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\section{Background}
\label{background}
The following notation will hold
throughout the paper.
Let $\bar X$ be a closed Riemann surface
with an integrable
meromorphic quadratic differential $q$.
We remind the reader that $q$ may have poles of order $1$.
We denote the vertical and
horizontal foliations of $q$ by $\lambda^+$ and $\lambda^-$
respectively. Let $\PP$ be a finite subset of $\bar X$
that includes the poles of $q$ if any, and let
$X = \bar X \ssm \PP$.
Let $\mathrm{sing}(q)$ denote the union of $\PP$ with the set of zeros
of $q$.
We require further that $q$ has no horizontal or
vertical saddle connections, that is no leaves of $\lambda^\pm$ that
connect two points of $\mathrm{sing}(q)$.
This situation holds in particular if
$\lambda^\pm$ are the stable/unstable foliations of a pseudo-Anosov
map $f:X\to X$, which will often be the case for us.
If $\PP=\mathrm{sing}(q)$ (i.e. $\PP$ contains all zeros of $q$)
we say $X$ is {\em fully-punctured}.
Let $\hat X$ denote the metric completion of the universal cover $\til
X$ of $X$, and note that there is an infinite branched covering
$\hat X \to \bar X$, infinitley branched over the points of $\PP$. The
preimage $\hat\PP$ of $\PP$ is the set of completion points.
The space $\hat X$ is a complete CAT$(0)$ space with the metric induced by
$q$.
\subsection{Veering triangulations}
\label{veering defs}
In this section let $\PP=\mathrm{sing}(q)$.
The veering triangulation, originally defined by Agol in
\cite{agol2011ideal} in the case
where $q$ corresponds to
a pseudo-Anosov $f:X\to X$, is an ideal
layered triangulation of $X\times\mathbb{R}$ which projects to a triangulation
of the mapping torus $M$ of $f$. The
definition we give here is due to Gu\'eritaud \cite{gueritaud}.
(Agol's ``veering'' property itself will not actually play a role in
this paper, so we will not give its definition).
A {\em singularity-free rectangle} in $\hat X$ is an embedded rectangle whose
edges consist of leaf segments of the lifts of $\lambda^\pm$ and whose
interior contains no singularities of $\hat X$.
If $R$ is a {\em maximal} singularity-free rectangle in $\hat X$ then
it must contain a singularity on each edge. Note that there cannot be
more than one singularity on an edge since $\lambda^\pm$ have no
saddle connections.
We associate to $R$ an ideal tetrahedron whose vertices are $\partial R
\cap \hat\PP$, as in \Cref{gue-tetra}.
This tetrahedron comes equipped with a ``flattening'' map into $\hat X$ as pictured.
\realfig{gue-tetra}{A maximal singularity-free rectangle $R$ defines a
tetrahedron equipped with a map into $R$.}
The tetrahedron comes with a natural orientation, inherited from the
orientation of $\hat X$ using the convention that the edge connecting
the horizontal boundaries of the rectangle lies {\em above} the edge
connecting the vertical boundaries. This orientation is indicated in \Cref{gue-tetra}.
The union of all these ideal tetrahedra, with faces identified whenever they
map to the same triangle in $\hat X$, is Gu\'eritaud's construction of
the veering triangulation of $\til X \times \mathbb{R}$.
\begin{theorem}\label{gueritaud construction} {\rm\cite{gueritaud}}
Suppose that $X$ is fully-punctured.
The complex of tetrahedra associated to maximal rectangles of $q$ is
an ideal triangulation $\til\tau$ of $\til X\times \mathbb{R}$, and the maps of
tetrahedra to their defining rectangles piece together to a fibration
$\pi:\til X \times \mathbb{R} \to \til X$. The action of $\pi_1(X)$ on $(\til
X,\til q)$ lifts simplicially
to $\til\tau$, and equivariantly with respect to $\pi$.
The quotient is
a triangulation of $X \times \mathbb{R}$.
If $q$
corresponds to a pseudo-Anosov $f:X\to X$
then the action of $f$ on $(X,q)$ lifts simplicially and
$\pi$-equivariantly to $\Phi:X\times\mathbb{R}\to X\times\mathbb{R}$.
The quotient is
a triangulation $\tau$ of the mapping torus $M$. The fibers of $\pi$
descend to flow lines for the suspension flow of $f$.
\end{theorem}
We will frequently abuse notation and use $\tau$ to refer to the
triangulation both in $M$ and in its covers.
We note that a saddle connection $\sigma$ of $q$ is an edge of $\tau$
if and only if $\sigma$ spans a singularity-free rectangle in $X$. See
\Cref{extend-rect}.
\realfig{extend-rect}{The singularity-free rectangle spanned by $\sigma$ can be
extended horizontally (or vertically) to a maximal one.}
If $e$ and $f$ are two crossing $\tau$-edges spanning rectangles $R_e$ and $R_f$,
note that $R_e$ crosses $R_f$ from top to bottom, or from left to
right -- any other configuration would contradict the singularity-free
property of the rectangles (\Cref{edges-cross}). If $\sl(e)$ denotes
the absolute value of the slope of $e$ with respect to $q$, we can see
that $R_e$ crosses $R_f$ from top to bottom if and only if
$e$ crosses $f$ and
$\sl(e) > \sl(f)$. We say that $e$ is {\em more vertical} than $f$ and
also
write $e>f$. We will see that $e>f$ corresponds to $e$ lying higher
than $f$ in the uppward flow direction.
Indeed we can see already that the relation $>$ is transitive, since
if $e>f$ and $f>g$ then the rectangle of $g$ is forced to intersect
the rectangle of $e$.
\realfig{edges-cross}{The rectangle of $e$ crosses $f$ from top to
bottom and we write $e>f$.}
We conclude with a brief description of the local structure of $\tau$ around
an edge $e$: The rectangle spanned by $e$ can be extended
horizontally to define a tetrahedron lying below $e$ in the flow direction (\Cref{extend-rect}),
and vertically to define a tetrahedron lying above $e$ in the flow
direction. Call these $Q_-$ and $Q_+$ as in
\Cref{edge-swing}. Between these, on each side of $e$,
is a sequence of tetrahedra $Q_1,\ldots,Q_m$ $(m\ge 1)$ so that two successive
tetrahedra in the sequence $Q_-,Q_1,\ldots,Q_m,Q_+$ share a triangular
face adjacent to $e$.
We find this sequence by starting with one
of the two top faces of $Q_-$, extending its spanning rectangle vertically until it hits
a singularity, and calling $Q_1$ the tetrahedron whose projection is inscribed in the new rectangle. If the new singularity belongs to $Q_+$ we are done $(m = 1)$, otherwise we repeat from the top face of $Q_1$ containing $e$ to find $Q_2$, and continue in this manner.
\Cref{edge-swing} illustrates this structure on one side of an edge
$e$. Repeating on the other side, note that the link of the edge $e$ is a circle, as expected.
\realfig{edge-swing}{The tetrahedra adjacent to an edge $e$ on one
side form a sequence ``swinging'' around $e$}
\subsection{Arc and curve complexes}
\label{sec: arc_complex}
The arc and curve complex $\A(Y)$ for a compact surface $Y$ is usually
defined as follows:
its vertices are essential homotopy classes of
embedded circles and properly embedded arcs $([0,1],\{0,1\}) \to
(Y,\partial Y)$, where ``essential'' means not homotopic to a point or
into the boundary \cite{MM2}. We must be clear about the meaning of homotopy
classes here, for the case of arcs: If $Y$ is not an annulus,
homotopies of arcs are assumed to be homotopies of maps of pairs. When
$Y$ is an annulus the homotopies are also required to fix the endpoints.
Simplices of $\A(Y)$, in all cases, correspond to tuples of vertices
which can be simultaneously realized by maps that are disjoint on
their interiors. We endow $\A(Y)$ with the simplicial distance on its
$1$-skeleton.
It will be useful, in the non-annular case, to observe that the
following definition is equivalent: Instead of maps of closed
intervals consider proper embeddings $\mathbb{R} \to \int(Y)$ into the
interior of $Y$, with equivalence arising from proper homotopy. This
definition is independent of the compactification of
$\int(Y)$. The natural isomorphism between these two versions of
$\A(Y)$ is induced by
a straightening construction in a collar
neighborhood of the boundary.
If $Y\subset S$ is an essential subsurface (meaning the inclusion of
$Y$ is $\pi_1$-injective and is not homotopic to a point or to an end
of $S$), we have subsurface projections $\pi_Y(\lambda)$ which are
defined for simplices $\lambda\subset \A(S)$ that intersect $Y$
essentially. Namely, after lifting $\lambda$ to the
cover $S_Y$ associated to $\pi_1(Y)$ (i.e. the cover to which $Y$
lifts homeomorphically and for which $S_Y \cong \int(Y)$),
we obtain a collection of
properly embedded disjoint essential arcs and curves,
which determine a simplex of $\A(Y)$.
We let $\pi_Y(\lambda)$ be the union of these vertices \cite{MM2}.
We make a similar definition for a lamination $\lambda$ that
intersects $Y$ essentially, except that we include not just the leaves
of $\lambda$ but all leaves that one can add in the complement of
$\lambda$ which accumulate on $\lambda$. This is natural when we
realize $\lambda$ as a measured {\em foliation} (as we do in most of
the paper), and need to include {\em generalized leaves}, which are
leaves that are allowed to pass through singularities.
Note that the diameter of $\pi_Y(\lambda)$ in $\A(Y)$ is at most 2.
Note that when $Y$ is an annulus these arcs have natural endpoints
coming from the standard compactification of $\til S = \HH^2$ by a
circle at infinity. We remark that $\pi_Y$ does not depend on any choice
of hyperbolic metric on $S$.
When $Y$ is not an annulus and $\lambda$ and $\partial Y$ are in
minimal position, we can also identify $\pi_Y(\lambda)$ with the
isotopy classes of components of $\lambda\cap Y$.
These definitions naturally extend to
immersed surfaces arising from covers of $S$.
Let $\Gamma$ be a finitely generated subgroup of $\pi_1(S)$. Then the
corresponding cover $S_\Gamma \to S$ has a compact core $W$ -- a
compact subsurface $W \subset S_\Gamma$ such that $S_\Gamma \ssm
W$ is a collection of boundary parallel annuli. For curves or
laminations $\lambda^\pm$ of $S$, we have lifts
$\widetilde{\lambda}^\pm$ to $S_\Gamma$ and define
$d_W(\lambda^-,\lambda^+) = d_{S_\Gamma}(\widetilde{\lambda}^-,
\widetilde{\lambda}^+)$.
Throughout this paper, when $\lambda,\lambda'$ are two laminations or
arc/curve systems, we denote by $d_Y(\lambda,\lambda')$ the {\em
minimal} distance between their images in $\A(Y)$,
that is
$$
d_Y(\lambda,\lambda') = \min\{d_Y(l,l') : l \in \pi_Y(\lambda), l' \in \pi_Y(\lambda') \}.
$$
To denote the \emph{maximal} distance between $\lambda$ and $\lambda'$ in $\A(Y)$ we write
$$
\mathrm{diam}_Y(\lambda,\lambda') = \mathrm{diam}_{\A(Y)}(\pi_Y(\lambda)\cup\pi_Y(\lambda')).
$$
\subsection{Flat geometry}
\label{AY in flat geometry}
In this section we return to the singular Euclidean geometry of $(X,q)$
and describe a circle at infinity for the flat metric
induced by $q$ on the universal cover $\til X$.
We identify $\til X$ with $\HH^2$
after fixing a reference hyperbolic metric on $X$.
Because of incompleteness of the flat metric
at the punctures $\PP$, the connection between the circle we will describe
and the usual circle at infinity for
$\HH^2$ requires a bit of care. A related
discussion appears in Gu\'eritaud \cite{gueritaud}, although he deals
explicitly only with the fully-punctured case.
With this picture of the
circle at infinity we will be able to describe $\pi_Y$ in terms of
$q$-geodesic representatives, and to describe a
$q$-convex hull for essential subsurfaces of $X$. In this section we do
not assume that $X$ is fully-punctured.
The completion points $\hat \PP$ in $\hat X$ correspond
to parabolic fixed points for $\pi_1(X)$ in $\partial \HH^2$, and
we abuse notation slightly by identifying $\hat\PP$ with this subset
of $\partial \HH^2$.
A {\em complete $q$-geodesic ray} is either a geodesic ray
$r:[0,\infty)\to\hat X$ of infinite
length, or a finite-length geodesic segment that
terminates in $\hat\PP$. A complete $q$-geodesic line is a geodesic
which is split by any point into two complete $q$-geodesic rays.
Our goal in this section is to describe a
circle at infinity that corresponds to endpoints of these rays.
\begin{proposition}\label{same compactification}
There is a compactification $\beta(\til X)$ of $\til X$ on which $\pi_1(X)$ acts
by homeomorphisms, with the following properties:
\begin{enumerate}
\item There is a $\pi_1(X)$-equivariant homeomorphism $\beta(\til X) \to
\overline{\HH^2}$, extending the identification of $\til X$ with $\HH^2$ and
taking $\hat \PP$ to the corresponding
parabolic fixed points in $\partial \HH^2$.
\item If $l$ is a complete $q$-geodesic line in $\hat X$ then its
image in $\overline{\HH^2}$ is an embedded arc with endpoints on
$\partial\HH^2$ and interior points in $\HH^2 \cup \hat \PP$. Conversely, every pair of distinct points $x,y$ in
$\partial\beta(\til X) = \beta(\til X) \ssm \til X$ are the
endpoints of a complete $q$-geodesic line. The termination point in
$\partial\HH^2$ of a complete $q$-geodesic
ray is in $\hat\PP$ if and only if it has finite length.
\item The $q$-geodesic line connecting distinct
$x,y\in\partial\beta(\til X)$ is either unique, or there is a
family of parallel geodesics making up an infinite Euclidean strip.
\end{enumerate}
\end{proposition}
One of the tricky points of this picture is that $q$-geodesic rays and
lines may meet points of the boundary $\partial\beta(\til X)$ not just at their
endpoints.
\begin{proof}
When $\PP = \emptyset$ and $X$ is a closed surface, $\til X$ is
quasi-isometric to $\HH^2$ and the proposition holds for the standard
Gromov compactification. We assume from now on that
$\PP\ne\emptyset$.
We begin by setting $\hat \HH^2 = \HH^2 \cup \hat \PP$ and endowing
it with the topology obtained
by taking, for each $p \in \hat \PP$, horoballs based at $p$ as a
neighborhood basis for $p$.
\begin{lemma}\label{hat same}
The natural identification of $\widetilde{X}$ with $\HH^2$
extends to a homeomorphism from $\hat X$ to $\hat \HH^2$.
\end{lemma}
\begin{proof}
First note that $\hat \PP$ is discrete as both a subspace of $\hat X$
and of $\hat \HH^2$. Hence, it suffices to show that a sequence of
points $x_i$ in $\widetilde{X} = \HH^2$ converges to a point $p \in
\hat \PP$ in $\hat X$ if and only if it converges to $p$ in $\hat
\HH^2$. This follows from the fact that the horoball neighborhoods of
$p$ descend to cusp neighborhoods in $X$ which form a
neighborhood basis for the puncture that is equivalent to the
neighborhood basis of $q$-metric balls.
\end{proof}
Our strategy now is to form the {\em Freudenthal space} of $\hat X$
and equivalently $\hat \HH^2$, which appends a space of {\em
ends}. This space will be compact but not Hausdorff, and after a
mild quotient we will obtain the desired compactification which can be
identified with $\overline{\HH^2}$. Simple properties of this
construction will then allow us to obtain the geometric conclusions in
part (2) of the proposition.
Let $\epsilon(\hat X)$ be the space of ends of $\hat X$, that is the
inverse limit of the system of path components of complements of
compact sets in $\hat X$. The Freudenthal space $\operatorname{Fr}(\hat X)$ is the
union $\hat X\cup \ep(\hat X)$ endowed with the toplogy generated by
using path components of complements of compacta to describe
neighborhood bases for the ends. Because $\hat X$ is not locally
compact, $\operatorname{Fr}(\hat X)$ is not guaranteed to be compact, and we have to take a bit of
care to describe it.
The construction can of course be repeated for $\hat\HH^2$, and
the homeomorphism of \Cref{hat same} gives rise to a
homeomorphism $\operatorname{Fr}(\hat X) \to \operatorname{Fr}(\HH^2)$.
Let us work in $\hat\HH^2$ now, where we can describe the ends
concretely using the following observations:
Every compact set
$K\subset \hat\HH^2$ meets $\hat\PP$ in a finite set $A$ (since $\hat
\PP$ is discrete in $\hat\HH^2$), and such a $K$ is
contained in an embedded closed disk $D$ which also meets $\hat\PP$ at
$A$. (This is not hard to see but does require attention to deal
correctly with the horoball neighborhood bases).
The components of $\hat\HH^2\ssm D$ determine a partition of
$\ep(\hat\HH^2)$, which in fact depends only on the set $A$ and not on
$D$ (if $D'$ is another disk meeting $\hat\PP$ at $A$, then $D\cup
D'$ is contained in a third disk $D''$, and this common refinement
of the neighborhoods gives the same partition).
Thus we have a more manageble (countable) inverse system of
neighborhoods in $\ep(\hat\HH^2)$, and with this description it is not
hard to see that $\ep(\hat\HH^2)$ is a Cantor set.
For each $p\in\hat\PP$ there are two distinguished ends $p^+,p^-\in
\ep(\hat\HH^2)$ defined as follows: For each finite subset $A\subset\hat\PP$
with at least two
points one of which is $p$, the two partition terms adjacent to $p$ in the
circle (or equivalently, in the boundary of any $D\subset \hat \HH^2$
meeting $\hat\PP$ in $A$)
define neighborhoods in
$\ep(\hat\HH^2)$, and this pair of neighborhood systems determines $p^+$ and
$p^-$ respectively.
One can also see that $p^+$ (and $p^-$) and $p$ do not admit disjoint
neighborhoods, and this is why $\operatorname{Fr}(\hat\HH^2)$ is not Hausdorff. We
are therefore led to define the quotient space
\[
\beta(\hat \HH^2) = \operatorname{Fr}(\hat\HH^2) / \sim ,
\]
where we make the identifications $p^- \sim p \sim p^+$, for each $p\in\hat\PP$.
We can make the same definitions in $\hat X$, obtaining
\[
\beta(\hat X) = \operatorname{Fr}(\hat X) / \sim ,
\]
which we rename $\beta(\til X)$.
Since the definitions are purely in terms of the topology of the spaces
$\hat\HH^2$ and $\hat X$,
the homeomorphism of
\Cref{hat same} extends to a homeomorphism $\beta(\til X) \to \beta(\hat\HH^2)$.
Part (1) of
\Cref{same compactification} follows once we establish that the
identity map of $\HH^2$ extends to a homeomorphism
$$
\beta(\hat\HH^2) \cong \overline{\HH^2}.
$$
This is not hard to see once we observe that the disks used above to
define neighborhood systems can be chosen to be ideal hyperbolic polygons. Their
halfspace complements serve as neighborhood systems for points of
$\partial\HH^2\setminus\hat\PP$. A sequence converges in
$\overline{\HH^2}$ to a point $p\in \hat\PP$
if it is eventually contained in any union of a horoball centered at p and two half-planes adjacent to $p$ on opposite sides.
This is modeled exactly by the equivalence relation $\sim$.
For part (2), let $D_0$ be a fundamental domain for $\pi_1(X)$ in
$\hat X$, which may be chosen to be a disk with vertices at points of
$\hat\PP$, and of finite $q$-diameter. Translates of $D_0$ can be glued
to build a sequence of nested disks $D_n$ exhausting $\hat X$, each of
which meets $\hat\PP$ in a finite set of vertices, and whose boundary is composed
of arcs of bounded diameter between successive vertices.
A complete $q$-geodesic ray $r$ either has finite length and terminates in
a point of $\hat\PP$, or has infinite length in which case it leaves
every compact set of $\hat X$, and visits each point of $\hat\PP$ at
most once. Thus it must terminate in a point of
$\ep(\hat X)$ in the Freudenthal space. We claim that this point
cannot be $p^+$ or $p^-$ for $p\in\hat\PP$. If $r$ terminates in
$p^+$, then for each disk $D_n$ ($n$ large) it must pass through the edge of
$\partial D_n$ adjacent to $p$ on the side associated to $p^+$. Any
two such consecutive edges meet in $p$ at one of finitely many angles (images of
corners of $D_0$), and hence the accumulated angle between edges goes
to $\infty$ with $n$. If we replace these edges by their $q$-geodesic
representatives, the angles still go to $\infty$.
This means that $r$ contains infinitely many disjoint subsegments
whose endpoints are a bounded distance from $p$, but this contradicts the
assumption that $r$ is
a geodesic ray.
The image of $r$ in the quotient $\beta(\til X)$ therefore terminates
in a point of $\hat\PP$ when it has finite length, and a point in
$\partial\beta(\til X)\ssm \hat\PP$ otherwise. The same is true for
both ends of a complete $q$-geodesic line $l$, and we note that both
ends of $l$
cannot land on the same point because then we would have a sequence of
segments $l_n\subset l$ of length going to $\infty$ with both
endpoints of $l_n$ on the same edge or on two consecutive edges
of $\partial D_n$, a
contradiction to the fact that $l_n$ is a geodesic and the arcs in
$\partial D_n$ have bounded $q$-length.
Now let $x,y$ be two distinct points in $\partial\beta(\til
X)$. Assume first that both are not in $\hat\PP$. Then for large
enough $n$, they are in separate components of the complement of
$D_n$. If we let $x_i \to x$ and $y_i\to y$ be sequences in $\beta(\til X)$, then eventually $x_i$ and
$y_i$ are in the same components of the complement of $D_n$ as $x$ and
$y$, respectively. The
geodesic from $x_i$ to $y_i$ must therefore pass through the
corresponding boundary segments of $D_n$ and in particular through $D_n$,
so we can extract a
convergent subsequence as $i\to\infty$. Letting $n\to\infty$ and diagonalizing we
obtain a limiting geodesic which terminates in $x,y$ as desired. If
$x\in \hat\PP$ or $y\in\hat\PP$ the same argument works except that we
can take $x_i \equiv x$ or $y_i \equiv y$. This establishes part (2).
Now let $l$ and $l'$ be two $q$-geodesics terminating in $x$ and $y$.
If $x$ and $y$ are in $\hat\PP$ then $l=l'$ since the metric is
CAT(0). If $x\notin \hat\PP$ then both $l$ and $l'$ pass through
infinitely many segments of $\partial D_n$ on their way
to $x$. Since these segments have uniformly bounded lengths, $l$ and
$l'$ remain a bounded distance apart. If $y\in\hat\PP$ then again
CAT(0) implies that $l=l'$, and if $y\notin\hat\PP$ then $l$ and $l'$
must cobound an infinite flat strip. This establishes part (3).
\qedhere
\end{proof}
With \Cref{same compactification} in hand we can consider
each complete $q$-geodesic line $l$ in $\hat X = \hat \HH^2$ as an arc
in the closed disk $\overline{\HH^2}$, which by the Jordan curve
theorem separates the disk ${\HH^2}$ into at least
$2$ components. Each component is an open disk whose closure meets
$\partial\HH^2$ in a subarc of one of the complementary arcs of the endpoints of
$l$. We call the union of disks whose closures meet one of these complementary arcs
of the endpoints of $l$
an {\em open side} $\openside{l}$ of $l$. The closure of each open side in $\overline \HH^2$ is then a connected union
of closed disks, attached to each other along the points of $\hat\PP$
that $l$ meets on the circle.
We call the closure of the open side $\openside{l}$ of $l$ in $\overline{\HH^2}$ the {\em side} $\side{l}$.
Note that $\openside{l} = \int (\side{l} \cap \HH^2) = \side{l} \ssm (\partial \HH^2 \cup l)$, and if $\side{l}$ and $\side{l}'$ are the two sides of $l$, then $\side{l} \cap \side{l}' = l$.
See \Cref{line-disks}.
\realfig{line-disks}{A complete $q$-geodesic line $l$ ands its endpoints on $\partial \HH^2$.}
With this picture we can state the
following:
\begin{corollary} \label{cor:side_coherence}
Let $a,b$ be disjoint arcs in $\HH^2$ with well-defined, distinct endpoints on $\partial \HH^2$ and let $a_q,b_q$ be $q$-geodesic lines with the same endpoints as $a$ and $b$, respectively. Then $b_q$ is contained in a single side of $a_q$.
\end{corollary}
\realfig{ab-intersect}{Disjoint arcs with their $q$-geodesic representatives.}
\begin{proof}
Letting $L$ and $R$ be the arcs of $\partial\HH^2$
minus the endpoints of $a$,
the endpoints of $b$ must lie in one of them, say $L$, since
$a$ and $b$ are disjoint.
Since $a_q$ and $b_q$ are geodesics in the CAT$(0)$ space $\hat X$,
their intersection is connected. If their intersection is empty, then
the corollary is clear. Otherwise, $b_q\ssm a_q$ is one or
two arcs, each with one endpoint on $a_q$ and the other on $L$. It follows
that $b_q\ssm a_q$ is on one open side of $a_q$, and the corollary
follows.
\end{proof}
\subsection*{Subsurfaces and projections in the flat metric}
Let $Y \subset X$ be an essential compact subsurface, and let
$X_Y=\til X/\pi_1(Y)$ be the associated cover of $X$. (Here we have identified $\pi_1(X)$ with the deck transformations of $\widetilde{X} \to X$ and fixed $\pi_1(Y)$ within its conjugacy class.)
For any
lamination $\lambda$ in $X$, we want to show that the projection
$\pi_Y(\lambda)$ can be
realized by subsegments of the $q$-geodesic representative of $\lambda$.
Recall that $X$ is not necessarily
fully-punctured.
We say a boundary component of $Y$ is {\em puncture-parallel} if it bounds a
disk in $\bar X \ssm Y$ that contains a single point of $\PP$. We
denote the corresponding subset of $\PP$ by $\PP_Y$ and refer to them
as the \emph{punctures} of $Y$. Let $\til{\PP}_Y$ denote the subset of
punctures of $X_Y$ which are encircled by the boundary components of
the lift of $Y$ to $X_Y$.
In terms of the completed space $\bar X_Y$, $\til \PP_Y$ is exactly the set of completion points which have finite total angle.
Let $\partial_0Y$ denote the union of the puncture-parallel components of
$\partial Y$ and let $\partial'Y$ denote the rest. Observe that the
components of $\partial_0 Y$ are in natural bijection with $\PP_Y$ and set
$Y' = Y\ssm\partial_0Y$.
Identifying $\til X$ with $\HH^2$,
let $\Lambda\subset \partial\HH^2$ be the limit set of
$\pi_1(Y)$, $\Omega =
\partial\HH^2 \ssm \Lambda$, and $\hat\PP_Y\subset \Lambda$
the set of parabolic fixed points of $\pi_1(Y)$.
Let $C(X_Y)$ denote the compactification of $X_Y$ given by
$(\HH^2 \cup \Omega\cup \hat\PP_Y)/\pi_1(Y)$, adding a point for each
puncture-parallel end of $X_Y$, and a circle for each of the other
ends. Now given a lamination (or foliation) $\lambda$, realized geodesically in the
hyperbolic metric on $X$, its lift to $X_Y$ extends to properly
embedded arcs in $C(X_Y)$, of which the ones that
are essential give
$\pi_Y(\lambda)$.
\Cref{same compactification}
allows us to
perform the same construction with the $q$-geodesic representative of
$\lambda$. Note that the leaves we obtain may
meet points of $\til \PP_Y$
in their interior, but a slight perturbation
produces properly embedded lines in $X_Y$ which are properly isotopic
to the leaves coming from $\lambda$.
If $Y$ is an annulus the same construction works, with the observation
that the ends of $Y$ cannot be puncture-parallel and hence $C(Y)$ is
a closed annulus and the leaves have well-defined endpoints in its
boundary. We have proved:
\begin{lemma}
\label{q arcs for AY}
Let $Y\subset X$ be an essential subsurface.
If $\lambda$ is a proper arc or lamination in $X$ then the lifts of its $q$-geodesic
representatives to $X_Y$, after discarding inessential components, give representatives of $\pi_Y(\lambda)$.
\end{lemma}
\subsection*{$q$-convex hulls}
We will need a flat-geometry analogue of the hyperbolic convex hull.
The main idea is simple -- pull the boundary
of the regular
convex hull tight using $q$-geodesics. The only difficulty comes from
the fact that
these geodesics can pass through parabolic fixed points, and
fail to be disjoint from each other, so
the resulting object may fail to be an embedded surface.
Our discussion is similar to Section $3$ of
Rafi \cite{rafi2005characterization}, but the discussion there
requires adjustments to handle correctly the incompleteness at punctures.
As above, identify $\til X$ with $\HH^2$. Let
$\Lambda \subset \partial \HH^2$ be a closed set and let
${\operatorname{CH}}(\Lambda)$ be the convex hull of $\Lambda$ in $\HH^2$. We define
${\operatorname{CH}}_q(\Lambda)$ as follows.
Assume first that $\Lambda$ has at least 3 points.
Each boundary geodesic $l$ of ${\operatorname{CH}}(\Lambda)$ has the same
endpoints as a
(biinfinite) $q$-geodesic $l_q$.
By part (3) of \Cref{same compactification},
$l_q$ is
unique unless it is part of a parallel family of geodesics, making a
Euclidean strip.
The plane is divided by $l_q$ into two sides as in the discussion
before \Cref{cor:side_coherence},
and one of the sides, which we call
$\side{l}$, meets $\partial \HH^2$
in a subset of the complement of $\Lambda$.
Recall that $\side{l}$ is either a disk
or a string of disks attached along puncture
points.
If $l_q$ is one of
a parallel family of geodesics, we include this family in $\side{l}$.
After deleting from $\hat X$ the interiors of $\side{l}$ for all $l$
in $\partial {\operatorname{CH}}(\Lambda)$ (which are disjoint by \Cref{cor:side_coherence}),
we obtain ${\operatorname{CH}}_q(\Lambda)$, the
$q$-convex hull.
If $\Lambda$ has 2 points then ${\operatorname{CH}}_q(\Lambda)$ is the closed Euclidean strip
formed by the union of $q$-geodesics joining those two points.
\medskip
Now fixing a subsurface $Y$ we can define a $q$-convex hull for the
cover $X_Y$, by taking a quotient of the $q$-convex hull of the limit
set $\Lambda_Y$ of $\pi_1(Y)$. This quotient, which we will denote by
${\operatorname{CH}}_q(X_Y)$, lies in the completion $\bar{X}_Y$.
Because ${\operatorname{CH}}_q(X_Y)$
may not be homeomorphic to $Y$, we pay explicit attention to a marking
map between $Y$ and its hull.
Let $\hat\iota:Y \to X_Y$ be the lift of the inclusion map to the
cover.
\begin{lemma}
\label{q tight}
The lift $\hat\iota:Y\to X_Y$ is homotopic to a map $\hat\iota_q:Y\to \bar
X_Y$ whose image is the $q$-hull ${\operatorname{CH}}_q(X_Y)$ such that
\begin{enumerate}
\item The homotopy $(h_t)_{t \in[0,1]}$ from $\hat\iota$ to $\hat\iota_q$ has the property that
$h_t(Y) \subset X_Y$ for all $t \in [0,1)$.
\item Each
component of $\partial_0 Y$
is taken by
$\hat\iota_q$ to the corresponding completion point of $\til{\PP}_Y$.
\item If $Y$ is an annulus then the image of $\hat\iota_q$ is either a maximal flat cylinder in $\bar X_Y$ or the unique geodesic representative of the core of $Y$ in $\bar X_Y$.
\item If $Y$ is not an annulus then
each component $\gamma$ of $\partial' Y$
is taken by $\hat\iota_q$ to a
$q$-geodesic representative in $\bar X_Y$. If there is a flat
cylinder in the homotopy class of $\gamma$ then the interior of
the cylinder is disjoint from $\hat\iota_q(Y)$.
\item There is a deformation retraction $r:\bar X_Y \to
\hat\iota_q(Y)$. For each component $\gamma$ of $\partial'Y$, the
preimage $r^{-1}(\hat\iota_q(\gamma))$ intersects $X_Y$ in either
an open annulus or a union of open disks joined in a cycle along
points in their closures.
\item If the interior $\int({\operatorname{CH}}_q(\Lambda_Y))$ is a disk then
$\hat\iota_q$ is a homeomorphism from $Y' = Y\ssm\partial_0Y$ to its image.
\end{enumerate}
\end{lemma}
\begin{proof}
Let $\Gamma = \pi_1 Y$ and let
$\Lambda =\Lambda_Y \subset \partial \HH^2$ denote the limit set of $\Gamma$.
As usual, ${\operatorname{CH}}(\Lambda)/\Gamma$ can be identified with $Y' = Y \ssm \partial_0 Y$. After
isotopy we may assume $\hat\iota:Y'\to {\operatorname{CH}}(\Lambda)/\Gamma$ is this
identification.
First assume that $Y$ is not an annulus.
Form ${\operatorname{CH}}_q(\Lambda)$ as above,
and for a boundary geodesic $l$ of
${\operatorname{CH}}(\Lambda)$ define $l_q$ and its side $\side{l}$ as in the
discussion above. The quotient of $l_q$ is
a geodesic representative of a component of $\partial Y$, and
the quotient of the open side $\openside{l}$ in $X_Y$
is either an open annulus or a
union of open disks joined in a cycle along points in their completion.
The $q$-geodesic may pass
through points of $\hat \PP$,
so that there is a homotopy from $l$ to $l_q$ rel endpoints which
stays in $\HH^2$ until the last instant.
We may equivariantly deform the identity to a map
${\operatorname{CH}}(\Lambda) \to {\operatorname{CH}}_q(\Lambda)$, which takes each $l$ to
$l_q$: since ${\operatorname{CH}}_q(\Lambda)$ is contractible, it suffices to give a
$\Gamma$-invariant triangulation of ${\operatorname{CH}}(\Lambda)$ and define the
homotopy successively on the skeleta. This homotopy descends to a map
from $Y'$ to ${\operatorname{CH}}_q(\Lambda)/\Gamma$, and can be chosen so that the
puncture-parallel boundary components map to the corresponding points of $\PP_Y$. This
gives the desired map $\hat\iota_q$ and establishes properties (1-4).
Using the description of the sides $\side{l}$, we may equivariantly
retract $\overline\HH^2$ to ${\operatorname{CH}}_q(\Lambda)$, giving rise to the
retraction $r$ of part (5).
Finally, if the interior of ${\operatorname{CH}}_q(\Lambda)$ is a disk, then its
quotient is a surface. Our homotopy yields a
homotopy-equivalence of $Y'$ to this surface which preserves peripheral
structure and can therefore be deformed rel boundary to a
homeomorphism. We let $\hat\iota_q$ be this homeomorphism, giving part $(6)$.
When $Y$ is a (nonperipheral) annulus, $\Lambda_Y$ is a pair of points
and we recall from above that ${\operatorname{CH}}_q(\Lambda)$ is either a flat strip
in $\hat{X}$ which descends to a flat cylinder in $\bar X_Y$, or it is
a single geodesic. The proof in the annular case now proceeds exactly
as above.
\end{proof}
Let $\iota_q : Y \to \bar X$ be the composition of $\hat \iota_q$ with
the (branched) covering $\bar X_Y \to \bar X$ and set
$\partial_q Y = \iota_q(\partial' Y)$. Note that this will be a 1-complex of saddle connections and not necessarily a homeomorphic image of $\partial' Y$.
\subsection{Fibered faces of the Thurston norm}
A fibration $\sigma\colon M\to S^1$ of a finite-volume hyperbolic
3-manifold $M$ over the circle comes with the following structure:
there is an integral cohomology class in $H^1(M;\mathbb{Z})$
represented by $\sigma_*:\pi_1M\to \mathbb{Z}$, which is the Poincar\'e dual
of the fiber $F$. There is a
representation of $M$ as a quotient $F\times\mathbb{R}/\Phi$
where $\Phi(x,t) = (f(x),t-1)$ and $f:F\to F$ is called the monodromy
map. This map is pseudo-Anosov and has stable and unstable (singular) measured foliations
$\lambda^+$ and $\lambda^-$ on $F$. Finally there is the suspension
flow inherited from the natural $\mathbb{R}$ action on $F\times\mathbb{R}$, and
suspensions $\Lambda^\pm$ of $\lambda^\pm$ which are flow-invariant 2-dimensional
foliations of $M$. All these objects are defined up to isotopy.
The fibrations of $M$ are organized by the {\em Thurston norm}
$||\cdot||$ on $H^1(M;\mathbb{R})$ \cite{thurston1986norm} (see also \cite{candel2000foliations}). This norm has a
polyhedral unit ball $B$ with the following properties:
\begin{enumerate}
\item Every cohomology class dual to a fiber is in the
cone $\mathbb{R}_+\mathcal{F}$ over a top-dimensional open face $\mathcal{F}$ of $B$.
\item If $\mathbb{R}_+\mathcal{F}$ contains a cohomology class dual to a fiber
then {\em every} irreducible integral class in $\mathbb{R}_+\mathcal{F}$ is dual to a
fiber. $\mathcal{F}$ is called a {\em fibered face} and its irreducible integral
classes are called fibered classes.
\item For a fibered class $\omega$ with associated fiber $F$,
$||\omega||=-\chi(F)$.
\end{enumerate}
In particular if $\dim H^1(M;\mathbb{R})\ge 2$ and $M$ is fibered then there
are infinitely many fibrations, with fibers of arbitrarily large
complexity.
We will abuse terminology a bit by saying that a fiber (rather than
its Poincar\'e dual) is in $\mathbb{R}_+\mathcal{F}$.
The fibered faces also organize the suspension flows and the
stable/unstable foliations: If $\mathcal{F}$ is a fibered face then there is a
single flow $\psi$ and a single pair $\Lambda^\pm$ of foliations whose leaves
are invariant by $\psi$, such that {\em every} fibration
associated to $\mathbb{R}^+\mathcal{F}$ may be isotoped so that its suspension flow is
$\psi$ up to a reparameterization, and the foliations $\lambda^\pm$ for the monodromy of its fiber $F$ are
$\Lambda^\pm\cap F$.
These results were proven by Fried \cite{fried1982geometry}; see also
McMullen \cite{mcmullen2000polynomial}.
\subsection*{Veering triangulation of a fibered face}
A key fact for us is that the veering triangulation of the manifold
$M$ depends only on the fibered face $\mathcal{F}$ and not on a particular
fiber. This was known to Agol for his original construction (see
sketch in \cite{agol-overflow}), but
Gu\'eritaud's construction makes it almost immediate.
\begin{proposition}[Invariance of $\tau$] \label{prop:invariance}
Let $M$ be a hyperbolic 3-manifold with fully-punctured fibered face
$\mathcal{F}$.
Let $S_1$ and $S_2$ be
fibers of $M$ each contained in $\mathbb{R}_+ \mathcal{F}$
and let $\tau_1$ and $\tau_2$ be the corresponding veering
triangulations of $M$. Then, after an isotopy preserving
transversality to the suspension flow,
$\tau_1 = \tau_2$.
\end{proposition}
\begin{proof}
The suspension flow associated to $\mathcal{F}$ lifts to the universal cover
$\til M$, and any fiber $S$ in $\mathbb{R}_+\mathcal{F}$ is covered
by a copy
of its universal cover $\til S$ in $\til M$ which meets every flow
line transversely, exactly once. Thus we may
identify $\til S$ with the leaf space ${\mathcal L}$ of this flow. The lifts
$\til\Lambda^\pm$ of the suspended laminations project to the leaf
space where they are identified
with the lifts $\til\lambda^\pm$ of $\lambda^\pm$ to $\til S$.
The foliated rectangles used in the construction of $\tau$ from
$\til{q}$ on $\til{S}$ depend
only on the (unmeasured) foliations $\til\lambda^\pm$.
Thus the abstract cell structure of $\tau$ depends
only on the fibered face $\mathcal{F}$ and not on the fiber. The map $\pi$ from each tetrahedron
to its rectangle does depend a bit on the fiber, as we choose
$q$-geodesics for the edges (and the metric $q$ depends on the
fiber); but the edges are always mapped to arcs
in the rectangle that are transverse to both foliations. It follows
that there is a transversality-preserving isotopy between the
triangulations associated to any two fibers.
\end{proof}
\subsection*{Fibers and projections}
We next turn to a few lemmas relating subsurface projections over the various fibers in a fixed face of the Thurston norm ball.
\begin{lemma}\label{lem:subgroup_projection}
If $\mathcal{F}$ is a fibered face for $M$
and $Y \to S$ is an infinite covering where
$S$ is a fiber in $\mathbb{R}_+\mathcal{F}$ and $\pi_1(Y)$ is finitely generated,
then the projection distance $d_Y(\lambda^-,\lambda^+)$ depends only on $\mathcal{F}$ and
the conjugacy class of the subgroup $\pi_1(Y) \le \pi_1(M)$ (and not
on $S$).
\end{lemma}
Note that $Y$ need not correspond to an embedded subsurface of $S$.
\begin{proof}
As in the proof of \Cref{prop:invariance}, $\til S$ can be
identified with the leaf space ${{\mathcal L}}$ of the flow in $\til M$.
The action of $\pi_1(M)$ on $\til M$ descends to ${\mathcal L}$, and
thus the cover $Y = \til S/\pi_1(Y)$ is identified with the quotient
${{\mathcal L}}/\pi_1(Y)$ and the lifts of $\lambda^\pm$ to $Y$ are identified
with the images of $\til\Lambda^\pm$ in ${{\mathcal L}}/\pi_1(Y)$. Thus the
projection $d_Y(\lambda^+,\lambda^-)$ can be obtained without
reference to the fiber $S$.
\end{proof}
This lemma justifies the notation $d_Y(\Lambda^+,\Lambda^-)$ used in
the introduction.
We will also require the following lemma, where we allow maps homotopic to fibers which are not necessarily embeddings.
\begin{lemma}\label{lem:flow_to_fiber_2}
Let $F$ be a fiber of $M$. Let $Y\subset M$ be a
compact surface and let $h \colon F \to M$ be a map which is
homotopic to the inclusion. Suppose that $h(F) \cap Y$ is inessential
in $Y$, i.e. each component of the intersection is homotopic into the
ends of $Y$. Then the image of $\pi_1(Y)$ is
contained in $\pi_1(F) \vartriangleleft \pi_1(M)$.
\end{lemma}
\begin{proof}
Let $\zeta$ be the cohomology class dual to $F$. Since $h(F)$
meets $Y$ inessentially, every loop in $Y$ can be pushed off of $h(F)$
so $\zeta$ vanishes on $\pi_1(Y)$. But the
kernel of $\zeta$ in $\pi_1(M)$ is exactly $\pi_1(F)$, so the image of
$\pi_1(Y)$ is in $\pi_1(F)$.
\end{proof}
\section{Rectangle and triangle hulls}
\label{hulls}
In this section we discuss a number of constructions that associate a
configuration of $\tau$-edges to
a saddle connection of the quadratic differential $q$. These
will be used later to show that subsurfaces with large projection are
compatible with the veering triangulation in the appropriate sense.
As a byproduct of our investigation, we prove the (to us) unexpected result
(\Cref{th:total geodesic})
that the edges of the veering triangulation form a totally
geodesic subgraph of the curve and arc graph of $X$.
We emphasize that in \Cref{sec:rectangles_along_saddles} and
\Cref{sec:t_hulls}, the surface $X$ is not necessarily
fully-punctured. Thus by $\tau$ we mean the veering triangulation
associated to the fully-punctured surface $X \ssm \mathrm{sing}(q)$. We will
say that a saddle connection of $X$ is a {\em $\tau$-edge} if its interior
is an edge of this veering triangulation. In particular this means
that its lift to $\til X$ spans a singularity-free rectangle.
\subsection{Maximal rectangles along a saddle connection}
\label{sec:rectangles_along_saddles}
Let $\sigma$ be a saddle connection, for the moment in the completed universal
cover $\hat X$. Consider the set $\mathcal{R}(\sigma)$ of all rectangles which are {\em maximal
with respect to the property that $\sigma$ passes through a diagonal}.
Thus each $R\in\mathcal{R}(\sigma)$ contains singularities in at least two
edges. Let $h(R)$ be the convex hull in $R$ of the singularities
in the boundary of $R$ and let $h^{(1)}(R)$ denote its $1$-skeleton
(see \Cref{rect-hulls}).
\realfig{rect-hulls}{The eight possible (up to symmetry) convex hulls $h(R)$, assuming
at most one singularity per leaf of $\lambda^\pm$. The saddle
connection $\sigma$ is in blue.}
Let
$$
\rhull(\sigma) = \bigcup \{ h^{(1)}(R): R\in \mathcal{R}(\sigma) \}.
$$
See \Cref{r-example} for an example.
Note that all the saddle connections in $\rhull(\sigma)$ are edges of $\tau$ ---
each of these arcs spans a singularity-free rectangle by construction.
Moreover, $\rhull(\sigma) = \{\sigma\}$ if $\sigma$ is itself a $\tau$-edge.
\realfig{r-example}{Example of $\rhull(\sigma)$ (in red)}
The following lemma will play an important role throughout
this paper.
\begin{lemma}\label{r disjoint}
If saddle connections $\sigma_1$ and $\sigma_2$ have no transversal intersections then
neither do $\rhull(\sigma_1)$ and $\rhull(\sigma_2)$.
\end{lemma}
\begin{proof}
Say that two rectangles meet {\em crosswise} if their interiors
intersect, and no corners of one are in the interior of the
other. Note that when two distinct rectangles meet crosswise,
any two of their diagonals intersect. We say that the rectangles meet
{\em properly crosswise} if they also do not share any corners, in
which case any two diagonals intersect in the interior.
Let $\tau_1$ and $\tau_2$ be saddle connections in $\rhull(\sigma_1)$
and $\rhull(\sigma_2)$, respectively, and suppose that they intersect
transversely. Hence their spanning rectangles $Q_1$ and $Q_2$ must
cross as in \Cref{edges-cross}. Assume that $Q_1$ is the taller and
$Q_2$ the wider.
Now let $R_1$ and $R_2$ be the rectangles of $\mathcal{R}(\sigma_1)$ and
$\mathcal{R}(\sigma_2)$ containing $Q_1$ and $Q_2$, respectively.
Because of the singularities in the corners of $Q_1$ and $Q_2$, $R_2$
is no taller than $Q_1$ and $R_1$ is no wider than $Q_2$. Hence $R_1$
and $R_2$ meet crosswise. (See \Cref{crossing-rects}).
\realfig{crossing-rects}{Three examples of the crossing pattern. The rectangles $R_1$
and $R_2$ are in blue, $\tau_1$ and $\tau_2$ are in red, and $Q_1$ and $Q_2$ are shaded. In {\em (i)} and
{\em (ii)} the
crossing is proper. In {\em (iii)} the corner $c$ is shared.}
If they met properly crosswise then $\sigma_1$ and $\sigma_2$ would
have an interior intersection, which is a contradiction. Hence $R_1$
and $R_2$ share a corner $c$. But the edges meeting at $c$ would
have to pass through boundary edges of $Q_1$ and $Q_2$. Those edges already
have the singularities of $\tau_1$ and $\tau_2$, and so $c$ cannot be
a singularity. Thus if $c$ is the intersection of the diagonals
contained in $\sigma_1$ and $\sigma_2$ it would be in the interior of
both saddle connections, again a contradiction.
We conclude that $\tau_1$ and $\tau_2$ cannot cross.
\end{proof}
An immediate consequence of \Cref{r disjoint} is that we can carry out the
construction downstairs: If $\sigma$ is a saddle connection in $\bar X$ we
can construct $\rhull(\hat \sigma)$ for each of its lifts $\hat \sigma$
to $\hat X$, and the lemma tells us none of them intersect
transversally. Thus the construction projects downstairs to give a
collection of $\tau$-edges with disjoint interior.
Moreover if $K$ is {\em any} collection
of saddle connections with disjoint interiors then $\rhull(K)$ makes sense as a subcomplex of
$\tau$ supported on some section by \Cref{lem:extension}.
Hence, we will continue to use $\rhull(\cdot)$ to denote
the corresponding map on saddle connections of $\bar X$. We remark that although
$\rhull(\cdot)$ takes collections of saddle connections with disjoint interiors to collections of
$\tau$-edges with disjoint interiors, it may do so with multiplicity.
\subsection{Triangle hulls} \label{sec:t_hulls}
Now let us consider a similar operation that uses right triangles
instead of rectangles, and associates to a transversely oriented
saddle connection in the universal cover a homotopic path of saddle
connections.
If $\sigma$ is a saddle connection in $\hat X$ equipped with a
transverse orientation, let $\cT(\sigma)$ denote the collection of
Euclidean right triangles which are {\em maximal with respect to the
property that they are attached along the hypotenuse to $\sigma$ along
the side given by its transverse orientation}. A triangle $t$ in
$\cT(\sigma)$ must have exactly one singularity in each of its legs,
and so their convex hull $h(t)$ is a single saddle connection.
The set $\cT(\sigma)$ must be finite, and its hypotenuses cover
$\sigma$ in a sequence
of non-nested intervals,
ordered by their left (or right) endpoints. See \Cref{t-example}.
Let $\thull(\sigma)$ be the union of segments $h(t)$ for $t\in\cT(\sigma)$.
\realfig{t-example}{An example of $\thull(\sigma)$ and $P(\sigma)$.}
\begin{lemma}\label{thull structure}
Either $\thull(\sigma) = \sigma$ or
$\sigma\cup\thull(\sigma)$ is the boundary of an embedded Euclidean
polygon $P(\sigma)$ in $\hat X$ which is foliated by arcs of $\lambda^\pm$.
\end{lemma}
\begin{proof}
Suppose that $t$ and $t'$ are triangles of $\cT(\sigma)$ and $p\in
t\cap t'$ is in the interior of $t$. Let $l$ and $l'$ be the vertical
line segments in $t$ and $t'$, respectively, joining $p$ to the
respective hypotenuses ($l'$ could be a single point). If $l$ and
$l'$ leave $p$ in opposite directions then $l\cup l'$ is a
vertical geodesic connecting two points of $\sigma$, which
contradicts the uniqueness of geodesics in $\hat X$. If they leave
$p$ in the same direction but are not equal, then their difference is a vertical
geodesic with endpoints on $\sigma$, again a contradiction.
We conclude that if $t$ and $t'$ intersect they do so on a common
subarc of their hypotenuses. This subarc spans a (nonmaximal) right triangle which
is exactly $t\cap t'$.
Now given $t\in\cT(\sigma)$, the vertical and
horizontal legs of $t$ each contain a single singularity of $\hat X$;
denote these singularities by $v_t$ and $h_t$, respectively. By
construction of $\cT(\sigma)$, there is a unique triangle $t' \in \cT(\sigma)$ such
that $h_{t'} = v_{t}$, unless $v_{t}$ is an endpoint of
$\sigma$. Hence, given an orientation on $\sigma$, the edges of
$\thull(\sigma)$ come with a natural ordering induced by moving along
$\sigma$. By our observations above, we see that $\thull(\sigma)$ is
an embedded arc and meets $\sigma$ only at its endpoints.
Since $\hat X$ is contractible, $\sigma$ and $\thull(\sigma)$ must be
homotopic and hence cobound a disk $P(\sigma)$. In fact this disk is foliated by
both $\lambda^+$ and $\lambda^-$, as we can see by noting that each
edge of $\thull(\sigma)$ cobounds a vertical (similarly a horizontal)
strip with a segment in $\sigma$. Hence $P(\sigma)$ admits an isometry
to a polygon in $\mathbb{R}^2$.
\end{proof}
Let us define a map $\thull^+_\sigma:\sigma\to \thull(\sigma)$ (resp. $\thull^-_\sigma$) which
is the result of pushing the points of $\sigma$ along the
vertical (resp. horizontal) foliation to the other side of $P(\sigma)$.
If $f\colon I \to \hat X$ is an embedding of an oriented 1-manifold $I$ that parametrizes
some union of saddle connections, we let
\begin{equation}\label{thull f}
\thull^+ f\colon I \to \hat X
\end{equation}
be the map that sends each $p\in I$ to $\thull^+_\sigma(f(p))$, where
$\sigma$ is the saddle connection containing $f(p)$ with transverse orientation induced by the orientation on $I$. By composing with
covering maps we can use the same notation for the resulting operation
in quotients $\hat X_Y$ or $\bar X$.
Unlike the rectangle hulls, the edges of $\thull(\sigma)$ are not
necessarily $\tau$-edges. (See the upper-right red saddle connection in \Cref{t-example}.)
Moreover, the $\thull$-version of \Cref{r disjoint} is in general not true.
That is, the image of $\thull$ may not project to an embedded complex in $\bar X$ since $\sigma_1$ and $\sigma_2$ can be disjoint while $\thull(\sigma_1)$ and $\thull(\sigma_2)$ cross. However, we do have the following:
\begin{lemma}\label{disjoint_thulls}
Let $\sigma,\sigma'$ be saddle connections in $\hat X$ with disjoint interiors. Let $l$ be an
arc of $\lambda^+$ with endpoints on $\sigma$ and $\sigma'$, and give
$\sigma$ and $\sigma'$ the transverse orientation pointing toward the
interior of $l$. Then the polygons $P(\sigma)$ and $P(\sigma')$ of $\hat X$ (from \Cref{thull structure}) have disjoint interiors.
\end{lemma}
\begin{proof}
Suppose towards a contradiction that there is a point $p$ which is in
the interior of each of the polygons $P = P(\sigma)$ and $P' =
P(\sigma')$.
Since $P$ and $P'$ are foliated by $\lambda^+$, let $m$ and $m'$ be
the arcs of $\lambda^+$ which are properly embedded in $P$ and $P'$
respectively, and pass through $p$. Orient $m$ so that it begins in
$\sigma$, and $m'$ so that it terminates in $\sigma'$. These
orientations agree at $p$: if they did not we would obtain a
contradiction by applying Gauss--Bonnet to the circuit passing through
$m$,$\sigma$,$l$,$\sigma'$ and $m'$.
Thus, the union $J=m\cup m'$ is an interval in a leaf of $\lambda^+$ with endpoints on
$\sigma$ and $\sigma'$, with $p$ in the interior of $m\cap m'$. (If $p$ were in $l$ already then
we would have $J=l$.)
Orienting $J$ as $[y,y']$ where $y\in \sigma$ and $y'\in\sigma'$, we
can write $m=[y,x]$ and $m'=[x',y']$, where $x = J\cap
\thull(\sigma)$ and $x'= J\cap \thull(\sigma')$. These points
appear, in order along $J$, as $y,x',p,x,y'$.
\realfig{disjoint-P}{The point $p$ cannot lie in the interior of both
$P(\sigma)$ and $P(\sigma')$.}
Let $t$ and $t'$ be the triangles of $\cT(\sigma)$ and $\cT(\sigma')$
containing $x$ and $x'$, respectively. Then $p\in t\cap t'$.
Let $\kappa$ and $\kappa'$ be the
saddle connections of $\thull(\sigma)$ and
$\thull(\sigma')$ spanning $t$ and $t'$, respectively
(See \Cref{disjoint-P}).
The fact that the endpoints of $\kappa$ and $\kappa'$ are disjoint
from the intersection of $t$ and $t'$ implies that $\kappa\cap
J$, which is $x$, lies below $\kappa'\cap J$, which is
$x'$. This contradicts the ordering of the points in $J$.
\qedhere
\end{proof}
\subsection{Retractions in $\A$} \label{sec:totally_geo}
In this subsection, $X$ is fully-punctured.
Let $\A(\tau) \subset \A(X)$ be the span of the vertices of $\A(X)$
which are represented by edges of $\tau$. We will
construct a \emph{coarse 1-Lipschitz retraction} from $\A(X)$ to $\A(\tau)$.
By this, we mean a coarse map which takes diameter $\le 1$ sets to diameter $\le 1$
sets and restricts to the identity on the 0-skeleton of $\A(\tau) \subset \A(X)$.
First, let $\mathcal{SC}(q) \subset \A(X)$ be the arcs of $X$ which
can be realized by saddle connections of $q$. Hence,
$\A(\tau) \subset \mathcal{SC}(q) \subset \A(X)$.
For any $a \in \A(X)$
define $\mathbf{s}(a)\subset \mathcal{SC}(q)$ as follows: If $a_q$ is the
$q$-geodesic representative of $a$ in $\bar X$, then let $\mathbf{s}(a)$
be the set of saddle connections of $q$ composing
$a_q$. If $a$ is a cylinder curve of $q$, then we take $\mathbf{s}(a)$ to be
the set of saddle connections appearing in the boundary of the maximal
cylinder of $a$. Note that if $a \in \A(X)$ is itself represented by a saddle
connection of $q$, then $\mathbf{s}(a)=\{a\}$.
The following lemma shows that $\mathbf{s}$ is well-defined and is a
coarse $1$-Lipschitz retraction, in the above sense.
\begin{lemma} \label{saddle_proj}
For adjacent vertices $a,b \in \A(X)$, the vertices of $\mathbf{s}(a)$ and
$\mathbf{s}(b)$ are pairwise adjacent or equal.
\end{lemma}
\begin{proof}
Recall that adjacency of vertices in $\A(X)$ corresponds to disjointness of their
hyperbolic geodesic representative, and for vertices realized by
saddle connections, this corresponds to the lack of transverse
intersection of their interiors.
But if any arcs of $\mathbf{s}(a)$ and $\mathbf{s}(b)$ have crossing interiors,
\Cref{cor:side_coherence} implies that the hyperbolic geodesic
representatives of $a$ and $b$ must cross as well. The lemma follows.
\end{proof}
Combining this lemma with \Cref{r disjoint} gives us the proof of
\Cref{th:total geodesic}, which we restate here in somewhat more
precise language:
\restate{th:total geodesic}{
{\rm (Geodesically connected theorem).}
Let $(X,q)$ be fully punctured with associated veering triangulation $\tau$.
The composition $\rhull \circ \mathbf{s} \colon \A(X) \to \A(\tau)$ is a coarse
$1$--Lipschitz retraction in the sense that it takes diameter $\le 1$ sets
to diameter $\le 1$ sets, and is the identity on the $0$-skeleton of $\A(\tau)$.
Hence, any two vertices in $\A(\tau)$ are joined by a geodesic of $\A(X)$ that lies
in $\A(\tau)$.}
\begin{proof}
\Cref{saddle_proj} says that $\mathbf{s}:\A(X)\to\mathcal{SC}(q)$ is a coarse $1$-Lipschitz
retraction. \Cref{r disjoint}, interpreted as a statement about the
arc and curve complexes, says the same for
$\rhull:\mathcal{SC}(q)\to\A(\tau)$. The theorem follows.
\end{proof}
\section{Introduction}
\label{intro}
Let $M$ be a 3-manifold fibering over the circle with fiber $S$ and
pseudo-Anosov monodromy $f$. The stable/unstable laminations
$\lambda^+,\lambda^-$ of $f$ give rise to a function on the essential
subsurfaces of $S$,
$$
Y \mapsto d_Y(\lambda^+,\lambda^-),
$$
where $d_Y$ denotes distance in the curve and arc complex of $Y$
between the lifts of $\lambda^\pm$ to the cover of $S$ homeomorphic to $Y$. This distance
function plays an important role in the geometry of the mapping class
group of $S$ \cite{MM2,BKMM, masur2013geometry}, and in the hyperbolic
geometry of the manifold $M$ \cite{ECL1, ELC2}.
In this paper we study the function $d_Y$ when $M$ is fixed
and the fibration is varied. The fibrations of a given manifold are
organized by the faces of the unit ball of Thurston's norm on
$H_2(M,\partial M)$, where each {\em fibered face} $\mathcal{F}$ has the
property that every irreducible integral class in the open cone $\RR_+\mathcal{F}$
represents a fiber.
There is a pseudo-Anosov flow which is transverse to
every fiber represented by $\mathcal{F}$, and whose stable/unstable
laminations $\Lambda^\pm\subset M$ intersect each fiber to give the laminations
associated to its monodromy. With this we note that
the projection distance $d_Y(\lambda^+,\lambda^-)$ can be defined for any
subsurface $Y$ of any fiber in $\mathcal{F}$. We use $d_Y(\Lambda^+,\Lambda^-)$ to
denote this quantity.
Our main results give explicit connections between $d_Y$ and
the {\em veering triangulation} of $M$, introduced by Agol \cite{agol2011ideal} and refined by
Gu\'eritaud \cite{gueritaud}, with the main feature being that when $d_Y$ satisfies
explicit lower bounds, a thickening of $Y$ is realized as
an embedded subcomplex of
the veering triangulation. In this way, the ``complexity'' of the
monodromy $f$ is visible directly in the triangulation in a way that
is independent of the choice of fiber in the face $\mathcal{F}$.
This is in contrast with the results of \cite{ELC2} in which the estimates
relating $d_Y$ to the hyperbolic geometry of $M$ are
heavily dependent on the genus of the fiber.
The results are cleanest in the setting of a {\em fully-punctured}
fiber, that is when the singularities of the monodromy $f$ are assumed
to be punctures of the surface $S$ (one can obtain such examples by
starting with any $M$ and puncturing the singularities and their
flow orbits). All fibers in a face $\mathcal{F}$ are fully-punctured when any one
is, and in this case we say that $\mathcal{F}$ is a {\em fully-punctured face.}
In this setting $M$ is a cusped manifold and the veering triangulation
$\tau$ is an ideal triangulation of $M$.
We obtain bounds on $d_W(\Lambda^+,\Lambda^-)$ that hold for $W$ in any
fiber of a given fibered face:
\begin{theorem}[Bounding projections over a fibered
face] \label{th:bounding projections}
Let $M$ be a hyperbolic 3-manifold with fully-punctured fibered face
$\mathcal{F}$ and veering triangulation $\tau$.
For any essential subsurface $W$ of any fiber of $\mathcal{F}$,
\[
\alpha \cdot (d_W(\Lambda^- ,\Lambda^+) -\beta) < |\tau|,
\]
where $|\tau|$ is the number of tetrahedra in $\tau$,
$\alpha = 1$ and $\beta = 10$ when $W$ is an annulus and
$\alpha = 3|\chi(W)|$ and $\beta = 8$ when $W$ is not an annulus.
\end{theorem}
Note that
this means that $d_W \le |\tau| +10$ for each subsurface $W$,
no matter which fiber $W$ lies in.
Further, the complexity $|\chi(W)|$ of any subsurface $W$ of any fiber
of $\mathcal{F}$ with $d_W(\Lambda^+,\Lambda^-) \ge 9$ is also bounded in
terms of $M$ alone.
In addition, given one fiber with a collection of subsurfaces
of large $d_Y$, we obtain control over the appearance of
high-distance subsurfaces in all other fibers:
\begin{theorem}[Subsurface dichotomy] \label{th:sub_dichotomy_fully_punctured}
Let $M$ be a hyperbolic 3-manifold with fully-punctured fibered face
$\mathcal{F}$ and suppose that $S$ and $F$ are each fibers in $\mathbb{R}_+\mathcal{F}$.
If $W$ is a subsurface of $F$, then either $W$ is isotopic
along the flow to a subsurface of $S$, or
$$3|\chi(S)| \ge d_W(\Lambda^-,\Lambda^+) -\beta,$$
where $\beta =10$ if $W$ is an annulus and $\beta = 8$ otherwise.
\end{theorem}
One can apply this theorem with $S$ taken to be the
smallest-complexity fiber in $\mathcal{F}$. In this case there is some finite
list of ``large'' subsurfaces of $S$, and
for all other fibers and all subsurfaces $W$ with $d_W$ sufficiently large,
$W$ is already accounted for on this finite list.
For a sample
application of \Cref{th:sub_dichotomy_fully_punctured},
let $W$ be an essential annulus with core
curve $w$ in a fiber $F$ of $M$
and suppose that $d_W(\Lambda^-,\Lambda^+) \ge K$ for some $K > 10$. (We note
that it is easy to construct explicit examples of $M$ with $d_W(\Lambda^-,\Lambda^+)$
as large as one wishes by starting with a pseudo-Anosov homeomorphism of $F$
with large twisting about the curve $w$.) If $w$ is trivial
in $H_1(M)$, then \Cref{th:sub_dichotomy_fully_punctured}
(or more precisely \Cref{always subsurface}) implies that $w$ is actually isotopic
to a simple closed curve in \emph{every} fiber in the open cone $\RR_+\mathcal{F}$ containing
$F$. When $w$ is nontrivial in $H_1(M)$ it determines a codimension-$1$ hyperplane
$P_w$ in $H^1(M) = H_2(M,\partial M)$ consisting of cohomology classes which
vanish on $w$. For each fiber $S$ of $\RR_+\mathcal{F}$ either $S$ is contained in $P_w$,
in which case $w$ is isotopic to a simple closed curve in $S$ as before, or $S$ lies
outside of $P_w$ and $|\chi(S)| \ge \frac{K-10}{3}$.
We remark that the second alternative is non-vacuous so long as
$H^1(M)$ has rank at least 2.
The general (non-fully-punctured) setting is also approachable with
our techniques, but a number of complications arise and
the connection to the veering triangulation of the fully-punctured manifold
is much less explicit.
An extension of the results in this paper to the
general setting will be the subject of a subsequent paper.
\subsection*{Pockets in the veering triangulation}
When $Y$ is a subsurface of a fiber $X$ in $\mathcal{F}$ and
$d_Y(\Lambda^+,\Lambda^-)>1$, we show (\Cref{thm: tau-compatible})
that $Y$ is realized simplicially in the veering triangulation lifted
to the cover $X\times\mathbb{R}$. If $d_Y(\Lambda^+,\Lambda^-)$ is even larger then
this realization can be thickened to a ``pocket'', which is a
simplicial region bounded by two isotopic copies of $Y$. With
sufficiently large assumptions this pocket can be made to embed in $M$
as well, and this is our main tool for connecting arc complexes to the
veering triangulation and establishing Theorems \ref{th:bounding
projections} and \ref{th:sub_dichotomy_fully_punctured}:
\begin{theorem}\label{thm:pocket summary}
Suppose $Y$ is a subsurface of a fiber $X$ with
$d_Y(\lambda^-,\lambda^+) > \beta$, where $\beta=8$ if $Y$ is
nonannular and $\beta=10$ if $Y$ is an annulus.
Then there is an embedded simplicial pocket $V$ in $M$ isotopic to a
thickening of $Y$, and
with $d_Y(V^-,V^+) \ge d_Y(\lambda^-,\lambda^+) - \beta$.
\end{theorem}
In this statement, $V^+$ and $V^-$ refer to the triangulations of the
top and bottom surfaces of the pockets, regarded as simplices in
the curve and arc complex $\A(Y)$. Also, $d_Y(V^-,V^+)$ denotes
the smallest $d_Y$-distance between an arc of $V^ -$ and an arc of $V^+$.\\
The veering triangulation in fact
recovers a number of aspects of the geometry of curve
and arc complexes in a fairly concrete way. As an illustration we prove
\begin{theorem}\label{th:total geodesic}
In the fully punctured setting, the arcs of the veering triangulation
form a geodesically connected subset $\A(\tau)$ of the curve and arc graph, in the sense that any two points in $\A(\tau)$ are connected by a geodesic that lies in $\A(\tau)$.
\end{theorem}
\subsection*{Hierarchies of pockets}
One is naturally led to generalize \Cref{thm:pocket summary} from a
result embedding one pocket at a time to a description of all pockets
at once. Indeed \Cref{prop:disjoint_pockets} tells us that whenever
subsurfaces $Y$ and $Z$ of $X$ have large enough projection distances and are
not nested,
they have associated pockets $V_Y$ and $V_Z$ which are disjoint in
$X \times \RR$.
These facts, taken together with
\Cref{th:total geodesic}, strongly suggest that the veering triangulation $\tau$
encodes the hierarchy of curve complex geodesics between $\lambda^\pm$ as
introduced by Masur-Minsky in \cite{MM2}. We expect that, using a
version of \Cref{th:total geodesic} that applies to subsurfaces and
adapting the notion of ``tight geodesic'' from \cite{MM2}, one can
carry out a hierarchy-like construction within the veering triangulation
and recover much of the structure found in \cite{MM2}, with more
concrete control, at least in the
fully-punctured setting. We plan to explore this approach in future
work.
\subsection*{Related and motivating work}
The theme of using fibered 3-manifolds to study infinite families of
monodromy maps is deeply explored in McMullen \cite{mcmullen2000polynomial} and
Farb-Leininger-Margalit \cite{farb-leininger-margalit}, where the focus is on
Teichm\"uller translation distance.
Distance inequalities analogous to
\Cref{th:sub_dichotomy_fully_punctured}, in the setting of Heegaard
splittings rather than surface bundles, appear in Hartshorn \cite{hartshorn},
and then more fully
in Scharlemann-Tomova \cite{scharlemann-tomova}. Bachman-Schleimer
\cite{BSc} use Heegaard surfaces to give bounds on the
curve-complex translation distance of the monodromy of a fibering. All
of these bounds apply to entire surfaces and not to subsurface
projections. In Johnson-Minsky-Moriah
\cite{johnson-minsky-moriah:subsurface}, subsurface projections are
considered in the setting of Heegaard splittings. A basic difficulty
in these papers which we do not encounter here is the compressibility of
the Heegaard surfaces, which makes it tricky to control essential
intersections. On the other hand,
unlike the surfaces and handlebodies that are used to obtain control
in the Heegaard setting, the foliations we consider here are infinite
objects, and the connection between them and finite arc systems in the
surface is a priori dependent on the fiber complexity. The veering
triangulation provides a finite object that captures this connection
in a more uniform way.
The totally-geodesic statement of \Cref{th:total geodesic} should be compared to
Theorem 1.2 of Tang-Webb \cite{tang-webb}, in which Teichm\"uller disks give rise to
quasi-convex sets in curve complexes. While the results of
Tang-Webb are more general, they are coarse, and it is interesting
that in our setting a tighter statement holds. Finally, we note that work by several authors
has focused on geometric aspects of the veering triangulation, including \cite{hodgson2011veering,futer2013explicit,hodgson2016non}.
\subsection*{Summary of the paper}
In \Cref{background} we set some notation and give Gu\'eritaud's
construction of the veering triangulation.
We also recall basic facts
about curve and arc complexes, subsurface projections and Thurston's
norm on homology. We spend some time in this section describing the
flat geometry of a punctured surface with an integrable
holomorphic quadratic
differential, and in particular giving an explicit description of the
circle at infinity of its universal cover (\Cref{same compactification}).
While this is a fairly familiar picture, some delicate issues arise
because of the incompleteness of the metric at the punctures.
In \Cref{sections} we study {\em sections} of the veering
triangulations, which are simplicial surfaces isotopic to $X$ in the
cover $X\times\mathbb{R}$, and transverse to the suspension flow of the
monodromy. These can be thought of as triangulations of the surface
$X$ using only edges coming from the veering triangulation.
We prove \Cref{lem:extension} which says that a partial triangulation
of $X$ using only edges from $\tau$ can always be extended to a full section, and
\Cref{prop:connect} which says that any two extensions of a partial
triangulation are connected by a sequence of ``tetrahedron
moves''. This is what allows us to define and study the ``pockets''
that arise between any two sections.
In \Cref{hulls} we define a simple but useful construction, rectangle and
triangle hulls, which map saddle connections in our surface to unions
of edges of the veering triangulation. An immediate consequence of
the properties of these hulls is a proof of \Cref{th:total
geodesic}.
In \Cref{surface_reps} we apply the flat geometry developed in
\Cref{background} to control the convex hulls of subsurfaces of the
fiber, and then use \Cref{hulls} to construct what we call
$\tau$-hulls, which are representatives of the homotopy class of a
subsurface that are simplicial
with respect to the veering triangulations. \Cref{thm: tau-compatible}
states that quite mild assumptions on $d_Y(\lambda^+,\lambda^-)$ imply
that the $\tau$-hull of $Y$ has embedded interior. The idea here is that any
pinching point of the $\tau$-hull is crossed by leaves of $\lambda^+$ and
$\lambda^-$ that intersect each other very little.
The main results of both \Cref{hulls} and \Cref{surface_reps} apply
in a general setting and do not require that the surface $X$ be fully-punctured.
In \Cref{pockets} we put these ideas together to prove our main
theorems for fibered manifolds with a fully-punctured fibered face.
In \Cref{Y pocket} we describe the maximal
pocket associated to a subsurface $Y$ with $d_Y(\Lambda^+,\Lambda^-)$
sufficiently large (greater than 2, for nonannular $Y$).
We then introduce the notion of an {\em isolated pocket},
which is a subpocket of the maximal pocket
that has good embedding properties in the manifold $M$. The existence
and embedding properties of these pockets are established in
\Cref{lem:iso_pocket} and \Cref{prop:disjoint_pockets}, which
together allow us to prove \Cref{thm:pocket summary}.
From here, a simple counting argument gives \Cref{th:bounding projections}: the size of the
embedded isolated pockets is bounded from below in terms of
$d_Y(\Lambda^+,\Lambda^-)$ and $\chi(Y)$, and from above by the total number
of veering tetrahedra.
To obtain \Cref{th:sub_dichotomy_fully_punctured}, we use the pocket
embedding results to show that, if $Y$ is a subsurface of one fiber
$F$ and $Y$ essentially intersects another fiber $S$, then $S$ must
cross every level surface of the isolated pocket of $Y$, and hence the
complexity of $S$ gives an upper bound for $d_Y(\Lambda^+,\Lambda^-)$. To
complete the proof we need to show that, if $Y$ does not essentially
cross $S$, it must be isotopic to an embedded (and not merely immersed)
subsurface of $S$. This is handled by
\Cref{lem:embedding_fullly_punctured}, which may be of independent
interest. It gives a uniform upper bound for $d_Y(\Lambda^+,\Lambda^-)$ when
$Y$ corresponds to a finitely generated subgroup of $\pi_1(S)$, unless
$Y$ covers an embedded subsurface.
\subsection*{Acknowledgments}
The authors are grateful to Ian Agol and Fran\c{c}ois Gu\'eritaud for explaining their work to us. We also thank Tarik Aougab, Jeff Brock, and Dave Futer for helpful conversations and William Worden for pointing out some typos in an earlier draft. Finally, we thank the referee for a thorough reading of our paper and comments which improved its readability.
\section{Embedded pockets of the veering triangulation and bounded projections}
\label{pockets}
In this section, let $X$ be fully-punctured with respect to the
foliations $\lambda^\pm$ of a pseudo-Anosov $f:X\to X$, and let $M$ be
the mapping torus. Recall that every fiber associated to the fibered
face $\mathcal{F}$ of $X$ must also be fully-punctured because they are transverse
to the same suspension flow, and hence that $\mathcal{F}$ is
a \emph{fully-punctured fibered face}.
We now prove our two main theorems on the structure of subsurface projections
in a fully-punctured fibered face, \Cref{th:bounding projections} and
\Cref{th:sub_dichotomy_fully_punctured}. The main tools in the proof
are the structure and embedding theorems for pockets associated with
high-distance subsurfaces, which we develop below. Recall that $\mathrm{diam}_Z(\cdot)$ denotes the diameter of $\pi_Z(\cdot)$ in $\A(Z)$ and that subsurfaces $Y$ and $Z$ \emph{overlap} if, up to isotopy, they are neither disjoint nor nested.
\subsection{Projections and $\tau$--compatible subsurfaces}
We begin by discussing projection to $\tau$-compatible subsurfaces.
\begin{lemma} \label{lem:overlap_tau}
Let $Y$ and $Z$ be $\tau$-compatible subsurfaces of $X$ and let $K \subset X$
be a disjoint collection of saddle connections which correspond to edges from $\tau$.
Then
\begin{enumerate}
\item If $K$ meets $\int_\tau(Y)$, then $\pi_Y(K) \neq \emptyset$, and $\mathrm{diam}_Y(\pi_Y (K)) \le 1$.
\item If $Y$ and $Z$ are disjoint, then so are $\int_\tau(Y)$ and $\int_\tau(Z)$.
\item If $Y$ and $Z$ overlap, then $\mathrm{diam}_Z(\partial Y \cup \partial_\tau Y) \le 1$.
\item The subsurface $\int_\tau(Y)$ is in minimal position with the foliations $\lambda^\pm$. In particular, the arcs of $\int_\tau(Y) \cap \lambda^\pm$ agree with the arcs of $\pi_Y(\lambda^\pm)$.
\end{enumerate}
\end{lemma}
\begin{proof}
For item (1), the main point is to show that an edge of $K$ that
meets $\int_\tau(Y)$ lifts to an {\em essential edge} in $\bar X_Y$.
This is true for edges meeting $\int_q(Y)$, using the local CAT(0) geometry
of $\bar X_Y$ and the fact that $\hat\iota_q(Y')$ is a locally convex embedding.
Thus it will suffice to show that any $\tau$-edge $e$ meeting
$\int_\tau(Y)$ must also meet $\int_q(Y)$.
Suppose, on the contrary, that $e$ meets $\int_\tau(Y)$ but not $\int_q(Y)$.
Then $e$ meets the interior of a polygon $P(\sigma)$ where $\sigma$ is
an outward-oriented saddle connection in $\partial_q Y$
(recall from \Cref{rmk:fully}
that, since $X$ is fully-punctured, the
inner $\thull$ step in the construction of $\hat\iota_\tau$ is the
identity, and the outer $\thull$ is in fact a rectangle hull).
Let
$R$ be the singularity-free rectangle spanned by $e$. If $e$ is
contained in $P(\sigma)$ then $R$ can be extended to a rectangle whose
diagonal lies in $\sigma$, and hence $e$ is one of the edges of
$\rhull(\sigma)$; but this contradicts the assumption that $e$ meets
$\int_\tau(Y)$. Thus $e$
crosses some edge $f$ of
$\rhull(\sigma)$. However, $f$ is contained in a singularity-free
triangle whose hypotenuse lies along $\sigma$ and so $\sigma$ must
cross the rectangle $R$ either top-to-bottom or side-to-side. In
either case, we see that $e$ crosses $\sigma \subset \partial_q Y$,
a contradiction.
We conclude that if a $\tau$-edge meets $\int_\tau(Y)$, then it also meets $\int_q(Y)$
and hence has a well-defined projection to $Y$.
The diameter bound in item $(1)$ is then immediate since $K$ is a disjoint collection of essential arcs of $\A(X)$.
For item $(2)$, first note that when $Y$ and $Z$ are disjoint subsurfaces of $X$,
the interiors $\int_q(Y)$ and $\int_q(Z)$ are also disjoint. This follows from \Cref{cor:side_coherence} and the $q$-hulls construction in \Cref{q tight}. More precisely,
let $\Lambda_Y$ and $\Lambda_Z$ be the limit sets of $Y$ and $Z$ in $\partial \HH^2$ (using our identifications from \Cref{AY in flat geometry}). Since $Y$ and $Z$ do not intersect, $\Lambda_Y$ and $\Lambda_Z$ do not link in $\partial \HH^2$ and so ${\operatorname{CH}}_q(\Lambda_Y)$ and ${\operatorname{CH}}_q(\Lambda_Z)$ have disjoint interiors by \Cref{cor:side_coherence}. This implies that $\int_q(Y)$ and $\int_q(Z)$ are disjoint in $X$.
To obtain $\int_\tau (Y)$ from $\int_q (Y)$ we append to each saddle
connection $\sigma$ in $\partial_q Y$ the (open) polygon $P(\sigma)$,
where $\sigma$ is oriented out of $Y$. We obtain $\int_\tau (Z)$ from
$\int_q (Z)$ by the same construction.
Since $\int_q(Y)$ and $\int_q(Z)$ are disjoint in $X$, it suffices to show that $P(\sigma)$ and $P(\kappa)$ have disjoint interiors, where $\sigma \subset \partial_qY$ and $\kappa \subset \partial_q Z$. If $\sigma = \kappa$, then this saddle connection spans a singularity-free rectangle and $P(\sigma) = \sigma = \kappa = P(\kappa)$. Otherwise, $\sigma$ and $\kappa$ have disjoint interiors and \Cref{disjoint_thulls} implies that $P(\sigma)$ and $P(\kappa)$ have disjoint interiors, as required.
This proves item (2).
Since $\int_\tau(Y)$ is an embedded representative of the interior of $Y$, $\partial Y$
has a representative disjoint from the collection of saddle
connections in $\partial_\tau Y$. Hence $\mathrm{diam}_Z(\partial Y \cup
\partial_\tau Y) \le 1$, proving item $(3)$. For
item $(4)$, first note that the subsurface $\int_q(Y)$ is in minimal position with the foliations $\lambda^\pm$. This is immediate from the local CAT$(0)$ geometry in $\bar X_Y$ and
the fact that $\lambda^\pm$ are geodesic: any bigon in $\bar X_Y$ between $\hat \iota_q(\partial' Y)$ and a leaf of $\lambda^\pm$ would lift to a bigon in $\hat X$ bounded by two geodesic segments, a contradiction to uniqueness of geodesics in $\hat X$.
The statement for
$\int_\tau(Y)$ then follows from the fact that the homotopy from
$\partial_q Y$ to $\partial_\tau Y$ can be taken to move either along
vertical or along horizontal leaves, using either $\thull^+$ or $\thull^-$ as in
the proof of \Cref{thm: tau-compatible}.
\end{proof}
\subsection{Pockets for a $\tau$-compatible subsurface}
Suppose that $Y \subset X$ is \linebreak $\tau$--compatible. By
\Cref{cor:top}, the set $T(\partial_\tau Y)$ of sections containing
$\partial_\tau Y$ contains a top and a bottom section, denoted $T^+ =
T^+(\partial_\tau Y)$
and $T^- = T^-(\partial_\tau Y)$, which between them bound a number of
pockets. See \Cref{sections} for terminology related to sections and pockets.
Our assumption on $d_Y(\lambda^-,\lambda^+)$ will imply that one
of these pockets is isotopic to a thickening of $Y$, as explained in
the following proposition:
\begin{proposition}[Pockets in $\tau$]\label{Y pocket}
Let $(X,q)$ be fully-punctured and $Y\subset X$ an essential
nonannular subsurface.
\begin{enumerate}
\item If $d_Y(\lambda^-,\lambda^+) > 0$ then
$d_Y(T^+,\lambda^+) = d_Y(T^-,\lambda^-) = 0$.
\item If $d_Y(\lambda^-,\lambda^+) > 2$ then
$T^+$ and $T^-$ bound
a pocket $U_Y$ whose interior is isotopic to a thickening of
$\int(Y)$.
\end{enumerate}
When $Y$ is an annulus,
\begin{enumerate}
\item If $d_Y(\lambda^-,\lambda^+) > 1$ then
$d_Y(T^+,\lambda^+) = d_Y(T^-,\lambda^-) = 1$.
\item If $d_Y(\lambda^-,\lambda^+) > 4$ then
$T^+$ and $T^-$ bound
a pocket $U_Y$ whose interior is isotopic to a thickening of
$\int(Y)$.
\end{enumerate}
\end{proposition}
\begin{proof}
Begin with the following lemma:
\begin{lemma}\label{near lambda}
Suppose that $Y \subset X$
is $\tau$-compatible,
let $e$ be an edge of $\partial_\tau Y$ and let $f$ be a $\tau$-edge
crossing $e$ with $f>e$. Then $d_Y(f,\lambda^+) \le 1$ if $Y$ is an annulus and $d_Y(f,\lambda^+) =0$ otherwise. Similarly if
$f<e$ then the same statement holds for $d_Y(f,\lambda^-)$.
\end{lemma}
\realfig{f-above-e_2}{Local picture near the $\tau$-edge $e$ of $\partial_\tau Y$ with $\int_\tau(Y) \subset X$ shaded. When $f>e$, the edge $l^+$ of $Q$ represents
$\pi_Y(\lambda^+)$ and is disjoint from $f$. Note that $Q$ is \emph{immersed} in $X$.}
The key idea of the proof is pictured in \Cref{f-above-e_2}. Here it is shown that if $f$ crosses $e \subset \partial_\tau Y$ with $f>e$, then some component of the intersection of $f$ with $\int_\tau(Y)$ is disjoint from some arc in $\pi_Y(\lambda^+)$. However, the spanning rectangle $Q$ for $f$ is immersed in $X$ (rather than necessarily embedded).
To handle this issue, we work in the cover $\widetilde X$.
\begin{proof}
Let $C^{\mathrm{o}}$ be a component of the preimage of $\int_\tau(Y)$ under $\widetilde X \to X$ and choose a saddle connection $\til e$ in the boundary of $C^{\mathrm{o}}$ which projects to $e$.
Further, let $\til f$ be any lift of $f$ which crosses $\til e$.
Since $f$ is a $\tau$-edge, $\til f$ spans a singularity-free rectangle $\til Q$ whose immersed image in $X$ we denote by $Q$.
Every $\tau$-edge which crosses $\til Q$ does so either
top to bottom or side to side.
Since $f>e$, $\til e$ must cross $\til Q$ from side to side (see
\Cref{sections}).
Since all $\tau$-edges in $\partial C^{\mathrm{o}}$ are disjoint, they all must
cross $\til Q$ from side to side.
Since $\int_\tau(Y)$ is in minimal position with $\lambda^+$
(\Cref{lem:overlap_tau}), $C^{\mathrm{o}}$ intersects each leaf of the vertical
foliation in a connected set.
Together these observations
imply that $\til Q \cap C^{\mathrm{o}}$ is a single polygon $\til B$,
bounded by at least one edge crossing $\til Q$ from side to side
(which we have called $\til e)$. See \Cref{f-above-e_cover}.
\begin{figure}[htbp]
\begin{center}
\includegraphics[scale = .7]{f-above-e_cover}
\caption{The 3 possibilities for $\til B$. The lightly shaded region is part of $C^{\mathrm{o}}$ in $\widetilde X$.}
\label{f-above-e_cover}
\end{center}
\end{figure}
\begin{claim*}
$\til B$ embeds in $\int_\tau (Y)$ under the covering $\til X \to X$.
\end{claim*}
\begin{proof}[Proof of claim]
Since $\til B \subset C^{\mathrm{o}}$, the image of $\til B$ is contained in $\int_\tau (Y)$.
Suppose that $x,y \in \til B$ map to the same point in $\int_\tau(Y)$, and denote by $l_x$ and $l_y$ the vertical leaf segments in $\til X$ starting at $x$ and $y$, respectively, and continuing to $\til e$. Since $\til B$ is convex,
$l_x,l_y \subset \til B$. Suppose that $l_x$ is no longer than $l_y$ and let $l_y'$ be the subsegment of $l_y$ with length equal to that of $l_x$. Then $l_x$ and $l_y'$ are identified under the map $\til X \to X$. But the identification of $ \partial l_x \ssm \{x\} \subset \til e$ and $ \partial l'_y \ssm \{y\} \subset \til B \cup \til e \subset C^{\mathrm{o}} \cup \til e$ gives a contradiction, unless $x=y$: the edge $\til e$ is mapped injectively into $X$ with image $e\subset \partial_\tau Y$ disjoint from the image of $C^{\mathrm{o}}$, which is $\int_\tau (Y)$.
\end{proof}
Let $\til s$ be the vertex of $\til f$ which
is on the same side of $\til e$ as $\til B$.
Let $\til l$ be the vertical side of $\til Q$ starting at $\til s$.
Let $B$ be the image of $\til B$ in $X$. By the claim, $B$ is a
singularity-free quadrilateral in $X$ whose interior is contained in
$\int_\tau(Y)$. The images in $X$ of $\til f \cap \til B$ and $\til l
\cap \til B$ are therefore disjoint proper arcs in
$\int_\tau(Y)$, which by
\Cref{lem:overlap_tau} are representatives of
$\pi_Y(f)$ and $\pi_Y(\lambda^+)$, respectively. Moreover, these arcs are properly
homotopic in $\int_\tau(Y)$ by a homotopy supported in $B$.
Hence, when $Y$ is nonannular, we conclude that $d_Y(f,\lambda^+) =0$.
If $Y$ is an annulus, we project the picture to the annular cover
$X_Y$, where
we note that the image $l$ of $\til l$, continued to infinity, cannot intersect
$f$ without meeting $Q$, and hence $e$, again. Since $l$ can only
meet $\partial_q Y$ once in the annular cover, we conclude it is
disjoint from $f$ and so
$d_Y(f,\lambda^+) =1$.
The case $f<e$ is similar, so \Cref{near lambda} is proved.
\end{proof}
We return to the proof of \Cref{Y pocket}.
Let $Y$ be nonannular.
Note that by definition the only
upward-flippable edges in $T^+$ must lie in $\partial_\tau Y$. Let
$e$ be such an edge and consider the single flip move that replaces
$e$ with an edge $f$. Then $f>e$, so by \Cref{near lambda},
$d_Y(f,\lambda^+) = 0$. On the other hand $f$ and $e$ are diagonals
of a quadrilateral made of edges of $T^+$, at least one of which, $e'$,
gives the same element of $\A(Y)$ as $f$. Hence
$d_Y(T^+,\lambda^+) = 0.$
If $Y$ is an annulus, we note that $e'$ and the vertical leaf in the
proof of \Cref{near lambda} give adjacent vertices of $\A(Y)$, so
$d_Y(T^+,\lambda^+)\le 1$. Note that $d_Y(T^+,\lambda^+) \ne 0$ because no
leaf of the foliation $\lambda^+$ has both its endpoints terminating at
completion points.
To prove the statements about pockets, let $K$ be the common edges of
$T^+$ and $T^-$,
viewed as a subcomplex of $X$.
If $\int_\tau(Y)$ contains an edge of $K$ then from the triangle inequality,
together with the first part of the proposition,
we obtain $d_Y(\lambda^+,\lambda^-) \le 2$ when $Y$ is
nonannular, and
$d_Y(\lambda^+,\lambda^-) \le 4$ when $Y$ is an annulus. By our
hypotheses this does not happen, so we conclude that
$T^+,T^- \in T(\partial_\tau Y)$ have no common edges contained
in $\int_\tau (Y)$. Hence $T^+$ and $T^-$ bound a pocket $U_Y$ whose base is
$\int_\tau(Y)$. This completes the proof.
\end{proof}
\subsection{Isolated pockets and projection bounds}
Let $X$ be a fiber in $\mathbb{R}_+\mathcal{F}$, and
let $Y$ be a $\tau$--compatible subsurface of $X$
such that $d_Y(\lambda^-,\lambda^+)>4$.
An \emph{isolated pocket} for $Y$ in $(X \times \mathbb{R}, \tau)$ is a subpocket $V = V_Y$ of $U_Y$ with base $\int_\tau (Y)$ such that
\begin{enumerate}
\item For each edge $e$ of $V$ which is not contained in $\partial_\tau Y$,
\[
d_Y(e,\lambda^+) \ge 3 \quad \text{and} \quad d_Y(e,\lambda^-) \ge 3
\]
if $Y$ is nonannular, and
\[
d_Y(e,\lambda^+) \ge 4 \quad \text{and} \quad d_Y(e,\lambda^-) \ge 4
\]
if $Y$ is an annulus.
\item Denoting by $V^\pm$ the top and bottom of $V$ with their induced triangulations,
\[
d_Y(V^-, V^+) \ge 1.
\]
\end{enumerate}
Note that condition $(2)$ guarantees that $\mathrm{int}(V_Y) \cong \int_\tau(Y) \times (0,1)$ is still a pocket just as in \Cref{Y pocket}. The next lemma shows that for $Y$ with $d_Y(\lambda^-,\lambda^+)$ sufficiently large, $Y$ has an isolated pocket with $d_Y(V^-,V^+)$ roughly $d_Y(\lambda^-,\lambda^+)$.
\begin{lemma} \label{lem:iso_pocket}
Suppose that $Y$ is a nonannular subsurface of $X$ with
$d_Y(\lambda^-,\lambda^+) > 8$. Then $Y$ has an isolated pocket $V$
with $d_Y(V^-,V^+) \ge d_Y(\lambda^-,\lambda^+) - 8$.
If $Y$ is an annulus with
$d_Y(\lambda^-,\lambda^+) > 10$, then $Y$ has an isolated pocket $V$
with $d_Y(V^-,V^+) \ge d_Y(\lambda^-,\lambda^+) - 10$.
\end{lemma}
\begin{proof}
Let $c=4$ if $Y$ is an annulus and $c=3$ otherwise, and assume that
$d_Y(\lambda^+,\lambda^-) > 2c+2$.
Since the pocket $U = U_Y$ is connected (\Cref{prop:connect}), there is a sequence of
sections $T^- = T_0, T_1, \ldots, T_N = T^+$ in $T(\partial_\tau Y)$
such that $T_{i+1}$ differs from $T_i$
by an upward diagonal exchange. From \Cref{Y pocket}, we know that
$d_Y(T^- , \lambda^-) \le 1$ and $d_Y(T^+ , \lambda^+) \le 1$. Let $0
< a < N$ be largest integer such that
$d_Y(T_{a-1}, \lambda^-) < c$; hence $d_Y(T_{i}, \lambda^-) \ge c$
for all $i\ge a$. Now let $b<N$ be the smallest integer greater than
$a$ such that
$d_Y(T_{b+1},\lambda^+) < c$; then $d_Y(T_{i},\lambda^+) \ge c$ for
all $a\le i \le b$.
Note that these indices exist since $d_Y(\lambda^-,\lambda^+) \ge 2c+1$.
Now let $V$ be the pocket between $T_a$ and $T_b$ with base contained in
$\int_\tau(Y)$ and note that $V$ is a subpocket of $U$.
Any edge $e$ of $V$ not contained in $\partial_\tau Y$ is
contained in a section
$T_i \in T(\partial_\tau Y)$ for $a \le i \le b$. Since we have
$d_Y(T_i,\lambda^\pm)\ge c$, we have $d_Y(e,\lambda^\pm)\ge c$. Thus it
only remains to get a lower bound on $d_Y(V^+,V^-)$.
The triangle
inequality (and diameter bound on $T_a$ and $T_b$) gives
\[
d_Y (V^-,V^+) = d_Y(T_a,T_b) \ge d_Y(\lambda^-,\lambda^+) - 2c -2 \ge 1.
\]
This implies that $\int_\tau (Y)$ is the base of $V$ and completes the proof.
\end{proof}
The following proposition shows that isolated pockets coming from either disjoint or overlapping subsurfaces of $X$ have interiors which do not meet.
\begin{proposition}[Disjoint pockets] \label{prop:disjoint_pockets}
Suppose that $Y$ and $Z$ are subsurfaces of $X$ with isolated pockets $V_Y$ and $V_Z$. Then, up to switching $Y$ and $Z$, either $Y$ is nested in $Z$, or the isolated pockets $V_Y$ and $V_Z$ have disjoint interiors in $X \times \mathbb R$.
\end{proposition}
\begin{proof}
If the subsurfaces $Y$ and $Z$ are disjoint, then $\int_\tau(Y)$ and $\int_\tau(Z)$ are also disjoint by \Cref{lem:overlap_tau}. Hence, the maximal pockets $U_Y$ and $U_Z$ have disjoint interiors by definition.
Now suppose that $Y$ is not an annulus.
We claim that if $Y$ and $Z$ overlap then either
\[
d_Y(\partial_\tau Z, \lambda^+)\le 1 \; \text{ or } \; d_Y(\partial_\tau Z,\lambda^-) \le 1.
\]
To see this, first note that there is some edge $f$
contained in $\int_\tau(Z)$
such that $f$ crosses some edges of $\partial_\tau Y$.
Otherwise, every triangulation of $\int_\tau(Z)$ by $\tau$--edges
would contain edges from $\partial_\tau Y$. But then applying this to
$T^\pm(\partial_\tau Z)$ and using \Cref{Y pocket},
we would have that
\[
d_Z(\lambda^-,\lambda^+) \le 2 + \mathrm{diam}_Z(\partial_\tau Y) \le 3,
\]
contradicting our assumption on the subsurface $Z$.
Now if $f$ intersects an edge $e$ of $\partial_\tau Y$ and $f>e$, then
by \Cref{near lambda}, $d_Y(\partial_\tau Z, \lambda^+)\le
d_Y(\partial_\tau Z, f) \le 1$. If $f<e$ then \Cref{near lambda} gives
$d_Y(\partial_\tau Z, \lambda^-)\le d_Y(\partial_\tau Z, f) \le 1$.
Now suppose that $e$ is an edge of $U_Y \cap U_Z$ which is not
contained in $\partial_\tau Y \cup \partial_\tau Z$. Then $e$, as a
$\tau$-edge in $X$, is disjoint from $\partial_\tau Z$ and so
$d_Y(e,\lambda^+) \le 2$ or
$d_Y(e,\lambda^-) \le 2$.
Hence $e$ cannot be contained in $V_Y$.
We conclude that $V_Y \cap V_Z \subset \partial_\tau Y \cup
\partial_\tau Z$. This completes the proof when $Y$ is not an
annulus.
When $Y$ is an annulus, then a similar argument using the annular case of \Cref{near lambda} shows that if $Y$ and $Z$ overlap then either
\[
d_Y(\partial_\tau Z, \lambda^+)\le 2 \; \text{ or } \; d_Y(\partial_\tau Z,\lambda^-) \le 2.
\]
Hence, if $e$ is an edge of $U_Y \cap U_Z$ which is not
contained in $\partial_\tau Y \cup \partial_\tau Z$, then
$d_Y(e,\lambda^\pm) \le 3$. So again $e$ cannot be contained in $V_Y$ and we conclude that $V_Y \cap V_Z \subset \partial_\tau Y \cup \partial_\tau Z$ as required.
\end{proof}
We next prove that isolated pockets embed into the fibered manifold
$M$. This is \Cref{thm:pocket summary}, which we restate here in more
precise language.
\restate{thm:pocket summary}{
{\rm (Embedding the pocket).}
Suppose $Y$ is a subsurface of a fully-punctured fiber $X$ with
$d_Y(\lambda^-,\lambda^+) > \beta$, where $\beta=8$ if $Y$ is
nonannular and $\beta=10$ if $Y$ is an annulus.
Then $Y$ has an isolated pocket $V_Y$ in $X \times \mathbb{R}$, and the
covering map $X \times \mathbb{R} \to M$ restricts to an embedding of the
subcomplex $V_Y \to M$.
}
\begin{proof}
Let $\Phi$ be the simplicial isomorphism of $X \times \mathbb{R}$ induced by $f$ as in \Cref{gueritaud construction}.
Note that if $T$ is a section of $\tau$, then $\Phi (T)$ is the section of $\tau$ whose corresponding triangulation of $X$ is $f(T)$.
Hence, $\Phi(T(\partial_\tau Y)) = T(\partial_\tau{f (Y)})$.
By \Cref{lem:iso_pocket}, $Y$ has an
isolated pocket $V =V_Y$. Note that $V$ embeds into $M$ if and only if it is disjoint from its translates $V_i = \Phi^i(V)$ for each $i \neq 0$. By the remark above, each $V_i$ is itself an isolated pocket for the subsurface $Y_i = f^i(Y)$, and any two of these subsurfaces are either disjoint or overlap in $X$. Hence, by \Cref{prop:disjoint_pockets} the isolated pockets $V_i$ are disjoint as required.
\end{proof}
We will now prove \Cref{th:bounding projections}, whose
statement we recall here:
\restate{th:bounding projections}{
Let $M$ be a hyperbolic 3-manifold with fully-punctured fibered face
$\mathcal{F}$ and veering triangulation $\tau$.
For any subsurface $W$ of any fiber of $\mathcal{F}$,
\[
\alpha \cdot (d_W(\lambda^- ,\lambda^+) -\beta) < |\tau|,
\]
where $|\tau|$ is the number of tetrahedra in $\tau$,
$\alpha = 1$ and $\beta = 10$ when $W$ is an annulus and
$\alpha = 3|\chi(W)|$ and $\beta = 8$ when $W$ is not an annulus.
}
\begin{proof}
Suppose that $W$ is any nonannular subsurface of any fiber $F$ in $\mathbb{R}_+ \mathcal{F}$.
We may assume that $d_W(\lambda^-,\lambda^+) >8$.
Then \Cref{lem:iso_pocket} implies that $W$ has an isolated pocket $V_W$ in $(F \times \mathbb{R}, \tau)$ such that $d_W(V_W^-,V_W^+)\ge d_Y(\lambda^-,\lambda^+) -8$.
By \Cref{thm:pocket summary}, the isolated pocket $V_W \subset (F \times
\mathbb{R}, \tau)$ embeds into $(M,\tau)$. Hence
$|V_W| \le |\tau|$, where $|V_W|$ denotes the number of
tetrahedra of $V_W$.
Now each tetrahedron of $V_W$ corresponds to a diagonal exchange between
the triangulations $V_W^-$ and $V_W^+$ of $W_\tau$ and each diagonal
exchange replaces a single edge of the triangulation.
There are at least $3|\chi(W)| + 1$ non-boundary edges to each triangulation of $W$,
and the diameter in $\A(W)$ of an ideal triangulation is 1, so we conclude
\begin{align} \label{ineq:pocket_growth}
|\tau| &\ge |V_W| = \#\{\text{diagonal exchanges from } V_W^- \text{ to } V_W^+\}\\
&> 3|\chi(W)| \cdot d_W(V^-,V^+) \nonumber \\
&\ge 3|\chi(W)| \cdot (d_W(\lambda^-,\lambda^+) - 8) \nonumber.
\end{align}
This completes the proof when $W$ is nonannular.
When $W$ is an annulus, we use the annular case of
\Cref{lem:iso_pocket} to obtain an isolated pocket $V_W$ in $(F \times
\mathbb{R}, \tau)$ such that $d_W(V_W^-,V_W^+)\ge d_Y(\lambda^-,\lambda^+)
-10$. Noting that a triangulation of the annulus contains at least 2
(non-boundary) edges, the same argument implies that
\begin{align*}
|\tau| &\ge |V_W| = \#\{\text{diagonal exchanges from } V_W^- \text{ to } V_W^+\}\\
&> d_W(V^-,V^+) \nonumber \\
&\ge d_W(\lambda^-,\lambda^+) - 10 \nonumber,
\end{align*}
as required.
\end{proof}
\subsection{Sweeping through embedded pockets}
We are now ready to prove \Cref{th:sub_dichotomy_fully_punctured},
whose statement we reproduce below.
This theorem relates subsurfaces of large projections among different fibers of a
fixed face.
\restate{th:sub_dichotomy_fully_punctured}{
Let $M$ be a hyperbolic 3-manifold with fully-punctured fibered face
$\mathcal{F}$ and suppose that $S$ and $F$ are each fibers in $\mathbb{R}_+\mathcal{F}$.
If $W$ is a subsurface of $F$, then either $W$ is isotopic
along the flow to a subsurface of $S$, or
$$3|\chi(S)| \ge d_W(\lambda^-,\lambda^+) -\beta,$$
where $\beta =10$ if $W$ is an annulus and $\beta = 8$ otherwise.
}
Recall from \Cref{lem:subgroup_projection} that
we can identify $d_W(\lambda^+,\lambda^-)$ with
$d_W(\Lambda^+,\Lambda^-)$, agreeing with the statement given in the introduction.
We will require the following lemma, which essentially states that immersed subsurfaces with large projection are necessarily covers of subsurfaces. Recall that in \Cref{sec: arc_complex} we defined the distance $d_W(\lambda^+,\lambda^-)$ when $W$ is a compact core of a cover $X_\Gamma \to X$ corresponding to a finitely generated subgroup $\Gamma \le \pi_1(X)$.
\begin{lemma}[Immersion to cover] \label{lem:embedding_fullly_punctured}
Suppose that $(X,q)$ is a fully-punctured surface.
Let $\Gamma$ be a finitely generated subgroup of $\pi_1(X)$ and let $W$ be a compact core of the cover $X_\Gamma \to X$.
If $W$ is nonannular and $d_W(\lambda^-,\lambda^+) > 4$ or
if $W$ is an annulus and
$d_W(\lambda^-,\lambda^+) >6$,
then there is a subsurface $Y$ of $X$ such that
$W \to X$ is homotopic to a finite cover $W \to Y \subset X$.
In particular, $\Gamma$ is
a finite index subgroup of $\pi_1(Y)$.
\end{lemma}
\begin{proof}
Suppose that $d_W(\lambda^-,\lambda^+) > 4$ if $W$ is nonannular and
$d_W(\lambda^-,\lambda^+) >6$ if $W$ is an annulus.
Let $p \colon \check X \to X$ be a finite cover to which $W \to X$
lifts to an embedding $W \to \check{X}$ (this exists since surface
groups are LERF \cite{scott-LERF}),
and identify $W$ with its
image in $\check{X}$. Lift $q$ along with the veering triangulation to
$(\check{X} \times \mathbb{R},\tau)$. By \Cref{thm: tau-compatible},
$W$ is a $\tau$--compatible subsurface of $\check X$, and
by \Cref{thm: tau-compatible}
and \Cref{prop:connect},
$T_{\check{X}}(\partial_\tau W)$ is nonempty and connected. To prove the lemma, we
show that $\int_\tau(W) \to X$ covers a subsurface of $X$. For this, it suffices to prove
that each edge of $p^{-1}(p(\partial_\tau W))$ is disjoint from $\int_\tau(W)$. Indeed, since
$W$ is $\tau$--compatible, one component of $\check X \ssm \partial_\tau W$ is $\int_\tau(W)$. If $p^{-1}(p(\partial_\tau W))$ is disjoint from $\int_\tau(W)$, then $\int_\tau(W)$ is also a component of $\check X \ssm p^{-1}(p(\partial_\tau W))$. As components of $\check X \ssm p^{-1}(p(\partial_\tau W))$ cover components of $X \ssm p(\partial_\tau W)$, this will show that $\int_\tau(W) \to X$ covers a subsurface of $X$.
Hence, we must show that each edge of $p^{-1}(p(\partial_\tau W))$ is disjoint from $\int_\tau(W)$. This is equivalent to the statement that no edge of $p^{-1}(p(\partial_\tau W))$ crosses $\partial_\tau W$ nor is contained in $\int_\tau(W)$.
First suppose that $W$ is not an annulus.
If $\check T$ is a section
of $(\check{X} \times \mathbb{R},\tau)$ with an edge $f$ such that $f>e$ for
an edge $e$ of $\partial_\tau W$,
then \Cref{near lambda} implies that
$d_W(\check T,\lambda^+) = 0$. Similarly if $f<e$ then $d_W(\check T,\lambda^-) =
0$. Hence, if $T$ is \emph{any section of} $(X \times \mathbb{R},\tau)$ such that
$d_W(T,\lambda^\pm) \ge 1$, then its lift
$\check{T} = p^{-1}(T)$ to $\check{X}$ must contain the edges of
$\partial_\tau W$ and so $\check{T} \in T_{\check{X}}(\partial_\tau
W)$. Moreover, such a section $T$ of $(X \times \mathbb{R},\tau)$ with $d_W(T,\lambda^\pm) \ge 1$ must exist.
This is because
by \Cref{gue-sweep}, we may sweep through $X\times\mathbb{R}$ with sections going from
near $\lambda^-$ to near $\lambda^+$. If all sections were to have $d_W$--distance
$0$ from either $\lambda^-$ or $\lambda^+$, then there would be a pair $T,T'$ differing by
a single diagonal exchange such that $d_W(T, \lambda^-)= d_W(T',\lambda^+) = 0$. But this would imply that
$d_W(\lambda^-,\lambda^+) \le 2$, contradicting our assumption on distance.
Putting these facts together, we conclude that
there exists a section $T$ of $(X \times \mathbb{R},\tau)$ with $d_W(T,\lambda^\pm)\ge 1$, and that
for each such section
\[
p^{-1}(T) \in T_{\check{X}}(p^{-1}(p(\partial_\tau W))).
\]
Note that this in particular implies that no edge of $p^{-1}(p(\partial_\tau W))$
crosses an edge of $\partial_\tau W$.
We claim now that no edge
$e$ in $p^{-1}(p(\partial_\tau W))$ can be
contained in $\int_\tau (W)$. Such an edge would have
a well-defined projection to
$\A(W)$ and
would necessarily appear in each section of $T_{\check{X}}(p^{-1}(p(\partial_\tau W)))$ (by definition of $T_{\check X}(\cdot)$).
Using our conclusion from above, this would imply that
$d_W(p^{-1}(T),e) = 0$ whenever $d_W(T,\lambda^\pm)\ge 1$.
But just as before, by sweeping through $X\times\mathbb{R}$ with sections going from
near $\lambda^-$ to near $\lambda^+$,
we produce sections $T_1, T_2$ with $d_W(T_1, \lambda^-) =d_W(T_2,\lambda^+)=1$.
Since each of these sections' preimage in $\check X$ contains the edge $e$, we get that
$d_W(\lambda^\pm,e)\le 2$, which contradicts our hypothesis that
$d_W(\lambda^+,\lambda^-) > 4$.
This shows that no edge of $p^{-1}(p(\partial_\tau W))$ can meet $\int_\tau(W)$ and
completes the proof when $W$ is nonannular.
When $W$ is an annulus, one proceeds exactly as above using the annular version of \Cref{near lambda}.
\end{proof}
\begin{proof}[Proof of \Cref{th:sub_dichotomy_fully_punctured}]
We may assume that $W$ is a subsurface of $F$ such that
$d_W(\lambda^-,\lambda^+) > \beta$.
First suppose that $\pi_1(W)$ is contained in $\pi_1(S)$.
Then by \Cref{lem:embedding_fullly_punctured}, there is a subsurface
$Y$ of $S$ such that, up to conjugation in $\pi_1(S)$, $\pi_1(W) \le
\pi_1(Y)$ is a finite index subgroup; let
$n \ge 1$ denote this index. If $\eta_F \colon \pi_1(M) \to
\mathbb{Z}$ is the homomorphism representing the cohomology class dual to
$F$, then $\eta_F | \pi_1(Y)$ vanishes on the index $n$ subgroup
$\pi_1(W)$.
Since $\mathbb{Z}$ is torsion-free we must have that $\eta$ vanishes on
$\pi_1(Y)$ and hence $\pi_1(Y)$ is contained in $\pi_1(F)$.
However, since the fundamental group of an embedded subsurface, in this case $W \subset F$, can not be nontrivially finite-index inside another subgroup of $\pi_1(F)$, we see that $n=1$ and $\pi_1(W) = \pi_1(Y)$.
That $W$ is isotopic along the flow in $M$ to $Y \subset S$ can be seen by lifting $W$ and $Y$ to the cover $S \times \mathbb{R} \to M$.
Hence, we may suppose by \Cref{lem:flow_to_fiber_2} that the image of
any $S \to M$ homotopic to the fiber $S$ intersects any isotope of $W
\subset F$ essentially. Since $d_W(\lambda^-,\lambda^+) > \beta$, $W$
has a nonempty isolated pocket $V_W \subset F \times \mathbb R$
which simplicially embeds into $(M, \tau)$ by
\Cref{thm:pocket summary}. Let $\{W_i\}$ denote a sequence of sections of $V_W$ from $V^-_W$ to $V^+_W$ with $W_{i+1}$ differing from $W_i$ by an upward diagonal flip. Also, fix a simplicial map $f \colon S \to (M,\tau)$ which is obtained by composing a section of $(S \times \mathbb{R},\tau)$ with the covering map $S \times \mathbb{R} \to M$.
Note that for each $i$, $f(S)$ meets at least one edge of the interior of $W_i$. Otherwise, the image of $S$ in $M$ misses the interior of $W_i$ contradicting our assumption. In fact, even more is true: Call a component $c$ of $f(S) \cap W_i$ \emph{ removable} if the triangles of $f(S)$
incident to the edges of $c$
lie locally to one side of $W_i$ in $M$. If $c$ is removable, then
there is an isotopy of $W_i$ supported in a neighborhood of $c$ which
removes $c$ from the intersection $f(S) \cap W_i$. Hence, if we denote
by $E_i$ the edges of $f(S) \cap W_i$ which do not lie in removable components , then $E_i$ must be nonempty for each $i$.
We claim that for each $i$, $E_i$ shares an edge with $E_{i+1}$. Otherwise, both $E_i$ and $E_{i+1}$ consist of a single edge and
the tetrahedron corresponding to the diagonal exchange from $W_i$ to
$W_{i+1}$ has $E_i$ as its bottom edge and $E_{i+1}$ as its top
edge. But then both of these edges must be removable since pushing the bottom two faces of the tetrahedron slightly upward makes that intersection disappear, and similarly for the top. This contradicts our above observation and establishes that $E_i$ and $E_{i+1}$ have a common edge.
We obtain a sequence in $\A(W)$,
\[
V^-_W \supset E_0 , E_1, \ldots, E_n \subset V^+_W,
\]
having the property that for each edge $e_i$ of $E_i$ there is an edge $e_{i+1}$ of $E_{i+1}$ such that $e_i$ and $e_{i+1}$ are disjoint. We conclude that the number of distinct edges in the sequence $E_0 , E_1, \ldots, E_n$ is at least $d_W(V^-_W, V^+_W)$.
Combining this with the fact that the number of edges in an ideal triangulation
of $S$ is $3|\chi(S)|$ and \Cref{lem:iso_pocket}, we see that
\[
3|\chi(S)| \ge d_W(V^-_W, V^+_W) \ge d_W(\lambda^-,\lambda^+) - \beta,
\]
as required.
\end{proof}
\medskip
We conclude the paper by recording the following corollary of
\Cref{lem:embedding_fullly_punctured} and the proof of
\Cref{th:sub_dichotomy_fully_punctured}.
\begin{corollary}\label{always subsurface}
Let $M$ be a hyperbolic manifold with fully-punctured fibered face
$\mathcal{F}$. Let $W$ be a subsurface of a fiber $F\in\mathbb{R}_+\mathcal{F}$ such that
$d_W(\Lambda^+,\Lambda^-) > 4$ if $W$ is nonannular and
$d_W(\Lambda^+,\Lambda^-) > 6$ if $W$ is an annulus. If $S$ is any
fiber in $\mathbb{R}_+\mathcal{F}$ such that $\pi_1(W) < \pi_1(S)$, then $W$ is isotopic
to a subsurface of $S$.
\end{corollary}
\section{Sections and pockets of the veering triangulation}
\label{sections}
In this section the surface $X$ is fully-punctured.
A {\em section} of the veering triangulation $\tau$ is an
embedding $(X,T) \to (X \times \mathbb{R}, \tau)$ which is simplicial with
respect to an ideal triangulation $T$ of $X$, and is a section of the
fibration $\pi \colon X \times \mathbb{R} \to X$ (hence transverse to the vertical flow). By \emph{simplicial} we
mean that the map takes simplices to simplices.
The edges of $T$ are saddle connections of $q$ that are also edges of $\tau$ (i.e.
those which span singularity-free rectangles), and indeed any
triangulation by $\tau$-edges gives rise to a section.
We will abuse
terminology a bit by letting $T$ denote both the triangulation and the
section.
A {\em diagonal flip} $T\to T'$ between sections is an isotopy that
pushes $T$ through a single tetrahedron of $\tau$, either above it or below
it. Equivalently, if $R$ is a maximal rectangle and $Q$ its associated
tetrahedron, the bottom two faces of $Q$ might appear in $T$, in which
case $T'$ would be obtained by replacing these with the top two
faces. This is an upward flip, and the opposite is a downward flip.
We will refer to the transition as both a \emph{diagonal flip/exchange} and a \emph{tetrahedron move}, depending on the perspective.
An edge $e$ of $T$ can be flipped downward exactly when it is the
tallest edge, with respect to $q$, among the edges in either of the
two triangles adjacent to it. This makes $e$ the top edge of a
tetrahedron (i.e. the diagonal of a quadrilateral that connects the
horizontal sides of the corresponding rectangle).
Similarly it can be flipped upward when it is the widest
edge among its neighbors.
See \Cref{flippability2}.
\realfig{flippability2}{The edge $e$ is upward flippable, $g$ is
downward flippable, and $f$ is not flippable.}
In particular it follows that every section has to admit both an
upward and downward flip -- simply find the tallest edge and the
widest edge.
However it is not a priori obvious that a section even
exists. Gu\'eritaud gives an argument for this and more:
\begin{lemma}[\cite{gueritaud}]\label{gue-sweep}
There is a sequence of sections $\cdots \to T_i\to
T_{i+1}\to\cdots$ separated by upward diagonal flips, which sweeps through the
entire manifold $(X\times\mathbb{R},\tau)$.
Moreover, when $(X\times\mathbb{R},\tau)$ covers the manifold $(M,\tau)$, this sequence is invariant by
the deck translation $\Phi$.
\end{lemma}
We remark that Agol had previously proven a version of \Cref{gue-sweep} with his original definition of the veering triangulation \cite{agol2011ideal}.
For an alternative proof that sections exist, see the second proof of \Cref{lem:extension}.
We remark that \Cref{gue-sweep} does not give a complete picture of all possible
sections of $\tau$. In this section we will establish a bit more
structure.
\medskip
For a subcomplex $K \le \tau$, denote by $T(K)$ the collection of
sections $T$ of $\tau$ containing the edges of $K$. A necessary
condition for $T(K)$ to be nonempty is that $\pi(K)$ is an
embedded complex in $X$ composed of $\tau$-simplices. We will continue
to blur the distinction between $K$ and $\pi(K)$.
Our first result states that the necessary condition is sufficient:
\begin{lemma}[Extension lemma] \label{lem:extension}
Suppose that $E$ is a collection of
$\tau$-edges in $X$ with
pairwise disjoint interiors. Then $T(E)$ is nonempty.
\end{lemma}
The second states that $T(K)$ is always connected by tetrahedron
moves. This includes in particular the case of $T(\emptyset)$, the set
of all sections.
\begin{proposition}[Connectivity] \label{prop:connect}
If $K$ is a collection of
$\tau$-edges in $X$ with
pairwise disjoint interiors,
then $T(K)$ is connected
via tetrahedron moves.
\end{proposition}
\subsection*{Finding flippable edges}
Let $T$ be a section and let $\sigma$ be an edge of $\tau$, which is
not an edge of $T$. Any edge $e$ of $T$ crossing $\sigma$ must do so
from top to bottom ($e>\sigma$) or left to right ($e<\sigma$), as in
\Cref{veering defs}, and we further note that all
edges of $T$ that cross $\sigma$ do it consistently, all top-bottom or all
left-right, since they are disjoint from each other.
\begin{lemma} \label{lem:down_flip}
Let $T$ be a section and suppose that an edge $\sigma$ of $\tau$ is
crossed by an edge $e$ of $T$. If $e>\sigma$, then
there is an edge of $T$ crossing $\sigma$ which is downward flippable.
Similarly if $e<\sigma$ then
there is an edge of $T$ crossing $\sigma$ which is upward flippable.
\end{lemma}
\begin{proof}
Assuming the crossings of $\sigma$ are top to bottom,
let $e$ be the edge crossing $\sigma$ that has largest height with
respect to $q$. Let $D$ be a triangle of $T$ on either side of
$e$ and let $f$ be its tallest edge.
Drawing the rectangle $M$ in which $D$ is inscribed (\Cref{tallest-crossing})
one sees that $R$, the rectangle of $\sigma$, is forced to cross it
from left to right. Hence, the edge $f$ must also cross $\sigma$.
Therefore, $f=e$ by choice of $e$.
It follows that $e$ is a downward flippable edge.
\end{proof}
\realfig{tallest-crossing}{The tallest $T$-edge crossing $\sigma$ must
also be tallest in its own triangles.}
\subsection*{Pockets}
Let $T$ and $T'$ be
two sections and $K$ their intersection, as a subcomplex in $X\times\mathbb{R}$. Because both sections are embedded copies of $X$
transverse to the suspension flow, their union $T \cup T'$ divides
$X \times \mathbb{R}$ into two unbounded regions and some number of bounded
regions. Each bounded region $U$ is a union of tetrahedra bounded by two isotopic
subsurfaces of $T$ and $T'$, which correspond to a component $W$ of
the complement of $\pi(K)$ in $X$. The isotopy is obtained by
following the flow, and if it takes the subsurface of $T'$ upward to
the subsurface of $T$ we say that
{\em $T$ lies above $T'$ in $U$}. We call $U$ a \emph{pocket over
$W$}, and sometimes write $U_W$. We call $W$ the \emph{base} of the pocket $U$.
\begin{lemma}\label{lem:slope_drop}
With notation as above, $T$ lies above $T'$ in the pocket $U_W$ if and only if,
for every edge $e$ of $T$ in $W$ and edge $e'$ of $T'$ in $W$, if $e$ and $e'$ cross then $e>e'$.
\end{lemma}
Note that, for each edge $e$ of $T$ in $W$ there is in fact an edge $e'$ of
$T'$ in $W$ which crosses $e$, since both $T$ and $T'$ are
triangulations, with no common edges in $W$.
\begin{proof}
Suppose that $T$ lies above $T'$ in $U_W$ and let $e$ be an edge of
$T$ in $W$; hence, it is in the top boundary of
$U$. Let $Q$ be the tetrahedron of $\tau$ for which $e$ is the top
edge. Via the local picture around $e$ (see \Cref{veering defs} and
\Cref{edge-swing}), we see that $Q$ lies locally
below $T$. Its interior is of course disjoint from $T$ and $T'$ (and
the whole $2$- skeleton), hence it is inside $U$. Let $e_1$ be the
bottom edge of $Q$.
Note $e > e_1$. If $e_1$ is in $T'$,
stop (with $e' = e_1$). Otherwise it is in the interior of $U$, and we can repeat with
the tetrahedron for which $e_1$ is the top edge. We get a sequence of
steps terminating in some $e'$ in $T'$, which must be in the boundary
of $U$, and conclude $e > e'$ (by the transitivity of $>$ as in
\Cref{veering defs}). Now from the paragraph before \Cref{lem:down_flip},
the same slope relation holds for every edge of $T'$
crossing $e$, hence giving the first implication of the lemma. For the
other direction, exchange the roles of $T$ and $T'$ in the proof.
\end{proof}
\subsection*{Connectedness of $T(K)$}
We can now prove \Cref{prop:connect}.
\begin{proof}
Let us consider $T$, $T'$ in $T(K)$. Let $U$ be one of the pockets,
and suppose $T$ lies above $T'$ in $U$. \Cref{lem:slope_drop} together
with \Cref{lem:down_flip} implies that $T$ has a downward flippable
edge $e$ which crosses an edge of $T'$ that is in $W$. In particular
$e$ itself is in $W$.
Performing this flip we reduce the number of tetrahedra contained in pockets. Thus a finite number of moves will take $T$ to $T'$, without disturbing $K$.
\end{proof}
As a consequence of \Cref{prop:connect} and its proof we have:
\begin{corollary}\label{cor:top}
If $K$ is a nonempty subcomplex of $\tau$ and $T(K) \neq \emptyset$,
then there are unique sections $T^+(K)$ and $T^-(K)$ in $T(K)$ such
that every $T \in T(K)$ can be upward flipped to $T^+(K)$ and downward flipped
to $T^-(K)$.
\end{corollary}
\begin{proof}
First note that $T(K)$ is finite: because $\tau$ is locally finite at the edges, there are only finitely many choices for a triangle adjacent to $K$. We then enlarge $K$ successively, noting that there is a bound on the number of triangles in a section.
Thus there exists a section $T^+$ in $T(K)$ which is not upward
flippable in $T(K)$.
For any two sections $T_1,T_2\in T(K)$ there is a $T_3\in
T(K)$ obtained as the union of the tops of the pockets of $T_1$ and
$T_2$ and their intersection. Thus $T_1$ is upward flippable unless
$T_1=T_3$, and similarly for $T_2$. This implies that $T^+$ is the
unique section in $T(K)$ which is not upward flippable, and every
other section is upward flippable to $T^+$.
We define $T^-$ analogously.
\end{proof}
The section $T^+(K)$ is called the \emph{top of $T(K)$} and the
section $T^-(K)$ is called the \emph{bottom of $T(K)$}. Note that any
section obtained from $T^+(K)$ by upward diagonal exchanges is not in
$T(K)$.
\subsection*{Extension lemma}
We conclude this section with two proofs of \Cref{lem:extension}.
\begin{proof}[Proof one]
\Cref{gue-sweep} gives us, in particular, the existence of at
least one section $T_0$ which is disjoint from $E$, which we may
assume lies above every edge of $E$.
Then by \Cref{lem:down_flip} there is a downward
flippable edge $e$ in $T_0$. The tetrahedron involved in the move lies
above $E$, so $E$ still lies below (or is contained in) the new
section $T_1$. We repeat this process, and at each stage every edge
of $E$ is either contained in $T_i$ or crosses an edge of $T_i$ and
lies below it. Thus by \Cref{lem:down_flip}, unless $E\subset T_i$ each $T_i$
contains a downward flippable edge that is not contained in
$E$.
Because $\tau$ is locally finite at each
edge, {\em any} sequence of downward flips is a proper sweepout of
the region below $T_0$, and hence
must eventually meet every edge of $\tau$ below $T_0$. Thus we may
continue until every edge of $E$ lies in $T_i$.
\end{proof}
\begin{proof}[Proof two] Our second proof does not use \Cref{gue-sweep}, and in
particular it gives an independent proof of the existence of
sections.
Let $D$ be a component of the complement of $E$ which is not a triangle.
Let $e$ be an edge of $\partial D$ and consider the collection of
$\tau$-tetrahedra adjacent to $e$. These contain a sequence
$Q_-,Q_1,\ldots Q_m,Q_+$, as in \Cref{edge-swing}, where $Q_-$ is the
tetrahedron with $e$ as its top
edge, $Q_+$ is the tetrahedron with $e$ as its bottom edge, and the
rest are adjacent to $e$
on the same side as $D$ (if $D$ meets $e$ on two sides we just choose one).
Two successive tetrahedra in this sequence
share a triangular face. We claim that one of
these faces must be contained in $D$. Equivalently we claim that one
of the triangles is not crossed by any edge of $E$.
Since each tetrahedron $Q$ is inscribed in a singularity free rectangle $R$, if an edge
$f$ of $E$ crosses any edge of $Q$ its rectangle crosses
all of $R$. It follows immediately, since the edges of $E$
have disjoint interiors, that they consistently cross $R$ all vertically, or
all horizontally. Because successive tetrahedra in the sequence share
a face it follows inductively that, if all the faces are crossed
by $E$, then they are all consistently crossed horizontally,
or all vertically.
However, $Q_-$ can
only be crossed vertically by $E$ (since $E$ does
not cross $e$). Similarly $Q_+$ can only be crossed horizontally. It
follows that there must be a triangular face $F$ that is {\em not} crossed
by $E$. Thus $F$ is contained in $D$. Since $D$ is not a triangle,
at least one edge of $F$ passes through the
interior of $D$. We add this edge to $E$ and
proceed inductively.
\end{proof}
\section{Projections and compatible subsurfaces}
\label{surface_reps}
In this section we show that if $Y\subset X$ is a compact essential subsurface of large projection distance $d_Y(\lambda^+,\lambda^-)$, then $Y$ has
particularly nice representations with respect to, first, the quadratic
differential $q$ and, second, the veering triangulation $\tau$. We
emphasize that in this section, the surface $X$ is not necessarily
fully-punctured.
\subsection{Projection and $q$--compatibility}
Recall the $q$-convex hull map $\hat\iota_q \colon Y \to \bar X_Y$
constructed in \Cref{q tight}. We
say that $Y$ is {\em $q$-compatible}
if $\hat\iota_q$ is an embedding of $Y' = Y\ssm \partial_0 Y$, as in part (6) of \Cref{q tight}.
(Recall that $\partial_0 Y$
maps to completion points of $\til \PP_Y$).
This condition implies
a little more:
\realfig{Y_q_cartoon_2}{The image of a $q$-compatible subsurface $Y$ in $\bar X_Y$ under $\hat \iota_q$. Open circles are points of $\til \PP_Y$ (corresponding to the image of $\partial_0 Y$) and dots are singularities not contained in $\til \PP_Y$. The ideal boundary of $X_Y$ is in blue.}
\begin{lemma} \label{lem:int_embed}
If $Y \subset X$ is $q$-compatible, then
\begin{enumerate}
\item the projection $\iota_q \colon Y \to \bar X$ of $\hat
\iota_q$ to $\bar X$ is an embedding from $\int(Y)$ into $X$
which is homotopic to the inclusion, and
\item $\hat\iota_q(\partial'Y)$ does not pass through points of $\til\PP_Y$.
\end{enumerate}
\end{lemma}
Recall that $\partial'Y = \partial Y \ssm \partial_0Y$.
\begin{proof}
Recall from \Cref{q tight} that $q$-compatibility of $Y$ is equivalent
to the statement that
the interior of the $q$-hull ${\operatorname{CH}}_q(\Lambda) \subset
\hat X$ is a disk (i.e. it is not pinched along singularities or
saddle connections).
If $\iota_q \colon \int(Y) \to X$ fails to be an
embedding, then it must be that for some deck transformation $g$ of
the universal covering $\til X \to X$ the interiors of ${\operatorname{CH}}_q(\Lambda)$
and $g \cdot {\operatorname{CH}}_q(\Lambda)$ are distinct and overlap. But then it
follows immediately from \Cref{cor:side_coherence} that the distinct
hyperbolic convex hulls ${\operatorname{CH}}(\Lambda)$ and $g \cdot {\operatorname{CH}}(\Lambda)$
overlap, contradicting that $Y$ is a subsurface of $X$. This proves
part (1).
For part (2), let $\beta$ be a component of $\partial_0 Y$. Since
$\hat\iota_q$ embeds $Y\ssm \partial_0Y$, a collar
neighborhood $U$ of $\beta$ in $Y$ maps to a neighborhood $V$ of the puncture
$p = \hat\iota_q(\beta)$. Now if $\gamma$ is a component of
$\partial'Y$, $q$-compatibility again implies its
image must avoid $V\ssm p$. Since $\hat\iota_q(\gamma)$ cannot
equal $p$, it must be disjoint from it.
\end{proof}
Note that $Y$ is a $q$-compatible annulus if and only if the core of $Y$ is a cylinder curve in $X$. In this case, the corresponding open flat cylinder in $X$ is $\iota_q(\int (Y))$. In general, if $Y$ is $q$-compatible then one component of $X \ssm \partial_q Y$ is an open subsurface isotopic to the interior of $Y$; this is the image $\iota_q(\int(Y))$ and is denoted $\int_q(Y)$.
The following proposition shows that mild assumptions on
$d_Y(\lambda^+,\lambda^-)$ imply that
$Y$ is $q$-compatible.
\begin{proposition}[$q$-Compatibility] \label{prop: q_compatible}
Let $Y\subset X$ be an essential subsurface.
If $Y$ is non-annular and $d_Y(\lambda^+,\lambda^-) > 0$, then $Y$ is $q$-compatible.
If $Y$ is an annulus and $d_Y(\lambda^+,\lambda^-) > 1$, then
$Y$ is $q$-compatible. In this case, $\int_q(Y)$ is a flat cylinder.
\end{proposition}
\begin{proof}
We treat the non-annular case first. Suppose that $d_Y(\lambda^+,\lambda^-)>0$.
Recall from \Cref{AY in flat geometry} that we have identified $\til X$ with $\HH^2$,
set $\Lambda\subset \partial\HH^2$ to be the limit set of
$\Gamma = \pi_1(Y)$, set $\Omega =
\partial\HH^2\ssm \Lambda$, and defined $\hat\PP_Y\subset \Lambda$
to be the set of parabolic fixed points of $\pi_1(Y)$. Note that $\hat \PP_Y = \Lambda \cap \hat \PP$.
Further recall from part (6) of \Cref{q tight} that the
map from $Y'$ to ${\operatorname{CH}}_q(X_Y)$ is an embedding,
provided the interior of ${\operatorname{CH}}_q(\Lambda)$ is a disk.
Since ${\operatorname{CH}}_q(\Lambda)$ is the result of deleting the interior of the side $\side{l}$ from $\hat X$ for each
hyperbolic geodesic line $l$ in $\partial {\operatorname{CH}}(\Lambda)$, it suffices to show that
\begin{enumerate}
\item for each geodesic line $l$ in $\partial {\operatorname{CH}}(\Lambda)$, the
interior of the corresponding $q$-geodesic $l_q$ does not meet $\partial \HH^2 \ssm \side{l}$, and
\item if $l$ and $l'$ are distinct geodesic lines in $\partial {\operatorname{CH}}(\Lambda)$ then
$l_q$ and $l'_q$ do not meet in $\widetilde X$.
\end{enumerate}
First suppose that condition $(1)$ is violated for some geodesic line $l$ in $\partial {\operatorname{CH}}(\Lambda)$ and point $\hat p \in \partial \HH^2 \ssm \side{l}$. Set $p$ to be the image of $\hat p$ in $\bar X_Y$. Letting $\gamma$ be the boundary component of $\partial' Y$ that is the image of $l$ in $X_Y$, we see that the image of $l_q$ in $\bar X_Y$, which equals $\gamma_q = \hat \iota_q(\gamma)$, passes through the point $p$.
Since $l_q$ is a geodesic in $\hat X$, we see that $\hat p$ is a completion point and so either $\hat p \in \hat \PP_Y$ or $\hat p \in \hat \PP \ssm \hat \PP_Y$.
Assume that $\hat p\in \hat \PP_Y$. Then
$p\in \widetilde \PP_Y$ corresponds to a puncture of $Y$.
Recall that by \Cref{q tight}, the image of the open side
$\openside{l} = \int(\side{l} \cap \widetilde X)$
in $X_Y$ is either an open annulus or a disjoint union of open disks; in either case, set $A_\gamma$ equal to the component which contains $p$ in its boundary.
The angle at $p$ in $A_\gamma$ between the incoming and
outgoing edges of $\gamma_q$ is at least $\pi$, which implies that
$A_\gamma$ contains a horizontal and a vertical ray $l^-,l^+$
emanating from $p$. (\Cref{p_gamma}.)
\realfig{p_gamma}{When $\hat\iota_q(\partial' Y)$ passes through a
point of $\widetilde \PP_Y$, $d_Y(\lambda^+,\lambda^-) =0$.}
These rays are proper $q$-geodesic lines in $X_Y$ (because $p$ is a
puncture, not a point of $X_Y$), and hence by \Cref{q arcs for
AY} represent vertices of $\pi_Y(\lambda^-)$ and
$\pi_Y(\lambda^+)$, respectively. Further, since the rays only intersect within the annulus or disk $A_\gamma$ and $Y$ is itself nonannular, we see that $l^-$ and $l^+$ in fact represent the same point in $\A(Y)$. (Actually, if $A$ does not contain a flat cylinder, then the interiors of $l^-$ and $l^+$ are disjoint as we show below). Either way, it follows that
$$
d_Y(\lambda^+,\lambda^-) =0,
$$
a contradiction.
Next assume that $\hat p \in \hat \PP \ssm \hat \PP_Y$. Since $\hat p \notin \side{l} \cap \partial \HH^2$ we may set $A$ to be the component of the image of $\openside{l}$
in $X_Y$ which contains $p \in \hat X_Y$ in its boundary.
As before, the angle subtended by $\gamma_q$ at $x$ in the boundary of $A$
is at least $\pi$ (see
\Cref{modified_pinch-puncture}). A pair of rays $l^\pm$
emanating from $x$ into $A$ are properly embedded lines and again
represent the same vertex of $\A(Y)$, giving us
$d_Y(\lambda^+,\lambda^-) =0$.
\realfig{modified_pinch-puncture}{$Y_q$ is pinched at a completion point.}
We conclude that condition $(1)$ is satisfied.
Next suppose that geodesics $l$ and $l'$ in the boundary of ${\operatorname{CH}}(\Lambda)$ violate $(2)$, i.e. $l_q$ and $l'_q$ meet in $\til X$. Let $\til I = l_q \cap l'_q \subset \hat X$ which, since $\hat X$ is CAT$(0)$, is a connected subset of each of $l_q,l'_q$.
In general, the intersection in $\hat X$ of two $q$-geodesic lines is either a single singularity (possibly a completion point) or a union of saddle connections.
Because $l_q$ and $l'_q$ meet in $\widetilde X$, $\til I$ contains either a saddle connection or a singularity which is not a completion point.
Let $\gamma,\gamma',\gamma_q,\gamma'_q, I$, be the images in $\bar X_Y$ of $l,l',l_q,l'_q,\til I$, respectively.
Suppose first that $I$ contains a saddle connection $\sigma$.
In this case, let $A$ be the component of the image of
the open side $\openside{l}$
in $X_Y$ which contains $\sigma$ in its boundary, and define $A'$ similarly.
(Note that it is possible that $A = A'$ and that $A$ and $A'$ meet along other saddle connections and singularities besides $\sigma$, but this will not change the discussion.)
Any point of $\sigma$ is crossed
by a pair $l^+,l^-$ of leaves of $\lambda^+,\lambda^-$, which
as proper arcs of $X_Y$ determine the same vertex of $\A(Y)$. Hence,
we conclude once again that $d_Y(\lambda^+,\lambda^-) =0.$
\realfig{common-saddle}{$Y_q$ is pinched along a saddle connection.}
Finally, suppose that $I$ contains a singularity $x$ in $X_Y$ (i.e. $x$ is not a completion point). Again, set $A$ to be the component of the image of $\openside{l}$
in $X_Y$ which contains $x$ in its boundary and $A'$ to be the component of the image of $\openside{l'}$ in $X_Y$ which contains $x$ in its boundary.
As before, there is an angle of at least $\pi$ on the $A$ side of
$\gamma_q$ and on the $A'$ side of $\gamma'_q$,
so we can find pairs of rays $r_0^\pm$ emanating from $x$ on
the $A$ side, and $r_1^\pm$ emanating on the $A'$ side (see \Cref{common-sing}).
The unions
$l^+ = r_0^+\cup_x r_1^+$ and $l^- = r_0^-\cup_x r_1^-$ are
generalized leaves of $\lambda^+$ and $\lambda^-$, respectively, and
again determine the same point in $\A(Y)$ so we conclude
that $d_Y(\lambda^+,\lambda^-) =0. $
\realfig{common-sing}{$Y_q$ is pinched at a singularity which is not a completion point.}
We conclude that if $Y$ is nonannular and $d_Y(\lambda^+,\lambda^-) >0$, then $Y$ is $q$-compatible.
When $Y$ is an annulus, almost the same argument applies. The
difference is that the arcs $l^\pm$ we obtain are not homotopic with
fixed endpoints, and so do not determine the same vertex of
$\A(Y)$. However, in each case we will show they have disjoint interiors,
concluding $d_Y(l^+,l^-) \le 1$, and so
$$
d_Y(\lambda^+,\lambda^-) \le 1.
$$
To see this, let $\gamma$ denote the core of $Y$ and let $\gamma_q$ be a geodesic
representative in $\bar X_Y$. Supposing that $\int_q(Y)$ is not a flat annulus, we first claim the following: For any singular point $p$ crossed by $\gamma_q$, if $l^+$ and $l^-$ are rays of $\lambda^+$ and $\lambda^-$, respectively, meeting with angle $\pi/2$ at $p$,
then the interiors of $l^+$ and $l^-$ do not meet.
\realfig{GB_annulus_2}{The $q$-geodesic $\gamma_q$ is the black hexagon. An interior
intersection between $l^+$ and $l^-$ contradicts the Gauss--Bonnet
theorem.}
To establish the claim, assume that the interiors of $l^{\pm}$ meet
and refer to \Cref{GB_annulus_2}. Let $A_\gamma$ be the complementary
region of $\gamma_q$ in $\bar X_Y$ containing $p'$, the interior intersection of
$l^{\pm}$. If $A_\gamma$ is a disk, then the claim follows
immediately from the uniqueness of geodesics in a CAT(0)
space. Hence, we may assume that $A_\gamma$ is an annulus. Let
$l^+_\ep$ be leaf of $\lambda^+$ parallel to $l^+$ and slightly
displaced to the interior of $A_\gamma$, so that the region $R$
bounded by $\gamma_q$ and the segments of $l^-$ and $l^+_\ep$
is an annulus. The total curvature of the $l^-l^+_\ep$ boundary of
$R$ is 0 since it is straight except for two right turns of opposite
signs, and the total curvature of $\gamma_q$ as measured from inside
$R$ is nonpositive (since each singularity on $\gamma_q$ subtends at
least angle $\pi$ within $R$). Since $\chi(R)= 0$ and the Gaussian
curvature in $R$ (including singularities) is nonpositive, the
Gauss--Bonnet theorem implies that the total curvature of $\partial
R$ is nonnegative. This implies that the total curvature of
$\gamma_q$ is 0, which means that $\gamma_q$ bounds a flat cylinder,
contradicting our assumption. This establishes the claim.
We now return to the proof of the proposition. First suppose that $\gamma_q$ passes through a completion point $x$ of $\bar X_Y$. Then, just as in \Cref{modified_pinch-puncture}, we can find a pair of rays $l^\pm$ emanating from $x$ into $A_\gamma$. By the claim above, the interiors of these rays do not meet and so $d_Y(\lambda^+,\lambda^-) \le 1$ as desired.
Finally, suppose that $\gamma_q$ remains in $X_Y$, i.e. it does not
pass through any completion points. It must still pass through a singularity $x$,
and we note that the total angle at $x$ is at
least $3\pi$. Recall that $\gamma_q$ subtends at least angle $\pi$ at
$x$ to either of its sides and we note that some side of $\gamma$ sees
angle at least $3\pi /2$ at $x$. Let $A$ denote this
side of $\gamma_q$ and let $A'$ denote the other side.
Note that $A \neq A'$ since $X_Y$ is an annulus which $\gamma_q$ separates.
The angle of $3\pi/2$ tells us there
are at least $3$ rays of $\lambda^\pm$ emanating into $A$. Now choose
rays $r_0^\pm$ of $\l^\pm$ emanating from $x$ on the $A'$ side.
Because the $3$ (or more) rays of $\lambda^\pm$ emanating from $x$ into
$A$ alternate between $\lambda^+$ and $\lambda^-$, we can choose from
them two rays $r_1^\pm$ of $\l^\pm$ such that
$r_0^+,r_1^+,r_1^-,r_0^-$ are listed
in the cyclic ordering of directions at $x$ (either
clockwise or counterclockwise).
The generalized leaves $l^+ = r_0^+\cup_x r_1^+$
and $l^- = r_0^-\cup_x r_1^-$ then represent arcs in the projections
$\pi_Y(\l^+)$ and $\pi_Y(\l^-)$ and after a slight perturbation these
leaves have disjoint interiors. Hence, again we see that
$d_Y(\l^+,\l^-)\le 1$.
We conclude that if $Y$ is an annulus with $d_Y(\l^+,\l^-)\ge 1$ then $Y$ is
$q$-compatible. \qedhere
\end{proof}
\subsection{Projections and $\tau$-compatibility}
\label{sec: hulls_punctured}
We now show how to associate to a subsurface $Y$ of
large projection a representative of $Y$ which is ``simplicial'' with
respect to the veering
triangulation. This will later be used to prove that such a subsurface induces a
pocket of the veering triangulation $\tau$.
Informally, we start with a $q$-compatible subsurface $Y \subset X$
and homotope $\hat \iota_q$ by pushing $\partial_q Y$ onto
$\tau$-edges (this process is depicted locally in \Cref{thull-twice}). Formally, this is done in two steps using the map $\thull(\cdot)$
described in \Cref{sec:t_hulls}, although some care must be taken in
order to ensure that the resulting object gives an embedded
representative of $\int(Y)$.
Call a subsurface $Y \subset X$ \emph{$\tau$-compatible} if the map $\hat\iota_q:Y \to \bar X_Y$ is homotopic rel $\partial_0 Y$ to a map
$\hat\iota_\tau:Y\to \bar X_Y$ which is an embedding on $Y' = Y\ssm \partial_0Y$ such that
\begin{enumerate}
\item $\hat\iota_\tau$ takes each component of $\partial'Y = \partial Y \ssm \partial_0 Y$ to a simple curve in $\bar X_Y \ssm \til{\PP}_Y$ composed of
a union of $\tau$-edges and
\item the map $\iota_\tau \colon Y \to \bar X$ obtained by composing
$\hat \iota_\tau$ with $\bar X_Y \to \bar X$ restricts to an embedding from $\int(Y)$ into $X$.
\end{enumerate}
We will show that when $d_Y(\lambda^-,\lambda^+)$ is sufficiently large, the subsurface $Y$ is $\tau$-compatible and in this case we set $\partial_\tau Y = \iota_\tau(\partial'Y)$ which is a collection of $\tau$-edges with disjoint interiors. We call $\partial_\tau Y$ the \emph{$\tau$--boundary} of $Y$ and consider it as a $1$-complex of $\tau$-edges. Similar to the situation of a $q$-compatible subsurface, if $Y$ is $\tau$-compatible then one component of $X \ssm \partial_\tau Y$ is an open subsurface isotopic to the interior of $Y$; this is the image $\iota_\tau(\int(Y))$ and is denoted $\int_\tau (Y)$.
\begin{theorem}[$\tau$-Compatibility]\label{thm: tau-compatible}
Let $Y\subset X$ be an essential subsurface.
\begin{enumerate}
\item If $Y$ is nonannular and $d_Y(\lambda^+,\lambda^-) > 0$,
then $Y$ is $\tau$-compatible.
\item If $Y$ is an annulus and $d_Y(\lambda^+,\lambda^-) > 1$, then
$Y$ is $\tau$-compatible.
\end{enumerate}
\end{theorem}
\begin{proof}
Suppose that $d_Y(\lambda^+,\lambda^-) > 0$ if $Y$ is nonannular and
$d_Y(\lambda^+,\lambda^-) > 1$ otherwise.
By \Cref{prop: q_compatible}, $Y$ is $q$-compatible and so $\hat \iota_q:Y\to \bar X_Y$ is an
embedding on $Y'$.
Let $Y_q$ denote its image. We first suppose that $Y$ is not an annulus.
Give $\partial ' Y$ the transverse orientation pointing into $Y$. For
any saddle connection $\sigma$ in $\hat\iota_q(\partial' Y)$ and any
triangle $t \in \cT(\sigma)$ pointing into $Y$ (see
\Cref{sec:t_hulls} for definitions), note that the
singularities of $\bar X_Y$ in $\partial t$ are \emph{not} completion
points of $\bar X_Y$, that is they do not correspond to punctures of
$X$. This is because any completion point lying in $t$ is the
endpoint of leaves $l^\pm$ of $\lambda^\pm$ whose initial segments
lie in $t$. These leaves correspond to essential proper arcs of $X_Y$
which are homotopic giving $d_Y(\lambda^-,\lambda^+) =0$, a
contradiction.
Similarly, we can conclude that for each saddle connection $\sigma$
in $\hat\iota_q(\partial' Y)$ and any $t \in \cT(\sigma)$ pointing
into $Y$, the triangle $t$ is entirely contained in $Y_q$. Otherwise,
similar to the proof of \Cref{prop: q_compatible}, we find leaves
$l^+$ and $l^-$ in $\bar X_Y$ whose intersection with $Y_q$ is
contained in $t$ and hence whose projections to $\A(Y)$ are
equal. See the left side of \Cref{modified_thull-overlap}. Since $d_Y(\lambda^+,\lambda^-)>0$ this is impossible.
Hence, the map $\thull^+(\hat\iota_q|_{\partial' Y})$ (as defined in
(\ref{thull f}) in \Cref{sec:t_hulls}) is
homotopic to $\hat\iota_q|_{\partial' Y}$ in $\bar X_Y \ssm \til{\PP}_Y$
by pushing across the polygonal regions
given by \Cref{thull structure} along leaves of $\lambda^+$. This
extends to a homotopy of $\hat
\iota_q$ to a map $\hat \iota' \colon Y \to \bar X_Y$
which we claim is still an embedding.
(Note that, in the case that $X$ is fully-punctured,
$\hat \iota' = \hat\iota_q$,
since all singularities of fully-punctured surfaces are completion points.)
To prove that $\hat\iota'$ is an embedding, let $C$ be a component of the preimage of
$\hat\iota_q(Y')$ in
$\hat X$
(using the notation of \Cref{AY in flat geometry}, $C$ is a translate of ${\operatorname{CH}}_q(\Lambda)$).
If $\alpha$ is a geodesic segment in $\partial C$, the
triangles used in the hull construction are attached to $\alpha$ and are contained in $C$.
If such a triangle $t$ intersects a triangle $t'$ from
a different segment $\alpha'$, they overlap as in the right side of
\Cref{modified_thull-overlap}. Any two
arcs $l^+,l^-$ of $\lambda^+$ and $\lambda^-$ passing through a point
in the overlap must intersect both $\alpha$ and $\alpha'$.
These arcs are
at distance 0 in $\A(Y)$, since they can be isotoped to each other rel $\partial
Y$.
Hence $d_Y(\lambda^-,\lambda^+) = 0$, contradicting the
hypothesis. Therefore, $t,t'$ cannot overlap.
\realfig{modified_thull-overlap}{Left: If $t \in \cT(\sigma)$ (in red) is not contained in $Y_q$ then $d_Y(\lambda^+,\lambda^-) =0$. Right:
An overlap of two hull triangles. Any completion point in the boundary of a hull triangle does not correspond to a puncture in $\til{\PP}_Y$.}
We conclude that the polygonal regions of our homotopy are embedded
and disjoint, and thus the homotopy can be chosen so that
$\hat \iota'$ is an
embedding. Since the image of $\hat \iota'$ is contained in the image of $\hat \iota_q$, we apply \Cref{lem:int_embed} to get that the projection $\iota' \colon Y \to \bar X$ restricts to an embedding on $\int(Y)$.
Now orient $\partial'Y$ in the opposite direction, pointing out of
the surface, and apply $\thull$ again, this time to $\hat \iota'(\partial' Y)$.
The triangles in the construction now extend outside the surface,
and the result of the operation is the rectangle hull
$\rhull(\thull(\hat\iota_q(\partial' Y)))$,
which is therefore composed of $\tau$-edges.
Using the homotopy pushing $\hat \iota'|_{\partial' Y}$
outward along leaves of $\lambda^+$ to $\thull^+(\hat\iota'|_{\partial' Y})$ (again using
\Cref{thull structure}) we obtain our final map
$\hat\iota_\tau$. See \Cref{thull-twice}. It remains to show that
$\hat\iota_\tau \colon Y \to \bar X_Y$ has the required properties.
To prove this, let us recapitulate the construction in the universal
cover.
\realfig{thull-twice}{An inner $\thull$ followed by outer $\thull$
yields $\tau$-edges. This locally depicts the homotopy from $\hat \iota_q$ to $\hat \iota_\tau$.}
As before, let $C = {\operatorname{CH}}_q(\Lambda)$. The map $\hat \iota'$ lifts to a
$\pi_1(Y)$-equivariant homeomorphism $C \to C'$, where $C'$ is
obtained by giving each saddle connection $\kappa$ in the boundary of
$C$ the transverse orientation pointing into $C$ and removing the
polygons $P(\kappa)$ given in \Cref{thull structure}. This map is
equivariantly homotopic to the identity by pushing along leaves of the
vertical foliation.
The outward step of our construction then pushes back along leaves of
the vertical foliation to obtain a $\pi_1(Y)$-equivariant map $C'\to
C_\tau\subset \hat X$, so that the composition $C\to C'\to C_\tau$ is a lift of the map
$\hat\iota_\tau \colon Y'
\to \bar X_Y$.
To show that $\hat\iota_\tau \colon Y' \to
\bar X_Y$ is an embedding, it suffices to show that the composition
$C\to C_\tau$ is a homeomorphism.
For every non-singular point $p\in \partial C$ there is an arc $n_p$ in
$\lambda^+$ such that the deformation of $C$ to $C_\tau$ is supported
on the union $\bigcup n_p$, and preserves each $n_p$. Thus to show
that $C\to C_\tau$ is a homeomorphism it suffices to show that $n_p
\cap n_{p'} =\emptyset$ for each $p\ne p'$ in $\partial C$.
The interior pieces, $n_p\cap C$, are already disjoint for
distinct points, by our
construction. Thus if $n_p$ intersects $n_{p'}$ their union is an
interval $J$ in a leaf of $\lambda^+$ with some subinterval between $p$ and $p'$ lying outside
$C$. This contradicts the convexity of $C$.
To show that $\iota_\tau$ is an embedding when restricted to $\int(Y)$, it suffices to check that the interior of $C_\tau$ is disjoint from all its translations under the entire deck group $\pi_1(X)$. To see this, take $g \in \pi_1(X)$ so that $C_\tau$ and $g \cdot C_\tau$ are distinct and intersect. Since $\iota' \colon \int(Y) \to X$ is an embedding, $C'$ and $g \cdot C'$ meet only along their boundary. Further, if $\sigma$ is a saddle connection in $\partial C' \cap \partial (g \cdot C')$, then $\sigma$ is the hypotenuse of a singularity-free triangle pointing into $C'$ as well as one pointing into $g\cdot C'$. Hence, $\sigma$ is a $\tau$-edge and so is fixed under the map $C' \to C_\tau$.
Now if the interiors of $C_\tau$ and $g\cdot C_\tau$ intersect there must be saddle connections $\sigma,\kappa \subset \partial C'$
such that
$P(\sigma)$ and $P(g \cdot \kappa)$ have intersecting interiors. (Here, $\sigma,\kappa$ are oriented out of $C'$.)
By the previous paragraph, $\sigma$ and $g\cdot \kappa$ are distinct.
As $C'$ and $g \cdot C'$ meet only along their boundary, $\sigma$ and
$g \cdot \kappa$ have disjoint interiors and any arc $l$ of $\lambda^+$ joining $\sigma$ to $g \cdot \kappa$ within $P(\sigma) \cup P(g \cdot \kappa)$ lives outside of $C'$ and $g \cdot C'$. In particular, the chosen transverse orientations on $\sigma$ and $g \cdot \kappa$ point to the interior of $l$.
However, by \Cref{disjoint_thulls}, in this situation, the interiors
of $P(\sigma)$ and $P(g \cdot \kappa)$ do not intersect. It follows that $\iota_\tau \colon \int(Y) \to X$ is an embedding.
It only remains to prove property $(1)$ of the definition of $\tau$-compatible.
Since $\hat \iota_\tau \colon Y' \to
\bar X_Y$ is an embedding, it follows that
$\hat \iota_\tau|_{\partial' Y}$ is an embedding, and its image
does not meet
$\widetilde P_Y$ by the same argument used to prove item $(2)$ of
\Cref{lem:int_embed}.
By construction the image $\hat \iota_\tau (\partial' Y)$ is composed of
$\tau$-edges.
Now suppose that $Y$ is an annulus. Then $\hat \iota_q(Y)$ is the
(nondegenerate) maximal flat cylinder of $\bar X_Y$ by \Cref{prop:
q_compatible}. Choosing the inward-pointing orientation for
$\partial Y$, we claim that
$\thull^+(\hat \iota_q|_{\partial Y}) = \hat \iota_q|_{\partial Y}$:
Otherwise, there must be a
saddle connection $\sigma$ on the boundary of the flat annulus
$\hat \iota_q(Y)$, and a triangle $t$ pointing into the annulus
with hypotenuse on $\sigma$, which encounters a singularity or
puncture $x$ on the other side of the annulus.
The picture is similar to the left side of \Cref{modified_thull-overlap}.
A variation on the Gauss--Bonnet argument
in the annulus case of \Cref{prop: q_compatible} then produces
vertical and horizontal leaves passing through $x$ which have disjoint
representatives, and hence $d_Y(\lambda^+,\lambda^-) \le 1$.
Thus the inward step of the process is the identity, and the outward
step and the rest of the proof proceed just as in the nonannular case.
\end{proof}
\begin{remark} \label{rmk:fully}
From the proof of \Cref{thm: tau-compatible}, we record the fact that if $X$ is fully-punctured and $Y$ satisfies
the hypotheses of \Cref{thm: tau-compatible}, then $\thull^+(\hat \iota_q|_{\partial Y}) = \hat \iota_q|_{\partial Y}$
and $\iota' = \hat \iota_q$.
Hence, in this case we have that $\partial_\tau Y = \rhull(\partial_q Y)$.
\end{remark}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,364
|
from __future__ import print_function
from peyotl.phylesystem.phylesystem_umbrella import Phylesystem
from peyotl.nexson_syntax import extract_tree_nexson
import sys
try:
phylsys = Phylesystem()
except Exception as e:
sys.stderr.write('count_trees.py: Exception: {}\n'.format(e.message))
sys.exit('count_trees.py: There was a problem creating a wrapper around your phylesystem '
'instance. Double check your configuration (see '
'http://opentreeoflife.github.io/peyotl/configuration/ for info).')
try:
print_freq = 500
num_trees = 0
num_studies = 0
max_trees_per_study = 0
biggest_study = None
studies_without_trees = []
sys.stderr.write('count_trees.py: beginning loop over studies...\n')
for study_id, nexson in phylsys.iter_study_objs():
num_studies += 1
try:
nt = len(extract_tree_nexson(nexson, tree_id=None))
except:
sys.stderr.write('Problem extracting trees from study {}'.format(study_id))
raise
if nt == 0:
studies_without_trees.append(study_id)
else:
num_trees += nt
if nt > max_trees_per_study:
biggest_study = study_id
max_trees_per_study = nt
if num_studies % print_freq == 0:
sys.stderr.write(' ...{d} studies read. Still going...\n'.format(d=num_studies))
except:
sys.exit('Unexpected error in iteration, please report this bug.')
output = '''{s:d} = # studies
{e:d} = # studies without any trees
{t:d} = # trees total
{m:d} = maximum # trees in any study ({b})
The tree-less studies are: {a}
'''.format(s=num_studies,
e=len(studies_without_trees),
t=num_trees,
m=max_trees_per_study,
b=biggest_study,
a=studies_without_trees)
print(output)
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,411
|
\section{Introduction}
Coronal mass ejections (CMEs) are among the most powerful solar events.
The CMEs transfer solar energetic particles to the Earth and cause geomagnetic storms,
which can produce severe space weather conditions. Previous studies have found that
the CME plasmas are strongly heated in the low solar corona.
Ultraviolet Coronagraph Spectrometer (UVCS) on board {\it{Solar and Heliospheric Observatory}} (SOHO) observations
have shown that the heating energy of CME plasma is comparable to or even larger than its kinetic energy
\citep{akmal2001, ciaravella2001, lee2009, landi2010, murphy2011}.
Ion charge composition from in situ measurements by the {\it{Advanced Composition Explorer}} (ACE) have shown that
strong and rapid heating are required around 2~R$_\sun$ by ionization state models \citep{gruesbeck2011, rakowski2011,lynch2011}.
Recent studies using the {\it{Solar Dynamic Observatory}}/Atmospheric Imaging Assembly (AIA) observations have shown that
CME core regions are strongly heated, and their temperatures can be higher than 10 MK \citep{reeves2011, cheng2012, hannah2013, tripathi2013}.
The association between hot X-ray plasma ejections and CMEs has been studied
since \citet{harrison1985} who found X-ray plasma ejections to be a signature of CME onset using observations by the
Coronagraph/Polarimeter \citep{macqueen1980} and the hard X-ray imaging spectrometer \citep{vanbeek1980}
on board the Solar Maximum Mission.
\citet{shibata1995} suggested that hot plasma ejections, observed by the soft X-ray telescope (SXT; \citealp{tsuneta1991}) on board {\it{Yohkoh}} \citep{ogawara1991},
might be miniature versions of the much larger scale CME events. The temperatures and masses of ejected plasmas
have been estimated to be higher than 10 MK and about 10$^{13}\sim$10$^{14}$~g, respectively \citep{tsuneta1997, ohyama1997, ohyama1998, tomczak2004}.
\citet{nitta1999} made the first systematic comparison between flare-associated plasma ejections in SXT and CMEs observed by the
Large Angle and Spectrometric Coronagraph Experiment (LASCO) on board {\it{SOHO}}.
They proposed that the occurrence of a hot plasma ejection depends on the presence of open field lines created by a preceding CME.
A statistical study of the relationship between flare-associated X-ray plasma ejections and CMEs shows that the events with X-ray plasma ejections
are more correlated with CMEs \citep{kim2005a}.
Recently, a catalogue of X-ray plasma ejections observed by SXT has been developed by \citet{tomczak2012}.
They suggests that the erupting loop-like structure characteristic of X-ray plasma ejections is a promising candidate to be a high temperature precursor of CMEs.
This idea is consistent with an earlier result that the X-ray plasma ejections with both loop and jet-type structures show a high association with CMEs \citep{kim2004}.
A spectroscopic study of hot plasma associated with a CME using the EUV Imaging Spectrometer (EIS) and the X-ray Telescope (XRT) on board {\it{Hinode}} \citep{landi2013} shows that
the temperature of X-ray plasma ejection is about 8$-$12.5~MK with the absence of the hot spectral lines in EIS, which might come from the limit
of sensitivity of EIS for the high temperatures.
Several studies have investigated the physical properties of erupting hot X-ray plasmas associated
with CMEs \citep{tomczak2004, kim2005b, landi2010}.
\citet{tomczak2004} investigated the energy balance of an X-ray plasma ejection associated both an X-class flare and a CME.
He suggests that the mass of the X-ray ejection event, 1.2$-$1.5$\times$10$^{15}$~g, can be
responsible for an additional acceleration of the CME.
A study of kinematic properties shows that the majority of X-ray plasma ejections are not likely to be the X-ray
counterpart of CMEs but outflows generated by magnetic reconnections with no statistical correlation between the
speed of X-ray plasma ejections and the corresponding CME speeds \citep{kim2005b}.
In this analysis we investigate energies of eruptive plasmas by estimating the temperatures and masses using the {\it{Hinode}}/XRT observations.
We find the temperatures using the filter ratio method \citep{narukage2011, dudik2011, kariyappa2011,reeves2012},
because there are not enough filters available for a more sophisticated differential emission measure (DEM) analysis for our observed events.
We determine the mass constraints of eruptive plasma by
calculating the emission measures and assuming simplified geometrical structures to determine the densities.
These assumptions provide the upper limit for the masses of the observed eruptive plasmas.
The masses of CMEs have been studied previously using the {\it{SOHO}}/LASCO observations \citep[e.g.][]{vour2010}.
We compare the estimated masses from X-ray observations with those calculated from the coronagraph measurements.
Finally, we investigate the radiative loss, thermal conduction, thermal, and kinetic energies of eruptive X-ray plasma.
In Section 2, we describe the observations used in this analysis. In Section 3, we explain the analysis method.
In Section 4, we discuss the estimated temperatures, masses, and energies of erupting X-ray plasmas.
In Section 5, we present our conclusions.
\section{Observations}
\label{sec:obs}
The XRT \citep{golub2007, kano2008} on board {\it{Hinode}} \citep{kosugi2007} observes
the solar corona at high ($\sim$\,1$''$ pixels) spatial resolution in multiple bandpasses
with a wide field of view of 34 $\times$ 34 arcmin and a 2048$\times$2048 CCD camera.
We investigate 7 examples of eruptive X-ray plasma observed by XRT (Figure~\ref{fig:xrt} and Table~\ref{tb:xrt}).
Four events are observed at the full resolution with $\sim$\,1$''$ pixels with a field of view (FOV) of $\sim$\,512$''\times$512$''$.
Two events are observed with 4 $\times$ 4 pixel binning. In this mode, XRT can observe the full Sun in 512$\times$512 pixels with $\sim$\,4 arcsec/pixel resolution.
One event is observed with a 2$\times$2 pixel binning with a FOV of $\sim$\,1024$\times$1024$''$.
Five events among the seven events are observed in a few passbands,
which allows us to determine the temperature of the erupting plasma using the filter ratio method.
We show the observational time cadences in Table~\ref{tb:xrt}.
Corresponding EUV and/or white light CME features are visible in some events.
Several events are observed in EUV bandpasses by the Extreme ultraviolet Imaging Telescope (EIT; \citealp{dela1995}) on board {\it{SOHO}}
and the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI)
Extreme UltraViolet Imager (EUVI; \citealp{wuelser2004, howard2008}) on board {\it{Solar TErrestrial RElations Observatory}} (STEREO; \citealp{kaiser2008}).
We summarize the EUV observations for each event in Table~\ref{tb:euv}.
The EIT and EUVI observations show associated prominence eruptions in absorption or emission for several events with the eruptive plasmas in X-rays.
Five events are observed in 195~\AA\ by {\it{SOHO}}/EIT with a 12 minute cadence.
All seven events are observed by {\it{STEREO}}/EUVI with various time cadences from a few minutes to 20 minutes for most of observations.
Two events are associated with B class flares by the {\it{Geostationary Operational Environmental Satellite}} (GOES).
Four events are associated with CMEs observed by LASCO \citep{brue1995} on board {\it{SOHO}},
while we do not find the associated CMEs for other three events.
One event on 2008 December 30 among the four events is associated with a very poor CME.
The EUVI observations on 2009 January 11 show brightening in 171~\AA, 195~\AA, and 284~\AA\ and,
especially, a brightening along a filament in 304~\AA.
Observations near the East limb on 2010 January 22 show that the erupting material moves to the southeast along a larger loop in the EIT observation,
subsequently causing another eruption associated with a CME.
A large filament is placed on the eruption region on 2010 January 30.
The 304~\AA\ observations of the event show that some materials move along the large filament.
\section{Analysis}
We estimate the temperature and mass of erupting plasma observed in X-rays,
and compare the mass constraints with the masses
obtained from white light coronagraph observations by the LASCO.
In addition, we evaluate the radiative loss, thermal conduction, thermal, and kinetic energies of eruptive plasmas observed in the X-rays.
\subsection{Temperature estimation of eruptive X-ray plasma}
\label{sec:temp}
We use the filter ratio method \citep{narukage2011, narukage2014} to find the temperatures of erupting plasma
for 5 events observed
in a few passbands by the XRT (Table~\ref{tb:temp}).
Filter ratio methods using the XRT observations have been used previously to estimate
the temperatures of bright points \citep{kariyappa2011}, the coronal emission for an active region \citep{dudik2011},
and a coronal cavity \citep{reeves2012}.
In this analysis, the temperatures of the erupting plasma are estimated using relatively thinner filter observations
since the thicker filter observations do not have enough signal for the temperature estimation.
We exclude the pixels that show contamination spots
,which are spot-like patterns over the CCD that accumulated after the second bakeout on 3 September 2007 (see details \citealp{narukage2011}).
The observed data are calibrated by a procedure (xrt\_prep.pro) in {\it{SolarSoft}} \citep{kobelski2014}.
We use a procedure (xrt\_teem.pro) in SolarSoft to estimate the temperatures by a filter ratio method \citep{narukage2011, narukage2014}.
Figure~\ref{fig:temp} shows the regions used for the temperature estimation.
We use the black colored pixels in the fourth panels of Figure~\ref{fig:temp} for the estimation.
In addition, we estimate the temperatures using averaged intensities for the regions which are included by contours on both the second and third panels of Figure~\ref{fig:temp}.
We subtract a pre-event image for each passband observation before we apply the filter ratio method.
The images at the first column show the eruptive plasmas before the pre-event subtractions.
The regions of eruptive plasma are shown in the second and third columns for two XRT passbands via enclosed solid lines on the pre-event subtracted images.
The time differences of the observations in two passbands are within 1 minute for most of the events.
We use thresholds for the temperature error and photon noise \citep{narukage2011} of less than 50\% and 20\%, respectively.
The images at the last column show the pixels within the thresholds by a black color on the XRT observations.
We estimate the signal to noise ratio (S/N) by using the procedure xrt\_cvfact.pro in {\it{SolarSoft}}.
We present the averaged S/N values of the selected pixels for the temperature estimation in Table~\ref{tb:temp}.
The corresponding temperatures to the averages of the observed data ratios are shown in Figure~\ref{fig:ratio}.
The slight difference in the model filter ratios on 2007 May 23 compared with the ratios on 2009 January 22 and 30
come from small changes of the temperature response due different levels of contamination on the CCD as a function of time.
The Al/mesh filter observations have been more affected by the contamination \citep{narukage2011}.
In case of two events on 2008 April 9 and 2009 December 13 observed by a single filter,
we assume the temperature of the eruptive plasma at the maximum of the temperature response function for that filter (See Section~\ref{sec:mass}).
\subsection{Mass estimation of eruptive X-ray plasma}
\label{sec:mass}
We determine the mass constraints of eruptive plasma
by assuming simplified geometrical structures.
For most of events in this analysis, the eruptive plasmas expand with a loop-like structure.
We assume a simple cylindrical structure for the loop-like eruptive plasmas.
The widths and lengths of the cylinder structures are shown in Figure~\ref{fig:temp} and also in Figure~\ref{fig:mass}.
The width of the cylinder structure is assumed to equal the line of sight depth.
With these assumptions, the volume of the eruptive plasma of each event
can be estimated as a cylinder.
For the event on 2008 April 8 in Figure~\ref{fig:mass}, we select two regions (A and B) of the eruptive plasmas because the region `B' appears to consist of
ambient corona plasma surrounding region `A'.
The region `A' of erupting plasma shown in the second column in Figure~\ref{fig:mass} is taken as a blob structure.
In this case, we take the width at each row (w$_{\rm i}$, see the second column in Figure~\ref{fig:mass}), assume a short cylinder at that position,
and sum the masses of these short cylinders for the total mass of the region `A'.
The region `B' shown in the third column is assumed to be a cylinder structure like the other events.
The above assumptions of the structure provide the upper limit to the masses of the observed eruptive plasmas
since any clumping will cause an overestimate of the mass.
Once we define the structure of the eruptive plasma for each event,
we find an emission measure (EM) of the erupting plasma
which can be used to estimate the densities of the plasmas.
The observed data number (DN) is given by
\begin{equation}
DN = R_t (T) \times \rm{EM},
\end{equation}
\noindent where DN is normalized number of DN sec$^{-1}$pix$^{-1}$ and R$_{t}$(T) ([DN cm$^5$ sec$^{-1}$pix$^{-1}$]) is the temperature response function
from procedures (make\_xrt\_wave\_resp.pro and make\_xrt\_temp\_resp.pro) in {\it{SolarSoft}}.
The EM [cm$^{-5}$] is defined as
\begin{equation}
EM = < n_e^2 > dl,
\end{equation}
\noindent where {\it n$_e$} and {\it dl} are the electron density and line of sight depth of the observed plasma, respectively.
Therefore, we can derive the electron density of the eruptive plasma with the assumption of the line of sight depth as explained above.
For the events in Figure~\ref{fig:temp}, we use the temperature response at the estimated temperatures given by the filter ratio method.
For the two events observed with a single passband, we assume the maximum temperature response for that filter, and the corresponding temperatures
are assumed as the temperatures of the eruptive plasmas for these events.
Under this assumption, the estimated density gives the lower limit to the mass.
We show the temperature response functions with the estimated (five events using the filter ratio method) or
assumed (two events with a single filter observation) temperatures in Figure~\ref{fig:resp}.
Finally, we estimate the masses of the eruptive plasmas in X-rays using the averaged density of the selected region for each event.
For this we assume a plasma with a 10$\%$ of Helium content with a mass of 1.974 $\times$ 10$^{-24}$~g per ion.
Table~\ref{tb:mass} shows the geometrical parameters, density, and mass for each event.
We show the S/N values for the regions used for the mass estimation in Table~\ref{tb:mass}.
These are estimated by the same procedure as the S/N values in the Table~\ref{tb:temp}.
\subsection{Energies of eruptive X-ray plasma}
\label{sec:energies}
We estimate the radiative loss, thermal conduction, thermal energy, and kinetic energy of the eruptive plasma
using the physical quantities in Table~\ref{tb:mass}.
The radiative loss (L$_r$) is given by
\begin{equation}
\rm{L_r} ~[erg] = EM \times P(T) \times \bigtriangleup{t},
\end{equation}
\noindent where EM is in unit of cm$^{-3}$ and P(T) is plasma radiative loss function.
We use analytical fits, P(T)=10$^{-21.94}$ for temperatures lower than 10$^{6.3}$ K and P(T)=10$^{-17.73}$~T$^{-2/3}$
for temperatures higher than or equal to 10$^{6.3}$K, for the radiative loss function given by \citet{rosner1978}.
The quantity $\bigtriangleup$t is the duration of eruptive plasma (column four in Table~\ref{tb:energy}).
We define the beginning of the duration right after the eruption starts.
In the case of the event on 2009 December 13, the eruption is first observed at 09:08~UT, but there is a data gap between 08:40~UT and 09:08~UT.
Therefore, the duration could be longer. The field of view of the event on 2010 January 30 is not enough to follow the eruption.
It appears that the bright eruptive plasma could persist longer than the duration
since the eruptive plasma moves out of the FOV in the observations later the duration in Table~\ref{tb:energy}.
In addition, most of eruptions start from pre-existing bright structures in the XRT observations.
Thus, the duration of the eruptive plasma could be longer than the time used in this analysis.
The radiative loss time scale \citep[e.g.][]{golub2009} is estimated by
\begin{equation}
\tau_{rad} = \frac{3~(n_e+n)~k_B~T}{2~n_e~n~P(T)},
\end{equation}
\noindent where n is the number density assuming 0.8 times of the electron number density, k$_B$ is the Boltzmann constant, and T is the temperature.
We assume that the the thermal conduction (F$_c$) is mainly along the magnetic field lines and estimate the thermal conduction using the conductivity flux defined as
\begin{equation}
F_c ~ \rm{[erg]} = \kappa~T_{max}^{5/2}~\frac{T_{max}}{{\it{l}}/2}~A \times \bigtriangleup{t},
\end{equation}
\noindent where $\kappa$ is 1.8$\times$10$^{-5}$/$\rm{ln}$$\Lambda$($\approx$ 7.0$\times$10$^{-7}$~erg~cm$^{-1}$~K$^{-7/2}$~s$^{-1}$),
T$_{max}$ is the temperature at the loop top, $l$ is the length of the loop, and A is the cross-sectional area.
Here, the \rm{ln}$\Lambda$ is the Coulomb logarithm. We apply the half lengths and depths of the cylinder structures to estimate the thermal conduction.
The thermal conduction time scale is estimated by
\begin{equation}
\tau_{cond} = \frac{3~(n_e + n)~k_B~(l/2)^2}{\kappa~{T_{\rm{max}}}^{5/2}}.
\end{equation}
\noindent We use the estimated temperatures in the Section~\ref{sec:temp} for the T$_{\rm{max}}$.
However, the estimated temperature is during the eruption of the plasma.
The temperature of the eruptive plasma may decrease due to its expansion.
Therefore, the estimated thermal conduction time scale can be larger than our estimation.
In the case of the events on 2009 January 11 and 2010 January 22, the length of the cylinder structure of the eruptive plasma in Figure~\ref{fig:temp}
is the half of the length of the loop. Therefore, the length in Table~\ref{tb:mass} is used for the {\it{l}}/2 in equations~(5) and~(6).
We estimate the thermal energy (=3(n + n$_e$)k$_B$T $\times$ Volume) and kinetic energy (=1/2mv$^2$) with the mass, m, in Table~\ref{tb:mass}.
The volume is calculated using the geometrical parameters in Table~\ref{tb:mass}.
The projected speeds of the erupting plasma are estimated using several sequence images during the times (column eight) in Table~\ref{tb:energy}.
Thus, the kinetic energy could be larger than these estimates.
In addition, we estimate the potential energy, which is required to lift the erupting plasma against solar gravity, given by
\begin{equation}
U = GM_\sun m(\frac{1}{R_\sun} - \frac{1}{r}),
\end{equation}
\noindent where G is the gravitational constant, M$_\sun$ is the solar mass, and R$_\sun$ is the solar radius.
We define the final heights (r, column eleven in Table~\ref{tb:energy}) of the eruptive plasma from the observations
just before the plasmas are blown out by losing their structures in the images, except for three events (marked by $^\flat$ in Table~\ref{tb:energy}).
The FOVs of the XRT observations for the three events are not enough to see the final heights of the eruptive plasmas.
For these events, we define the final heights as the highest height of eruptive plasma that can be measured in the limited FOV.
Thus, the final heights could be higher than the measured values.
\section{Results and discussion}
\label{sec:results}
We estimate the temperature, mass, and energies of eruptive plasma for seven events observed in {\it{Hinode}}/XRT.
The temperatures estimated by the filter ratio of the plasma vary from 1.6 to 10~MK in Table~\ref{tb:temp}.
Using the black pixels in the fourth column of Figure 2, we find that the event on 2007 May 23 shows a high temperature of $\sim$10~MK using the filter ratio method.
This measurement confirms the results of temperature analysis studies of CME plasmas, which show that
the temperatures of the CMEs observed in EUV can include high temperature plasma over 10~MK \citep{reeves2011, cheng2012, hannah2013, tripathi2013}.
The temperature of erupting plasma on 2009 January 22 is $\sim$6.3~MK
while the temperatures for other three events on 2008 December 30, 2009 January 11, and 2010 January 30 are relatively low, from 1.6 to 2.5~MK.
Using the areas enclosed in the contours shown in the second and third panels of Figure 2,
we find temperatures of 16, 2.2, 2.2, 7.9, and 2.5~MK for the events on 2007 May 23, 2008 December 30, 2009 January 11, 2010 January 22, and 2010 January 30, respectively.
The estimated temperatures are higher than or similar to the temperatures estimated by using the black pixels as explained in section 3.1.
Lower DNs in faint regions of erupting plasma within the contours might be removed by the background subtraction.
This effect is more likely for Al/mesh filter observations, which are relatively more sensitive for the lower temperature plasma, meaning that
the contribution of lower intensity pixels could be disproportionately prevalent in the Al/mesh filter.
Thus the average Al/mesh intensity could be lower than it should be, which would increase the filter ratio, thereby increasing the measured temperature.
Two events on 2007 May 23 and 2009 December 13 are associated with B-class flares.
The temperature of erupting plasma on 2007 May 23 is higher than other events.
The event on 2009 December 13 is observed with a single filter of Al-med, which is sensitive for high temperature ($> \sim$5~MK).
Therefore, this observation may indicate the high temperature of the erupting plasma.
In addition, the source location of the event on 2008 April 9 is behind of the limb.
This event has been studied with regard to supra-arcade downflows observed by XRT
that have been interpreted as evidence for reconnection in a current sheet trailing a flux rope eruption \citep{savage2010}.
Therefore, there is a possibility of a flare behind the limb. We can not see an evidence of the flare in the STEREO observations
since the active region is seen at the west limb by the STEREO at heliocentric longitude 24$^\circ$.
One event on 2010 January 22 shows a relatively high temperature of $\sim$6.4~MK without an associated flare.
The results of our study suggest that the events of erupting plasma in X-rays can be seen without any flare.
However, the higher temperature plasma events are possibly more associated with flares
as found in a previous study using observations by SXT on board {\it Yohkoh} by \citet{tomczak2012}.
The masses estimated by using a simplified geometrical structure are from $\sim$3$\times$10$^{13}$ $-$ $\sim$5$\times$10$^{14}$~g.
The averaged densities of eruptive plasma are in the range between $\sim$7$\times$10$^7$ and $\sim$2$\times$10$^9~\rm cm^{-3}$.
These results are smaller than earlier studies using {\it{Yohkoh}} observations \citep{tsuneta1997, ohyama1997, ohyama1998, ohyama2008, tomczak2007}
probably because their X-ray plasma ejections are associated with mostly M-class flares.
Several of our events are cooler, but the hotter events have temperatures similar to those listed in \citet{tomczak2007}.
The event on 2008 April 9 has been intensively studied on its energetics and physical properties of current sheet and flux rope
\citep{savage2010, landi2010, patsourakos2011, thompson2012, landi2013}.
The density, 8.8$\times$10$^7$ cm$^{-3}$, in this analysis is similar with the result, $\sim$10$^8$ cm$^{-3}$, of \citet{landi2010}.
The temperature, log T = 6.9 $-$ 7.1 K, from the analysis using the EIS and XRT \citep{landi2013} is
similar with our assumption at the maximum temperature response in this analysis.
The masses of the eruptive plasma in lower corona are smaller than those calculated from coronagraph observations by LASCO, as shown in Table~\ref{tb:euv}.
The coronagraph observations represent the total mass of CME materials measured through electron scattering,
while the mass in X-rays represents only the hot plasma. There might also be mass that falls down to the Sun.
In addition, the CMEs accumulate mass including cooler plasma as they expand through the corona,
so observations at 2.3 R$_\sun$ and above should give larger masses.
Three events among the seven events have no corresponding CME observations by LASCO.
The event on 2010 January 22 shows a failed eruption in the EIT and EUVI observations.
The observations in EUV on 2010 January 30 show a large filament near the region where the eruption is observed.
The 195~\AA\ EUVI observations appear to show eruptions on 2010 January 30.
However, the observations show that some of the erupting plasma falls back to the Sun.
The event on 2009 January 11 also shows a brightening along a filament in 304~\AA\ EUVI observations.
Thus, this event also has a possibility that some plasmas might fall back to the Sun along the filament.
Two events on 2007 May 23 and 2009 December 13 are associated with CMEs in the LASCO observations.
The event on 2008 December 30 is very slow ($\sim$5 km/s) in the low corona.
The event is possibly associated with a very faint narrow CME appeared in C2 FOV at 21:30~UT about 3 hours later than the event observation time in XRT.
Only about half of the eruptions in X-rays are associated with the CMEs in the LASCO
observations, either because the erupting material falls back to the Sun or because
the ejected mass is too small to be seen given the sensitivity and cadence of LASCO.
Two events have corresponding EUV observations by {\it the Transition Region and Coronal Explorer} (TRACE; \citealp{handy1999}) available for comparison.
Figure~\ref{fig:trace} shows the co-alignment between the TRACE and XRT observations.
The event on 2007 May 23 shows the eruptive plasma as an absorption from $\sim$07:12~UT to $\sim$07:42~UT in 171~\AA\ and 195~\AA\ by {\it{STEREO}}/EUVI.
The 304~\AA\ EUVI observations show the eruption in emission at $\sim$07:22~UT, but later, it appears in absorption in the same 304~\AA\ band.
The eruption in X-rays starts at $\sim$07:02~UT and then all the plasma erupts before $\sim$07:20~UT.
This indicates that the eruptive hot plasma in X-ray cools down, so then it appears as absorption in 195~\AA\, then in 304~\AA\ as emission and finally as absorption in 304~\AA.
The co-alignment image on the left bottom in Figure~\ref{fig:trace} demonstrates that
the erupting plasma observed by both TRACE and XRT is spatially coincident.
The erupting loop on the TRACE observations contains a filament which is seen as an absorption feature on the {\it STEREO}/EUVI observations.
The EUVI 171 \AA\ observations also show a loop eruption in emission.
Thus, it is also possible that a filament erupts with hot plasma which can be seen in emission.
On the other hand, the event on 2008 Apr. 9 shows that a prominence erupts in absorption around 09:05~UT in 171~\AA, 195~\AA, and 284~\AA\ observations
and then it appears as emission in the passbands, while it erupts in emission in 304~\AA\ and remains in emission until it moves out of the observational FOV.
Its eruption in X-ray starts around 09:16~UT from the behind of the limb.
Therefore, the eruption might start earlier than that time.
These observations indicate that the hot and cool plasmas erupt simultaneously and the cool plasmas seen in absorption are heated during their eruptions.
The co-alignment image on the right bottom in Figure~\ref{fig:trace} shows that
the plasmas seen in the TRACE and XRT observations are not spatially coincident.
Landi et al. interpret this observation as the XRT emission enveloping the tail of the erupted prominence.
Table~\ref{tb:energy} shows the radiative loss, thermal conduction, thermal, and kinetic energies.
The radiative loss energies are much smaller than the thermal conduction energies,
except for one event on 2010 January 30.
In this event, the radiative loss is larger than thermal conductive flux by a factor of 3-4.
We estimate the temperatures in this events to be the relatively low values of 1.6 MK
and the radiative loss time scale is smaller than the thermal conduction time scale.
Additionally, the event has much smaller thermal conduction flux than its thermal energies.
On the other hand, for two events on 2007 May 23 and 2009 December 13, we estimate high temperatures of 10 MK.
These events have relatively large thermal conductive flux compared to their thermal energies,
and their conductive cooling times are very short compared to the radiative cooling times.
Therefore, the plasma of the two events with the high temperatures of 10 MK is dominated by thermal conduction,
while the plasma of the two relatively low temperature events is dominated by radiative losses.
Three other events on 2008 April 9, 2009 January 11, and 2010 January 22 show similar conduction and thermal energies,
while one event on 2008 December 30 shows a relatively larger thermal conduction than its thermal energy.
These events are also dominated by the conductive cooling process, according to the calculated cooling times.
The thermal energies are much larger than the kinetic energies for all events from X-ray observations in low corona.
The kinetic energies from the observations in X-rays are much smaller than those of typical CMEs from the LASCO observations
because of their low speeds and masses.
Therefore, the eruptive plasma in the lower corona might be accelerated during its expansion to
the several solar radii when it is observed by coronagraphs.
The potential energies are higher than the kinetic energies
because of the very low speeds and masses in low corona.
On the other hand, the potential
energies are smaller than the thermal energies because the temperatures
are high and the gas is only lifted 0.1$-$0.3 R$_\sun$ above the solar surface.
\citet{emslie2012} studied energetics of large solar eruptive events.
In their study, the kinetic energies are much bigger than the potential energies ($\sim$10$^{30} - $10$^{31}$~erg), which are estimated from the LASCO observations.
The kinetic energies of their events, $\sim$10$^{31} - $10$^{33}$~erg, are larger than those of our three events, $\sim$10$^{30}$~erg,
taken from the LASCO CME catalogue\footnote{\label{catalogue}http://cdaw.gsfc.nasa.gov/CME$\_$list/}.
The events studied in \citet{emslie2012} are mostly associated with X-class flares,
and the potential and kinetic energies are estimated at larger heights.
Thus, the kinetic energies would be bigger than the potential energies if the speed exceeds the escape speed.
In addition, we investigate the energy evolution of two of the five events (2007 May 23 and 2008 December 30)
observed with multiple passbands.
Three other events are not available for this analysis
due to the lower cadence of the second filter observations and a limitation of the FOVs.
Especially, the event on 2008 December 30 is very slow with a velocity of about 3$\sim$7~km/s for about 4 hours.
This slow expansion makes it possible to see the eruption for a longer time in the XRT field of view.
We apply the velocities in Table~\ref{tb:energy} for both events since the velocities are similar in the time sequences.
Figure~\ref{fig:energy} shows the energy changes for two events.
The event on 2007 May 23 is observed for only three times.
The erupting plasma seems to heat up (or at least not cool down) even as the structure is expanding.
The thermal conduction, thermal, and kinetic energies increase as the structure and temperature become larger.
The event on 2008 December 30 shows a brightening at the beginning of its eruption.
The temperature of the plasma is higher, at about 9~MK at 14:41 UT.
Then, the erupting plasma cools down, but the temperature stays larger than 2~MK even after its slow decrease between 15:06 and 16:52 UT.
The kinetic and thermal energies increase with time as the volume and mass get larger.
For both events, we confirm that the thermal conduction time scales remain much shorter than the radiative loss time scales during expansion.
With above results, we confirm that the radiative loss and thermal conduction could cool the erupting hot plasma.
Thermal conduction does even out the temperature along the
loop. The reason that it is considered a cooling process is that
it transports heat from the X-ray emitting gas to temperatures
of a few times 10$^5$ K. The radiative cooling coefficient in this temperature range is
much higher, and the density is also higher, so the transition region
radiates the energy away very efficiently.
Especially, for 4 events on 2007 May 23, 2008 April 9, 2008 December 30, and 2009 December 13,
the thermal conduction timescales are much shorter than the duration of eruption (column four in Table~\ref{tb:energy}).
This result implies that additional heating energy for these four events is necessary
to explain the persistence of the high temperature plasma in X-ray observations during the eruption.
\section{Summary and Conclusion}
We investigate the temperatures, masses, and energies of seven eruptive plasma observed by {\it{Hinode}}/XRT.
We estimate the temperatures of X-ray plasma by a filter ratio method for five events observed by several passbands.
For other two events observed by a single passband, we assume the temperatures at the maximum of the temperature response
function for that filter. We find that the estimated isothermal temperatures vary from 1.6~MK to 10~MK.
About half of the erupting plasmas have no corresponding CME observed by the LASCO due to failed eruption
or the sensitivity and cadence of the LASCO.
We determine the mass constraints of eruptive plasmas in X-rays assuming simplified cylinder structures, which represent an upper limit to the mass.
The estimated masses are 3$\times$10$^{13} - $5$\times$10$^{14}$~g.
The masses in X-rays are smaller than
the masses in coronagraph observations.
The estimated mass in X-rays represents only the hot plasma while the mass from LASCO
is total CME mass. In addition, the CMEs accumulate mass including cooler plasma as they expand through the corona.
The radiative loss energies are much smaller than the thermal conduction energies in six events except for 2010 January 30.
Therefore, the plasmas for most of events cool down by the thermal conduction, while the plasmas for only one event cools down due to radiative loss.
The thermal conduction time scales for four events are much shorter than the duration of eruption.
This result indicates that additional heating for these four events is required to explain the hot plasmas observed by {\it{Hinode}}/XRT.
To investigate how much heating energy will be required to explain the hot plasma in X-rays
and the kinetic energies of the CMEs observed by coronagraphs,
we plan to analyze the time series observations in X-rays with high cadence {\it{SDO}}/AIA images.
\acknowledgments
This work was supported by NASA grants NNM07AA02C and NNX09AB17G and NSF SHINE grant AGS-1156076 to the
Smithsonian Astrophysical Observatory, Basic Science Research
program (NRF-2013R1A1A2058409, NRF-2013R1A1A2012763) and the BK21 plus program through the National Research
Foundation (NRF) funded by the Ministry of Education of Korea,
NRF of Korea Grant funded by the Korean Government (NRF-2013M1A3A3A02042232),
and the Korea Meteorological Administration/National Meteorological Satellite
Center.
``Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as
domestic partner and NASA and STFC (UK) as international partners. It is
operated by these agencies in co-operation with ESA and the NSC (Norway)."
The CME catalog is generated and maintained at the CDAW Data Center by
NASA and The Catholic University of America in cooperation with the Naval Research Laboratory.
SOHO is a project of international cooperation between ESA and NASA.
\bibliographystyle{apj}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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Four Star Playhouse è una serie televisiva statunitense in 129 episodi trasmessi per la prima volta nel corso di 4 stagioni dal 1952 al 1956.
È una serie di tipo antologico in cui ogni episodio rappresenta una storia a sé. Gli episodi sono storie di genere vario. A differenza delle altre serie antologiche dell'epoca, Four Star Playhouse utilizzava un cast fisso di base con quattro attori che a rotazione interpretavano i protagonisti degli episodi.
Interpreti
Quattro attori principali, Charles Boyer, David Niven, Dick Powell e Ida Lupino (i primi tre furono anche produttori), a turno, erano protagonisti degli episodi. Dick Powell interpreta, in otto episodi, il personaggio di Willie Dante, creato sulla sceneggiatura di Blake Edwards, operatore di una casa di gioco d'azzardo illegale. Il personaggio produrrà poi in seguito lo spin-off Ispettore Dante in cui è interpretato da Howard Duff. Altro spin-off generato dalla serie, con l'episodio del 25 febbraio 1954, è Meet McGraw (1957-1958, 41 episodi).
Molti altri artisti interpretarono diversi ruoli in più di un episodio.
Herb Vigran (15 episodi, 1952-1956)
Regis Toomey (8 episodi, 1952-1956)
Ralph Moody (7 episodi, 1953-1956)
Robert Bice (7 episodi, 1954-1956)
Ray Walker (6 episodi, 1952-1956)
Christopher Dark (6 episodi, 1955-1956)
Richard Hale (6 episodi, 1953-1956)
Rhys Williams (6 episodi, 1952-1955)
Joan Camden (5 episodi, 1953-1955)
Alan Mowbray (5 episodi, 1955-1956)
Richard Reeves (5 episodi, 1953-1955)
William Forrest (5 episodi, 1953-1955)
Dorothy Green (4 episodi, 1953-1956)
Gene Hardy (4 episodi, 1953-1956)
Ronald Colman (4 episodi, 1952-1954)
Merle Oberon (4 episodi, 1953-1955)
Beverly Garland (4 episodi, 1954-1956)
Nestor Paiva (4 episodi, 1953-1955)
Berry Kroeger (4 episodi, 1955-1956)
Joseph Waring (4 episodi, 1954-1956)
Walter Sande (4 episodi, 1952-1956)
Walter Kingsford (4 episodi, 1953-1956)
Hugh Beaumont (4 episodi, 1954-1956)
Walter Coy (4 episodi, 1955-1956)
Lewis Martin (4 episodi, 1954-1956)
John Harmon (4 episodi, 1953-1954)
John Doucette (4 episodi, 1954-1955)
Alex Frazer (4 episodi, 1953-1956)
William F. Leicester (4 episodi, 1952-1955)
Sam Flint (4 episodi, 1954-1955)
Brooks Benedict (4 episodi, 1952-1956)
Barbara Lawrence (4 episodi, 1953-1956)
Frank Lovejoy (3 episodi, 1953-1956)
Joanne Woodward (3 episodi, 1954-1956)
Jeanette Nolan (3 episodi, 1953-1956)
Jean Howell (3 episodi, 1953-1955)
Dick Foran (3 episodi, 1954-1955)
James Seay (3 episodi, 1953-1956)
Lawrence Dobkin (3 episodi, 1953-1955)
Arthur Space (3 episodi, 1954-1956)
Morris Ankrum (3 episodi, 1955-1956)
Craig Stevens (3 episodi, 1953-1956)
Joan Banks (3 episodi, 1953-1954)
Ted Stanhope (3 episodi, 1954)
Paul Bryar (3 episodi, 1954-1956)
Herbert Lytton (3 episodi, 1954-1956)
Noreen Nash (3 episodi, 1952-1955)
Jean Willes (3 episodi, 1953-1955)
Frances Rafferty (3 episodi, 1953-1954)
Jay Novello (3 episodi, 1952-1955)
Howard McNear (3 episodi, 1952-1955)
Chuck Connors (3 episodi, 1954-1955)
Edward Platt (3 episodi, 1954-1955)
Harry Bartell (3 episodi, 1953-1956)
John Hoyt (3 episodi, 1954-1956)
Frank J. Scannell (3 episodi, 1954-1956)
George Macready (3 episodi, 1952-1954)
Don Shelton (3 episodi, 1954-1956)
William Boyett (3 episodi, 1952-1955)
Leonard Bremen (3 episodi, 1953-1954)
John Alvin (3 episodi, 1953-1954)
Claire Carleton (3 episodi, 1952-1954)
Ross Elliott (3 episodi, 1954-1956)
John Dehner (3 episodi, 1954-1955)
Hugh Sanders (3 episodi, 1954-1955)
Alexander Campbell (3 episodi, 1955-1956)
Norbert Schiller (3 episodi, 1955-1956)
Nolan Leary (3 episodi, 1956)
Joan Fontaine (2 episodi, 1953-1955)
Virginia Grey (2 episodi, 1952-1954)
James Millican (2 episodi, 1953)
Beverly Washburn (2 episodi, 1954-1956)
Elisabeth Fraser (2 episodi, 1953)
Maxine Cooper (2 episodi, 1956)
Steven Geray (2 episodi, 1955)
Tristram Coffin (2 episodi, 1955-1956)
Willis Bouchey (2 episodi, 1954-1956)
Larry J. Blake (2 episodi, 1953-1954)
Ellen Corby (2 episodi, 1953-1954)
Alix Talton (2 episodi, 1953)
Harry Lauter (2 episodi, 1956)
Virginia Christine (2 episodi, 1953-1954)
Ralph Peters (2 episodi, 1954-1956)
Anthony Eustrel (2 episodi, 1954-1955)
Irene Tedrow (2 episodi, 1955-1956)
Tim Graham (2 episodi, 1955-1956)
William Swan (2 episodi, 1956)
Nick Dennis (2 episodi, 1953-1956)
Lucille Barkley (2 episodi, 1953)
Gloria Marshall (2 episodi, 1954-1956)
Jimmy Baird (2 episodi, 1955)
Frank Gerstle (2 episodi, 1953-1954)
Jack Lomas (2 episodi, 1954)
Jeanne Ferguson (2 episodi, 1956)
Tony Dante (2 episodi, 1956)
Martha Hyer (2 episodi, 1953-1954)
Angela Lansbury (2 episodi, 1954-1955)
Marguerite Chapman (2 episodi, 1954)
Vera Miles (2 episodi, 1954)
Hillary Brooke (2 episodi, 1952-1953)
Stacy Harris (2 episodi, 1953-1956)
Barbara Billingsley (2 episodi, 1953-1955)
Hal Baylor (2 episodi, 1954-1955)
Paul Picerni (2 episodi, 1954-1955)
Robert J. Wilke (2 episodi, 1954-1955)
Produzione
La serie fu prodotta da Four Star Productions e Official Films.
Registi
Tra i registi sono accreditati:
Roy Kellino in 41 episodi (1953-1956)
Robert Florey in 31 episodi (1952-1956)
Richard Kinon in 7 episodi (1956)
Robert Aldrich in 5 episodi (1953-1954)
Blake Edwards in 4 episodi (1953-1954)
Frank McDonald in 3 episodi (1954)
László Benedek in 3 episodi (1956)
William Asher in 2 episodi (1954)
William A. Seiter in 2 episodi (1955-1956)
Tay Garnett
Sceneggiatori
Tra gli sceneggiatori sono accreditati:
Gwen Bagni in 15 episodi (1952-1954)
John Bagni in 13 episodi (1952-1954)
Richard Carr in 13 episodi (1954-1956)
Frederick Brady in 9 episodi (1954-1956)
Blake Edwards in 7 episodi (1952-1954)
Seeleg Lester in 5 episodi (1953-1954)
Merwin Gerard in 4 episodi (1953)
Frederick J. Lipp in 4 episodi (1954-1955)
Larry Marcus in 3 episodi (1952-1954)
Milton Merlin in 3 episodi (1952-1953)
Marc Brandell in 3 episodi (1954-1956)
László Görög in 3 episodi (1955-1956)
James Bloodworth in 3 episodi (1956)
Amory Hare in 2 episodi (1953)
Octavus Roy Cohen in 2 episodi (1954-1955)
Milton Geiger in 2 episodi (1954-1955)
Thelma Robinson in 2 episodi (1954)
Oscar Millard in 2 episodi (1955-1956)
Willard Wiener in 2 episodi (1955)
Robert Eggenweiler in 2 episodi (1956)
Ida Lupino in 2 episodi (1956)
Roland Winters in 2 episodi (1956)
Distribuzione
La serie fu trasmessa negli Stati Uniti dal 25 settembre 1952 al 26 luglio 1956 sulla rete televisiva CBS. È stata distribuita anche in Finlandia con il titolo Aitiopaikka e nel Regno Unito con il titolo Four Star Theatre. La serie è conosciuta anche con il titolo Star Performance in una successiva riedizione.
Episodi
Note
Altri progetti
Collegamenti esterni
Scheda su Four Star Playhouse di TVRage
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 764
|
Мужун Хуан (, 297—348), взрослое имя Юаньчжэнь (元真) — сяньбийский вождь, основатель государства Ранняя Янь. Когда его сын провозгласил себя императором, то он посмертно тоже возвёл отца в императорское достоинство, провозгласив его императором с храмовым именем Тай-цзу (太祖) и посмертным именем Вэньминь-ди (文明帝).
Биография
Отец Мужун Хуана — Мужун Хуэй — изначально воевал против основателя империи Цзинь Сыма Яня, однако в 289 году признал себя цзиньским вассалом. Затем Мужун Хуэй женился на одной из дочерей Дуаньского правителя, и плодом этого союза и стал Мужун Хуан. В это время северные цзиньские земли постоянно страдали от крестьянских восстаний и вторжений северных варваров, и многие люди бежали от бедствий на остававшийся спокойным Ляодунский полуостров, что значительно усилило Мужун Хуэя. После того, как северные бывшие цзиньские земли оказались под властью хуннского государства Северная Хань и цзеского государства Поздняя Чжао, Мужун Хуэй, остававшийся лояльным к империи Цзинь, получил от цзиньских властей титул «Ляодунского гуна» (遼東公).
Мужун Хуэй доверял Мужун Хуану ответственные военные задачи — в частности, войны против Юйвэнь. В 322 году Мужун Хуэй официально сделал Мужун Хуана своим наследником, и вскоре после этого тот получил от цзиньских властей титул «Чаосянского гуна» (朝鲜公) и звание «Полководец — умиротворитель Севера» (平北将军). В 333 году Мужун Хуэй скончался, и Мужун Хуан объявил себя «Ляодунским удельным гуном» (辽东郡公). После этого началась его борьба за власть с братьями: Мужун Хань бежал в Дуань и стал там генералом, а Мужун Жэнь захватил ряд городов в восточной части сяньбийских земель и тоже провозгласил себя Ляодунским гуном. В 334 году Мужун Хань вторгся с дуаньским контингентом и нанёс поражение войскам Мужун Хуана, однако затем вернулся обратно. В начале 336 года Мужун Хуан, совершив неожиданную атаку по льду замёрзшего Бохайского залива, захватил Мужун Жэня врасплох, и вынудил его совершить самоубийство.
В 337 году Мужун Хуан провозгласил себя «Яньским князем» (燕王) — это считают началом государства Ранняя Янь. В том же году он, нарушив принцип отца «не иметь контактов с врагами Цзинь», отправил посольство в Позднее Чжао, признавая себя его вассалом и предлагая союз против Дуань. Чжаоский правитель Ши Ху согласился, и нападение состоялось в 338 году. Яньские силы нанесли первый удар, разгромили дуаньцев, разграбили города севернее дуаньской столицы, и ушли. Когда прибыли чжаоские войска, то дуаньский правитель, у которого не осталось войск, предпочёл бежать. Ши Ху был рад одержанной победе, но рассердился на то, что Мужун Хуан не стал соединяться с ним, и чжаоская армия повернула против Янь. Мужун Хуан сначала тоже хотел бежать, однако потом по совету своих генералов решил остаться и оборонять столицу Цзичэн, и после 20-дневной осады чжаоской армии пришлось отступить. Яньские силы преследовали отступающую чжаоскую армию, в результате чего та понесла серьёзные потери, и вновь взяли под контроль восставшие было города, включая бывшие дуаньские земли. Одержав победу над Поздней Чжао, Мужун Хуан отправил послов к цзиньскому императору Чэн-ди с просьбой о княжеском титуле, поясняя, что тот ему необходим чтобы упрочнить свою власть, но что он по-прежнему лоялен империи Цзинь. После некоторых споров, от империи Цзинь в 341 году ему был официально дарован титул «Яньского князя». В том же 341 году столица Ранней Янь была перенесена из Цзичэна в новопостроенный Лунчэн.
В 344 году Мужун Хуан разгромил юйвэней, вынудил их вождя бежать, а само племя насильно переселил южнее и заставил смешаться с собственным населением. В 345 году Мужун Хуан прекратил использовать летоисчисление империи Цзинь — этот шаг был равносилен формальному провозглашению независимости.
В 348 году Мужун Хуан заболел и умер. Ему наследовал сын Мужун Цзюнь.
Примечания
Ссылки
Официальная биография Мужун Хуана в «Книге Цзинь» (китайский язык)
Официальные биографии правителей Ранней Янь в «Вёсны и Осени Шестнадцати государств» (китайский язык)
Императоры Ранней Янь
Правители Азии IV века
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 9,299
|
Malana may refer to
Basti Malana - a town in Punjab, Pakistan
Malana, Himachal Pradesh - an ancient village in India
Malana, Khyber Pakhtunkhwa - a town in NWFP, Pakistan
Parachinar Malana - a town in Kurram Agency, Pakistan
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,666
|
extern "C" {
// If this header file is included as part of a generated recognizer that
// is being compiled as if it were C++, and this is Windows, then the const elements
// of the structure cause the C++ compiler to (rightly) point out that
// there can be no instantiation of the structure because it needs a constructor
// that can initialize the data, however these structures are not
// useful for C++ as they are pre-generated and static in the recognizer.
// So, we turn off those warnings, which are only at /W4 anyway.
//
#ifdef ANTLR3_WINDOWS
#pragma warning (push)
#pragma warning (disable : 4510)
#pragma warning (disable : 4512)
#pragma warning (disable : 4610)
#endif
#endif
typedef struct ANTLR3_CYCLIC_DFA_struct
{
/// Decision number that a particular static structure
/// represents.
///
const ANTLR3_INT32 decisionNumber;
/// What this decision represents
///
const pANTLR3_UCHAR description;
ANTLR3_INT32 (*specialStateTransition) (void * ctx, pANTLR3_BASE_RECOGNIZER recognizer, pANTLR3_INT_STREAM is, struct ANTLR3_CYCLIC_DFA_struct * dfa, ANTLR3_INT32 s);
ANTLR3_INT32 (*specialTransition) (void * ctx, pANTLR3_BASE_RECOGNIZER recognizer, pANTLR3_INT_STREAM is, struct ANTLR3_CYCLIC_DFA_struct * dfa, ANTLR3_INT32 s);
ANTLR3_INT32 (*predict) (void * ctx, pANTLR3_BASE_RECOGNIZER recognizer, pANTLR3_INT_STREAM is, struct ANTLR3_CYCLIC_DFA_struct * dfa);
const ANTLR3_INT32 * const eot;
const ANTLR3_INT32 * const eof;
const ANTLR3_INT32 * const min;
const ANTLR3_INT32 * const max;
const ANTLR3_INT32 * const accept;
const ANTLR3_INT32 * const special;
const ANTLR3_INT32 * const * const transition;
}
ANTLR3_CYCLIC_DFA;
typedef ANTLR3_INT32 (*CDFA_SPECIAL_FUNC) (void * , pANTLR3_BASE_RECOGNIZER , pANTLR3_INT_STREAM , struct ANTLR3_CYCLIC_DFA_struct * , ANTLR3_INT32);
#ifdef __cplusplus
}
#ifdef ANTLR3_WINDOWS
#pragma warning (pop)
#endif
#endif
#endif
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,443
|
Erik Cuba Chooses to Stay in Olney After Graduation
Ronni Walker
Publisher@olneyenterprise.com
Megargel resident and recent Olney High School graduate, Erik Cuba, said he has always known he wants to build a life in a small community. "It is not my world view or my political ideologies or my religious beliefs for wanting to stay in this community," Cuba said. "Toward the end of high school, many of my friends said they wanted to be someplace other than this small town. I never got that feeling. I love to travel. I've been to [Washington] D.C. multiple times, and I've toured Europe with my church group. At the end of those trips I always say the world is cool, but there's no place like home."
Cuba reminisced about growing up in a small town. "One of my favorite childhood memories is riding the school bus home on Fridays after the pep rally. Our bus driver, Mr. Bob, would give a Dr Pepper to every kid. I would tell him bye and run to grandpa's truck to spend the night. It is something I always looked forward to doing on the weekends. These are the memories that tie me to this community," Cuba said.
Cuba graduated from OHS last year with 32 college hours and was able to enroll as a sophomore at Midwestern State University (MSU) in Wichita Falls. He plans to graduate in May 2021 and hopes to join Olney High School Faculty in the Fall of 2021.
The math major says although his initial plan was to become a doctor, he has always gravitated toward teaching—a role he took on at an early age when tutoring his friends in math. Cuba's mother, Kim Cuba—a fifth-grade science teacher at Olney Elementary—did not persuade him to become a teacher but was still influential.
"One thing that cemented why I wanted to be a teacher was looking back at all of those plays, all of those band performances, all of the games, track meets and the different events that I have been part of in high school; One of the things that were prominent to me was the after moments. After the play was over or after I cut off the band and turned around to the audience to give a bow, my mom was always there. My family was always there. Being able to turn around to see the people that love you was there to support you, I can't trade that for anything." Cuba said.
Cuba mentioned the top four teachers who were his biggest inspirations. "Tom Lundy made me fall in love with math. Carol Wainscott developed my love for math in junior high school by pushing me to learn more. She saw my ability and molded it. In high school, Peter Allen was an excellent teacher. He was good at taking something that people didn't understand and putting it into terms they could understand. He gave me that aspect that helps me with the way I tutor my students. Dickey Scott is the person who ingrained the teaching bug into my mind before I knew it was there. He is one of the best math teachers and one of smartest people I know," Cuba said.
A few of Cuba's extra-curricular activities during high school include playing the lead in the One Act Play, playing the baritone, trumpet eventually leading to his role as drum major in high school and placing third on his debate team. It is easy to see how he manages his busy life now based on his ability to do well academically while juggling electives throughout middle and high school. In addition to his full-time student status at MSU, Cuba works three days at the Refuge as an after-school tutor and intern. He still has his job at Stewart's Food Store for the past three years.
Cuba made an interesting comparison of his job at Stewart's to social media. "I consider my job at Stewart's as my Facebook because I don't really [engage] on Facebook and don't find a need for it. Our small town is our social media hub. If you are active in the town, you get to know a lot of people the same way you do if you are active on social media. The difference is it's personal. I get a status update every time someone comes into the store," Cuba said. "I can't leave a community of people who have supported me while growing up."
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,025
|
package com.sksamuel.elastic4s.requests.searches.aggs.responses.bucket
import com.sksamuel.elastic4s.requests.searches.aggs.responses.{AggBucket, AggSerde, BucketAggregation}
case class GeoHashGrid(name: String, buckets: Seq[GeoHashGridBucket]) extends BucketAggregation
case class GeoHashGridBucket(key: String, override val docCount: Long, private[elastic4s] val data: Map[String, Any])
extends AggBucket
object GeoHashGrid {
implicit object GeoHashGridAggSerde extends AggSerde[GeoHashGrid] {
override def read(name: String, data: Map[String, Any]): GeoHashGrid = apply(name, data)
}
def apply(name: String, data: Map[String, Any]): GeoHashGrid = GeoHashGrid(
name,
data("buckets").asInstanceOf[Seq[Map[String, Any]]].map { map =>
GeoHashGridBucket(
map("key").toString,
map("doc_count").toString.toLong,
map
)
}
)
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,181
|
Telmo Irureta (Zumaya, 8 de enero de 1989) es un actor y humorista español.
Biografía
Con parálisis cerebral desde los dos años, es magíster en Pedagogía y estudia Psicología. Estuvo tres años en el taller de Artes Escénicas de Donostia. Es protagonista de cortometrajes, monólogos y obras de teatro.
En 2021 fue el protagonista de La consagración de la primavera de Fernando Franco García; la película se presentó en la sección oficial del Festival de Cine de Donostia 2022. En el teatro Sexberdina escribió la obra junto a Kepa Errasti. En 2023 ganó un Premio Goya en la categoría de Mejor Actor Revelación.
Vida personal
Es sobrino de la también actriz Elena Irureta.
Salió públicamente del armario como persona homosexual tras una polémica generada en redes sociales donde se le acusaba de promover la prostitución femenina por su discurso durante la entrega de Premios Goya de 2023, donde defendió la vida sexual de las personas discapacitadas.
Teatro
Sexberdinak, escrito junto a Kepa Errasti.
Filmografía
Robarte una noche (2018), cortometraje de Fernando Vera Moreno.
La consagración de la primavera (2022) de Fernando Franco.
Premios
Premios Goya
Referencias
Enlaces externos
Irureta: "Me alegro de que se hable de sexo y discapacidad" en RNE
Ganadores del Premio Goya al mejor actor revelación
Discapacitados de España
Actores de Guipúzcoa
Nacidos en Zumaya
Actores con discapacidad
Personas homosexuales de España
Actores LGBT de España
Actores gais
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,862
|
Q: Bootstrap: Reducing NavBar width and all its drop down option panels and text size I am using Bootstrap css for Nav Bar and it comes up very fine.
But the width appears to be big and I want to reduce it ( also ensure that it gets equally reduced/adjusted in other viewports also) and also reduce the options panels/text size that comes under the Nav Bar dropdown.
I'm using the following css class
navbar navbar-default navbar-fixed-top navbar-inverse
and the Nav Bar is coming in black ( which is giving the wow effect) and something that is needed but all the options under dropdown is coming as white. How to make this white background to black? Any bootstrap class already in place?
If navbar-inverse can make the top nav bar as black then there must be some class to provide the same effect for the dropdown panel options under the same Nav Bar
I want to avoid custom css at this point to achieve this.
Thanks,
Faraz
A: there is no way to change anything unless you want to create a custom css file, or edit the bootstrap css files.
If you are looking for something very simple, i have found this fantastic
http://pikock.github.io/bootstrap-magic/app/index.html#!/editor
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,600
|
Category Archives: Heatstroke
Better Laws, Child Abuse, Death, Good Parenting, Heatstroke, Physical Abuse
KS Steps Up For Children In Hot Vehicles
Image June 28, 2018 Blackhorn33
Amber Rollins, director of KidsAndCars.org, demonstrates how to safely break a window using a device, the Resqme emergency window breaker and seat belt cutter.
Kansas removes lawsuit fear for rescuers of
children, pets trapped in hot cars
Beginning Sunday, good Samaritans in Kansas won't have to think about getting sued for busting out the window of a hot car to save a child or pet trapped inside.
A new state law underscores that lives are more important than property when it comes to hot cars. Kansas joins 18 states — including Missouri — in giving rescuers legal immunity when they believe a person or a pet is in imminent danger. Two additional states have laws protecting pets only.
Amber Rollins, director of the non-profit Kids and Cars, on Monday demonstrated how a simple device can in seconds shatter the window of a locked vehicle, making rescue possible. Rollins used a disabled SUV at the 129 Auto Parts salvage lot in Spring Hill, Kansas.
A hand-held, spring-loaded device called "resqme" was the only tool she needed. It must be used on a side window because windshields and rear windows are made to not shatter. The device, which shoots a metal pin at the glass, should be applied to a corner of a side window. Applying it to the center of the window will not work.
The tool "resqme" can be ordered from kidsandcars.org for $7.50.
Regular nail punches available at hardware stores can also be used. In fact, Johnson County MedAct units each carry nail punches. A crowbar or stone or any other implement also can be used.
Some things to consider when busting out a window:
First check to see if the vehicle is locked. Obviously, if it is not the window does not need to be broken.
Use appropriate force against a side window furthest away from the child or animal inside as the glass can fly.
Get the victim to a cool place, remove clothing and apply water.
Stay until emergency responders arrive.
In addition to Kids and Cars, the Kansas law was championed by Safe Kids Kansas and the Humane Society Legislative Fund of Kansas.
Although Kids and Cars is not aware of any case in which a rescuer was later sued for causing property damage to a vehicle, Rollins pointed to a New Mexico hot-car death in which two witnesses told police they saw the victim in distress but did not act.
Rollins keeps two resqmes handy. One is attached to the driver's seat belt of her car so it will be immediately available to use in escaping if the vehicle becomes submerged in water. The resqme also has a blade to cut the seat belt if necessary.
Rollins keeps her other resqme on her key ring in case she notices a vulnerable child or pet in a hot car.
"A child's body heats up three to five times faster than an adult," said Cherie Sage, state coordinator for Safe Kids Kansas. "Their developing bodies are not as efficient at regulating their temperature. When a child's internal temperature reaches 104 degrees major organs begin to shut down. And when that child's temperature reaches 107 degrees that child can die."
During Monday's demonstration, the outside temperature was in the low 80s but the temperature inside the SUV was over 100 degrees. The air inside a vehicle can jump that much in a matter of minutes, even if the windows are partially open, because the windshield has a greenhouse effect.
There have been 18 child deaths in hot cars in the United States so far this year, about par with the average of 37 a year. But there are three other suspected cases this year awaiting autopsy results.
In most cases the parent did not know or simply forgot that their child was in the back seat.
Kids and Cars suggests that parents make a habit of putting their smart phones in the back seat so they will have to go there to retrieve them. Another idea is to keep a stuffed animal in the car seat and move it to the front seat when a child is strapped in to serve as a visible reminder for the parent.
#HotVehiclesChildrenDangerous EnvironmentGood ParentingHeat StrokeValues
Child Abuse, Death, Good Parenting, Heatstroke, Physical Abuse, StopChildAbuse
Hot Vehicle Claims First Child In 2018
Image March 24, 2018 Blackhorn33
#HotVehicles Are Not #BabySitters
Family Of 1-Year-Old Who Died In Hot Car Had No DCF History
MIAMI, FL – The Department of Children and Families says the family of a 1-year-old who died after being left in a hot car had no history with the child welfare system.
The department has opened a child protective investigation but says all details remain confidential.
DCF Secretary Mike Carroll did release a statement saying,
"My heart goes out to this family who have lost a precious child. It is easy to assume this could never happen to you, but time and time again I see caregivers who let themselves slip into a routine when transporting children and make a fatal mistake when that routine is disrupted. More than half of all child deaths from hot cars are the result of a parent inadvertently leaving the child in their car.."
The case prompted strong words from Miami-Dade Police spokesman, Detective Alvaro Zabaleta.
He told CBS4's Peter D'Oench, "This is something that we, in society, cannot allow to continue to happen. The precious cargo in your car is a child and there is no way that we as parents can forget the precious child in your car. This is happening way too often."
"No matter how hectic our schedule is, no matter how fast paced our lives are, we can not allow our kids to be put in danger," said Zabaleta. "We just need to learn how to slow down and concentrate on what we are doing."
The 1-year-old boy was apparently forgotten in the car Wednesday at a strip mall near Bird Road and 97th Avenue.
The baby's mother works at a beauty salon in the mall, according to witnesses. They said she was not supposed to work on Wednesday but came in on her day off.
She reportedly came to work at the Forever Young Spa around 9 a.m., parked the car in the back and, at about 12:30 p.m., they heard loud screams and commotion when she found her child.
The baby was a transported to Kendall Medical Center where he was pronounced dead.
It was a hot day Wednesday with temperatures in the mid-80s. Temperatures inside the car could've reached up to 100°.
Witnesses said the mother was devastated and screaming. She said something along the lines of because of work – this happened.
At this time, it is unclear if there will be any charges related to this incident. Zabaleta said the case is being referred to the Miami-Dade State Attorney's office. Witnesses said police have recovered surveillance tape from the scene but it is not being released.
A friend of the family said that family members were too upset to say anything right now.
At the salon, customers said they were upset after hearing the news.
"I can't imagine anything like this happening," said Cathy O'Sullivan, who also has children.
Another customer, Shanin Alvarez, said, "This is such a sad story to hear this. I don't know what happened, if she was distracted or if she is a first-time mother."
Customer Lidia Gutierrez said, "It is horrible. It is just so sad." Her friend and another customer, Iala Isarque, said, "I just really have no words to say."
Following the incident, Carroll did ask parents to find a safety strategy that works for them, suggesting the following:
Be sure to check the back seat every time you leave the vehicle.
Put your purse, briefcase, lunch, etc. in the backseat so you are sure to look before you lock the door.
Do not let your children play near vehicles; they may accidentally lock themselves in.
If there is a change in plans and someone else is dropping your kids off, have them call you at drop off so you know everyone made it safely.
For more information on tips to hot car preventions, click here.
On average, 37 children die from heat-related deaths after being trapped inside vehicles. Even the best of parents or caregivers can unknowingly leave a sleeping baby in a car; and the end result can be injury or even death.
KIDSANDCARS.org
Child AbuseDeathGood ParentingHeat StrokePhysical AbuseValues
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,937
|
# Copyright 2016 The Johns Hopkins University Applied Physics Laboratory
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import six
from abc import ABCMeta
from six.moves import configparser
from intern.service.mesh.service import MeshService, VoxelUnits
import os
CONFIG_FILE ='~/.intern/intern.cfg'
@six.add_metaclass(ABCMeta)
class Remote(object):
"""Base class for communicating with remote data stores.
Attributes:
_volume (intern.service.Service): Class that communicates with the volume service.
_metadata (intern.service.Service): Class that communicates with the metadata service.
_project (intern.service.Service): Class that communicates with the project service.
_object (intern.service.Service): Class that communicates with the object service.
"""
def __init__(self, cfg_file_or_dict=None):
"""Constructor.
Loads credentials in order from user provided dictionary > user provided file > default file > environment vars
Args:
cfg_file_or_dict (optional[str|dict]): Path to config file in INI format or a dict of config parameters.
"""
# Service Objects
self._volume = None
self._metadata = None
self._project = None
self._object = None
self._mesh = None
# Configuration data loaded from file or passed directly to the constructor
# Is available for children Remote classes to use as needed
self._config = None
# Tokens for Services
self._token_project = None
self._token_metadata = None
self._token_volume = None
self._token_object = None
if cfg_file_or_dict is None:
# Default to the config file in the user directory if no config file was provided
cfg_file_or_dict = os.path.expanduser(CONFIG_FILE)
if isinstance(cfg_file_or_dict, dict):
# A config dictionary was provided directly. Keep things consistent by creating an INI string.
cfg_str = "[Default]\n"
for key in cfg_file_or_dict:
cfg_str = "{}{} = {}\n".format(cfg_str, key, cfg_file_or_dict[key])
self._config = self.load_config_file(six.StringIO(cfg_str))
else:
# A file path was provided by the user
if os.path.isfile(os.path.expanduser(cfg_file_or_dict)):
with open(os.path.expanduser(cfg_file_or_dict), 'r') as cfg_file_handle:
self._config = self.load_config_file(cfg_file_handle)
else:
# Provided file or default file do not exist. Try loading from env variables
if "INTERN_PROTOCOL" in os.environ and "INTERN_HOST" in os.environ and "INTERN_TOKEN" in os.environ:
cfg_str = "[Default]\n"
cfg_str = "{}{} = {}\n".format(cfg_str, "protocol", os.environ['INTERN_PROTOCOL'])
cfg_str = "{}{} = {}\n".format(cfg_str, "host", os.environ['INTERN_HOST'])
cfg_str = "{}{} = {}\n".format(cfg_str, "token", os.environ['INTERN_TOKEN'])
self._config = self.load_config_file(six.StringIO(cfg_str))
else:
raise IOError("Configuration file not found: {}. Please provide credential file or set environment variables".format(cfg_file_or_dict))
self._init_mesh_service()
def load_config_file(self, config_handle):
"""Load config data for the Remote.
Args:
config_handle (io.StringIO): Config data encoded in a string.
Returns:
(configparser.ConfigParser)
"""
cfg_parser = configparser.ConfigParser()
cfg_parser.read_file(config_handle)
return cfg_parser
def _init_mesh_service(self):
"""
Method to initialize the Mesh Service
Args:
None
Returns:
None
Raises:
(KeyError): if given invalid version.
"""
self._mesh = MeshService()
@property
def volume_service(self):
return self._volume
@property
def project_service(self):
return self._project
@property
def metadata_service(self):
return self._metadata
@property
def object_service(self):
return self._object
@property
def mesh_service(self):
return self._mesh
def list_project(self, **kwargs):
"""Perform list operation on the project.
What this does is highly dependent on project's data model.
Args:
(**kwargs): Args are implementation dependent.
Returns:
(list)
"""
return self._project.list(**kwargs)
def get_cutout(self, resource, resolution, x_range, y_range, z_range, time_range=None, id_list=[], parallel: bool= True, **kwargs):
"""Get a cutout from the volume service.
Args:
resource (intern.resource.Resource): Resource compatible with cutout operations.
resolution (int): 0 indicates native resolution.
x_range (list[int]): x range such as [10, 20] which means x>=10 and x<20.
y_range (list[int]): y range such as [10, 20] which means y>=10 and y<20.
z_range (list[int]): z range such as [10, 20] which means z>=10 and z<20.
time_range (optional [list[int]]): time range such as [30, 40] which means t>=30 and t<40.
id_list (optional [list]): list of object ids to filter the cutout by.
parallel (bool: True): Whether downloads should be parallelized using multiprocessing
Returns:
(): Return type depends on volume service's implementation.
Raises:
RuntimeError when given invalid resource.
Other exceptions may be raised depending on the volume service's implementation.
"""
if not resource.valid_volume():
raise RuntimeError('Resource incompatible with the volume service.')
return self._volume.get_cutout(
resource, resolution,
x_range, y_range, z_range, time_range,
id_list, parallel = parallel, **kwargs
)
def create_cutout(self, resource, resolution, x_range, y_range, z_range, data, time_range=None):
"""Upload a cutout to the volume service.
Args:
resource (intern.resource.Resource): Resource compatible with cutout operations.
resolution (int): 0 indicates native resolution.
x_range (list[int]): x range such as [10, 20] which means x>=10 and x<20.
y_range (list[int]): y range such as [10, 20] which means y>=10 and y<20.
z_range (list[int]): z range such as [10, 20] which means z>=10 and z<20.
data (object): Type depends on implementation.
time_range (optional [list[int]]): time range such as [30, 40] which means t>=30 and t<40.
Returns:
(): Return type depends on volume service's implementation.
Raises:
RuntimeError when given invalid resource.
Other exceptions may be raised depending on the volume service's implementation.
"""
if not resource.valid_volume():
raise RuntimeError('Resource incompatible with the volume service.')
return self._volume.create_cutout(
resource, resolution, x_range, y_range, z_range, data, time_range)
def reserve_ids(self, resource, num_ids):
"""Reserve a block of unique, sequential ids for annotations.
Args:
resource (intern.resource.Resource): Resource compatible with annotation operations.
num_ids (int): Number of ids to reserve.
Returns:
(int): First id reserved.
"""
if not resource.valid_volume():
raise RuntimeError('Resource incompatible with the volume service.')
return self._volume.reserve_ids(resource, num_ids)
def get_extents(self, resource):
"""Get extents of data volume
Args:
resource (intern.resource.Resource): Data platform resource.
Returns:
extents (array): [[x-min, max-x], [y-min, max-y], [z-min, max-z]]
"""
return self._metadata.get_extents(resource)
def get_bounding_box(self, resource, resolution, id, bb_type='loose'):
"""Get bounding box containing object specified by id.
Currently only supports 'loose' bounding boxes. The bounding box
returned is cuboid aligned.
Args:
resource (intern.resource.Resource): Resource compatible with annotation operations.
resolution (int): 0 indicates native resolution.
id (int): Id of object of interest.
bb_type (optional[string]): Defaults to 'loose'.
Returns:
(dict): {'x_range': [0, 10], 'y_range': [0, 10], 'z_range': [0, 10], 't_range': [0, 10]}
"""
if not resource.valid_volume():
raise RuntimeError('Resource incompatible with the volume service.')
if bb_type != 'loose' and bb_type != 'tight':
raise RuntimeError("bb_type must be either 'loose' or 'tight'.")
return self._volume.get_bounding_box(resource, resolution, id, bb_type)
def get_ids_in_region(
self, resource, resolution,
x_range, y_range, z_range, time_range=[0, 1]):
"""Get all ids in the region defined by x_range, y_range, z_range.
Args:
resource (intern.resource.Resource): Resource compatible with annotation operations.
resolution (int): 0 indicates native resolution.
x_range (list[int]): x range such as [10, 20] which means x>=10 and x<20.
y_range (list[int]): y range such as [10, 20] which means y>=10 and y<20.
z_range (list[int]): z range such as [10, 20] which means z>=10 and z<20.
time_range (optional [list[int]]): time range such as [30, 40] which means t>=30 and t<40. Defaults to [0, 1].
Returns:
(list[int]): Example: [1, 2, 25].
Raises:
requests.HTTPError
TypeError: if resource is not an annotation channel.
"""
return self._volume.get_ids_in_region(
resource, resolution, x_range, y_range, z_range, time_range)
def mesh(self, resource, resolution,
x_range, y_range, z_range, time_range=None,
id_list=[], voxel_unit=VoxelUnits.nm,
voxel_size=[4,4,40], simp_fact = 0, max_simplification_error=60,
normals=False, **kwargs):
"""Generate a mesh of the specified IDs
Args:
resource (intern.resource.Resource): Resource compatible with cutout operations.
resolution (int): 0 indicates native resolution.
x_range (list[int]): x range such as [10, 20] which means x>=10 and x<20.
y_range (list[int]): y range such as [10, 20] which means y>=10 and y<20.
z_range (list[int]): z range such as [10, 20] which means z>=10 and z<20.
time_range (optional [list[int]]): time range such as [30, 40] which means t>=30 and t<40.
time_range (optional [list[int]]): time range such as [30, 40] which means t>=30 and t<40.
id_list (optional [list]): list of object ids to filter the volume by.
voxel_unit (optional VoxelUnit): voxel unit of measurement to derive conversion factor.
voxel_size (optional [list]): list in form [x,y,z] of voxel size. Defaults to 4x4x40nm
simp_fact (optional int): mesh simplification factor, reduces triangles by given factor
max_simplification_error (optional int): Max tolerable error in physical distance
normals (optional bool): if true will calculate normals
Returns:
mesh (intern.service.mesh.Mesh): mesh class
Raises:
RuntimeError when given invalid resource.
Other exceptions may be raised depending on the volume service's implementation.
"""
if not resource.valid_volume():
raise RuntimeError('Resource incompatible with the volume service.')
volume = self._volume.get_cutout(
resource, resolution, x_range, y_range, z_range, time_range, id_list, **kwargs)
mesh = self._mesh.create(
volume, x_range, y_range, z_range, time_range, id_list, voxel_unit, voxel_size,
simp_fact, max_simplification_error, normals)
return mesh
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,384
|
Marked for Life (Digital Audiobook)
By Emelie Schepp
MP3 CD (6/14/2016)
When a high-ranking head of the migration board is found shot to death in his living room, there is no shortage of suspects, including his wife. But no one expects to find mysterious, child-size fingerprints in this childless home.
Public prosecutor Jana Berzelius steps in to lead the investigation. Young and brilliant but emotionally cold, Berzelius, like her famous prosecutor father, won't be swayed by the hysterical widow or intimidated by the threatening letters the victim had tried to hide. She is steely, aloof, impenetrable. That is, until the boy…
A few days later on a nearby deserted shoreline, the body of a derelict preteen is discovered, and with him, the murder weapon that killed the official. Berzelius finds herself drawn more deeply into the case when, as she attends the boy's autopsy, she recognizes something familiar on his small, scarred, drug-riddled body. Cut deep into his flesh are initials that scream child trafficking and trigger in her a flash of memory from her own dark childhood. Her connection to this boy has been carved with deliberation and malice that penetrate to her very core.
Now, to protect her own horrific but hidden past, she must find the real suspect behind these murders before the police do.
International bestselling author Emelie Schepp introduces us to the enigmatic, unforgettable Jana Berzelius in this first novel of a suspenseful, chilling trilogy.
Emelie Schepp is an international bestselling Nordic crime author. She lives with her husband and two children in Sweden.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,614
|
Die Raiffeisenbank Landshuter Land eG ist eine Genossenschaftsbank mit Sitz in Ergolding (Bayern).
Geschichte
Die Raiffeisenbank Landshuter Land eG entstand im Jahr 2022 aus der Fusion der Raiffeisenbank Pfeffenhausen-Rottenburg-Wildenberg eG, der Raiffeisenbank Essenbach eG und der Raiffeisenbank Altdorf-Ergolding eG.
Verbundpartner
Die Bank ist Teil der Genossenschaftlichen Finanzgruppe Volksbanken Raiffeisenbanken. Sie vertreibt daher z. B. Bausparverträge der Bausparkasse Schwäbisch Hall, Investmentfonds von Union Investment und vermittelt Versicherungen der R+V Versicherung. Die Funktion der Zentralbank nimmt die DZ Bank wahr.
Gesellschaftliches Engagement
Die Bank fördert kulturelle, sportliche und soziale Organisationen und Veranstaltungen, sowie Schulen und Kindergärten im Geschäftsgebiet. Im Jahr 2021 belief sich das Spendenvolumen auf insgesamt ca. 133.000 Euro.
Weblinks
Webseite der Raiffeisenbank Landshuter Land eG
Einzelnachweise
LandshuterLand
Unternehmen (Landkreis Landshut)
Pfeffenhausen
Rottenburg an der Laaber
Wildenberg
Gegründet 1911
Friedrich Wilhelm Raiffeisen als Namensgeber
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,912
|
This Heckler and Koch UMP. 45 non-firing prop was screen used in the Summit Entertainment film John Wick: Chapter 2. Starring Keanu Reeves, directed by Chad Stahelski. Released by Lions Gate. This is a non-firing prop, with an all metal mock suppressor. This prop was signed out for multiple days and multiple locations. The Letter of Authenticity comes from the production company and is double signed by the assistant director and the production designer. This prop is guaranteed for life. An autographed production photo of Keanu Reeves is included with this sale. All documents and photos are embossed notarized for authenticity to guarantee originality. We are not memorabilia retailers. We provide prop weapons and clothing to the film industry in LA and ATL. We only sell used items to finance new gear. The item "JOHN WICK 2 Screen Used prop gun H&K UMP 45 w LOA Lifetime Guarantee" is in sale since Friday, December 15, 2017. This item is in the category "Entertainment Memorabilia\Movie Memorabilia\Props\Originals". The seller is "cha_ligh" and is located in Saint Augustine, Florida. This item can be shipped to United States.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,974
|
function readAcousticSensorData(readFolderPath,saveFolderPath,delay)
% readAcousticSensorData(readFolderPath,saveFolderPath)
% readAcousticSensorData(readFolderPath,saveFolderPath,delay)
% readAcousticSensorData(readFolderPath)
%
% Brian Goodwin, 2015-03-04
%
% 2016-07-12 -- v2
%
% File is saved under the name "acousticEmissionSensorData.mat"
%
% Make sure that the end of each path contains a '\' or '/' (depending on
% your system).
%
% This function also creates a "README_AEdata.txt" file indicating where
% the acoustic sensor data came from.
%
% "delay" variable is the set amount that aet needs to be added to "aet".
% The "delay" variable should have units of [ms] (milliseconds).
fid = dir(fullfile(readFolderPath,'*CH*.isf'));
fid = {fid.name};
nchan = length(fid);
ae = cell(1,nchan);
for k = 1:nchan
[out,~] = isfread3(fullfile(readFolderPath,fid{k}));
ae{k} = out.y;
end
if nargin<3
aet = out.x;
else
aet = out.x+delay/1e3;
end
if nargin>1 && ~isempty(saveFolderPath)
save(fullfile(saveFolderPath,'acousticEmissionSensorData.mat'),'ae','aet')
fid = fopen(fullfile(saveFolderPath,'README_AEdata.txt'),'w');
else
save(fullfile(readFolderPath,'acousticEmissionSensorData.mat'),'ae','aet')
fid = fopen(fullfile(readFolderPath,'README_AEdata.txt'),'w');
end
fprintf(fid,'The file named "acousticEmissionSensorData.mat" \ncame from data that is located in the folder:\n\n%s\n\nData is in raw form (unfiltered).\n\nVariables are "ae" and "aet" for the acoustic\nemission and time, respectively.',readFolderPath);
fclose(fid);
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,465
|
Q: Initializing a DatagramSocket in Java I'm going to create a simple server processing some UDP datagrams. My code is as follows:
public class UDPServer implements Runnable{
private static final Logger logger = Logger.getLogger("UDPServer");
private DatagramSocket datagramSocket = null;
private int port;
public UDPServer(int portNumber) {
this.port = portNumber;
try {
this.datagramSocket = new DatagramSocket(port, InetAddress.getLocalHost());
} catch (UnknownHostException ex) {
logger.info("Server creating failed 1...");
} catch (SocketException e) {
logger.info("Server creating failed 2...");
}
logger.info("Server created...");
logger.log(Level.INFO, "Datagram socket: INETAddress: {0} Port: {1}", new Object[]{datagramSocket.getInetAddress(), datagramSocket.getPort()});
}
private void runServer() {
logger.info("Starting the server...");
try {
while (true) {
byte[] buffer = new byte[64];
DatagramPacket receivedPacket = new DatagramPacket(buffer, buffer.length);
logger.log(Level.INFO, "Waiting for an incoming packet on {0}", this.datagramSocket.getInetAddress());
datagramSocket.receive(receivedPacket);
logger.log(Level.INFO, "Received packet from: {0}", receivedPacket.getSocketAddress());
new DatagramConsumer(receivedPacket).start();
}
} catch (SocketException ex) {
// logging...
} catch (IOException ex) {
// logging
}
}
@Override
public void run() {
this.runServer();
}
}
It simply creates a server, and provides a method for retrieving and processing datagrams...
Something I do not understand is, when I'm creating the server object:
UDPServer server = null;
try {
server = new UDPServer(12395);
Thread serverThread = new Thread(server);
serverThread.start();
serverThread.join();
}
I see the output like this:
INFO: Server created...
INFO: Datagram socket: INETAddress: null Port: -1
INFO: Starting the server...
INFO: Waiting for an incoming packet on null
I'm new to networking stuff and I do not know what I'm making wrong... I was expecting that my server should listen for incoming datagrams on definied port and local address...
A: Use datagramSocket.getLocalSocketAddress() for display instead.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,344
|
{"url":"http:\/\/algassert.com\/post\/1618","text":"# [Un]popular Qubits #4: Affecting Atoms by Looking at Emitted Light\n\n26 Jun 2016\n\nIn April, \"Mapping quantum state dynamics in spontaneous emission\" by M. Naghiloo et al was published in Nature Communications. The paper didn't get much coverage, but the authors released a YouTube video about the paper, titled \"How we look at light can affect the atom that emits it\":\n\nThat sounds pretty mind-blowing, but by the end of this post you might have a different opinion.\n\n# Two Circuits\n\nMy method for understanding papers basically amounts to translating the experiments they describe into analogous quantum logic circuits, then just thinking about those circuits. So, instead of talking directly about the paper, I'm going to talk about a couple circuits.\n\nIn these circuits, we have a qubit $A$ that starts in the state $\\ket 0 + \\ket 1$. Then we keep introducing fresh work qubits in the $\\ket 0$ state, performing a small rotation controlled by $A$, and measuring the result:\n\nWe use the measurement results to infer the state of $A$.\n\nSurprisingly, this process plays out in qualitatively different ways depending on how you go about measuring.\n\nZ axis\n\nLet's start by just measuring in the computational basis, i.e. along the Z axis, as shown in the previous diagram. For flavor, we also imagine our quantum computer is setup so that any On measurement will produce an audible CLICK!.\n\nWe run the circuit. What happens?\n\nThe qubit $A$ starts in a superposition of On and Off, and that continues to be true for as long as you wait without hearing a click. But the conditional rotation creates an asymmetry between the $A$-is-Off case and the $A$-is-On case: if $A$ is Off, the conditional rotation doesn't happen. Without any rotation, the work qubit would stay Off and so the measurement result would also have to be Off. But if $A$ is On (or partially On) then, every once in awhile... CLICK! and now you know for sure that $A$ is guaranteed 100% On.\n\nIn other words, when our measurements keep happening along the Z axis, $A$ behaves like it has a half-life. We can explore this behavior in Quirk by displaying some measurement chances and conditional states:\n\nNotice how anytime a state indicator has a black \"is On\" control, the state is straight up (i.e. $\\ket 1$), whereas the only-white-control \"all Off\" cases are essentially identically to the starting state. Also notice the chance-of-On staying pretty consistent. This circuit's measurements really do imply that $A$ is behaving as if its state has a half-life.\n\nOther axis\n\nNow lets try measuring along a different axis, by rotating the qubit a bit before the computational-basis measurement. When we do that, we see very different conditional states:\n\nInstead of jumping to 'all on all the time' as soon as any measurement returns On, $A$ is only being perturbed a little bit by each outcome. (I had to make the conditional rotations a big stronger for it to be visible.)\n\nIf you analyze the behavior more closely, as I did in 'Eve's quantum clone computer', you find that the qubit is actually performing a random walk! Instead of waiting for a solitary click that tells you everything, you'll be hearing a stream of CLI-CLI-CLICK! CLI-CLICK! CLICK! ... CLICK! CLI-CLI-CLI-CLI-CLICK! where each click, or pause, tells you the direction of a small step the qubit took.\n\n# Interpretation\n\nClearly the measurement we choose to make changes the experience quite drastically. In one case we're patiently waiting for a single click that reveals all. In the other case, we're hearing a stream of clicks that together slowly build up to the full story. But what does this all mean? And is it useful?\n\nThe authors end their video with the following claim:\n\n\"This gives us a way to control the atom by the way that we look at the light.\"\n\nThat's actually not quite right.\n\nUp until now, I've been showing conditional states in the circuit diagrams. But what does the qubit's unconditional state, i.e. what we can expect before even starting the experiment, look like?\n\nWell, when measuring along the Z axis, the qubit kinda rotates slowly while decaying towards the center:\n\nAnd, when measuring along another axis, the qubit... kinda rotates slowly while decaying towards the center...:\n\nThe above diagrams show that the qubit evolves in the same way, regardless of which measurements we plan to make. This demonstrates that changing the axis doesn't give us any control. (Though that was obvious from the start, since otherwise we could easily violate the no-communication theorem.)\n\nWhat's actually happening during these experiments is that we're learning different information about the qubit as we go. Although the unconditional expected-ahead-of-time states don't depend on the measurement choices, the conditional informed-by-measurement states differ by quite a lot. We're not deciding what happens, but we are finding out what happened.\n\nSo the authors are wrong when they say we've found a way to control the atom by looking at the light differently. A corrected quote would be... \"This gives us a way to find out if the atom is in the state we want by the way that we look at the light\". Which... sounds quite a lot more mundane, doesn't it?\n\nStill, it's very interesting that the experience changes so much when measuring different axes.\n\nUltimately, I think that the phenomena described by the paper is just an interesting example of how you learn different things by measuring different things. There's no control, at least not in the literal sense of the word.\n\n(That being said, I feel uncomfortable bluntly leaving things at \"there's no control\". It has the wrong connotations, and probably some people will disagree about the shades of meaning. The thing we are doing would require control if this was a classical system. This is yet another example of entanglement riding the line between \"I can predict that!\" and \"I can control that!\" in a way that's hard to summarize.)\n\n# Summary\n\nHow you measure entangled information about a qubit qualitatively changes the feel of the inference process. Sometimes it behaves like spontaneous decay, other times like a random walk.\n\nDespite the surprisingly different behaviors, we're not actually controlling the qubit. We're just revealing things about it at different rates.\n\nPeter de Rivaz - June 28, 2016\nDoes a similar circuit represent the Quantum Zeno effect?\n\nI know you had an earlier post about Zeno but it didn't have a circuit diagram in it. My guess is that the Qbit should have a fixed initial state and then small rotations applied along the top line, but that the presence of the conditional gates may help to preserve the Qbit in its original state?\nCraig Gidney - June 28, 2016\nYes, it's a similar circuit. The main difference is that, in the Zeno effect, the small rotation is applied *to* the qubit-of-interest. Here the qubit-of-interest is controlling the small rotation. Also the Zeno effect involves constantly directly measuring the qubit-of-interest, whereas here we're only measuring related information.\n\nHere's a mock Zeno circuit (normally eight X^(1\/8) gates would do a full NOT, but due to the intermediate CNOTs the qubit stays mostly off; the effect gets stronger with smaller rotations)\nPeter de Rivaz - June 28, 2016\nAh, that's brilliant! I'd tried a similar circuit, but I had the control gates upside down (which fails to have any effect at all).\n(By the way, the link is a bit hard to copy\/paste from the comment box - I had to use developer tools to get access to the full string)\nMahdi - July 05, 2016\nWe\u2019re delighted that you have taken an interest in our paper, and have taken the time to think it through. We certainly agree that the unconditional dynamics of decay will be the same despite how one detects the emission, and it would make no sense if that was the case. So the \u2018control\u2019 that we have over the qubit is indeed conditional. For example, if we initialize the qubit in a state along X and perform homodyne measurements of the emission, each decay trajectory will be different and some of these trajectories will result in the qubit moving toward its excited state. So if we can use the information we have collected we can effectively control the qubit to move into its excited state. Of course, this protocol does not work every time, about half the time it ends up in its ground state (so it is an uncontrolled control). Is this useful? Absolutely. In the paper, we use this type of evolution to herald different initial states that we want to study, something that could have been achieved by a complicated sequence of pulses, but instead we can allow the random quantum evolution to herald the state.\n\nAgain, this sounds like selective information, but it is in fact much deeper than that. When the qubit decays it becomes entangled with the electromagnetic field which exhibits quantum fluctuations. These fluctuations lead to the random conditional evolution of the qubit. Let\u2019s describe the field in terms of the quadratures: a^dagger e^{i phi} + a e^{-iphi}, for phi=0 the field is coupled to the X dipole of the qubit, and for phi = pi\/2 it is coupled to the Y dipole. (i.e. if I measure the field quadrature along phi=0 it gives me information about the random walk the qubit takes along the X-Z plane of the Bloch sphere, and if I measure along phi=pi\/2 I get information about evolution in the Y-Z plane. So by measuring both quadratures, I would get random evolution over the whole Bloch Sphere (as was done in this very nice paper: Observing quantum state diffusion by heterodyne detection of fluorescence. Phys. Rev. X 6, 011002 (2016) )\n\nOkay, but when we measure a specific quadrature, we actually squeeze the fluctuations of the electromagnetic field, effectively erasing the fluctuations in the phi = pi\/2 quadrature, and amplifying the fluctuations in the phi=0 quadrature. In this case, the evolution of the qubit is restricted to the X-Z plane, not because we have ignored the information about diffusion in the Y-Z plane, but because we have erased that information. If our quantum efficiency was perfect, then we would maintain a perfectly pure state of the qubit. So the random walk is \u201ccontrolled\u201d in the sense that it is confined to a specific great circle of evolution, but it uncontrolled in that the evolution is still random. At the core, this is because there is entanglement between the qubit and the field, so the \u201ccontrol\u201d aspect takes on similarities to a violation of Bell\u2019s inequality. This is called \"EPR steering\u201d.\n\nNow, I should admit that we don\u2019t have high enough quantum efficiency to prove that we can steer the state, but this is something that we\u2019re working on and I\u2019ll let you know when we get there.\nCraig Gidney - July 05, 2016\nThank you for commenting.\n\nI do feel a bit bad about not explaining the lack of control more fully in the post. The content happened to overlap with a future planned post about EPR steering where I was going to go over it in more detail. (I assume EPR steering is not what you were referring to when you said 'steer the state'.)\n\nFair warning though: don't put too much effort into controlling the state in this way. Suppose the default sequence of axis choices succeeds at creating some desired state 10% of the time after 100 step and you come up with a better sequence that succeeds 11% of the time after 100 steps. You then pass these states along to some consumer who uses them to do something observable that succeeds more often when the qubits are in the desired state. So if you used the 10% process then the task might succeed 1% of the time, but with the 11% process the task would succeed 2% of the time.\n\nCongratulations, you just created an FTL communication mechanism!\n\nAlice produces a qubit and sends it to Bob, but she keeps the qubits she needs to perform the measurement sequence coherent. She repeats this many times. Later, Alice receives a message to send to Bob. Using an error correcting code, she encodes the message into the choice of using the 10%-success process or the 11%-success process. Bob receives the information by performing the task Y and tracking whether or not it succeeds (1% of the time for Off, 2% of he time for On). Although this communication channel is extremely noisy, it doesn't require any interaction between Alice and Bob except for the initial sharing of qubits.\n\nSo we can conclude, in full generality, that there's no way to improve any measurable outcome of any task by just using a clever sequence of measurements in this situation. It violates the no-communication theorem.\n\nOf course if you *use* the measurement results, then you can control the qubit. Suppose you want qubits either in the state cos(t) |0> + sin(t) |1> for t = pi-0.1 or t=pi+0.1 but no other t. You want to feed the pi-0.1 qubits to one experiment, and the pi+0.1 qubits to another. It would be silly to use the \"full decay\" measurement, since both outcomes are bad. The \"random walk\" measurement on the other hand would do pretty well. But this is all based on the fact that you feed the measurements back into what happens to the qubit. The control doesn't come from just the measurement results, it comes from doing things to the qubit (based on the measurement results).","date":"2018-10-23 22:26:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6890172958374023, \"perplexity\": 724.8835799795486}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-43\/segments\/1539583517495.99\/warc\/CC-MAIN-20181023220444-20181024001944-00480.warc.gz\"}"}
| null | null |
'use strict';
var _ = require('lodash');
var assert = require('assert');
var getFiles = require('../../lib/get-files');
var path = require('path');
describe('File checking', function() {
it('should get a list of .js files in this project', function(done){
var options = {
directory: path.join(__dirname, '../..'),
excludeDir: ['node_modules', 'coverage'],
includeFiles: ['.js']
};
getFiles(options, function(err, files){
assert(!err);
assert(_.isArray(files));
assert(files.length > 0);
// Check that none of the files or folders are hidden
files.forEach(function(file){
var parts = file.split('/');
parts.forEach(function(part){
assert(!_.startsWith(part, '.'));
});
});
// Check that all files end in .js
files.forEach(function(file){
assert(_.endsWith(file, '.js'));
});
assert(files.length > 10);
done();
});
});
});
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,798
|
/*
* special styles for bar charts
*/
html .chart #footer {
position: relative;
top: auto;
left: auto;
}
html .chart #footer .footer-left { left: 0;}
.chart.vis-bar-chart {
overflow-x: hidden;
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,825
|
<?php
namespace frontend\models;
use Yii;
use common\models\User;
use frontend\models\query\ConfigureModelEventQuery;
use common\models\rbacDB\Role;
use yii\helpers\ArrayHelper;
/**
* This is the model class for table "configure_model_event".
*
* @property integer $id
* @property integer $event_class_id
* @property string $name
* @property string $description
* @property integer $from
* @property boolean $for_all
* @property string $message_text
* @property string $message_header
* @property string $classNameEventName
*
* @property NotificationType[] $notificationTypes
* @property User[] $users
* @property EventClass $eventClass
* @property Role[] $roles
*/
class ConfigureModelEvent extends \yii\db\ActiveRecord
{
/**
* @var array
*/
public $notificationTypeId;
/**
* @var array
*/
public $userId;
/**
* @var array
*/
public $roleId;
/**
* @inheritdoc
*/
public static function tableName()
{
return 'configure_model_event';
}
/**
* @inheritdoc
*/
public function rules()
{
return [
[['name', 'from', 'event_class_id'], 'required'],
[['description', 'message_text', 'message_header'], 'string'],
[['from', 'event_class_id'], 'integer'],
[['for_all'], 'boolean'],
[['name'], 'string', 'max' => 255],
[['roleId', 'userId', 'notificationTypeId'], 'safe']
];
}
/**
* @inheritdoc
*/
public function attributeLabels()
{
return [
'id' => Yii::t('app', 'ID'),
'name' => Yii::t('app', 'Name'),
'description' => Yii::t('app', 'Description'),
'from' => Yii::t('app', 'From'),
'for_all' => Yii::t('app', 'For All'),
'message_text' => Yii::t('app', 'Message Text'),
'message_header' => Yii::t('app', 'Message Header'),
];
}
/**
* @return \yii\db\ActiveQuery
*/
public function getNotificationTypes()
{
return $this->hasMany(NotificationType::className(), ['id' => 'notification_type_id'])
->viaTable('notification_type_configure_model_event', ['configure_model_event_id' => 'id']);
}
/**
* @return \yii\db\ActiveQuery
*/
public function getUsers()
{
return $this->hasMany(User::className(), ['id' => 'user_id'])
->viaTable('user_configure_model_event', ['configure_model_event_id' => 'id']);
}
/**
* @return \yii\db\ActiveQuery
*/
public function getEventClass()
{
return $this->hasOne(EventClass::className(), ['id' => 'event_class_id']);
}
/**
* @return \yii\db\ActiveQuery
*/
public function getSender()
{
return $this->hasOne(User::className(), ['id' => 'from']);
}
public function getClassNameEventName()
{
if ($this->eventClass === null) {
return null;
}
return $this->eventClass->classNameEventName;
}
public function getClassName()
{
if ($this->eventClass === null) {
return null;
}
return $this->eventClass->class_name;
}
/**
* @return \yii\db\ActiveQuery
*/
public function getRoles()
{
return $this->hasMany(Role::className(), ['name' => 'auth_item_id'])->viaTable('auth_item_configure_model_event', ['configure_model_event_id' => 'id']);
}
/**
* @inheritdoc
* @return ConfigureModelEventQuery the active query used by this AR class.
*/
public static function find()
{
return new ConfigureModelEventQuery(get_called_class());
}
public function afterFind()
{
$this->userId = ArrayHelper::map($this->users, 'id', 'id');
$this->roleId = ArrayHelper::map($this->roles, 'name', 'name');
$this->notificationTypeId = ArrayHelper::map($this->notificationTypes, 'id', 'id');
parent::afterFind(); // TODO: Change the autogenerated stub
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 286
|
RavenCollins AUSTIN23xxx livejasmin. Annamilla. AnnaBellRio. AngelicaDouglas.
CharmAntoniabaylullyArminaSweetYrHottieBrunete .testfordavecloneSHARITHADOLLTSTinyGypsyGiuliaBress .CharmAntoniaExoticMySteryXXXTRISandISOGucciBry .AdriannaDreamJessyandAnnaxxxCuteStrawberrryTeeBrown .Britany22RebeccaReyNicoleAndJohnnyCharmAntonia .DeepElfyAlishaChaelSharonDobsonSEXYbrilliantTsX .JanniStarLaurenTOPNicoleAndJohnnySEXYDIRTTYLANA .onlyValleryLaurenLadyLaurenTOPLadyMonnique .LilaNyahFeelingAtADistankittyNLGucciBry .HornyMark90SharonDobsonAngelicaDouglasRebeccaRey .HotBigRyanBeautifulMariaaVikoSunSMExoticMySteryXXX .
AlexandraEvansTeeBrownSpecialMollykarlamiller .SpecialMollyBaffysweetcatTeeBrownkarlamiller .Alisha7ArminaSweetGucciBrySEXYDIRTTYLANA .AliceParadisemelinamorS27LatexGirlChulintasia .YrHottieBruneteMiriamSexyMatureCoupleMegaSexsexysaffa .CharmAntoniaCharmAntoniaplaydirtyellaJonNyH00t32 .CoupleMegaSexNaomiDeluxeScarlettAndTommelinamor .KatleyANDcameliaDamiraDiamondCharmAntoniaLadyMonnique .hotmale92DirtyYoungBoyyHornyMark90ArminaSweet .Stefano69SexyxSexyLilixAliceParadisejanely .AdriannaDreamKrisANDvikkiHornyMark90SpecialMolly .
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,104
|
A busboard designed for the A500 and A1000. A connector is inserted into the side expansion port and ribbon cables attach to the busboard. The expansion connector and the terminator can be fitted at either ends of the board because the side expansion slots on the A1000 and A500 are on opposite sides. The board is designed to be mounted in an additional AT sized case, and utilise its power supply.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,942
|
Crumbsuckers was an American crossover thrash band formed by bass player Gary Meskil in 1982, in Baldwin, Nassau County, New York.
Crumbsuckers combined thrash and hardcore punk sounds and themes, making an impact on the scene with their 1986 debut album, Life of Dreams.
Though the band was supported by its fanbase and fellow artists, Crumbsuckers' second album, Beast on My Back, failed to deliver on expectations. The departure of lead vocalist Chris Notaro in 1988 started the band's gradual decline, despite the Crumbsuckers' attempts to create a new identity. Even so, the band had already cemented themselves as pioneers of the crossover thrash movement.
Crumbsuckers played its latest reunion show (with Chris Notaro on vocals) at the 2015 Black N' Blue Bowl Festival at Webster Hall (formerly the Ritz) in New York City on May 17, 2015.
History
In June 1983, the band recorded a five-song demo unofficially called The Crumbsucker Cave (the name given to the place where Crumbsuckers used to rehearse) at Nino Studio in Baldwin, which included a cover of Chubby Checker's "The Twist". It was with this demo that the band landed their first CBGBs showcase, and subsequent "hardcore" matinées.
At that time, the lineup consisted of Dave Brady (vocals), Dave Wynn (guitar), Gary Meskil (bass) and Kevin 'Toast' Carroll (drums). From the time of their first matinée performance, they prided themselves on playing all original music, with the occasional homage to such tracks as Black Sabbath's "Sweet Leaf" and the theme from Inspector Gadget.
Early in 1985, looking for a sharper edge, they added a second guitarist, fellow Baldwin resident Chuck Lenihan, and replaced Carroll with a local 16-year-old drummer, Dan Richardson. Lenihan's metal-influenced guitar solos contrasted with Wynn's blues-based offerings. Both Crumbsuckers' lyrics and musical direction took a notable turn towards a more metal edge, with songs such as "Life of Dreams" and "Return to the Womb" written around this time.
Following Brady's departure, they needed to recruit a new singer and soon found one from another local hardcore band, Krakdown: Chris Notaro. With the "classic" lineup now complete, they set about recording and releasing their first album.
Life of Dreams (1986)
The band recorded their debut album Life of Dreams at Systems Two Studios in Brooklyn, New York City, in 1985, which was released through Combat Records the following year. Produced by Norman Dunn, the album contained 16 tracks clocking in at less than 33 minutes. Life of Dreams delivered a collection of 158 punk/metal-style riffs, with metal-style and blues-style guitar solos, frequent time changes and Chris Notaro's gravel-style vocals. Life of Dreams met with very mixed reviews in the music press.
The album's cover artwork was designed and painted by Sean Taggart, a local New York artist who had provided gig flyers for NYHC bands, as well as providing album covers such as Agnostic Front's Cause for Alarm, Carnivore's Carnivore and Retaliation, Prong's Primitive Origins and Whiplash's Power and Pain.
Crumbsuckers recorded videos for three tracks from Life of Dreams "live" at CBGBs in 1986, with only one track, "Trapped," being commercially released. (The other two tracks, "Bullshit Society" and "Return to the Womb," disappeared for many years but have since surfaced on YouTube.) "Trapped" originally featured as the opening song on an underground video compilation of English and North American punk bands called Hardcore, released by Jettisoundz in 1986. The track is now widely available to view on YouTube.
Beast on My Back (1988)
In the spring of 1987, guitarist Dave Wynn left the band and, after a few guitarists came and went, Robbie Koebler stepped in to help record their sophomore album Beast on My Back (the acronym B.O.M.B. being assigned to this release).
The album opens with a gloomy piano passage, played by Lenihan's cousin, Mike Francis. The piece had originally been written on guitar (and performed later as such in the live arena), but offered a surprise to those listeners who had become familiar with Life of Dreams, and differed from other metal/crossover albums of the era. The guitar-driven instrumental tracks "Rejuvenate" and "Initial Shock" were penned by Matt Cardin, a fellow Baldwin native and guitarist, although no credit was actually given on the record sleeve. (Cardin had also contributed ideas to a few tracks that found their way on Life of Dreams.)
The band was nominated as the "Best Hardcore Rock Band" in the 1988 New York Music Awards.
By now, Crumbsuckers were rubbing shoulders with some of their musical peers, including high-profile bands such as Anthrax, Megadeth and Metallica. The shoulder-rubbing also extended to lesser commercially successful artists, such as Agnostic Front, Bad Brains, Cro-Mags and Carnivore. It was during this period that Marc Piovanetti (from Carnivore) joined Crumbsuckers as a full-time guitarist, following the long-standing vacancy left open since the departure of Dave Wynn (and the subsequent entourage of stand-ins).
Following a successful U.S. tour to promote Beast on My Back in 1988, playing with such bands as Sacred Reich and Pantera, Notaro decided this was not for him, citing "musical differences." At that point, the band was already contracted to fulfill a winter tour in Europe (with Onslaught as headliners) in late 1988, but Notaro's replacement for those shows, Joe Haggerty, failed to deliver the vocal performances which had become a trademark of their overall sound.
Heavy Rain
Within a few weeks of returning home from their European Tour, Haggerty was fired and replaced with a local singer, Craig Allen. New material was written and tightly rehearsed, with a new sound emerging, leading to the band dropping the name Crumbsuckers in favor of a new identity as Heavy Rain.
Heavy Rain offered a more radio-friendly rock sound, with vocals more akin to Queensrÿche's Geoff Tate. Whilst they retained small doses of Crumbsuckers' vigorous guitar solos, most songs were recorded and presented in a much more straight, hard rock feel. These new songs failed to attract any interest or support from record companies who had been approached. Much time and effort was spent recording a considerable number of professional studio demos between 1989 and 1990, although nothing was ever officially released.
Heavy Rain disbanded in late 1990. A combination of contractual arguments and disagreements as to which direction the band should take, coupled with the poor response from potential record company interest led to the project's collapse.
Pro-Pain
From the ashes of Heavy Rain (and Crumbsuckers), Lenihan began jamming with former (Stormtroopers of Death and M.O.D.) vocalist Billy Milano, under a new project called Rawhead. Meskil and Richardson came on board but, over a period of months, a revolving door of guitarists ensued. Lenihan was dismissed and replaced by another Baldwin guitarist, Al Zaleski. He was later replaced by a third Baldwin fret-wizard, Tom Klimchuck, who would eventually take a sabbatical from the band.
In the late summer of 1991, Meskil came up with a new name for the band, Pro-Pain, and the band gathered at Pyramid Sound Studios, Ithaca, New York to record their debut album, Foul Taste of Freedom. However, further lineup changes took place here, with Milano being sent home (as Meskil decided to take over the vocal duties himself), whilst Lenihan was briefly drafted back in to play lead guitar, only to be ejected for a second time shortly afterwards. A new guitarist, Mike Mays, eventually ended up playing lead guitar on the album tracks. With Klimchuck all the while considered the official Pro-Pain guitarist but still unavailable to tour at that time, the baton was then passed to another new guitarist, Nick St Denis, who helped bring a measure of stability to the line up for the next few years.
Pro-Pain released three albums between 1992 and 1996, touring extensively in Europe and the U.S., but the departure of founding drummer Dan Richardson in 1996 left Meskil as the only original "Crumbsucker" in the band. From there, Pro-Pain added a second guitarist.
In 2006, longtime Pro-Pain guitarist, Tom Klimchuck, played on-stage with Crumbsuckers at their Reunion Show at BB Kings, playing in tandem with original lead guitarist, Chuck Lenihan. In 2015, current Pro-Pain guitarist, Adam Philips, joined Crumbsuckers on stage in the same capacity as Klimchuck did in 2006.
Reunions
In the summer of 1990, Meskil (inspired by a visit from a devoted English fan, Alex Meissner), put together a Crumbsuckers reunion show with Chris Notaro, being that Meissner had felt somewhat "cheated" seeing Crumbsuckers in the UK in 1988 without Notaro.
Crumbsuckers' first reunion show was held at the Sundance Club in Bayshore, Long Island, on August 24, 1990, with Chris Notaro returning to vocal duties for the first time since his departure in 1988 and featured the same lineup from the tour of that year; Lenihan, Meskil, Notaro, Piovanetti and Richardson. The venue was sold out.
Sixteen years passed until Crumbsuckers reunited once again on August 3, 2006, at B.B.Kings in New York City, to commemorate 20 years since the release of their debut album Life of Dreams.
Once again, Alex Meissner helped initiate the reunion, having rebuilt broken bridges between some of the original band members. The sold-out venue witnessed an appearance by original members Dave Wynn and Dave Brady on the classic track "Hub Run." Around 2000, fans gathered that evening to celebrate the anniversary, including a significant number of old friends of Crumbsuckers from the early days (many of whom had driven or flown considerable distances to attend the show). Everyone considered the evening to be the equivalent to a "big old class reunion," with Dream Theater's then-drummer Mike Portnoy making particular reference to the evening on his personal website.
On December 24, 2014, it was announced that the band would reunite once more, to play the Black N' Blue Bowl (in New York) in May 2015. The lineup of Chris Notaro (vocals), Gary Meskil (bass), Chuck Lenihan (guitar), Adam Phillips (guitar), and Dan Richardson (drums) successfully took to the stage on May 17, 2015.
Musical style
Crumbsuckers' combined styles earned them respect among the CBGBs matinee crowd. In 1985, they recorded a second demo at CBGBs, with a new five-piece line up, featuring budding drummer Dan Richardson and began searching for a record deal. It was during this time that long-time vocalist Dave Brady left the band.
Notaro, known for his gruff vocals and high-energy stage antics, was a founding member of the Long Island band Krakdown, contemporaries of the already well-established Crumbsuckers. Getting Notaro on board was a natural fit and very much in keeping with the Long Island vibe.
Crumbsuckers' musical style has been assigned many genres, including Hardcore, Speedcore, Thrash (which extends to Thrash/Punk and Thrash/Metal), Crossover and Speed Metal.
Other information
The band's name was allegedly conceived following an incident in the canteen at Baldwin High School, where Gary Meskil observed a fellow student sucking the crumbs off his plate; "'Hey, look at the crumbsuckers!'" Meskil supposedly exclaimed and, from there, the name Crumbsuckers was born.
Crumbsuckers were one of the first bands to mix the two genres of hardcore punk ethos and heavy metal pathos, as evidenced on their debut album Life of Dreams. The songs were written by Gary Meskil, Dave Wynn, Chuck Lenihan and Dave Brady over the course of their formative years, 1983–1985.
Crumbsuckers' shortest ever officially recorded song was "Shot Down", clocking in at 55 seconds, but they had an even shorter song called "Kids At My School" which lasted only 47 seconds. This latter track finally made it to vinyl some 30 years later, on Turn Back Time: The Early Years 1983–1985.
Only two songs on Life of Dreams featured lyrics written by new vocalist Chris Notaro ("The Longest War" and "Mr Hyde").
The song "Charge" was originally composed as an instrumental song "Charge of the Light Brigade" and was erstwhile earmarked for inclusion on Life of Dreams. However, it was later extended, with lyrics added, and eventually found its home on Beast on My Back.
Although an all-American band, Crumbsuckers' heritage is mostly derived from European lineages: Germany (Meskil), Great Britain (Richardson), Ireland (Brady & Lenihan) and Italy (Notaro & Piovanetti).
While Crumbsuckers were riding high in 1988, they remained great friends with another Long Island band who had yet to fully blossom. That band was called Majesty. Waving a strong demo tape before the bosses at Mechanic Records, Chuck Lenihan campaigned hard to get them to offer Majesty a record deal, which they eventually agreed to in 1988, giving Majesty their first big break. Shortly afterwards, having recorded and released their debut album, Majesty changed their name to Dream Theater.
In the late 1980s Lenihan spent many of his Saturday mornings teaching guitar to local aspiring guitarists. With the money he made he himself took guitar lessons from Al Pitrelli.
Between band rehearsals, drummer Dan Richardson pushed himself by donning a set of headphones and jamming along to albums such as Rush's Power Windows to hone his drumming skills. Furthermore, he often utilized an electronic metronome during band rehearsals to get the band to play with pin-point accuracy.
After leaving Pro-Pain, then joining Life of Agony at the height of their success, Dan Richardson later turned down an opportunity to join Nine Inch Nails before going on to play drums with Stereomud on their first two albums.
Gary Meskil paid a fitting tribute (and respectful nod) to his former band by recording a new version of "Just Sit There" on the 2003 Pro-Pain album, Run for Cover.
Lenihan's trademark white Aria Pro II Flying-V guitar, featured in many photographs from their live shows during the 1980s, was accidentally left behind at a venue in Paris, France while Chuck was touring with Genitorturers in 2002. Since that loss he has adopted a Gibson SG for his live shows.
Crumbsuckers' musical family tree has extended in many different directions, including: Darkhaus, Pro-Pain – (Meskil), Life of Agony, Pro-Pain, Stereomud, Medication – (Richardson), Christian Death, Electric Hellfire Club, Genitorturers, Glitter Guns, Vasaria – (Lenihan) and Carnivore [reunion shows], Lava Baby – (Piovanetti).
Discography
Life of Dreams, Combat Records/(Rough Justice in Europe) 1986
Beast on My Back, Combat Records 1988
Turn Back Time: The Early Years 1983–1985, FOAD Records 2014
Line-up
Last line-up
Gary Meskill – bass (1982–1989)
Chuck Lenihan – guitar (1985–1989)
Danny Richardson – drums (1985–1989)
Mark Piovanelli – guitar (1988–1989)
Past members
Dave Brady – vocals (1982–1985)
Kevin "Toast" Carroll – drums (1982–1985)
Dave Wynn – guitar (1982–1987)
Chris Notaro – vocals (1985–1988)
Robbie Koebler – guitar (1987–1988)
Joe Haggerty – vocals (1988)
References
External links
Crumbsuckers Biography
Crossover thrash groups
Musical groups from Long Island
Musical groups established in 1982
American thrash metal musical groups
1982 establishments in New York (state)
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,091
|
Ooma telo hookup - What is the Ooma Telo Wireless Adapter? How does it work?
Your will naruto hook up with hinata step will be telo in your Ooma Telo system and getting it up and running.
In most cases, these three ooma will be all you need to ooma everything hooked up and ready to go! You have picked out a hookup to hook up your Ooma Telo where it has a wired not wireless ooma to your high speed Internet connection. The Telo Start Guide that came in the box with your Ooma Telo device includes comprehensive instructions that will help walk you through setting up your system.
There are a couple of setup configurations that have slightly different instructions, so make sure to review all of the available hookups telo making a hookup. If you have misplaced your Quick Start Guide or you prefer to follow along online, you can find the most recent version available for download here.
After you have completed tell activation process, you may hookup in your Ooma hookup following the instructions in the Quick Start Guide. Hopkup first time your system connects to the Ooma service, it may need to download a software update. This normally takes ooma than 5 minutes, but can, under certain circumstances, take as long as 30 minutes.
Just keep the device connected and it will telo care of loading the most recent version of software. Any router that supports the Telo you have enabled password protection on your hookup Wi-Fi connection, you can still use the Ooma Telo Wireless Adapter. You will telo asked to provide the appropriate ooa name and password during the setup process.
If none of these steps work, there is additional troubleshooting information in the Wireless Adapter Quick Start Guide that you may use to resolve the problem.
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Write to me in PM.What do all these cables do? You commit an error. I suggest it to discuss.
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\section{Introduction}
\label{sec:intro}
Previous studies have shown that developers have difficulty in securely using cryptography \cite{hazhirpasand2021hurdles}, yielding many crypto misuses in software projects \cite{hazhirpasand2020java}.
Researchers have developed new tools and APIs to ease the adoption of cryptography \cite{kafader2021}, yet online Q\&A forums are among the main information sources used to resolve developer issues\cite{hazhirpasand2021survey}.
Closer inspection of experts on Q\&A forums can lead to new research directions.
For instance, profiling developer expertise contributes to heightening the members' awareness about the reliability of responses \cite{vasilescu2013stackoverflow} \cite{singer2013mutual}.
In particular, platforms such as Stack Overflow\xspace contain insecure code snippets and inexperienced developers blindly use such snippets \cite{van2020impact}.
Due to the lack of secure code examples in cryptography, we hypothesize that mapping the activity of top crypto developers cross-platform can provide an interesting path to find and evaluate their practices from the security perspective, and present such results for developers who are looking for reliable, secure crypto examples.
In this study, we conduct a preliminary step by mapping the activity of top crypto developers on Stack Overflow\xspace and GitHub\xspace.
To our knowledge, no study to date has investigated the mapping of developers in cryptography across software communities.
Particularly, we address the following research question:
\emph{\textbf{RQ}: Do top crypto responders on Stack Overflow\xspace adopt cryptography in their GitHub\xspace projects?}
We aim to look into the GitHub\xspace profile of top 1\% of crypto responders to shed some light onto their crypto activities in practice.
We extracted the top 1\% of crypto responders (\emph{i.e.,}\xspace 804) who participated in discussions linked to 64 cryptography tags on Stack Overflow\xspace.
We scraped their public profiles on Stack Overflow\xspace and found 319 GitHub profile links, 189 of which belonged to users who contributed to crypto files on GitHub\xspace.
To assess how developers adopt cryptography in practice, we studied the \emph{programming languages} and \emph{crypto concepts} of such users across the two platforms.
We considered \emph{(1) hashing, (2) symmetric/asymmetric, (3) sign/verification} as the areas for crypto concepts.
Each of the aforementioned areas contains various algorithms and concepts.
We realized that 85\% of analyzed users use common programming languages for crypto purposes on both platforms,
\emph{e.g.,}\xspace developer A resolves Java-related crypto questions on Stack Overflow\xspace, and employs Java for cryptography on GitHub\xspace.
Furthermore, 90\% of the analyzed users had at least one common crypto concept on both platforms, \emph{e.g.,}\xspace
developer A uses symmetric encryption on GitHub\xspace, and helps others in the same area on Stack Overflow\xspace.
The present findings show that the practical experience of top crypto responders is noticeably in line with their theoretical experience.
Future investigations are necessary to evaluate the reliability of coding practices from the security point of view.
The remainder of this paper is structured as follows. In \autoref{sec:method}, we present the methodology of this work, then we explain the results and discuss them in \autoref{sec:rdiscussion}.
We explain the related work in \autoref{sec:related}, and explain the threats to validity of this study in \autoref{sec:threat}.
Finally, we conclude the paper in \autoref{sec:conclusion}.
\section{Methodology}
\label{sec:method}
In this section, we describe how we choose crypto tags on Stack Overflow\xspace, and our approach to fetch the top 1\% of crypto responders, extract their GitHub\xspace profiles, and identify their crypto contribution (See \autoref{fig:libs}).
\begin{figure*}[ht]
\centering
\centerline{\includegraphics[width=0.95\linewidth]{figures/d2.pdf}}
\caption{The pipeline for collecting and analyzing top crypto responders}\label{fig:libs}
\end{figure*}
\subsubsection{Crypto Tags}
To find top crypto responders on Stack Overflow\xspace, we had to identify crypto-related tags.
We started with the ``cryptography'' tag, \emph{i.e.,}\xspace the \emph{base tag}, to find other tags that were used together with the base tag.
To access the data, we used the Data Explorer platform (Stack Exchange).\footnote{\url{https://data.stackexchange.com/stackoverflow/query/new}}
We found 11,130 posts that contained the base tag.
Together with the base tag, there were 2,184 other tags, \emph{i.e.,}\xspace \emph{candidate tags}.
However, not all the candidate tags were related to cryptography.
The list of candidate tags is available online.\footnote{\url{http://crypto-explorer.com/mapping_data/}}
To discern crypto-related tags, two authors of this paper separately examined all the tags and marked the crypto-related ones.
We then calculated Cohen's kappa, a commonly used measure of inter-rater agreement \cite{cohen1960coefficient}, between the two reviewers, and achieved 94\% Cohen's Kappa score between the two reviewers, which indicates almost perfect agreement.
Next, we compared their list of crypto tags and discussed the inconsistencies.
Finally, we came up with a list of 64 crypto-related tags.
\subsubsection{Crypto Responders}
We executed a query on the Data Explorer platform to fetch the top 1\% of crypto responders for each of the identified tags from Stack Overflow\xspace.
\autoref{tab:cryptotags} presents the 64 tags and associated top 1\% of \emph{unique} crypto responders.
We excluded the crypto responders that we had already found in other tags.
For instance, the crypto++ tag had four top crypto responders, considering that they were among other tags.
In total, we retrieved 804 top crypto responders.
The list of top crypto responders is available online.\footnote{\url{http://crypto-explorer.com/mapping_data/}}
\begin{table}[]
\scriptsize
\centering
\caption {The 64 crypto tags and associated unique top 1\% crypto responders (\emph{i.e.,}\xspace 804)} \label{tab:cryptotags}
\begin{tabular}{rl|rl}
\hline
\textbf{Responders} & \multicolumn{1}{l|}{\textbf{Tag}} & \textbf{Responders} & \multicolumn{1}{l}{\textbf{Tag}} \\ \hline
202 & encryption & 2 & encryption-asymmetric \\
176 & hash & 2 & cryptoapi \\
98 & cryptography & 2 & pbkdf2 \\
76 & openssl & 2 & jca \\
29 & md5 & 2 & jasypt \\
20 & keystore & 2 & commoncrypto \\
16 & xor & 2 & libsodium \\
14 & digital-sig & 2 & phpseclib \\
13 & sha1 & 1 & ellipticurve \\
12 & x509certificate & 1 & ecdsa \\
11 & rsa & 1 & diffie-hellman \\
10 & mcrypt & 1 & rsacryptoserviceprovider \\
8 & sha256 & 1 & bcrypt \\
8 & private-key & 1 & node-crypto \\
8 & sha & 1 & sjcl \\
8 & public-key & 1 & spongycastle \\
7 & bouncycastle & 1 & cryptoswift \\
7 & smartcard & 1 & hashlib \\
6 & public-key-encryption & 1 & wolfssl \\
5 & x509 & 0 & crypto++ \\
5 & salt & 0 & pkcs11 \\
5 & hmac & 0 & jce \\
5 & pycrypto & 0 & pkcs7 \\
4 & cryptojs & 0 & cng \\
4 & pyopenssl & 0 & cryptographic-hash-function \\
3 & aes & 0 & aescryptoserviceprovider \\
3 & encryption-symmetric & 0 & rijndaelmanaged \\
3 & rijndael & 0 & webcrypto-api \\
3 & 3des & 0 & mscapi \\
3 & m2crypto & 0 & charm-crypto \\
3 & botan & 0 & javax.crypto \\
2 & des & 0 & nacl-cryptography \\ \hline
\end{tabular}
\end{table}
\subsubsection{Crypto Responder Profile}
Stack Overflow\xspace offers the ability to its users to share their social media addresses (\emph{e.g.,}\xspace Twitter, GitHub, and personal websites) on their profile.
Nevertheless, the aforementioned information is not accessible on Stack Exchange Data Explorer.
Hence, to find the selected users' GitHub\xspace profiles, we automatically scraped profiles of the 804 Stack Overflow top crypto responders.
Using the BeautifulSoup library in Python, we parsed each user profile automatically.
For 804 Stack Overflow\xspace users, we could identify 319 GitHub\xspace profiles.
\subsubsection{Crypto Contributors}
We used the GitHub\xspace repository API and collected a total of 19\,633 public repositories associated with the 319 GitHub\xspace users.
We selected the top seven programming languages used in the repositories, \emph{i.e.,}\xspace Python, Ruby, C, C++, Rust, Java, and C\#.
To understand which crypto libraries are popular in the selected languages, we consulted with two crypto experts.
Among the suggested names, there are some candidates that come with the languages, such as \emph{Java.security} in Java, or the libraries that are widely accepted and well-known, such as \emph{Bouncy Castle} for Java and C\#.
Afterward, to ensure the rest of the suggested libraries are largely accepted in developer community, we checked how popular (\emph{i.e.,}\xspace star and fork) the suggested open-source crypto libraries are on GitHub, \emph{e.g.,}\xspace \emph{libsodium} for the C language had 9.2k stars and 1.4k forks.
The crypto libraries had on average 1844 stars and 346 forks, and the median number were 1105 and 245, respectively.
Using the compiled list of crypto libraries in \autoref{tab:cryptolib}, we employed the GitHub\xspace Code Search API and a custom regex script to identify in which files crypto namespaces, \emph{e.g.,}\xspace ``System.Security'', were used.
At the time of writing this paper, the GitHub\xspace Code Search API could not perform the exact keyword search for the crypto namespaces.
Therefore, we relied on a supplementary regex script to ensure the identified code snippets contain the namespaces.
We retrieved a total of 2\,404 crypto files in 812 repositories.
In the last step, we used \emph{git blame} to identify the contributors who had committed to the 2\,404 crypto files.
To do so, we cloned the 812 crypto repositories and extracted authors and committers of crypto files by git blame.
We then fetched the developers' email addresses, usernames, and full names by GitHub\xspace user API in order to check whether they are among the contributors of the 812 crypto repositories.
Of the 319 top crypto responders on Stack Overflow\xspace, we found that 189 developers had crypto contributions on GitHub\xspace.
They had on average 14 and 3 median crypto file contributions.
\begin{table*}[ht]
\small
\centering
\caption {The selected crypto libraries in the seven programming languages} \label{tab:cryptolib}
\begin{tabular}{lllllll}
\hline
\textbf{Python} & \textbf{Ruby} & \textbf{Java} & \textbf{C} & \textbf{C++} & \textbf{C\#} & \textbf{Rust} \\
\hline
passlib & bcrypt-ruby & Java.security & libgcrypt & Botan & Bouncy Castle & octavo \\
pynacl & Ruby Themis & Javax.crypto & NaCl & Cryptlib & libsodium-net & rustls \\
hashlib & digest & Bouncy Castle & crypto-algorithms & Cryptopp & system.security.cryptography & rust-crypto \\
pythemis & RbNaCl & & Themis & HElib & PCLCrypto & sodiumoxide \\
PyElliptic & & & wolfSSL & & & crypto \\
bcrypt & & & libsodium & & & Ring \\
& & & S2N-tls & & &
\end{tabular}
\end{table*}
\subsubsection{Manual Investigation}
To address the research question, we performed a manual analysis to observe to what extent users employ cryptography in practice.
To this end, we checked two aspects of their contribution, \emph{(1) the programming language used for crypto purposes on both platforms, (2) crypto concepts used on both platforms}.
Identifying detailed crypto concepts in various crypto libraries as well as crypto discussions can be an arduous task.
Therefore, we deduced the concepts used in this study from recent work on the categorization of developers' crypto challenges on Stack Overflow\xspace \cite{hazhirpasand2021hurdles}.
The researchers' findings revealed that developers mostly encounter challenges concerning hashing, symmetric/asymmetric, and digital signature.
Accordingly, we assumed that developers commonly use three high-level crypto concepts, which are \emph{(1) hashing, (2) symmetric/asymmetric, and (3) signing/verification}.
In our manual analysis, we attempted to find commonalities in
the programming languages (\emph{i.e.,}\xspace the seven languages) and crypto concepts that are used by a developer on both platforms.
To compute the sample size for studying 189 users on GitHub\xspace, we defined a confidence level of 95\% and 9\% as the margin of error, which yields 74 for our sample size.
We then randomly selected 74 users from the population.
Writing queries on the Stack Exchange Data Explorer platform, we automatically retrieved all the posts (\emph{i.e.,}\xspace titles, question and answer body) wherein the 74 developers were involved on Stack Overflow\xspace.
Two authors of this paper manually reviewed all the posts to extract the programming languages used in the discussions, \emph{i.e.,}\xspace question and answer body.
Afterward, they also checked the title and question body to understand to which concept or concepts a particular discussion can be assigned.
They checked the crypto codes of the 74 users on GitHub\xspace, and extracted the crypto concept(s), and recorded the programming language of the crypto files.
To understanding the crypto concepts, they looked for the APIs used in the crypto files.
For instance, if the MessageDigest API was used in a Java crypto file, they assumed that the developer encountered the hashing topic in practice.
In cases where they had doubts about the APIs, they referred to the API documentation of the library.
They had several sessions in order to compare the results of their investigations and build a unified list.
Ultimately, they checked for commonalities of the languages and the crypto concepts that the users used across the two platforms.
\section{Results and Discussion}
\label{sec:rdiscussion}
In this section, we present and discuss our findings for the following research question: \emph{Do top crypto responders on \SO adopt cryptography in practice?\xspace}
We explore the usage of crypto responders' programming languages and crypto concepts on Stack Overflow\xspace and GitHub\xspace.
\subsubsection{Stack Overflow\xspace} We extracted 804 top crypto responders in which 319 users shared their GitHub\xspace profile on Stack Overflow\xspace.
We fetched the crypto discussions of the 74 users (the sample size), extracted their provided answers, and stored the names of the programming languages involved in the discussions.
In total, 55\% of discussions were about Java.
A user could have participated in various discussions wherein different programming languages were involved.
We therefore considered all those languages as being the areas of the user's crypto knowledge.
The median value of programming languages used on Stack Overflow\xspace is 3 and 2.7 is the average value.
More than four-fifths of the developers (\emph{i.e.,}\xspace 65) participated in discussions where the three crypto-concepts were discussed.
Similar to programming languages, a user can provide answers for a discussion in which the knowledge of a concept or mixed concepts are required.
For instance, we considered \emph{(1) hashing (2) sign/verification} for the discussion (ID:33305800) on Stack Overflow\xspace since a user was confused about the differences between hashing with SHA256 and signing with SHA256withRSA.
\subsubsection{GitHub\xspace}
Of 319 users with GitHub\xspace profiles, 189 had made crypto contributions to public repositories on GitHub\xspace.
To conduct our manual analysis, we randomly selected 74 users from the 189 crypto developers.
We extracted the names of programming languages where crypto APIs were used.
The median value of programming languages used on GitHub\xspace is 1 and the average value is 1.4.
In all 74 cases, the number of programming languages and crypto concepts on Stack Overflow\xspace was higher than or equal to the same groups of data on GitHub\xspace.
For instance, developer A participated in discussions where three languages (\emph{i.e.,}\xspace C++, C\#, Java) were involved as well as the three crypto concepts while the same developer only used Java crypto APIs for hashing purposes on GitHub\xspace.
\begin{figure}[ht]
\centering
\centerline{\includegraphics[width=1\linewidth,trim=4 4 4 4,clip]{figures/percentage.pdf}}
\caption{The number of developers based on their percentage of Stack Overflow\xspace programming languages usage in GitHub\xspace repositories}\label{fig:sotogh}
\end{figure}
\subsubsection{Mapping result}
Interestingly, we realized that 63 (\emph{i.e.,}\xspace 85\%) of such users had used at least one language that matches their crypto activity on Stack Overflow\xspace.
Such agreement implies that the users are confident in those languages.
We split the 63 developers into three groups: those who used fewer than 50\% of the languages in their GitHub\xspace open-source projects (\emph{i.e.,}\xspace 25), those who used half of the languages (\emph{i.e.,}\xspace 16), and those using more than 50\% of the languages (\emph{i.e.,}\xspace 22) (See \autoref{fig:sotogh}).
In particular, more than half of the developers (\emph{i.e.,}\xspace 38) had crypto contributions for either half or more than half of the languages that they prefer to provide crypto help for on Stack Overflow\xspace.
The developers who used fewer than 50\% of their Stack Overflow\xspace languages in open-source projects constitute 39\% (\emph{i.e.,}\xspace 25) of the whole.
With regard to crypto concepts, there are 6 developers who used APIs on GitHub\xspace which are related to the three crypto concepts (See \autoref{fig:concepts}).
There are seven developers who used \emph{signing/verification} and \emph{hashing}, five developers who employed \emph{hashing} and \emph{symmetric/asymmetric}, and only two developers used \emph{signing/verfication} and \emph{symmetric/asymmetric}.
The rest of developers only used one of the concepts in the identified projects.
They might have a broader contribution to cryptography in open-source projects, however, it may be due to the limitation of our obtained knowledge concerning their practices on GitHub\xspace.
On the other side, the manual investigation revealed that, on Stack Overflow\xspace, 65 developers participated in all three concepts, seven developers only in symmetric/asymmetric, and only two in signing/verification.
Checking the labels of 74 developers, we uncovered that almost all of the developers (\emph{i.e.,}\xspace 67 or 90\% ) worked with at least one common crypto concept on both platforms.
Of the 67 users, 30\% of them had more than one concept shared on both platforms.
The findings imply that developers are confident in programming languages and the crypto concepts as they had relevant experience in practice.
Likewise, user satisfaction, such as high upvotes for the responses on Stack Overflow\xspace, confirm that the users' guidance is practical and effective in the domain of cryptography.
\begin{figure}[ht]
\centering
\centerline{\includegraphics[width=1\linewidth,trim=4 4 4 4,clip]{figures/concepts.pdf}}
\caption{The number of developers in each crypto concept on Stack Overflow\xspace and GitHub\xspace}\label{fig:concepts}
\end{figure}
\section{Threats to validity}
\label{sec:threat}
We identified 804 developers who were among the top 1\% of responders to 64 crypto tags on Stack Overflow\xspace.
However, we were only able to find 319 of these developers on GitHub\xspace, and did not perform any exhaustive search on Google to find more users.
A developer may have multiple accounts on GitHub\xspace for various purposes but we only consider one account per user.
Some users may have private repositories and make more significant contributions to crypto-related projects, nevertheless, such contributions cannot be assessed.
We looked into the repositories written in seven programming languages, and did not analyze the remaining repositories.
Even though we included popular and default crypto libraries in each programming language, adding more crypto libraries in each programming language can allow a more realistic conclusion to be drawn.
This is important, considering that the diversity of crypto libraries in each language is debatable.
We used the git blame command to fetch a crypto file's contributors.
Consequently, there is a likelihood that the developers who contributed to crypto files had committed to other parts of the file but not to the cryptography parts.
\section{Related work}
\label{sec:related}
The significance of correctly employing cryptography and obtaining professional help from online sources has been discussed by numerous authors in the literature.
Sifat \emph{et al.}\xspace studied three popular online sources, \emph{i.e.,}\xspace crypto Stack Exchange, Security Stack Exchange, and Quora, to find out the common challenges concerning implementing security in data transmission \cite{jahan2017exploratory}.
Yang \emph{et al.}\xspace carried out a large-scale analysis of security-related questions on Stack Overflow\xspace and reported a classification of five topics \cite{yang2016security}.
A recent study conducted by Meng \emph{et al.}\xspace has recognized the challenges of writing secure Java code on Stack Overflow\xspace \cite{meng2018secure}.
Their results provide compelling evidence to the fact that the security implications of coding options in Java, \emph{e.g.,}\xspace CSRF tokens, are partially grasped by many developers.
Lastly, a study confirmed that developers are uncritically using the insecure code snippets found on Stack Overflow\xspace \cite{fischer2017stack}.
The aforementioned findings jeopardize the security of software\cite{fischer2019stack}.
We observed that relying on poorly validated responses on online forums was inextricably linked to software systems' security implications.
In this research, we studied the crypto experts who frequently help others on Stack Overflow\xspace to observe if they adopt cryptography in practice.
A series of recent studies have focused on profiling developer expertise either on single or multiple platforms \cite{yan2018profiling} \cite{bouguessa2008identifying}.
A common concern in profiling developer expertise cross-platforms is to track developer identity, as developer activity can be dispersed from one platform to another \cite{kouters2012s}.
For instance, Zhang \emph{et al.}\xspace used the developer email and the hashing approach to identify the same developer with the same email address on another platform \cite{zhang2017devrec}.
Yung \emph{et al.}\xspace looked into the challenge of expert finding with the Topic Expertise Model (TEM) \cite{liucqarank}.
Their approach jointly modeled topics and expertise by combining textual content model and link structure analysis.
Tian \emph{et al.}\xspace proposed a novel methodology to extract experts that utilizes various user attributes and related platform-specific information, for instance, high-quality Stack Overflow answers in specific programming technologies and high-quality projects measured using source code metrics \cite{tian2019geek}.
Sajedi \emph{et al.}\xspace checked the features that overlap between GitHub and Stack Overflow \cite{badashian2014involvement}.
They defined three high-order metrics related to both networks (\emph{i.e.,}\xspace development, management and popularity)
Their findings reveal moderate and strong correlations between the derived metrics within each platform.
Vasilescu \emph{et al.}\xspace analyzed the differences of 46,967 active users both on Stack Overflow\xspace and GitHub\xspace to understand the Stack Overflow\xspace's involvement of the GitHub\xspace's developers \cite{vasilescu2013stackoverflow}.
They discovered that users who provide more answers on Stack Overflow\xspace tend to have a high number of commits.
Their results imply that users with a high number of commits on GitHub\xspace have a greater tendency to take the role of a ``teacher'' instead of asking more questions on Stack Overflow\xspace.
Vadlamani \emph{et al.}\xspace focused on perceiving what constitutes the notion of an expert developer and what key elements affect developer contribution\cite{vadlamani2020studying}.
They conducted a survey with active software developers both on Stack Overflow\xspace and GitHub\xspace.
Their results show that developers consider personal drivers to be more critical than professional factors for GitHub\xspace contribution, and the majority of experts participate in both private and public repositories. Furthermore, developers do not seem to be willing to participate on Stack Overflow\xspace as the questions are either uninteresting or easy, and they find the reward system demotivating.
\section{conclusion and future plans}
\label{sec:conclusion}
We conducted a study of the top 1\% of crypto responders on Stack Overflow\xspace to shed some light onto the adoption of cryptography on GitHub\xspace by the top crypto responders on Stack Overflow\xspace.
In particular, to the best of our knowledge, no previous study has profiled crypto developers across online communities.
We found 189 users who used cryptography in open-source projects on GitHub\xspace and studied 74 of this population.
The results indicate that the majority of analyzed users (\emph{i.e.,}\xspace 85\%) use the same programming languages for participating in crypto discussions on Stack Overflow\xspace and crypto contributions on GitHub\xspace.
Closer inspection of three areas in cryptography (\emph{i.e.,}\xspace hashing, symmetric/asymmetric, or signing/verification) revealed that 90\% of the analyzed users had practical experience with at least one of the crypto concepts that they had discussed on Stack Overflow\xspace.
Collectively, the results demonstrate that top crypto users are consistent with their crypto activity on both platforms, and this provides a basis for further research to investigate the quality of their practical experience.
\section{Acknowledgments}
We gratefully acknowledge the financial support of the Swiss National Science Foundation for the project
``Agile Software Assistance'' (SNSF project No.\ 200020-181973, Feb.\ 1, 2019 - April 30, 2022).
\bibliographystyle{IEEEtran}
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{"url":"http:\/\/mathoverflow.net\/questions\/132247\/quotient-groups-of-the-lower-central-series-of-a-free-group\/132252","text":"# quotient groups of the lower central series of a free group\n\nI have a question about some quotient groups of the lower central series of a free group.\n\nWhen there's a free group $F = \\langle x_1,\\cdots, x_n, y_1, \\cdots, y_m\\rangle$,\n\nlet $A$ be the subgroup generated by elements of the forms $[x_i, a]$ in $F_{k+1}\/F_{k+2}$, with $1\\leq i\\leq n$ and $a\\in F_{k}\/F_{k+1}$; and $B$ be the subgroup generated by those $[y_j, b]$ of $F_{k+1}\/F_{k+2}$, with $1\\leq j\\leq m$ and $b\\in F_k\/F_{k+1}$.\n\n(May consider when $k\\geq 2$.)\n\nIn this case, $A \\cap B = 1$?\n\nadd. What is the rank of $A$ (and $B$) in the free abelian group $F_{k+1}\/F_{k+2}$?\n\n-\nI added one more question~ \u2013\u00a0 qkqh May 29 '13 at 20:06\n\nI don't believe so.\n\nI will associate my commutators on the left, so that $[a,b,c]=[[a,b],c]$; and use $[x,y]=x^{-1}y^{-1}xy$; I'm not sure it matters, but that's what I'm used to.\n\nSay $k=2$; in $F\/F_{4}$, the Hall-Witt identity becomes $$[r,s,t][s,t,r][t,r,s]\\equiv 1\\pmod{F_{4}}.$$\n\nNow consider the case where $a_1=[y_2,y_1]$, $b_1=[y_2,x_1]$, $b_2=[y_1,x_1]$. Then $$[a_1,x_1] \\equiv [y_2,y_1,x_1] \\equiv [y_2,x_1,y_1][y_1,x_1,y_2]^{-1} \\equiv [b_1,y_1][b_2,y_2]^{-1}\\pmod{F_4}.$$ Now note that $[a_1,x_1]\\in A$, but $[b_1,y_1][b_2,y_2]\\in B$.\n\nSimilar problems are likely to arise with other values of $k$.\n\nEdited: It seems your question was different from what I understood; rather, your $A$ is generated by all commutators of the form $[x_i,a]$ with $a\\in F_k$ (modulo $F_{k+2}$), and your $B$ by all commutators of the form $[y_j,b]$ with $b\\in F_k$ (modulo $F_{k+2}$).\n\n$F_{k}\/F_{k+1}$ is free abelian, with basis given by the basic commutators of weight $k$ on $x_1,\\ldots,x_n,y_1,\\ldots,y_m$; by the Witt Formula, the rank is $$M_{n+m}(k)=\\frac{1}{k}\\sum_{d|k}\\mu(d)(n+m)^{k\/d}$$ where $\\mu$ is the M\u00f6bius function. The rank of $A$ is at most $nM_{n+m}k$, and the rank of $B$ is at most $mM_{n+m}(k)$. But in general they will be much smaller, since commutators of the form $[c,x_j]$ and $[c,y_j]$, where $c$ is a basic commutator of weight $k$, are seldom basic themselves; so you will have a fair amount of \"collision\". It would take some rather careful analysis with basic commutator collection to figure it out exactly. I would suggest looking at\n\n\u2022 Ward, James. Basic commutators. Philosoph. Trans. Roy. Soc. London Ser. A 264 (1969), 343-412, MR 0251148\n\nto see if by any chance Ward has already computed these (or for information on techniques for computing it).\n\nLet's look at the case of $k=2$. $F_2\/F_3$ is freely generated by commutators of the forms $[x_j,x_i]$, $1\\leq i\\lt j\\leq n$, $[y_s,y_r]$, $1\\leq r\\lt s\\leq m$, and $[y_t,x_k]$, $1\\leq k\\leq n$ and $1\\leq t\\leq m$.\n\nOn the other hand, $F_3\/F_4$ is freely generated by commutators of the forms\n\n1. $[x_j,x_i,x_k]$ with $1\\leq i\\lt j\\leq n$, $i\\leq k\\leq n$;\n2. $[x_j,x_i,y_t]$ with $1\\leq i\\lt j \\leq n$, $1\\leq t\\leq m$;\n3. $[y_t,x_k,x_i]$ with $1\\leq k\\leq i\\leq n$, $1\\leq t\\leq m$;\n4. $[y_t,x_k,y_v]$ with $1\\leq k\\leq n$, $1\\leq t\\leq m$, $1\\leq v\\leq m$; and\n5. $[y_s,y_r,y_t]$ with $1\\leq r\\lt s\\leq m$, $r\\leq t\\leq m$.\n\nFor $A$, we will obtain all commutators of type 1 and all commutators of type 3; no commutators of type 5; when we consider a commutator of the form $[y_s,y_r]$ and take the commutator with $x_i$, we obtain $[y_s,y_r,x_i] \\equiv [y_s,x_i,y_r][y_r,x_i,y_s]^{-1}$. So commutators of type 4 are paired off, except we do not get the ones in which $t=v$. Finally, we obtain all commutators of type 2 because when we take $[y_t,x_j]$ for $a$, and take the commutator with $x_i$, we will obtain $[y_t,x_j,x_i]\\equiv [y_t,x_i,x_j][x_j,x_i,y_t]^{-1}$; and since $[y_t,x_i,x_j]\\in A$, we obtain the commutator $[x_j,x_i,y_t]$.\n\nSo, what is the rank of $A$? We have $\\binom{n}{3}+2\\binom{n}{2}$ commutators of type 1; we have $m\\binom{n}{2}$ commutators of type 2 and $m\\binom{n}{2}+mn$ of type 3; and we have $n\\binom{m}{2}$ generators corresponding to commutators of type 4. This gives $$\\mathrm{rank}(A) = \\binom{n+1}{3} + (2m+1)\\binom{n}{2}+n\\binom{m+1}{2}.$$\n\nAs for $B$, the argument is similar: we get no commutators of type 1, all commutators of type 5 (of which there are $\\binom{m}{3}+2\\binom{m}{2}$); all commutators of type 2 (of which there are $m\\binom{n}{2}$); we also get all of type 4, which gives $nm^2$ commutators; as for type 3, these cannot occur from expressions of the form $[b,y_j]$ with $b\\in F_2\/F_3$. So the rank of $B$ will be $$\\mathrm{rank}(B) = \\binom{m+1}{3}+\\binom{m}{2} + m\\binom{n}{2} + nm^2.$$\n\nFinally, for the overlap: according to the Witt formula, the rank of $F_3\/F_4$ is $$\\frac{1}{3}(n+m)\\left( (n+m)^2 - 1\\right).$$ So this allows you to compute the rank of the overlap.\n\nFor larger values of $k$ the computations become more difficult, because not all basic commutators are of the form $[c,x_i]$ or $[c,y_j]$. But this should give you an idea of the kind of thing that is going on (and why I don't want to try doing this for $k=3$).\n\n-\nOh, thank you for your kind answer. My $A$ means not a subgroup generated by $n$ element with some fixed $a_i$'s, but the one generated by all elements of that form $[x_i,a_i]$ where $a_i$'s range over $F_k\/ F_{k+1}$. so, $A$ doesn't depend on the choice of $a_i$. sorry to give confusion. \u2013\u00a0 qkqh May 30 '13 at 9:00\n@qkqh: That's lousy notation, then. You are really looking at $\\langle [F_k,x_1],\\ldots,[F_k,x_n]\\rangle\\bmod F_{k+2}$, and similarly for $B$. I'll have to think about it. \u2013\u00a0 Arturo Magidin May 30 '13 at 14:55\nThank you for your deep considering and editing my deficient questions. It seems to have small mistakes. In my thought, for $A$, there are $2n\\binom{m}{2}$ commutators of type 4, and $B$ has $m\\binom{n}{2}$ commutators of type 3, so \\begin{eqnarray*} \\textrm{rank}(B) &=& \\binom{m+1}{3} + \\binom{m}{2} + 2m\\binom{n}{2} + nm^2 \\\\ &=& \\binom{m+1}{3} + (2n+1)\\binom{m}{2} + mn^2 \\end{eqnarray*} Am I right? \u2013\u00a0 qkqh Jun 9 '13 at 15:01\n@qkqh: I'm wrong in type $4$ (there's no factor of $\\frac{1}{2}$, but how do you get $2n\\binom{m}{2}$ commutators of type 4? You choose two indices between $1$ and $m$ for the $y$s, which gives $\\binom{m}{2}$; then you choose the index for $x$, which has $n$ possibilities. For this choice, we get the generator $[y_t,x_k,y_s][y_s,x_k,y_t]^{-1}$. So it's only $n\\binom{m}{2}$. And I do not see how you get any commutators of type 3 in $B$ at all. \u2013\u00a0 Arturo Magidin Jun 9 '13 at 19:57\nYes, you are right. I have wanted that rank$(A)$ and rank$(B)$ are symmetric (i.e. by changing $n$ and $m$, we get the other), and now it's right. Thank you \u2013\u00a0 qkqh Jun 11 '13 at 3:17\n\nNot necessarily. By the Jacobi Identity, in $F\/F_4$ we have for example\n\n$[x_1,[x_2,y_1]][x_2,[y_1,x_1] = [y_1,[x_1,x_2]]^{-1}$.\n\nFor your second question, the rank of $A$ is clearly at most $n$. For $k=2$, you could choose $a_i=x_i$, so it could be anything between 0 and $n$. For $k>2$, the relation above shows that it can be strictly less than $n$. It is possible that there is some lower bound in this case.\n\n-\nThank you, I understand the first answer. And sorry, too. \u2013\u00a0 qkqh May 30 '13 at 9:03\nI have edit my definition of $A$ and $B$. \u2013\u00a0 qkqh May 30 '13 at 9:10","date":"2015-10-10 03:48:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.961814284324646, \"perplexity\": 184.9939170646429}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-40\/segments\/1443737940789.96\/warc\/CC-MAIN-20151001221900-00078-ip-10-137-6-227.ec2.internal.warc.gz\"}"}
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Dallas County, Iowa Records
Dallas County, Iowa Courthouse Records
Dallas County, Iowa Census Records
Dallas County, Iowa Vital Records
Dallas County, Iowa Resources
Dallas County, Iowa External Links
Dallas County, Iowa (Map It) was created on January 13, 1846 (Organized in March 1, 1847) from Unorganized Territory. Dallas County was named in honor of George Mifflin Dallas(1792–1864), the eleventh vice president of the United States
Dallas County is bordered by Boone County (north), Polk County (east), Madison County (south), Guthrie County (west), Greene County (northwest).
Dallas County Cities and Towns include Adel, Bouton, Clive , Dallas Center, Dawson, De Soto, Dexter, Granger, Grimes , Linden, Minburn, Perry, Redfield, Urbandale , Van Meter, Waukee, West Des Moines , Woodward.
A Dallas County, Iowa County and City Maps contains detailed information about roads and boundaries, these maps may include rural communities, churches, and cemeteries.
Dallas County, IA Courthouse
The Dallas County Courthouse is located in Adel, Iowa. Dallas County was attached to Polk County and Mahaska County for a breif time prior to organization March 1, 1847. Some early records may be found there. Learn More About State of Iowa Court, Tax, Land and Probate Records.
The following dates indicates what vital, land, probate, and court records are in Dallas county. The date listed for each record is usually the earliest registration filed. The date does not indicate that there are alot records for that year and does not mean that all such events were actually filed with the clerk.
Dallas County Recorder's Office has Birth / Death Records from 1880, has Marriage Records from 1847 and has Land Records from 1850. he County Recorder's Office maintains official records of documents affecting title to real estate. Every real estate transaction that takes place begins in the Recorder's Office. One of the major duties of the office is the management of public records. As a result, accuracy and preservation of records are a must in the Recorder's Office. In addition to real estate transactions, the Recorder's Office issues titles and liens; records veterans discharge papers; processes passport applications; accepts marriage applications and issues the subsequent license; issues certified copies of birth, death and marriage records as well as other numerous duties.
Dallas County Clerk of Court has Probate Records from 1851and has Court Records from 1855. The County Clerk of Court manages and maintains all trial court records, including pleadings, evidence and orders. The clerks of court have hundreds of administrative duties. They accept and process fines, fees and court costs owed to the state, child support checks, and civil judgments owed to litigants. They maintain a record of liens on all real estate in the county. Clerks help with involuntary hospitalization cases. They have the authority to dispose of scheduled violations which are not contested and do not require a court hearing. Clerks are also responsible for informing state and local government agencies of court orders.
Dallas County Tax Assessor is responsible for assess and appraise all real estate and personal property, to have access to all public records of the county for the purpose of securing information pertaining to accurate listings of taxable property.
U.S. Federal Population Schedules: 1850, 1860, 1870, 1880 (free index), 1890 (fragmented), 1900, 1910, 1920, 1930, 1940
Dallas County Genealogical Society, P.O. Box 264, Dallas Center 50063-0246
Dallas County, Iowa Message Boards
Dallas County, Iowa Books - Amazon
Iowa Genealogical Society Publications for Dallas County
Dallas Co., Iowa - FindaGrave
Dallas County, Iowa Links - Cyndi's List
Dallas Co. IAGenweb
Dallas County, Iowa Ancestry Database Collections
Dallas County, Iowa Military Records
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Q: Oracle count (*) is taking too much time I was trying to fetch the count(*) from the table, which has almost 7 million records and it taking more than an hour for returning the result.
Also the table has 153 columns out of which index has been created for column 123, so tried to run the following query in parallel, but it didn't help.
select /*+ parallel (5) */ count(123) from <table_name>
Please suggest if there is alternative way.
When I ran desc on the table in Toad, the index tab holds the value of no. of rows. Any idea how that value is getting updated there?
A: A few issues to mention:
*
*For "select count(*) from table" to use an index, the indexed column must be non-nullable, or the index must be a bitmap type.
*If there are known to be no nulls in the column but there is no not null constraint on it, then use "select count(*) from table where column_name is not null".
*It does of course have to be more efficient to scan the index than the table, but with so many table columns you're probably fine there.
*If you really want a parallel index scan, use the parallel_index hint, not parallel. But with only 7 million rows you might not find any need for parallelism.
*You need to check the execution plan to see if an index and/or parallel query is in use.
*If you can use an estimated number of rows then consider using the sample clause: for example "select 1000*count(*) from table sample(0.1)"
A: Counting the number of rows of large table takes long time. It's natural. Some DBMS stores the number of records, however, this kinds of DBMS limits concurrency. It should lock the entire table before DML operation on the table. (The entire table lock is necessary to update the count properly.)
The value in ALL_TABLES.NUM_ROWS (or USER_TABLES.NUM_ROWS) is just a statistical information generated by analyze table ... or dbms_stats.gather_table_stats procedure. It's not accurate, not real-time information.
If you don't need the exact number of rows, you can use the statistical information. However you shouldn't depend on it. It's used by Oracle optimizer, but shouldn't in application program.
I'm not sure why you have to count the number of rows of the table. If you need it in the batch program which is run infrequently, you can partition the table to increase the parallelism. If you need the count in online program, you should find a way not to use the count.
A: select /*+ parallel (5) */
Seems like odd number for degree of parallelism. Well, obvious 5 is an odd number, and that is strange. The DoPs ought to be a power multiple of two (see below for more).
Anyway, do you have a reason for using parallel query? Do you have at least five spare processors? If not, there is a good chance the overhead of managing the PQ slaves is at least contributing to the poor performance.
Why should DOP = n*2? There is an established heuristic based on Queuing Theory that running more than two batch jobs simultaneously leads to degraded performance. Find out more. (I think queuing theory actually recommends a figure of 1.8, but as database jobs are often bound by I/O or disk we can usually get away with 2.)
I originally said "power of 2" but that's mainly because multi-core servers tend to have a number of CPUs which is a power of 2, but multiple of 2 is more accurate, because some boxes have 12 CPUs or some other number.
Now, if we have a 64 core box, a DOP of 5 or 37 is fine, because we have enough CPUs to run that many threads simultaneously. But if we have got a small quadcore box, only 2, 4 or 8 makes sense, because those are the only values which will ensure an even distribution of work across all four processors. Running five threads on a quadcore box means one CPU will be doing a lot more work than the other three; there is a possibility that it will take longer to finish, leaving the other three slaves waiting. So DOP=5 can actually lead to a greater elapsed time than DOP=4.
DOP=n*2 is only a rule of thumb, and not set in stone. However, it is based on sound reasoning, and we should know why we're doing something different. Obviously, we should have conducted some experiments to confirm that we have chosen the right DOP (whatever value we settle on).
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Q: Parsing Paypal Response with javascript Paypal is returning the following two http responses (one success and one failure). I sure could use some help figuring out how to parse them using javascript? So, I need to pull out ACK= "Success" (or "Failure" and "Date". THANKS!
SUCCESS:
{"result":{"uuid":"6bd97902-33fd-70d8-8a30-cebd03756d38","status":200,"headers":{"Connection":"close","Content-Length":"104","Content-Type":"text/plain; charset=utf-8","Date":"Thu, 13 Mar 2014 20:08:56 GMT","Server":"Apache"},"text":"TIMESTAMP=2014%2d03%2d13T20%3a08%3a56Z&CORRELATIONID=4ed210495e962&ACK=Success&VERSION=93&BUILD=10030158","buffer":[84,73,77,69,83,84,65,77,80,61,50,48,49,52,37,50,100,48,51,37,50,100,49,51,84,50,48,37,51,97,48,56,37,51,97,53,54,90,38,67,79,82,82,69,76,65,84,73,79,78,73,68,61,52,101,100,50,49,48,52,57,53,101,57,54,50,38,65,67,75,61,83,117,99,99,101,115,115,38,86,69,82,83,73,79,78,61,57,51,38,66,85,73,76,68,61,49,48,48,51,48,49,53,56],"cookies":{}}}
AND Failure
{"result":{"uuid":"022f4f52-8caf-deae-fd7b-94daf0d787ad","status":200,"headers":{"Connection":"close","Content-Length":"359","Content-Type":"text/plain; charset=utf-8","Date":"Thu, 13 Mar 2014 19:23:12 GMT","Server":"Apache"},"text":"TIMESTAMP=2014%2d03%2d13T19%3a23%3a12Z&CORRELATIONID=ca98a083b004e&ACK=Failure&VERSION=93&BUILD=10030158&L_ERRORCODE0=10314&L_SHORTMESSAGE0=Masspay%20input%20parse%20error&L_LONGMESSAGE0=The%20input%20to%20the%20masspay%20server%20is%20incorrect%2e%20Please%20make%20sure%20that%20you%20are%20using%20a%20correctly%20formatted%20input%2e&L_SEVERITYCODE0=Error","buffer":[84,73,77,69,83,84,65,77,80,61,50,48,49,52,37,50,100,48,51,37,50,100,49,51,84,49,57,37,51,97,50,51,37,51,97,49,50,90,38,67,79,82,82,69,76,65,84,73,79,78,73,68,61,99,97,57,56,97,48,56,51,98,48,48,52,101,38,65,67,75,61,70,97,105,108,117,114,101,38,86,69,82,83,73,79,78,61,57,51,38,66,85,73,76,68,61,49,48,48,51,48,49,53,56,38,76,95,69,82,82,79,82,67,79,68,69,48,61,49,48,51,49,52,38,76,95,83,72,79,82,84,77,69,83,83,65,71,69,48,61,77,97,115,115,112,97,121,37,50,48,105,110,112,117,116,37,50,48,112,97,114,115,101,37,50,48,101,114,114,111,114,38,76,95,76,79,78,71,77,69,83,83,65,71,69,48,61,84,104,101,37,50,48,105,110,112,117,116,37,50,48,116,111,37,50,48,116,104,101,37,50,48,109,97,115,115,112,97,121,37,50,48,115,101,114,118,101,114,37,50,48,105,115,37,50,48,105,110,99,111,114,114,101,99,116,37,50,101,37,50,48,80,108,101,97,115,101,37,50,48,109,97,107,101,37,50,48,115,117,114,101,37,50,48,116,104,97,116,37,50,48,121,111,117,37,50,48,97,114,101,37,50,48,117,115,105,110,103,37,50,48,97,37,50,48,99,111,114,114,101,99,116,108,121,37,50,48,102,111,114,109,97,116,116,101,100,37,50,48,105,110,112,117,116,37,50,101,38,76,95,83,69,86,69,82,73,84,89,67,79,68,69,48,61,69,114,114,111,114],"cookies":{}}}
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|
Q: Troouble in inserting value in database using php I have a DB (using phpmyadmin). I want to enter data in the master table but the problem is I want to take the details from the user in two different HTML pages.
If I am able to store data from htmlpage1 into the DB the next HTML page doesn't store any data.
I have tried;
1 - using where command in the second page. no help.
2 - tried to save data into variables and store all the data together when I have it from htmlpage2 as well.
NOTE:
HTML page 1 has a submit button "register"
HTML page 2 has a submit button "submit"
here is the code.;
<?php
session_start();
$enrollment = "";
$username = "";
$email = "";
$password = "";
$fathername = "";
$dateofbirth = "";
$course = "";
$contact = "";
$gender = "";
$address = "";
$city = "";
$state = "";
$country = "";
$tenth = "";
$twth = "";
$ug = "";
$pg = "";
$phd = "";
$sem1 = "";
$sem2 = "";
$sem3 = "";
$sem4 = "";
$train1 = "";
$train2 = "";
$ts1 = "";
$ts2 = "";
$ts3 = "";
$errors = array();
$db= mysqli_connect('localhost','root', '', 'spaarc');
if (isset($_POST['register'])){
$enrollment = mysqli_real_escape_string($db, $_POST['enrollment']);
$username = mysqli_real_escape_string($db, $_POST['sname']);
$email = mysqli_real_escape_string($db, $_POST['email']);
$password = mysqli_real_escape_string($db, $_POST['password']);
$fathername = mysqli_real_escape_string($db, $_POST['fname']);
$dateofbirth = mysqli_real_escape_string($db, $_POST['dob']);
$course = mysqli_real_escape_string($db, $_POST['course']);
$contact = mysqli_real_escape_string($db, $_POST['contact']);
$gender = mysqli_real_escape_string($db, $_POST['gender']);
$address = mysqli_real_escape_string($db, $_POST['address']);
$city = mysqli_real_escape_string($db, $_POST['city']);
$pin = mysqli_real_escape_string($db, $_POST['pincode']);
$state = mysqli_real_escape_string($db, $_POST['state']);
$country = mysqli_real_escape_string($db, $_POST['country']);
if (empty($username)){
array_push($errors, "Username is required");
}
if (empty($email)){
array_push($errors, "Email is required");
}
if (empty($password)){
array_push($errors, "Password is required");
}
}
if (isset($_POST['submit'])){
$tenth = mysqli_real_escape_string($db, $_POST['ClassX_Percentage']);
$twth = mysqli_real_escape_string($db, $_POST['ClassXII_Percentage']);
$ug = mysqli_real_escape_string($db, $_POST['Graduation_Percentage']);
$pg = mysqli_real_escape_string($db, $_POST['Masters_Percentage']);
$phd = mysqli_real_escape_string($db, $_POST['PhD_Percentage']);
$sem1 = mysqli_real_escape_string($db, $_POST['topic1']);
$sem2 = mysqli_real_escape_string($db, $_POST['topic2']);
$sem3 = mysqli_real_escape_string($db, $_POST['topic3']);
$sem4 = mysqli_real_escape_string($db, $_POST['topic4']);
$train1 = mysqli_real_escape_string($db, $_POST['train1']);
$train2 = mysqli_real_escape_string($db, $_POST['train2']);
$ts1 = mysqli_real_escape_string($db, $_POST['sub']);
$ts2 = mysqli_real_escape_string($db, $_POST['prog']);
$ts3 = mysqli_real_escape_string($db, $_POST['cer']);
if (empty($ts1)){
array_push($errors, "ts is required");
}
if (empty($ts2)){
array_push($errors, "ts is required");
}
if (empty($ts3)){
array_push($errors, "ts is required");
}
if (count($errors)==0){
$password = md5($password);
$sql="INSERT INTO studetails (enrollment, name, email, password, fname, dob, course, contact, gender, address, city, pin, state, country, tenth, twth, ug, pg, phd, sem1, sem2, sem3, sem4, train1, train2, ts1, ts2, ts3) VALUES ('$enrollment','$username', '$email', '$password','$fathername','$dateofbirth','$course','$contact','$gender','$address','$city','$pin','$state','$country','$tenth','$twth','$ug','$pg','$phd','$sem1','$sem2','$sem3','$sem4','$train1','$train1','$ts1','$ts2','$ts3')";
mysqli_query($db, $sql);
$_SESSION['sname'] = $username;
$_SESSION['success'] = "You are now logged in";
header('location: preview.php');
}
}
?>
NOTE:
$enrollment = "";
$username = "";
$email = "";
$password = "";
$fathername = "";
$dateofbirth = "";
$course = "";
$contact = "";
$gender = "";
$address = "";
$city = "";
$state = "";
$country = "";
this is to be stored from HTML page1
and the rest from HTML page2
And what values in the DB should accept NULL in this condition??
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| 2,516
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Fabrizio Pinelli (born 4 March 1985 in Torino) is an Italian footballer. He currently plays for F.C. Canavese.
References
F.C. Canavese players
1985 births
Living people
Association football goalkeepers
Italian footballers
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{"url":"http:\/\/citizendia.org\/Surface_area","text":"Surface area is the measure of how much exposed area an object has. Area is a Quantity expressing the two- Dimensional size of a defined part of a Surface, typically a region bounded by a closed Curve. It is expressed in square units. If an object has flat faces, its surface area can be calculated by adding together the areas of its faces. In Geometry, a face of a Polyhedron is any of the Polygons that make up its boundaries Even objects with smooth surfaces, such as spheres, have surface area.\n\n## Formulas\n\nSphere: The surface area of a sphere is the integral of infinitesimal circular rings of width dx\nThe radius of the circular ring is $f(x) = \\sqrt{r^2-x^2}$. \"Globose\" redirects here See also Globose nucleus. A sphere (from Greek \u03c3\u03c6\u03b1\u03af\u03c1\u03b1 - sphaira, \"globe The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space The length of the circular ring is equal to $2\\pi\\cdot f(x)$\nThe width of the ring can be determined by using Pythagoras' formula for a rectangular triangle with side lengths dx and $f'(x) \\cdot dx$, which leads to $\\sqrt{1+f'(x)^2}\\,dx$\nThe infinitesimal surface area of the circular ring thus is equal to $2\\pi f(x)\\cdot \\sqrt{1+f'(x)^2}\\,dx$\nThe derivative of f(x) is equal to $f'(x) = \\frac{-x}{\\sqrt{r^2-x^2}}$\nThe surface area of the sphere can be calculated as\n\n$\\int_{-r}^r 2\\pi f(x)\\cdot \\sqrt{1+f'(x)^2}\\,dx$ = $\\int_{-r}^r 2\\pi \\sqrt{r^2-x^2} \\cdot \\sqrt(1+\\frac{x^2}{r^2-x^2})\\,dx = \\int_{-r}^r 2\\pi \\sqrt {r^2}\\,dx = 2\\pi r \\int_{-r}^r 1\\,dx$\n\nThe antiderivative needed is the simple linear function x\nThus, the sphere surface area amounts to\n\nAsphere = $2\\pi r[r-(-r)] = 4\\pi r^2 \\ \\!$\n\n## Surfaces whose area cannot be defined\n\nWhile areas of many simple surfaces have been known since antiquity, a rigorous mathematical definition of area requires a lot of care. \"Pythagoras of Samos\" redirects here For the Samian statuary of the same name see Pythagoras (sculptor. In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change In Calculus, an antiderivative, primitive or indefinite integral of a function f is a function F whose Derivative Various approaches to defining the surface area were developed in the late nineteenth and the early twentieth century by Henri Lebesgue and Hermann Minkowski. Henri L\u00e9on Lebesgue le\u0254\u0303 l\u0259\u02c8b\u025bg ( June 28, 1875, Beauvais &ndash July 26, 1941, Paris) was a French Hermann Minkowski ( June 22 1864 \u2013 January 12 1909) was a Russian born German Mathematician, of Jewish For a very wide class of geometric surfaces called piecewise-smooth all these approaches result in the same notion of area. However, if a surface is very irregular, or rough, then it may not be possible to assign any area at all to it. A typical example is given by a surface with spikes spread throughout in a dense fashion. Many surfaces of this type occur in the theory of fractals. A fractal is generally \"a rough or fragmented geometric shape that can be split into parts each of which is (at least approximately a reduced-size copy of the whole\" Extensions of the notion of area which partially fulfill its function and may be defined even for very badly irregular surfaces are studied in the geometric measure theory. In Mathematics, geometric measure theory ( GMT) is the study of the geometric properties of the measures of sets (typically in A specific example of such an extension is the Minkowski content of a surface. The Minkowski content of a set or the boundary measure, is a basic concept in Geometry and Measure theory which generalizes to arbitrary\n\n## In chemistry\n\nSurface area is important in chemical kinetics. Chemical kinetics, also known as reaction kinetics is the study of rates of chemical processes Increasing the surface area of a substance generally increases the rate of a chemical reaction. The reaction rate or rate of reaction for a Reactant or product in a particular reaction is intuitively defined as how fast a reaction takes A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called For example, iron in a fine powder will combust, while in solid blocks it is stable enough to use in structures. Iron (\u02c8\u0430\u026a\u025an is a Chemical element with the symbol Fe (ferrum and Atomic number 26 Combustion or burning is a complex sequence of Exothermic chemical reactions between a Fuel and an Oxidant accompanied by the production of For different applications a minimal or maximal surface area may be desired.\n\n## In biology\n\nThe surface area-to-volume ratio (SA:V) of a cell imposes upper limits on size, as the volume increases much faster than does the surface area, thus limiting the rate at which substances diffuse from the interior across the cell membrane to interstitial spaces or to other cells. The cell is the structural and functional unit of all known living Organisms It is the smallest unit of an organism that is classified as living and is often called The cell membrane (also called the plasma membrane, plasmalemma, or \"phospholipid bilayer\" is a Selectively permeable Lipid bilayer If you consider the math, you'll see the relation between SA and V much more intuitively: V = 4\/3 \u03c0 r3; SA = 4 \u03c0 r2, where r is the radius of the cell. Do the math and the resulting ratio becomes 3\/r. If a cell has a radius of 1 \u03bcm, the SA:V ratio is 3. Increase the cell's radius to 10 \u03bcm and the SA:V ratio becomes 0. 3. With a cell radius of 100, SA:V ratio is 0. 03. Using the previous simple example, we can see how the surface area falls off steeply with increasing volume.","date":"2013-05-21 01:39:55","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 9, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.786415696144104, \"perplexity\": 541.6916596439578}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368699632815\/warc\/CC-MAIN-20130516102032-00027-ip-10-60-113-184.ec2.internal.warc.gz\"}"}
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Kennel Cough in dogs is similar to the common cold in humans and is considered to be one of the most common canine diseases across the world.
It can be caused by several different bacteria or viruses, usually in a combination of two or more.
Easily transmitted, generally fairly mild in terms of symptoms and usually the 'patient' recovers within ten to fourteen days.
Treatment often isn't necessary, but if secondary infection sets in then antibiotics might be prescribed by your veterinarian.
Kennel Cough is also more formally known as 'Tracheobronchitis' , or, more commonly, as 'Bordatella' because the bacteria that is responsible for many, many cases of Kennel Cough is the Bordatella Bronchiseptica virus.
What Causes Kennel Cough in Dogs?
Your dog could 'catch' Kennel Cough by being infected with one, or often more, of several different different viruses or bacteria.
Many others are thought to play a role in some cases, including the Distemper virus, Staphylococcus (Staph), Streptococcus (Strep) and E-coli, to name a few.
As with most illnesses, if your dogs' immune system is already weak (ie by another disease or age), or if it is immature (as with puppies) the chances of catching Kennel Cough are increased.
Kennel Cough is very easily transmitted from dog to dog.
It's about as easy to pass Kennel Cough from dog to dog as it is for the common cold to pass from one person to another.
It can travel through the air (in droplets spread by coughing, sneezing or just breathing).
The viruses/bacteria can also be transmitted through direct contact with sick dogs (face to face, licking etc.) or with objects that have been touched by those same sick dogs.
People can also carry the virus or bacteria on their hands and clothing and pass it between dogs.
Toys, bedding, hard surfaces, water bowls... they're all potential sources of contamination.
Because of how easily Kennel Cough spreads, environments where there are a lot of dogs are often hot-beds for infection and can spark a mini epidemic.
These can include boarding kennels, large-scale dog breeding operations, doggie day care facilities, dog pounds, rescue organizations and other similar establishments.
Puppies or dogs who have made a full recovery from Kennel Cough are still considered to be infectious for up to three months as the virus is still being shed from their bodies.
Although the viral causes of Canine Kennel Cough can't be transmitted to humans, some of the bacterial ones can.
Including Bordatella Bronchoseptica , Staphylococcus (Staph), Streptococcus (Strep) and more.
Not surprisingly, the most noticeable symptom of Kennel Cough is... a cough!
And this particular cough is pretty easy to recognize.
It's a dry, honking, snorting, hacking sort of cough.
In children, the cough caused by the Croup virus is a dry, barking type of cough due to the inflammation of the trachea and bronchial tubes.
Severe coughing 'fits' which end in gagging, retching and gasping are common.
Kennel Cough causes the same inflammation in dogs and results in a similar type of cough and 'fits'. Quite distinctive.
Other symptoms might be seen as well, the exact combination depends on which combination of virus/bacteria has causes the illness.
Symptoms usually appear sometime within 2 - 14 days of exposure to the the bacteria/virus.
If you think your dog may have Kennel Cough, always have him examined by your veterinarian.
Other conditions also have a cough as an early symptom and you need a firm diagnosis.
Your veterinarian may want to prescribe an antibiotic as a preventative measure (to prevent secondary infections from developing), and if your dog is very young, has another health condition or is a senior this can be important.
Even given that list of symptoms, most dogs don't really seem, or act, too sick.
Again with the analogy to the human common cold. You might feel 'yukky' but you can function normally and go about your daily business.
Most dogs are the same way with Kennel Cough.
They may seem a little 'under the weather' (and obviously have that distressing cough) but they shouldn't appear to be really sick.
Sometimes the virus/bacteria will develop into a secondary infection which can lead to serious problems if not recognized and treated.
Symptoms of a worsening infection might include coughing up mucus, extreme lethargy, refusal to eat, continuous fever, difficulty breathing, thickening mucus discharge from eyes/nose etc.
If you see any of these, or Fido seems to be feeling really unwell, then get him examined by your veterinarian right away. He may need additional help.
As with many other canine illnesses, some dogs can catch Kennel Cough and be contagious, without showing any symptoms. They're basically silent 'carriers' of the disease.
Because Kennel Cough in dogs is usually a self-limiting disease (ie dogs will generally recover by themselves within two weeks), treatment isn't always needed.
'Supportive care' can be given at home and is pretty straightforward.
Plenty of rest, extra fluids and a nutritious diet will help him fight off the infection.
Avoid strenuous exercise, lots of excitement/stress, or smoky/dusty environments because these can trigger coughing fits.
If you're walking your dog, try to use a harness instead of a collar as putting pressure on his throat/trachea can also get that cough all riled up.
If it's really cold outdoors, keep your dog inside as much as possible because the cold is likely to trigger his coughing.
But, just as if we catch a cold we may end up with an ear infection, chest infection, pneumonia etc., a dog with Kennel Cough may develop similar secondary infections.
Pneumonia is a the most dangerous potential problem and it can be very dangerous, even fatal.
Secondary infections often need to be treated with antibiotics to prevent serious problems.
There are a couple of antibiotics that are usually used to treat Kennel Cough infections.
This combination results in medications like Clavamox and Clavulox.
A blend of these two antibiotics is usually much more effective than giving straight Amoxycillin because many bacteria are now becoming immune to this common medication.
Popular antibiotics which are especially effective against Bordatella and mycoplasma.
These can include plain Doxycycline as well as Vibramycin or VibraVet.
When combined, these two types of antibiotic are effective in killing many of the bacteria found in dogs with Kennel Cough.
In some cases they can be more effective than the Amoxycillin blend.
There are other antibiotics that your vet may prescribe based on your individual dogs' infection, general health and so on.
These can include Baytril (Enrofloxacin), Gentamicin, Chloramphenicol and more.
Sometimes your vet may feel prescribing other medications such as a cough-suppressant, bronchodilator or steroid to help relieve inflammation and other symptoms.
Don't give Fido anything NOT prescribed/recommended by your vet!
Please don't ever give your dog antibiotics, cough medicine or any other medication that you or another family member or pet has been prescribed.
Each case is unique and people medicine often isn't suitable (or is downright dangerous) for dogs.
There are some things you can do at home to help Fido if he has Kennel Cough.
I wouldn't recommend using home remedies and natural treatments instead of mainstream veterinary care and medications (if prescribed).
But natural, homeopathic or herbal remedies for Kennel Cough can be a great addition to other treatments, or used alone if your vet feels that Fido doesn't need prescription meds.
Natural remedies can be used to relieve symptoms of upper respiratory tract infections, such as coughing and sneezing.
They can also help boost your dogs' immune system so that he's better able to fight off the virus/bacteria.
The perfect 'cold remedy' for dogs & cats.
Designed to calm bronchial irritation, reduce congestion and make breathing easier.
Unique blend of five scientifically selected natural ingredients.
100% homeopathic. Safe, effective, non-addictive.
Gentle, natural blend of herbal ingredients designed to soothe and support your dogs' upper respiratory tract.
Also helps to break up mucus and relieve congestion.
Boosts immune function to help Fido feel better, faster.
A natural organic, herbal remedy.
Fights infection, is anti-microbial and boosts the immune system.
It helps to reduced coughing, relieve congestion and help your dogs' body fight the bacteria and viruses that are making him sick.
* NOT to be take if your dog has been prescribed Baytril or an anti-viral medication.
Essential oils have some wonderful properties and can be effective in so many ways.
I found a natural aromatherapy blend which was designed specifically to soothe a dogs' cough, ease breathing and boost immunity... it's also antibacterial and antiviral.
Check out Aromadog Cough Drop and you'll see what I mean.
There are a few things you can do to help your dog feel better, and recover from his bout of Kennel Cough.
It's important to keep Fido well-hydrated as this helps his body flush out the virus and bacteria that are making him sick.
Extra fluids can also prevent him from getting dehydrated, which is a dangerous condition all on it's own.
But when your pooch doesn't feel that great it can be tricky to get him to drink enough, let alone extra.
Adding a little warm low-sodium chicken broth to his kibble will encourage your dog to gobble it up.
The broth will smell good and taste good (and if he's congested his senses of smell and taste may be dulled) so he's going to enjoy that.
If you don't have any broth on hand, even soaking his dry kibble in warm water for 10 minutes before feeding it to him will release aroma and flavor, and add some valuable fluids to his meal.
Canned food contains a much higher percentage of water than dry kibble does.
It's not as nutritionally dense and I don't recommend it as a regular diet for any other than very tiny dogs, senior dogs or those with health problems that make eating dry dog food difficult or unwise.
However, pretty much all dogs love this type of food and adding some of it to Fidos' mealtimes will encourage him to eat and increase his fluid intake.
Just be aware that you will have to 'wean him off' this once he's 100% healthy again!
When my kids were young and would have a bout of Croup (a human virus that produces similar symptoms to Kennel Cough), I'd sit in the bathroom with the shower running full blast to ease the irritation in their chests.
This works well for dogs too.
The warm, moist steam soothes and reduces inflammation while thinning mucus and dilating bronchial tubes.
Setting up a humidifier in the room/s where he spends most of his time can achieve something similar (although for acute coughing episodes the steamy shower is far more effective) and is a more long-term solution.
If you don't have enough humidifiers, setting a bowl of water near radiators, air vents or other sources of heat will help moisten the air in any room.
Coconut oil has so many amazing benefits, and one of them is its' anti-viral properties.
Try adding two teaspoons of Coconut Oil per 10lbs of body weight to his food daily.
It will likely improve his willingness to eat and help his body fight the virus/es that are making him sick.
Honey has a whole host of health-inducing properties!
It's anti-viral, anti-bacterial, anti-microbial, anti-inflammatory... and it's soothing and tastes good too.
Adding one teaspoon of honey to your dogs' food daily will help his immune system and soothe his irritated throat.
There's nothing to stop you using both Coconut Oil and Honey.
Because there are several viruses and bacteria that can cause Kennel Cough in dogs (either separately or in combination), there are at least two vaccinations that your pup needs to be protected.
These are the Bordatella vaccine and the Canine Adenovirus-2 (CAV-2) vaccine.
The CAV-2 vaccines is one of the CORE puppy shots recommended by the American Animal Hospital Associaion.
The Bordatella vaccine is highly recommended if your pup is to be spending time in an environment where there are lots of other dogs.
Many veterinarians' recommend it even if this isn't the case, simply because Kennel Cough is SO easily transmitted and so common.
Vaccinating your puppy and being meticulous about keeping those vaccinations up to date is the very best way to keep Fido safe.
While the Canine Adenovirus-2 vaccine is always given as an injection, the Bordatella vaccine can be given either as an injection, or as intra-nasal drops. Or both.
Veterinary studies have shown that the intra-nasal delivery provides better immunity within the respiratory tract, provides that immunity quickly (often within 72 hours), only needs to be administered once, and can be given to puppies as young as 3 - 4 weeks.
The injection needs to be given twice. The first between 6 and 8 weeks of age, and the second one three weeks later.
Protection doesn't start until around 10 - 14 days after the second shot.
However the shots do provide stronger immunity in other areas of the body.
Some veterinarians recommend both types of vaccination for puppies and dogs who are at high risk of contracting Kennel Cough (especially in pound/rescue/kennel situations).
Also, dogs in high-risk environments may need to be vaccinated every six months rather than annually.
Some puppies may show mild signs of a Kennel Cough infection after being vaccinated with the intra-nasal form of the vaccine.
These symptoms might last for two or three days, and your puppy/dog may be able to spread a very mild form of disease during this time. He/she will recover fully within the same period of time.
Don't be too worried about this, I've never personally had any issues stemming from this, and the intra-nasal delivery is the most popular and veterinary recommended method.
I have my puppies and dogs vaccinated intra-nasally and have always been happy with that, having not had any pup/dog catch kennel cough (and we do use boarding kennels from time to time and attend classes and dog events too).
The choice is one that is something best discussed with your own vet and taking into account your own situation and plans for your pooch.
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Also, it had been shown that TGF-and simply by modulating laminin receptor 37/67 dependent regulation of cardiac performance signaling pathway (13)
August 14, 2021 Mia Hayes
Also, it had been shown that TGF-and simply by modulating laminin receptor 37/67 dependent regulation of cardiac performance signaling pathway (13). on the usage of biomolecules, such as for example angiotensin II and changing development factor-it was as effectual as widely used chemical substance compound 5-azacytidine and much more effective than various other biomolecules, for instance, IGF-1, bFGF, dynorphin B, insulin or oxytocin (11). As opposed to angiotensin II, TGF-by intramyocardial transplantation of differentiated rat bone tissue marrow mesenchymal stem cells in to the wounded rat center (12). Also, it had been proven that TGF-and by modulating laminin receptor 37/67 reliant legislation of cardiac functionality signaling pathway (13). Nevertheless, to our greatest knowledge, a lot of the research investigated the consequences of the biomolecules on the gene and protein amounts but few investigated other pivotal procedures, such as for example epigenetic or metabolic alterations. In this scholarly study, the potential of angiotensin II and TGF-and and expands the data of individual amniotic fluid-derived mesenchymal stem cells efficiency at the original levels of induced differentiation. Components and Methods Individual amniotic liquid mesenchymal stem cells isolation and cultivation Amniotic liquid mesenchymal stem cells had been isolated from amniocentesis examples from second-trimester amniotic liquid obtained from healthful women who required prenatal diagnostics but no SU 5205 hereditary abnormalities had been detected (protocols accepted by the Ethics Committee of Biomedical Analysis of Vilnius Region, No 158200-123-428-122). A two-stage process was utilized as previously defined (2). Preferred and isolated cells had been preserved in the development moderate AmnioMAX-C100 basal with Amnio-MAX-C100 dietary supplement (Gibco, Thermo Fisher Scientific, NY, USA), 100 U/ml penicillin and 100 is normally a binary picture, which contains just centers of fluorescent dots proclaimed as one white pixels. Wilcoxon rank amount test was utilized to check the hypothesis over the equality of medians of two examples. Statistical need for changes SU 5205 between examples was provided over Tukey-style container plots. Extracellular flux evaluation Full of energy profile of differentiated and control cells was driven using Seahorse XFp Extracellular Flux Analyzer and Cell Energy Phenotype Test Package (Agilent Technology, CA, USA). Mitochondrial respiration was assessed using Cell Mito Tension Test Kit. Air consumption price (OCR) and extracellular acidification price (ECAR) had been measured simultaneously, without inhibitors from the electron transfer string (oligomycin first of all, FCCP, rotenone and antimycin A) C the baseline, and following the addition from the above-mentioned inhibitors then. Following the measurements, cells had been gathered and lysed using RIPA buffer (150 mM NaCl, 10 mM EDTA, pH 8.0, 10 mM Tris, pH 7.4, 0.1% SDS, 1% deoxycholate, 1% NP-40 in PBS, pH 7.6). Total protein concentrations had been assessed using DC Protein Assay (BioRad Laboratories, CA, USA) and spectrophotometer Infinite M200 Pro (Tecan, Switzerland). In every computations, OCR and ECAR beliefs had been normalized to the quantity of protein in each well and portrayed per (Fig. 1C) as established using RT-qPCR. Open up in another screen Fig. 1 Characterization of individual AF-MSCs. (A) The normal spindle-shaped morphology of individual Alox5 amniotic fluid-derived mesenchymal stem cells, cultivated in cell lifestyle. Scale club=400 so that as dependant on RT-qPCR. Data, relative to GAPDH, are presented as meanSD (n=3). Assessment of alterations during the induced cardiomyogenic differentiation Cardiomyogenic differentiation was induced with two concentrations of angiotensin II and two concentrations of TGF-and C regulating the expression of structural and functional genes of cardiomyocytes was assessed. SU 5205 As shown in Fig. 2B and Supplementary tables, obtained from STRING database, NKX2-5 interacts with other TFs TBX5 and GATA4 forming the network of transcription factors that cooperate with MYH6 (as well as of was upregulated in AF-MSCs induced.
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Titan Trust Bank completes takeover of Union Bank
Union Bank Plc on Thursday said it had completed its core investors' sale of a majority shareholding to Titan Trust Bank Ltd., a subsidiary of TGI Group.
In a statement signed by Somuyiwa Sonubi, the bank's company Secretary, made available to the Nigerian Exchange Ltd., in Lagos, the bank said there was a board change that resulted to the resignation of directors.
This, it added, subsequently led to retirement of the directors from its Board, while others new ones were appointed.
The statement said, "Union Bank hereby notifies Nigerian Exchange Limited (NGX), the Securities & Exchange Commission and members of the public of the completion of the transaction under the Share Sale and Purchase Agreement (SSPA)."
It said it effectively transferred 93.41per cent of Union Bank's issued share capital to TTB.
It added that the transaction followed Union Bank's notification in December 2021 of the execution of the SSPA between the bank's majority shareholders – Union Global Partners Ltd., Atlas Mara Ltd, et al. – and Titan Trust Bank Ltd. (TTB).
"Consequently, in compliance with NGX, Rulebook and the Amendments to the Listing Rules, Union Bank hereby notifies NGX, our esteemed stakeholders and the investing public of the following.
"Union Bank, hereby, notifies NGX that with the completion of the transaction, TGI Group, parent of TTB, now becomes the majority shareholder and core investor in Union Bank.
"Union Bank, hereby, notifies NGX of the completion of the divestment of the Bank's entire shareholding interest (direct and indirect) in its subsidiary, Union Bank (UK) Plc ("UBUK"), to all the shareholders in the Bank's records as of March 4, pro rata to their existing shareholding interests in the Bank.
"Consequently, UBUK is not included in the transaction with Titan Trust Bank," said the statement.
The bank also notified the NGX of retirement of directors, the Chief Executive Officer, Mr Emeka Okonkwo, with effective from June 2.
Other directors that retired included: Mrs Beatrice Hamza Bassey, Chairman/Non-Executive Director; Mrs Obafunke Alade-Adeyefa, Independent Non-Executive Director; Mr Richard Burrett, Non-Executive Director and Mr Ian Clyne, Non-Executive Director.
Others are: Mr Kenroy Dowers, Non-Executive Director; Mr Paul Kokoricha, Non-Executive Director; Mr Taimoor Labib, Non-Executive Director; Mr Mark Patterson, Non-Executive Director; and Mr Emeka Ogbechie Non-Executive Director.
The bank also appointed Mr Mudassir Amray as the Chief Executive Officer, and Mr Farouk Mohammed Gumel as the bank's Chairman effective June 2.
According to the bank, Amray is a seasoned banker with over 25 years in senior management roles.
Prior to being appointed the Chief Executive Officer for Union Bank, Amray led the establishment of Titan Trust Bank and subsequently became the Bank's pioneer CEO in October 2019.
He holds an MBA from the University of Santo Tomas and a Bachelor of Commerce from National College, University of Karachi.
Aldo, Gumel is Group Executive Director for TGI Group. He is also the Chairman, Board of Directors at Wacot Rice Ltd., a subsidiary of TGI Group, and Non, Executive Chairman at the Nigeria Sovereign Investment Authority (NSIA).
Prior to joining TGI, Gumel was a Partner at PwC and Head of the West African Advisory/Consulting business, covering Nigeria, Ghana, Liberia, Sierra Leone, and Angola.
Gumel holds a BSc. in Materials Technology (Leather) from the University of Northampton and an MSc, in Clean Technology from Newcastle University.
He is also a chartered accountant with the Institute of Chartered Accountants of Nigeria and a Fellow of the Institute of Chartered Accountants in England and Wales.
Other new appointments to the board include: Mr Andrew Ojei, Non-Executive Director; Alhaji Abubakar Mohammed, Non-Executive Director; and Mr Lawrence Mackombo, Non-Executive Director.
Commenting on behalf of the outgoing Directors, erstwhile Chairman of the Board, Mrs Bassey, said the bank reached a significant milestone with the completion of the transaction between its core shareholders and Titan Trust Bank.
"As is normal for transactions such as this, the current board and CEO Mr Emeka Okonkwo retired and handed over the reins of the bank to a new Board and to Mr Mudassir Amray as CEO.
"The entire Board congratulates the parties on this landmark transaction.
It has been a privilege and honor to have chaired and served on the Board that oversaw the preservation and transformation of one of Nigeria's most iconic institutions.
"I extend my heartfelt gratitude to Mr Okonkwo, the Management team and entire Staff of the bank as well as the retiring directors for their diligent and committed service over the years.
"I am also grateful for the trust that our minority investors placed in us for managing and running the bank.
Titan Trust Bank
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"Spend, Spend, Spend" is the 12th episode of seventh season of the British BBC anthology TV series Play for Today. The episode was a television play that was originally broadcast on 15 March 1977. "Spend, Spend, Spend" was written by Jack Rosenthal, directed by John Goldschmidt, produced by Graeme McDonald, and starred Susan Littler and John Duttine.
"Spend, Spend, Spend" is based on the book of the same name by Nicholson and Stephen Smith and recounts Nicholson's life story from the 1950s to the early 1970s in a non-linear fashion.
Development
Rosenthal was a colleague of the PR man who, on behalf of Littlewoods Pools, persuaded Nicholson to allow publicity for her pools win. He wrote in his autobiography: "From that day on, I followed her wild, seemingly stupid adventures in the papers - and believed every snide, snooty, biased word the relentless publicity said. All adding up to one word - that she was a cow." Being given Nicholson's book by director John Goldschmidt caused Rosenthal to reassess his attitude and "become a fan" eager to put across an explanation of her behaviour.
Critical response
The production won the British Academy Television Awards for Best Single Play and Royal Television Society's Writer's Award 1977.
Home media
The work was released on DVD as part of Jack Rosenthal at the BBC by Acorn media in 2011, alongside other works for television written by Rosenthal.
References
External links
Spend Spend, Spend at the TV Cream website
1977 British television episodes
1977 television plays
British television plays
Play for Today
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{
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Alexander Berntsson (born 30 March 1996) is a Swedish footballer who plays for Halmstads BK as a defender.
References
External links
1996 births
Living people
Association football defenders
Halmstads BK players
Swedish footballers
Allsvenskan players
Superettan players
Sweden youth international footballers
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require('../modules/web.timers');
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\section{Introduction}
Centaurus A (NGC 5128, hereafter Cen A) is a nearby elliptical galaxy and the prototypical
Faranoff-Riley Class I source with spectacular twin radio lobes extending out to $\sim$ 4$\degr$
($\sim$ 250 kpc) from the nucleus (see Israel 1998 for an excellent review). The morphology as well as
a bimodal metallicity distribution of the globular cluster population indicate the galaxy has
experienced a major merger event in the past (perhaps as recently as 1.6 $\times$ 10$^{8}$ yr ago;
Quillen et al. 1993). On nuclear scales, evidence for a central super massive black hole (SMBH) comes
from variable x-ray and radio observations. Estimates of the black hole mass by Silge et al. (2005),
Marconi et al. (2006), and Haring-Neumayer et al. (2006) suggest it to be $\sim$10$^{8}$ M$_{\sun}$.
Despite intensive studies of Cen A, observations at UV and optical wavelengths have been especially
hampered by the dust lane that bisects the galaxy and heavily obscures the nuclear regions.
Additionally, unified theories of AGN (Krolik \& Begelman 1988; Antonucci 1993: Urry \& Padovani 1995),
suggest the central SMBH is obscured from our line-of-sight by a geometrically and optically thick
torus of gas and dust that further extinguishes radiation arising from accretion onto the SMBH. High
spatial resolution mid-IR observations now available with 8m class telescopes such as Gemini offer an
ideal way to study the obscured central region of Cen A, having extinction 25-75 times lower than
observations at optical wavelengths. High spatial resolution mid-IR imaging of other nearby AGNs (e.g.
Radomski et al. 2002, 2003, 2003b; Packham et al. 2005, Soifer et al. 2000, 2001, 2003; Perlman et al.
2001, Mason et al. 2007, Alonso-Herrero et al. 2006) highlight the value of such observations in
separating and modeling emission from nuclear star formation regions, the torus, and dusty narrow
emission line regions.
Previous mid-IR observations of Cen A have produced somewhat contradictory
results. Thus, the true nature and extent of the nuclear emission remains controversial. Observations
by Whysong \& Antonucci (2004) on the Keck I detected an unresolved nucleus at 11.7$\micron$ and
17.75$\micron$ at resolutions of $\sim$ 0$\farcs$3 and 0$\farcs$5 respectively, placing limits of 5.6pc
and 8.85pc on the size of the mid-IR emitting region. However, Karovska et al. (2003) (hereafter K03)
claim to resolve the nucleus of Cen A based on 8.8$\micron$ and N-band imaging with the Magellan 6.5m
telescope, calculating a size of 0$\farcs$17 $\pm$ 0$\farcs$02 or 3pc after subtracting a PSF in
quadrature. Further observations by Siebenmorgen, Kr{\"u}gel, \& Spoon (2004) with a resolution of
$\sim$ 0$\farcs$5 were unable to directly resolve the nucleus at 10.4$\micron$, but showed that the
growth curve indicated weak extended emission over 2$\arcsec$ with a surface brightness a factor of ten
lower than the peak of the nucleus. Most recently, observations by Hardcastle, Kraft, and Worrall
(2006) (herein HKW06) find the nuclear FWHM of Cen A to be slightly resolved calculating a conservative
upper limit of 0$\farcs$27 or $\leq$ 4.6pc at N-band ($\lambda$$_0$ = 10.4$\micron$). If the nucleus of
Cen A is resolved, this could be the first galaxy in which the emission from dust associated with the
torus has been resolved with single-telescope mid-IR observations. In order to address the controversy
of the central nuclear resolution of Cen A, we have methodically observed Cen A and corresponding
calibration sources at high-resolution in the mid-IR to (1) test the hypothesis that the nucleus is
resolved and (2) characterize the mid-IR emission mechanisms. In addition, we draw upon publicly
accessible archived observations in the mid-IR in addition to our own data to further explore low-level
extended emission surrounding the nucleus of Cen A. Our observations are discussed in $\S$ 2 while
results and analysis are presented in $\S$ 3 and $\S$ 4 respectively. Throughout this paper we assume a
distance to Cen A of D= 3.5 Mpc (1$\arcsec$=17pc).
\section{Observations and Data Reduction}
Observations of Cen A were made over two epochs. Epoch A occurred on 2004 January 28 and 29 (UT) and
was initiated by the authors of this paper. Epoch B was observed on 2004 March 6, 11, and 12 and was
retrieved from the Gemini Science Archive (GSA) based on data first published by HKW06. Both sets of
data were obtained using the facility mid-IR camera/spectrograph T-ReCS (Telesco et al. 1998) on the
Gemini South telescope. T-ReCS uses a Raytheon 320 x 240 pixel Si:As IBC array, providing a plate scale
of 0$\farcs$089 pixel$^{-1}$, corresponding to a field of view of 28$\farcs$5 x 21$\farcs$4. The
detector was read out in correlated quadruple sampling (CQS) mode (Sako et al 2003). The standard
chop-nod technique was used to remove time-variable sky background, telescope thermal emission, and the
so-called ``1/f" detector noise. The chop throw was 15$\arcsec$ and the telescope was nodded every 30
sec. All data were reduced using IDL.
\subsection{Epoch A 2004 January 28 and 29}
We carefully observed Cen A over a period of two nights. Images were obtained in the Si-2
($\lambda$$_0$ = 8.74$\mu$m, $\Delta$$\lambda$ = 0.78$\micron$) and Qa ($\lambda$$_0$ = 18.3$\micron$,
$\Delta$$\lambda$ = 1.5$\micron$) filters to optimize resolution and sensitivity in both the 10 and
20$\micron$ atmospheric windows. The chop and nod direction was fixed at 0$\degr$ (North-South). The
first night we observed at 8.8$\micron$ for about 3.5 hours real-time
(real-time$\sim$3.5$\times$on-source time due to chop-nod procedure, not including time for telescope
slewing and calibration) using an iterative procedure which repeatedly interleaved observations of a
point spread function (PSF) star (65 sec on-source) with those of Cen A (455 sec on-source). This
resulted in a total of 5 PSF observations (5.4 min on-source total) and 5 galaxy observations (34 min
on-source total). We used the same procedure on the second night at 18.3$\micron$; however, the initial
PSF star had too low a S/N ratio so a new PSF was chosen resulting in only 3 high S/N PSF measurements
(3.3 min on-source total). A total of 4 galaxy observations (26.4 min on-source total) at 18.3$\micron$
were obtained. Estimates of the FWHM of the galaxy and PSF were done by fitting a Moffat function
(Moffat 1969).
The stars PPM318494 and PPM291667, located 1.5$\degr$ and 4.2$\degr$ from Cen
A, were used for PSF comparison to look for extended emission in the galaxy.
Each of the PSF observations was made immediately prior to or
after the Cen A observations and using an identical observational setup to accurately sample the
delivered image quality of those observations. PSF images were not rotated to correct for changes in
the pupil due to the small rotation angle of the pupil between observations of the galaxy and PSF
(typically $<$ 6$\degr$). This was done to avoid the slight smoothing of the FWHM that occurs when an
image is digitally rotated to correct for pupil rotation. Line cuts taken at similar pupil angles on
the galaxy justify this. These showed the profiles to be radially symmetric hence an azimuthally
averaged FWHM was adequate for investigating any resolved emission in the nucleus of Cen A.
Observations of HD110458 were used for flux calibration through both Si-2 and Qa filters at a similar
airmass as the Cen A observations. Absolute calibration was achieved using the TIMMI2 photometric
standard list where the flux densities of HD 110458 at 8.8 $\micron$ and 18.3 $\micron$ are 6.95 Jy and
1.72 Jy respectively. Observations of HD110458 and Cen A at 8.8 $\micron$ show variations of $\lesssim
5$\%. At 18.3 $\micron$ only one observation of the flux calibrator was taken. However, observations of
the relative flux of Cen A at 18.3 $\micron$ showed variations of $\sim$ 25\%.
The differences in the intrinsic spectra of the stellar sources and Cen A as observed through the Si-2
and Qa filters requires a color correction. This color correction not only affects the observed fluxes
but also the FWHM. A stellar spectra peaking at shorter wavelengths (T$\sim$4000K) will dominate the
shorter wavelength portion of the filter. A cooler source such as Cen A (T$\sim$200K) will peak at
longer wavelengths and dominate the longer wavelength portion of the filter. The resultant effect will
not only alter the flux calibration but also cause the FWHM of ``hot" stellar sources to be smaller
than the relatively ``cool" Cen A when observed through the same filter. This effect is significant in
large bandpass mid-IR filters such as N-band ($\lambda$$_0$ = 10.4$\mu$m, $\Delta$$\lambda$ =
5.3$\micron$). The difference between a T$\sim$4000K and T$\sim$200K source in the N-band will result
in a color correction of the observed flux density up to 21\% and the observed FWHM of the stellar
source will appear 12\% smaller. Due to the relatively small bandwith of the Si-2 and Qa filters
($\Delta$$\lambda$ = 0.78 and 1.5$\micron$) this effect is much smaller. The color correction between a
T$\sim$4000K and T$\sim$200K source is $<$ 4\% and the difference in the FWHM is $<$ 0.05\%, both
within the errors of our observations.
\subsection{Epoch B 2004 March 6, 11, and 12}
Epoch B data were first published by HKW06 and was retrieved from the GSA after its proprietary period
to compare with our observations. Images were obtained in the N-band ($\lambda$$_0$ = 10.4$\mu$m,
$\Delta$$\lambda$ = 5.3$\micron$) over the nights of 2004 March 6, 11, and 12. The chop angle was
121$\degr$ and the instrument position angle was set at 172$\degr$. The nucleus was positioned in the
corner of the array in order to concentrate on possible extended mid-IR emission along the synchrotron
jet emanating from the AGN. On March 6th HD110458 was observed for a PSF and flux calibrator (43 sec
on-source) followed by 6 successive observations of Cen A (each 825 sec on-source) for a total
on-source time of 82.5 minutes on the galaxy. On the following night March 11th, Cen A was observed
twice (each observation 825 sec on-source) followed by a PSF and calibrator star HD 108903 (36 sec
on-source). The same observation sequence was repeated on March 12th.
\section{Results}
In both Epoch A and B we detect low-level extended mid-IR emission near the nucleus of Cen A at
8.8$\micron$, N-band, and 18.3$\micron$. Using multiple observations of the AGN and nearby stellar
targets in Epoch A we determine the central nucleus of Cen A to be unresolved at both 8.8$\micron$ and
18.3$\micron$ and place firm limits on the size based on the FWHM. We make a distinction between the
unresolved nucleus and the surrounding emission and discuss both separately in $\S$ 3.1 and $\S$ 3.2,
followed by analysis of the source of such emission in $\S$ 4.
\subsection{The Central Nucleus}
Figure 1 shows the FWHM of the
nucleus of Cen A and corresponding PSFs over time. Observations of the galaxy were split up into
nod-sets to match the same integration times of the PSF for careful comparison (65 sec on-source at
8.8$\micron$ and 109 sec on-source at 18.3$\micron$). The overall decrease in FWHM in the 8.8$\micron$
plot corresponds to the lower airmass through the observations as well as an improvement in seeing
throughout the night. A similar plot is shown for 18.3$\micron$ in Figure 1 also. Though there is some
variation in the FWHM, the bright nucleus of Cen A is unresolved. Figure 2 shows azimuthally averaged
radial profiles of the total coadded Cen A data at 8.8$\micron$ and 18.3$\micron$ in comparison to
coadd of all the PSF observations at each wavelength. Given the 3$\sigma$ variation of the PSF it is
clear the bright nucleus of Cen A is unresolved at both wavelengths. Neither the extension claimed by
K03 nor by HKW06 is detected. In the case of K03 it was noted that several hours passed between galaxy
and PSF observations while HKW06 compared individual galaxy exposures of 825 sec on-source with a
single short 43 sec on-source observation of the PSF. As can be seen in Figure 1, the PSF and galaxy
vary significantly over time with changes in seeing and airmass, highlighting the potential dangers in
comparing a single, short PSF measurement to a set of longer galaxy observations.
We agree with the observations of Whysong \& Antonucci (2004) that the nucleus of Cen A is unresolved,
though with multiple PSF observations we are able to place a tighter statistical constraint of the size
of the bright mid-IR nucleus. Following the analysis of Soifer et al. (2000) and Packham et al. (2005),
we suggest that any nuclear extensions would be readily detected at 3 times the standard deviation of
the PSF standard. For our 8.8$\micron$ data the median size of the PSF $\theta$$_{PSF}$=0.3$\arcsec$,
3$\sigma$=0$\farcs$057 ($\theta$$_{sd}$) which excludes the first PSF observation taken under poor
seeing and high airmass that is not representative of the group. For our 18.3$\micron$ data median size
of the PSF $\theta$$_{PSF}$=0.53$\arcsec$, 3$\sigma$=0$\farcs$039 ($\theta$$_{sd}$), based on all 3 PSF
observations. The maximum angular extension $(\theta_{max})$ is defined
\begin{equation}
\theta^{2}_{max} = \theta^{2}_{tot} - \theta^{2}_{PSF}
\end{equation}
\noindent where $\theta$$^{2}_{tot}$ is ($\theta$$_{PSF}$ + $\theta$$_{sd}$)$^{2}$. Thus, any bright
nuclear extended emission must occur on scales $<$0$\farcs$19 ($\lesssim$3.2pc) at 8.8$\micron$ and
$<$0$\farcs$21 ($\lesssim$3.5pc) at 18.3$\micron$ at the level of the FWHM.
\subsection{The Extended Emission}
Although the mid-IR nucleus of Cen A is unresolved when compared to the FWHM of corresponding PSFs
there is clear evidence of surrounding low-level extended emission detected in both Epoch A and B. This
mid-IR emission is faint and only becomes apparent after a 10 pixel (0.89$\arcsec$) gaussian smooth is
applied. Figure 3 clearly shows this emission at 8.8$\micron$ and 18.3$\micron$ from Epoch A overlaid
on Pa-$\alpha$ emission observed by Marconi et al. (2000). Similar structure to that at 8.8$\micron$ is
seen in N-band data from Epoch B (Figure 4). This emission has no effect on the FWHM of the central
nucleus and could not have been the cause of previous detections of a ``resolved" nucleus by K03 or
HKW06. It also is too faint, $>$ 250$\times$ fainter than the peak at both 8.8$\micron$ and N-band of
the 10 pixel smoothed image, to be associated with the 2$\arcsec$ extended emission claimed by
Siebenmorgen et al. (2004) which was only at a level of 1/10th the peak at 10.4$\micron$ (Figure 5).
Low-level extended mid-IR emission is known to exist near the nucleus of Cen A. Observations using the
Infrared Space Observatory (ISO) by Mirabel et al. (1999) and most recently Spitzer observations by
Quillen et al. (2006; 2006b) show the nucleus is surrounded by a dusty warped disk. Observations in
this paper however represent to date the highest resolution mid-IR images that clearly detect this
emission surrounding the nucleus. Analysis of this emission however is limited due to the chop throw of
15$\arcsec$ which results in some chopping onto emission, compromising detailed examination of the flux
and morphological parameters. Though a minor effect with respect to the bright nucleus, the faint
extended emission does show some evidence of negative chop regions. However, the similar mid-IR
structure of this emission at 8.8$\micron$ and N-band despite chopping onto different regions would
seem to show that much of the structure observed is real. In addition the correspondence of the mid-IR
with emission regions of Pa-$\alpha$ detected by Schreier et al. (1998) and Marconi et al. (2000)
reinforces that in fact what we see are primarily real structures (Figures 3 and 4).
\section{Analysis: Sources of emission}
In this section we discuss the possible origins of the mid-IR emission of both the bright unresolved
central nucleus and the low-level extended emission. Due to the the contamination from chopping onto
nearby emission, the analysis of the low-level extended emission is presented in a broad overview.
Additional imaging data resulting in a more detailed analysis of this emission will be put forth by
Leeuw et al. (in preparation).
\subsection{The Nucleus}
\subsubsection{Nucleus: Stellar Activity}
Starburst activity in the nucleus of Cen A has been modeled by Alexander et al. (1999), who fit the
nuclear ($<$ 4$\arcsec$) IR flux $\leq$ 60$\micron$ with approximately equal parts dusty torus and
starburst emission. However, their nuclear starburst component depends strongly on fitting the
11.3$\micron$ PAH feature from Mirabel et al. (1999) that is not seen in the higher spatial resolution
($\sim$ 3$\arcsec$) Siebenmorgen et al. (2004) data. In addition, estimates of the high intrinsic
polarization from near-IR observations by Packham et al. (1996) and Capetti et al. (2000) on order of
11\% to 17\% are consistent with optically thin scattering from a compact torus surrounding the central
engine rather than a starburst.
Combining our data with bolometric luminosity measurements, we can evaluate the likely contribution of
a starburst using a ``luminosity density" analysis similar to that by Soifer et al. (2000, 2001, 2003)
and Evans et al. (2003). They have calculated the surface brightnesses from infrared luminous AGN and
starburst galaxies. This was done by measuring the size or upper limit of the mid-IR size of a compact
region and assuming that this mid-IR region is representative of the infrared emitting region as a
whole. Using the total IR luminosity as an approximation of the bolometric luminosity in these galaxies
and assuming it originates from this region resulted in an estimate of the luminosity density. In
general, they found that galactic HII regions have surface brightnesses ranging from 2 $\times$
10$^{11}$ to 2 $\times$ 10$^{12}$ L$_{\sun}$ kpc$^{-2}$, starburst galaxies range from 2 $\times$
10$^{11}$ to 10$^{13}$ L$_{\sun}$ kpc$^{-2}$, while ULIRGS typically range from 2 $\times$ 10$^{12}$ to
6 $\times$ 10$^{13}$ L$_{\sun}$ kpc$^{-2}$. On small scales ($\leq$ 10 pc) Meurer et al. (1997) found
that star clusters may have a global (UV, IR, and radio) surface brightness as high as 5 $\times$
10$^{13}$ L$_{\sun}$ kpc$^{-2}$. Soifer et al. (2003) found in three Seyferts surface brightnesses on
order of a few times 10$^{14}$ L$_{\sun}$ kpc$^{-2}$, which they argued must be primarily AGN emission,
being well above the luminosity density of bright star clusters and starbursts.
Based on our observations we measure a mid-IR luminosity of the nucleus of Cen A of 1.8 $\times$
10$^{8}$ L$_{\sun}$. This value is similar to the 1.5 $\times$ 10$^{8}$ L$_{\sun}$ value of Whysong \&
Antonucci (2004) based on their 11.7$\micron$ measurement and represents a lower limit to the total
luminosity. Assuming a normal quasar SED Whysong \& Antonucci (2004) estimate the bolometric luminosity
of the AGN to be $\sim$ 2.5 $\times$ 10$^{9}$ L$_{\sun}$. This is similar to the value calculated by
Israel (1998) and within a factor of $\sim$ 2 quoted by Marconi et al. (2001). Given the lower
estimated bolometric luminosity and our maximum size limit of 3.5pc from our 18.3$\micron$ observations
we calculate a luminosity density for Cen A of 2.8 $\times$ 10$^{14}$ L$_{\sun}$ kpc$^{-2}$. These
values are similar to those found by Soifer et al. (2003) for Seyferts in which starburst activity was
considered negligible in regions with a luminosity density $>$ 10$^{14}$ L$_{\sun}$ kpc$^{-2}$. Even a
bright star cluster as suggested by Meurer et al. (1997) (5 $\times$ 10$^{13}$ L$_{\sun}$ kpc$^{-2}$)
could only contribute $<$ 18\% to the overall luminosity density. Thus, this general analysis in
addition to the lack of PAH emission detected by Siebenmorgen et al. (2004) and the strong polarization
observations obtained by Packham et al. (1996) and Capetti et al. (2000) indicate that any starburst
activity in the nucleus of Cen A is negligible compared to the emission from the AGN.
\subsubsection{Nucleus: Narrow Line Region (NLR) Dust} In order to explore the possibility
of central heating of a dusty NLR we calculate color temperatures from the ratio of our 8.8 $\micron$
and 18.3 $\micron$ fluxes (see Radomski et al. 2003). Based on this ratio we calculate a temperature of
the nucleus of $\sim$ 210 K. A similar temperature is obtained if we use the ratio of fluxes at 11.7
$\micron$ and 17.75 $\micron$ from Whysong \& Antonucci (2004). This value is slightly higher than the
$\sim$ 160 K calculated by K03 based on their single 8.8$\micron$ flux. However, we can achieve
approximately the same temperature using their formula for our 8.8$\micron$ measurement so the
difference is entirely due to the calculation method. Taking into account extinction from the dust lane
across Cen A as proposed by K03 of $\tau$ $\sim$ 1 at 10 $\micron$ raises the color temperature by only
20 K to 230 K.
We derive an approximation of the dust grain properties using the methodology applied to NGC 4151
(Radomski et al. 2003) and Circinus (Packham et al. 2005). Assuming a simple uniform dust distribution,
a first-order determination of the size of the region that could be heated by a central source can be
made. Given that dust grains primarily absorb UV-optical radiation and re-emit in the infrared, the
equilibrium temperature of dust in a strong UV field is given by (Sellgren et al. 1983)
\begin{equation}
T\sim \left( \frac{L_{UV}}{16\pi R^{2}\sigma }\frac{Q_{UV}}{Q_{IR}}\right) ^{1/4}
\end{equation}
In the above equation, T is the dust temperature, $L_{UV}$ is the approximate UV-optical luminosity of
the central source, $R$ is the radius from the source in parsecs, $\sigma $ is the Stefan-Boltzman
constant, and $Q_{UV}/Q_{IR}$ is the ratio of the Planck averaged UV absorption coefficient to the
infrared emission coefficient. Values of $Q_{UV}/Q_{IR}$ are dependent on the dust grain size and
composition and are given by Draine \& Lee (1984), Laor \& Draine (1993), and Weingartner \& Draine
(2001) for graphite and ``smoothed astronomical'' (SA) silicate.
Using the bolometric luminosity of 2.5 $\times$ 10$^{9}$ L$_{\sun}$ as an estimate and a dust
temperature of 200 K, Cen A could heat NLR dust similar to that in Circinus and NGC 4151
(0.003-0.01$\micron$ silicate; 0.015-0.04$\micron$ graphite) up to a radial distance of 9 - 14pc
($\sim$0$\farcs$5 - 0$\farcs$8) from the the central engine. This is much larger than the maximum size
of the unresolved mid-IR nucleus (0$\farcs$21; 3.5 pc diameter) and shows that the central AGN is
capable of heating all the dust in the core. With these observations it is difficult to determine how
much of this unresolved emission may be distributed between a compact NLR and torus. However, if we
assume a similar scenario as in NGC 4151 then the NLR may only contribute $\sim$ 10-20\% of the mid-IR
emission (Radomski et al. 2003; Groves, Dopita, \& Sutherland 2006).
\subsubsection{Nucleus: Dusty Torus} The maximum size we obtain for the mid-IR
emission from dust associated with a compact geometrically and optically thick torus at the level of
the FWHM is $<$0$\farcs$19 ($\lesssim$3.2pc) at 8.8$\micron$ and $<$0$\farcs$21 ($\lesssim$3.5pc) at
18.3$\micron$. This is consistent with observations at K-band (2.2$\micron$) FWHM $<$ 0.2$\arcsec$
($<$3.4pc) (Schreier et al. 1998) as well as the polarization observations of Capetti et al. (2000),
which suggest scattering off a 2pc disk. It is also close to the 4.07pc x 3.05pc (scaled to 3.5 Mpc)
torus modeled by Alexander et al. (1999), although as discussed above their starburst fit may not be
accurate if there is no nuclear PAH emission.
Applying the recent models of Nenkova et al. (2002), we in fact predict that the mid-IR emission of the
Cen A torus is unresolvable in the present observations. These models are far more robust than our
earlier calculations of dust in the relatively optically thin NLR, taking into account radiative
transfer and cloud shadowing necessary in the optically thick environment of a torus. In these models
the inner radius of the torus scales with the square root of the AGN luminosity and inversely with
temperature to the 5/2 power. At the dust sublimation temperature (1200 K), the inner radius of the
Cen A torus may be only 0.07 pc. While the outer edge of the torus may be large ($\sim 5$ pc), in these
inhomogeneous torus models the cloud distribution declines rapidly ($\propto r^{-q}$, where $q = 1$, 2,
or 3). Thus, most of the clouds are strongly concentrated within the inner parsec (Figure 6). Also
though the hottest dust has $T =1200 $K, the contributions of the many cooler indirectly-heated clouds
are significant, and the net spectrum of the clumpy torus appears much cooler. For the models
presented above, $F_\nu$ peaks around 25 $\mu$m, with the color temperature of the
8.8$\micron$/18.3$\micron$ flux density ratio indicating $T\approx 200$K.
The model mid-IR emission does not always trace the cloud distribution. Because of the large optical
depths through the densest regions of the torus, the heating and subsequent emission can be suppressed
in the torus midplane. These effects are strongest at shorter wavelengths and for less compact cloud
distributions, where the strongest observable emission extends along the torus axis. In such
instances, some hot, luminous material (on the projected front or rear of the torus) is not completely
obscured. We modeled a range of torus parameters, which include the radial distribution, $q$, the
optical depth per cloud measured in the $V$ band, $\tau_V$, and the total number of clouds through the
equatorial plane, $N_C$. We show the results for a model that fits the observed 10$\micron$ nuclear
spectrum of NGC 1068 well (Mason et al. 2006), with $q = 2$ and $N_C = 8$, and a comparison model in
which $q = 1$ and $N_C = 5$. In both models, $\tau_V = 40$, the outer radius is 30 times the dust
sublimation radius, and the cloud distribution is gaussian in elevation above the torus mid-plane,
without a sharp cutoff. These two sets of parameters yield cloud distributions and images that are
characteristic of the full parameter space we explored.
The torus is viewed edge-on in the simulated images at 8.8 and 18.3$\micron$ (Figure 6). The
18.3$\micron$ emission generally traces the cloud distribution because optical depth effects are not
significant, both for heating the clouds and their subsequent emission. Directly-heated clouds that
are not blocked along the line of sight dominate the emission at 8.8$\micron$. The resulting images
are extended perpendicular to the cloud distribution, and in the less compact ($q=1$) distribution,
this extension persists on larger scales. The exact emission profile does depend on the model
parameters, but in all cases the strong extended emission (which the FWHM of the simulated images
themselves indicates) is confined to scales of $0\farcs02$. In the simulations, the flux declines to
10\% of the peak strength on scales of $0\farcs08$ or less. In general, the emission is more compact in
the steeper cloud distributions, and it is always much smaller than the $0\farcs2$ upper limit we
measure in the data. This approaches the scales of HST STIS observations of Marconi et al. (2006) which
indicate the central dark object in Cen A is no more than 0$\farcs$036-0$\farcs$04 (0.6-0.7pc) in
radius. Thus, careful interferometry will be required to resolve this structure.
\subsubsection{Nucleus: Synchrotron Emission}
As in the case of M87 (Perlman et al. 2001), the powerful radio jet of Cen A could provide a
significant fraction of the mid-IR emission through synchrotron radiation. Chiaberge et al. (2001)
claim the entire nuclear SED of Cen A can be fit with a synchrotron self-Compton (SSC) model. Also
recent mid-IR interferometry models by Meisenheimer et al. (2007) suggest a tiny predominantly SSC core
($<$0.2pc). They model that the SSC core contributes between 80-60\% of the emission between 8 and 13
$\micron$ respectively. However there are several problems with this scenario.
First, the lack of polarization at $\sim$ 1000$\micron$ (Packham et al. 1996) is difficult to
reconcile with a predominantly synchrotron core. Second, Meisenheimer et al. (2007) reference the
variability seen at L-band ($\sim$3.5$\micron$) by Lepine et al. (1984) detailing an increase in flux
by a factor of 5 between 1971-1981 as evidence of the variable synchrotron nature of the IR core. If
the mid-IR core is dominated by synchrotron emission then similar variability should be seen at $\sim$
10$\micron$. However mid-IR (10$\micron$) measurements taken coincident with the L-band observations
(Becklin et al. 1971, Kleinmann et al. 1974, Grasdalen et al. 1976) seem inconsistent with variability
trends seen at X-ray and radio wavelengths (Beall et al. 1978; Abraham et al. 1982). Indeed Telesco
(1978) comparing mid-IR (10$\micron$) observations from 1971-1978 concluded that there was no evidence
of mid-IR variability during this period. Comparing mid-IR observations taken from 1984 to 2004 also
show no significant variation at $\sim$10$\micron$ after accounting for filter and calibration
differences (Alexander et al. 1999; Mirabel et al. 1999; Krabbe et al. 2001; Siebenmorgen et al. 2004;
Karovska et al. 2003; Weedman et al. 2005; Hardcastle et al. 2006; this paper). And finally, the
fluxes measured by Meisenheimer et al. (2007) for the SSC core at 11.4$\micron$ are a factor of $\sim$
4 smaller that the unresolved core measured by Whysong \& Antonucci (2004) at 11.7$\micron$. Given that
the high spatial resolution Siebenmorgen et al. (2004) spectra show no PAH emission it is unlikely that
this could affect the flux. Thus at least at the longer portion of the 10$\micron$ window it appears
that there is ample excess emission possibly from a torus that could dominate the mid-IR on scales $<$
0$\farcs$3.
Another method to estimate the synchrotron emission in the nucleus of Cen A is to use a simple power
law model such as that used for M87 (Perlman et al. 2001). A strong linear correlation between the
optical and radio core values of FR I galaxies found by Chiaberge, Capetti, and Celotti (1999) hinted
at a common synchrotron origin for this emission. Capetti et al. (2000) used this correlation and the
radio core flux of Cen A of 9.1 Jy at 15GHz (Clarke, Burns, \& Norman 1992) to predict the synchrotron
emission at 2$\micron$ of 10mJy. This trend also follows closely with the synchrotron models of HKW06
which fit the non-nuclear ``inner", ``middle" and ``outer" lobes of the radio jet in Cen A. Assuming
this trend and a radio core flux of 9.1Jy we predict a nonthermal mid-IR flux density between 8 and
18$\micron$ of 30 to 50mJy; more than an order of magnitude less than what is measured. This may
indicate that synchrotron emission in the nucleus of Cen A is negligible in the mid-IR in comparison to
emission from dust.
\subsection{The Extended Emission}
\subsubsection{Extended: Stellar Activity}
The nucleus of Cen A is most likely dominated by the AGN, however much of the surrounding extended
emission is likely due to stars. The close correspondence between much of this emission
$\gtrsim$5$\arcsec$ from the nucleus at 8.8$\micron$ and N-band and the Pa-$\alpha$ data from Marconi
et al. (2000) (Figures 3 and 4) indicate much of what we are seeing is associated with regions of star
formation. The same has been seen in other extragalactic star forming regions by Alonso-Herrero et al.
(2006). In general, these clumps as well as much of the emission outline the twin parallel lanes of
emission seen as part of the large scale warped disk in the lower resolution Spitzer mid-IR data
(Quillen et al. 2006; Figure 1). At 8.8$\micron$ and N-band the Pa-$\alpha$ clumps C, D, E, F, and G
seen by Schreier et al. (1998) are all detected along the direction of the top lane of emission seen by
Spitzer. Along the bottom lane only the Pa-$\alpha$ clump K is detected. Several other mid-IR sources
of emission associated with regions of Pa-$\alpha$ emission are also obvious in Figures 3 and 4. At
18.3$\micron$ little evidence of this emission is seen. This is most likely due to two reasons: (1) the
lower sensitivity of the 18$\micron$ (Qa) filter and (2) star formation regions typically have a PAH
component at 8.6$\micron$ and 11.3$\micron$ which is readily detected in the 8.8$\micron$ and N-band
filters. However, at both 8.8$\micron$ and N-band some Pa-$\alpha$ clumps are devoid of mid-IR
emission. Unfortunately this may be due to the limited chop throw (15$\arcsec$) of the data discussed
previously which is certainly chopping onto other regions of low level emission creating negative areas
in the field of view. Thus extensive analysis of theses star formation regions is not feasible at this
time. However, there is an overall good correspondence between the Pa-$\alpha$ and mid-IR.
\subsubsection{Extended: Narrow Line Region (NLR) Dust}
Although the nucleus can be heated entirely by the AGN it is unlikely that the bulk of the extended
emission could be heated by the central engine. This low level-extended mid-IR emission, in some cases
up to 10$\arcsec$ (170pc) away from the nucleus would have to be extremely cool on order of $\sim$ 60K
assuming the same simple formula as in $\S$ 4.1.2. Assuming a normal blackbody SED of dust this cool
however would cause significant emission (on order of a few Jy) at longer wavelengths such as
18.3$\micron$ where no significant extended emission is seen on scales $>$3$\arcsec$. This provides
further evidence that much of this mid-IR emission, especially that coincident with the Pa-$\alpha$
emission, is associated with local stellar activity.
The only significant 18.3$\micron$ emission detected is a small clump of emission at a distance of
2.8$\arcsec$ (48pc) from the nucleus (PA=64$\degr$; measured North through East) approximately
coincident with Pa-$\alpha$ clump A from Schreier et al. (1998) (see Figure 3). Krajnovi{\'c}, Sharp,
\& Thatte (2006) suggest this clump as well as clump B may be due to jet induced star formation.
Emission is detected in both clumps at 8.8$\micron$ while there is a $\sim$2$\sigma$ detection of clump
B at 18.3$\micron$. If this mid-IR emission is truly associated with shock induced star formation
regions then we would expect heating of the surrounding dust to be local.
We measure the the flux density in a 2$\arcsec$ diameter area near clump A to be $\sim$ 4mJy at
8.8$\micron$ and $\sim$ 40mJy at 18$\micron$, given the possibility of emission being chopped onto
these can be considered rough estimates. Near clump B the mid-IR emission is similar to that of clump A
$\sim$ 4mJy at 8.8$\micron$ with very little emission ($\sim$ 17mJy) at 18.3$\micron$. This results in
an optically thin estimate of the temperature of 150-200K near clump A and even warmer near clump B
which is farther away at 3.5$\arcsec$ (60pc). Given that we estimate that 14pc is approximately the
maximum distance that the AGN (2.5 $\times$ 10$^{9}$ L$_{\sun}$) can heat dust to 200K this would rule
out mid-IR emission near clump B as being centrally heated dust. Even for clump A at a temperature of
150K only the smallest grains of graphite (0.003-0.005um) could be heated by the central engine. Though
these are very simple estimates it does imply that local heating of dust due to shock induced star
formation associated with the radio ejecta is a possible explanation for mid-IR emission near clumps A
and B. However, if there is an enhancement in luminosity in the direction of the NLR along the radio
axis (NE of the nucleus), as would be the case if the ionizing luminosity is anisotropic, then it may
be possible to heat dust out to a radius consistent with clumps A and B. This could also explain the
faint mid-IR extension seen on the opposite side (SW of the nucleus) at 8.8$\micron$. This is thought
to be the case in NGC 4151 (Radomski et al. 2003) where extended mid-IR emission on either side of the
nucleus along the radio axis is thought to arise from a dusty NLR within the ionization cone heated by
the central engine. In this case the NLR of NGC 4151 may see an ionizing luminosity a factor of
$\sim$13$\times$ greater than that seen from Earth (Penston et al. 1990). Anisotropies and beaming
along the NLR has been predicted as strong as 200$\times$ in some galaxies (Baldwin, Wilson \& Whittle
1987). In Cen A a beaming factor or underestimate of the true luminosity of 10-20$\times$ would be
needed to be consistent with the central heating of clumps A and B within an ionization cone.
\subsubsection{Extended: Dusty Torus} CO and H$_{2}$ measurements of Cen A show a nuclear ring of outer radius 80-140pc,
with an inner hole of diameter 40pc enclosing a mass of 10$^{9}$ L$_{\sun}$ (Israel et al 1990, 1991;
Rydbeck et al. 1993; Marconi et al. 2001). This ring is aligned perpendicular to the radio jet and has
been speculated to be associated with the very outer parts of a torus. This would seem to contradict
our earlier results which indicate a highly compact torus $<$3.5pc. The difference however is entirely
due to what is defined as the ``torus" in AGN. Shi et al. (2006) describes the ``torus" as a
multilayered system with and ``inner" ($<$0.1pc) ``middle" (0.1-10pc) and ``outer" (10-300pc)
structure. In this scenario the compact torii seen in the mid-IR would typically correspond to the
``middle" disk while the CO/H$_{2}$ is associated with the ``outer" disk. Similar to Cen A, NGC 1068
also contains a compact mid-IR torus $<$15pc (Mason et al. 2006) surrounded by a large 100pc scale CO
disk. Mid-IR polarization observations of NGC 1068 by Packham et al. (2007) provide continuity between
these structures suggesting that the compact geometrically and optically thick torus is often
surrounded by a larger and more diffuse structure associated with the dusty central regions of the host
galaxy. Other dusty structures such as nuclear galactic bars may further merge into this scenario.
Observations by Marconi et al. (2001b) even suggest that the H$_{2}$ structure shows kinematical
evidence consistent with a galactic bar fueling the AGN, though they cannot entirely rule out a
disk/torus structure.
Possible evidence for mid-IR emission associated with this ``outer" torus/nuclear bar can be seen at
both 8.8$\micron$ and N-band (Figures 3 and 4). At both wavelengths there appears to be a ridge of
emission extending up from the NW of the nucleus towards Pa-$\alpha$ clump G. At 8.8$\micron$ some
mid-IR emission is also seen on the SE side. In all cases this emission seems devoid of corresponding
Pa-$\alpha$ emission associated with stellar activity as discussed earlier. Given that the data at
8.8um and N-band is chopping on different areas of the galaxy (see Observations $\S$ 2) it is unlikely
that at least the NW structure seen at both wavelengths is excessively distorted due to improper chop
subtraction. This structure possibly indicates that the emission detected in CO/H$_{2}$ contains a
dusty component. However, using simple calculations from $\S$ 4.1.2, even dust as small as
0.003$\micron$ at this distance (5-7$\arcsec$) would have to be on order of 70-80K to be heated by the
central AGN. This is not reasonable as such cool dust should emit substantially more (on order of a few
Jy) at 18$\micron$ where no significant emission is detected along this ridge. A more likely
possibility is this emission is due to PAH emission as detected by ISO and Spitzer at least at
8.8$\micron$ and possibility also 11.3$\micron$ in the N-band.
NICMOS imaging by Schreier et al. (1998) shows a 1$\arcsec$x2$\arcsec$ (20pc radius) emission line
region interpreted as a gaseous disk also possibly associated with a multi-layered torus which is
nearly parallel to the radio jet and perpendicular to the CO disk. Schreier et al. (1998) hypothesized
this peculiar angle may be caused by one of two scenarios. Either that it had formed recently enough
(possibly associated with a merger or infall event) such that it had not time to become aligned with
the black hole spin axis, or because it was along the major axis of the bulge that it was dominated by
the galaxy gravitational potential rather than that of the black hole. In either case these
observations indicate that there may be an outer gaseous ring of material that is highly warped with
respect to the inner compact mid-IR torus. Though we do generally detect low-level mid-IR emission
along this direction we detect no extension associated with this structure at the level of the FWHM.
\subsubsection{Extended: Synchrotron Emission}
As discussed earlier, in both Epoch A and B data extended mid-IR emission is detected approximately
coincident with Pa-$\alpha$ clumps A and B from Schreier et al. (1998). This emission also falls very
near the axis of the powerful radio jet in Cen A. At N-band especially (Figure 4) emission is seen
along the inner part of the radio jet extending out past the Pa-$\alpha$ clumps A and B. As discussed
above it is difficult to rule out shock induced star formation and/or dusty NLR emission. Furthermore
due to the possibility of inadequate chop-subtraction attempting to fit a synchrotron model to evaluate
its contribution, if any, is difficult. Thus we cannot confirm nor rule out some contribution from
synchrotron radiation emanating from the jet near the nucleus. Farther out along the jet axis in the NE
direction negative emission from improper chop subtraction becomes more apparent in both Epoch A and B
data and some faint mid-IR emission associated with the jet is most likely lost. However in Epoch B at
N-band there is clear evidence of mid-IR emission located farther out and coincident with the radio
axis. This new source is denoted as RPL 1 (Figure 4).
RPL 1 is located in a very bright area of the radio jet at a distance of 18.4$\arcsec$ PA=(53$\degr$
measured North to East). It is outside the field of view of the Epoch A data and thus cannot be
characterized at 8.8$\micron$ and 18.3$\micron$. Given the distance as projected on sky 18.4$\arcsec$
is equal to $>$300 pc. This rules out dust heated by the central source, as it would take a beaming
factor of $>$500 to heat even the smallest dust grains to a temperature of 200K. If no beaming is
assumed the maximum temperature that a blackbody heated by the central AGN could obtain at that
distance is 42K, which given an approximate flux density of 2mJy at N-band would require a 25$\micron$
flux several hundred thousand times what is measured by IRAS. Confidence in the detection of this
source is strong as it is seen on all three nights observed at N-band and after a 20 pixel
(1.78$\arcsec$) offset/dither between nights. Stacking all three nights of data results in a
3-4$\sigma$ detection (Figure 4). Mid-IR emission from a synchrotron jet has been seen in M87 (Perlman
et al. 2001) and at larger radii from Cen A by Spitzer (HKW06), however in these cases the mid-IR
morphology and position showed a strong spatial and morphological correspondence to that of the radio
emission from the jet. This does not seem to be the case in RPL 1 which is located offset
$\sim$2$\arcsec$ from a bright radio knot and with a much less elongated shape. Another possible
explanation is a dusty clump heated by the impact or shock of the outflow impinging on surrounding
material associated with jet induced star formation. However it is possible that the morphology of this
weak source is affected by improper chop subtraction of the crowded mid-IR emission in Cen A and thus
it requires further investigation.
\section{Conclusions}
We detect a bright unresolved mid-IR nucleus surrounded by low-level emission in the central region of
Centaurus A. We find the bright central nucleus of Cen A to be unresolved in the mid-IR at the level of
the FWHM. Using multiple PSF measurements and their variation, we place an upper limit on the size of
the mid-IR nucleus of Cen A of 3.2 pc (0$\farcs$19) at 8.8$\micron$ and 3.5 pc (0$\farcs$21) at
18.3$\micron$. This is consistent with our models which predict the mid-IR emission from a torus in Cen
A to be unresolved with a size of 0$\farcs$05 or less. The primary source of the nuclear mid-IR
emission is likely to be associated with this dusty torus and NLR emission with minimal contributions
from starburst and synchrotron emission.
Extended mid-IR emission in Cen A is generally coincident with Pa-$\alpha$ regions most likely due to
stellar activity. A ridge of mid-IR emission perpendicular to the radio axis and devoid of much
Pa-$\alpha$ emission may be associated with a CO, H$_{2}$ outer ring/bar. Emission associated with
Pa-$\alpha$ clumps A and B from Schreier et al. (1998) could be due to shock heating or possibly
centrally heated dust in a NLR if anisotropic beaming of radiation along the radio axis is taken into
account. A new mid-IR source RPL 1, is detected along the radio axis at a distance of 18.4$\arcsec$
(PA=53$\degr$) and is possibly due to shock heating of material impacted by the jet or synchrotron
emission. Overall the mid-IR emission in the nuclear region is shown to be very complex and in need of
further study.
\section{Acknowledgments}
JTR, JMD, and RM acknowledge the support of the NSF based on observations obtained at the Gemini
Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc.,
under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science
Foundation (United States), the Particle Physics and Astronomy Research Council (United Kingdom), the
National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq
(Brazil), and CONICET (Argentina). We also thank Matthew Sirocky for his assistance with the torus
simulations and NAL acknowledges support from NSF award AST-0237291. JTR would also like to acknowledge
Craig Markwardt for his very useful IDL routines which were used to fit Moffat profiles and Alessandro
Marconi for trying to find his original Pa-$\alpha$ images. CP would like to acknowledge NSF grant
0206617. All authors would also like to thank the referee for the helpful comments that improved this
paper.
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{"url":"https:\/\/puzzling.stackexchange.com\/questions\/85443\/help-the-it-guy-heal-one-of-his-hard-drives","text":"# Help the IT guy heal one of his hard drives [duplicate]\n\nThere are $$64$$ hard drives each with one extra bit (\"flag\"), the value of which you don't know (it can be '$$0$$' or '$$1$$'). One hard drive is infected with virus that you need to heal.\n\nYou have two softwares in your disposal to help you: a detector and an antivirus. The detector always identifies the infected hard drive, but may only set\/unset one flag (out of the $$64$$ flags) and can peek to see the values of each flag. The antivirus can inspect each flag as well, but may only attempt to heal one hard drive. If the antivirus is given a clean hard drive it stays clean, and if it is given an infected one it heals it.\n\nHow would you coordinate the work of the detector and the antivirus such that you always fulfill your objective?\n\n## marked as duplicate by hexomino, Rubio\u2666Jun 24 at 11:52\n\nBecause the original question and answer of this dupe are a bit.. hard to read, I'll try to write up a simpler solution:\n\nFirst, the detector identifies the borkened drive. Then it\n\nenumerates the disks from 0 to 63, and XORs (bitwise) together all the disk numbers that have their flag bit set to 1.\n\nThis gives some result\n\nfrom 0 to 63, which the decoder can always change into any other result by flipping only one disk's flag bit: the numbers from 0 to 63 represent all possible 6 bit sequences, which is useful, because XORring works by flipping bits that correspond to 1s in the other operand, so any combination of bits can be flipped as desired.\n\nFor example,\n\nLet's say that the XORring resulted in 13, and the broken disk was 27. The detector wants to set the total XOR to 27, so it can now compute (using the property of XOR that adding a XOR is the same operation as removing a XOR) $$27 \\ominus 13 = 27 \\oplus 13 = 22$$, and flip the flag on the 22nd disk.\n\nThe antivirus can now\n\ncalculate the XOR of all disk numbers with the flag set to 1, and it will end up with the number of the broken disk, 27, because $$13 \\oplus 22 = 27$$.\n\n\u2022 Ideally you'd put improved solutions on the dup target, not on the dup post where it's likely to be ignored. \u2013\u00a0Rubio Jun 24 at 11:52","date":"2019-11-12 17:13:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 6, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4738483428955078, \"perplexity\": 1327.4381053369793}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-47\/segments\/1573496665575.34\/warc\/CC-MAIN-20191112151954-20191112175954-00283.warc.gz\"}"}
| null | null |
Study the temperature dependence of resistivity of high purity aluminum fine showed that up to temperatures of 10-12K a mechanism of electron scattering at grain boundaries dominates the electron-dislocation scattering, then the effect is suppressed by electron-phonon scattering. Analysis of the results of the first studies show that the problem of producing and studying fine (in the limit of nanocrystalline) of pure metals is relevant to a winding giperprovodyaschih cryogenic electromagnetic systems.
Results of the study of quantum oscillations of the kinetic coefficients in terms of magnetic breakdown obtained for dilute alloys of Al-Y and Zn-In, indicate that the doping metals properly chosen type and concentration of impurities lead to a change in geometry and size of sheets of the Fermi surface.
Conducting highly-pures aluminum fibres are placed into the matrix of high-strength Al alloy, which is suitable for their joint working and operation. This fabrication technology allows a reliable electrical and thermal contact of a matrix and a conductor.
A multi-fibre conductor, consisting of the Al-Mn-Mg alloy with the 94% aluminum content, which has a high yield limit σy = 360 МPа при Т = 4.2 К, and also heat conductivity and linear expansion coefficient being close to those of pure Al.
A physical model of current flow in from high-purity aluminum giperprovodnike, taking into account the effect of the magnetic stray field of the self-field coil, which allowed to optimize the design of the winding because of its banding on the mechanical loads and flow-through cooling with liquid hydrogen. When choosing a winding structure the main criterion is to protect the plastic guide from the radial and axial strain. This is ensured by a special coil banding and strong material allows to maintain the high conductive properties of high-purity aluminum and provide a current density of 200 A/mm. Obtained at this stage of the assignment results confirm the fundamental possibility of generating strong magnetic fields in compact solenoidal systems promising for use in power systems on board spacecraft.
Investigated the temperature dependence of resistivity of ionic compounds [C4mim] PF6 and [C6mim] NTf2. In all cases the samples are cooled to 77 K there is growing resistance to a law close to parabolic. When heated to the crystallization temperature on the curves of lnR (T) anomalies in the temperature range corresponding to the supercooled liquid state. The value of resistivity in the crystalline state are different for these compounds. In the case of [C4mim] PF6 resistance less than the state of the glass, for [C6mim] NTf2 the opposite is true.
Using frozen lactic acid bacteria in the atmosphere of liquid nitrogen can increase the number of living cells and has no effect on the ratio of bacterial cultures in the starter.
Scientific-technical principles and an experimental model system for kriozamorazhivaniya microbial biomass.
|
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Apple is spending up to $15M per episode on its TV shows, as Netflix starts spending less
Andy Meek @aemeek
There was a time, not that long ago in fact, where HBO's reported budget of $5 million spent on each episode of Game of Thrones sounded pretty extreme. Like something approaching a small movie budget. Not that Westeros fans would argue such spending bordered on anything close to profligacy, with the attention to detail and quality so high, but it still was an eye-popping number. And now here we are, with major new entrants like Apple about to plunge into the Streaming Wars — and to start dedicating the equivalent of feature film budgets to their own new TV shows in the hopes of guaranteeing they'll have something you'll like or at least want to try.
The amount of money we're talking about here, in many cases, is bigger than ever. Apple, for example, will launch its subscription-based Apple TV+ this fall, taking the iPhone maker into a whole new market that it's never attempted before (premium TV content creation). Say what you will about its chances of being competitive with rivals like Netflix, at least the company is apparently going all-in here. If there's one thing Apple can do to increase its chances of producing a show or multiple shows mainstream viewers will end up liking, they can spend a ridiculously huge amount of money. Which is exactly what the company is reportedly doing.
One of the shows Apple has green-lit to be an early part of Apple TV+ is See, a 60-minute drama starring Jason Momoa that's set in the far future on Earth after a virus wipes out the population and leaves survivors blind — and unable to, you guessed it, see. One source told The Wall Street Journal Apple is spending almost $15 million per episode on the show, no doubt pushing the total well north of $100 million for the show.
Image Source: Photo by Matt Rourke/AP/Shutterstock
What's interesting is that this comes at a time when Netflix is apparently going to start going in the opposite direction. The streamer's chief content officer Ted Sarandos recently told a group of mid- and high-level film and TV executives at the company that spending needs to be more cost-effective going forward.
To be sure, the level of spending is not a guaranteed barometer of a show's success. Consider Netflix's short-lived 2016 series The Get Down from Baz Luhrmann, a drama about the '70s music scene, that was canceled after one season despite Netflix spending $7.5 million per episode.
Netflix is, of course, a near-impregnable obstacle to any new streamer entering this space, which is why the giants seem to feel like spending big piles of cash is pretty much a prerequisite here. Disney, for example, is doing the same thing — pouring an estimated $15 million per episode into The Mandalorian, a series set within the Star Wars universe that's coming to its new Disney+ streamer also launching this fall.
Same with Amazon, which spent a quarter of a billion dollars acquiring the rights to develop a Lord of the Rings-themed series for its streaming platform. These and other companies are practically breaking the bank to ensure we'll have tons of great content to watch, so no matter who the winner is among them, at least we know one thing. We sure will be.
Image Source: Photo by Tony Avelar/AP/Shutterstock
Tags: Apple TV Plus, netflix
From 'Stranger Things' superstar to Marvel superhero? Millie Bobbie Brown to star in new MCU Phase 4 movie
Red wine may hold a secret that will keep Mars travelers fit
Hurry Before It's Gone!
Who needs Prime Day when LED light strips are just $7.99 each right now?
By Zach Epstein 10 hours ago
Galaxy Note 10 might be even faster than the S10 and OnePlus 7 Pro, new leak teases
By Chris Smith 2 days ago
7 paid iPhone apps on sale for free on July 17th
By Zach Epstein 1 day ago
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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City EP
Re-pressed on demand! Our original debut EP featuring six songs:
Double Happiness (I want my)
Taking A Dive
With a strong call back to the pioneers of post-punk and early surf rock, listeners will love the sprinkling of Joy Division, Sonic Youth, The Shadows and The Go-Betweens as well as the nod to the early 90's Flying Nun sounds. - John Russell, Valley Heat Records/4000 Records.
Released March 14, 2018 on Valley Heat Records, and re-pressed June, 2021.
Kristin (Black) Fergusson - guitar, vocals. Peter Fergusson - guitar, vocals. Meg Welchman - bass, vocals. Simon Welchman - drums.
Produced, Recorded, Mixed and Mastered by Peter Fergusson
The Double Happiness is based in Brisbane, AUSTRALIA. Their music is released via 4000 Records
For all gig enquiries and other info: Email us here
We'd love you to follow us!
© 2023 by The Silent South. Proudly created with Wix.com
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{"url":"https:\/\/en.wikibooks.org\/wiki\/Linear_Algebra\/Dimension","text":"# Linear Algebra\/Dimension\n\nJump to: navigation, search\nLinear Algebra\n \u2190\u00a0Basis Dimension Vector Spaces and Linear Systems\u00a0\u2192\n\nIn the prior subsection we defined the basis of a vector space, and we saw that a space can have many different bases. For example, following the definition of a basis, we saw three different bases for ${\\displaystyle \\mathbb {R} ^{2}}$. So we cannot talk about \"the\" basis for a vector space. True, some vector spaces have bases that strike us as more natural than others, for instance, ${\\displaystyle \\mathbb {R} ^{2}}$'s basis ${\\displaystyle {\\mathcal {E}}_{2}}$ or ${\\displaystyle \\mathbb {R} ^{3}}$'s basis ${\\displaystyle {\\mathcal {E}}_{3}}$ or ${\\displaystyle {\\mathcal {P}}_{2}}$'s basis ${\\displaystyle \\langle 1,x,x^{2}\\rangle }$. But, for example in the space ${\\displaystyle \\{a_{2}x^{2}+a_{1}x+a_{0}\\,{\\big |}\\,2a_{2}-a_{0}=a_{1}\\}}$, no particular basis leaps out at us as the most natural one. We cannot, in general, associate with a space any single basis that best describes that space.\n\nWe can, however, find something about the bases that is uniquely associated with the space. This subsection shows that any two bases for a space have the same number of elements. So, with each space we can associate a number, the number of vectors in any of its bases.\n\nThis brings us back to when we considered the two things that could be meant by the term \"minimal spanning set\". At that point we defined \"minimal\" as linearly independent, but we noted that another reasonable interpretation of the term is that a spanning set is \"minimal\" when it has the fewest number of elements of any set with the same span. At the end of this subsection, after we have shown that all bases have the same number of elements, then we will have shown that the two senses of \"minimal\" are equivalent.\n\nBefore we start, we first limit our attention to spaces where at least one basis has only finitely many members.\n\nDefinition 2.1\n\nA vector space is finite-dimensional if it has a basis with only finitely many vectors.\n\n(One reason for sticking to finite-dimensional spaces is so that the representation of a vector with respect to a basis is a finitely-tall vector, and so can be easily written.) From now on we study only finite-dimensional vector spaces. We shall take the term \"vector space\" to mean \"finite-dimensional vector space\". Other spaces are interesting and important, but they lie outside of our scope.\n\nTo prove the main theorem we shall use a technical result.\n\nLemma 2.2 (Exchange Lemma)\n\nAssume that ${\\displaystyle B=\\langle {\\vec {\\beta }}_{1},\\dots ,{\\vec {\\beta }}_{n}\\rangle }$ is a basis for a vector space, and that for the vector ${\\displaystyle {\\vec {v}}}$ the relationship ${\\displaystyle {\\vec {v}}=c_{1}{\\vec {\\beta }}_{1}+c_{2}{\\vec {\\beta }}_{2}+\\cdots +c_{n}{\\vec {\\beta }}_{n}}$ has ${\\displaystyle c_{i}\\neq 0}$. Then exchanging ${\\displaystyle {\\vec {\\beta }}_{i}}$ for ${\\displaystyle {\\vec {v}}}$ yields another basis for the space.\n\nProof\n\nCall the outcome of the exchange ${\\displaystyle {\\hat {B}}=\\langle {\\vec {\\beta }}_{1},\\dots ,{\\vec {\\beta }}_{i-1},{\\vec {v}},{\\vec {\\beta }}_{i+1},\\dots ,{\\vec {\\beta }}_{n}\\rangle }$.\n\nWe first show that ${\\displaystyle {\\hat {B}}}$ is linearly independent. Any relationship ${\\displaystyle d_{1}{\\vec {\\beta }}_{1}+\\dots +d_{i}{\\vec {v}}+\\dots +d_{n}{\\vec {\\beta }}_{n}={\\vec {0}}}$ among the members of ${\\displaystyle {\\hat {B}}}$, after substitution for ${\\displaystyle {\\vec {v}}}$,\n\n${\\displaystyle d_{1}{\\vec {\\beta }}_{1}+\\dots +d_{i}\\cdot (c_{1}{\\vec {\\beta }}_{1}+\\dots +c_{i}{\\vec {\\beta }}_{i}+\\dots +c_{n}{\\vec {\\beta }}_{n})+\\dots +d_{n}{\\vec {\\beta }}_{n}={\\vec {0}}\\qquad \\qquad (*)}$\n\ngives a linear relationship among the members of ${\\displaystyle B}$. The basis ${\\displaystyle B}$ is linearly independent, so the coefficient ${\\displaystyle d_{i}c_{i}}$ of ${\\displaystyle {\\vec {\\beta }}_{i}}$ is zero. Because ${\\displaystyle c_{i}}$ is assumed to be nonzero, ${\\displaystyle d_{i}=0}$. Using this in equation ${\\displaystyle (*)}$ above gives that all of the other ${\\displaystyle d}$'s are also zero. Therefore ${\\displaystyle {\\hat {B}}}$ is linearly independent.\n\nWe finish by showing that ${\\displaystyle {\\hat {B}}}$ has the same span as ${\\displaystyle B}$. Half of this argument, that ${\\displaystyle [{\\hat {B}}]\\subseteq [B]}$, is easy; any member ${\\displaystyle d_{1}{\\vec {\\beta }}_{1}+\\dots +d_{i}{\\vec {v}}+\\dots +d_{n}{\\vec {\\beta }}_{n}}$ of ${\\displaystyle [{\\hat {B}}]}$ can be written ${\\displaystyle d_{1}{\\vec {\\beta }}_{1}+\\dots +d_{i}\\cdot (c_{1}{\\vec {\\beta }}_{1}+\\dots +c_{n}{\\vec {\\beta }}_{n})+\\dots +d_{n}{\\vec {\\beta }}_{n}}$, which is a linear combination of linear combinations of members of ${\\displaystyle B}$, and hence is in ${\\displaystyle [B]}$. For the ${\\displaystyle [B]\\subseteq [{\\hat {B}}]}$ half of the argument, recall that when ${\\displaystyle {\\vec {v}}=c_{1}{\\vec {\\beta }}_{1}+\\dots +c_{n}{\\vec {\\beta }}_{n}}$ with ${\\displaystyle c_{i}\\neq 0}$, then the equation can be rearranged to ${\\displaystyle {\\vec {\\beta }}_{i}=(-c_{1}\/c_{i}){\\vec {\\beta }}_{1}+\\dots +(1\/c_{i}){\\vec {v}}+\\dots +(-c_{n}\/c_{i}){\\vec {\\beta }}_{n}}$. Now, consider any member ${\\displaystyle d_{1}{\\vec {\\beta }}_{1}+\\dots +d_{i}{\\vec {\\beta }}_{i}+\\dots +d_{n}{\\vec {\\beta }}_{n}}$ of ${\\displaystyle [B]}$, substitute for ${\\displaystyle {\\vec {\\beta }}_{i}}$ its expression as a linear combination of the members of ${\\displaystyle {\\hat {B}}}$, and recognize (as in the first half of this argument) that the result is a linear combination of linear combinations, of members of ${\\displaystyle {\\hat {B}}}$, and hence is in ${\\displaystyle [{\\hat {B}}]}$.\n\nTheorem 2.3\n\nIn any finite-dimensional vector space, all of the bases have the same number of elements.\n\nProof\n\nFix a vector space with at least one finite basis. Choose, from among all of this space's bases, one ${\\displaystyle B=\\langle {\\vec {\\beta }}_{1},\\dots ,{\\vec {\\beta }}_{n}\\rangle }$ of minimal size. We will show that any other basis ${\\displaystyle D={\\langle {\\vec {\\delta }}_{1},{\\vec {\\delta }}_{2},\\ldots \\rangle }}$ also has the same number of members, ${\\displaystyle n}$. Because ${\\displaystyle B}$ has minimal size, ${\\displaystyle D}$ has no fewer than ${\\displaystyle n}$ vectors. We will argue that it cannot have more than ${\\displaystyle n}$ vectors.\n\nThe basis ${\\displaystyle B}$ spans the space and ${\\displaystyle {\\vec {\\delta }}_{1}}$ is in the space, so ${\\displaystyle {\\vec {\\delta }}_{1}}$ is a nontrivial linear combination of elements of ${\\displaystyle B}$. By the Exchange Lemma, ${\\displaystyle {\\vec {\\delta }}_{1}}$ can be swapped for a vector from ${\\displaystyle B}$, resulting in a basis ${\\displaystyle B_{1}}$, where one element is ${\\displaystyle {\\vec {\\delta }}}$ and all of the ${\\displaystyle n-1}$ other elements are ${\\displaystyle {\\vec {\\beta }}}$'s.\n\nThe prior paragraph forms the basis step for an induction argument. The inductive step starts with a basis ${\\displaystyle B_{k}}$ (for ${\\displaystyle 1\\leq k) containing ${\\displaystyle k}$ members of ${\\displaystyle D}$ and ${\\displaystyle n-k}$ members of ${\\displaystyle B}$. We know that ${\\displaystyle D}$ has at least ${\\displaystyle n}$ members so there is a ${\\displaystyle {\\vec {\\delta }}_{k+1}}$. Represent it as a linear combination of elements of ${\\displaystyle B_{k}}$. The key point: in that representation, at least one of the nonzero scalars must be associated with a ${\\displaystyle {\\vec {\\beta }}_{i}}$ or else that representation would be a nontrivial linear relationship among elements of the linearly independent set ${\\displaystyle D}$. Exchange ${\\displaystyle {\\vec {\\delta }}_{k+1}}$ for ${\\displaystyle {\\vec {\\beta }}_{i}}$ to get a new basis ${\\displaystyle B_{k+1}}$ with one ${\\displaystyle {\\vec {\\delta }}}$ more and one ${\\displaystyle {\\vec {\\beta }}}$ fewer than the previous basis ${\\displaystyle B_{k}}$.\n\nRepeat the inductive step until no ${\\displaystyle {\\vec {\\beta }}}$'s remain, so that ${\\displaystyle B_{n}}$ contains ${\\displaystyle {\\vec {\\delta }}_{1},\\dots ,{\\vec {\\delta }}_{n}}$. Now, ${\\displaystyle D}$ cannot have more than these ${\\displaystyle n}$ vectors because any ${\\displaystyle {\\vec {\\delta }}_{n+1}}$ that remains would be in the span of ${\\displaystyle B_{n}}$ (since it is a basis) and hence would be a linear combination of the other ${\\displaystyle {\\vec {\\delta }}}$'s, contradicting that ${\\displaystyle D}$ is linearly independent.\n\nDefinition 2.4\n\nThe dimension of a vector space is the number of vectors in any of its bases.\n\nExample 2.5\n\nAny basis for ${\\displaystyle \\mathbb {R} ^{n}}$ has ${\\displaystyle n}$ vectors since the standard basis ${\\displaystyle {\\mathcal {E}}_{n}}$ has ${\\displaystyle n}$ vectors. Thus, this definition generalizes the most familiar use of term, that ${\\displaystyle \\mathbb {R} ^{n}}$ is ${\\displaystyle n}$-dimensional.\n\nExample 2.6\n\nThe space ${\\displaystyle {\\mathcal {P}}_{n}}$ of polynomials of degree at most ${\\displaystyle n}$ has dimension ${\\displaystyle n+1}$. We can show this by exhibiting any basis\u2014 ${\\displaystyle \\langle 1,x,\\dots ,x^{n}\\rangle }$ comes to mind\u2014 and counting its members.\n\nExample 2.7\n\nA trivial space is zero-dimensional since its basis is empty.\n\nAgain, although we sometimes say \"finite-dimensional\" as a reminder, in the rest of this book all vector spaces are assumed to be finite-dimensional. An instance of this is that in the next result the word \"space\" should be taken to mean \"finite-dimensional vector space\".\n\nCorollary 2.8\n\nNo linearly independent set can have a size greater than the dimension of the enclosing space.\n\nProof\n\nInspection of the above proof shows that it never uses that ${\\displaystyle D}$ spans the space, only that ${\\displaystyle D}$ is linearly independent.\n\nExample 2.9\n\nRecall the subspace diagram from the prior section showing the subspaces of ${\\displaystyle \\mathbb {R} ^{3}}$. Each subspace shown is described with a minimal spanning set, for which we now have the term \"basis\". The whole space has a basis with three members, the plane subspaces have bases with two members, the line subspaces have bases with one member, and the trivial subspace has a basis with zero members. When we saw that diagram we could not show that these are the only subspaces that this space has. We can show it now. The prior corollary proves that the only subspaces of ${\\displaystyle \\mathbb {R} ^{3}}$ are either three-, two-, one-, or zero-dimensional. Therefore, the diagram indicates all of the subspaces. There are no subspaces somehow, say, between lines and planes.\n\nCorollary 2.10\n\nAny linearly independent set can be expanded to make a basis.\n\nProof\n\nIf a linearly independent set is not already a basis then it must not span the space. Adding to it a vector that is not in the span preserves linear independence. Keep adding, until the resulting set does span the space, which the prior corollary shows will happen after only a finite number of steps.\n\nCorollary 2.11\n\nAny spanning set can be shrunk to a basis.\n\nProof\n\nCall the spanning set ${\\displaystyle S}$. If ${\\displaystyle S}$ is empty then it is already a basis (the space must be a trivial space). If ${\\displaystyle S=\\{{\\vec {0}}\\}}$ then it can be shrunk to the empty basis, thereby making it linearly independent, without changing its span.\n\nOtherwise, ${\\displaystyle S}$ contains a vector ${\\displaystyle {\\vec {s}}_{1}}$ with ${\\displaystyle {\\vec {s}}_{1}\\neq {\\vec {0}}}$ and we can form a basis ${\\displaystyle B_{1}=\\langle {\\vec {s}}_{1}\\rangle }$. If ${\\displaystyle [B_{1}]=[S]}$ then we are done.\n\nIf not then there is a ${\\displaystyle {\\vec {s}}_{2}\\in [S]}$ such that ${\\displaystyle {\\vec {s}}_{2}\\not \\in [B_{1}]}$. Let ${\\displaystyle B_{2}=\\langle {\\vec {s}}_{1},{\\vec {s_{2}}}\\rangle }$; if ${\\displaystyle [B_{2}]=[S]}$ then we are done.\n\nWe can repeat this process until the spans are equal, which must happen in at most finitely many steps.\n\nCorollary 2.12\n\nIn an ${\\displaystyle n}$-dimensional space, a set of ${\\displaystyle n}$ vectors is linearly independent if and only if it spans the space.\n\nProof\n\nFirst we will show that a subset with ${\\displaystyle n}$ vectors is linearly independent if and only if it is a basis. \"If\" is trivially true\u2014 bases are linearly independent. \"Only if\" holds because a linearly independent set can be expanded to a basis, but a basis has ${\\displaystyle n}$ elements, so this expansion is actually the set that we began with.\n\nTo finish, we will show that any subset with ${\\displaystyle n}$ vectors spans the space if and only if it is a basis. Again, \"if\" is trivial. \"Only if\" holds because any spanning set can be shrunk to a basis, but a basis has ${\\displaystyle n}$ elements and so this shrunken set is just the one we started with.\n\nThe main result of this subsection, that all of the bases in a finite-dimensional vector space have the same number of elements, is the single most important result in this book because, as Example 2.9 shows, it describes what vector spaces and subspaces there can be. We will see more in the next chapter.\n\nRemark 2.13\n\nThe case of infinite-dimensional vector spaces is somewhat controversial. The statement \"any infinite-dimensional vector space has a basis\" is known to be equivalent to a statement called the Axiom of Choice (see (Blass 1984).) Mathematicians differ philosophically on whether to accept or reject this statement as an axiom on which to base mathematics (although, the great majority seem to accept it). Consequently the question about infinite-dimensional vector spaces is still somewhat up in the air. (A discussion of the Axiom of Choice can be found in the Frequently Asked Questions list for the Usenet group sci.math. Another accessible reference is (Rucker 1982).\n\n## Exercises\n\nAssume that all spaces are finite-dimensional unless otherwise stated.\n\nThis exercise is recommended for all readers.\nProblem 1\n\nFind a basis for, and the dimension of, ${\\displaystyle {\\mathcal {P}}_{2}}$.\n\nProblem 2\n\nFind a basis for, and the dimension of, the solution set of this system.\n\n${\\displaystyle {\\begin{array}{*{4}{rc}r}x_{1}&-&4x_{2}&+&3x_{3}&-&x_{4}&=&0\\\\2x_{1}&-&8x_{2}&+&6x_{3}&-&2x_{4}&=&0\\end{array}}}$\nThis exercise is recommended for all readers.\nProblem 3\n\nFind a basis for, and the dimension of, ${\\displaystyle {\\mathcal {M}}_{2\\!\\times \\!2}}$, the vector space of ${\\displaystyle 2\\!\\times \\!2}$ matrices.\n\nProblem 4\n\nFind the dimension of the vector space of matrices\n\n${\\displaystyle {\\begin{pmatrix}a&b\\\\c&d\\end{pmatrix}}}$\n\nsubject to each condition.\n\n1. ${\\displaystyle a,b,c,d\\in \\mathbb {R} }$\n2. ${\\displaystyle a-b+2c=0}$ and ${\\displaystyle d\\in \\mathbb {R} }$\n3. ${\\displaystyle a+b+c=0}$, ${\\displaystyle a+b-c=0}$, and ${\\displaystyle d\\in \\mathbb {R} }$\nThis exercise is recommended for all readers.\nProblem 5\n\nFind the dimension of each.\n\n1. The space of cubic polynomials ${\\displaystyle p(x)}$ such that ${\\displaystyle p(7)=0}$\n2. The space of cubic polynomials ${\\displaystyle p(x)}$ such that ${\\displaystyle p(7)=0}$ and ${\\displaystyle p(5)=0}$\n3. The space of cubic polynomials ${\\displaystyle p(x)}$ such that ${\\displaystyle p(7)=0}$, ${\\displaystyle p(5)=0}$, and ${\\displaystyle p(3)=0}$\n4. The space of cubic polynomials ${\\displaystyle p(x)}$ such that ${\\displaystyle p(7)=0}$, ${\\displaystyle p(5)=0}$, ${\\displaystyle p(3)=0}$, and ${\\displaystyle p(1)=0}$\nProblem 6\n\nWhat is the dimension of the span of the set ${\\displaystyle \\{\\cos ^{2}\\theta ,\\sin ^{2}\\theta ,\\cos 2\\theta ,\\sin 2\\theta \\}}$? This span is a subspace of the space of all real-valued functions of one real variable.\n\nProblem 7\n\nFind the dimension of ${\\displaystyle \\mathbb {C} ^{47}}$, the vector space of ${\\displaystyle 47}$-tuples of complex numbers.\n\nProblem 8\n\nWhat is the dimension of the vector space ${\\displaystyle {\\mathcal {M}}_{3\\!\\times \\!5}}$ of ${\\displaystyle 3\\!\\times \\!5}$ matrices?\n\nThis exercise is recommended for all readers.\nProblem 9\n\nShow that this is a basis for ${\\displaystyle \\mathbb {R} ^{4}}$.\n\n${\\displaystyle \\langle {\\begin{pmatrix}1\\\\0\\\\0\\\\0\\end{pmatrix}},{\\begin{pmatrix}1\\\\1\\\\0\\\\0\\end{pmatrix}},{\\begin{pmatrix}1\\\\1\\\\1\\\\0\\end{pmatrix}},{\\begin{pmatrix}1\\\\1\\\\1\\\\1\\end{pmatrix}}\\rangle }$\n\n(The results of this subsection can be used to simplify this job.)\n\nProblem 10\n\nRefer to Example 2.9.\n\n1. Sketch a similar subspace diagram for ${\\displaystyle {\\mathcal {P}}_{2}}$.\n2. Sketch one for ${\\displaystyle {\\mathcal {M}}_{2\\!\\times \\!2}}$.\nThis exercise is recommended for all readers.\nProblem 11\nWhere ${\\displaystyle S}$ is a set, the functions ${\\displaystyle f:S\\to \\mathbb {R} }$ form a vector space under the natural operations: the sum ${\\displaystyle f+g}$ is the function given by ${\\displaystyle (f+g)\\,(s)=f(s)+g(s)}$ and the scalar product is given by ${\\displaystyle (r\\cdot f)\\,(s)=r\\cdot f(s)}$. What is the dimension of the space resulting for each domain?\n1. ${\\displaystyle S=\\{1\\}}$\n2. ${\\displaystyle S=\\{1,2\\}}$\n3. ${\\displaystyle S=\\{1,\\ldots ,n\\}}$\nProblem 12\n\n(See Problem 11.) Prove that this is an infinite-dimensional space: the set of all functions ${\\displaystyle f:\\mathbb {R} \\to \\mathbb {R} }$ under the natural operations.\n\nProblem 13\n\n(See Problem 11.) What is the dimension of the vector space of functions ${\\displaystyle f:S\\to \\mathbb {R} }$, under the natural operations, where the domain ${\\displaystyle S}$ is the empty set?\n\nProblem 14\n\nShow that any set of four vectors in ${\\displaystyle \\mathbb {R} ^{2}}$ is linearly dependent.\n\nProblem 15\n\nShow that the set ${\\displaystyle \\langle {\\vec {\\alpha }}_{1},{\\vec {\\alpha }}_{2},{\\vec {\\alpha }}_{3}\\rangle \\subset \\mathbb {R} ^{3}}$ is a basis if and only if there is no plane through the origin containing all three vectors.\n\nProblem 16\n1. Prove that any subspace of a finite dimensional space has a basis.\n2. Prove that any subspace of a finite dimensional space is finite dimensional.\nProblem 17\n\nWhere is the finiteness of ${\\displaystyle B}$ used in Theorem 2.3?\n\nThis exercise is recommended for all readers.\nProblem 18\n\nProve that if ${\\displaystyle U}$ and ${\\displaystyle W}$ are both three-dimensional subspaces of ${\\displaystyle \\mathbb {R} ^{5}}$ then ${\\displaystyle U\\cap W}$ is non-trivial. Generalize.\n\nProblem 19\n\nBecause a basis for a space is a subset of that space, we are naturally led to how the property \"is a basis\" interacts with set operations.\n\n1. Consider first how bases might be related by \"subset\". Assume that ${\\displaystyle U,W}$ are subspaces of some vector space and that ${\\displaystyle U\\subseteq W}$. Can there exist bases ${\\displaystyle B_{U}}$ for ${\\displaystyle U}$ and ${\\displaystyle B_{W}}$ for ${\\displaystyle W}$ such that ${\\displaystyle B_{U}\\subseteq B_{W}}$? Must such bases exist? For any basis ${\\displaystyle B_{U}}$ for ${\\displaystyle U}$, must there be a basis ${\\displaystyle B_{W}}$ for ${\\displaystyle W}$ such that ${\\displaystyle B_{U}\\subseteq B_{W}}$? For any basis ${\\displaystyle B_{W}}$ for ${\\displaystyle W}$, must there be a basis ${\\displaystyle B_{U}}$ for ${\\displaystyle U}$ such that ${\\displaystyle B_{U}\\subseteq B_{W}}$? For any bases ${\\displaystyle B_{U},B_{W}}$ for ${\\displaystyle U}$ and ${\\displaystyle W}$, must ${\\displaystyle B_{U}}$ be a subset of ${\\displaystyle B_{W}}$?\n2. Is the intersection of bases a basis? For what space?\n3. Is the union of bases a basis? For what space?\n4. What about complement?\n\n(Hint. Test any conjectures against some subspaces of ${\\displaystyle \\mathbb {R} ^{3}}$.)\n\nThis exercise is recommended for all readers.\nProblem 20\n\nConsider how \"dimension\" interacts with \"subset\". Assume ${\\displaystyle U}$ and ${\\displaystyle W}$ are both subspaces of some vector space, and that ${\\displaystyle U\\subseteq W}$.\n\n1. Prove that ${\\displaystyle \\dim(U)\\leq \\dim(W)}$.\n2. Prove that equality of dimension holds if and only if ${\\displaystyle U=W}$.\n3. Show that the prior item does not hold if they are infinite-dimensional.\n? Problem 21\n\nFor any vector ${\\displaystyle {\\vec {v}}}$ in ${\\displaystyle \\mathbb {R} ^{n}}$ and any permutation ${\\displaystyle \\sigma }$ of the numbers ${\\displaystyle 1}$, ${\\displaystyle 2}$, ..., ${\\displaystyle n}$ (that is, ${\\displaystyle \\sigma }$ is a rearrangement of those numbers into a new order), define ${\\displaystyle \\sigma ({\\vec {v}})}$ to be the vector whose components are ${\\displaystyle v_{\\sigma (1)}}$, ${\\displaystyle v_{\\sigma (2)}}$, ..., and ${\\displaystyle v_{\\sigma (n)}}$ (where ${\\displaystyle \\sigma (1)}$ is the first number in the rearrangement, etc.). Now fix ${\\displaystyle {\\vec {v}}}$ and let ${\\displaystyle V}$ be the span of ${\\displaystyle \\{\\sigma ({\\vec {v}})\\,{\\big |}\\,\\sigma {\\text{ permutes }}1,\\ldots ,n\\}}$. What are the possibilities for the dimension of ${\\displaystyle V}$? (Gilbert, Krusemeyer & Larson 1993, Problem 47)\n\nSolutions\n\n## References\n\n\u2022 Blass, A. (1984), \"Existence of Bases Implies the Axiom of Choice\", in Baumgartner, J. E., Axiomatic Set Theory, Providence RI: American Mathematical Society, pp.\u00a031\u201333\u00a0.\n\u2022 Rucker, Rudy (1982), Infinity and the Mind, Birkhauser\u00a0.\n\u2022 Gilbert, George T.; Krusemeyer, Mark; Larson, Loren C. (1993), The Wohascum County Problem Book, The Mathematical Association of America\u00a0.\nLinear Algebra\n \u2190\u00a0Basis Dimension Vector Spaces and Linear Systems\u00a0\u2192","date":"2017-04-24 05:39:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 219, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9933162331581116, \"perplexity\": 2694.225146108719}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-17\/segments\/1492917119080.24\/warc\/CC-MAIN-20170423031159-00178-ip-10-145-167-34.ec2.internal.warc.gz\"}"}
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{"url":"http:\/\/thepasqualian.com\/?p=1145","text":"## 1.3 Exercise 2\n\nThis problem is interesting because it shows that restrictions of equivalence relations are also equivalence relations.\n\n\"Let\u00a0 $C$ be a relation on a set $A$.\u00a0 If\u00a0 $A_0 \\subset A$, define the restriction of\u00a0 $C$ to\u00a0 $A_0$ to be the relation\u00a0 $C \\cap (A_0 \\times A_0)$. Show that the restriction of an equivalence relation is an equivalence relation.\"\n\n(Taken from\u00a0Topology\u00a0by James R. Munkres, Second Edition, Prentice Hall, NJ, 2000. Page 28.)\n\n----------\n\nSOLUTION\n\nReflexivity: Notice that\u00a0 $A_0 \\times A_0$ will naturally contain those reflexive elements that belong to it (pick a fixed element $a \\in A_0$, then $(a, a) \\in A_0 \\times A_0$).\u00a0 By hypothesis of reflexivity of\u00a0 $C$, such are included in\u00a0 $C$ too, because\u00a0 $C$ contains all reflexive elements in\u00a0 $A \\times A$. It follows that such a point is also in the restriction.\n\nSymmetry:\u00a0 We want to show that, picking any point in the restriction, its symmetric point is also in the restriction.\u00a0 First, notice that for any (fixed) element\u00a0 $(a, b) \\in A_0 \\times A_0$, its symmetric partner\u00a0 $(b, a) \\in A_0 \\times A_0$ because of the set's square-symmetry.\u00a0 Now pick\u00a0 $(x, y) \\in C \\cap A_0 \\times A_0$.\u00a0 Of course, such\u00a0 $(x, y) \\in A_0 \\times A_0$, and also\u00a0 $(x, y) \\in C$ by the definition of intersection.\u00a0 Since\u00a0 $(x, y) \\in C$, there exists a point\u00a0 $(y, x) \\in C$ by hypothesis of its symmetry in\u00a0 $A \\times A$. \u00a0 $(y, x)$ is also a point in\u00a0 $A_0 \\times A_0$ by its square-symmetry.\u00a0 Therefore\u00a0 $(y, x) \\in C \\cap A_0 \\times A_0$ and the restriction is symmetric.\n\nTransitivity:\u00a0 First, notice that transitivity holds in\u00a0 $A_0 \\times A_0$, because it contains all elements\u00a0that belong to\u00a0 $A_0$\u00a0in combination with themselves.\u00a0 Thus, having chosen any three (fixed) elements\u00a0 $a, b, c \\in A_0$, specifically these elements\u00a0 $(a, b), (b, c), (a, c)$ are in\u00a0 $A_0 \\times A_0$.\u00a0 Now pick two elements\u00a0 $(x, y), (y, z) \\in C \\cap A_0 \\times A_0$.\u00a0 There is an element\u00a0 $(x, z) \\in C$ by hypothesis of its transitivity in\u00a0 $A \\times A$.\u00a0 Such exists in\u00a0 $A_0 \\times A_0$ as well by our aforementioned observation.\u00a0 Since the element is in both\u00a0 $C$ and\u00a0 $A_0 \\times A_0$, it is in their intersection and therefore in the restriction of\u00a0 $C$.\n\nCategories:","date":"2018-01-22 02:10:24","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 36, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 36, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9498976469039917, \"perplexity\": 2047.2923899867008}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-05\/segments\/1516084890947.53\/warc\/CC-MAIN-20180122014544-20180122034544-00502.warc.gz\"}"}
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\section{Introduction }
For centuries, it was thought that Euclidean geometry is the only geometric system until the discoveries of hyperbolic geometry that is a non-Euclidean geometry. In 1870, it was shown by Cayley-Klein that there are 9 different geometries in the plane including Euclidean geometry. These geometries are determined by parabolic, elliptic, and hyperbolic measures of angles and lengths.
The main aim of this work is to study some special curves in Galilean geometry which is also among foregoing geometries. The conventional view about Galilean geometry is that it is relatively simpler than Euclidean geometry. There are some problems that cannot be solved in Euclidean geometry, however they are an easy matter in Galilean geometry. For instance, the problem of determination of position vector of an arbitrary curve and the problem that we study in this article can be considered as good examples for the case. Another advantageous of Galilean geometry is that it is associated with the Galilean principle of relativity. For more details about Galilean geometry, we refer the interested reader to the book by Yaglom \cite{yag}.
The theory of curves forms an important and useful class of theories in differential geometry. The curves emerge from the solutions of some important physical problems. Also, mathematical models are often used to describe complicated systems that arising in many different branch of science such as engineering, chemistry, biology, etc. \cite{biyo, kimya}
A curve in space is studied by assigning at each point a moving frame.
The method of moving frame is a central tool to study a curve or a surface. The fundamental theorem of curves states that curves are determined by curvatures and Frenet vectors \cite{krey}. Thus, curvature functions provide us with some special and important information about curves. For example; line, circle, helix (circular or generalized), Salkowski curve, geodesic , asymptotic and line of curvature etc. All of these curves are characterized by the specific conditions imposed on their curvatures. To examine the characteristics of this curves, it is important that the position vectors of the curves are given according to the curvature functions. However, this is not always possible in all geometries. For example, the problem of determination of the position vector of a curve in Euclidean or Minkowski spaces can only be solved for some special curve such as plane line, helix and slant helix.
However, this problem can be solved independent of type of curves in Galilean space \cite{ali,buket}.
Curves can also be produced in many different ways, such as solution of physical problems, trajectory of a moving particle, etc. \cite{krey}. In addition, one can produce a new curve by using Frenet vector fields of a given curve, such as Evolutes and involutes, spherical indicatrix, and Smarandache curves.
If the position vector of $\alpha$ curve is formed by frame vectors of $\beta$ curve, then $\alpha$ is called Smarandache curve of $\beta$ \cite{suha}.
Recently, many researchers have studied special Smarandache curves with respect to different frames in different spaces. In \cite{suha}, the authors introduced a special case of Smarandache curves in the space $E_4^1$. \cite{ali10} studied special Smarandache curve in Euclidean space $E^3$. In \cite{yuce, cetin}, the authors investigate the curves with respect to Bishop and Darboux frame in $E^3$, respectively. Also, \cite{saad17} investigated the curves with respect to Darboux frame in Minkowski $3-$space.
Among these studies, only \cite{saad} used general position vector with respect to Frenet frame of curve to obtain Samarandache curves in Galilean space.
The main aim of this paper is to determine position vector of Smarandache curves of arbitrary curve on a surface in $G_3$ in terms of geodesic, normal curvature and geodesic torsion with respect to the standard frame. The results of this work include providing Smarandache curves of some special curves such as geodesic, asymptotic curve, line of curvature on a surface in $G_3$ and Smarandache curves for special cases of curves such as, Smarandache curves of geodesics that are circular helix, genaralized helix or Salkowski, etc. Finally, we elaborate on some special curves by giving their graphs.
\section{Introduction and Preliminaries}
The Galilean space $G^{3}$ is one of the Cayley-Klein spaces associated with the projective metric of signature $\left( 0,0,+,+\right) $ \cite{mol}. The absolute figure of the Galilean space is the ordered triple $\{w,f,I\}$, where $w$ is an ideal (absolute) plane,
$f$ is a line (absolute line) in $w$, and $I$ is a fixed eliptic involution of points of $f$.
In non-homogeneous coordinates the group of isometries of $G^{3}$ has the following form:
\begin{eqnarray}
\overline{x} &=&a_{11}+x, \notag \\
\overline{y} &=&a_{21}+a_{22}x+y\cos \varphi +z\sin \varphi , \\
\overline{z} &=&a_{31}+a_{32}x-y\sin \varphi +z\cos \varphi, \notag
\end{eqnarray}%
where $a_{11}, a_{21}, a_{22}, a_{31}, a_{32}$, and $\varphi$ are real numbers \cite{pav}.
If the first component of a vector is zero, then the vector is called as isotropic, otherwise it is called non-isotropic vector \cite{pav}.
In $G^{3}$, the scalar product of two vectors $\mathbf{v}=(v_{1},v_{2},v_{3})$ and $\mathbf{w}=(w_{1},w_{2},w_{3})$ is defined by
$$\mathbf{v}\cdot _{G}\mathbf{w} = \left\{
\begin{array}{lr}
v_{1}w_{1} , & \text{if } v_{1}\neq 0 \text{ or } w_{1}\neq 0\, \ \ \ \\
v_{2}w_{2}+v_{3}w_{3} ,& \text{if } v_{1}=0 \text{ and } w_{1}=0\,.
\end{array}\right.$$
The Galilean cross product of these vectors is defined by
\begin{eqnarray}
\mathbf v\times _{G}\mathbf w=%
\begin{vmatrix}
0 & \mathbf e_{2} &\mathbf {e_{3}} \\
v_{1} & v_{2} & v_{3} \\
w_{1} & w_{2} & w_{3}%
\end{vmatrix}.%
\end{eqnarray}
If $\mathbf{v}\cdot _{G}\mathbf{w}=0$, then $\mathbf{v}$ and $\mathbf{w}$
are perpendicular.
The norm of $\mathbf{v}$ is defined by
$$\Vert \mathbf{v}\Vert_{G}=\sqrt{\vert\mathbf{v}\cdot_{G}\mathbf{v}\vert}.$$
Let $I\subset \mathbb R$ and let $\gamma :I\rightarrow G^{3}$ be a unit speed curve
with curvature $\kappa>0$ and torsion $\tau$.
Then the curve $\gamma$ is defined by
\begin{eqnarray*}
\gamma \left( x\right) =\left( x,y\left( x\right) ,z\left( x\right) \right) ,
\end{eqnarray*}
and that the Frenet frame fields are given by
\begin{eqnarray}{\label{fframe}}
T\left(x\right) &=&\alpha ^{\prime }\left( x\right),
\notag \\
N\left( x\right) &=& \frac{\gamma''(x)}{\Vert \gamma''(x)\Vert_{G}}
\\
B\left( x\right) &=&T(x)\times _{G}B(x) \notag \\&=&\frac{1}{\kappa \left( x\right) }\left( 0,
-z^{\prime \prime }\left( x\right) , y^{\prime \prime }\left(
x\right) \right), \notag
\end{eqnarray}%
where
\begin{equation}
\kappa \left( x\right) ={\Vert \gamma''(x) \Vert }_{G} \quad \text{and} { \ \ }\tau
\left( x\right) =\frac{\det \left( \gamma ^{\prime }\left( x\right) ,\gamma
^{\prime \prime }\left( x\right) ,\gamma ^{\prime \prime \prime }\left(
x\right) \right) }{\kappa ^{2}\left( x\right) }\,.
\end{equation}%
The vector fields $\mathbf{T, N} $ and $\mathbf{B}$ are called the tangent vector field, the principal normal
and the binormal vector field, respectively \cite{pav}. Therefore, the Frenet-Serret formulas can be written in matrix form as
\begin{eqnarray}
\begin{bmatrix}
\mathbf{T} \\
\mathbf{N} \\
\mathbf{B}%
\end{bmatrix}%
^{\prime }=%
\begin{bmatrix}
0 & \kappa & 0 \\
0 & 0 & \tau \\
0 &- \tau & 0%
\end{bmatrix}%
\begin{bmatrix}
\mathbf{T} \\
\mathbf{N} \\
\mathbf{B}%
\end{bmatrix}\,.
\end{eqnarray}%
There is another useful frame for study curves on a surface. For an easy reference we call this surface $M$. This frame can be formed by two basic vectors. These vectors are a unit tangent vector field $\mathbf{T}$ of the curve $\gamma$ on $M$ and the unit normal vector field $\mathbf{n}$ of $M$ at the point $\gamma(x)$ of $\gamma$. Therefore, the frame field $\{\mathbf{T, Q, n}\}$ is obtained and is called Darboux frame or the tangential-normal frame field. Here, $\mathbf{Q=n}\times_{G}\mathbf{T}$.
\begin{theorem}Let $\gamma :I\subset \mathbb{R}\rightarrow M\subset G^{3}$ be a unit-speed curve, and let $\{\mathbf{T, Q, n}\}$ be the Darboux frame field of $\gamma$ with respect to M. Then the Frenet formulas in matrix form is given by
\begin{eqnarray}\label{Darboux}
\begin{bmatrix}
\mathbf{T} \\
\mathbf{Q} \\
\mathbf{n}
\end{bmatrix}
^{\prime }=
\begin{bmatrix}
0 & \kappa_g & \kappa_n \\
0 & 0 & \tau_g \\
0 & -\tau_g & 0
\end{bmatrix}
\begin{bmatrix}
\mathbf{T} \\
\mathbf{Q} \\
\mathbf{n}
\end{bmatrix}\, ,
\end{eqnarray}
where $\kappa_g$, $\kappa_n$ and $\tau_g$ are called geodesic curvature, normal curvature and geodesic torsion, respectively.
\end{theorem}
\begin{proof} It follows from solving \eqref{Darboux} componentwise \cite{buket, tevfik} .
\end{proof}
Also, (\ref{Darboux}) implies the important relations
\begin{eqnarray}\label{kt}
\kappa^2(x)=\kappa^2_g(x)+\kappa^2_n(x), \hskip .5cm \tau(x)=-\tau_g(x)+\frac{\kappa'_g(x)\kappa_n(x)-\kappa_g(x)\kappa'_n(x)}{\kappa^2_g(x)+\kappa^2_n(x)}
\end{eqnarray}
where $\kappa(x)$ and $\tau(x)$ are the curvature and the torsion of $\beta$, respectively.
We refer to \cite{pav, ros, yag} for detailed treatment of Galilean and pseudo-Galilean geometry.
\section{Special Smarandache Curves with Darboux Apparatus with Respect to Frenet Frame in $G_{3}$}
In this section, we will give special Smarandache curves with Darboux apparatus with respect to Frenet frame of a curve on a surface in $G_3$. In order to the position vector of an arbitrary curve with geodesic curvature $\kappa_{g}$, normal curvature $\kappa_{n}$ and geodesic torsion $\tau_{g}$ on the surface in $G_{3}$ \cite{buket}.
Based on the definition of Smarandache curve in \cite{saad,suha}, we will state the following definition.
\begin{definition}\label{smadef}
Let $\gamma(x)$ be a unit speed curve in $G_3$ and ${\mathbf{T, N, B}}$ be the Frenet frame field along with $\gamma$. Special Smarandache $\mathbf{TN, TB}$ and $\mathbf{TNB}$ curves are, respectively, defined by
\begin{eqnarray}
\gamma_{\mathbf{TN}}&=&\mathbf{T}+\mathbf{N}\\
\gamma_{\mathbf{TB}}&=&\mathbf{T}+\mathbf{B}\\
\gamma_{\mathbf{TNB}}&=&\mathbf{T}+\mathbf{N}+\mathbf{B}.
\end{eqnarray}
\end{definition}
The following result which is stated as theorem is our main work in this article.
\begin{theorem}\label{posmat}
The $\mathbf{TN}$, $\mathbf{TB}$ and $\mathbf{TNB}$ special Smarandache curves with Darboux apparatus of $\gamma$ with respect to Frenet frame are, respectively, written as
\begin{eqnarray}{\label{posma}}
\gamma_{\mathbf{TN}}&=&\left(
\begin{array}{c}
1,\int N_1 dx+ \frac{1}{\sqrt{{\kappa_g}^2+{\kappa_n}^2}}N_1, \,
\int N_2 dx+\frac{1}{\sqrt{{\kappa_g}^2+{\kappa_n}^2}}N_2
\end{array}\notag
\right) \\\notag
&& \\
\gamma_{\mathbf{TB}} &=&\left(
\begin{array}{c}
\ 1\ ,\ \int N_1 dx - \frac{1}{\sqrt{{\kappa_g}^2+{\kappa_n}^2}}N_2,\,
\int N_2 dx+\frac{1}{\sqrt{{\kappa_g}^2+{\kappa_n}^2}}N_1
\end{array}
\right) \\\notag
&& \\\notag
\gamma_{\mathbf{TNB}} &=&\ \left(
\begin{array}{c}
1, \, \int N_1 dx+\frac{1}{\sqrt{{\kappa_g}^2+{\kappa_n}^2}}(N_{1}-N_{2}),\,
\int N_2 dx+\frac{1}{\sqrt{{\kappa_g}^2+{\kappa_n}^2}}(N_{1}+N_{2})%
\end{array}%
\right)
\end{eqnarray}
where
\begin{eqnarray*}
{N_1}&=&\kappa _{g}\sin \Big(\int\tau _{g}dx\Big)+\kappa _{n}\cos
\Big(\int \tau _{g}dx\Big),\\
N_2&=&\kappa _{g}\cos \Big(\int \tau _{g}dx\Big)-\kappa _{n}\sin \Big(\int \tau
_{g}dx\Big).
\end{eqnarray*}
\end{theorem}
\begin{proof}
The position vector of an arbitrary curve with geodesic curvature $\kappa_{g}$, normal curvature $\kappa_{n}$ and geodesic torsion $\tau_{g}$ on the surface in $G_{3}$ which is introduced by \cite{buket} as follows
\begin{eqnarray}\label{pos}
\gamma(x)\ =\left(
\begin{array}{c}
x,\, \int (\int (\kappa _{g}(x)\sin (\int \tau _{g}(x)dx)-\kappa _{n}(x)\int \tau
_{g}(x)\sin (\int \tau _{g}(x)dx)dx)dx)dx,\\
\\
\int (\int (\kappa _{g}\cos (\int \tau _{g}dx)-\kappa _{n}\int \tau _{g}\cos
(\int \tau _{g}dx)dx)dx)dx
\end{array}
\right)
\end{eqnarray}
The derivatives of this curve are, respectively, given by;
\begin{eqnarray}
\notag
\gamma^{\prime}(x) &=&\left(
\begin{array}{c}
1, \, \int (\kappa _{g}\sin (\int \tau _{g}dx)-\kappa _{n}\int \tau _{g}\sin
(\int \tau _{g}ds)dx)dx, \\
\\
\ \int (\kappa _{g}\cos (\int \tau _{g}dx)-\kappa _{n}\int \tau _{g}\cos(\int \tau _{g}dx)dx)dx%
\end{array}
\right)\notag \\
&& \notag \\
\gamma^{\prime \prime }(x) &=&\left(
\begin{array}{c}
0, \, \kappa _{g}\sin (\int \tau _{g}dx)-\kappa _{n}\int \tau _{g}\sin
(\int \tau _{g}dx)dx, \\
\\
\kappa _{g}\cos (\int \tau _{g}dx)-\kappa _{n}\int \tau _{g}\cos (\int \tau
_{g}dx)dx
\end{array}
\right) \notag
\end{eqnarray}
The Frenet frame vector fields with Darboux apparatus of $\gamma$ are determined as follows
\begin{eqnarray*}
\mathbf{T} &=&\left(
\begin{array}{c}
1, \, \int (\kappa _{g}\sin (\int \tau _{g}dx)-\kappa _{n}\int \tau _{g}\sin
(\int \tau _{g}dx)dx)dx, \\
\\
\ \int (\kappa _{g}\cos (\int \tau _{g}dx)-\kappa _{n}\int \tau _{g}\cos
(\int \tau _{g}dx)dx)dx%
\end{array}%
\right) \\
&& \\
\mathbf{N} &=&\frac{1}{\sqrt{{\kappa_g}^2+{\kappa_n}^2}}\left(
\begin{array}{c}
0,\, \kappa _{g}\sin(\int \tau _{g}dx)+\kappa _{n}\cos(\int \tau _{g}dx),
\\ \\ \kappa _{g}\cos(\int \tau _{g}dx)-\kappa _{n}\sin(\int \tau _{g}dx)
\end{array}
\right)\\
&& \\
\mathbf{B} &=&\frac{1}{\sqrt{{\kappa_g}^2+{\kappa_n}^2}}\left(
\begin{array}{c}
0,\, -\kappa _{g}\cos(\int \tau _{g}dx)+\kappa _{n}\sin(\int \tau _{g}dx),
\\ \\ \kappa _{g}\sin(\int \tau _{g}dx)+\kappa _{n}\cos(\int \tau _{g}dx)
\end{array}
\right)
\end{eqnarray*}
Using the definition (\ref{smadef}), we obtain desired results.
We now provide some applications of this theorem for some special curves.
\end{proof}
\section{Applications}
We begin with studying Smarandache curves of important special curves lying on surfaces such as geodesic, asymtotic and curvature (or principal) line. Also, we will provide special cases such as helix and Salkowski curve of these curves.
Let $\gamma$ be regular curve on a surface in $G^3$ with the curvature $\kappa$, the torsion $\tau$, the geodesic curvature $\kappa_g$, the normal curvature $\kappa_n$ and the geodesic torsion $\tau_g$.
\begin{definition}\label{defgap}
\cite{krey} We can say that $\gamma$ is
\begin{eqnarray*}
\begin{split}
geodesic \, curve &\Longleftrightarrow \kappa_g\equiv 0,
\\asymptotic \, curve & \Longleftrightarrow \kappa_n\equiv 0,
\\line \, of \, curvature & \Longleftrightarrow \tau_g\equiv 0.
\end{split}
\end{eqnarray*}
Also, We can say that $\gamma$ is called:
\begin{eqnarray}\label{helsal}
\begin{array}{ccc}
\kappa, \tau & \hskip 1cm& r\\
\hline
\kappa\equiv0 &\Longleftrightarrow &\textbf{a straight line.}\\
\tau\equiv0 &\Longleftrightarrow &\textbf{a plane curve.}\\
\kappa\equiv\textit{cons.$>$0},\tau\equiv\textit{cons.$>$0} &\Longleftrightarrow &\textbf{a circular helix or W-curve.}\\
\frac{\tau}{\kappa}\equiv\textit{cons.} &\Longleftrightarrow &\textbf{a generalized helix.}\\
\kappa\equiv\textit{cons.}, \tau\neq\textit{cons.} &\Longleftrightarrow &\textbf{Salkowski curve \cite{mon,sal}.}\\
\kappa\neq\textit{cons.}, \tau\equiv\textit{cons.} &\Longleftrightarrow &\textbf{anti-Salkowski curve \cite{sal}.}\\
\end{array}
\end{eqnarray}
\end{definition}
\subsection{The position vectors of Smarandache curves of a general geodesic curve in $G_3$}
\begin{theorem}{\label{thmgeo}}
The position vectors $\alpha_g(x)$ of Smarandache curves of a family of geodesic curve in $G_3$ are provided by
%
%
\begin{eqnarray*}
\alpha^g _{\mathbf{TN}} &=&\left(
\begin{array}{c}
1, \, \int \kappa _{n}\cos (\int \tau _{g}dx)dx+\cos (\int \tau _{g}dx),
-\int \kappa _{n}\sin (\int \tau _{g}dx)dx-\sin (\int \tau _{g}dx)
\end{array}
\right) \\
&& \\
\alpha^g _{\mathbf{TB}} &=&\left(
\begin{array}{c}
1, \, \int \kappa _{n}\cos (\int \tau _{g}dx)dx+\sin (\int \tau _{g}dx),
-\int \kappa _{n}\sin (\int \tau _{g}dx)dx+\cos (\int \tau _{g}dx)
\end{array}
\right)\\
&&\\
\alpha^g _{\mathbf{TNB}} &=&\left(
\begin{array}{c}
1, \, \int \kappa _{n}\cos (\int \tau _{g}dx)dx+\cos (\int \tau _{g}dx)+\sin (\int \tau _{g}dx),\\
\\
-\int \kappa _{n}\sin (\int \tau _{g}dx)dx+\cos (\int \tau _{g}dx)-\sin (\int \tau _{g}dx)
\end{array}%
\right) \notag
\end{eqnarray*}
\end{theorem}
\begin{proof}
The above equations are obtained as general position vectors for $\mathbf{TN}, \, \mathbf{TB}$ and $\mathbf{TNB}$ special Smarandache curves with Darboux apparatus of a geodesic curve on a surface in $G_3$ by using the definition (\ref{defgap}) and Theorem \ref{posmat}.
\end{proof}
Now, we will give the position vectors for special Smarandache curves of some special cases of a geodesic curve in $G_3$.
\begin{corollary}
The position vectors of special Smarandache curves of a family of geodesic curve that is a circular helix in $G_3$ are given by the equations
%
%
%
%
%
\begin{eqnarray*}
\alpha^g_{ch}{_\mathbf{TN}}(x) &=& \left(
\begin{array}{c}
1, \, \frac{e}{c}\sin(cx+c_{1})+\frac{e}{c}\cos(cx+c_{1}), \\ \\
\frac{e}{c}\cos(cx+c_{1})-\frac{e}{c}\sin(cx+c_{1})
\end{array}
\right)\\
\\
\alpha^g_{ch}{_\mathbf{TB}}(x) &=& \left(
\begin{array}{c}
1, \, (\frac{e+c}{c})\sin(cx+c_{1}), \, (\frac{e+c}{c})\cos(cx+c_{1})
\end{array}
\right)\\
\\
\alpha^g_{ch}{_\mathbf{TNB}}(x) &=&\left(
\begin{array}{c}
1, \,
(\frac{e+c}{c})\sin(cx+c_{1})+\cos(cx+c_{1}), \\
\\
(\frac{e+c}{c})\cos(cx+c_{1})-\sin(cx+c_{1}) \\
\\
\end{array}%
\right)
\end{eqnarray*}
where $c, \, c_1$ and $e$ are integral constants.
\end{corollary}
\begin{corollary}
The position vectors of special Smarandache curves of a family of geodesic curve that is a generalized helix in $G_3$ are given by the equations
%
%
%
%
%
\begin{eqnarray*}
\alpha^g_{gh}{_\mathbf{TN}}(x)&=&\left(
\begin{array}{c}
1, \, \frac{1}{d}\sin(d\int\kappa_{n}dx)+\cos(d\int\kappa_{n}dx), \\
\\ \frac{1}{d}\cos(d\int\kappa_{n}dx)-\sin(d\int\kappa_{n}dx)\\
\end{array}
\right)\\
\\
\alpha^g_{gh}{_\mathbf{TB}}(x)&=&\left(
\begin{array}{c}
1, \, \frac{1}{d}\sin(d\int\kappa_{n}dx)+\sin(d\int\kappa_{n}dx), \\
\\ \frac{1}{d}\cos(d\int\kappa_{n}dx)+\cos(d\int\kappa_{n}dx)\\
\end{array}%
\right) \\
\\
\alpha^g_{gh}{_\mathbf{TNB}}(x)&=&\left(
\begin{array}{c}
1, \, \frac{d+1}{d}\sin(d\int\kappa_{n}dx)+\cos(d\int\kappa_{n}dx), \\
\\
\frac{d+1}{d}\cos(d\int\kappa_{n}dx)-\sin(d\int\kappa_{n}dx) \\
\end{array}
\right)
\end{eqnarray*}
where $d$ is integral constant.
\end{corollary}
\begin{corollary}
The position vectors of Smarandache curves of a family of geodesic that is a Salkowski curve in $G_3$ are given by the equations
%
%
%
%
%
%
\begin{eqnarray*}
\alpha^g_{s}{_\mathbf{TN}}(x)&=&\left(
\begin{array}{c}
1, \, m\int\cos(\int\tau_{g}dx)dx+\cos(\int\tau_{g}dx), \\
\\ -m\int\sin(\int\tau_{g}dx)dx-\sin(\int\tau_{g}dx) \\
\end{array}%
\right) \\
\\
\alpha^g_{s}{_\mathbf{TB}}(x)&=&\left(
\begin{array}{c}
1, \, m\int\cos(\int\tau_{g}dx)dx+\sin(\int\tau_{g}dx), \\
\\ -m\int\sin(\int\tau_{g}dx)dx+\cos(\int\tau_{g}dx) \\
\end{array}%
\right)\\
\\
\alpha^g_{s}{_\mathbf{TNB}}(x)&=&\left(
\begin{array}{c}
1, \, m\int\cos(\int\tau_{g}dx)dx+\cos(\int\tau_{g}dx)+\sin(\int\tau_{g}dx),\\
\\ -m\int\sin(\int\tau_{g}dx)dx+\cos(\int\tau_{g}dx)-\sin(\int\tau_{g}dx) \\
\end{array}%
\right)
\end{eqnarray*}
where $m$ is an integral constant.
\end{corollary}
\begin{corollary}
The position vectors of Smarandache curves of a family of geodesic that is a anti-Salkowski curve in $G_3$ are given by the equations
%
%
%
\begin{eqnarray*}
\alpha^g_{as}{_\mathbf{TN}}(x)&=&\left(
\begin{array}{c}
1, \, \int\kappa_{n}\cos(cx+c_{1})dx+\cos(cx+c_{1}),\\
\\ -\int\kappa_{n}\sin(cx+c_{1})dx-\sin(cx+c_{1})
\end{array}%
\right)\\
\\
\alpha^g_{as}{_\mathbf{TB}}(x)&=&\left(
\begin{array}{c}
1, \, \int\kappa_{n}\cos(cx+c_{1})dx+\sin(cx+c_{1}) , \\
\\ -\int\kappa_{n}\sin(cx+c_{1})dx+\cos(cx+c_{1})
\end{array}%
\right)\\
\alpha^g_{as}{_\mathbf{TNB}}(x)&=&\left(
\begin{array}{c}
1, \, \int\kappa_{n}\cos(cx+c_{1})dx+\cos(cx+c_{1})+\sin(cx+c_{1}), \\
\\ -\int\kappa_{n}\sin(cx+c_{1})dx+\cos(cx+c_{1})-\sin(cx+c_{1})
\end{array}%
\right)
\end{eqnarray*}
where $c$ and $c_{1}$ are integral constants.
\end{corollary}
We want to note that above corollaries can be proved by using the equations (\ref{kt}), (\ref{helsal}) and Theorem \ref{thmgeo}.
\subsection{The position vectors of Smarandache curves of an general asymptotic curve in $G_3$}
\begin{theorem}{\label{thmasy}}
The position vectors $\alpha_g(x)$ of Smarandache curves of a family of asymptotic curve in $G_3$ are provided by
%
%
%
%
%
%
%
%
\begin{eqnarray*}
\beta^a _{\mathbf{TN}} &=&\left( 1, \, \int \kappa _{g}\sin (\int \tau _{g}dx)dx+\sin
\int \tau _{g}dx\ ,\ \int \kappa _{g}\cos (\int \tau _{g}dx)dx+\cos \int
\tau _{g}dx\right) \\
&& \notag \\
\beta^a _{\mathbf{TB}} &=&\left( 1, \, \int \kappa _{g}\sin (\int \tau _{g}dx)dx-\cos
\int \tau _{g}dx\ ,\ \int \kappa _{g}\cos (\int \tau _{g}dx)dx+\sin \int
\tau _{g}dx\right) \notag \\
&& \notag \\
\beta^a _{\mathbf{TNB}} &=&\left(
\begin{array}{c}
1, \, \int \kappa _{g}\sin (\int \tau _{g}dx)dx+\sin \int \tau _{g}dx-\cos
\int \tau _{g}dx, \, \\ \\
\int \kappa _{g}\cos (\int \tau _{g}dx)dx+\cos \int \tau _{g}dx+\sin \int
\tau _{g}ds%
\end{array}%
\right) \notag
\end{eqnarray*}
\end{theorem}
\begin{proof}
By using the definition (\ref{defgap}) in Theorem \ref{posmat}, then the above equations are obtained as general position vectors for $\mathbf{TN}, \, \mathbf{TB}$ and $\mathbf{TNB}$ special smarandache curves with Darboux apparatus of an asymptotic curve on a surface in $G_3$.
\end{proof}
Now, we will give the position vectors for Smarandache curves of some special cases of an asymptotic curve in $G_3$
\begin{corollary}
The position vectors of Smarandache curves of a family of asymptotic curve that is a circular helix in $G_3$ are given by the equations
%
%
%
%
\begin{eqnarray*}
\beta^a_{ch}{_\mathbf{TN}}(x)&=&\left(
\begin{array}{c}
1, \, -\frac{f}{c}\cos(cx+c_{1})+\sin(cx+c_{1})\ , \\
\\ \frac{f}{c}\sin(cx+c_{1})+\cos(cx+c_{1}) \\
\end{array}%
\right)\\ \\
\beta^a_{ch}{_\mathbf{TB}}(x)&=&\left(
\begin{array}{c}
1, \, -(\frac{c+f}{c})\cos(cx+c_{1}),
\, (\frac{c+f}{c})\sin(cx+c_{1}) \\
\end{array}
\right)\\ \\
\beta^a_{ch}{_\mathbf{TNB}}(x)&=&\left(
\begin{array}{c}
1, \, -(\frac{c+f}{c})\cos(cx+c_{1})+\sin(cx+c_{1}),\\
\\ (\frac{c+f}{c})\sin(cx+c_{1})+\cos(cx+c_{1})
\end{array}%
\right)
\end{eqnarray*}
where $c, c_{1}$ and $f$ are integral constants.
\end{corollary}
\begin{corollary}
The position vectors of Smarandache curves of a family of asymptotic curve that is a generalized helix in $G_3$ are given by the equations
%
%
\begin{eqnarray*}
\beta^a_{gh}{_\mathbf{TN}}(x)&=&\left(
\begin{array}{c}
1, \, -\cos(k\int \kappa_{g}dx)+\sin(k \int \kappa_{g}dx), \\
\\
\sin(k\int \kappa_{g}dx)+\cos(k \int \kappa_{g}dx) \\
\end{array}%
\right) \\
\\
\beta^a_{gh}{_\mathbf{TB}}(x)&=&\Big(
\begin{array}{c}
1, \, -2\cos(k\int \kappa_{g}dx), \,
2\sin(k\int \kappa_{g}dx) \\
\end{array}%
\Big)\\
\\
\beta^a_{gh}{_\mathbf{TNB}}(x)&=&\left(
\begin{array}{c}
1, \, -2\cos(k\int \kappa_{g}dx)+\sin(k\int \kappa_{g}dx), \\
\\
2\sin(k\int \kappa_{g}dx)+\cos(k\int \kappa_{g}dx) \\
\end{array}%
\right)
\end{eqnarray*}
where $k$ is integral constant.
\end{corollary}
\begin{corollary}
The position vectors of Smarandache curves of a family of asymptotic curve that is a Salkowski curve in $G_3$ are given by the equations
\begin{eqnarray*}
\beta^a_{s}{_\mathbf{TN}}(x)&=&\left(
\begin{array}{c}
1, \, \int(f\sin(\int \tau_{g}dx))dx+\sin(\int \tau_{g}dx), \\
\\
\int(f\cos(\int \tau_{g}dx))dx+\cos(\int \tau_{g}dx) \\
\end{array}%
\right)\\
\\
\beta^a_{s}{_\mathbf{TB}}(x)&=&\left(
\begin{array}{c}
1, \, \int(f\sin(\int \tau_{g}dx))dx-\cos(\int \tau_{g}dx), \\
\\
\int(f\cos(\int \tau_{g}dx))dx+ \sin(\int \tau_{g}dx) \\
\end{array}%
\right)\\
\\
\beta^a_{s}{_\mathbf{TNB}}(x)&=&\left(
\begin{array}{c}
1, \, \int(f\sin(\int \tau_{g}dx))dx+\sin(\int \tau_{g}dx)-\cos(\int \tau_{g}dx), \\
\\
\int(f\cos(\int \tau_{g}dx))dx+\cos(\int \tau_{g}dx)+ \sin(\int \tau_{g}dx) \\
\end{array}%
\right)
\end{eqnarray*}
where $f$ is constant.
\end{corollary}
\begin{corollary}
The position vectors of Smarandache curves of a family of asymptotic curve that is an anti-Salkowski curve in $G_3$ are given by the equations
%
%
\begin{eqnarray*}
\beta^a_{as}{_\mathbf{TN}}(x)&=&\left(
\begin{array}{c}
1, \, \int(\kappa_{g}\sin(cx+c_{1}))dx+\sin(cx+c_{1}),\\ \\ \int(\kappa_{g}\cos(cx+c_{1}))dx+\cos(cx+c_{1}) \\
\end{array}
\right)\\
\\
\beta^a_{as}{_\mathbf{TB}}(x)&=&\left(
\begin{array}{c}
1, \, \int(\kappa_{g}\sin(cx+c_{1}))dx-\cos(cx+c_{1}), \\ \\
\int(\kappa_{g}\cos(cx+c_{1}))dx+\sin(cx+c_{1}) \\
\end{array}
\right)\\
\\
\beta^a_{as}{_\mathbf{TNB}}(x)&=&\left(
\begin{array}{c}
1, \, \int(\kappa_{g}\sin(cx+c_{1}))dx+\sin(cx+c_{1})-\cos(cx+c_{1}), \\
\\
\int(\kappa_{g}\cos(cx+c_{1}))dx+\cos(cx+c_{1})+\sin(cx+c_{1})
\end{array}
\right)
\end{eqnarray*}
where $c$ and $c_1$ are constants.
\end{corollary}
\begin{proof}
We want to point out that above corollaries can be proved by using the equations (\ref{kt}), (\ref{helsal}) and Theorem \ref{thmasy}.
\end{proof}
\subsection{The position vectors of Smarandache curves of a general curvature line in $G_3$}
\begin{theorem}{\label{thmcur}}
The position vectors $\gamma^c(x)$ of Smarandache curves of a family of curvature line in $G_3$ are provided by
%
%
%
%
%
%
%
%
%
\begin{eqnarray*}
\gamma^c _{_\mathbf{TN}} &=&\left(
\begin{array}{c}
1,\, \int (\kappa _{g}\sin a + \kappa_n \cos a)dx+\frac{1}{\sqrt{\kappa_g^2+\kappa_n^2}}(\kappa _{g}\sin a + \kappa_n \cos a),\\
\, \int (\kappa _{g}\cos a - \kappa_n \sin a)dx-\frac{1}{\sqrt{\kappa_g^2+\kappa_n^2}}(\kappa _{g}\cos a - \kappa_n \sin a)
\end{array}
\right) \\
&& \notag \\
\gamma^c _{_\mathbf{TB}} &=&\left(
\begin{array}{c}
1,\, \int (\kappa _{g}\sin a + \kappa_n \cos a)dx-\frac{1}{\sqrt{\kappa_g^2+\kappa_n^2}}(\kappa _{g}\cos a - \kappa_n \sin a),\\
\, \int (\kappa _{g}\cos a - \kappa_n \sin a)dx+\frac{1}{\sqrt{\kappa_g^2+\kappa_n^2}}(\kappa _{g}\sin a + \kappa_n \cos a)
\end{array}
\right) \\
&& \notag \\
\gamma^c _{_\mathbf{TNB}} &=&\left(
\begin{array}{c}
1,\, \int (\kappa _{g}\sin a + \kappa_n \cos a)dx\\-\frac{1}{\sqrt{\kappa_g^2+\kappa_n^2}}(\kappa _{g}(\sin a-\cos a) + \kappa_n(\sin a+\cos a)),\\
\, \int (\kappa _{g}\cos a - \kappa_n \sin a)dx\\+\frac{1}{\sqrt{\kappa_g^2+\kappa_n^2}}(\kappa _{g}(\sin a+\cos a) + \kappa_n (\cos a-\sin a))
\end{array}
\right) \notag
\end{eqnarray*}
\end{theorem}
\begin{proof}
By using the definition (\ref{defgap}) in Theorem \ref{posmat}, then the above equations are obtained as general position vectors for $\mathbf{TN}, \, \mathbf{TB}$ and $\mathbf{TNB}$ special smarandache curves with Darboux apparatus of a curvature line on a surface in $G_3$.
\end{proof}
Now, we will give the position vectors for Smarandache curves of some special cases of a curvature line in $G_3$
\begin{corollary}
The position vectors $\gamma^c(x)$ of Smarandache curves of a family of curvature line with $\kappa_{g}\equiv$ const. and $\kappa_{n}\equiv$ const. is a circular helix in $G_3$ are provided by
%
%
%
%
\begin{eqnarray*}
\gamma^c_{ch}{_\mathbf{TN}}(x)&=&\left(
\begin{array}{c}
1, \, (a_{1}\sin a+a_{2}\cos a)x+\frac{1}{\sqrt{a_1^2+a_2^2}}(a_{1}\sin a+a_2\cos a), \\
\\ (a_{1}\cos a-a_{2}\sin a)x-\frac{1}{\sqrt{a_1^2+a_2^2}}(a_{1}\cos a-a_2\sin a)
\end{array} \right) \\
\\
\gamma^c_{ch}{_\mathbf{TB}}(x)&=&\left(
\begin{array}{c}
1, \, (a_{1}\sin a+a_{2}\cos a)x-\frac{1}{\sqrt{a_1^2+a_2^2}}(a_{1}\cos a-a_2\sin a), \\
\\ (a_{1}\cos a-a_{2}\sin a)x+\frac{1}{\sqrt{a_1^2+a_2^2}}(a_{1}\sin a+a_2\cos a)
\end{array}
\right)\\
\\
\gamma^c_{ch}{_\mathbf{TNB}}(x)&=&\left(
\begin{array}{c}
1, \, (a_{1}\sin a+a_{2}\cos a)x\\+\frac{1}{\sqrt{a_1^2+a_2^2}}(a_{1}(\sin a-\cos a)+a_2(\cos a+\sin a)), \\
\\ (a_{1}\cos a-a_{2}\sin a)x\\-\frac{1}{\sqrt{a_1^2+a_2^2}}(a_{1}(\sin a+\cos a)-a_2(\cos a-
\sin a))
\end{array}
\right)
\end{eqnarray*}
%
\end{corollary}
\begin{proof}
By using the equations (\ref{kt}) and (\ref{helsal}) in Theorem \ref{thmcur}, we obtain the above equation.
\end{proof}
We will now provide some illustrative examples for arbitrary curve on a surface.
\begin{example}
In \eqref{pos}, if we let $\kappa_g(x)=\sin x, \, \kappa_n(x)=\cos x$ and $\tau_g(x)=x$, we obtain the following curve:
\begin{eqnarray}
\gamma(x)= \left(
\begin{array}{c}
x, \\\\ \sqrt{\pi } \left( x\cos \left( 1/2 \right) -\cos \left( 1/2 \right) \right) {\it FresnelC} \left( {\frac {x-1}{ \sqrt{\pi }}} \right) \\
\mbox{}+ \sqrt{\pi } \left( x\sin \left( 1/2 \right) -\sin \left( 1/2 \right) \right) {\it FresnelS} \left( {\frac {x-1}{ \sqrt{\pi }}} \right) \\
\mbox{}-\cos \left( 1/2 \right) \sin \left( 1/2\, \left( x-1 \right) ^{2} \right) +\sin \left( 1/2 \right) \cos \left( 1/2\, \left( x-1 \right) ^{2} \right),\\\\
- \sqrt{\pi } \left( \sin \left( 1/2 \right) -x\sin \left( 1/2 \right) \right) {\it FresnelC} \left( {\frac {x-1}{ \sqrt{\pi }}} \right) \\
\mbox{}- \sqrt{\pi } \left( x\cos \left( 1/2 \right) -\cos \left( 1/2 \right) \right) {\it FresnelS} \left( {\frac {x-1}{ \sqrt{\pi }}} \right) \\-\cos \left( 1/2\, \left( x-1 \right) ^{2} \right) \cos \left( 1/2 \right)
\mbox{}-\sin \left( 1/2\, \left( x-1 \right) ^{2} \right) \sin \left( 1/2 \right)
\end{array}
\right)
\end{eqnarray}
where $$FresnelS(x)=\int \sin\left(\frac{\pi x^2}{2}\right) dx, \hskip .5cm FresnelC(x)=\int \cos\left(\frac{\pi x^2}{2}\right).$$
The special Smaradache curves of $\gamma$ can be obtained directly from Definition \ref{smadef}, or replacing $\kappa_g(x)$, $\kappa_n(x)$ and $\tau_g(x)$ by $\sin x, \cos x$ and $x$ in Theorem 3, respectively.
In this case, the graphs of $\gamma$ curve and its $\mathbf{TN, TB, TNB}$ special Smarandache curves are given as follows Figure 1.
\end{example}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.4 \textwidth]{alfa_Tg=x,Kg=sinx,Kn=cosx_.png}
\includegraphics[width=0.4\textwidth]{TNB-TB-TN.png}
\caption{$\gamma$ curve and the right figure is printed from outside to inside $\gamma_{TNB}, \gamma_{TB}, \gamma_{TN}$ Smarandache curves of $\gamma$} \label{fig1}
\end{center}
\end{figure}
We now consider another example for geodesic curve on surface along with their graphs.
\begin{example} Let the surface $M$ be defined by
$$\phi(u,v)=\Bigg(u+v, \frac{u-\sin(u+v)\cos(u+v)}{4}, \frac{\sin(u+v)^2-u^2}{4}\Bigg)$$
and define the curve $\gamma$ which lies on the surface $M$ as follows
$$\displaystyle \gamma(x) = \Bigg(x, \frac{x-\sin(x)\cos(x)}{4}, \frac{\sin(x)^2-x^2}{4}\Bigg).$$
Thus, $\gamma$ is a geodesic curve with $\kappa(x)=\sin x$ and $\tau(x)\equiv1$ on $M$ in $G_3$. Also, $\mathbf {T, Q, n}$ vector fields and $\kappa_n(x), \tau_g(x)$ curvatures are obtained by using equation (\ref{Darboux}), (\ref{kt}). Using these curvatures in Theorem \ref{thmgeo}, we derive special Smarandache curves of $\gamma$.
\end{example}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.6\textwidth]{buketsekil1.png}%
\includegraphics[width=0.4\textwidth]{buketsekil2.png}
\caption{$\phi(u,v)$ surface and $\gamma(x)$ curve}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.3\textwidth]{BuketTN.png}%
\includegraphics[width=0.3\textwidth]{BuketTB.png}%
\includegraphics[width=0.3\textwidth]{BuketTNB.png}
\caption{$\gamma_\mathbf{TNB}, \gamma_\mathbf{TB}, \gamma_\mathbf{TN}$ special Smarandache curves of $\gamma$, respectively.} \label{fig1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.3\textwidth]{alfa_Tn.png}%
\includegraphics[width=0.3\textwidth]{alfa_TQ.png}%
\includegraphics[width=0.3\textwidth]{alfa_TQn.png}
\caption{$\gamma_\mathbf{Tn}, \gamma_\mathbf{TQ}, \gamma_\mathbf{TQn}$ special Smarandache curves with respect to Darboux frame of $\gamma$, respectively.} \label{fig1}
\end{center}
\end{figure}
\newpage
\section{Conclusion}
In this work, we studied general position vectors of special Smarandache curves with Darboux apparatus of an arbitrary curve on a surface in the three-dimensional Galilean space $G^{3}$. As a result of this, we also provided special Smarandache curves of geodesic, asymptotic and curvature line on the surface in $G^{3}$ and provided some related examples of special Smarandache curves with respect to Frenet and Darboux frame of an arbitrary curve on a surface. Finally, we emphasize that one can investigate position vectors of elastic curves on a surface using the general position vectors of curves on a surface in Galilean space. Last but not least, we want to point out that the results of this study can be easily generalized to families of surfaces that have common Smarandache curves.
\section*{Acknowledgements}
This study was supported financially by the Research Centre of Amasya University (Project No: FMB-BAP16-0213).
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,184
|
Q: Reading from FTDI sync FT245 FIFO returns zero bytes Hello I am developing simple DSO and I have problem with FT245 sync FIFO.
Reading from FT245 works normally when I read 4byte acknowledges, but when I want to retrieve sampled data it returns zero bytes (meaning ftdi_read_data returns 0, consecutive reads returns -84 then -32 (there is no documentation what these codes means)).
Function for readig:
int Ft245sync::read(unsigned char * buf)
{
int res = ftdi_read_data(ftdic, buf, getReadChunkSize());
std::cerr << "res rd: " << res << std::endl;
return res;
}
Code where reading happens:
Part which works (reading acknowledge):
//send SET TRIGGER
recvbuf[0] = 0;
while(recvbuf[0] != DATA_OK)
{
unsigned char buf3[10] = { SET_TRIGGER, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
if(ft245.write(buf3) < 0)
{
std::cerr << "Error writing data3\n";
}
if(ft245.read(recvbuf) < 0)
{
std::cerr << "Error receiving data\n";
}
}
Part which doesn't work:
//send START CAPTURE
unsigned char buf5[10] = { START_CAPTURE, 0x05, 0, 0, 0, 0, 0, 0, 0, 0 };
if(ft245.write(buf5) < 0)
{
std::cerr << "Error writing data5\n";
}
usleep(700);
std::cout << "Capture started\n";
for (int i = 0; i < 30; ++i)
{
if(ft245.read(recvbuf) < 0)
{
std::cerr << "Error reading data\n";
}
}
Screenchots from chipscope from working read:
Screenshot from faulty read:
As could be seen WR is put low in both situations two clocks after TXE goes low.
Part of VHDL code of working read:
when SEND_ACKNOWLEDGE0 =>
if to_boolean(ft245busy) then
state <= SEND_ACKNOWLEDGE0;
else
state <= SEND_ACKNOWLEDGE1;
end if;
when SEND_ACKNOWLEDGE1 =>
ft245rw <= '1';
responseCounter <= "000";
ft245din <= "10000000";
if (ft245wr = '0') then
state <= SEND_ACKNOWLEDGE2;
ft245strobe <= '0';
else
ft245strobe <= '1';
state <= SEND_ACKNOWLEDGE1;
end if;
when SEND_ACKNOWLEDGE2 =>
if (responseCounter < 1) then
responseCounter <= (responseCounter + 1);
ft245din <= "10000000";
state <= SEND_ACKNOWLEDGE2;
else
ft245dataWaitIn <= '1';
ft245rw <= '0';
responseCounter <= "000";
case command is
when "10101110" =>
state <= INIT0;
when "00010000" =>
state <= SET_VREF0;
when "00010001" =>
state <= SET_VLOG0;
when "00100000" =>
state <= SET_ATTENUATORS;
when "00100001" =>
state <= SET_COUPLINGS;
when "00110000" =>
state <= SET_DECIMATION;
when "00110001" =>
state <= SET_ANALOGTRIGGER;
when "00110010" =>
state <= SET_DIGITALTRIGGER;
when "01000000" =>
state <= START_CAPTURE;
when others =>
state <= IDLE;
end case;
end if;
Part of faulty read:
when DUMP_DATA_PREPFT =>
if to_boolean(ft245busy) then
state <= DUMP_DATA_PREPFT;
else
state <= DUMP_DATA0;
end if;
when DUMP_DATA0 =>
adc1pd <= '1';
adc2pd <= '1';
ft245rw <= '1';
bufferDataDirection <= '0';
answerNumber <= "00";
ft245din <= "01010000";
if ((ft245wr = '0') and to_boolean(bufferReady)) then
state <= DUMP_DATA1;
ft245strobe <= '0';
else
ft245strobe <= '1';
state <= DUMP_DATA0;
end if;
when DUMP_DATA1 =>
ft245din <= "01010000";
ft245dataWaitIn <= '0';
answerNumber <= (answerNumber + 1);
if (answerNumber = 3) then
state <= DUMP_DATA2;
bufferOutputInputReady <= '1';
else
state <= DUMP_DATA1;
end if;
And there's code of my ft245 controller responsible for reading (writing from FPGA point of view):
when IDLE =>
if (strobe = '1') then
busy <= '1';
if (rw = '1') then
state <= WRITE_PREP;
else
state <= READ_PREP;
end if;
else
busy <= '0';
state <= IDLE;
end if;
when WRITE_PREP =>
if (txe = '0') then
state <= WRITE;
else
state <= WRITE_PREP;
end if;
when WRITE =>
if ((txe = '0') and (not to_boolean(dataWaitIn))) then
wr_int <= '0';
else
wr_int <= '1';
state <= IDLE;
busy <= '0';
end if;
And there is listing of program output:
res wr: 10
res rd: 4
res wr: 10
Capture started
res rd: 0
res rd: 0
res rd: -84
Error reading data
res rd: -32
Error reading data
res rd: -32
...
From my point of view everything in FPGA is OK (according to chipscope) and reading in program is also the same so I don't know why it works and then don't (I can successfully do more (tens) write/read cycles with 4byte acknowledge, but then it always stops at this faulty read)...
//Edit:
When you set ridiculously large incoming buffer (more than 16000 bytes) then it suprisingly works. But still I don't understand why..
A: Chipscope only shows you the internals.
More things you ought to check:
*
*Have you constrained the timing correctly on all the IO pins to the FTDI chip?
*Are you sure (using a fast scope) that you have met every timing requirement at the pins of the FTDI chip?
You might find that the logic in your failing path is causing something to be out of spec.
A: I kind of solved it by setting incoming buffer to 32768 bytes which is maximum byte count I would transfer.. It works well now, just having some unaligned bytes (off one byte) after every 506 bytes.. But that's probably some error in my FPGA design.
//Edit:
Just for note, biggest problem is not timing (even if you violate 11ns hold timing it will work correctly, I only have 7ns setup for example) but making state machine aware of situation when input buffers are full ant TXE goes high and correctly continue in transfer when TXE goes back low.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 532
|
A couple weeks ago I shared some fitting room pictures of white rehearsal dinner dress options (this post). Shortly after posting, I found this romper online. At one third of the price of my previous top choice, I knew I had to give it a try. It fits beautifully and I love the ruffle detail so I'm definitely keeping it! My romper is almost sold out but I found some similar options under $100 below. I also really like this new arrival at Rent the Runway - I'm swooning over the lace.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,382
|
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|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,261
|
\section{Introduction}
Holography has provided insights into the emergence of locality in quantum gravity. Early work on this topic includes the reconstruction of bulk operators using causal approaches \cite{BDHM98,HKLL06}. However, Ryu-Takayanagi (RT) surfaces \cite{RT06} reach outside of the region causally connected to a boundary subregion \cite{probes12,maximin12,dual_density_matrix12} and so it was appreciated that they must have some role to play in reconstructing the bulk from the boundary. Regions that are not crossed by RT surfaces, or their covariant generalisations due to Hubeny-Rangamani-Takayanagi (HRT) \cite{HRT07}, are known as an entanglement shadows \cite{entwinement14,shadows14}.
However, the precise meaning of these regions is not fully understood.
In recent years, an understanding of subregion-subregion duality in holography has lead to a new perspective on bulk locality. It has been understood that boundary locality leads to a well defined notion of local algebras of operators and that this local algebra can be associated to an appropriate algebra of bulk operators localised in the entanglement wedge
associated with that boundary subregion \cite{HQECC14,JLMS15,EW_reconstruction16}.
In this picture, HRT surfaces separate a bulk Cauchy slice into two parts, each reconstructible from complementary regions on the boundary. Because entanglement shadows can be contained in entanglement wedges, those bulk regions do not seem to be an obstruction to the reconstruction of the bulk from the boundary in this regard.
This analysis does not however have anything to say about whether the operators are localised at points in the bulk, it just restricts them to the entanglement wedge.
Nonetheless, this machinery can be used to identify local operators \cite{stereoscopic16,KL17,SW,Locality_from_Modular17}. An operator that can be reconstructed independently in different boundary regions must lie in the intersection of the entanglement wedges of those regions. Therefore if a family of boundary regions can be found such that the intersection of their entanglement wedges includes only a single point in the bulk, then an operator that can be reconstructed in any of those regions must be localised at that point \cite{SW}.
This work defined the localisable region as the set of bulk points that can be identified in this way.
Not all points in the bulk need to have this property and so the points that do not are known as non-localisable.
The existence of local operators in semi-classical quantum gravity at non-localisable points cannot be established using this method. We will see that in some cases, causal reconstruction methods can be used to reconstruct operators in the non-localisable region. However, these causal methods only provide locality order by order in perturbation theory and lead to various confusions which were resolved using entanglment wedge reconstruction methods in \cite{HQECC14,EW_reconstruction16}.
When the non-localisable region is behind a horizon it is not clear how to establish the existence of local operators.
The boundaries of entanglement wedges, which include the HRT surface, play an important role in the determination of the localisable region. However, the boundary of entanglement wedges also include the lightsheets emanating from the HRT surface towards the boundary and \cite{SW} proposed methods for localising points on these lightsheets. Clearly the non-localisable region is not in general the same as the entanglement shadows that were considered in \cite{entwinement14,shadows14}, but their interpretations have some similarities and we will see that they do coincide in some cases.
\subsection{Set-up}
Let us start by collecting the necessary notation. We will consider spacetimes, $M$, which are asymptotically AdS. Given an achronal subregion $R$ of the boundary, the set of points on the boundary spacetime for which every inextensible causal curve passing through the point also crosses $R$ is called the boundary domain of dependence of $R$, $D[R]$. The future/past domain of dependence of $R$ are denoted by $D^\pm[R]$. Let $J^\pm[S]$ denote the causal future/past of the subset $S$ of our spacetime. It was argued in \cite{BLR_CW12,HR_CW12,dual_density_matrix12} that a bulk field $\phi(x)$ can be reconstructed, to leading order in $1/N$, on a boundary subregion $D[R]$ whenever $x$ lies in the so-called causal wedge,
\begin{equation}
W_C(R) = \mathcal{J}^{+}[D[R]] \cap \mathcal{J}^{-}[D[R]].
\end{equation}
of the subregion $R$. This bulk reconstruction method is known as causal wedge reconstruction.
We will denote the HRT surface anchored on a region $R$ by $\gamma_R$. This HRT surface can be taken to lie on a Cauchy slice of the bulk, $\Sigma_R$. It separates this Cauchy slice into $H_R$, the homology region connecting $R$ to $\gamma_R$, and $H'_R$.
$W_{\mathcal{E}}(R) \equiv D[H_R]$ is known as the entanglement wedge of $R$ and is the bulk region dual to $R$ in what is known as entanglement wedge reconstruction or subregion-subregion duality \cite{HQECC14,JLMS15,EW_reconstruction16}.
In \cite{SW}, a criterion was proposed for diagnosing whether a typically non-local boundary operator $\phi$ acting on a given code subspace $G$ (dual to an unknown bulk spacetime) corresponds to a local operator in the bulk. We will briefly summarise their proposal and recall the purpose of the localisable region, but refer to \cite{SW} for further details. The argument is based on the map $Q$ which associates the following set of boundary regions with $\phi$
\begin{equation}
\mathcal{Q}(\phi)=\{R\in\mathcal{R}|\phi \text{\ is reconstructable in\ } R\}.
\end{equation}
This map defines equivalent classes $[\phi]$, where $\phi_1\sim\phi_2$ if and only if $\mathcal{Q}(\phi_1)=\mathcal{Q}(\phi_2)$. On these equivalent classes, one can associate the ordering $[\phi_1]\leq[\phi_2]$ if $\mathcal{Q}(\phi_1)\subseteq\mathcal{Q}(\phi_2)$. A set of operators $[\phi] \neq [1_G]$ with the property that for every operator $\phi'$ such that $[\phi] \leq [\phi']$ we also have $[\phi'] \in \{[\phi],[1_G]\}$, are called superficially local. This boundary characterisation of operators on the code subspace encodes the general intuition that the more local a bulk operator is, the more boundary regions it can be reconstructed on. In some sense, the superficially local operators in $[\phi]$ are as local in the bulk as it can be using the map $\mathcal{Q}$. However, not all superficially local operators are true local bulk operators\footnote{Note that the reverse is also true.}.
The localisable region of the bulk (whose semi-classical Hilbert space is dual to the code subspace) is the subspace of bulk points for which superficial locality implies true bulk locality. A useful (bulk) criterion to determine if a bulk point $p$ belongs to the localisable region is proved as theorem III.1 in \cite{SW}, which will be a central tool in this work. It requires the existence of a subset of the collection of all boundary regions such that the intersection of their entanglement wedges contains only the point $p$, that is there is some family of boundary regions $\mathcal{R}_0$ such that
\begin{gather}
\bigcap_{R\in \mathcal{R}_0} W_{\mathcal{E}}(R) = \{p\}\,.
\label{eqn:SW_condition_localisability}
\end{gather}
In some asymptotically AdS spacetimes, such as pure AdS, the localisable region is the entire bulk. In that case, superficial locality coincides with locality.
Points which are not in the localisable region are known as non-localisable. %
By taking the converse of \eqref{eqn:SW_condition_localisability}, a non-localisable point is one such that there exists another point $q$ so that
\begin{align}
p \in W_{\mathcal{E}}(R) \implies q \in W_{\mathcal{E}}(R)\, ,
\end{align}
for all $R \in R_0$.
Operators at these two points cannot be split into different entanglement wedges, so that the argument for bulk micro-causality in \cite{HQECC14,JLMS15,EW_reconstruction16} does not apply.
In a simple spacetime such as global AdS$_3$, where a Cauchy slice is completely probed by RT surfaces, finding a set of boundary regions with a single bulk point in the intersection of their entanglement wedges can be very simple.
Namely, one can consider a bulk point as the intersection of two spatial geodesics. Because each geodesic is the set of points in the intersection of the two entanglement wedges bounded by that geodesic, the intersection of those four entanglement wedges contain only one bulk point.
This is very similar to the intuition used to reconstruct bulk operators using invariance under modular flows proposed in \cite{KL17}.
However, such an arguments only works for spacetimes entirely probed by RT surfaces, i.e. spacetimes without an entanglement shadow.
It was argued in \cite{SW} that, even in the presence of an entanglement shadow, the entire bulk is in the localisable region when entanglement wedges probe the entire spacetime.
This argument was based on an implicit assumption on the geometry of entanglement wedges, namely that the future and past boundaries of a cross-section of the entanglement wedge as depicted in figure \ref{fig: assumption wedges} are monotonic.
In that case, it was argued that a set of entanglement wedges as shown in figure \ref{fig: assumption wedges}
would be sufficient to localise a point in the entanglement wedges of conical deficit spacetimes.
\begin{figure}[th]
\centering
\includegraphics[width=.5\textwidth]{assumptionWedge.pdf}
\vskip 2mm
\caption{This figure is based on figure 3 of \cite{SW} demonstrating how to localise a point inside the entanglement shadow in the conical deficit spacetime. It depicts a conformal diagram, where light rays move at 45$^\circ$, of a $(r,t)$ slice of this spacetime with deficit angle $2 \pi/3$.
The entanglement shadow is shown in gray. Four HRT surfaces associated to large boundary regions are drawn in blue.
The boundaries of the corresponding entanglement wedges are shown, in green and purple for HRT surfaces centered at $\theta = 0$ and $\theta = \pi$ respectively. This boundary is set by a light ray departing the HRT surface and reaching the defect at $r=0$. Behind the defect a caustic forms reaching the boundary at the other side of the cylinder.
Provided that the corner between the light ray and the caustic is not too sharp, one can use such a set of boundary regions to localise a point in the entanglement shadow of a conical deficit.}
\label{fig: assumption wedges}
\end{figure}
In this work, we investigate this assumption by deriving the precise form of entanglement wedges and the caustics bounding them in asymptotically-AdS$_3$ geometries using the embedding space formalism. This will allow us to identify the non-localisable regions in some simple spacetimes by using the techniques proposed in \cite{SW}. As the lightsheets bounding entanglement wedges include caustics, an understanding of their shape is required to determine the extent of these non-localisable regions.
In section \ref{sec:cone}, we study entanglement wedges in the conical deficit geometry. We find an unexpected behaviour of the caustics bounding the entanglement wedges for deficit angles $\pi \leq \Delta \theta < 2\pi$ which implies a breakdown of the general analysis proposed in \cite{SW}. In this case, the non-localisable region coincides with the region not probed by HRT surfaces. For smaller deficit angles, the caustics have the behaviour anticipated by \cite{SW} and the whole spacetime is localisable.
In section \ref{sec:two-sided}, we derive the shape of some of entanglement wedges in the maximally extended two-sided BTZ black hole. Again, we will start by understanding the shape of the entanglement wedges and the caustics bounding them in this spacetime. HRT surfaces that stretch from one boundary to the other, which correspond to boundary regions including components in both boundaries, allowed \cite{SW} to localise points behind the horizon. Yet there is a region near the singularity that is not localisable. We prove a lemma demonstrating that entanglement shadows hidden behind event horizons lead to non-localisable regions. When given access to only one asymptotic region, as is the case for black holes formed by collapse, we find that there is a non-localisable region near the horizon which coincides with the entanglement shadow present in that case.
\section{Conical deficit}
\label{sec:cone}
The conical deficit spacetime is obtained by identifying the global angular coordinate $\theta$ of AdS$_3$ with $\theta+2 \pi \alpha$, with $0<\alpha<1$.
Defining a new angular coordinate with the usual $2\pi$ periodicity, while simultaneously rescaling the other global coordinates,
one obtains the conical deficit metric,
\begin{equation}
\label{linecon}
ds^2=-\left(r^2+\alpha^2 \right)dt^2+\frac{dr^2}{r^2+\alpha^2 }+r^2d\theta^2.
\end{equation}
Determining the localisable region of a conical deficit spacetime necessitates understanding the HRT surfaces and corresponding entanglement wedges associated to arbitrary boundary regions. These geometric constructs can be considered in the embedding space formalism, where AdS$_3$ is understood as a hyperboloid embedded in $\mathbb{R}^{2,2}$. We will use the convention that this space has signature $(-,-,+,+)$. The AdS hyperboloid is defined by $X^2=-L^2$, where $L$ is the AdS scale. This hyperboloid has a closed timelike curve which must be unravelled by taking its universal cover. We will work in units where $L=1$. Global coordinates on AdS$_3$ can be used to parametrise this hyperboloid as follows
\begin{align}
X^A_{global} (r,t,\theta) = \left( \sqrt{r^2+1} \cos t, \sqrt{r^2+1} \sin t, r \sin \theta, r \cos \theta \right) \, .
\label{eqn:global_param}
\end{align}
The metric of AdS$_3$ in global coordinates is the one induced by the embedding of the hyperboloid into flat $\mathbb{R}^{2,2}$,
\begin{align}
ds^2 = dX \cdot dX = -\left(r^2+1\right) dt^2 + \frac{dr^2}{r^2+1} + r^2 d\theta^2 \,.
\end{align}
The identification of the angular coordinate required to obtain the conical deficit spacetime can be understood directly in the embedding space if one considers hyperpolar coordinates on $\mathbb{R}^{2,2}$ of the form
\begin{align}
\left( r_1 \cos \tau, r_1 \sin \tau, r_2 \sin \phi, r_2 \cos \phi \right)\,.
\label{eqn:hyperpolar}
\end{align}
The action of $\phi \rightarrow \phi + 2\pi \alpha$ preserves the hyperboloid $X^2 = -1$. Once this identification is restricted to the hyperboloid, parametrised by \eqref{eqn:global_param}, it reproduces the usual identification of $\theta$ with $\theta+2 \pi \alpha$. The vector normal to 3-planes of constant $\phi_0$ is given by
\begin{align}
P_{plane}(\phi_0) = \left(0 ,0 , \cos\phi_0 , - \sin \phi_0 \right)\, ,
\end{align}
and under the identification of the angular coordinate $\theta \sim \theta + 2 \pi \alpha$, the points $X$ satisfying $X \cdot P_{plane}(\phi_0)=0$ are being identified with those at $X \cdot P_{plane}(\phi_0+2 \pi \alpha)=0$.
A fundamental region of this identification can be covered by using global coordinates rescaled as
\begin{align}
\theta_{global} = \alpha \theta_{cone}\,, \qquad
t_{global} = \alpha t_{cone}\,, \qquad
r_{global} = \frac{r_{cone}}{\alpha} \,,
\end{align}
with $0<\theta<2 \pi$. This leads to a parametrisation of the AdS hyperboloid by
\begin{align}
X^A_{cone} (r,t,\theta) = \frac{1}{\alpha} \left( \sqrt{r^2+\alpha^2} \cos \alpha t, \sqrt{r^2+\alpha^2} \sin \alpha t, r \sin \alpha \theta, r \cos \alpha \theta \right) \, .
\label{eqn:cone_param}
\end{align}
The metric induced by the embedding into $\mathbb{R}^{2,2}$ reproduces the conical deficit metric \eqref{linecon}.
\subsection{HRT surfaces}
In AdS$_3$, HRT surfaces are given by spacelike geodesics.
The geodesics of a conical deficit spacetime can be obtained from the AdS$_3$ geodesics subject to the appropriate identifications. In the ambient $\mathbb{R}^{2,2}$ planes intersecting the hyperboloid $X^2=-1$ give the relevant geodesics \cite{integral_geometry15, causal_diamonds16}.
Such a plane is spanned by the $\mathbb{R}^{2,2}$ vectors corresponding to a point on the geodesic, $X_0$, as well as the tangent at this point, $X_1$. Given a geodesic \begin{align}
\gamma^\mu(\lambda) = (r(\lambda),t(\lambda),\theta(\lambda)) \,,
\end{align}
the points on the geodesic are given by
$X^A_{cone}(\gamma(\lambda))$, so that
\begin{align}
X_0 = X^A_{cone}(\gamma(\lambda_0)) \qquad \mathrm{and}\qquad X_1 \propto \partial_\lambda X^A_{cone}(\gamma(\lambda_0))
\end{align}
for a given reference point $\lambda_0$. For example, a geodesic with\footnote{This tangent vector, $\partial_\lambda \gamma^\mu(\lambda_0)$, is chosen for future convenience. Note that it has unit length and points in the $\partial_\theta$ direction for $\eta=0$. For $\eta\neq 0$ this HRT surface is anchored to an interval that is not centered at $\theta=0$.}
\begin{align}
\gamma^\mu(\lambda_0) &= (r_0,\, 0,\, 0)\,, \\
\partial_\lambda \gamma^\mu(\lambda_0) &= (-\eta \sqrt{r_0^2 + \alpha^2},\, \frac{\eta}{\sqrt{r_0^2 + \alpha^2}} ,\, \frac{1}{r_0}) \,.
\end{align}
has
\begin{align}
X_0 &= X^A_{cone} (r_0,0,0) = \frac{1}{\alpha} \left( \sqrt{r_0^2+\alpha^2}, 0,0, r_0 \right) \, , \\
X_1 &= \partial_\lambda \gamma^\mu(\lambda_0) \partial_\mu X^A_{cone} (r_0,0,0)
= \left(- \eta \frac{ r_0}{\alpha} , \eta, 1 ,-\eta \frac{ \sqrt{r_0^2+\alpha^2} }{\alpha} \right)
\,.
\label{eqn:hrt_cone}
\end{align}
This plane can also be described by the plane spanned by the vectors orthogonal to it, its normal space.
A co-dimension 2 HRT surface always has a 2-dimensional normal plane. The 2-dimensional space normal to the HRT surface has one timelike and one spacelike direction, therefore the normal plane in $\mathbb{R}^{2,2}$ can be described either by a timelike and a spacelike unit vector $(S,T)$ such that $S^2 =1$, $T^2=-1$ and $S\cdot T=0$ or by a pair of null vectors $(N_1,N_2)$ such that $N_1^2=0$, $N_2^2=0$ and $N_1\cdot N_2 = -2$. These two descriptions are related by $N_1=T+S$ and $N_2 = T-S$. The HRT surface itself lives on a 2-plane spanned by $X_0$ and $X_1$, with $X_0^2=-1$ and $X_1^2 = 1$. so that $(X_0, X_1, S, T)$ form an orthonormal basis for $\mathbb{R}^{2,2}$. The intersection of this 2-plane with the AdS hyperboloid leads to a parametrisation of the HRT surface as
\begin{align}
Y(\xi) = \sec \xi X_0 + \tan \xi X_1 \qquad
\mathrm{for}~-\frac\pi2< \xi< \frac\pi2 \,.
\end{align}
The HRT surface reaches the boundary for $\xi = \pm \frac{\pi}{2}$. These boundary points are described by the null rays $X_0 \pm X_1$ in the ambient $\mathbb{R}^{2,2}$.
In terms of the parametrisation given in \eqref{eqn:hrt_cone}, the boundary points of HRT surfaces are described by the null rays in the direction of
\begin{align}
X_0 \pm X_1
= \left(
\frac{\sqrt{r_0^2 + \alpha^2} \mp \eta r_0}{\alpha} ,\pm \eta ,\pm 1, \frac{r_0 \mp \eta \sqrt{r_0^2 + \alpha^2}}{\alpha}
\right)\,.
\end{align}
The conformal boundary of AdS$_3$ is given by null rays, $Z^2=0$ with $Z \sim \lambda Z$. In terms of the coordinates used to describe the conical deficit, this is
\begin{align}
Z^A_{cone} (t,\theta) \propto
\lim_{r\rightarrow \infty} \frac{\alpha}{r} X^A_{cone}(r,t,\theta) = \left(
\cos \alpha t, \sin \alpha t, \sin \alpha \theta, \cos \alpha \theta
\right) \,.
\end{align}
Comparing these two expressions gives the endpoints of the boundary interval to which our HRT surface is attached
\begin{align}
\theta_\pm = \pm \frac{1}{\alpha} \arctan \frac{\alpha}{r_0 \mp \eta \sqrt{r_0^2 + \alpha^2}}
\,,\qquad
t_\pm = \pm \frac1\alpha \arctan \frac{\eta \alpha}{\sqrt{r_0^2 + \alpha^2} \mp \eta r_0 }
\,.
\end{align}
This characterisation of the spacelike geodesics in AdS$_3$ allows us to construct the HRT surface anchored to a boundary interval. For the conical deficit spacetime, we can similarly construct all of the candidate HRT surfaces by looking at all the surfaces anchored to images of the boundary points at the edges of the boundary region. The true HRT surface is the one of minimal length. This condition causes conical deficit spacetimes to develop an entanglement shadow, a bulk region that no HRT surface can reach, around the conical singularity at $r=0$. The minimal radius probed by the HRT surfaces can be found to be \cite{entwinement14}
\begin{equation}
r_{\text{min}} = \alpha \cot \alpha \frac{ \pi}{2}.
\end{equation}
A few HRT surfaces together with the entanglement shadow are drawn in figure \ref{FigHRTSurfCon} for $\alpha = 1/2$. Any simply connected boundary subregion has the same HRT surface as its complement. The red geodesic in figure \ref{FigHRTSurfCon} can be therefore be thought of as the HRT surface to the black or the yellow subregion of the boundary. Note that the entanglement shadow is included in the homology surface of the black boundary region, in contrast to $H_R$ of the yellow boundary region.
\begin{figure}[th]
\centering
\begin{subfigure}[b]{0.45\textwidth}
\includegraphics[width=.9\textwidth]{RTsConical.pdf}
\caption{}
\vskip 2mm
\label{fig: RTsConical}
\end{subfigure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=.9\textwidth]{RTsCovering.pdf}
\vskip 2mm
\caption{}
\label{fig: RTsCovering}
\end{subfigure}
\caption{A constant time slice of conical AdS$_3$ with $\alpha=1/2$ is shown. The boundary is pulled to a finite value by using the radial coordinate, $\rho=\arctan r$. The entanglement shadow is shown in gray. A few representative HRT surfaces are shown in orange, blue and red on the fundamental domain in (a). The same geodesics are shown on the covering space (AdS$_3$) in (b) together with their images. The fundamental domain is obtained by identifying points under a rotation by $\pi$.}
\label{FigHRTSurfCon}
\end{figure}
The presence of this region unprobed by HRT surfaces makes the determination of the localisable region more subtle than in AdS$_3$. \cite{SW} suggested that those entanglement shadows nevertheless belong to the localisable region because, by their theorem III.1, the geometric objects that matter in the determination of the localisable region are entanglement wedges. They argued, based on their figure 3, that the entire spacetime was localisable. This argument is recapped in our figure \ref{fig: assumption wedges}. We will now construct the entanglement wedges in the conical deficit spacetime in order to verify whether the behaviour depicted in this figure in generic.
\subsection{Entanglement wedges}
Given an HRT surface, the entanglement wedge can be obtained by lightsheet construction outlined in \cite{HRT07}. The idea is that from each point on the HRT surface two light rays are shot orthogonally to the HRT surface in the direction of the $H_R$ hypersurface (one future- and one past-directed). The collection of these light rays together with the boundary causal diamond of the HRT surface forms the boundary of the entanglement wedge. In this construction, one should take into account that the lightsheet must be terminated whenever light rays intersect. Such intersections are called caustics. In this section, we will derive the location of the lightsheets and caustic analytically. In Appendix \ref{sec: Numerical approach to the lightsheet construction}, a numerical approach to this construction is summarised for the case of a conical deficit, which is also applicable to other spacetimes.
The light rays generating the lightsheet are null geodesics and so they can be described by a 2-plane in $\mathbb{R}^{2,2}$ spanned by a timelike unit vector $Y(\xi)$ where the null ray leaves the HRT surface and a null tangent vector $N$. This light ray must be orthogonal to the HRT surface so that $N \cdot X_1 =0$. This means that $N$ must live on the 2-plane normal to the HRT surface so that each of the two lightsheets are generated by one of the two null vectors spanning the normal plane, $N_1$ and $N_2$,\footnote{Note that the same two null vectors $N_1$ and $N_2$ generate the normal space along the entire HRT surface. In AdS, the normal space rotates as we move along the HRT surface. However the HRT surfaces lift to planes in $\mathbb{R}^{2,2}$ where parallel transport is trivial. The rotation of the normal space in AdS therefore comes from pulling back these fixed vectors through the map \eqref{eqn:cone_param}. This was discussed in \cite{higher_dim_diff_ent18}. } %
\begin{align}
L_i(\lambda,\xi) = Y(\xi) + \lambda N_i\,, \qquad \mathrm{for}~\lambda>0~\mathrm{and}~i=1,2\,.
\end{align}
For the conical deficit, explicit expressions for this lightsheet can be obtained. We will focus on the entanglement wedges of boundary intervals covering more than half of the boundary, so that the lightsheets will initially point towards decreasing $r$. The construction of the lightsheets of the complementary region (of size smaller than half the boundary) is straightforward and similar, although these regions will not have caustics in the bulk for conical deficits.
We shall parametrise the HRT surface by the location of the point whose future light ray along the lightsheet will hit the conical singularity at $r=0$. Without loss of generality, we can choose coordinates such that this point lies at $t=0$ and $\theta=0$. Therefore,
\begin{align}
X_0 = \left( \frac{\sqrt{r_0^2+\alpha^2}}{\alpha}, 0,0, \frac{r_0}\alpha \right) \,,
\end{align}
as before. We will now choose a basis for embedding space by pushing forward the tangent space of this point. By pushing forward the unit vectors in each coordinate direction, we can construct the following embedding space vectors
\begin{align}
R &= \sqrt{r_0^2 + \alpha^2} \partial_r X^A_{cone} (r_0,0,0)
= \alpha^{-1} \left( r_0, 0 ,0, \sqrt{r_0^2 + \alpha^2} \right)\,,\\
T &= \frac{1}{\sqrt{r_0^2 + \alpha^2}} \partial_t X^A_{cone}(r_0,0,0)
= \left( 0,1,0,0 \right) \,, \\
\Theta &= \frac1{r_0} \partial_\theta X^A_{cone}(r_0,0,0)
= \left( 0,0,1,0 \right)\,.
\end{align}
Taken together, $(X_0,\,T,\,\,R,\,\Theta)$ form an orthonormal basis for $\mathbb{R}^{2,2}$. Using this basis, we can provide an intuition for the parametrisation of the HRT surfaces that we used in \eqref{eqn:hrt_cone}. The future-directed light ray leaving $X_0$, which will hit the conical singularity, is characterised by the fact that it will leave the HRT surface in a null direction with no angular component. Since the metric has no cross terms or $\theta$ dependence, a geodesic that starts with no velocity in the $\theta$ direction will never acquire one. This inward pointing future-directed null vector, orthogonal to $X_0$, with no angular component can be constructed as
\begin{align}
N_1 = T - R \,.
\end{align}
We want to construct an HRT surface such that the null ray in this direction will be the generator of the lightsheet leaving from $X_0$. Therefore, this null vector must be one of the $N_i$ characterising the space orthogonal to the $X_0$--$X_1$ plane. We must therefore choose $X_1$ so that it is orthogonal to this vector. A general spacelike unit vector orthogonal to both $X_0$ and $N_1$ can be parametrised by a single parameter $\eta \in \mathbb{R}$,
\begin{align}
X_1 = \Theta + \eta \left( T-R \right)\,.
\end{align}
For $\eta=0$, this tangent vector has no component in the time direction, so the resulting HRT surface will stay at a fixed time. One can therefore think of $\eta$ as parametrising the tilt of the boundary interval away from the constant time slice.
The final null vector completing our orthonormal frame is determined by the requirement that it be (i) orthogonal to $X_0$ and $X_1$, (ii) null and (iii) satisfy $N_1 \cdot N_2 = -2$,
\begin{align}
N_2 =(\eta^2-1) R -(\eta^2+1)T - 2\eta \Theta \,.
\end{align}
The future lightsheet is therefore located at
\begin{align}
L_1 (\xi,\lambda) %
&=\sec \xi \, X_0 + \tan \xi \, \Theta + (\lambda + \eta \tan\xi ) \, T- (\lambda + \eta \tan\xi) \, R \,,\nonumber\\
&= \Bigg(\frac{\sqrt{r_0^2 + \alpha^2} \sec\xi - r_0 (\lambda + \eta \tan\xi) }{\alpha}
,\, \lambda + \eta \tan\xi ,\, \label{eqn:lightsheet_cone}\\
& \qquad\qquad \tan \xi ,\,
\frac{r_0 \sec\xi - \sqrt{r_0^2 + \alpha^2} (\lambda + \eta \tan\xi)}{\alpha} \Bigg)\, ,
\nonumber
\end{align}
and is shown in figure \ref{fig: Lightsheets} for a few cases.
\begin{figure}
\centering
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=.75\textwidth]{LightsheetN2_front.pdf}
\vskip 2mm
\caption{$\alpha=\frac{1}{2}, r_0=2,\eta=0.5$}
\label{fig: LightsheetN2a}
\end{subfigure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=.75\textwidth]{Time_slice_futurepast_caustic.pdf}
\caption{$\alpha=\frac{1}{2}, r_0=2,\eta=0.5$}
\vskip 2mm
\label{fig: LightsheetN2b}
\end{subfigure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=.75\textwidth]{LightsheetN1_5.pdf}
\vskip 2mm
\caption{$\alpha=\frac{2}{3}, r_0=2.5,\eta=0$}
\label{fig: LightsheetN1_5}
\end{subfigure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=.75\textwidth]{LightsheetN3.pdf}
\vskip 2mm
\caption{$\alpha=\frac{1}{3}, r_0=2.5,\eta=0$}
\label{fig: LightsheetN3}
\end{subfigure}
\caption{Plots of the lightsheet bounding the entanglement wedges corresponding to intervals, shown in yellow, that cover more than half of the boundary. The HRT surface is displayed in blue. A few light rays generating the lightsheet are drawn in purple. The light ray that hits the conical singularity at $r=0$ is drawn in green and the caustic where the lightsheet terminates is in red.
In (a) and (b) the front and top view respectively of the full lightsheet which bounds the entanglement wedge of a non-equal time slice HRT surface is displayed, with the dashed lines in (b) referring to the past lightsheet and the solid lines to the future lightsheet. For $\alpha=\frac12$, the caustic is at constant $t$. In (c) and (d) only the future lightsheet is displayed, so as to reduce clutter.}
\label{fig: Lightsheets}
\end{figure}
This lightsheet must be terminated whenever two generators cross, so that $L_i(\lambda_1,\xi_1) = L_i(\lambda_2,\xi_2)$. In the case of AdS$_3$, that is $\alpha=1$, the planes in $\mathbb{R}^{2,2}$ containing these generators intersect only along the null ray $N_i$, which corresponds to the boundary point at the tip of the boundary causal diamond associated to the region on which the HRT surface is anchored. This is the fact that in AdS, the lightsheets are free of caustics in the bulk and terminate at the tip of the boundary causal diamond.
The new ingredient in the conical deficit spacetime is the identification. When the interval covers more than half of the boundary, this leads to new solutions to $L_i(\lambda_1,\xi_1) = L_i(\lambda_2,\xi_2)$ as two vectors can be related by the identification. Recall that this identification corresponds to a rotation by $2\pi\alpha$ of $\phi$ in the hyperpolar coordinates \eqref{eqn:hyperpolar}, which parametrises the angle in the positive signature coordinates of $\mathbb{R}^{2,2}$.
In general, identifying a caustic requires tuning three of the four parameters $(\xi_1,\lambda_1,\xi_2,\lambda_2)$. However, in this case we can exploit symmetries in our set-up to simplify our task. From the explicit expression for $L_1^A$, we see that $L_1^3$ is odd in $\xi$. Since we can apply our identification symmetrically under a $X^3 \rightarrow -X^3$ reflection by identifying the plane $P_{plane}(\pi \alpha)$ with $P_{plane}(-\pi \alpha)$, we should look for caustics where the lightsheets reach these planes. We find a caustic where $L_1(\lambda_1,\xi) \cdot P_{plane}(\pi \alpha) =0$ and $L_1(\lambda_2,-\xi) \cdot P_{plane}(- \pi \alpha) =0$.
This occurs at
\begin{align}
\lambda_1 = - \frac{Y(\xi)\cdot P_{plane}(\pi \alpha) }{N_1\cdot P_{plane}(\pi \alpha) } \,, \qquad
\lambda_2 = - \frac{Y(-\xi)\cdot P_{plane}(-\pi \alpha) }{N_1\cdot P_{plane}(-\pi \alpha) } \,.
\label{eqn:self_intersection_soln}
\end{align}
The caustic is located at
\begin{align}
L_1(\lambda_1,\xi) &= \left(
\frac{\alpha \sec\xi - r_0 \cot\pi \alpha \tan\xi}{\sqrt{r_0^2 + \alpha^2 }},
\frac{r_0 \sec\xi + \alpha \cot\pi\alpha \tan\xi}{\sqrt{r_0^2 + \alpha^2}},
\tan\xi, -\cot \pi \alpha \tan\xi
\right) \,, \nonumber\\
L_1(\lambda_2,-\xi) &= \left(
\frac{\alpha \sec\xi - r_0 \cot\pi \alpha \tan\xi}{\sqrt{r_0^2 + \alpha^2 }},
\frac{r_0 \sec\xi + \alpha \cot\pi\alpha \tan\xi}{\sqrt{r_0^2 + \alpha^2}},
-\tan\xi, -\cot \pi \alpha \tan\xi
\right) \,.
\end{align}
In terms of the coordinates covering the conical deficit defined in \eqref{eqn:cone_param}, $L_1(\lambda_1,\xi)$ and $L_1(\lambda_2,-\xi)$ are located at $\theta = \pm \pi$ respectively along the same curve,\footnote{The branch of $\arctan$ which has range $[0,\pi]$ must be used. This branch ensures that $t(r)$ is continuous as $\alpha$ is varied near $\alpha=\frac12$.}
\begin{align}
t(r)
= \frac1\alpha \left( \arctan \frac{\sqrt{\alpha^2 + r^2 \sin^2 \pi \alpha}}{r \cos \pi \alpha}
-\arctan \frac{\alpha}{r0}
\right) \,,
\label{eq: caustic conical}
\end{align}
confirming that this is a caustic.
There is a simple expression for $\partial_r t(r)$, which makes manifest its definite sign:
\begin{align}
\partial_r t(r) = -
\frac{\alpha \cos \pi\alpha}{\left(r^2+\alpha ^2\right) \sqrt{\alpha ^2+r^2
\sin ^2 \pi\alpha}} \,.
\label{eqn:dtdr_cone_caustic}
\end{align}
\begin{figure}
\centering
\begin{subfigure}[b]{0.7\textwidth}
\centering
\includegraphics[width=.95\textwidth]{Caustic2.pdf}
\vskip 2mm
\caption{$\alpha = \frac{1}{2}$}
\label{fig: caustic2}
\end{subfigure}
\begin{subfigure}[b]{0.7\textwidth}
\centering
\includegraphics[width=.95\textwidth]{Caustic1_5.pdf}
\vskip 2mm
\caption{$\alpha = \frac{2}{3}$}
\label{fig: caustic1_5}
\end{subfigure}
\begin{subfigure}[b]{0.7\textwidth}
\centering
\includegraphics[width=.95\textwidth]{Caustic3.pdf}
\caption{$\alpha = \frac{1}{3}$}
\vskip 2mm
\label{fig: caustic3}
\end{subfigure}
\caption{A side view of the entanglement wedge for regions covering more than half of the boundary in the conical deficit for various values of $\alpha$. The HRT surface is depicted in blue, the ingoing light ray in green, the caustic in red and the interior of the entanglement wedge is shaded in light blue. }
\label{fig: caustics}
\end{figure}
This result has three interesting features. The first is that it does not depend on $\eta$ used to parametrise the tilt of the HRT surface. The caustic leaves the conical singularity at $r=0$ and moves towards the boundary at constant $\theta$. It hits the boundary at the future tip of the boundary causal diamond, at $\theta = \pm \pi$ and
\begin{align}
t(r=\infty)
=
\pi - \frac1\alpha \arctan \frac{\alpha}{r_0} \,.
\label{eq: time boundary tip}
\end{align}
That the caustic does not depend on $\eta$ reflects the fact that its shape does not depend on whether the past tip of the boundary causal diamond is at the same angular position as the future tip.
In effect, we have chosen our coordinates so that the future caustic and the future tip of the causal diamond all lie at $\theta=\pm \pi$. In these coordinates, the choice of $r_0$ and $\eta$ determine where the past tip will lie. By the time reflection symmetry of the metric, it must be that the caustic on the past lightsheet also lies at the angle of the past tip. Hence for tilted HRT surfaces, the past caustic will not lie at $\theta=\pm \pi$ anymore, as illustrated in figure \ref{fig: LightsheetN2a} and \ref{fig: LightsheetN2b}.
The second feature is that its shape does not depend on $r_0$. The only effect of $r_0$ is to shift the caustic in $t$, as the value of $r_0$ determines the position of the future tip where the caustic meets the boundary.
The last feature is that $t(r)$ is monotonic, since \eqref{eqn:dtdr_cone_caustic} does not change sign as a function of $r$. $t(r)$ is decreasing for $0<\alpha<\frac12$ and increasing for $\frac12 < \alpha <1$, as shown in figure \ref{fig: caustics}. For $\alpha = \frac12$, the caustic is flat since $\partial_r t(r) =0$. Moreover, the difference between the time at which the radial light ray reaches the singularity and the time of the future tip of the boundary causal diamond can be seen to be
\begin{align*}
t(\infty)-t(0)= \pi - \frac{\pi}{2 \alpha} \,.
\label{eq: time difference tip singularity}
\end{align*}
Lightsheets of intervals containing less than half of the boundary can be constructed in a similar way and are shown for completeness in figure \ref{fig: entanglement wedges interval less than half}.
\begin{figure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=.9\textwidth]{LightSheet_outwardsN3r1_1_face.pdf}
\vskip 2mm
\end{subfigure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=.85\textwidth]{LightSheet_outwardsN3r1_1.pdf}
\vskip 2mm
\end{subfigure}
\caption{Plot of the lightsheet bounding the entanglement wedge corresponding to an interval, shown in yellow, that covers less than half of the boundary with $r_0 = 1.1$, $\eta = 0$ and $\alpha = 1/3$. A few light rays generating the lightsheet are drawn in purple.}
\label{fig: entanglement wedges interval less than half}
\end{figure}
\subsection{Localisable region}
Let us now turn to determining the localisable region in the conical deficit spacetime. The argument given in \cite{SW} for localisability in the conical deficit, reviewed in our figure \ref{fig: assumption wedges}, assumed that $t(r)$ describing the caustics is monotonically increasing, but we have seen that this is not the case for $0< \alpha \leq 1/2$. In particular, this assumption does not hold for any of the conical deficit spacetimes obtained by a $\mathbb{Z}_n$ identification, which have $\alpha = \frac{1}{n} $ \cite{coneZn}. These are the spacetimes where entwinement was proposed as a quantity that could probe inside the entanglement shadow \cite{entwinement14,entwinement16,entwinement18}.
We have found that $t(r)$ is indeed monotonically increasing for conical deficits $\frac12<\alpha<1$, so their argument goes through and we conclude that the entire spacetime is localisable. However, for $0 < \alpha \leq \frac12$ this is not the case. In those cases, we can show that there is a non-localisable region coinciding with the entanglement shadow as follows. Points inside the entanglement shadow are only inside the entanglement wedge of boundary intervals that cover more than half of the boundary. These entanglement wedges are bounded by the radial light ray heading from the HRT surface directly to the conical singularity along a direction $\theta=\theta_0$ and by the caustic at $\theta=\theta_0 \pm \pi$. Since $t(r)$ is monotonically decreasing for both the caustic and the ingoing light ray, these entanglement wedges will always include a whole interval $[0,r]$ at fixed time $t(r)$ and $\theta$. Therefore any entanglement wedge that includes a point $(r_*, t_*, \theta_*)$ along this ingoing light ray or the caustic will also include all the points $(r,t_*,\theta_*)$ with $r<r_*$. By theorem III.1 of \cite{SW}, this implies that the point $(r_*, t_*, \theta_*)$ cannot be localisable.
Although points inside the entanglement shadow are not in the localisable region, the total radial extent of an operator near the conical singularity can be determined from where it can be reconstructed on the boundary.\footnote{We would like to thank Sean Weinberg for emphasising this fact in correspondence on this topic.} The obstruction is that an operator supported on a ring at fixed radius can be reconstructed in exactly the same regions as an operator that is supported on the disk inside this ring.
\subsection{Disconnected boundary regions}
To complete the argument that the entanglement shadow is not in the localisable region for $0 < \alpha \leq \frac12$, we should also analyse regions with multiple disconnected components. Start with the 2 interval case, where the region on the boundary is $R = I_1 \cup I_2$.
The boundary of this boundary region, $\partial R$, consists of 4 points. The HRT surface must be anchored at these 4 points, and therefore has two components, each consisting of a spatial geodesic connecting two boundary points. There are two possible ways of connecting the 4 boundary points: either the spatial geodesics connect the endpoints of each interval independently or they connect the intervals to each other. In the first case, the homology surface is the union of two disconnected homology surfaces, each corresponding to a homology surface associated to a single interval of less than half the boundary circle. This situation only has the trivial caustics at the tips of the two boundary diamonds. In the second case, the homology surface connects the two intervals across the bulk and includes the central region around the conical singularity. This situation is the more interesting one with non-trivial caustics.
The caustic in this situation is depicted in figure \ref{fig: two_intervals caustic} and can be seen to form a Y-shape. It generically starts at the conical deficit and moves outwards until it splits into two branches, one going to each of the future tips of the two boundary diamonds. A first branch gets formed by the lightsheet emanating from the HRT surface closest to the singularity, where light rays near the radial generator of the lightsheet meet on the other side of the deficit, much as in the single interval case. The other branches come from where the second lightsheet meets this one. The first branch follows exactly the analysis in the previous sections, with the appropriate HRT surface connecting the pair of boundary points that are further apart. The other two branches can be found by looking for the intersection of the lightsheets.
\begin{figure}
\centering
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=1\textwidth]{two_intervals_0_85_3_5.pdf}
\vskip 2mm
\label{fig: two_intervals_0_85_3_5}
\end{subfigure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=0.85\textwidth]{two_intervals_top.pdf}
\vskip 2mm
\label{fig: two_intervals_top}
\end{subfigure}
\caption{The entanglement wedge of a disconnected boundary region $R$, shown in yellow, on the constant time slice $t=0$, for $\alpha = \frac{1}{2.2}$. The HRT surfaces are at $r_0^{(a)}=0.8$, $r_0^{(b)}=3.5$, $\theta_0^{(a)}=0$, $\theta_0^{(b)}=\pi$ and are shown in blue. The caustic, depicted in red, forms a Y-shape that is monotonically decreasing in time as a function of $r$. The green lines represent the two radial light rays starting from the HRT surfaces and meeting the caustic. The purple lines bound the future boundary causal diamonds. \textit{Left.} The complete entanglement wedge seen from the side. \textit{Right.} The caustic seen from the top. The gray segment is a boundary region $R'$ associated to $\gamma^{(a)}$ alone. The position of the tips of the boundary causal diamonds for the two interval boundary region are illustrated with red dots while the gray dot shows the position of the tip of the single causal diamond of region $R'$.}
\label{fig: two_intervals caustic}
\end{figure}
Denote the two HRT surfaces and lightsheets by $(a)$ and $(b)$, where $(a)$ is the one which meets the deficit first and leads to the first branch of the caustic. In the ambient $\mathbb{R}^{2,2}$, the two HRT surfaces are parametrised by
\begin{align}
Y^{(a)}(\xi^{(a)}) &= \sec \xi^{(a)} X_0^{(a)} + \tan \xi^{(a)} X_1^{(a)} \,, \\
Y^{(b)}(\xi^{(b)}) &= \sec \xi^{(b)} X_0^{(b)} + \tan \xi^{(b)} X_1^{(b)} \,,
\end{align}
and the lightsheets are
\begin{align}
L^{(a)} (\xi^{(a)},\lambda^{(a)}) &= Y^{(a)}(\xi^{(a)}) + \lambda^{(a)} N_1^{(a)}\,, \\
L^{(b)} (\xi^{(b)},\lambda^{(b)}) &= Y^{(b)}(\xi^{(b)}) + \lambda^{(b)} N_1^{(b)}\,.
\end{align}
Notice that these lightsheets are simply the intersection of the 3-plane generated by $(X_0,X_1,N_1)$ with the AdS hyperboloid $X^2=-1$. Therefore, the new branch of the caustic will occur along the intersection of these 3-planes. The 3-plane generating the lightsheet is specified by
\begin{align}
N_1 \cdot L =0\,.
\end{align}
Therefore the intersection of the lightsheets occurs when
\begin{align}
N_1^{(a)} \cdot L^{(b)}(\xi^{(b)},\lambda^{(b)}) =0 \,,
\qquad \mathrm{or} \qquad
N_1^{(b)} \cdot L^{(a)}(\xi^{(a)},\lambda^{(a)}) =0 \,.
\end{align}
These two conditions are the same and must be satisfied at the same points in $\mathbb{R}^{2,2}$, so whichever is more convenient can be used. These conditions are easily solved in terms of the parameter along each generator where this intersection can occur,
\begin{align}
\lambda_*^{(a)} = - \frac{N_1^{(b)} \cdot Y^{(a)}(\xi^{(a)})}{N_1^{(b)} \cdot N_1^{(a)} }\,,
\qquad \mathrm{and} \qquad
\lambda_*^{(b)} = - \frac{N_1^{(a)} \cdot Y^{(b)}(\xi^{(b)})}{N_1^{(a)} \cdot N_1^{(b)} } \,.
\label{eqn:lightsheet_intersection}
\end{align}
The last step is to figure out whether each generator is terminated first by crossing the opposite lightsheet or intersecting with an image of the same lightsheet under the identification required to produce the conical deficit. This amounts to combining the correct branches of the solutions to \eqref{eqn:self_intersection_soln} and \eqref{eqn:lightsheet_intersection}. When doing so, we have implemented the effects of the conical deficit by considering all of the relevant images.
Let us now return to the question of whether the entanglement shadow near the conical deficit is in the localisable region. Since no HRT surfaces pass through the entanglement shadow, the only possibility for localisation is if a region whose entanglement wedge includes the conical singularity has a caustic on the future lightsheet with increasing $t(r)$. This caustic departs the singularity where the first light ray on one of the lightsheets meets it. We denoted by $\gamma^{(a)}$ the HRT surface which emitted this light ray. One can also identify a single interval, $R'$, such that $\gamma^{(a)}$ is its HRT surface and such that its entanglement wedge also includes the conical singularity, as shown in figure \ref{fig: two_intervals caustic}. The lightsheet bounding the entanglement wedge of $R'$ also includes this same light ray that hits the conical singularity. We saw that $t(r)$ parametrising the caustic on the lightsheet of $R'$ was decreasing since, from \eqref{eq: time difference tip singularity}, the time of the future tip of the boundary causal diamond associated to $R'$, $t_{R'}(r=\infty)$, was earlier than $t_{R'}({r=0})$ where the light ray hit the conical singularity,
\begin{align}
t_{R'}(r=0) \geq t_{R'}(r=\infty)\,.
\end{align}
Since $R \subset R'$, the time of the future tips of the causal diamonds associated to $I_1$ and $I_2$, must be less than $t_{R'}(r=\infty)$.
We therefore expect the branches of the caustic connecting these tips to the branch starting at the conical singularity at $t_{R'}({r=0}) = t_{R}({r=0})$ to be decreasing. In any case, the behaviour right near the conical deficit is controlled by the branch of the caustic that matches that found in the single interval case. Therefore any entanglement wedge constructed in this way includes the same points in the near deficit region and they are not useful in a family of wedges that localises a point through \eqref{eqn:SW_condition_localisability}.
More boundary regions leads to more richness in the possible caustics, but it seems unlikely to us that they will allow us to localise points inside the entanglement shadow. The behaviour of the entanglement wedge near the conical singularity will always be controlled by the first lightsheet to reach it wrapping around the deficit. This leads to the sharp corners we have observed which impede localisability. We can also see that adding more boundary regions will only force the tips of the boundary diamonds, where the caustics must reach the boundary, to earlier times which is not conducive to the type of geometry required to localise new bulk points.
\subsection{Causal reconstruction in the conical deficit spacetime}
It is interesting to note that causal reconstruction in the conical deficit spacetime also behaves differently for $0<\alpha \leq \frac12$, where the non-localisable region appears, than for $\frac12 <\alpha \leq 1$ where the central region is localisable.
It should first be emphasised that the conical deficit spacetime has no horizons, so that the entire interior can be reconstructed using causal methods when we have access to the entire boundary \cite{BDHM98,HKLL06,dual_density_matrix12,BLR_CW12,HR_CW12}. Since we have an example of a spacetime without a horizon but with a non-localisable region, this demonstrates that being in the localisable region cannot be a necessary condition for whether a local operator can be reconstructed in the boundary theory.
However, the conical deficit spacetime for $0<\alpha \leq \frac12$ does exhibit a certain type of fragility towards causal reconstruction: omitting even a point from the boundary region means that the causal wedge will no longer include a region around the conical singularity. On the other hand, for $ \frac12 < \alpha \leq 1$, the causal reconstruction of the central region is robust in the sense that the causal wedge corresponding to omitting a single point from the boundary still includes an open region around the conical singularity.
This can be diagnosed by studying a light ray departing from the conical singularity and seeing how long it takes to reach the boundary. The causal diamond corresponding to the entire boundary minus a point terminates at $t = \pi$, where the boundary light rays emitted from the omitted point cross at the other side of the boundary circle. In order for the region near the conical singularity to be reconstructible using causal methods, a light ray departing from it must reach the boundary at $t<\pi$ so that it stays within this causal wedge. A radial outgoing light ray starting at $(r_0,t_0,\theta_0)$ in the conical deficit spacetime follows
\begin{align}
t(r) = t_0 + \frac{1}{\alpha} \left( \arctan \frac{\alpha}{r_0} - \arctan \frac{\alpha}{r} \right) \,.
\end{align}
Setting $r_0=0$ and $t_0=0$, we see that a radial light ray departing from the conical singularity reaches the boundary at a time $t= \frac{\pi}{2 \alpha}$ confirming the picture discussed above.
\section{BTZ black hole}
\label{sec:two-sided}
In this section we will consider localisability in the BTZ black hole. Localisability in two-sided eternal black holes was considered by \cite{SW} and our analysis will confirm their results. We start by proving a lemma valid in any number of dimensions which provides a sufficent condition for identifying non-localisable regions inside entanglement shadows behind horizons. Turning to the case of the 3-dimensional BTZ black hole, we will find the caustics bounding the entanglement wedges of regions comprising the entirety of one boundary in addition to part of the other. Since these caustics do not impede the innermost light ray from reaching the singularity, the picture form \cite{SW} goes through unchanged. We will then comment on localisability in the one-sided BTZ, where we will conclude that the entanglement shadow is non-localisable.
\subsection{Localisability of entanglement shadows behind horizons}
In the conical deficit spacetime, \cite{SW} proposed a technique, that was reviewed in figure \ref{fig: assumption wedges}, for localising points that cannot be reached by HRT surfaces but that lie on the intersection of lightsheets approaching the point from a future and a past direction. In this section, we will prove that a region cannot be localised if there are no HRT surfaces in its future light-cone. This provides a connection between regions which are not probed by extremal surfaces, $S$, and localisability in the sense of \cite{SW}: a neighbourhood $U \subset M$ such that $J^+(U) \subset S$ is not localisable.
Many spacetimes are known to have regions that are not probed by extremal surfaces \cite{plateaux13,entwinement14,shadows14}. However, the region near an asymptotically AdS boundary will always be probed by extremal surfaces attached to small boundary regions.\footnote{See for example \cite{EE_from_1st_13} for a discussion of surfaces attached to such small regions.} This means that $S$, the region not probed by extremal surfaces a.k.a. the entanglement shadow, cannot reach the asymptotic boundary. If the future of a neighbourhood is to be contained within the entanglement shadow $S$, and therefore not reach the asymptotic boundary, the spacetime must contain a horizon. Our lemma therefore applies to spacetimes with event horizons, although as we saw in section \ref{sec:cone} in the conical deficit spacetime, event horizons are not necessary for the existence of a non-localisable region.
\begin{lemma}
\label{thm:need-HRT}
Let $U \subset M$ be an open neighbourhood of $M$ such that $J^+(U) \cap \gamma_R=\emptyset$ for all boundary subregions $R$.
Then $U \subset Loc(M)^c$: this neighbourhood is not localisable.
\end{lemma}
Proof. We will argue by contradiction. Suppose there exists $p \in U$ that is localisable. Theorem III.1 from \cite{SW} tells us that this is true if and only if there is a family of boundary regions, $\mathcal{R}_0$, such that
\begin{gather}
\bigcap_{R\in \mathcal{R}_0} W_{\mathcal{E}}(R) = \{p\}\,.
\end{gather}
Now consider another point $q\in U\cap J^-(p)$, $q\neq p$. This intersection must be non-empty since $U$ is open.
Since no HRT surface can intersect the future of $q$, any of the HRT surfaces, $\gamma_R$, anchored to a region $R\in \mathcal{R}_0$ must either enter the past of $q$ or else be entirely spacelike separated from $q$. In either case, it is possible to choose the Cauchy slice of the bulk, $\Sigma_R$, which the HRT surface $\gamma_R$ separates into $H_R$ and $H'_R$, such that $q$ lies to the future of $\Sigma_R$.\footnote{See for example \cite{maximin12} for a discussion of the freedom in choosing this Cauchy slice.}
$p \in W_{\mathcal{E}}(R)$ implies that $p\in D(H_R)$. In fact $p\in D^+(H_R)$, since $p$ is in the future of $q$ and therefore $p$ must also be the future of $H_R \subset \Sigma_R$.
But then, any past-directed causal curve starting at $q$, $\Gamma_q^-$, could be continued to the future along a causal curve connecting $q$ to $p$. Since any inextensible past-directed causal curve through $p$ must cross $H_R$ ($p\in D^+(H_R)$), any such $\Gamma_q^-$ must cross $H_R$ as well. This means that $q\in D^+(H_R)$ and so that $q\in W_{\mathcal{E}}(R)$ for all $R\in \mathcal{R}_0$, in contradiction to the assumption that $p$ is localisable. $\Box$
By simply inverting future and past we can prove another lemma.
\begin{lemma}
\label{thm:need-HRT-past}
Let $U \subset M$ be an open neighbourhood of $M$ such that $J^-(U) \cap \gamma_R=\emptyset$ for all boundary subregions $R$. Then $U \subset Loc(M)^c$.
\end{lemma}
Thus we see that entanglement shadows provide an obstruction to localisability if they include the entire future or past of a region. The technique proposed by \cite{SW} and depicted in figure \ref{fig: assumption wedges}, for localising points inside entanglement shadows requires that both the future and the past of the point in question reach outside the entanglement shadow. These lemmas show that this is necessary.
\subsection{Entanglement wedges in the BTZ black hole}
To identify the entanglement wedges and hence the non-localisable region of BTZ, we will
use a similar approach to the previous section on the conical deficit spacetime and describe it as a quotient of AdS$_3$. For the case of non-rotating BTZ, the identification required for taking this quotient can be obtained by an identification of the ambient $\mathbb{R}^{2,2}$, which once restricted to the AdS hyperboloid gives the correct identification. This will allow us to again obtain a closed form expression for the location of the caustic bounding the relevant entanglement wedges.
The identification required to obtain BTZ is most easily described in different (hyperbolic) hyperpolar coordinates on $\mathbb{R}^{2,2}$ of the form
\begin{align}
\left( r_1\sinh\tau, r_2 \cosh\mu , r_1 \cosh\tau, r_2 \sinh\mu \right)\,,
\label{eqn:hyperpolar_BTZ}
\end{align}
where the required identification is $\mu \sim \mu + 2\pi R$. $R$ is the horizon radius in the resulting BTZ measured in units where $L=1$.
This identifies the plane at $X\cdot{P_{plane}}(\mu_0) =0$ with that at $X\cdot P_{plane}(\mu_0+2\pi R) =0$ where
\begin{align}
P_{plane}(\mu_0) = \left( 0, \sinh\mu_0 , 0, \cosh\mu_0 \right)\,.
\end{align}
Note that the identification required to describe rotating BTZ has a more complicated form and it is not immediately obvious that there is a simple identification of embedding space that restricts correctly to the $X^2=-1$ hyperboloid to reproduce it.
A fundamental domain of this quotient can be covered by coordinates $(u,v,\theta)$,
\begin{align}
X_{BTZ}^A(u,v,\theta) = \left( \frac{v+u}{1+ uv}, \frac{1-uv}{1+uv} \cosh(R \theta),
\frac{v-u}{1+ uv} , \frac{1-uv}{1+uv} \sinh(R \theta) \right)\,.
\label{eqn:BTZcoords}
\end{align}
The metric induced from this embedding is the BTZ metric in Kruskal-like coordinates\footnote{The BTZ black hole was introduced in \cite{BTZ92}. The embedding of BTZ into $
\mathbb{R}^{2,2}$ using these coordinates is reviewed in
\cite{butterfly13}.
}
\begin{gather}
ds^2 = dX_{BTZ} \cdot dX_{BTZ} = \frac{-4 du dv +R^2 (1-uv)^2 d\theta^2}{(1+uv)^2} \,.
\end{gather}
In these coordinates, the singularity is at $uv=1$ and the right exterior region is $u<0$ and $v>0$.
The boundary is located at $1+uv=0$. A time coordinate can be introduced so that $u=-e^{-R t}$ and $v=e^{R t}$ at the boundary, which is associated to the null rays
\begin{align}
Z_{BTZ}^A (t,\theta) &\propto \frac{1+uv}{2} X^A_{BTZ}(u,v,\theta) \big|_{u=-e^{-R t},\, v=e^{R t}}\\
&= \left( \sinh R t , \cosh R \theta,
\cosh R t ,\sinh R \theta \right)\,. \label{eqn:BTZ_bdy}
\end{align}
Now we wish to identify the entanglement wedges associated to two types of regions: connected regions contained in the right boundary, as well as the complement of this type of region, which includes the entirety of the left boundary plus a part of the right asymptotic region. Denote the region of interest by $A$. In either case, the corresponding HRT surface is anchored to the right boundary at $\partial A$ and the entanglement wedge is bounded by the radially outward or inward pointing lightsheets respectively from the HRT surface. Regions contained entirely in the right boundary will have HRT surfaces that stay within one fundamental domain of the identification, so they will not develop any new caustics beyond the one at the tip of the boundary diamond. We will therefore focus mostly on the complement type regions. The future-directed lightsheets associated with these regions depart the HRT surface in the $\partial_u$ direction and the past-directed one towards $-\partial_v$. We will focus on the future-directed lightsheet in what follows. As was the case in the last section, the past-directed lightsheet can be understood by exploiting the time reflection symmetry of this metric.
The lightsheet is obtained by following null geodesics orthogonal to each point on the HRT surface to generate a co-dimension 1 surface. Similar to our experience with the conical deficit spacetime, since the metric is rotationally invariant and has no $d\theta$ cross terms, a null geodesic that leaves the surface with no $\partial_\theta$ component to its velocity will fall directly into the singularity in a radial direction. The most important question will then be whether this null generator continues until it hits the singularity or whether nearby generators are bent inwards to cross this ray and form a caustic before this can happen.
We will again label the HRT surfaces by the point which emits this radial light ray.
This point is described by a vector $X_0(u_0,v_0,\theta_0)$ in the form of \eqref{eqn:BTZcoords}, such that $X_0^2=-1$. We can set $\theta_0=0$ by using the rotational symmetry. The tangent space of the BTZ spacetime can be embedded in embedding space by pushing it forward through the map in \eqref{eqn:BTZcoords}. Similar to the approach taken in the last section, the image of the vectors $\partial_u$, $\partial_v$ and $\partial_\theta$ along with $X_0$, can be normalised to produce an orthonormal frame for the embedding space $(X_0, U,V, \Theta)$,
\begin{align}
X_0&=\Big(\frac{u_0+v_0}{1+u_0 v_0},\frac{1-u_0 v_0}{1+u_0 v_0},\frac{v_0-u_0}{1+u_0
v_0},0\Big) \,,\\
U&=\Big(\frac{1-v_0^2}{1+u_0 v_0},\frac{-2 v_0}{1+u_0 v_0},\frac{-1-v_0^2}{1+u_0 v_0},0\Big)\,,\\
V&=\Big(\frac{1-u_0^2}{1+u_0 v_0},\frac{-2 u_0}{1+u_0 v_0},\frac{1+u_0^2}{1+u_0 v_0},0\Big)\,,\\
\Theta&=\Big(0,0,0,1\Big)\,. \label{eqn:BTZ_frame}
\end{align}
We now repeat the approach used in the previous section for determining the lightsheet in terms of the ambient $\mathbb{R}^{2,2}$. The first orthogonal null vector defining HRT surface must be chosen to point in the $\partial_u$ direction. This means that $N_1 = U$.
Now we must determine $X_1$ and $N_2$. We will use a similar parametrisation where
\begin{align}
X_1 = \Theta + \eta U, \qquad N_2 = -2 \eta \Theta - V - \eta^2 U\,,
\end{align}
so that $\eta=0$ describes the surface lying on a constant time slice and $\eta\in \mathbb{R}_0$ describes a boosted or tilted surface.
The resulting HRT surface
\begin{align}
Y(\xi) = \sec \xi X_0 + \tan \xi X_1 \,,
\end{align}
is obtained by imposing $Y^2=-1$ within the $X_0$--$X_1$ plane.
The lightsheets are given by
\begin{align}
L_i(\lambda,\xi) &= Y(\xi)+\lambda N_i \,, \\
L_1 (\lambda,\xi) &= \bigg(
\frac{\left(u_0+v_0\right)\sec\xi
+\left(1-v_0^2\right) (\lambda+\eta \tan\xi)}{1+u_0 v_0},
\frac{ (1-u_0 v_0) \sec\xi -2 \eta v_0 \tan\xi -2 \lambda v_0 }{1+u_0 v_0}, \nonumber\\
&\qquad \qquad
\frac{ (v_0-u_0) \sec\xi -\eta\left(1+v_0^2\right) \tan\xi
-\lambda \left(1+v_0^2\right) }{1+u_0 v_0},
\tan (\xi )
\bigg)\,.
\end{align}
By the same argument as before, new bulk caustics only occur due to the identifications required to take the quotient to obtain BTZ from AdS$_3$. This rules out the possibility that the caustic cuts off the inward pointing light ray before it hits the singularity, since the singularity is reached within a fundamental domain of the identification. Instead the caustics will extend from the singularity back to the boundary where the generators on opposite sides of the radial light ray meet at the surface fixed by the identification.
This time the last component of $L_1$ is odd under $\xi \rightarrow -\xi$, so that the caustic occurs on the identified planes $P_{plane}(\pi R)$ and $P_{plane}(-\pi R)$.
The solutions to $L_1(\lambda_1,\xi)\cdot P_{plane}(\pi R)=0$ and $L_1(\lambda_2,-\xi)\cdot P_{plane}(-\pi R)=0$ are
\begin{align}
\lambda_1 = - \frac{Y(\xi)\cdot P_{plane}(\pi R) }{N_1\cdot P_{plane}(\pi R) } \,, \qquad
\lambda_2 = - \frac{Y(-\xi)\cdot P_{plane}(-\pi R) }{N_1\cdot P_{plane}(-\pi R) } \,.
\end{align}
The caustic is located at
\begin{align}
L_1(\lambda_1,\xi) &= \bigg(
\frac{\left(v_0^2+1\right) \sec\xi
+\left(v_0^2-1\right) \coth \pi R \tan\xi }{2 v_0},
\coth \pi R \tan\xi , \nonumber\\ &\qquad \qquad
\frac{\left(v_0^2-1\right) \sec\xi +\left(v_0^2+1\right) \coth \pi R \tan\xi }{2 v_0},
\tan \xi \bigg) \,,
\\
L_1(\lambda_2,-\xi) &= \bigg(
\frac{\left(v_0^2+1\right) \sec\xi
+\left(v_0^2-1\right) \coth \pi R \tan\xi }{2 v_0},
\coth \pi R \tan\xi , \nonumber\\ &\qquad \qquad
\frac{\left(v_0^2-1\right) \sec\xi +\left(v_0^2+1\right) \coth \pi R \tan\xi }{2 v_0},
-\tan \xi \bigg) \,. \nonumber
\end{align}
In the hyperpolar coordinates of \eqref{eqn:hyperpolar_BTZ}, $L_1(\lambda_1,\xi)$ and $L_1(\lambda_2,-\xi)$ are located at $\mu = \pm \pi R$ respectively, which are to be identified, confirming that this is the location of a caustic. This can be related to a position in the Kruskal-like coordinates by inverting \eqref{eqn:BTZcoords}.
This determines the future caustic to lie along $\theta=\pm \pi$ at
\begin{align}
v(u) = v_0 \frac{u v_0 + \cosh \pi R}{1 + u v_0 \cosh \pi R}\,.
\label{eqn:2-sided_BTZ_caustic}
\end{align}
This is illustrated in figure \ref{fig: caustic btz penrose}.
Notice that \eqref{eqn:2-sided_BTZ_caustic} is independent of both the boost of the boundary region, $\eta$, and of $u_0$.
Similarly to the result we found in the conical deficit, the caustic only depends on the location of the future tip of the boundary causal diamond. By following the caustic out to the boundary, that is comparing the light ray in the direction of
\begin{align}
\lim_{\xi\rightarrow \frac\pi2 } \frac{\sinh\pi R}{\tan\xi} L_1(\lambda_1,\xi) &=
\bigg(
\frac{\left(v_0^2+1\right) \sinh \pi R
+\left(v_0^2-1\right) \cosh \pi R }{2 v_0},
\cosh \pi R ,
\\ &\qquad \qquad
\frac{\left(v_0^2+1\right) \cosh \pi R + \left(v_0^2-1\right) \sinh \pi R }{2 v_0},
\sinh \pi R \bigg) \,, \nonumber
\end{align}
to our parametrisation of the boundary, \eqref{eqn:BTZ_bdy}, we see that this future tip is located at $\theta=\pm \pi$ and
\begin{align}
t(r=\infty) = \pi + \frac{1}{R} \log v_0\,.
\end{align}
\begin{figure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=0.9\textwidth]{TimeSliceBTZ.pdf}
\caption{Schwarzschild-like $(r,\theta)$ diagram}
\vskip 2mm
\label{fig: caustic btz t projected out}
\end{subfigure}
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=.9\textwidth]{CausticBTZ.pdf}
\caption{Penrose diagram}
\vskip 2mm
\label{fig: caustic btz penrose}
\end{subfigure}
\caption{The red line represents the future caustic of a boundary region in the one- and two-sided BTZ black hole. The boundary region, shown in yellow, comprises more than half of the $t=0$ slice of the right boundary and the complete left boundary time slice. The HRT surface is shown in blue and is chosen at $r_0 = 1$. A few representative orthogonal light rays are drawn in purple in (a) and meet at the caustic. The radial light ray reaching the singularity is shown in green. The horizon is chosen at $R=0.5$ and is indicated in dashed orange.}
\label{fig: caustic penrose btz}
\end{figure}
\subsection{Localisability in two-sided BTZ}
In this section we will discuss the localisable region in the two-sided eternal BTZ black hole. This region will be quite different from that in the one-sided BTZ black hole that could be formed by collapse, due to the existence of spacelike geodesics stretching from one boundary to the other. In the two-sided case, the entanglement shadow is behind the horizon near the singularity. In fact, the entire spacetime is probed by spacelike geodesics stretching between the two boundaries, but the length of these geodesics grows as they approach the singularity. Since regions to which these geodesics can be anchored also admit candidate extremal surfaces consisting of disconnected geodesics that stay outside of the horizon, these disconnected geodesics will dominate once the geodesic that crosses gets close enough to the singularity. This leads to an entanglement shadow near the singularity in the interior of the black hole \cite{shadows14}.
This entanglement shadow behind the horizon allows us to use our lemma \ref{thm:need-HRT} to argue that there is a non-localisable region near the horizon.
In particular, given the explicit form of the entanglement wedges of regions that include the entire left boundary as well as a subregion of the right boundary derived in the previous section (see figure \ref{fig: caustic btz penrose}), we confirm that everything to the left, on the conformal diagram, of the central ingoing light ray that hits the singularity is included in the entanglement wedge. This confirms the picture in figure 5 used by \cite{SW} in their argument establishing the non-localisability of a region near the singularity of the two-sided BTZ.
\subsection{Localisability in one-sided BTZ}
If we only have access to one boundary of the BTZ black hole, then there is a region near the horizon that cannot be reached by HRT surfaces, much as in the conical deficit spacetime \cite{plateaux13,shadows14}. Here again we could try to use the strategy proposed by \cite{SW} for the conical deficit to localise points in this region. However, from figure \ref{fig: caustic t(r) btz} we can see that this strategy will not work for the same reasons that it failed for $0<\alpha\leq \frac12$ in the conical deficit. To analyse this, it is useful to introduce Schwarzschild-like coordinates covering the exterior region of BTZ. These have the form
\begin{align}
X_{BTZ'}^A &= \left( \frac{\sqrt{r^2-R^2}}{R} \sinh R t, \frac{r}{R} \cosh R \theta,
\frac{\sqrt{r^2-R^2}}{R} \cosh R t, \frac{r}{R} \sinh R \theta \right) \,, \\
ds^2 &= dX_{BTZ'} \cdot dX_{BTZ'} = -(r^2-R^2) dt^2 + \frac{dr^2}{r^2-R^2} +r^2 d\theta^2\,.
\end{align}
These coordinates are related to the Kruskal-like ones by\footnote{The Schwarzschild-like coordinates cover the right exterior region, where $v>0$ and $u<0$.}
\begin{align}
\frac{r}{R}=& \frac{1-uv}{1+uv}\,, & v =& \sqrt{\frac{r-R}{r+R}} e^{R t} \,, \\
e^{R t} =& \sqrt{\frac{v}{-u}}\,, & u=&-\sqrt{\frac{r-R}{r+R}} e^{-R t} \,.
\end{align}
An example of a caustic in BTZ is shown in figure \ref{fig: caustic penrose btz} in both set of coordinates.
In the previous section, our HRT surfaces were parametrised by $(u_0,v_0)$. We can use the time-translation symmetry of the metric in Schwarzschild-like coordinates to fix $t_0=0$. This means that $u_0 = -v_0$ and
\begin{align}
r_0 = R \frac{1+v_0^2}{1-v_0^2} \,.
\end{align}
Applying this change of coordinates to the expression for the caustics obtained in \eqref{eqn:2-sided_BTZ_caustic}, the caustic is found to lie at
\begin{align}
\label{eq: caustic btz}
t(r) &=
\frac{1}{R} \left(
\mathrm{arctanh}\, \frac{ \sqrt{R^2 + r^2 \sinh^2 \pi R} }{r \cosh \pi R} - \mathrm{arctanh}\, \frac{R}{r_0}
\right)\,,\\
\partial_r t(r) &= - \frac{ R \cosh \pi R }{(r^2-R^2) \sqrt{R^2+r^2 \sinh^2 \pi R} }\,.
\end{align}
This expression makes explicit that $t(r)$ is a monotonically decreasing function of $r>R$ which diverges as $r \rightarrow R$, as shown in figure \ref{fig: caustic t(r) btz}. Note that \eqref{eq: caustic btz} can also be found from \eqref{eq: caustic conical} by analytically continuing $\alpha \rightarrow i R$.
\begin{figure}
\centering
\includegraphics[width=.6\textwidth]{caustic_t_r_btz.pdf}
\vskip 2mm
\caption{The time dependence of the caustic outside the horizon of a BTZ black hole as a function of $r$, with a horizon of radius $R = 0.5$ for an HRT surface with $r_0=1$. The solid red line is the caustic and the orange dashed line depicts the location of the horizon.}
\label{fig: caustic t(r) btz}
\end{figure}
This implies that any entanglement wedge whose caustic passes through the point $(r_*,t_*,\theta_*)$, will include all the points along a line at fixed $t$ going inwards from this point, that is the points \begin{align}
(r,t_*,\theta_*) ~ \mathrm{for}~ r \in (R,r_*) \,.
\end{align}
By the same logic used in the conical deficit spacetime, this demonstrates that the non-localisable region of the one-sided BTZ black hole coincides with the entanglement shadow.
\section{Outlook}
In this work we studied the detailed form of the caustics bounding the entanglement wedges in simple spacetimes. Entanglement wedges play an essential role in understanding the emergence of bulk locality \cite{HQECC14,JLMS15,EW_reconstruction16} and in the diagnosis of bulk locality from the error correcting structure of holography proposed in \cite{SW}, the shape of the caustics bounding these entanglement wedges is important in determining the bulk region for which local bulk operators can be identified as local using boundary techniques.
Our analysis of the detailed form of these caustics revealed unexpected features that contradicts the assumptions in some of their analysis, while confirming those made in other parts. In particular, in the setting of asymptotically AdS$_3$ spacetimes, we find a non-localisable region near the horizon of a one-sided BTZ black hole and near conical singularities with sufficiently large angular deficits which coincides with the entanglement shadow. In the conical deficit, the non-localisable region appears when the caustics bend sufficiently sharply away from the trajectory of the light rays approaching the conical singularity leading to a sharp corner in the entanglement wedge near the conical singularity.
It would be interesting to better understand the caustics appearing on the boundaries of entanglement wedges in higher dimensions. Since the lightsheets will be higher dimensional objects, there is a more complicated zoo of caustics that could occur with the possibility of lower dimensional caustics where higher dimensional caustics pinch off. There is also a variety of boundary regions that can be considered, whereas a 2-dimensional boundary only admits intervals. Less symmetric boundary regions will generally lead to the presence of more caustics, even in empty AdS space. A better understanding of the possible shapes of these caustics is required to understand the entanglement wedges in these geometries with all the ensuing implications for understanding bulk locality.
The study of the caustics in more complicated settings, such as higher dimensions will require numerical techniques. Finding the locations of caustics becomes the problem of finding where light rays cross in the bulk. As the number of dimensions grows the number of parameters which must be tuned for this to occur grows as well, not to mention that even finding the HRT surfaces, which emit these lightsheets, in higher dimensions requires solving PDEs rather than ODEs. In appendix \ref{sec: Numerical approach to the lightsheet construction}, we discuss a numerical approach to determining the caustics in the simple setting we studied in this work. This numerical approach was used to confirm our analytic results and provides a starting point for further studies in more complicated settings.
\section*{Acknowledgements}
We would like to thank Ben Craps and Sean Weinberg for discussions.
This work is supported in part by FWO-Vlaanderen through projects G044016N and G006918N and by Vrije Universiteit Brussel through the Strategic Research Program ``High-Energy Physics.'' M.~D.~C.~is supported by a PhD fellowship from the Research Foundation Flanders (FWO).
C.~R.~also acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC) funding reference number PDF-517316-2018 and from a Postdoctoral Fellowship from the Research Foundation Flanders (FWO).
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,206
|
Paul Salvator Goldengruen (de son vrai nom Paul Ricken, né le à Warburg) est un peintre allemand d'art brut.
Biographie
Après une formation de vendeur au détail de 1976 à 1979 à Warburg et les 15 mois de service militaire obligatoire à Münster et à Lunebourg en 1980 et 1981, Paul Salvator Goldengruen obtient son abitur en suivant les cours d'une école pour des personnes qui reprennent des études à Paderborn de début 1982 à fin 1984. Il commence des études de biologie à l'automne 1985 à Münster et Bielefeld qu'il abandonne ensuite. Il se réoriente vers la littérature anglaise et va jusqu'en licence.
Dans les années 1990, un an après le décès de sa mère, Paul Salvator Goldengruen développe une maladie psychiatrique qu'il canalise par l'expression artistique. Il s'investit dans cette activité et développe une forme d'art brut.
Ses peintures se diffusent entre psychiatres par Internet et se retrouvent en Amérique du Nord (International Society for the Study of Trauma and Dissociation) et latine (Artecomunicarte) dans des expositions consacrées à l'art brut. En , 20 tableaux sont acquis par la collection Hans Prinzhorn à Heidelberg comme La divinité primitive (Die Urgottheit).
Son œuvre croissante compte environ 500 pièces, pour la plupart des images de grand format qui se caractérisent par l'expressivité et la richesse des couleurs et souvent un symbolisme énigmatique, ainsi que des petites sculptures et quelque 200 poèmes.
Source, notes et références
Liens externes
Site consacré à l'œuvre de Paul Salvator Goldengruen
Artiste contemporain allemand
Art brut en Allemagne
Peintre d'art brut
Peintre allemand du XXIe siècle
Naissance en août 1960
Naissance à Warburg
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,213
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Narikkalpatti is a village in the Dindigul District of the South Indian state of Tamil Nadu, located 11 km from Palani. The River Shanmuganadhi flows through this village. At the time of the Census of India 2001, Narikkalpatti had a population of more than 4500 people. The majority of the people belong to the Kongu Vellalar Gounder caste and devangars.
The postal code of the village is 624618.
The Union Primary school and a Govt Aided Higher secondary school (CGM) are situated there, as well as Indian overseas bank branch
The main income sources of the village are agriculture and weaving. The main agricultural products include coconuts, rice and sugar cane. The village is located between Dharapuram and Palani via Alangiyam.
References
Villages in Dindigul district
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,884
|
Partalansaari is an island located in lake Saimaa. A large portion of the island belongs to the municipality of Sulkava while a smaller part belongs to Puumala.
The island is surrounded by the largest watersheds — on the east is Lepistönselkä, on the northwest is Enonvesi and on the southwest Haapaselkä. There are more than 80 lakes and ponds within the island and the largest are lakes Kulkemusjärvi and Saajuu. The island has a road connection to the mainland. The villages that are covered by the municipality of Sulkava are Kaartilankoski in the north, Karjulanmäki in the west and Auvila in the southeast. Puumala includes the villages of Keriniemi and Kietävälä. The island has approximately 400 permanent residents. There are a lot of summer residents as well.
A book about Partalansaari — Partalansaaren poluilla — was published in 1999. It was written by Rauno Pelkonen, a former resident of the island.
The 60-kilometer route of Sulkavan Suursoudut (The Grand Rowing Races of Sulkava), revolves around Partalansaari. Halfway through the trip lies the Varviranta accommodation area, where tour rowers stay overnight.
History
Partalansaari has been inhabited since the prehistoric times. Many Stone Age settlements were found in Sulkava.
Partanlasaari was formerly known as Kulkemussalo island and it was later abbreviated to Kulkemussaari.
Gallery
References
Islands of Finland
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 461
|
Skinny ain't what it used to be.
the kind that could dethrone a man if you allow it.
can I say, grease paint's good for murderabilia.
chillax with your border, something taller's on the way.
could advance someone as fakely as me.
of so slender a truth.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,418
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/*
* Mesh object with texture and skinning information
*/
#include "precompiled.h"
#include "Model.h"
#include "Decal.h"
#include "ModelDef.h"
#include "maths/Quaternion.h"
#include "maths/BoundingBoxAligned.h"
#include "SkeletonAnim.h"
#include "SkeletonAnimDef.h"
#include "SkeletonAnimManager.h"
#include "MeshManager.h"
#include "ObjectEntry.h"
#include "lib/res/graphics/ogl_tex.h"
#include "lib/res/h_mgr.h"
#include "lib/sysdep/rtl.h"
#include "ps/Profile.h"
#include "ps/CLogger.h"
#include "renderer/Renderer.h"
#include "simulation2/Simulation2.h"
#include "simulation2/components/ICmpTerrain.h"
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Constructor
CModel::CModel(CSkeletonAnimManager& skeletonAnimManager, CSimulation2& simulation)
: m_Flags(0), m_Anim(NULL), m_AnimTime(0), m_Simulation(simulation),
m_BoneMatrices(NULL), m_AmmoPropPoint(NULL), m_AmmoLoadedProp(0),
m_SkeletonAnimManager(skeletonAnimManager)
{
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Destructor
CModel::~CModel()
{
ReleaseData();
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// ReleaseData: delete anything allocated by the model
void CModel::ReleaseData()
{
rtl_FreeAligned(m_BoneMatrices);
for (size_t i = 0; i < m_Props.size(); ++i)
delete m_Props[i].m_Model;
m_Props.clear();
m_pModelDef = CModelDefPtr();
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// InitModel: setup model from given geometry
bool CModel::InitModel(const CModelDefPtr& modeldef)
{
// clean up any existing data first
ReleaseData();
m_pModelDef = modeldef;
size_t numBones = modeldef->GetNumBones();
if (numBones != 0)
{
size_t numBlends = modeldef->GetNumBlends();
// allocate matrices for bone transformations
// (one extra matrix is used for the special case of bind-shape relative weighting)
m_BoneMatrices = (CMatrix3D*)rtl_AllocateAligned(sizeof(CMatrix3D) * (numBones + 1 + numBlends), 16);
for (size_t i = 0; i < numBones + 1 + numBlends; ++i)
{
m_BoneMatrices[i].SetIdentity();
}
}
m_PositionValid = true;
return true;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// CalcBound: calculate the world space bounds of this model
void CModel::CalcBounds()
{
// Need to calculate the object bounds first, if that hasn't already been done
if (! (m_Anim && m_Anim->m_AnimDef))
{
if (m_ObjectBounds.IsEmpty())
CalcStaticObjectBounds();
}
else
{
if (m_Anim->m_ObjectBounds.IsEmpty())
CalcAnimatedObjectBounds(m_Anim->m_AnimDef, m_Anim->m_ObjectBounds);
ENSURE(! m_Anim->m_ObjectBounds.IsEmpty()); // (if this happens, it'll be recalculating the bounds every time)
m_ObjectBounds = m_Anim->m_ObjectBounds;
}
// Ensure the transform is set correctly before we use it
ValidatePosition();
// Now transform the object-space bounds to world-space bounds
m_ObjectBounds.Transform(GetTransform(), m_WorldBounds);
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// CalcObjectBounds: calculate object space bounds of this model, based solely on vertex positions
void CModel::CalcStaticObjectBounds()
{
m_ObjectBounds.SetEmpty();
size_t numverts=m_pModelDef->GetNumVertices();
SModelVertex* verts=m_pModelDef->GetVertices();
for (size_t i=0;i<numverts;i++) {
m_ObjectBounds+=verts[i].m_Coords;
}
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// CalcAnimatedObjectBound: calculate bounds encompassing all vertex positions for given animation
void CModel::CalcAnimatedObjectBounds(CSkeletonAnimDef* anim, CBoundingBoxAligned& result)
{
result.SetEmpty();
// Set the current animation on which to perform calculations (if it's necessary)
if (anim != m_Anim->m_AnimDef)
{
CSkeletonAnim dummyanim;
dummyanim.m_AnimDef=anim;
if (!SetAnimation(&dummyanim)) return;
}
size_t numverts=m_pModelDef->GetNumVertices();
SModelVertex* verts=m_pModelDef->GetVertices();
// Remove any transformations, so that we calculate the bounding box
// at the origin. The box is later re-transformed onto the object, without
// having to recalculate the size of the box.
CMatrix3D transform, oldtransform = GetTransform();
CModelAbstract* oldparent = m_Parent;
m_Parent = 0;
transform.SetIdentity();
CRenderableObject::SetTransform(transform);
// Following seems to stomp over the current animation time - which, unsurprisingly,
// introduces artefacts in the currently playing animation. Save it here and restore it
// at the end.
float AnimTime = m_AnimTime;
// iterate through every frame of the animation
for (size_t j=0;j<anim->GetNumFrames();j++) {
m_PositionValid = false;
ValidatePosition();
// extend bounds by vertex positions at the frame
for (size_t i=0;i<numverts;i++)
{
result += CModelDef::SkinPoint(verts[i], GetAnimatedBoneMatrices());
}
// advance to next frame
m_AnimTime += anim->GetFrameTime();
}
m_PositionValid = false;
m_Parent = oldparent;
SetTransform(oldtransform);
m_AnimTime = AnimTime;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
const CBoundingBoxAligned CModel::GetWorldBoundsRec()
{
CBoundingBoxAligned bounds = GetWorldBounds();
for (size_t i = 0; i < m_Props.size(); ++i)
bounds += m_Props[i].m_Model->GetWorldBoundsRec();
return bounds;
}
const CBoundingBoxAligned CModel::GetObjectSelectionBoundsRec()
{
CBoundingBoxAligned objBounds = GetObjectBounds(); // updates the (children-not-included) object-space bounds if necessary
// now extend these bounds to include the props' selection bounds (if any)
for (size_t i = 0; i < m_Props.size(); ++i)
{
const Prop& prop = m_Props[i];
if (prop.m_Hidden || !prop.m_Selectable)
continue; // prop is hidden from rendering, so it also shouldn't be used for selection
CBoundingBoxAligned propSelectionBounds = prop.m_Model->GetObjectSelectionBoundsRec();
if (propSelectionBounds.IsEmpty())
continue; // submodel does not wish to participate in selection box, exclude it
// We have the prop's bounds in its own object-space; now we need to transform them so they can be properly added
// to the bounds in our object-space. For that, we need the transform of the prop attachment point.
//
// We have the prop point information; however, it's not trivial to compute its exact location in our object-space
// since it may or may not be attached to a bone (see SPropPoint), which in turn may or may not be in the middle of
// an animation. The bone matrices might be of interest, but they're really only meant to be used for the animation
// system and are quite opaque to use from the outside (see @ref ValidatePosition).
//
// However, a nice side effect of ValidatePosition is that it also computes the absolute world-space transform of
// our props and sets it on their respective models. In particular, @ref ValidatePosition will compute the prop's
// world-space transform as either
//
// T' = T x B x O
// or
// T' = T x O
//
// where T' is the prop's world-space transform, T is our world-space transform, O is the prop's local
// offset/rotation matrix, and B is an optional transformation matrix of the bone the prop is attached to
// (taking into account animation and everything).
//
// From this, it is clear that either O or B x O is the object-space transformation matrix of the prop. So,
// all we need to do is apply our own inverse world-transform T^(-1) to T' to get our desired result. Luckily,
// this is precomputed upon setting the transform matrix (see @ref SetTransform), so it is free to fetch.
CMatrix3D propObjectTransform = prop.m_Model->GetTransform(); // T'
propObjectTransform.Concatenate(GetInvTransform()); // T^(-1) x T'
// Transform the prop's bounds into our object coordinate space
CBoundingBoxAligned transformedPropSelectionBounds;
propSelectionBounds.Transform(propObjectTransform, transformedPropSelectionBounds);
objBounds += transformedPropSelectionBounds;
}
return objBounds;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// BuildAnimation: load raw animation frame animation from given file, and build a
// animation specific to this model
CSkeletonAnim* CModel::BuildAnimation(const VfsPath& pathname, const CStr& name, int frequency, float speed, float actionpos, float actionpos2, float soundpos)
{
CSkeletonAnimDef* def = m_SkeletonAnimManager.GetAnimation(pathname);
if (!def)
return NULL;
CSkeletonAnim* anim = new CSkeletonAnim();
anim->m_Name = name;
anim->m_Frequency = frequency;
anim->m_AnimDef = def;
anim->m_Speed = speed;
if (actionpos == -1.f)
anim->m_ActionPos = -1.f;
else
anim->m_ActionPos = actionpos * anim->m_AnimDef->GetDuration();
if (actionpos2 == -1.f)
anim->m_ActionPos2 = -1.f;
else
anim->m_ActionPos2 = actionpos2 * anim->m_AnimDef->GetDuration();
if (soundpos == -1.f)
anim->m_SoundPos = -1.f;
else
anim->m_SoundPos = soundpos * anim->m_AnimDef->GetDuration();
anim->m_ObjectBounds.SetEmpty();
InvalidateBounds();
return anim;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Update: update this model to the given time, in msec
void CModel::UpdateTo(float time)
{
// update animation time, but don't calculate bone matrices - do that (lazily) when
// something requests them; that saves some calculation work for offscreen models,
// and also assures the world space, inverted bone matrices (required for normal
// skinning) are up to date with respect to m_Transform
m_AnimTime = time;
// mark vertices as dirty
SetDirty(RENDERDATA_UPDATE_VERTICES);
// mark matrices as dirty
InvalidatePosition();
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// InvalidatePosition
void CModel::InvalidatePosition()
{
m_PositionValid = false;
for (size_t i = 0; i < m_Props.size(); ++i)
m_Props[i].m_Model->InvalidatePosition();
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// ValidatePosition: ensure that current transform and bone matrices are both uptodate
void CModel::ValidatePosition()
{
if (m_PositionValid)
{
ENSURE(!m_Parent || m_Parent->m_PositionValid);
return;
}
if (m_Parent && !m_Parent->m_PositionValid)
{
// Make sure we don't base our calculations on
// a parent animation state that is out of date.
m_Parent->ValidatePosition();
// Parent will recursively call our validation.
ENSURE(m_PositionValid);
return;
}
if (m_Anim && m_BoneMatrices)
{
// PROFILE( "generating bone matrices" );
ENSURE(m_pModelDef->GetNumBones() == m_Anim->m_AnimDef->GetNumKeys());
m_Anim->m_AnimDef->BuildBoneMatrices(m_AnimTime, m_BoneMatrices, !(m_Flags & MODELFLAG_NOLOOPANIMATION));
}
else if (m_BoneMatrices)
{
// Bones but no animation - probably a buggy actor forgot to set up the animation,
// so just render it in its bind pose
for (size_t i = 0; i < m_pModelDef->GetNumBones(); i++)
{
m_BoneMatrices[i].SetIdentity();
m_BoneMatrices[i].Rotate(m_pModelDef->GetBones()[i].m_Rotation);
m_BoneMatrices[i].Translate(m_pModelDef->GetBones()[i].m_Translation);
}
}
// For CPU skinning, we precompute as much as possible so that the only
// per-vertex work is a single matrix*vec multiplication.
// For GPU skinning, we try to minimise CPU work by doing most computation
// in the vertex shader instead.
// Using g_Renderer.m_Options to detect CPU vs GPU is a bit hacky,
// and this doesn't allow the setting to change at runtime, but there isn't
// an obvious cleaner way to determine what data needs to be computed,
// and GPU skinning is a rarely-used experimental feature anyway.
bool worldSpaceBoneMatrices = !g_Renderer.m_Options.m_GPUSkinning;
bool computeBlendMatrices = !g_Renderer.m_Options.m_GPUSkinning;
if (m_BoneMatrices && worldSpaceBoneMatrices)
{
// add world-space transformation to m_BoneMatrices
const CMatrix3D transform = GetTransform();
for (size_t i = 0; i < m_pModelDef->GetNumBones(); i++)
m_BoneMatrices[i].Concatenate(transform);
}
// our own position is now valid; now we can safely update our props' positions without fearing
// that doing so will cause a revalidation of this model (see recursion above).
m_PositionValid = true;
// re-position and validate all props
for (size_t j = 0; j < m_Props.size(); ++j)
{
const Prop& prop=m_Props[j];
CMatrix3D proptransform = prop.m_Point->m_Transform;
if (prop.m_Point->m_BoneIndex != 0xff)
{
CMatrix3D boneMatrix = m_BoneMatrices[prop.m_Point->m_BoneIndex];
if (!worldSpaceBoneMatrices)
boneMatrix.Concatenate(GetTransform());
proptransform.Concatenate(boneMatrix);
}
else
{
// not relative to any bone; just apply world-space transformation (i.e. relative to object-space origin)
proptransform.Concatenate(m_Transform);
}
// Adjust prop height to terrain level when needed
if (prop.m_MaxHeight != 0.f || prop.m_MinHeight != 0.f)
{
CVector3D propTranslation = proptransform.GetTranslation();
CVector3D objTranslation = m_Transform.GetTranslation();
CmpPtr<ICmpTerrain> cmpTerrain(m_Simulation, SYSTEM_ENTITY);
if (cmpTerrain)
{
float objTerrain = cmpTerrain->GetExactGroundLevel(objTranslation.X, objTranslation.Z);
float propTerrain = cmpTerrain->GetExactGroundLevel(propTranslation.X, propTranslation.Z);
float translateHeight = std::min(prop.m_MaxHeight,
std::max(prop.m_MinHeight, propTerrain - objTerrain));
CMatrix3D translate = CMatrix3D();
translate.SetTranslation(0.f, translateHeight, 0.f);
proptransform.Concatenate(translate);
}
}
prop.m_Model->SetTransform(proptransform);
prop.m_Model->ValidatePosition();
}
if (m_BoneMatrices)
{
for (size_t i = 0; i < m_pModelDef->GetNumBones(); i++)
{
m_BoneMatrices[i] = m_BoneMatrices[i] * m_pModelDef->GetInverseBindBoneMatrices()[i];
}
// Note: there is a special case of joint influence, in which the vertex
// is influenced by the bind-shape transform instead of a particular bone,
// which we indicate with the blending bone ID set to the total number
// of bones. But since we're skinning in world space, we use the model's
// world space transform and store that matrix in this special index.
// (see http://trac.wildfiregames.com/ticket/1012)
m_BoneMatrices[m_pModelDef->GetNumBones()] = m_Transform;
if (computeBlendMatrices)
m_pModelDef->BlendBoneMatrices(m_BoneMatrices);
}
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// SetAnimation: set the given animation as the current animation on this model;
// return false on error, else true
bool CModel::SetAnimation(CSkeletonAnim* anim, bool once)
{
m_Anim = NULL; // in case something fails
if (anim)
{
m_Flags &= ~MODELFLAG_NOLOOPANIMATION;
if (once)
m_Flags |= MODELFLAG_NOLOOPANIMATION;
if (!m_BoneMatrices && anim->m_AnimDef)
{
// not boned, can't animate
return false;
}
if (m_BoneMatrices && !anim->m_AnimDef)
{
// boned, but animation isn't valid
// (e.g. the default (static) idle animation on an animated unit)
return false;
}
if (anim->m_AnimDef && anim->m_AnimDef->GetNumKeys() != m_pModelDef->GetNumBones())
{
// mismatch between model's skeleton and animation's skeleton
LOGERROR("Mismatch between model's skeleton and animation's skeleton (%lu model bones != %lu animation keys)",
(unsigned long)m_pModelDef->GetNumBones(), (unsigned long)anim->m_AnimDef->GetNumKeys());
return false;
}
// reset the cached bounds when the animation is changed
m_ObjectBounds.SetEmpty();
InvalidateBounds();
// start anim from beginning
m_AnimTime = 0;
}
m_Anim = anim;
return true;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// CopyAnimation
void CModel::CopyAnimationFrom(CModel* source)
{
m_Anim = source->m_Anim;
m_AnimTime = source->m_AnimTime;
m_Flags &= ~MODELFLAG_CASTSHADOWS;
if (source->m_Flags & MODELFLAG_CASTSHADOWS)
m_Flags |= MODELFLAG_CASTSHADOWS;
m_ObjectBounds.SetEmpty();
InvalidateBounds();
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// AddProp: add a prop to the model on the given point
void CModel::AddProp(const SPropPoint* point, CModelAbstract* model, CObjectEntry* objectentry, float minHeight, float maxHeight, bool selectable)
{
// position model according to prop point position
// this next call will invalidate the bounds of "model", which will in turn also invalidate the selection box
model->SetTransform(point->m_Transform);
model->m_Parent = this;
Prop prop;
prop.m_Point = point;
prop.m_Model = model;
prop.m_ObjectEntry = objectentry;
prop.m_MinHeight = minHeight;
prop.m_MaxHeight = maxHeight;
prop.m_Selectable = selectable;
m_Props.push_back(prop);
}
void CModel::AddAmmoProp(const SPropPoint* point, CModelAbstract* model, CObjectEntry* objectentry)
{
AddProp(point, model, objectentry);
m_AmmoPropPoint = point;
m_AmmoLoadedProp = m_Props.size() - 1;
m_Props[m_AmmoLoadedProp].m_Hidden = true;
// we only need to invalidate the selection box here if it is based on props and their visibilities
if (!m_CustomSelectionShape)
m_SelectionBoxValid = false;
}
void CModel::ShowAmmoProp()
{
if (m_AmmoPropPoint == NULL)
return;
// Show the ammo prop, hide all others on the same prop point
for (size_t i = 0; i < m_Props.size(); ++i)
if (m_Props[i].m_Point == m_AmmoPropPoint)
m_Props[i].m_Hidden = (i != m_AmmoLoadedProp);
// we only need to invalidate the selection box here if it is based on props and their visibilities
if (!m_CustomSelectionShape)
m_SelectionBoxValid = false;
}
void CModel::HideAmmoProp()
{
if (m_AmmoPropPoint == NULL)
return;
// Hide the ammo prop, show all others on the same prop point
for (size_t i = 0; i < m_Props.size(); ++i)
if (m_Props[i].m_Point == m_AmmoPropPoint)
m_Props[i].m_Hidden = (i == m_AmmoLoadedProp);
// we only need to invalidate here if the selection box is based on props and their visibilities
if (!m_CustomSelectionShape)
m_SelectionBoxValid = false;
}
CModelAbstract* CModel::FindFirstAmmoProp()
{
if (m_AmmoPropPoint)
return m_Props[m_AmmoLoadedProp].m_Model;
for (size_t i = 0; i < m_Props.size(); ++i)
{
CModel* propModel = m_Props[i].m_Model->ToCModel();
if (propModel)
{
CModelAbstract* model = propModel->FindFirstAmmoProp();
if (model)
return model;
}
}
return NULL;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Clone: return a clone of this model
CModelAbstract* CModel::Clone() const
{
CModel* clone = new CModel(m_SkeletonAnimManager, m_Simulation);
clone->m_ObjectBounds = m_ObjectBounds;
clone->InitModel(m_pModelDef);
clone->SetMaterial(m_Material);
clone->SetAnimation(m_Anim);
clone->SetFlags(m_Flags);
for (size_t i = 0; i < m_Props.size(); i++)
{
// eek! TODO, RC - need to investigate shallow clone here
if (m_AmmoPropPoint && i == m_AmmoLoadedProp)
clone->AddAmmoProp(m_Props[i].m_Point, m_Props[i].m_Model->Clone(), m_Props[i].m_ObjectEntry);
else
clone->AddProp(m_Props[i].m_Point, m_Props[i].m_Model->Clone(), m_Props[i].m_ObjectEntry, m_Props[i].m_MinHeight, m_Props[i].m_MaxHeight, m_Props[i].m_Selectable);
}
return clone;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// SetTransform: set the transform on this object, and reorientate props accordingly
void CModel::SetTransform(const CMatrix3D& transform)
{
// call base class to set transform on this object
CRenderableObject::SetTransform(transform);
InvalidatePosition();
}
//////////////////////////////////////////////////////////////////////////
void CModel::AddFlagsRec(int flags)
{
m_Flags |= flags;
if (flags & MODELFLAG_IGNORE_LOS)
{
m_Material.AddShaderDefine(str_IGNORE_LOS, str_1);
m_Material.RecomputeCombinedShaderDefines();
}
for (size_t i = 0; i < m_Props.size(); ++i)
if (m_Props[i].m_Model->ToCModel())
m_Props[i].m_Model->ToCModel()->AddFlagsRec(flags);
}
void CModel::RemoveShadowsRec()
{
m_Flags &= ~MODELFLAG_CASTSHADOWS;
m_Material.AddShaderDefine(str_DISABLE_RECEIVE_SHADOWS, str_1);
m_Material.RecomputeCombinedShaderDefines();
for (size_t i = 0; i < m_Props.size(); ++i)
{
if (m_Props[i].m_Model->ToCModel())
m_Props[i].m_Model->ToCModel()->RemoveShadowsRec();
else if (m_Props[i].m_Model->ToCModelDecal())
m_Props[i].m_Model->ToCModelDecal()->RemoveShadows();
}
}
void CModel::SetMaterial(const CMaterial &material)
{
m_Material = material;
}
void CModel::SetPlayerID(player_id_t id)
{
CModelAbstract::SetPlayerID(id);
for (std::vector<Prop>::iterator it = m_Props.begin(); it != m_Props.end(); ++it)
it->m_Model->SetPlayerID(id);
}
void CModel::SetShadingColor(const CColor& color)
{
CModelAbstract::SetShadingColor(color);
for (std::vector<Prop>::iterator it = m_Props.begin(); it != m_Props.end(); ++it)
it->m_Model->SetShadingColor(color);
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,237
|
\section{Introduction}
Topological defects appear everywhere in physics. Ranging from gravitation and cosmology to Bose-Einstein condensates they are associated to symmetry-breaking phase transitions. In particular, they appear in the isotropic-to-nematic phase transition of calamitic liquid crystals in the form of hedgehogs, disclinations, domain walls or more complicated textures \cite{kleman,repnik}. The deflection of light rays by these defects is an old issue. Grandjean \cite{grand}, already in 1919, calculated the light paths of extraordinary rays passing by disclination lines \cite{prob}. More recently, Joets and Ribotta \cite{joets} used a geometrical model to describe the light propagation in anisotropic and inhomogeneous media like liquid crystals. Inspired by their work we studied the propagation of light near disclination lines in nematics from a geometric point of view \cite{caio1,caio2,caio3}. In particular, in \cite{caio1} we observed lensing effects due the deflection of the beams in regions near the defect. There, we calculated the light trajectories from a geometry resulting from the application of Fermat's principle\footnote{Kline and Kay \cite{kline} were probably the first to prove that light rays in inhomogeneous anisotropic media are extremals of Fermat's functional.} associated to an effective refractive index $N$ \cite{born} given in terms of $n_o$ and $n_e$, the ordinary and extraordinary refractive index, respectively. In a few words, what we did was to consider the bent light rays as geodesics of a model space of unknown geometry. By identifying Fermat's principle with the geodesic variational principle we were able to find the effective geometries for each defect studied. Knowing the effective geometry, the geodesics were obtained numerically. Incidentally, a geometric model describing elastic properties of nematic liquid crystals which also leads to an effective geometry, appeared recently in the literature \cite{sim}.
Since the refractive indices of a nematic depend both on the temperature and on the wavelenght of the light, a more realistic model incorporating these effects is in order. Li, Gauza and Wu \cite{jun1} modeled the temperature effect on the nematic refractive index based on Vuks equation \cite{vuks} and, by fitting their final expression to experimental data of selected materials, found the unknown coefficients.The same group derived Cauchy formulae (see page 100 of \cite{born}) for the refractive indices of a nematic sample as a function of the wavelenth of the light \cite{jun2}. Again, by fitting their final expression to experimental data, all coeficients were determined. In this work, we incorporate their models to our geometric model for propagation of light in nematics with topological defects, in order to study temperature and wavelength effects. Although in \cite{caio1} we studied both the symmetric ($k=1$) and asymmetric ($k\neq 1$) defects, without loss of generality, we keep our analysis here mostly for the symmetric cases since their effective geometry is simpler and more intuitive than the asymmetric cases. Since, in all cases, the effective geometry depends only on the ratio $\alpha=n_e/n_o$ it is how the temperature and the wavelength affect this ratio what matters. In section II we review the geometric model and discuss the simplest effective geometry for light traveling by a disclination. In section III we use the results of \cite{jun1} and \cite{jun2} to show how $\alpha$ is affected by temperature and wavelength and study the effect of the variation of this ratio on the light paths near selected defects.
\section{Geometric Model}
Disclinations in nematics are classified according to the topological index (or strength) $k$ which gives a measure of how much the director rotates as one goes around the defect. That is, the director configurations, in the plane $x-y$, are given by \cite{kleman}
\begin{equation}
\varphi(\theta)=k\theta+c , \label{phi}
\end{equation}
where $\varphi$ is the angle between the molecular axis and the $x$-axis, $\theta$ is the angular polar coordinate and $c=\varphi(0)$. Selected director configurations can be seen on Figure 11.4 of \cite{kleman}. We assume the disclinations are straight and lie along the $z$-axis and the light rays propagate in the $x$-$y$ plane so, effectively, we have a two-dimensional problem.
We consider an optical medium constituted by a nematic liquid crystal with disclinations \cite{repnik}, where the effective geometry for the light is defined by the line element (equation (25) of \cite{caio1})
{\small
\begin{eqnarray}
& ds^2 & = \left\{n_o^2 \cos^{2}[(k-1)\phi+c]+n_e^2 \sin^{2}[(k-1)\phi+c]\right\}dr^{2} \nonumber\\
& + & \left\{n_o^2 \sin^{2}[(k-1)\phi+c]+n_e^2 \cos^{2}[(k-1)\phi+c]\right\}r^{2}d\phi^{2} \nonumber\\
& - & \left\{2(n_e^2-n_o^2)^{2}\sin[(k-1)\phi+c]\cos[(k-1)\phi+c]\right\}rdrd\phi. \nonumber\\
& & \label{kmetric}
\end{eqnarray}}
The metric (\ref{kmetric}) was obtained by identifying Fermat's principle with the variational principle that determines the geodesics in Riemannian geometry. Let
\begin{equation}
{\cal F}=\int_{A}^{B} N d \ell , \label{fermat}
\end{equation}
where, $d\ell$ is the element of arc length along the path between points $A$ and $B$ and the effective refractive index
\begin{equation}
N^2=n_o^2\cos^2\beta +n_e^2\sin^2\beta , \label{nr}
\end{equation}
where $\beta = (\widehat{\vec{n},\vec{S}})$ is the local angle between the director $\vec{n}$ and the Poynting vector $\vec{S}$. Then, among all possible paths between the generic points $A$ and $B$, Fermat's principle for the extraordinary rays grants us that the path actually followed by the energy is the one that minimizes ${\cal F}$.
In Riemannian geometry the line element $ds$ depends on the position coordinates $x^i$ of the point of the manifold under consideration. That is,
\begin{equation}
ds^2 = \sum_{i,j}g_{ij}dx^idx^j, \label{riemline}
\end{equation}
where $g_{ij}=g_{ij}(x^i)$ is the metric tensor. The geodesic joinning points $A$ and $B$ in such manifold is obtained by minimizing $\int_A^B ds$, just like Fermat's principle. This leads to a nice interpretation of the light paths as geodesics in an effective geometry \cite{born}. Thus, we may identify
\begin{equation}
N^{2}d\ell^2 = \sum_{i,j}g_{ij}dx^idx^j. \label{interp}
\end{equation}
The meaning of this equation is the following: the line element of the optical path, in an Euclidean space with refractive properties, is identified with the line element of an effective geometry characterized by $g_{ij}$.
In \cite{caio2} we showed that the effective geometry for the vortex-like $k=1$, $c=\frac{\pi}{2}$ disclination is that of a cone. The effective metric for this case is obtained by substituting these values in metric (\ref{kmetric}) and rescaling the coordinate $r$ to $\rho=n_e r$. That is, the two-dimensional line element for this effective geometry, in polar coordinates, is \cite{caio1}
\begin{equation}
ds^2 = d\rho^{2} + \alpha^2 \rho^{2}d\theta^{2}, \label{metr1}
\end{equation}
where $\alpha=n_o/n_e$ is the ratio between the refractive indices. The geodesic equation in a Riemannian space like the cone is \cite{man}
\begin{equation}
\frac{d^{2}x^i}{dt^2}+\sum_{j,k}\Gamma^{i}_{jk}\frac{dx^j}{dt}\frac{dx^k}{dt}=0,\label{georie}
\end{equation}
where $t$ is a parameter along the geodesic and $\Gamma^{i}_{jk}$ are the Christoffel symbols, given by
\begin{equation}
\Gamma^{i}_{jk}=\frac{1}{2}\sum_{m}g^{mi}\left\{ \frac{\partial g_{km}}{\partial x^j}+\frac{\partial g_{mj}}{\partial x^k}-\frac{\partial g_{jk}}{\partial x^m}\right\} . \label{chris}
\end{equation}
For metric (\ref{metr1}) equation (\ref{georie}) reduces to the coupled system of ordinary differential eaquations
\begin{equation}
\frac{d^2\rho}{dt^2}-\alpha^2\rho\left(\frac{d\theta}{dt}\right)^2=0 \label{eq1}
\end{equation}
and
\begin{equation}
\frac{d^2\theta}{dt^2}+\frac{2}{\rho}\frac{d\rho}{dt}\frac{d\theta}{dt}=0. \label{eq2}
\end{equation}
The solution to the coupled system (\ref{eq1}) and (\ref{eq2}) is easily obtained \cite{padua}:
\begin{equation}
\rho(t)=\sqrt{\frac{C^2}{E\alpha^2}+2E(t+D)^2}, \label{r(t)}
\end{equation}
\begin{equation}
\theta(t)=\frac{1}{\alpha}\arctan\left(\frac{2E\alpha(t+D)}{c}\right)+\frac{F}{\alpha}, \label{theta(t)}
\end{equation}
where $C$, $D$, $E$ and $F$ are integration constants.
In figure 1 we show the light paths in the nematic medium with the $k=1$, $c=\frac{\pi}{2}$ disclination as given by (\ref{r(t)}) and (\ref{theta(t)}). In figure 2 the geodesics on a cone are shown for comparison.
\begin{figure}[!h]
\begin{center}
\includegraphics[height=5cm]{1.eps}
\caption{Light trajectories in a nematic liquid crystal with a topological defect given by a disclination $k=1$ and $c=\pi/2$.}
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
\includegraphics[height=5cm]{geocone.eps}
\caption{Geodesics on the cone.}
\end{center}
\end{figure}
Metric (\ref{metr1}) describes a cone. Fig. 3 shows the making of a cone from a planar sheet where an angular section was removed with posterior identification of the edges. If $\gamma$ is the angle that defines the removed section then the remaining surface corresponds to an angular sector of $2\pi\alpha=2\pi-\gamma$. This is exactly what metric (\ref{metr1}) describes. The incorporation of the term $\alpha^2$ to the Euclidean metric in polar coordinates makes the total angle on the surface be $\int_{0}^{2\pi} \alpha d\theta=2\pi\alpha <2\pi$, since $n_o<n_e$. It is clear then that $\alpha$ tells how ``pointed'' is the cone. The closer $\alpha$ gets to 1 the flatter is the cone. For $\alpha=1$ the cone turns into a plane.
\begin{figure}[!h]
\begin{center}
\includegraphics[height=1.5cm]{conec2.eps}
\caption{Conical surface of angular deficit $\gamma$.}
\end{center}
\end{figure}
The solutions (\ref{r(t)}) and (\ref{theta(t)}) still hold for the radial defect with $k=1$ and $c=0$ since, in this case, the line element (\ref{kmetric}) reduces to
\begin{equation}
ds^2 = d\rho^{2} + \frac{1}{\alpha^2} \rho^{2}d\theta^{2}, \label{metr2}
\end{equation}
where, $\alpha=n_o/n_e$ still. Consequently, equations (\ref{r(t)}) and (\ref{theta(t)}) become
\begin{equation}
\rho(t)=\sqrt{\frac{C^2 \alpha^2}{E}+2E(t+D)^2}, \label{r(t)2}
\end{equation}
\begin{equation}
\theta(t)=\alpha\arctan\left(\frac{2E(t+D)}{c\alpha}\right)+F\alpha, \label{theta(t)2}
\end{equation}
where, as before, $C$, $D$, $E$ and $F$ are integration constants.
\section{Refractive index variation}
The refractive indices $n_o$ and $n_e$ of a nematic liquid crystal depend both on the temperature ($T$) and on the wavelenth ($\lambda$) of the light. In this section, based in \cite{jun1} and \cite{jun2}, we analyse how these parameters affect the ratio $\alpha=n_o/n_e$, which characterizes the effective geometry associated to disclinations. By changing either $T$ or
$\lambda$, $\alpha$ is changed and so is the effective geometry. This causes a deformation of the geodesics associated to the light rays in our model.
In \cite{jun1} we can find expressions to the ordinary and extraordinary refractive index given in terms of the birefringence $\Delta n$ and of its average value $\left\langle n\right\rangle$, such that
\begin{equation}
n_o=\left\langle n\right\rangle-\frac{1}{3}\Delta n,\label{a1}
\end{equation}
\begin{equation}
n_e=\left\langle n\right\rangle+\frac{2}{3}\Delta n.\label{a2}
\end{equation}
In $(\ref{a1})$ and $(\ref{a2})$ the behavior of $\left\langle n\right\rangle$ as function of the temperature \cite{jun1} is given through a linear dependence given by
\begin{equation}
\left\langle n\right\rangle=A-BT,\label{med}
\end{equation}
where the parameters $A$ and $B$ are obtained experimentally.
The birefringence can be written in terms of the approximated \cite{haller} order parameter $S=\left(1-\frac{T}{T_c}\right)^{\beta}$ as
\begin{equation}
\Delta n=(\Delta n)_0\left(1-\frac{T}{T_c}\right)^{\beta},\label{birre}
\end{equation}
where $(\Delta n)_0$ is the birefringence at $T=0\,K$, $\beta$ is a constant associated to the material and $T_c$ is the isotropic-nematic transition temperature.
Therefore, substituting the equations $(\ref{med})$ and $(\ref{birre})$ into $(\ref{a1})$ and $(\ref{a2})$, we have
\begin{equation}
n_o=A-BT-\frac{(\Delta n)_0}{3}\left(1-\frac{T}{T_c}\right)^{\beta},\label{ind1}
\end{equation}
\begin{equation}
n_e=A-BT+\frac{2(\Delta n)_0}{3}\left(1-\frac{T}{T_c}\right)^{\beta}.\label{ind2}
\end{equation}
The liquid crystal considered was the 5CB or 4-cyano-4-n-pentylbiphenyl and the wavelength of the incident beam was $589$nm \cite{jun1}. For this material the parameters are given in the table below obtained from \cite{jun1}. The parameters A, $\beta$ and $(\Delta n)_0$ are adimensional.
\begin{center}
\begin{tabular}{|c|c|c|c|c|} \hline
A & B & $\beta$ &$(\Delta n)_0$ &$T_c$\\ \hline
1.7546 & 0.0005360 K$^{-1}$ & 0.2391 & 0.3768 &306.6 K\\ \hline
\end{tabular}
\end{center}
In figure 4 we show the ratio $\alpha=n_o/n_e$ as a function of the temperature as obtained from equations (\ref{ind1}) and (\ref{ind2}). As shown in \cite{caio2} these parameters are associated to the effective geometry perceived by the light traveling in the vicinity of $k=1$ disclinations. For these defects the geometry is conical with the radial disclination ($k=1$, $c=0$) behaving as a negative curvature cone and the vortex-like disclination ($k=1$, $c=\pi/2$) like the ordinary cone. The value $\alpha=1$, reached at $T_c$ corresponds to the Euclidean geometry which describes the isotropic phase.
\begin{figure}[h]
\begin{center}
\includegraphics[height=7cm]{alphatemp2.eps}
\caption{Effective geometry parameter $\alpha$ as function of the temperature for 5CB in the nematic phase at 589 nm.}
\end{center}
\end{figure}
Next, we consider the wavelength dependence of the effective geometry at a fixed temperature. Li and Wu \cite{jun2} modeled the ordinary and extraorinary refractive indices wavelength dependence based on the extended Cauchy formulae. Their model is described by the following equations:
\begin{equation}
n_e=A_e-\frac{B_e}{\lambda^2}+\frac{C_e}{\lambda^4},\label{lambda1}
\end{equation}
\begin{equation}
n_o=A_o-\frac{B_o}{\lambda^2}+\frac{C_o}{\lambda^4}.\label{lambda2}
\end{equation}
The coefficients appearing in equations (\ref{lambda1}) and (\ref{lambda2}) were obtained \cite{jun2} by fitting experimental data. For 5CB at 25.1 $^o$C they are given in the tables below.
\begin{center}
\begin{tabular}{|c|c|c|} \hline
$A_e$ & $B_e$ & $C_e$ \\ \hline
1.6795 & 0.0048 $\mu m^2$& 0.0027 $\mu m^4$\\ \hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{|c|c|c|} \hline
$A_o$ & $B_o$ & $C_o$\\ \hline
1.5174 & 0.0022 $\mu m^2$ & 0.0011 $\mu m^4$\\ \hline
\end{tabular}
\end{center}
In figure 5 we show the ratio $\alpha=n_o/n_e$ as a function of the wavelength as obtained from equations (\ref{lambda1}) and (\ref{lambda2}).
\begin{figure}[!h]
\begin{center}
\includegraphics[height=7cm]{alphacomp2.eps}
\caption{Effective geometry parameter $\alpha$ as function of the wavelength for 5CB in the nematic phase at 25.1 $^o$C.}
\end{center}
\end{figure}
Since both temperature and wavelength cause $\alpha$ to change we can summarize their effect on the light paths by studying the geodesics for different values of $\alpha$. Substituting the metric (\ref{kmetric}) in (\ref{chris}) and this one in (\ref{georie}) we can calculate the geodesics for different values of $\alpha$. As described in Section II, the geodesic equations (\ref{georie}) have exact solutions for the $k=1$ case. The remaining cases can be solved by a numerical method. In figures 6 and 7 we show the effects of the variation of the parameter $\alpha$ on the light paths near the $k=1$ defects, using the exact solution of Section II. In figure 8 we show the same effects for the $k=-1$ disclination, using the Runge-Kutta numerical method to solve the geodesic equation. In all cases, the solid line corresponds to $\alpha$=0,8912, the dotted line to $\alpha$=0,9120 and the dash-dotted line to $\alpha$=0,9355. These values, for 5CB, probed by a 589 nm light beam, correspond to the temperatures of 290 K, 300 K and 305 K, respectively. Notice that as $\alpha$ approaches 1 the light paths straighten out, as it should.
\begin{figure}[!h]
\begin{center}
\includegraphics[height=5cm]{div.eps}
\caption{Influence of the parameter $\alpha$ on the light trajectories in a nematic liquid crystal with a disclination $k=1$ and $c=0$.}
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
\includegraphics[height=5cm]{vort.eps}
\caption{Influence of the parameter $\alpha$ on the light trajectories in a nematic liquid crystal with a disclination $k=1$ and $c=\pi/2$.}
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
\includegraphics[height=5cm]{assim.eps}
\caption{Influence of the parameter $\alpha$ in the light trajectories in a nematic liquid crystal with a disclination $k=-1$ and $c=\pi/2$.}
\end{center}
\end{figure}
\newpage
\section{Conclusion}
Topological defects in nematics cause light passing by to deflect, as shown in \cite{caio1}. In that article, we associated the light paths to geodesics in a curved space specified by the defect. The deflection is due to the particular orientation of the director field associated to the defect, which may be translated into curvature. The intensity of the deflection depends on the ratio $\alpha$ between the ordinary and extraordinary refractive indices, which, in turn, depend on the temperature of the liquid crystal and on the wavelength of the light. Taking as example 5CB, which has been extensively characterized with respect to temperature and wavelength dependence of the refractive indices \cite{jun1,jun2}, we solved the geodesic equations for a realistic range of values of $\alpha$ corresponding to temperature and/or wavelength variation. The graphical result illustrates the influence of these parameters on the light deflection caused by the defect. The further $\alpha$ gets from 1 the strong is the deflection. This can be achieved by either lowering the temperature or shortening the wavelength. In conclusion, the study of the influence of measurable physical parameters, like temperature and wavelength, helps us to understand better the behavior of light propagation in liquid crystals where topological defects are relevant.
\begin{acknowledgement}
This work has been supported by CNPq, CNPq/FACEPE, PRONEX/FAPESQ-PB and CAPES/PROCAD. We are indebted to Eduardo R. da Costa for helping with the graphs.
\end{acknowledgement}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,113
|
\section{Introduction}
\emph{Bilateral trade} is a fundamental economic scenario comprising a buyer and a seller.
The seller holds one item, and can possibly trade this item with the buyer for some price.
The buyer and the seller each have a (non-negative real-valued) valuation for the item that is up for trade.
The buyer's valuation is only known by the buyer and the seller's valuation is only known by the seller. The buyer and seller both want to maximise their utility, which is assumed to be \emph{quasi-linear}, i.e., of the form $x \cdot v - p$, where $x$ is a $0/1$-variable that is set to $1$ if and only if the agent holds the item, $v$ is the agent's value for the item, and $p$ is the price paid/received by the agent. In the buyer's case $p$ is non-negative and represents how much the buyer has to pay. In the seller's case, the price $p$ is non-positive because the seller receives money to transfer her item.
The main problem studied for this bilateral trade setting is one in mechanism design: which mechanism maximises the \emph{social welfare} (i.e., total utility of both players)? A direct revelation mechanism for this setting solicits the valuations of the buyer and the seller. Subsequently it determines whether the buyer and the seller should trade and which prices they have to pay or receive. We would like any mechanism to satisfy the following properties:
\begin{itemize}
\item Dominant strategy incentive compatibility (DSIC): It should be a dominant strategy for the buyer and seller to submit their true valuations to the mechanism.
\item Ex-post individual rationality (ex-post IR): Neither agent should end up with a negative utility if the agent's true valuation is submitted to the mechanism.
\item Strong budget balance (SBB): The price paid by the buyer is equal to the price received by the seller, i.e., the mechanism does not extract money from the market, nor does it inject money into the market.
\end{itemize}
While the valuations of the buyer and seller are known by the buyer and seller only, it is assumed that there is still distributional public knowledge about their valuations. More precisely, it is assumed that there are two publicly known distributions from which the buyer and seller independently draw their valuations. The mechanism may thus make use of these distributions in order to determine the outcome.
Ideally, we would want the mechanism to have the seller trade with the buyer whenever the buyer's valuation exceeds the seller's valuation. The expected total utility that would result from trading as such is referred to as the \emph{optimal} social welfare. Unfortunately the optimal social welfare is not achievable, as shown by Myerson and Satterthwaite~\cite{myersonsatterthwaite}: No bilateral trade mechanism is simultaneously DSIC, IR, {\em weakly} budged balanced, and social-welfare optimizing. Weak budget balance (WBB) is less restrictive than strong budget balance, as WBB only requires that no money be injected into the market, while the mechanism is allowed to extract money from the market.
For the classic bilateral trade setting, it was recently shown \cite{doubleauctions} that the only direct revelation mechanisms that are simultaneously incentive compatible, strongly budget balanced, and ex-post individually rational, are \emph{fixed price} mechanisms, i.e., mechanisms that are parametrised by a price $p$, and trade occurs if and only if the valuation of the buyer is at least $p$ and the valuation of the seller is at most $p$.
An alternative ---and more challenging to approximate--- objective to the social welfare is the \emph{gain from trade}, which measures the expected increase in total utility that is achievable by applying the mechanism, with respect to the initial allocation.
For example, if a seller holds an item that she values $\$4$ and a buyer values the same item $\$10$, whenever a fix price mechanism sets a price $4 \leq p \leq 10$, the buyer and the seller trade producing a gain from trade of $\$6$. Whenever the price $p$ is set lower than $\$4$ or greater than $\$10$ no trade occur, and the gain from trade is $0$.
McAfee~\cite{mcafee} has shown that if the median of the distribution of the seller's valuation is less than the median of the distribution of the buyer's valuation, then there is a fixed price mechanism for which the expected gain from trade is at least half of the optimal gain from trade. In fact, it was shown for this special case that by setting the fixed price anywhere in between the two medians, half of the optimal gain from trade is guaranteed. We extend this result by showing that the optimal gain from trade is at least $2/r$ times the gain from trade achievable by a fixed price mechanism, where $r$ is the probability that the seller's valuation does not exceed the buyer's valuation (which is the condition under which a gain from trade is possible in the first place).
Subsequently, we improve this approximation factor in an asymptotic sense, by showing that a more sophisticated rule for setting the fixed price results in an expected gain from trade within a factor $O(\log(1/r))$ of the optimal gain from trade. This is asymptotically the best approximation factor possible, which is shown by an appropriate example of a bilateral trade setting for which every fixed price achieves an expected gain from trade of $\Omega(\log(1/r))$ times the expected gain from trade.
It follows from our results that our mechanisms cannot approximate the gain from trade if the probability of trading is small. Indeed, we prove a general negative result showing that the ratio between the gain from trade of a DSIC mechanism and the optimal gain from trade can be arbitrarily small as the support of the distribution grows. A similar result has been proved independently in \cite{BD16}.
We finally extend our study to the \emph{double auction} setting, where there are multiple buyers and sellers, each seller holding one item and each buyer having a demand for obtaining at most one item. The valuations of the $n$ buyers are independently drawn from a common probability distribution, and the same holds for the $m$ sellers, although the probability distribution of the sellers may be distinct from that of the buyers.
\subsection{Our Results}
The first results presented in this paper concern the bilateral trade problem. It is known that if a mechanism has to satisfy IR, DSIC, and SBB, then it must be a fixed price mechanism \cite{doubleauctions}, i.e., the mechanism fixes a price $p$ and posts it to the buyer and the seller. We want to understand how this price $p$ has to be chosen.
McAfee's result of \cite{mcafee} states that in case the seller's median is less than the buyer's median, then setting the price in between the medians of the buyer and the seller results in a $2$-approximation to the optimal gain from trade.
Our first result is a strict generalization of \cite{mcafee} where the approximation to the optimal gain from trade is given as a function of the probability that a trade is efficient, in other words: the probability that the valuation drawn from the buyer is greater than the valuation drawn from the seller. This parameter is referred to as $r = \mathbf{Pr}_{v \sim f, w \sim g}[v \geq w]$, where $f$ is the buyer's distribution and $g$ is the seller's distribution.
In particular, we show that setting the price $p$ such that $\mathbf{Pr}_{v \sim f}[v \geq p] = \mathbf{Pr}_{w \sim g}[w \leq p]$ results in a $r/2$-approximation to the optimal gain from trade.
Then, we show how that it is possible to improve the approximation factor of $2/r$ considerably in an asymptotic sense: We prove that by using a more complex rule for determining the fixed price $p$, the optimal gain from trade is at most a factor of $O(\log(1/r))$ times the gain from trade when trading at price $p$. When $r$ is small, this results in a big improvement when compared to the approximation factor that we established in the previous section.
Our mechanism works by showing that we can decompose ``roughly'' the entire probability space into at most $\log(1/r) + 1$ such events, so that choosing the best fixed price corresponding to each of these events results in a gain from trade that is an $O(\log(1/r))$-approximation to the optimal gain from trade.
Finally, we want to consider the double auction setting. In this setting, we extend the definition of a fixed price mechanism in a natural way: the mechanism computes a single price $p$, buyers with a valuation greater than $p$ and sellers with a valuation lower than $p$ will be allowed to trade. If the sets of allowed buyers and allowed sellers have different cardinalities, agents will be removed from the biggest set uniformly at random so that the cardinality of the two sets will be equal
The fixed price mechanism that we propose for the double auction setting achieves a gain from trade that is a $1-\epsilon$ approximation to the optimal gain from trade with probability $(1 - 1/e^{\epsilon^2\#T/2})$ where $\#T$ is the expected number of trades of the mechanism. This implies that if the double auction instance is such that a relatively small expected number of trades can happen at this price, then a reasonably good approximation factor is achieved by our mechanism (see Section \ref{sec:double-auctions} for a detailed discussion). One may also interpret our result as a ``large market'' result: the approximation factor approaches $1$ as we let the number of buyers and sellers in the market grow proportionally, since in that case the number of trades grows arbitrarily large. This is, to the best of our knowledge, the first fixed price mechanism that is DSIC, SBB, and ex-post IR, and achieves a near-optimal gain from trade under mild conditions on the size of the market.
\subsection{Related Literature}
The impossibility result of \cite{myersonsatterthwaite} proved that no two-sided mechanism can be simultaneously BIC, IR, WBB, and optimise the social welfare even in the simple bilateral trade setting. Thus, many subsequent works studied how it is possible to relax some of the constraints to achieve positive results in the context of maximise the social welfare or the gain from trade.
In \cite{Blumrosen2016}, a BIC mechanism is devised that approximates the expected gain from trade in bilateral trade up to a
factor of $1/e$ when the buyer's distribution function satisfies a property known as the monotone hazard rate condition. The mechanism of \cite{Blumrosen2016} is not DSIC since it achieves this approximation factor from a Bayes-Nash equilibrium by using the valuation of the seller in the price offered to the buyer. It is also shown in the same work that no BIC mechanism can achieve an approximation bound better than $2/e$.
Mechanisms that are DSIC/BIC, IR, and SBB have been given for bilateral trade in \cite{bd14}. In addition to this, the authors proposed a WBB mechanism for a general class of markets known as combinatorial exchange markets.
Mechanisms for double auctions with near-optimal gain from trade have been previously proposed for the prior-free setting. McAfee~\cite{mcafee92} has shown a WBB, DSIC, IR mechanism which achieves a $1-1/k$-approximation to the optimal gain from trade if the number of trades under the optimum allocation is $k$. This rate of convergence requires the prior distributions of traders to be bounded above zero, over an interval $[0,1]$, but the mechanism is not a function of the priors. More recently, Segal-Halevi et al.~\cite{HHA16} devised a SBB mechanism with the same performance guarantee.
The mechanisms of \cite{mcafee92,HHA16} are direct revelation mechanisms where the price depends crucially on the reported valuations.
In contrast, the goal in our present paper is to find out how much gain from trade can be generated by means of setting a single fixed price, independent of the valuations of the players, at which all agents trade. Such mechanisms have the advantage that they are conceptually simpler and have a pricing scheme that is extremely easy to understand. They also can be implemented as posted price mechanisms where buyers and sellers merely have to indicate whether they would be willing to trade at the given price. Thus, they require a minimum amount of valuation revelation.
In \cite{DBLP:journals/corr/Segal-HaleviHA16}, the authors present a mechanism that combines random sampling and random serial dictatorship techniques which is IR, SBB and DSIC, and asymptotically approaches the optimum gain from trade. Recently, \cite{DBLP:conf/sigecom/BrustleCWZ17} provides an IR, SBB, and BIC mechanism that achieves a constant approximation to the best gain from trade achievable among the IR, WBB, and BIC mechanisms, which is an alternative (more permissive) benchmark. Two recent papers by Feldman and Gonen \cite{feld1,feld2} study a multi-unit variant of double auctions for online advertising purposes. They design in \cite{feld1} IR, WBB, and DSIC mechanisms that well-approximate the gain from trade under certain technical conditions, as a function of the number of trades under the optimum allocation. In \cite{feld2} they develop further mechanisms for an online variant of this setting, where additional sellers and buyers may enter the market over time.
Our paper contributes to a recent line of computational work on {\em market intermediation}, in which a mechanism is assumed to interact
with both buyers and sellers of some good, or goods. The objective is to maximise (or, approximately maximise) either revenue for the mechanism, or welfare of the buyers/sellers. Deng et al.~\cite{DGTZ14} study revenue maximisation, in a setting of multiple buyers and sellers, with uncorrelated priors and a single type of item being traded. The same objective was studied by \cite{dghk02} yet in the \emph{prior-free} model. Gerstgrasser et al.~\cite{GGK16} also study the objective of maximising expected revenue, in a setting where there is a small number of buyers and seller, who have a prior distribution whose support size represents the complexity of instances of the problem. In \cite{GGK16}, this distribution is otherwise unrestricted, and in particular may be correlated.
Giannakopoulos et al.~\cite{gkl17} study a similar double auction setting to the one studied here in Section~\ref{sec:double-auctions}: there are multiple buyers and sellers and one kind of item, with unit supply and demand. Buyers have a common prior distribution on their valuations, as do sellers. \cite{gkl17} study market intermediation from the perspective of welfare maximisation, and revenue maximisation. Colini-Baldeschi et al.~\cite{CGKLRT17} also study market intermediation, in the context of buyers and seller of a collection of heterogenous items, aiming to maximise welfare and achieve a strong notion of budget balance.
In the context of social welfare in the economics literature it is often studied a setting in which the valuation of the sellers and the buyers are independently drawn from identical regular distributions, while satisfying IR and WBB. And in this setting the goal is to find an approximation of the optimal social welfare as a function of the number of agents. \cite{gs89} showed that duplicating the number of agents by $\tau$ results in a market where the optimal IR, IC, WBB mechanism's expected social welfare approximation factor approaches $1$ at a rate of $O(\log{\tau} / \tau^2)$. \cite{rsw94} and \cite{sw02} investigated a family of non-IC double auctions, and study the inefficiency and the extent to which agents misreport their valuations in these double auctions.
\section{Preliminaries}\label{sec:prelims}
As a general convention, we use $[a]$ to denote the set $\{1, \ldots, a\}$. We will use $\mathbf{1}(X)$ to denote the indicator function that maps to $1$ if and only if event/fact $X$ holds.
\paragraph{Double Auction Setting.}
In a double auction setting there are $n$ buyers and $m$ sellers. Initially, each seller $j \in [m]$ holds one item and has a valuation $w_{j}$ for it. The sellers are not interested in possess more than one item.
Each buyer $i \in [n]$ is interested in obtaining no more than one item and has a valuation $v_{i}$ for it. Moreover, they are indifferent among the different items.
The valuations of the buyers and the sellers are private knowledge, but they are independently drawn from publicly known distributions $f$ and $g$, where $f$ is the probability distribution for the valuation of a buyer and $g$ is the probability distribution for the valuation of a seller.
We treat $f$ and $g$ as probability density functions. All the buyers share the same distribution $f$ and all the sellers share the same mass probability distribution $g$, but $f$ and $g$ may be distinct.
Moreover, let $G$ be the corresponding cumulative distribution functions of $g$ and let $\bar{F}$ be the corresponding complementary cumulative distribution function (or survival function) of $f$.
Given a double auction setting $(n, m, f, g)$, our goal is to redistribute the items from the sellers to the buyers. An \emph{allocation} for a double auction setting $(n, m, f, g)$ is a pair of vectors $(\bm{X},\bm{Y}) = ((X_1, \ldots, X_n),(Y_1,\ldots,Y_m))$ such that all the elements $X_1, \ldots, X_n, Y_1, \ldots, Y_m \in \{0, 1\}$, and $\sum_{i \in [n]} X_{i} + \sum_{j \in [m]} Y_{j} = m$. The set $\mathcal{A}$ represents the set of all allocations for the double auction setting.
The redistribution of the items from sellers to buyers is done by running a \emph{mechanism} $\mathbb{M}$.
A mechanism receives input from the agents, and outputs an allocation $(\bm{X},\bm{Y})$ and a price $p$.
The allocation $(\bm{X},\bm{Y})$ and the price $p$ represents the \emph{outcome} of the mechanism $\mathbb{M}$.
Thus, an outcome is a tuple $(\bm{X},\bm{Y}, p)$. The price $p$ represents how much a buyer has to pay to obtain an item and how much a seller has to receive to sell her item.\footnote{More generally, we may define the notion of a mechanism such that more complex pricing schemes are possible, but our definition suffices for the mechanisms that we will define later in this paper.}
Agents are assumed to be utility maximisers. The \emph{utility} is defined as the valuation for the items that they possess with respect to the allocation vector, minus the payment charged by the mechanism. Specifically, the utility of a buyer $i$ will be $u_{i}^B(\bm{X},\bm{Y}, p) = (v_{i} - p)\cdot X_{i}$. Similarly, the utility of a seller $j$ will be $u_{j}^S(\bm{X},\bm{Y}, p) = w_{j} Y_{j} + p \cdot (1-Y_j)$.
Furthermore, agents are assumed to be fully rational, so that they will strategically interact with the mechanism to achieve their goal of maximising utility. Our goal is to design a mechanism that is DSIC, IR, SBB (as defined in the introduction) such that the the \textit{gain from trade} is high. For an outcome $(\bm{X}, \bm{Y}, p)$, the gain from trade $\textrm{GFT}(\bm{X},\bm{Y}, p)$ is defined as
\begin{equation*}
\textrm{GFT}(\bm{X},\bm{Y}, p) = \sum_{i=1}^n v_i X_i + \sum_{j=1}^m w_j (Y_j - 1)
\end{equation*}
For a double auction setting $(n, m, f, g)$, the \textit{expected optimal gain from trade} is defined as
\begin{equation*}
\text{OPT}_{n,m,f,g} = \mathbf{E}_{v \sim f^n, w \sim g^m}\left[\max\left\{\sum_{i=1}^n v_i X_i + \sum_{i=1}^m w_j (Y_j - 1)\ \middle|\ (\bm{X}, \bm{Y}) \in \mathcal{A} \right\}\right].
\end{equation*}
We will sometimes omit the subscript, as in those cases the instance being discussed will be clear from context.
We say that a mechanism $\mathbb{M}$ \emph{$\alpha$-approximates the optimal gain from trade} for some $\alpha > 1$ if and only if $\text{OPT} \leq \alpha \mathbf{E}[\text{GFT}(\bm{X},\bm{Y}, p)]$, where $(\bm{X},\bm{Y},p)$ is the random allocation that the mechanism generates, when valuations $v$ and $w$ are drawn from $f^n$ and $g^m$ respectively. Our goal is to find a DSIC, ex-post IR, and SBB mechanism that $\alpha$-approximates the optimal gain from trade for a low $\alpha$.
\paragraph{Bilateral Trade Setting.}
The bilateral trade setting is a special case of the double auction setting where there is only one unit-demand buyer and one unit-supply seller. Thus, we can represent a bilateral trade setting as a pair of valuation distribution function, one for the buyer $f$ and one for the seller $g$, i.e., $(f,g)$.
It is known that if a mechanism has to satisfy IR, DSIC, and SBB, then it must be a fixed price mechanism \cite{doubleauctions}, i.e., the mechanism fixes a price $p$ a priori, and trade happens if and only if both the buyer's valuation is at least $p$ and the seller's valuation is at most $p$.
For a bilateral trade instance, the gain from trade of a fixed price mechanism with fixed price $p$ will be denoted by $\text{GFT}_{f,g}(p)$. That is,
\begin{equation*}
\text{GFT}_{f,g}(p) = \mathbf{E}_{v \sim f, w \sim g}[\max\{0,v-w\}\mathbf{1}(w \leq p \leq v)].
\end{equation*}
Moreover, note that for the bilateral trade setting we can express $\text{OPT}_{f,g}$ as $\mathbf{E}_{v \sim f, w\sim g}[\max\{0,v-w\}]$.
For the bilateral trade setting, the goal of this paper is to study how to set the price $p$ such that the gain from trade achieved by the fixed price mechanism with price $p$ is as close as possible to the optimal gain from trade.
We will design fixed price mechanisms where the ratio between $\text{OPT}_{f,g}$ and $\text{GFT}_{f,g}(p)$ is a function of the probability that the buyer has a value greater than the seller, i.e., the provability that a trade is efficient.
This probability will be represented by the parameter $r$. Thus,
\begin{equation*}
r = \mathbf{Pr}_{v \sim f, w \sim g}[v \geq w].
\end{equation*}
Due to space constraints, the proofs of various theorems and lemmas have been deferred to the appendix.
\section{An $O(1/r)$-Approximation Mechanism for Bilateral Trade}
In the bilateral trade setting there is only one unit-demand buyer and one unit-supply seller. It can be proven that if a mechanism has to satisfy IR, DSIC, and SBB, then it must be a fixed price mechanism \cite{doubleauctions}, i.e., the mechanism fixes a price $p$ and posts it to the buyer and the seller. Trade happens if and only if both the buyer's valuation is at least $p$ and the seller's valuation is at most $p$.
We will show in this section that there exists a fixed price mechanism that achieves an expected gain from trade that is at least $r/2$ times the expected optimal gain from trade. In the fixed price mechanism that we propose for this, the fixed price $p$ is set such that $\mathbf{Pr}_{v \sim f}[v \leq p] = \mathbf{Pr}_{w \sim g}[w \leq p]$. The main theorem that we prove is thus as follows.
\begin{theorem}\label{mainthm}
Let $(f,g)$ be a bilateral trade instance, let $p \in \mathbb{R}_{\geq 0}$ be any fixed price, and let $q$ be the minimum of $\mathbf{Pr}_{v \sim f}[v \geq p]$ and $\mathbf{Pr}_{w \sim g}[w \leq p]$. Then,
\begin{equation}\label{eq:1}
\frac{1}{q} \text{GFT}_{f,g}(p) \geq \text{OPT}_{f,g} .
\end{equation}
Moreover, if $p$ is chosen such that $q$ is maximised (i.e., $p$ is such that $\mathbf{Pr}_{w \sim g}[w \leq p] = \mathbf{Pr}_{v \sim f}[v \geq p]$), it holds that
\begin{equation}\label{eq:2}
\frac{2}{r} \text{GFT}_{f,g}(p) \geq \text{OPT}_{f,g}.
\end{equation}
\end{theorem}
Note that this theorem strictly generalises McAfee's result of \cite{mcafee}, which states that in case the seller's median is less than the buyer's median, then setting the price in between the medians of the buyer and the seller results in a $2$-approximation to the optimal gain from trade: If we take $p$ to be any price in between the median of the seller and the buyer, then $q$ is at least $1/2$, and (\ref{eq:1}) then states that the gain from trade at fixed price $p$ is at least half the optimal gain from trade.
\section{Improving the Asymptotic Dependence on $r$}
In this section, we show how it is possible to improve the approximation factor implementing a more involved rule to determine the fixed price $p$. When the trading price $p$ will be set with the new rule the approximation factor will improve from $2/r$ to $O(\log(1/r))$. Notice that when $r$ is small, this is a big improvement with respect to the approximation shown in the previous section.
All logarithms used in this section are to base 2.
Let us first give a high level description of how we determine the fixed price of the mechanism. Let us consider any two points $z$ and $z'$ such that $\mathbf{Pr}[v \geq z] = 2 \mathbf{Pr}[v \geq z']$. Let $E$ be the event that the buyer's valuation exceeds $z$, and that the sellers valuation lies in between $z$ and $z'$. Let $\overline{F}_{E}$ be the complementary cumulative distribution function of the buyer conditioned on $E$ and let $G_{E}$ be the cumulative distribution function of the seller conditioned on $E$. We now see that on the interval $[z,z']$, the function $\overline{F}_{E}$ decreases from $1$ to $1/2$ and the function $G_{E}$ increases from $0$ to $1$. Thus, the functions cross each other in $[z,z']$ at a value of at least $1/2$, which means that the median of the buyer exceeds the median of the seller when conditioning on $E$. Using Theorem \ref{mainthm}, we thus obtain that when conditioning on $E$ there exists a fixed price that achieves a $2$-approximation to the optimal gain from trade.
Our mechanism works by showing that we can decompose ``roughly'' the entire probability space into at most $\log(1/r) + 1$ such events, so that choosing the best fixed price corresponding to each of these events results into an $O(\log(1/r))$ approximation to the optimal gain from trade. More precisely, we show that there are two sets of roughly $\log(1/r) + 1$ such events, and we prove that in case one of these sets does not cover a fraction of the probability space that accounts for at least $1/2$ of the optimal gain from trade, then the other set of events does. To determine the desired fixed price, we can thus
\begin{enumerate}
\item first determine which of the two event sets ``covers'' a large part of the optimal gain from trade,
\item and subsequently select the best fixed price among the $\log(1/r) + 1$ prices corresponding to the event set.
\end{enumerate}
The two event sets have the following properties: one of them excludes the part of the probability space where the buyer's complementary CDF is below the threshold $r/2$. The other one switches the roles of the seller and buyer, and excludes the part of the probability space where the seller's CDF is below a the threshold $r/2$. From this property of the event sets (i.e., having these particular thresholds on the tails of the two distributions), we are able to show that one of the event sets covers a large part of the optimal gain from trade.
We now proceed by making these ideas precise.
We first describe how we determine the price, which we denote by $p^*$, for a given instance $(f,g)$. In contrast with the last section, we assume (for convenience of exposition) without loss of generality that $f$ and $g$ are continuous distributions without point masses, where we treat $f$ and $g$ as probability density functions, and we let $F$ and $G$ be the corresponding cumulative distribution functions. We write $\overline{F}$ to denote the buyer's complementary cumulative distribution function $1 - F$. Let $r$ be the probability $\mathbf{Pr}_{v \sim f, w \sim g}[v \geq w]$ of a trade being possible (as before). Let $x$ be the value such that $F(x) = r/2$ and let $y$ be the value such that $\overline{G}(y) = r/2$.
We distinguish between two cases.
\begin{itemize}
\item If $\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge w > y)]
\geq \text{OPT}_{f,g}/2$, then let $p^*$ be the price that achieves the maximum gain from trade among the prices $p_1, \ldots, p_{\lceil\log(2/r)\rceil}$, where for $i \in [\lceil\log(2/r)\rceil]$, price $p_i$ is such that
\begin{equation*}
\mathbf{Pr}_{w \sim g}\left[w \leq p_i\ \middle|\ \overline{F}^{-1}\left(\frac{1}{2^{i-1}}\right) \leq w \leq \overline{F}^{-1}\left(\frac{1}{2^i}\right)\right] = \mathbf{Pr}_{v \sim f}\left[v > p_i\ \middle|\ \overline{F}^{-1}\left(\frac{1}{2^{i-1}}\right) \leq v\right].
\end{equation*}
\item Otherwise, let $p^*$ be the price that achieves the maximum gain from trade among the prices $p_1', \ldots, p_{\lceil\log(2/r)\rceil}'$, where for $i \in [\lceil\log(2/r)\rceil]$, price $p_i'$ is such that
\begin{equation*}
\mathbf{Pr}_{v \sim f}\left[v > p_i\ \middle|\ G^{-1}\left(\frac{1}{2^{i}}\right) \leq v \leq G^{-1}\left(\frac{1}{2^{i-1}}\right)\right] = \mathbf{Pr}_{w \sim g}\left[w \leq p_i\ \middle|\ G^{-1}\left(\frac{1}{2^{i}}\right) \leq w\right],
\end{equation*}
where we define $G^{-1}(1) = \infty$ if there exists no point $t \in \mathbb{R}_{\geq 0}$ such that $G(t) = 1$.
\end{itemize}
This completes the definition of the fixed price $p^*$.
First we prove that if the first of the two cases does not apply (i.e., if the inequality $\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge w > y)] \leq \text{OPT}_{f,g}/2$ does not hold), then the symmetric inequality $\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge w < x)] \leq \text{OPT}_{f,g}/2$ holds for the second case.
\begin{lemma}\label{caseslemma}
If $\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge w > y)] > \text{OPT}_{f,g}/2$, then $\mathbf{E}_{w \sim f, v \sim g}[(v-w)\mathbf{1}(w \leq v \wedge v < x)] \leq \text{OPT}_{f,g}/2$.
\end{lemma}
\begin{proof}
It suffices to prove that the events $w \leq v \wedge w > y$ and $w \leq v \wedge v < x$ are disjoint, since then the value $\text{OPT}_{f,g}$ can be decomposed into three terms:
\begin{eqnarray*}
\text{OPT}_{f,g} & = & \mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v)\mathbf{1}(w > y)] + \mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v)\mathbf{1}(w < x)] \\
& & \qquad + \mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v)\mathbf{1}(v \leq y \wedge w \geq x)],
\end{eqnarray*}
from which it follows that at least one of the first two terms does not exceed $\text{OPT}_{f,g}/2$, which proves the claim.
In order to show that $w \leq v \wedge w > y$ is disjoint from $w \leq v \wedge v < x$, in turn it suffices to prove that $y \geq x$. To see this, suppose for contradiction that $y < x$. Then we can derive
\begin{eqnarray*}
\mathbf{Pr}_{v \sim f, w \sim g}[w \leq v] & \leq & \mathbf{Pr}_{v \sim f, w \sim g}[w \leq x \cap w \leq v] + \mathbf{Pr}_{v \sim f, w \sim g}[w > x \cap w \leq v] \\
& \leq & \mathbf{Pr}_{w \sim g}[w \leq x] + \mathbf{Pr}_{v \sim f}[v > x] \\
& < & \mathbf{Pr}_{w \sim g}[w \leq x] + \mathbf{Pr}_{v \sim f}[v > y] \\
& = & \frac{r}{2} + \frac{r}{2} = r,
\end{eqnarray*}
which contradicts the definition $r = \mathbf{Pr}_{v \sim f, w \sim g}[w \leq v]$.
\qed
\end{proof}
With the above lemma in mind, we can prove our intended approximation factor for price $p^*$.
\begin{theorem}\label{thm:log-approx}
Let $(f,g)$ be any bilateral trade instance, and let $p^*$ be the price for $(f,g)$, as defined above. It holds that
\begin{equation*}
\text{OPT}_{f,g} \leq 4\log\left(\left\lceil\frac{2}{r}\right\rceil\right) \text{GFT}_{f,g}(p^*) .
\end{equation*}
\end{theorem}
\begin{proof}
We divide the proof into two cases, corresponding to the case distinction by which $p^*$ is defined. In the first case, it holds that $\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge w > y)] \leq \text{OPT}_{f,g}/2$. This implies that $\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge w \leq y)] \geq \frac{\text{OPT}_{f,g}}{2}$. For $i \in [\lceil\log(2/r)\rceil]$, let $E(i)$ denote the event
\begin{equation*}
\overline{F}^{-1}\left(\frac{1}{2^{i-1}}\right) \leq w \leq \overline{F}^{-1}\left(\frac{1}{2^i}\right) \wedge \overline{F}^{-1}\left(\frac{1}{2^{i-1}}\right) \leq v,
\end{equation*}
and let $f_{E(i)}$ and $g_{E(i)}$ be the probability distributions $f$ and $g$ conditioned on the event $E(i)$. Moreover, we define $\overline{F}_{E(i)}$ as the complementary cumulative distribution function of $f_{E(i)}$ and $G_{E(i)}$ as the cumulative distribution function of $g_{E(i)}$.
By definition, the price $p^*$ is the price among the prices $\{p_i : i \in [\lceil\log(2/r)\rceil]\}$ that achieves the highest gain from trade.
We proceed to show that we can write the expectation on the left hand side as a convex combination of $\lceil\log(2/r)\rceil$ values $T_1, \ldots, T_{\lceil\log(2/r)\rceil}$ (and $0$), such that $T_i \leq 2 \text{GFT}_{f_{E(i)},g_{E(i)}}(p_i)$ for all $i \in [\lceil\log(2/r)\rceil]$. Define
\begin{equation*}
T_i = \mathbf{E}_{v \sim f, w \sim g}\left[(v-w)\mathbf{1}(w \leq v)\ \middle|\ E(i) \right] = \text{OPT}_{f_{E(i)},g_{E(i)}}.
\end{equation*}
We prove first that $T_i \leq 2 \text{GFT}_{f_{E(i)},g_{E(i)}}(p_i)$ for $i \in [\lceil\log(2/r)\rceil]$.
We see that the function $\overline{F}_{E(i)}$ is at least $1/2$ on the interval $I_i = [\overline{G}^{-1}(1/2^{i-1}), \overline{G}^{-1}(1/2^i)]$, because $F$ is in the range $[1/2^{i-1}, 1/2^i]$ on interval $I_i$.
The function $G_{E(i)}$ crosses $\overline{F}_{E(i)}$ in $I_i$, and the price $p_i$ is, per definition, exactly the point in $I_i$ where the two functions are equal, i.e., the point $p_i \in I_i$ such that $\overline{F}_{E(i)}(p_i) = G_{E(i)}(p_i)$. Therefore, $1/2 \leq \overline{F}_{E(i)}(p_i) = G_{E(i)}(p_i)$.
Now we apply the first part of Theorem \ref{mainthm} to the instance $(f_{E(i)},g_{E(i)})$ with price $p_i$. Because of the above inequality, we know that the value of $q$ in Theorem \ref{mainthm} is at least $1/2$, so we obtain $\text{GFT}_{f_{E(i)},g_{E(i)}}(p_i) \geq (1/2)\text{OPT}_{f_{E(i)},g_{E(i)}} = (1/2)T_i$, as we wanted to show. We also derive that
\begin{align*}
& \mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge w \leq y)] \\
& \qquad \leq \sum_{i = 1}^{\lceil\log(2/r)\rceil} \mathbf{Pr}\left[\overline{F}^{-1}\left(\frac{1}{2^{i-1}}\right) \leq w \leq \overline{F}^{-1}\left(\frac{1}{2^i}\right) \wedge \overline{F}^{-1}\left(\frac{1}{2^{i-1}}\right) \leq v\right] T_i \\
& \qquad = \sum_{i = 1}^{\lceil\log(2/r)\rceil} \mathbf{Pr}_{v \sim f, w \sim g}[E(i)] T_i,
\end{align*}
is indeed a convex combination of $T_1, \ldots, T_{\lceil\log(2/r)\rceil}$ (and $0$). (Note that the inequality in the above derivation is an equality in case $\log(2/r)$ is an integer.)
It follows that
\begin{align*}
& \text{OPT}_{f,g}/2 \leq 2 \sum_{i = 1}^{\lceil\log(2/r)\rceil} \mathbf{Pr}_{v \sim f, w \sim g}[E(i)] \text{GFT}_{f_{E(i)},g_{E(i)}}(p_i) \\
& \qquad = 2 \sum_{i = 1}^{\lceil\log(2/r)\rceil} \mathbf{Pr}_{v \sim f, w \sim g}[E(i)]\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq p_i \leq v)\ |\ E(i)] \\
& \qquad = 2 \sum_{i = 1}^{\lceil\log(2/r)\rceil} \mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq p_i \leq v)\mathbf{1}(E(i))] \\
& \qquad \leq 2 \sum_{i = 1}^{\lceil\log(2/r)\rceil} \mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq p_i \leq v)] \leq 2 \sum_{i = 1}^{\lceil\log(2/r)\rceil} \text{GFT}_{f,g}(p_i) \\
& \qquad \leq 2 \log\left(\left\lceil\frac{2}{r}\right\rceil\right) \max\left\{\text{GFT}_{f,g}(p_i) : i \in \left[\log\left(\left\lceil\frac{2}{r}\right\rceil\right)\right]\right\} = 2 \log\left(\left\lceil\frac{2}{r}\right\rceil\right) \text{GFT}_{f,g}(p^*),
\end{align*}
which proves the desired result for our first case.
For the second case, it holds that $\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge w > y)] > \text{OPT}_{f,g}/2$. Then by Lemma \ref{caseslemma}, $\mathbf{E}_{v \sim f, w \sim g}[(v-w)\mathbf{1}(w \leq v \wedge v < x)] \leq (1/2) \text{OPT}_{f,g}$.
The analysis of this second case is from this point entirely analogous to that of the first case.
\qed
\end{proof}
Note that the approximation bound of $2/r$ that we established in the first section is better than the approximation bound of $4 \lceil \log(2/r) \rceil$ when $r$ is roughly greater than $0.05$. At $r = 0.05$, the approximation factor $4 \lceil \log(2/r)\rceil$ already takes a value around $20$. Hence, the result of this section is intended to provide theoretical insight into how the approximability of the gain from trade depends on $r$ asymptotically.
An (asymptotically) matching lower bound is given in the appendix of \cite{BD16}, which shows that $\Theta(\log(1/r))$ is asymptotically the best possible factor by which the optimal gain from trade that can always be approximated. We provide in Appendix \ref{apx:lowerbound} another independently discovered example of such a bilateral trade instance, in which the probability distributions of the buyer and the seller are discrete rather than continuous. Our example additionally shows that the approximation factor achievable by a fixed price mechanism can be no better than $\Omega(1/N)$, where $N$ is the number of points in the support of the distributions.
\section{A Fixed Price Double Auction}\label{sec:double-auctions}
We now turn to the double auction setting. Recall that in this setting there are $n \geq 1$ buyers and $m \geq 1$ sellers. The sellers each hold one item, and neither the buyers or the sellers are interested in holding more than one item. As before, we refer to $f$ for the probability distribution function from which the buyers' valuations are independently drawn, and to $g$ for the probability distribution from which the sellers' valuations are independently drawn. We denote the (random) valuation of buyer $i \in [n]$ by $v_i$ and the (random) valuation of seller $j \in [m]$ by $w_j$. See Section \ref{sec:prelims} for the definition.
In order to present the definition of a \emph{fixed price mechanism} for the double auction setting, let us first introduce the concept of \emph{feasible pair}.
\begin{definition}
Let $(n,m,f,g)$ be an instance of a double auction setting, let $(v,w) \in \mathbb{R}^n\times \mathbb{R}^m$ be a valuation profile for the buyers and sellers, and let $p \in \mathbb{R}_{\geq 0}$. We call $(i,j) \in [n]\times[m]$ a \emph{feasible pair} with respect to profile $(v,w)$ and fixed price $p$ iff $v_i \geq p \geq w_j$.
\end{definition}
\noindent Now, we can define a fixed price mechanism as follows.
\begin{definition}
We define a \emph{fixed price mechanism} $\mathbb{M}$ for a double auction setting $(n,m,f,g)$ as a direct revelation mechanism for which there is a price $p$ such that the mechanism selects a uniform random maximal subset of feasible pairs with respect to reported profile $(v,w)$ and $p$, and makes these pairs trade with each other. Moreover, for every selected trading pair $(i,j)$, the mechanism makes buyer $i$ pay an amount of $p$ to seller $j$. We refer to $p$ as the \emph{price} of $\mathbb{M}$.
\end{definition}
This is perhaps the most natural generalization of the notion of a fixed price mechanism that one may think of.
Please note that in a fixed price mechanism with price $p$, given a reported valuation profile $(v,w)$, the number of pairs that trade is always the minimum of $|\{v_i : v_i \geq p\}|$ and $|\{w_i : w_i \leq p\}|$.
It is easy to show that fixed price mechanisms clearly satisfy the three basic properties that we want:
\begin{theorem}\label{thm:properties}
For every double auction setting, every fixed price mechanism is ex-post IR, SBB, and DSIC.
\end{theorem}
Fixed price mechanisms have some additional advantanges.
\begin{itemize}
\item First, a fixed price mechanism is entirely symmetric: Each seller has the same expected utility, and each buyer has the same expected utility. The mechanism treats buyers with the same valuation entirely symetrically and does not break ties in favour of one over the other. This symmetricity is desirable from the point of view of fairness.
\item Secondly, the mechanism does not require the agents to fully reveal their entire valuation, since it can be implemented as a \emph{two-sided sequential posted price mechanism} \cite{doubleauctions}. Under such an implementation, the mechanisms goes over the buyers and sellers one by one. It proposes a take-it-or-leave-it price (equal to $p$, in this case) to each buyer and seller, which the buyers and sellers can choose to accept or reject. As soon as an accepting (buyer,seller)-pair is found, the mechanism lets this pair trade at price $p$. Taking a uniform random order of buyers and sellers will result in a random subset of feasible pairs who trade at price $p$, i.e., it will result in an implementation of the fixed price mechanism with price $p$. Under such an implementation, each buyer and seller has to reveal only one bit of information, which indicates whether her valuation is above or below $p$.
\end{itemize}
We aim to design a simple fixed price mechanism for which the gain from trade is a good approximation to the optimal gain from trade.
The mechanism we use is as follows.
\begin{definition}
Given an instance $(n,m,f,g)$ of a double auction setting, let $\overline{p}$ be the price such that $n\overline{F}(\overline{p})= mG(\overline{p})$. We refer to the fixed price mechanism with price $\overline{p}$ as the \emph{balanced fixed price double auction}.
For ease of presentation, we refer to $\overline{F}(\overline{p})$ as $\overline{q}^B$ and we refer to $G(\overline{p})$ as $\overline{q}^S$. We denote by $\text{GFT}(\overline{p})$ the expected gain from trade achieved by the balanced fixed price double auction, and we denote by $\#T$ the expected number of trades that the balanced fixed price double auction generates.
\end{definition}
Observe that the balanced fixed price double auction is a generalization of the mechanism of Theorem \ref{mainthm} that achieves for the bilateral trade setting a $2/r$-approximation of the optimal gain from trade. We note that the value $\#T$ is by definition equal to $n\overline{q}^B = m \overline{q}^S$.
The main result we prove in this section is as follows.
\begin{theorem}\label{thm:doubleauctions}
For all $\epsilon \in [0,1]$, with probability at least $1 - 2/e^{\#T \epsilon^2 /2}$, the balanced fixed price double auction achieves a gain from trade that is at least $(1-\epsilon)$ times the expected optimal gain from trade.
\end{theorem}
Note that $\#T$, the expected number of trades of the balanced fixed price double auction, needs to exceed $2\ln(2)/\epsilon^2$ by any constant for the above theorem to yield a constant approximation guarantee. The value $\#T$ can be regarded as a property of the instance $(n,m,f,g)$ on which the mechanism is run, and is equal to the value where the functions $n\overline{F}$ and $mG$ cross each other. The requirement on $\#T$ is reasonably mild: For example, the above theorem says that when $\#T$ is at least $10$, the balanced fixed price double auction yields an expected gain from trade that is a $(< 4)$-approximation to the optimal gain from trade, by taking $\epsilon \approx 0.61$ (since $(1 - 2/e^{0.61^2 \cdot 5}) \cdot (1-0.61) > 0.25$). The theorem provides a constant approximation ratio for all instances where $\#T > 2\ln(2) \approx 1.38$, but grows unbounded as $\#T$ approaches $2\ln2$ from above.
There is an interesting interpretation of this theorem in terms of large markets: Observe that increasing the number of buyers or sellers in the market also increases $\#T$. In particular, by increasing both the number of buyers and the number of sellers simultaneously, $\#T$ grows unboundedly. From our theorem we may therefore infer that the balanced fixed price double auction approximation approximates the gain from trade by a factor that goes to $1$ as the market grows.
\begin{figure}
{\centering
\begin{tikzpicture}[scale=0.5]
\def3pt{3pt}
\tikzstyle{xxx}=[ultra thick,loosely dotted]
\tikzstyle{nome}=[rectangle,align=right,anchor=east,minimum width=1cm,text width=2cm]
\usetikzlibrary{patterns,decorations.pathreplacing}
\draw[ultra thick](0,11)--(0,0)--(22,0);
\draw[thick,dashed](0,8)--(18,8);
\draw[thick]plot[smooth,tension=0.7]coordinates
{(0,0)(2,0.1)(4,0.4)(6,1.2)(8,2.8)(10,5.2)(12,6.8)(14,7.6)(16,7.9)(18,8)(20,8)};
\draw[thick]plot[smooth,tension=0.7]coordinates
{(0,11)(2,10.9)(4,10.5)(6,9)(8,7.2)(10,5.2)(12,3)(14,1.5)(16,0.5)(18,0.1)(20,0)};
\draw[thick,dashed](10,0)--(10,5);\node at(10,-0.5){$\overline{p}$};
\draw[thick,dashed](0,5.2)--(10,5.2);
\node at(17,8.5){$m \cdot G$ (sellers)}; \node at(3,11.5){$n \cdot\overline{F}$ (buyers)};
\node[nome] at(-0.5,11){$n$};
\node[nome] at(-0.5,8){$m$};
\node[nome] at(-0.5,5.2){$n\overline{q}^B = m\overline{q}^S$};
\end{tikzpicture}
\par}
\caption{The graphs of the functions $n \cdot \overline{F}$ and $m \cdot G$ are shown.
They cross at price $\overline{p}$.}
\label{fig:gft}
\end{figure}
To prove the desired approximation property of the balanced fixed price double auction, we note that due to symmetry, we may assume that under the optimum allocation every buyer has the same a priori probability of trading with a seller, and every seller has the same a priori probability of trading with a buyer. This motivates the following definition.
\begin{definition}
For a double auction setting $(n,m,f,g)$ we define the values $q^S$ as the probability that any buyer receives an item under the optimum allocation, and we define $q^S$ as the probability that any seller loses her item under the optimum allocation. We define the prices $p^B$ and $p^S$ as the prices closest to $\overline{p}$ such that $\overline{F}(p^B) = q^B$ and $G(p^S) = q^S$. That is: $p^B$ is such that a buyers' probability of her valuation exceeding $p^B$ is equal to the probability of obtaining an item under the optimum allocation, and if there multiple such prices then $p^B$ is defined as the unique one closest to $\overline{p}$. Likewise, $p^S$ is such that a sellers' probability of her valuation being at most $p^S$ is equal to the probability of losing her item under the optimum allocation. Lastly, we let $\text{OPT}$ denote the expected gain from trade achieved by the optimum allocation.
\end{definition}
The values $\text{GFT}(\overline{p})$, $\text{OPT}$, $\#T$, $\overline{p}$, $\overline{q}^B$, $\overline{q}^S$, $p$, $q^B$, and $q^S$ all depend (like $r$) on the instance $(n,m,f,g)$. We will leave this dependence implicit, as throughout this section there will be no ambiguity about the instance of the double auction setting that is being discussed.
\begin{lemma}\label{lem:optnumtrades}
For every instance $(n,m,f,g)$ of a double auction setting, the following property of the optimal allocation is satisfied.
\begin{equation*}
nq^B = mq^S.
\end{equation*}
\end{lemma}
\noindent The following lemma states that our price $\overline{p}$ always lies in between $p^B$ and $p^S$.
\begin{lemma}\label{lem:ordering}
For every instance $(n,m,f,g)$ of a double auction setting, $p^{B} \geq \overline{p} \geq p^{S}$ or $p^{S} \geq \overline{p} \geq p^{B}$.
\end{lemma}
\noindent The following lemma provides a useful bound on $\text{OPT}$
\begin{lemma}\label{prob:gftopt}
For every instance $(n,m,f,g)$ of a double auction setting, it holds that
\begin{equation*}
\text{OPT} \leq n q^B \mathbf{E}[v_1\ |\ v_1 \geq p^B] - m q^S \mathbf{E}[w_1\ |\ w_1 \leq p^S].
\end{equation*}
\end{lemma}
We will use the following technical Lemma to bound $\text{OPT}$ further.
\begin{lemma}\label{lem:bound1}
For every instance $(n,m,f,g)$ of a double auction setting, it holds that
\begin{equation*}
n q^B \mathbf{E}[v_1\ |\ v_1 \geq p^B] - m q^S \mathbf{E}[w_1\ |\ w_1 \leq p^S] \leq n \overline{q}^B \mathbf{E}[v_1\ |\ v_1 \geq {\overline p}] - m \overline{q}^S \mathbf{E}[w_1\ |\ w_1 \leq {\overline p}]
\end{equation*}
\end{lemma}
We can now prove our main approximation result for the balanced fixed price double auction.
\begin{proof}[of Theorem \ref{thm:doubleauctions}]
Let us define the following random variables: $B_{i}$ is a random variable that is equal to $1$ if $v_{i} \geq \overline{p}$ and $0$ otherwise, similarly, $S_{j}$ is a random variable that is equal to $1$ if $w_{j} \leq \overline{p}$ and $0$ otherwise. Now, let $B = \sum_{i} B_{i}$ and $S= \sum_{j} S_{j}$. Moreover, let $B_i^*$ denote the event that $i$ trades under the balanced fixed price double auction, and similarly let $B_j^*$ be the event that $j$ trades under the balanced fixed price double auction. Denote by $E$ the event that the balanced fixed price double auction lets at least $(1-\epsilon)n\overline{q}^B = (1-\epsilon)m\overline{q}^S$ pairs of buyers and sellers trade. That is $E$ denotes the event that $B \geq (1-\epsilon)n \overline{q}^{B} \wedge S \geq (1-\epsilon) m \overline{q}^{S}$. First, we derive the following bound on the gain from trade of the balanced fixed price double auction conditioned on $E$.
\begin{eqnarray*}
& & \mathbf{E}\left[\sum_{i = 1}^n (v_i - \overline{p})\mathbf{1}(B_i^*) + \sum_{j=1}^m(\overline{p} - w_j)\mathbf{1}(S_j^*)\ \middle|\ E \right] \\
& = & \sum_{i = 1}^n \mathbf{E}\left[v_i - \overline{p}\ \middle|\ E \wedge B_i^*\right]\mathbf{Pr}\left[B_i^*\ \middle|\ E \right] + \sum_{j=1}^m \mathbf{E}\left[\overline{p} - w_j\ \middle|\ E \wedge S_j^* \right]\mathbf{Pr}\left[S_j^*\ \middle|\ E \right] \\
& = & \sum_{i = 1}^n \mathbf{E}\left[v_i - \overline{p}\ \middle|\ v_i \geq \overline{p} \right]\mathbf{Pr}\left[B_i^*\ \middle|\ E \right] + \sum_{j=1}^m \mathbf{E}\left[\overline{p} - w_j\ \middle|\ w_j \leq \overline{p} \right]\mathbf{Pr}\left[S_j^*\ \middle|\ E \right] \\
& \geq & \sum_{i = 1}^n \mathbf{E}\left[v_i - \overline{p}\ \middle|\ v_i \geq \overline{p} \right]\frac{n\overline{q}^B(1-\epsilon)}{n} + \sum_{j=1}^m \mathbf{E}\left[\overline{p} - w_j\ \middle|\ w_j \leq \overline{p} \right]\frac{m\overline{q}^S(1-\epsilon)}{m} \\
& = & n \mathbf{E}\left[v_1 - \overline{p}\ \middle|\ v_1 \geq \overline{p} \right]\overline{q}^B(1-\epsilon) + m \mathbf{E}\left[\overline{p} - w_1\ \middle|\ w_1 \leq \overline{p} \right]\overline{q}^S(1-\epsilon). \\
& = & n \mathbf{E}\left[v_1\ \middle|\ v_1 \geq \overline{p} \right]\overline{q}^B(1-\epsilon) - m \mathbf{E}\left[w_1\ \middle|\ w_1 \leq \overline{p} \right]\overline{q}^S(1-\epsilon). \\
\end{eqnarray*}
We bound as follows the probability of the event $E$ happening.
\begin{eqnarray*}
\mathbf{Pr}[E] & = & 1 - \mathbf{Pr}[B < (1-\epsilon)n \overline{q}^{B} \vee S < (1-\epsilon) m \overline{q}^{S}] \\
& \geq & 1 - \mathbf{Pr}[B < (1-\epsilon)n \overline{q}^{B}] - \mathbf{Pr}[S < (1-\epsilon) m \overline{q}^{S}]\\
& \geq & 1 - \frac{2}{e^{n\overline{q}^B \epsilon^2 / 2}} \\
& \geq & 1 - \frac{2}{e^{\#T \epsilon^2 / 2}} \\
\end{eqnarray*}
The second inequality follows from applying a standard Chernoff bound, which can be done since $B$ and $S$ are sums of $\{0,1\}$ independent random variables.
We conclude that with probability at least $1 - 2/e^{\#T \epsilon^2 / 2}$ the mechanism obtains at least $(1-\epsilon) \#T $ trades at price $\overline{p}$. Thus, using Lemmas \ref{prob:gftopt} and \ref{lem:bound1} we conclude that with probability at least $1 - 2/e^{\#T \epsilon^2 / 2}$ the gain from trade of the balanced fixed price double auction is at least
\begin{equation*}
(1-\epsilon) (n \overline{q}^B \mathbf{E}[v_1\ |\ v_1 \geq \overline{p}] - m \overline{q}^S \mathbf{E}[w_1\ |\ w_1 \leq \overline{p}]) \geq (1-\epsilon) \text{OPT},
\end{equation*}
which completes the proof.
\qed
\end{proof}
\begin{paragraph}{\bf{Acknowledgements.}}
We thank Tim Roughgarden for helpful discussions at the early stages of this work.
\end{paragraph}
\newpage
\bibliographystyle{plain}
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| null | null |
Q: Convert pandas (python) categorical x-axis to continuous values when plotting I am plotting a pandas series in python using the matplotlib plot command (i.e. series.plot(), where series is my series). Part of the series is as follows:
(1, 1.1] 0.000000
(1.1, 1.2] 0.000000
(1.2, 1.3] 0.000000
(1.3, 1.4] 0.003115
(1.4, 1.5] 0.002625
(1.5, 1.6] 0.000000
(1.6, 1.7] 0.001464
... ...
(4.9, 5.0] 0.737385
Name: series, dtype: float64
A plot of my dataframe is shown here (the red line in this case). I want the x-axis to go from 1.0 to 5.0 instead of showing the bin categories. How can I achieve this? Using plt.xticks doesn't seem to work.
A: Where does the series come from? Usually, I have a big dataframe of continuous-valued columns X and Y, and then define X-binss according to X values. After that, group by X-bins to calculate average (or weighted average, or sum, or any other aggregation function) of Y to get the series like yours. If that's the case, I would suggest calculate mean of X in this process and plot against average X instead of X-bins. This will be more precise than taking left/right end points or mid-points of the bins for plotting. E.g.,
df['Xbin'] = pd.cut(df['X'], np.arange(0,10,0.1))
Instead of
ser = df.groupby('Xbin')['Y'].mean()
ser.plot()
do
df2 = df.groupby('Xbin')[['X','Y']].mean()
df2.plot(x='X', y='Y')
A: Based on our discussion, your series has an index that is a string of the intervals, eg. '(1,1.1]' is the index of the first item in the series.
I was able to reproduce your issue using the following code:
import pandas as pd
import numpy as np
x1 = np.arange(0,5,.1)
x2 = np.arange(0.1,5.1,.1)
y = x1**2
df = pd.DataFrame(np.vstack((x1,x2,y)).T, columns=['x1','x2','y'])
df['xRange'] = '(' + df.x1.map(str) + ', ' + df.x2.map(str) + ']'
series = df.set_index('xRange', drop=True)['y']
series.plot()
To get the ticks labelled correctly using just the series object, you need to strip the index off and pull out the first part of the interval.
You can recover the dataframe for plotting purposes via:
new_df = pd.DataFrame(series)
new_index = series.index.map(lambda s: float(s.split(',')[0].replace('(','')))
new_df.set_index(new_index, inplace=True)
new_df.plot()
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\section{Introduction}
Multidimensional simulations shed light on how fluid instabilities arising in supernova explosions mix ejecta
\cite{herant1994,candace2009,candace2010,candace2011}. Unfortunately, computing the full self-consistent
three-dimensional (3D) stellar evolution initial models for the explosion setup is still beyond the
realm of contemporary computational power. One alternative is to first evolve the main sequence star in a 1D
stellar evolution code in which the equations of momentum, energy and mass are solved on a spherically
symmetric Lagrangian grid, such as \texttt{KEPLER}{} \cite{kepler} or \texttt{MESA}{} \cite{mesa}. Once the star reaches the
pre-supernova phase, its 1D profiles can then be mapped into multidimensional hydro codes such as \texttt{CASTRO}{}
\cite{zhang2011,ann2010} or \texttt{FLASH}{} \cite{flash} and continue to be evolved until the star explodes.
Differences between codes in dimensionality and coordinate mesh can lead to numerical issues such
as violation of conservation of mass and energy when profiles are mapped from one code to another. A first, simple
approach could be to initialize multidimensional grids by linear interpolation from corresponding mesh points
on the 1D profiles. However, linear interpolation becomes invalid when the new grid fails to resolve critical
features in the original profile such as the inner core of a star. This is especially true when porting profiles
from 1D Lagrangian codes, which can easily resolve very small spatial features in mass coordinate, to a
fixed or adaptive Eulerian grid. Besides conservation laws, some physical processes such as nuclear
burning are very sensitive to temperature, so slight errors in mapping can lead to very different outcomes
for the simulation. Only a few studies have examined mapping 1D profiles to 2D or 3D meshes
\cite{zingale2002}, and none address the conservation of physical quantities by such procedures.
We investigate these issues and introduce a new scheme for mapping 1D data sets to multidimensional
grids. We first describe our mapping algorithm in \Sect{method} and then present results of porting a
massive star model from \texttt{KEPLER}{} to \texttt{CASTRO}{} in \Sect{result}. Finally, we conclude in \Sect{conclusion}.
\section{Method}
\lSect{method}
Since the star is very nearly in hydrostatic equilibrium but we also map explosions where we want to conserve
the total energy , care must be taken in mapping its profile from the
non-uniform Lagrangian grid in mass coordinate to the new Eulerian spatial grid. Our method preserves
conservation of quantities such as mass and energy that are analytically conserved in the evolution
equations on the new mesh. Although this does not guarantee that a hydrostatic star will be fully hydrostatic
on the new grid because our construction does not, it is a physically motivated constraint and sufficient for our simulations. The algorithm we describe
below is specific to our stellar models but can be easily generalized to other mappings of 1D data to higher
dimensions.
\begin{figure}
\begin{center}
\includegraphics[scale=0.6]{mapping11.eps}
\caption{ Constructing a conservative profile. The rectangular bins illustrate the original 1D profile. The
areas of different colors represent conserved quantities such as mass and internal energy. Note that
uniform zones in mass lead to nonuniform bins in volume coordinate, as shown above. \label{mapping}}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.6]{fig1_b200.ps}
\caption{\texttt{KEPLER}{} densities and temperatures (red crosses) and our piecewise linear fits (green lines).
Since we map internal energy (a conserved quantity) rather than temperature, we calculate $T$ from the
equation of state using density, element abundance, and internal energy. \label{fig1}}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.6]{fig2_b200.ps}
\caption{Total mass of the star on the new 1D \texttt{CASTRO}{} grid vs. number of zones. Conservative
mapping (blue) preserves the mass of the star at all resolutions, while linear interpolation (orange)
converges to 200 {\ensuremath{\mathrm{M}_{\odot}}}{} at a resolution of $\sim$ a few $\times 10^4$, when the grid begins to
resolve the core of the star ($\sim 10^9$ cm). Even using a very high resolution, the linear interpolation
still fails to resolve the density gradient between the inner core and the out envelope (see Figure \ref{fig1}
$10^{9} \sim 10^{11}$ cm). So the curve of linear interpolation is saturated at zone number $\sim 10^5$,
its results are still off by a few $\%$. \label{fig2}}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.6]{fig3_b200.ps}
\caption{Total mass of the star on the new 2D \texttt{CASTRO}{} grid vs. number of zones in both $r$ and
$z$. Conservative mapping (blue) recovers the mass of the star at all resolutions and linear
interpolation (orange) approaches 200 {\ensuremath{\mathrm{M}_{\odot}}}{} at a resolution of $\sim$ $2048^2$. \label{fig3}}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.6]{fig4_b200.ps}
\caption{Total mass of the He core on the 2D \texttt{CASTRO}{} grid vs. number of zones in both $r$ and
$z$. Conservative mapping (blue) preserves the original mass of the core at all resolutions while
linear interpolation (orange) begins to converge to 100 {\ensuremath{\mathrm{M}_{\odot}}}{} at a resolution of $64^2$ but is still
off by $\sim 1 \%$ even as the resolution approaches $\sim 2048^2$ . \label{fig4}}
\end{center}
\end{figure}
First, we construct a continuous (C$^0$) function that conserves the physical quantity when it is mapped onto the
new grid. An ideal choice for interpolation is the volume coordinate $V$, the volume enclosed by a given radius from the center of
the star. Then, integrating a density $\rho_X$ (which can represent mass or internal energy density) with respect to the volume coordinate yields a conserved quantity $X$
\begin{equation}
X=\int _{V_1}^{V_2}\rho_X\,\mathrm{d}V,
\end{equation}
such as the total mass or internal total energy lying in the shell between $V_1$ and $V_2$.
Next, we define a piecewise linear function in volume $V$ that represents the conserved quantity $\rho_X$,
preserves its monotonicity (no new artificial extrema), and is bounded by the extrema of the original data.
The segments are constructed in two stages. First, we extend a line across the interface between adjacent
zones that either ends or begins at the center of the smaller of the two zones, as shown in Figure
\ref{mapping} (note that uniform zones in mass coordinate do not result in uniform zones in $V$). The
slope of the segment is chosen so that the area trimmed from one zone by the segment ($a$ and $b$) is
equal to the area added under the segment in the neighboring bin ($a'=a$ and $b'=b$).
If the two segments bounding $a$ and $a'$ and $b$ and $b'$ are joined together by a third in the center zone in
Figure \ref{mapping}, two ``kinks'', or changes in slope, can arise in the interpolated quantity there; plus, the slope
of the flat central segment is usually a poor approximation to the average gradient in that interval. We therefore
construct two new segments that span the entire central zone and connect with the two original segments where
they cross its interfaces, as shown in Figure \ref{mapping}. The new segments join each other at the position in
the central bin where the areas $c$ and $c'$ enclosed by the two segments are equal (note that they in general
have different slopes). After repeating this procedure everywhere on the grid, each bin will be spanned by two
linear segments that represent the interpolated quantity $\rho_X$ at any $V$ within the bin and have no more
than one kink in $\rho_X$ across the zone. Our scheme introduces some smearing (or smoothing) of the data,
but it is limited to less than or equal to the width of one zone on the original grid.
The result of our interpolation scheme is a piecewise linear reconstruction in $V$ of the original profile in mass
coordinate, for which the quantity $\rho_X$ can be determined at any $V$, not just the radii associated with the
Lagrangian grid. We show this profile as a function of the radius associated with the volume coordinate $V$ for
a zero-metallicity 200 {\ensuremath{\mathrm{M}_{\odot}}}{} star with $r$ $\sim$ $2 \times 10^{13}$ cm from \texttt{KEPLER}{} \cite{heger2002,heger2010} in Figure \ref{fig1}.
We populate the new multidimensional grid with conserved quantities from the reconstructed stellar profiles
as follows. First, the distance of the selected mesh point from the center of the new coordinate grid is calculated.
We then use this radius to obtain its $V$ to reference the corresponding density in the piecewise linear profile of
the star. The density assigned to the zone is then determined from adaptive iterative subsampling. This is done by first
computing the total mass of the zone by multiplying its volume by the interpolated density. We then divide the
zone into equal subvolumes whose sides are half the length of the original zone. New $V$ are computed for
the radii to the center of each of these subvolumes and their densities are again read in from the reconstructed
profile. The mass of each subvolume is then calculated by multiplying its interpolated density by its volume element. These masses are then summed and
compared to the mass previously calculated for the entire cell. If the relative error between the two masses is larger
than some predetermined tolerance, each subvolume is again divided as before, masses are computed for all the
constituents comprising the original zone, and they are then summed and compared to the zone mass from the
previous iteration. This process continues recursively until the relative error in mass between the two most
recent consecutive iterations falls within an acceptable value, typically 10$^{-4}$. The density we assign to the
zone is just this converged mass divided by the volume of the entire cell. This method is used to map internal
energy density and the partial densities of the chemical species to every zone on the new grid. The total density
is then obtained from the sum of the partial densities; pressure and temperature in turn are determined from the
equation of state. This method is easily applied to hierarchy geometry of the target grid.
\section{Results}
\lSect{result}
We port a 1D stellar model from \texttt{KEPLER}{} into \texttt{CASTRO}{} to verify that our mapping is conservative. As an example here, we use the zero-metalicity pre-supernova 200 {\ensuremath{\mathrm{M}_{\odot}}}{} star whose profiles are shown in Figure \ref{fig1}. \texttt{KEPLER}{} is a
Lagrangian code that evolves stars in mass coordinate so its mesh is nonuniform in space, and \texttt{CASTRO}{} has an
Eulerian grid with uniform spatial zones.
We compare our piecewise linear fits to the \texttt{KEPLER}{} data in Figure \ref{fig1}, which shows that they reproduce
the original stellar profile. Because our fits smoothly interpolate the block histogram structure of the \texttt{KEPLER}{} bins
(especially at larger radii), they reduce the number of unphysical sound waves that would have been introduced in
\texttt{CASTRO}{} by the discontinuous interfaces between these bins in the original data. The density profile is key to the
hydrodynamic and gravitational evolution of the explosion, and the temperature profile is crucial to the nuclear
burning that powers the explosion.
We first map the profile onto a 1D grid in \texttt{CASTRO}{} and plot the mass of the star as a function of grid resolution
in Figure \ref{fig2}. The mass is independent of resolution for our conservative mapping because we subsample
the quantity in each cell
prior to initializing it, as described above. In contrast, the total mass from linear interpolation is very sensitive to
the number of grid points but does eventually converge when the number of zones is sufficient to resolve the core
of the star, in which most of its mass resides.
We next map the \texttt{KEPLER}{} profile onto a 2D cylindrical grid ($r,z$) and a 3D cartesian grid ($x,y,z$) in \texttt{CASTRO}{}.
The only difference between mapping to 1D, 2D, and 3D is the form of the volume elements used to subsample each
cell, which are $4\pi r^2 dr$, $2\pi r dr dz$, $dx dy dz$, respectively. We show the mass of the star as a
function of resolution in Figure \ref{fig3}. Conservative mapping again preserves its mass at all grid
resolutions. In 2D, more zones are required for linear interpolation to converge to the mass of the star. To further
validate our conservative scheme, we map just the helium core of star ($\sim$ 100 ${\ensuremath{\mathrm{M}_{\odot}}}$ with $r \sim$ 10$^{10}$
cm) onto the 2D grid. The helium core is crucial to modeling thermonuclear supernovae because it is where explosive
burning begins. We show its mass as a function of resolution in Figure \ref{fig4}. We again recover
all the mass of the core at all resolutions while linear interpolation overestimates the mass by at least $\sim$ 1 $\%$,
even with large numbers of zones.
Conservative mapping is effective in 3D but requires much more computational time to subsample each cell
to convergence. Furthermore, an impractical number of zones is needed for linear interpolation to reproduce the
original mass of the star, so we defer its comparison to our scheme in 3D to a later study. We note that our method
also works with adaptive mesh refinement (AMR) grids because both $V$ and the interpolated quantities can be determined
and subsampling can be performed on every grid in the hierarchy.
\section{Conclusion}
\lSect{conclusion}
Multidimensional stellar evolution and supernova simulations are numerically challenging because multiple physical
processes (hydrodynamics, gravity, burning) occur on many scales in space and time. For computational efficiency,
1D stellar models are often used as initial conditions in 2D and 3D calculations. Mapping 1D profiles onto
multidimensional grids can introduce serious numerical artifacts, one of the most severe of which is the violation of
conservation of physical quantities. We have developed a new mapping algorithm that guarantees that conserved
quantities are preserved at any resolution and reproduces the most important features in the original profiles. Our
method is practical for 1D and 2D calculations, and we are now developing integral methods (an explicit integral approach instead of using volume subsampling) that are numerically tractable in 3D.
\section*{Acknowledgments}
The authors thank Daniel Whalen for reviewing the earlier manuscript and providing many insightful comments,
the members of the CCSE at LBNL for help with \texttt{CASTRO}{}, and Hank Childs for assistance with {\it VisIt}. We
also thank Laurens Keek, Volker Bromm, Dan Kasen, Adam Burrows, and Stan Woosley for many useful discussions. All
numerical simulations were performed with allocations from the University of Minnesota Supercomputing Institute
and the National Energy Research Scientific Computing Center. This work has been supported by the DOE SciDAC
program under grants DOE-FC02-01ER41176, DOE-FC02-06ER41438, and DE-FC02-09ER41618, and by the US
Department of Energy under grant DE-FG02-87ER40328.
\section*{References}
\bibliographystyle{iopart-num}
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February 7, 2019 | Manufacturing & Prototyping| Materials
3D-Printed Rubber Repairs Itself
Billy Hurley, Digital Editorial Manager
Got a hole in your shoe? A team at USC is taking steps toward self-healing sneakers.
Researchers at the University of Southern California Viterbi School of Engineering have developed a 3D-printed rubber that repairs itself when broken or fractured.
Aside from busted footwear, the material may also help to someday support electronics and soft robotics.
We want to use those materials to 3D-print soldier armors or airplane wings.
— Professor Qiming Wang
The rubber is manufactured via a 3D-printing method known as photopolymerization, where light solidifies the liquid resin into a desired shape.
During photopolymerization, a chemical group called thiols reacts with an oxidizer to create the special self-healing component: disulfides. The disulfide group allows the broken bonds to be reformed — when the ratio is right at least.
"When we gradually increase the oxidant, the self-healing behavior becomes stronger, but the photopolymerization behavior becomes weaker," said USC Assistant Professor Qiming Wang. "There is competition between these two behaviors. And eventually we found the ratio that can enable both high self-healing and relatively rapid photopolymerization."
In the team's study, published in NPG Asia Materials, the researchers demonstrated their material's ability on a range of products, including a shoe pad, a soft robot, a multiphase composite, and an electronic sensor. (See a video demonstration below.)
Professor Wang spoke with Tech Briefs about where he wants to see the self-healing material appear next.
Tech Briefs: What inspired this idea?
Assistant Professor Qiming Wang, University of Southern California Viterbi School of Engineering: The idea is inspired by nature. Animal organs or trees can autonomously heal wounds by themselves. At the same time, they feature very complex geometries and microstructures. The existing self-healing polymers, however, cannot be easily shaped into 3D structures. This motivates us to conduct the research to search for a solution for 3D-printable self-healing materials.
A NASA 'Self-Healing'Innovation
NASA's microheater may help to repair chips and electronics.
Tech Briefs: How is the material able to repair itself? What are the essential components that enable this kind of capability?
Prof. Wang: The healing of the material is enabled by a chemical group called disulfide bonds. These bonds can autonomously reform after you break them.
The key is how to incorporate these bonds into a material that can also be 3D-printable. Eventually, we found a solution: we find that a chemical group called thiol can be incorporated with carbon double bonds to enable photopolymerization-based 3D printing, and the thiol group can be oxidized into disulfide groups by adding an oxidant. By playing with the oxidant, we find a way to synthesize a material that can be rapidly 3D-printed and rapidly self-healed.
Tech Briefs: In what industries and applications do you envision this being used?
Prof. Wang: This type of material may make impacts on the shoe companies, tire companies, robot industries, and flexible electronics. The major contribution of our research would be introducing a way to rapidly manufacture 3D structures that can heal themselves like human organs.
Tech Briefs: On what products have you have demonstrated this material so far?
Prof. Wang: We have demonstrated a number of fabricated samples. Some interesting examples include:
A shoe pad that can heal a fracture. (The shoe pad can sustain large angle twisting after healing)
A soft robot actuator that can lift a weight ten times of itself after healing a fatal fracture
A soft electronic sensor that can restore the flexibility and electric conductivity after healing a fracture.
Tech Briefs: How well did the test with the shoe go? How does the healing work exactly?
Prof. Wang: We first 3D-print a shoe pad and cut it with a blade. Then, we contact two parts with a small force and then put on a hot plate with the corresponding healing temperature (e.g., 40-60 °C). The disulfide bonds broken during the cutting process will reform around the interface to bridge the fracture interface. After healing for 2 hours, the fracture interface will be nicely healed with a smooth surface. (See Fig. 2bc in our paper for reference.)
Tech Briefs: What's next for you and your team regarding this development?
Prof. Wang: The next step is to develop 3D-printable and self-healable rigid polymers. We want to use those materials to 3D-print soldier armors or airplane wings. Just imagine when there are damages and fractures in those structures on the battlefield; they can autonomously self-heal and refunction.
The "steps" of the 3D-printer rubber as it heals. (Image Credit: Prof. Wang)
Tech Briefs: What is most exciting to you about this material and its possibilities?
Prof. Wang: The most exciting thing about this material is that it provides a new paradigm to rapidly make nature-like structures. Modern engineering is always learning from nature and acquiring inspirations from nature, but does not do better than nature. The living structures like human organs and trees can feature complex functional structures and, at the same time, heal wounds. The engineering materials and structures cannot do both.
Our research shows a possibility to borrow the wisdom of nature to enable better next-generation manufacturing engineering.
Professor Wang's research is a collaboration with Viterbi students Kunhao Yu, An Xin, and Haixu Du, and University of Connecticut Assistant Professor Ying Li.
What do you think? How do you envision this kind of self-healing material being used? Share your comments and questions below.
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Nicetius can refer to:
Nicetius, bishop of Trier
Nicetius of Lyon, bishop of Lyon
Nicetius of Provence, rector of Provence
|
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\section{Introduction}
The Stewart platform is a parallel manipulator with six degrees of freedom \cite{Merlet}.
We will use the (standard) variables $x, y, z, pitch, roll$ and $yaw$,
where $x,y$ and $z$ are
the coordinates of the centre of the top platform, and $pitch, roll$ and $yaw$ denote the Euler angles
defining the inclination of this platform with respect to the bottom platform,
see Figure \ref{fig1}.
\begin{figure}[ht]
\begin{center} \epsfig{figure=stewart.eps,width=8cm}
\caption{The Stewart platform.}
\label{fig1}
\end{center}
\end{figure}
The aim of this paper is to study the singular manifold which is defined by the
physical configurations for which it will not be possible to determine the
position of the platform uniquely by fixing the lengths of the legs. This is a
well-known problem in parallel manipulators\cite{Merlet}.
The solution to the forward kinematics problem naturally divides into two cases,
namely, a singular and a non-singular. In the non-singular case we recall the
work\cite{JiWu01} of Ji and Wu and show that there are $8$ possible isolated
singular solutions that correspond to the same legs lengths. In the singular
case we extend the previous analysis and show how to obtain, for a given set of
length legs, a set of singular solutions all of them parameterized by a scalar
parameter. These solutions are a continuous curves in position space and in
rotation space in which the platform moves without changing the values of the
leg lengths. This fully characterize the singular manifold and shows that the
platform is, in this case, completely singular.
Spatial rotations in three dimensions can be parameterized\cite{JiWu01,Diebel06} using both Euler
angles $(\phi, \theta,\psi)$
and unit quaternions $\mathbf{q}=(q_0,q_1,q_2,q_3)$, $\vert\vert
\mathbf{q}\vert\vert=1$. A unit quaternion may be described as a vector in
$\mathbbm{R}^4$
\begin{eqnarray}
\label{eq:quaternion}
\mathbf{q}&=&(q_0,q_1,q_2,q_3),\\
\mathbf{q}^T\mathbf{q}&=& q_0^2+q_1^2+q_2^2+q_3^2=1.
\end{eqnarray}
The rotation matrix is given by
\begin{eqnarray}
R=\left(
\begin{matrix}2q_0^2-1+2q_1^2&2q_1q_2-2q_0q_3&2q_0q_2+2q_1q_3\cr 2q_1q_2+2q_0q_3&2q_0^2-1+2q_2^2&2q_2q_3-2q_0q_1\cr
2q_1q_3-2q_0q_2&2q_0q_1+2q_2q_3&2q_0^2-1+2q_3^2
\end{matrix}
\right).
\end{eqnarray}
Consider the Stewart platform shown
in Figure \ref{fig1}. As shown there, the two coordinate systems $O$ and $O'$ are
fixed to the base and the mobile platforms. The
platform geometry can be described by vectors $\mathbf{L}_i$, $i=1,2,\ldots, 6$,
defined by $\mathbf{L}_i=\mathbf{P}+\mathbf{T}_i-\mathbf{B}_i$,
$i=1,2,\ldots, 6$, where $\mathbf{B}_i$ and $\mathbf{T}_i$ are the base and top
vertices coordinates, respectively, and $\mathbf{P}$ is the center point of the
top plate. We assume that these
points are related by
\begin{eqnarray}
\mathbf{T}_i= \mu A \mathbf{B}_i,\qquad i=1,2,\ldots, 6,
\end{eqnarray}
where $A$ is a $3\times 3$ orthogonal matrix ($A^T A=I$, where $I$ is the
$3\times 3$ identity matrix) and $\mu \in ]0,1[$ is called the rescaling
factor. The coordinates of the base vertices are given by
\begin{eqnarray}
\mathbf{B}_i=(x_i,y_i,0),\qquad i=1,2,\ldots, 6.
\end{eqnarray}
Given the position $\mathbf{P}=(x,y,z)$ and the transformation matrix $R$
between the two coordinate systems, the leg vectors may be written as
\begin{eqnarray}
\mathbf{L}_i&=&\mathbf{T}_i-\mathbf{B}_i+\mathbf{P},\\
&=& (\mu R A -I)\mathbf{B}_i + \mathbf{P},\qquad i=1,2,\ldots, 6.
\label{eq:Lv}
\end{eqnarray}
So the length for each $i$-leg is given by
\begin{equation}
\label{eq:L}
\mathbf{L}_i^{~T}\mathbf{L}_i = \left((\mu R A -I)\mathbf{B}_i + \mathbf{P}\right)^T \left((\mu R A -I)\mathbf{B}_i + \mathbf{P}\right)
\end{equation}
Given $\mathbf{q}$, $A$ and $\mathbf{P}$ the leg lengths are given by
\begin{equation}
\label{eq:Lnorm}
L_i = \sqrt{\left((\mu R A -I)\mathbf{B}_i + \mathbf{P}\right)^T \left((\mu R A -I)\mathbf{B}_i + \mathbf{P}\right)}.
\end{equation}
\section{Forward kinematics}
In the forward kinematics the six leg lengths $L_i$, $i=1,2,\ldots, 6$, are given, while $R$ and $\mathbf{P}$ are
unknown. Let ${\mathbf{e}_x}=(1,0,0)$, ${\mathbf{e}_y}=(0,1,0)$, ${\mathbf{e}_z}=(0,0,1)$ and expand (\ref{eq:L}), then one gets,
\begin{eqnarray}
L_i^2&=&\mathbf{P}^T\mathbf{P}+\mathbf{B}_i^{~T}\left((\mu (R A)^T-I)(\mu R A
-I)\right)\mathbf{B}_i\nonumber\\\qquad
&& + 2\mathbf{B}_i^{~T}(\mu(R A)^T-I)\mathbf{P},
\end{eqnarray}
or
\begin{eqnarray}
L_i^2&=&\mathbf{P}^T\mathbf{P}+2x_i\left({\mathbf{e}_x}^T(\mu (R A)^T \mathbf{P}-\mathbf{P})\right)+2y_i\left({\mathbf{e}_y}^T(\mu (R A)^T
\mathbf{P}-\mathbf{P})\right)\nonumber\\\qquad
&& -2\mu\left[x_i^2({\mathbf{e}_x}^T R A {\mathbf{e}_x})+x_i y_i({\mathbf{e}_x}^T R A {\mathbf{e}_y} +{\mathbf{e}_y}^T R A {\mathbf{e}_x})\right. \nonumber\\\qquad
&&\left.+y_i^2(\mu{\mathbf{e}_y}^T R A{\mathbf{e}_y})\right]+(1+\mu^2)(x_i^2+y_i^2).
\label{eq:L_F_K}
\end{eqnarray}
Define $\mathbf{w}=(w_1,w_2,w_3,w_4,w_5,w_6)$ as
\begin{eqnarray}
w_1&=&\mathbf{P}^T \mathbf{P}\label{eq:w1},\\
w_2&=& 2\mu{\mathbf{e}_x}^T((R A)^T\mathbf{P}-\mathbf{P})\label{eq:w2},\\
w_3&=& 2\mu{\mathbf{e}_y}^T((R A)^T\mathbf{P}-\mathbf{P}\label{eq:w3}),\\
w_4&=& -2\mu{\mathbf{e}_x}^T RA{\mathbf{e}_x}\label{eq:w4},\\
w_5&=& -2\mu(\left({\mathbf{e}_x}^T RA{\mathbf{e}_y} +{\mathbf{e}_y}^T RA{\mathbf{e}_x}\right)\label{eq:w5},\\
w_6&=& -2\mu{\mathbf{e}_y}^T RA{\mathbf{e}_y}\label{eq:w6},
\end{eqnarray}
and $\mathbf{d}=(d_1,d_2,d_3,d_4,d_5,d_6)$, where
\begin{eqnarray}
\label{eq:d}
d_i=L_i^2-(1+\mu^2)(x_i^2+y_i^2),\qquad i=1,2,\ldots, 6.
\end{eqnarray}
Then relation (\ref{eq:L_F_K}) can be written as a linear system with the form
\begin{eqnarray}
\label{eq:ls}
Q \mathbf{w}=\mathbf{d},
\end{eqnarray}
where the matrix $Q$ is given by
\begin{eqnarray}
\label{eq:Maux}
Q=\left(\begin{matrix}
1&x_1&y_1&x_1^2&x_1 y_1&y_1^2\cr
1&x_2&y_2&x_2^2&x_2 y_2&y_2^2\cr
1&x_3&y_3&x_3^2&x_3 y_3&y_3^2\cr
1&x_4&y_4&x_4^2&x_4 y_4&y_4^2\cr
1&x_5&y_5&x_5^2&x_5 y_5&y_5^2\cr
1&x_6&y_6&x_6^2&x_6 y_6&y_6^2\cr
\end{matrix}
\right).
\end{eqnarray}
Note that if the base points are all different and belong to a conic section then $\det Q =0$.
The matrix given by (\ref{eq:Maux}) corresponds to the well known Braikenridge-Maclaurin construction.
In the next sections we will show that one can obtain the rotation matrix $R$
and the position $\mathbf{P}$ in terms of
the solution $\mathbf{w}=(w_1,w_2,\ldots,w_6)$ of the linear system given by
(\ref{eq:ls}). The solution to the forward
kinematics problem naturally divides into two cases, namely, a non-singular case
where $\det Q\ne 0$ and a singular case where $\det Q=0$.
In the singular case, we
obtain for a given set of length legs, $L_1,L_2,\ldots,L_6$, a singular solution parameterized by a scalar
parameter. These solutions are curves in position space and in rotation space in
which the platform moves without changing the values of the leg lengths.
\subsection{Non-singular case}
In the case where the six base vertices are not on a conic section, one gets
$\det Q\ne 0$, and so the solution of (\ref{eq:ls}),
$\mathbf{w}=(w_1,w_2,w_3,w_4,w_5)$, can be obtained from
\begin{eqnarray}
\mathbf{w}=Q^{-1}d.
\end{eqnarray}
The first three equations (\ref{eq:w1}), (\ref{eq:w2}) and (\ref{eq:w3})
determines the rotation parameters, namely,
$\mathbf{q}$, and the last three (\ref{eq:w4}), (\ref{eq:w5}) and (\ref{eq:w6})
the position $\mathbf{P}=(x,y,z)$.
To determine the rotation parameters consider the equations
\begin{eqnarray}
w_4&=&-2 \mu \left(2 { q_1}^2+2 { q_0}^2-1\right),\\
w_5&=&-8 \mu { q_1} { q_2}\label{eq:q1q2}, \\
w_6&=&-2 \mu \left(2 { q_2}^2+2 { q_0}^2-1\right),
\end{eqnarray}
which are obtained from (\ref{eq:w4}), (\ref{eq:w5}) and (\ref{eq:w6}), respectively.
Eliminating $q_0$, one gets,
\begin{eqnarray}
{ q_1}^2- {q_2}^2&=&-(w_4-w_6)/(4\mu),\\
{ q_1} { q_2} &=&-w_5/(8\mu).
\end{eqnarray}
Let
\begin{eqnarray}
\alpha=\frac{w_4-w_6}{4\mu},\qquad \beta= -\frac{w_5}{8\mu}.
\end{eqnarray}
Then the above equations can be written as
\begin{eqnarray}
q_1^4+\alpha q_1^2-\beta^2&=&0,\\
q_2^4-\alpha q_2^2-\beta^2&=&0.
\end{eqnarray}
So,
\begin{eqnarray}
q_1^2&=& \frac{-\alpha+\gamma}{2},\label{eq:q1sol}\\
q_2^2&=& \frac{\alpha+\gamma}{2},\label{eq:q2sol}
\end{eqnarray}
where
\begin{eqnarray}
\gamma=\sqrt{\alpha^2+4\beta^2}.
\end{eqnarray}
Substituting yields
\begin{eqnarray}
q_3^2&=& \frac{1}{2} + \frac{w_4}{4\mu}-\frac{\alpha+\gamma}{2},\label{eq:q3sol}\\
q_0^2&=&\frac{1}{2}- \frac{w_4}{4\mu}+\frac{\alpha-\gamma}{2}.\label{eq:q0sol}
\end{eqnarray}
Assuming $q_0\ge 0$ and that (\ref{eq:q3sol}) and (\ref{eq:q2sol}) have two
roots each, then, $q_1$ is determined by (\ref{eq:q1q2}).
Consequently, we have a total of four different quaternions. These are
\begin{eqnarray}
\mathbf{s_1}&=&(\bar q_0,\bar q_1,\bar q_2,\bar q_3),\\
\mathbf{s_2}&=&(\bar q_0,\bar q_1,\bar q_2,-\bar q_3),\\
\mathbf{s_3}&=&(\bar q_0,-\bar q_1,-\bar q_2,\bar q_3),\\
\mathbf{s_4}&=&(\bar q_0,-\bar q_1,-\bar q_2,-\bar q_3),
\end{eqnarray}
where $(\bar q_0,\bar q_1,\bar q_2,\bar q_3)$ are the roots.
To determine the position, consider the equations
\begin{eqnarray}
\mathbf{u}^T&=&2\mu{\mathbf{e}_x}^T((R A)^T-I),\\
\mathbf{v}^T&=&2\mu{\mathbf{e}_y}^T((R A)^T-I).
\end{eqnarray}
Thus
\begin{eqnarray}
\mathbf{P}^T\mathbf{P}&=&w_1,\label{eq:sphere}\\
\mathbf{u}^T\mathbf{P} &=&w_2,\label{eq:plane1}\\
\mathbf{v}^T\mathbf{P} &=&w_3,\label{eq:plane2}
\end{eqnarray}
Obviously (\ref{eq:plane1}) and (\ref{eq:plane2}) represent two planes and their
intersection is a line with equation given by
\begin{eqnarray}
\label{eq:line}
\mathbf{P}=\mathbf{r}_0+t \mathbf{r}_1,
\end{eqnarray}
where $t$ is the parameter of the line. The vectors $\mathbf{r}_0$ and $\mathbf{r}_1$ are given by
\begin{eqnarray}
\mathbf{r}_0&=&\frac{(\mathbf{v}^T\mathbf{v})w_2-(\mathbf{u}^T\mathbf{v})w_3}{(\mathbf{u}^T
\mathbf{u})(\mathbf{v}^T\mathbf{v})-(\mathbf{u}^T\mathbf{v})^2}\mathbf{u}-
\frac{-(\mathbf{u}^T\mathbf{v})w_2+(\mathbf{u}^T\mathbf{u})w_3}{(\mathbf{u}^T
\mathbf{u})(\mathbf{v}^T\mathbf{v})-(\mathbf{u}^T\mathbf{v})^2}\mathbf{v},\\
\mathbf{r}_1&=&\frac{\mathbf{u}\times \mathbf{v}}{\vert\vert\mathbf{u}\times \mathbf{v}\vert\vert}.
\end{eqnarray}
The line (\ref{eq:line}) intersects the sphere (\ref{eq:sphere}) at two points $P_\pm$ given by
\begin{eqnarray}
P_\pm&=& \mathbf{r}_0\pm t^*\mathbf{r}_1,\\
\end{eqnarray}
where
\begin{eqnarray}
t^*=\sqrt{w_1-\mathbf{r}_0^T\mathbf{r}_0}.
\end{eqnarray}
Note that in order to $P_\pm$ exist one should have
\begin{eqnarray}
\label{eq:t*}
w_1\ge \mathbf{r}_0^T\mathbf{r}_0.
\end{eqnarray}
So, both $R$ and $\mathbf{P}$ are found, and totally they have eight possible
different solutions for a given set of leg lengths.
\subsection{Singular case\label{sing}}
In this case, we assume that all points belong to a circle $x_i^2+y_i^2=1$ (we can assume $r=1$ without loss of
generality), $i=1,2,\ldots,6$. In this case the matrix
\begin{eqnarray}
\label{eq:QCirc}
Q=\left(\begin{matrix}
1&x_1&y_1&x_1^2&x_1 y_1&1-x_1^2\cr
1&x_2&y_2&x_2^2&x_2 y_2&1-x_2^2\cr
1&x_3&y_3&x_3^2&x_3 y_3&1-x_3^2\cr
1&x_4&y_4&x_4^2&x_4 y_4&1-x_4^2\cr
1&x_5&y_5&x_5^2&x_5 y_5&1-x_5^2\cr
1&x_6&y_6&x_6^2&x_6 y_6&1-x_6^2\cr
\end{matrix}\right)
\end{eqnarray}
is singular, that is, $\det Q=0$ and in fact, if all points are different and
belong to a conic
section the rank of $Q$ is five (corresponding to the Braikenridge-Maclaurin
construction). This will be the case if
$x_i^2+y_i^2=1$, $i=1,2,\ldots,6$, and $(x_i,y_i)\ne(x_j,y_j)$ for $i\ne j$, $i,j=1,2,\ldots,6$.
This fact enables us to explicitly compute the $LU$ factorization of the matrix
$Q$ in terms of the coordinate of the vertices of the base $(x_i,y_i)$,
$i=1,2,\ldots,6$. These expressions are to big to be shown here but a script for
the Maxima computer algebra system\cite{Maxima:CAS} is available upon request to the author.
So the linear system $Q\mathbf{w}=d$ can be put into the for
\begin{eqnarray}
\label{eq:lnLU}
U\mathbf{w}=L^{-1}d,
\end{eqnarray}
where $\det L=1$ and $U$ is a matrix with rank $5$. The solution of
(\ref{eq:lnLU}) is given in terms of a
solution $(w_2,w_3,w_4,w_5,w_6)$ which depends on the value of $w_1$, which
we take to be a free parameter. Notice that any other quantity could be used
for this purpose, although expression (\ref{eq:sphere}) suggests that $w_1$ is
the good choice. So the
expressions given by (\ref{eq:q1sol}), (\ref{eq:q2sol}), (\ref{eq:q3sol}) and
(\ref{eq:q0sol}) can be used to determine
the the values of the quaternion $\mathbf{q}$, the rotation matrix, and the
point $\mathbf{P}$ as a function of the
free parameter $w_1$.
\section{Conclusions}
The singular manifold of a Stewart platform is define by
the physical configurations for which it will not be possible to determine the
position of the platform uniquely by fixing the lengths of the legs. By
considering a simple Stewart platform, for which the base vertices are in a
circle (although the result naturally holds for any conic section)
and the bottom and top plates are related by a rotation and a
contraction, it was shown that the platform is always in a singular configuration.
It was also shown how to characterize the singular manifold in this case and how it
can be parameterize by a scalar parameter.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,193
|
Mercedes SL-Class SL 400 AMG Line 2dr 9G-Tronic 2019 Review | What Car?
What Car? will save you at least £16,911, but our approved dealers could save you even more.
This twin-turbocharged is found in the SL 400 and offers the best mix of performance and running costs. It makes a decent noise, too.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,981
|
Virgisporangium aurantiacum is a species of bacteria. It is a motile and spored species found in soil.
References
Further reading
Whitman, William B., et al., eds. Bergey's manual® of systematic bacteriology. Vol. 5. Springer, 2012.
External links
LPSN
Type strain of Virgisporangium aurantiacum at BacDive - the Bacterial Diversity Metadatabase
Micromonosporaceae
Bacteria described in 2001
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,884
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,738
|
require 'spec_helper.rb'
describe 'UsAppToPerson' do
it "can create" do
@holodeck.mock(Twilio::Response.new(500, ''))
expect {
@client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person.create(brand_registration_sid: 'BNXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX', description: 'description', message_samples: ['message_samples'], us_app_to_person_usecase: 'us_app_to_person_usecase', has_embedded_links: true, has_embedded_phone: true)
}.to raise_exception(Twilio::REST::TwilioError)
values = {
'BrandRegistrationSid' => 'BNXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX',
'Description' => 'description',
'MessageSamples' => Twilio.serialize_list(['message_samples']) { |e| e },
'UsAppToPersonUsecase' => 'us_app_to_person_usecase',
'HasEmbeddedLinks' => true,
'HasEmbeddedPhone' => true,
}
expect(
@holodeck.has_request?(Holodeck::Request.new(
method: 'post',
url: 'https://messaging.twilio.com/v1/Services/MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX/Compliance/Usa2p',
data: values,
))).to eq(true)
end
it "receives create responses" do
@holodeck.mock(Twilio::Response.new(
201,
%q[
{
"sid": "QE2c6890da8086d771620e9b13fadeba0b",
"account_sid": "ACaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"brand_registration_sid": "BNaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"messaging_service_sid": "MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"description": "Send marketing messages about sales to opted in customers.",
"message_samples": [
"EXPRESS: Denim Days Event is ON",
"LAST CHANCE: Book your next flight for just 1 (ONE) EUR"
],
"us_app_to_person_usecase": "MARKETING",
"has_embedded_links": true,
"has_embedded_phone": false,
"campaign_status": "PENDING",
"campaign_id": "CXaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"is_externally_registered": false,
"rate_limits": {
"att": {
"mps": 600,
"msg_class": "A"
},
"tmobile": {
"brand_tier": "TOP"
}
},
"message_flow": "End users opt-in by visiting www.example.com and adding their phone number. They then check a box agreeing to receive text messages from Example Brand. Additionally, end users can also opt-in by texting START to (111) 222-3333 to opt in.",
"opt_in_message": "Acme Corporation: You are now opted-in. For help, reply HELP. To opt-out, reply STOP",
"opt_out_message": "You have successfully been unsubscribed from Acme Corporation. You will not receive any more messages from this number.",
"help_message": "Acme Corporation: Please visit www.example.com to get support. To opt-out, reply STOP.",
"opt_in_keywords": [
"START"
],
"opt_out_keywords": [
"STOP"
],
"help_keywords": [
"HELP"
],
"date_created": "2021-02-18T14:48:52Z",
"date_updated": "2021-02-18T14:48:52Z",
"url": "https://messaging.twilio.com/v1/Services/MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa/Compliance/Usa2p/QE2c6890da8086d771620e9b13fadeba0b",
"mock": false
}
]
))
actual = @client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person.create(brand_registration_sid: 'BNXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX', description: 'description', message_samples: ['message_samples'], us_app_to_person_usecase: 'us_app_to_person_usecase', has_embedded_links: true, has_embedded_phone: true)
expect(actual).to_not eq(nil)
end
it "receives create_with_defaults responses" do
@holodeck.mock(Twilio::Response.new(
201,
%q[
{
"sid": "QE2c6890da8086d771620e9b13fadeba0b",
"account_sid": "ACaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"brand_registration_sid": "BNaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"messaging_service_sid": "MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"description": "Send marketing messages about sales to opted in customers.",
"message_samples": [
"EXPRESS: Denim Days Event is ON",
"LAST CHANCE: Book your next flight for just 1 (ONE) EUR"
],
"us_app_to_person_usecase": "MARKETING",
"has_embedded_links": true,
"has_embedded_phone": false,
"campaign_status": "PENDING",
"campaign_id": "CXaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"is_externally_registered": false,
"rate_limits": {
"att": {
"mps": 600,
"msg_class": "A"
},
"tmobile": {
"brand_tier": "TOP"
}
},
"message_flow": "End users opt-in by visiting www.example.com and adding their phone number. They then check a box agreeing to receive text messages from Example Brand. Additionally, end users can also opt-in by texting START to (111) 222-3333 to opt in.",
"opt_in_message": "Acme Corporation: You are now opted-in. For help, reply HELP. To opt-out, reply STOP",
"opt_out_message": "You have successfully been unsubscribed. You will not receive any more messages from this number. Reply START to resubscribe.",
"help_message": "Reply STOP to unsubscribe. Msg&Data Rates May Apply.",
"opt_in_keywords": [
"START"
],
"opt_out_keywords": [
"STOP",
"STOPALL",
"UNSUBSCRIBE",
"CANCEL",
"END",
"QUIT"
],
"help_keywords": [
"HELP",
"INFO"
],
"date_created": "2021-02-18T14:48:52Z",
"date_updated": "2021-02-18T14:48:52Z",
"url": "https://messaging.twilio.com/v1/Services/MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa/Compliance/Usa2p/QE2c6890da8086d771620e9b13fadeba0b",
"mock": false
}
]
))
actual = @client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person.create(brand_registration_sid: 'BNXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX', description: 'description', message_samples: ['message_samples'], us_app_to_person_usecase: 'us_app_to_person_usecase', has_embedded_links: true, has_embedded_phone: true)
expect(actual).to_not eq(nil)
end
it "can delete" do
@holodeck.mock(Twilio::Response.new(500, ''))
expect {
@client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person('QEXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX').delete()
}.to raise_exception(Twilio::REST::TwilioError)
expect(
@holodeck.has_request?(Holodeck::Request.new(
method: 'delete',
url: 'https://messaging.twilio.com/v1/Services/MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX/Compliance/Usa2p/QEXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX',
))).to eq(true)
end
it "receives delete responses" do
@holodeck.mock(Twilio::Response.new(
204,
nil,
))
actual = @client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person('QEXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX').delete()
expect(actual).to eq(true)
end
it "can read" do
@holodeck.mock(Twilio::Response.new(500, ''))
expect {
@client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person.list()
}.to raise_exception(Twilio::REST::TwilioError)
expect(
@holodeck.has_request?(Holodeck::Request.new(
method: 'get',
url: 'https://messaging.twilio.com/v1/Services/MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX/Compliance/Usa2p',
))).to eq(true)
end
it "receives read_full responses" do
@holodeck.mock(Twilio::Response.new(
200,
%q[
{
"compliance": [
{
"sid": "QE2c6890da8086d771620e9b13fadeba0b",
"account_sid": "ACaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"brand_registration_sid": "BNaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"messaging_service_sid": "MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"description": "Send marketing messages about sales to opted in customers.",
"message_samples": [
"EXPRESS: Denim Days Event is ON",
"LAST CHANCE: Book your next flight for just 1 (ONE) EUR"
],
"us_app_to_person_usecase": "MARKETING",
"has_embedded_links": true,
"has_embedded_phone": false,
"campaign_status": "PENDING",
"campaign_id": "CXaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"is_externally_registered": false,
"rate_limits": {
"att": {
"mps": 600,
"msg_class": "A"
},
"tmobile": {
"brand_tier": "TOP"
}
},
"message_flow": "End users opt-in by visiting www.example.com and adding their phone number. They then check a box agreeing to receive text messages from Example Brand. Additionally, end users can also opt-in by texting START to (111) 222-3333 to opt in.",
"opt_in_message": "Acme Corporation: You are now opted-in. For help, reply HELP. To opt-out, reply STOP",
"opt_out_message": "You have successfully been unsubscribed from Acme Corporation. You will not receive any more messages from this number.",
"help_message": "Acme Corporation: Please visit www.example.com to get support. To opt-out, reply STOP.",
"opt_in_keywords": [
"START"
],
"opt_out_keywords": [
"STOP"
],
"help_keywords": [
"HELP"
],
"date_created": "2021-02-18T14:48:52Z",
"date_updated": "2021-02-18T14:48:52Z",
"url": "https://messaging.twilio.com/v1/Services/MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa/Compliance/Usa2p/QE2c6890da8086d771620e9b13fadeba0b",
"mock": false
}
],
"meta": {
"page": 0,
"page_size": 50,
"first_page_url": "https://messaging.twilio.com/v1/Services/MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa/Compliance/Usa2p?PageSize=50&Page=0",
"previous_page_url": null,
"next_page_url": null,
"url": "https://messaging.twilio.com/v1/Services/MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa/Compliance/Usa2p?PageSize=50&Page=0",
"key": "compliance"
}
}
]
))
actual = @client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person.list()
expect(actual).to_not eq(nil)
end
it "can fetch" do
@holodeck.mock(Twilio::Response.new(500, ''))
expect {
@client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person('QEXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX').fetch()
}.to raise_exception(Twilio::REST::TwilioError)
expect(
@holodeck.has_request?(Holodeck::Request.new(
method: 'get',
url: 'https://messaging.twilio.com/v1/Services/MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX/Compliance/Usa2p/QEXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX',
))).to eq(true)
end
it "receives fetch responses" do
@holodeck.mock(Twilio::Response.new(
200,
%q[
{
"sid": "QE2c6890da8086d771620e9b13fadeba0b",
"account_sid": "ACaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"brand_registration_sid": "BNaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"messaging_service_sid": "MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"description": "Send marketing messages about sales to opted in customers.",
"message_samples": [
"EXPRESS: Denim Days Event is ON",
"LAST CHANCE: Book your next flight for just 1 (ONE) EUR"
],
"us_app_to_person_usecase": "MARKETING",
"has_embedded_links": true,
"has_embedded_phone": false,
"campaign_status": "PENDING",
"campaign_id": "CXaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"is_externally_registered": false,
"rate_limits": {
"att": {
"mps": 600,
"msg_class": "A"
},
"tmobile": {
"brand_tier": "TOP"
}
},
"message_flow": "End users opt-in by visiting www.example.com and adding their phone number. They then check a box agreeing to receive text messages from Example Brand. Additionally, end users can also opt-in by texting START to (111) 222-3333 to opt in.",
"opt_in_message": "Acme Corporation: You are now opted-in. For help, reply HELP. To opt-out, reply STOP",
"opt_out_message": "You have successfully been unsubscribed from Acme Corporation. You will not receive any more messages from this number.",
"help_message": "Acme Corporation: Please visit www.example.com to get support. To opt-out, reply STOP.",
"opt_in_keywords": [
"START"
],
"opt_out_keywords": [
"STOP"
],
"help_keywords": [
"HELP"
],
"date_created": "2021-02-18T14:48:52Z",
"date_updated": "2021-02-18T14:48:52Z",
"url": "https://messaging.twilio.com/v1/Services/MGaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa/Compliance/Usa2p/QE2c6890da8086d771620e9b13fadeba0b",
"mock": false
}
]
))
actual = @client.messaging.v1.services('MGXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') \
.us_app_to_person('QEXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX').fetch()
expect(actual).to_not eq(nil)
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 274
|
\section{Introduction}
\file{elsarticle.cls} is a thoroughly re-written document class
for formatting \LaTeX{} submissions to Elsevier journals.
The class uses the environments and commands defined in \LaTeX{} kernel
without any change in the signature so that clashes with other
contributed \LaTeX{} packages such as \file{hyperref.sty},
\file{preview-latex.sty}, etc., will be minimal.
\file{elsarticle.cls} is primarily built upon the default
\file{article.cls}. This class depends on the following packages
for its proper functioning:
\begin{enumerate}
\item \file{natbib.sty} for citation processing;
\item \file{geometry.sty} for margin settings;
\item \file{fleqn.clo} for left aligned equations;
\item \file{graphicx.sty} for graphics inclusion;
\item \file{txfonts.sty} optional font package, if the document is to
be formatted with Times and compatible math fonts;
\item \file{hyperref.sty} optional packages if hyperlinking is
required in the document;
\item \file{endfloat.sty} optional packages if floats to be placed at
end of the PDF.
\end{enumerate}
All the above packages (except some optional packages) are part of any
standard \LaTeX{} installation. Therefore, the users need not be
bothered about downloading any extra packages. Furthermore, users are
free to make use of \textsc{ams} math packages such as
\file{amsmath.sty}, \file{amsthm.sty}, \file{amssymb.sty},
\file{amsfonts.sty}, etc., if they want to. All these packages work in
tandem with \file{elsarticle.cls} without any problems.
\section{Major Differences}
Following are the major differences between \file{elsarticle.cls}
and its predecessor package, \file{elsart.cls}:
\begin{enumerate}[\textbullet]
\item \file{elsarticle.cls} is built upon \file{article.cls}
while \file{elsart.cls} is not. \file{elsart.cls} redefines
many of the commands in the \LaTeX{} classes/kernel, which can
possibly cause surprising clashes with other contributed
\LaTeX{} packages;
\item provides preprint document formatting by default, and
optionally formats the document as per the final
style of models $1+$, $3+$ and $5+$ of Elsevier journals;
\item some easier ways for formatting \verb+list+ and
\verb+theorem+ environments are provided while people can still
use \file{amsthm.sty} package;
\item \file{natbib.sty} is the main citation processing package
which can comprehensively handle all kinds of citations and
works perfectly with \file{hyperref.sty} in combination with
\file{hypernat.sty};
\item long title pages are processed correctly in preprint and
final formats.
\end{enumerate}
\section{Installation}
The package is available at author resources page at Elsevier
(\url{http://www.elsevier.com/locate/latex}).
It can also be found in any of the nodes of the Comprehensive
\TeX{} Archive Network (\textsc{ctan}), one of the primary nodes
being
\url{http://tug.ctan.org/tex-archive/macros/latex/contrib/elsarticle/}.
Please download the \file{elsarticle.dtx} which is a composite
class with documentation and \file{elsarticle.ins} which is the
\LaTeX{} installer file. When we compile the
\file{elsarticle.ins} with \LaTeX{} it provides the class file,
\file{elsarticle.cls} by
stripping off all the documentation from the \verb+*.dtx+ file.
The class may be moved or copied to a place, usually,
\verb+$TEXMF/tex/latex/elsevier/+,
or a folder which will be read
by \LaTeX{} during document compilation. The \TeX{} file
database needs updation after moving/copying class file. Usually,
we use commands like \verb+mktexlsr+ or \verb+texhash+ depending
upon the distribution and operating system.
\section{Usage}\label{sec:usage}
The class should be loaded with the command:
\begin{vquote}
\documentclass[<options>]{elsarticle}
\end{vquote}
\noindent where the \verb+options+ can be the following:
\begin{description}
\item [{\tt\color{verbcolor} preprint}] default option which format the
document for submission to Elsevier journals.
\item [{\tt\color{verbcolor} review}] similar to the \verb+preprint+
option, but increases the baselineskip to facilitate easier review
process.
\item [{\tt\color{verbcolor} 1p}] formats the article to the look and
feel of the final format of model 1+ journals. This is always single
column style.
\item [{\tt\color{verbcolor} 3p}] formats the article to the look and
feel of the final format of model 3+ journals. If the journal is a two
column model, use \verb+twocolumn+ option in combination.
\item [{\tt\color{verbcolor} 5p}] formats for model 5+ journals. This
is always of two column style.
\item [{\tt\color{verbcolor} authoryear}] author-year citation style of
\file{natbib.sty}. If you want to add extra options of
\file{natbib.sty}, you may use the options as comma delimited strings
as arguments to \verb+\biboptions+ command. An example would be:
\end{description}
\begin{vquote}
\biboptions{longnamesfirst,angle,semicolon}
\end{vquote}
\begin{description}
\item [{\tt\color{verbcolor} number}] numbered citation style. Extra options
can be loaded with\linebreak \verb+\biboptions+ command.
\item [{\tt\color{verbcolor} sort\&compress}] sorts and compresses the
numbered citations. For example, citation [1,2,3] will become [1--3].
\item [{\tt\color{verbcolor} longtitle}] if front matter is unusually long, use
this option to split the title page across pages with the correct
placement of title and author footnotes in the first page.
\item [{\tt\color{verbcolor} times}] loads \file{txfonts.sty}, if
available in the system to use Times and compatible math fonts.
\item [{\tt\color{verbcolor} reversenotenum}] Use alphabets as
author--affiliation linking labels and use numbers for author
footnotes. By default, numbers will be used as author--affiliation
linking labels and alphabets for author footnotes.
\item [{\tt\color{verbcolor} lefttitle}] To move title and
author/affiliation block to flushleft. \verb+centertitle+ is the
default option which produces center alignment.
\item [{\tt\color{verbcolor} endfloat}] To place all floats at the end
of the document.
\item [{\tt\color{verbcolor} nonatbib}] To unload natbib.sty.
\item [{\tt\color{verbcolor} doubleblind}] To hide author name,
affiliation, email address etc. for double blind refereeing purpose.
\item[] All options of \file{article.cls} can be used with this
document class.
\item[] The default options loaded are \verb+a4paper+, \verb+10pt+,
\verb+oneside+, \verb+onecolumn+ and \verb+preprint+.
\end{description}
\section{Frontmatter}
There are two types of frontmatter coding:
\begin{enumerate}[(1)]
\item each author is
connected to an affiliation with a footnote marker; hence all
authors are grouped together and affiliations follow;
\pagebreak
\item authors of same affiliations are grouped together and the
relevant affiliation follows this group.
\end{enumerate}
An example of coding the first type is provided below.
\begin{vquote}
\title{This is a specimen title\tnoteref{t1,t2}}
\tnotetext[t1]{This document is the results of the research
project funded by the National Science Foundation.}
\tnotetext[t2]{The second title footnote which is a longer
text matter to fill through the whole text width and
overflow into another line in the footnotes area of the
first page.}
\end{vquote}
\begin{vquote}
\author[1]{Jos Migchielsen\corref{cor1}%
\fnref{fn1}}
\ead{J.Migchielsen@elsevier.com}
\author[2]{CV Radhakrishnan\fnref{fn2}}
\ead{cvr@sayahna.org}
\author[3]{CV Rajagopal\fnref{fn1,fn3}}
\ead[url]{www.stmdocs.in}
\end{vquote}
\begin{vquote}
\cortext[cor1]{Corresponding author}
\fntext[fn1]{This is the first author footnote.}
\fntext[fn2]{Another author footnote, this is a very long
footnote and it should be a really long footnote. But this
footnote is not yet sufficiently long enough to make two
lines of footnote text.}
\fntext[fn3]{Yet another author footnote.}
\address[1]{Elsevier B.V., Radarweg 29, 1043 NX Amsterdam,
The Netherlands}
\address[2]{Sayahna Foundations, JWRA 34, Jagathy,
Trivandrum 695014, India}
\address[3]{STM Document Engineering Pvt Ltd., Mepukada,
Malayinkil, Trivandrum 695571, India}
\end{vquote}
The output of the above \TeX{} source is given in Clips~\ref{clip1} and
\ref{clip2}. The header portion or title area is given in
Clip~\ref{clip1} and the footer area is given in Clip~\ref{clip2}.
\deforange{blue!70}
\src{Header of the title page.}
\includeclip{1}{130 612 477 707}{1psingleauthorgroup.pdf
\deforange{orange}
\deforange{blue!70}
\src{Footer of the title page.}
\includeclip{1}{93 135 499 255}{1pseperateaug.pdf
\deforange{orange}
Most of the commands such as \verb+\title+, \verb+\author+,
\verb+\address+ are self explanatory. Various components are
linked to each other by a label--reference mechanism; for
instance, title footnote is linked to the title with a footnote
mark generated by referring to the \verb+\label+ string of
the \verb=\tnotetext=. We have used similar commands
such as \verb=\tnoteref= (to link title note to title);
\verb=\corref= (to link corresponding author text to
corresponding author); \verb=\fnref= (to link footnote text to
the relevant author names). \TeX{} needs two compilations to
resolve the footnote marks in the preamble part.
Given below are the syntax of various note marks and note texts.
\begin{vquote}
\tnoteref{<label(s)>}
\corref{<label(s)>}
\fnref{<label(s)>}
\tnotetext[<label>]{<title note text>}
\cortext[<label>]{<corresponding author note text>}
\fntext[<label>]{<author footnote text>}
\end{vquote}
\noindent where \verb=<label(s)>= can be either one or more comma
delimited label strings. The optional arguments to the
\verb=\author= command holds the ref label(s) of the address(es)
to which the author is affiliated while each \verb=\address=
command can have an optional argument of a label. In the same
manner, \verb=\tnotetext=, \verb=\fntext=, \verb=\cortext= will
have optional arguments as their respective labels and note text
as their mandatory argument.
The following example code provides the markup of the second type
of author-affiliation.
\begin{vquote}
\author{Jos Migchielsen\corref{cor1}%
\fnref{fn1}}
\ead{J.Migchielsen@elsevier.com}
\address{Elsevier B.V., Radarweg 29, 1043 NX Amsterdam,
The Netherlands}
\author{CV Radhakrishnan\fnref{fn2}}
\ead{cvr@sayahna.org}
\address{Sayahna Foundations, JWRA 34, Jagathy,
Trivandrum 695014, India}
\author{CV Rajagopal\fnref{fn1,fn3}}
\ead[url]{www.stmdocs.in}
\address{STM Document Engineering Pvt Ltd., Mepukada,
Malayinkil, Trivandrum 695571, India}
\end{vquote}
\vspace*{-.5pc}
\begin{vquote}
\cortext[cor1]{Corresponding author}
\fntext[fn1]{This is the first author footnote.}
\fntext[fn2]{Another author footnote, this is a very long
footnote and it should be a really long footnote. But this
footnote is not yet sufficiently long enough to make two lines
of footnote text.}
\end{vquote}
The output of the above \TeX{} source is given in Clip~\ref{clip3}.
\deforange{blue!70}
\src{Header of the title page..}
\includeclip{1}{119 563 468 709}{1pseperateaug.pdf
\deforange{orange}
\pagebreak
Clip~\ref{clip4} shows the output after giving \verb+doubleblind+ class option.
\deforange{blue!70}
\src{Double blind article}
\includeclip{1}{124 567 477 670}{elstest-1pdoubleblind.pdf
\deforange{orange}
\vspace*{-.5pc}
The frontmatter part has further environments such as abstracts and
keywords. These can be marked up in the following manner:
\begin{vquote}
\begin{abstract}
In this work we demonstrate the formation of a new type of
polariton on the interface between a ....
\end{abstract}
\end{vquote}
\vspace*{-.5pc}
\begin{vquote}
\begin{keyword}
quadruple exiton \sep polariton \sep WGM
\end{keyword}
\end{vquote}
\noindent Each keyword shall be separated by a \verb+\sep+ command.
\textsc{msc} classifications shall be provided in
the keyword environment with the commands
\verb+\MSC+. \verb+\MSC+ accepts an optional
argument to accommodate future revisions.
eg., \verb=\MSC[2008]=. The default is 2000.\looseness=-1
\subsection{New page}
Sometimes you may need to give a page-break and start a new page after
title, author or abstract. Following commands can be used for this
purpose.
\begin{vquote}
\newpageafter{title}
\newpageafter{author}
\newpageafter{abstract}
\end{vquote}
\begin{itemize}
\leftskip-2pc
\item [] {\tt\color{verbcolor} \verb+\newpageafter{title}+} typeset the title alone on one page.
\item [] {\tt\color{verbcolor} \verb+\newpageafter{author}+} typeset the title
and author details on one page.
\item [] {\tt\color{verbcolor} \verb+\newpageafter{abstract}+}
typeset the title,
author details and abstract \& keywords one one page.
\end{itemize}
\section{Floats}
{Figures} may be included using the command, \verb+\includegraphics+ in
combination with or without its several options to further control
graphic. \verb+\includegraphics+ is provided by \file{graphic[s,x].sty}
which is part of any standard \LaTeX{} distribution.
\file{graphicx.sty} is loaded by default. \LaTeX{} accepts figures in
the postscript format while pdf\LaTeX{} accepts \file{*.pdf},
\file{*.mps} (metapost), \file{*.jpg} and \file{*.png} formats.
pdf\LaTeX{} does not accept graphic files in the postscript format.
The \verb+table+ environment is handy for marking up tabular
material. If users want to use \file{multirow.sty},
\file{array.sty}, etc., to fine control/enhance the tables, they
are welcome to load any package of their choice and
\file{elsarticle.cls} will work in combination with all loaded
packages.
\section[Theorem and ...]{Theorem and theorem like environments}
\file{elsarticle.cls} provides a few shortcuts to format theorems and
theorem-like environments with ease. In all commands the options that
are used with the \verb+\newtheorem+ command will work exactly in the same
manner. \file{elsarticle.cls} provides three commands to format theorem or
theorem-like environments:
\begin{vquote}
\newtheorem{thm}{Theorem}
\newtheorem{lem}[thm]{Lemma}
\newdefinition{rmk}{Remark}
\newproof{pf}{Proof}
\newproof{pot}{Proof of Theorem \ref{thm2}}
\end{vquote}
The \verb+\newtheorem+ command formats a
theorem in \LaTeX's default style with italicized font, bold font
for theorem heading and theorem number at the right hand side of the
theorem heading. It also optionally accepts an argument which
will be printed as an extra heading in parentheses.
\begin{vquote}
\begin{thm}
For system (8), consensus can be achieved with
$\|T_{\omega z}$
...
\begin{eqnarray}\label{10}
....
\end{eqnarray}
\end{thm}
\end{vquote}
Clip~\ref{clip5} will show you how some text enclosed between the
above code\goodbreak \noindent looks like:
\vspace*{6pt}
\deforange{blue!70}
\src{{\ttfamily\color{verbcolor}\expandafter\@gobble\string\\ newtheorem}}
\includeclip{2}{1 1 453 120}{jfigs.pdf}
\deforange{orange}
The \verb+\newdefinition+ command is the same in
all respects as its\linebreak \verb+\newtheorem+ counterpart except that
the font shape is roman instead of italic. Both
\verb+\newdefinition+ and \verb+\newtheorem+ commands
automatically define counters for the environments defined.
\vspace*{6pt}
\deforange{blue!70}
\src{{\ttfamily\color{verbcolor}\expandafter\@gobble\string\\ newdefinition}}
\includeclip{1}{1 1 453 105}{jfigs.pdf}
\deforange{orange}
The \verb+\newproof+ command defines proof environments with
upright font shape. No counters are defined.
\vspace*{6pt}
\deforange{blue!70}
\src{{\ttfamily\color{verbcolor}\expandafter\@gobble\string\\ newproof}}
\includeclip{3}{1 1 453 65}{jfigs.pdf}
\deforange{orange}
Users can also make use of \verb+amsthm.sty+ which will override
all the default definitions described above.
\section[Enumerated ...]{Enumerated and Itemized Lists}
\file{elsarticle.cls} provides an extended list processing macros
which makes the usage a bit more user friendly than the default
\LaTeX{} list macros. With an optional argument to the
\verb+\begin{enumerate}+ command, you can change the list counter
type and its attributes.
\begin{vquote}
\begin{enumerate}[1.]
\item The enumerate environment starts with an optional
argument `1.', so that the item counter will be suffixed
by a period.
\item You can use `a)' for alphabetical counter and '(i)' for
roman counter.
\begin{enumerate}[a)]
\item Another level of list with alphabetical counter.
\item One more item before we start another.
\end{vquote}
\deforange{blue!70}
\src{List -- Enumerate}
\includeclip{4}{1 1 453 185}{jfigs.pdf}
\deforange{orange}
Further, the enhanced list environment allows one to prefix a
string like `step' to all the item numbers.
\begin{vquote}
\begin{enumerate}[Step 1.]
\item This is the first step of the example list.
\item Obviously this is the second step.
\item The final step to wind up this example.
\end{enumerate}
\end{vquote}
\deforange{blue!70}
\src{List -- enhanced}
\includeclip{5}{1 1 313 83}{jfigs.pdf}
\deforange{orange}
\section{Cross-references}
In electronic publications, articles may be internally
hyperlinked. Hyperlinks are generated from proper
cross-references in the article. For example, the words
\textcolor{black!80}{Fig.~1} will never be more than simple text,
whereas the proper cross-reference \verb+\ref{tiger}+ may be
turned into a hyperlink to the figure itself:
\textcolor{blue}{Fig.~1}. In the same way,
the words \textcolor{blue}{Ref.~[1]} will fail to turn into a
hyperlink; the proper cross-reference is \verb+\cite{Knuth96}+.
Cross-referencing is possible in \LaTeX{} for sections,
subsections, formulae, figures, tables, and literature
references.
\section[Mathematical ...]{Mathematical symbols and formulae}
Many physical/mathematical sciences authors require more
mathematical symbols than the few that are provided in standard
\LaTeX. A useful package for additional symbols is the
\file{amssymb} package, developed by the American Mathematical
Society. This package includes such oft-used symbols as
$\lesssim$ (\verb+\lesssim+), $\gtrsim$ (\verb+\gtrsim+) or
$\hbar$ (\verb+\hbar+). Note that your \TeX{}
system should have the \file{msam} and \file{msbm} fonts installed. If
you need only a few symbols, such as $\Box$ (\verb+\Box+), you might try the
package \file{latexsym}.
Another point which would require authors' attention is the
breaking up of long equations. When you use
\file{elsarticle.cls} for formatting your submissions in the
\verb+preprint+ mode, the document is formatted in single column
style with a text width of 384pt or 5.3in. When this document is
formatted for final print and if the journal happens to be a double column
journal, the text width will be reduced to 224pt at for 3+
double column and 5+ journals respectively. All the nifty
fine-tuning in equation breaking done by the author goes to waste in
such cases. Therefore, authors are requested to check this
problem by typesetting their submissions in final format as well
just to see if their equations are broken at appropriate places,
by changing appropriate options in the document class loading
command, which is explained in section~\ref{sec:usage},
\nameref{sec:usage}. This allows authors to fix any equation breaking
problem before submission for publication.
\file{elsarticle.cls} supports formatting the author submission
in different types of final format. This is further discussed in
section \ref{sec:final}, \nameref{sec:final}.
\subsection*{Displayed equations and double column journals}
Many Elsevier journals print their text in two columns. Since
the preprint layout uses a larger line width than such columns,
the formulae are too wide for the line width in print. Here is an
example of an equation (see equation 6) which is perfect in a
single column preprint format:
\bigskip
\setlength\Sep{6pt}
\src{See equation (6)}
\deforange{blue!70}
\includeclip{4}{105 500 500 700}{1psingleauthorgroup.pdf}
\deforange{orange}
\noindent When this document is typeset for publication in a
model 3+ journal with double columns, the equation will overlap
the second column text matter if the equation is not broken at
the appropriate location.
\vspace*{6pt}
\deforange{blue!70}
\src{See equation (6) overprints into second column}
\includeclip{3}{59 421 532 635}{elstest-3pd.pdf}
\deforange{orange}
\vspace*{6pt}
\noindent The typesetter will try to break the equation which
need not necessarily be to the liking of the author or as it
happens, typesetter's break point may be semantically incorrect.
Therefore, authors may check their submissions for the incidence
of such long equations and break the equations at the correct
places so that the final typeset copy will be as they wish.
\section{Bibliography}
Three bibliographic style files (\verb+*.bst+) are provided ---
\file{elsarticle-num.bst}, \file{elsarticle-num-names.bst} and
\file{elsarticle-harv.bst} --- the first one can be used for the
numbered scheme, second one for numbered with new options of
\file{natbib.sty}. The third one is for the author year
scheme.
In \LaTeX{} literature, references are listed in the
\verb+thebibliography+ environment. Each reference is a
\verb+\bibitem+ and each \verb+\bibitem+ is identified by a label,
by which it can be cited in the text:
\verb+\bibitem[Elson et al.(1996)]{ESG96}+ is cited as
\verb+\citet{ESG96}+.
\noindent In connection with cross-referencing and
possible future hyperlinking it is not a good idea to collect
more that one literature item in one \verb+\bibitem+. The
so-called Harvard or author-year style of referencing is enabled
by the \LaTeX{} package \file{natbib}. With this package the
literature can be cited as follows:
\begin{enumerate}[\textbullet]
\item Parenthetical: \verb+\citep{WB96}+ produces (Wettig \& Brown, 1996).
\item Textual: \verb+\citet{ESG96}+ produces Elson et al. (1996).
\item An affix and part of a reference:
\verb+\citep[e.g.][Ch. 2]{Gea97}+ produces (e.g. Governato et
al., 1997, Ch. 2).
\end{enumerate}
In the numbered scheme of citation, \verb+\cite{<label>}+ is used,
since \verb+\citep+ or \verb+\citet+ has no relevance in the numbered
scheme. \file{natbib} package is loaded by \file{elsarticle} with
\verb+numbers+ as default option. You can change this to author-year
or harvard scheme by adding option \verb+authoryear+ in the class
loading command. If you want to use more options of the \file{natbib}
package, you can do so with the \verb+\biboptions+ command, which is
described in the section \ref{sec:usage}, \nameref{sec:usage}. For
details of various options of the \file{natbib} package, please take a
look at the \file{natbib} documentation, which is part of any standard
\LaTeX{} installation.
In addition to the above standard \verb+.bst+ files, there are 10
journal-specific \verb+.bst+ files also available.
Instruction for using these \verb+.bst+ files can be found at
\href{http://support.stmdocs.in/wiki/index.php?title=Model-wise_bibliographic_style_files}
{http://support.stmdocs.in}
\section{Graphical abstract and highlights}
A template for adding graphical abstract and highlights are available
now. This will appear as the first two pages of the PDF before the
article content begins.
\pagebreak
Please refer below to see how to code them.
\begin{vquote}
....
....
\end{abstract}
\begin{graphicalabstract}
\end{graphicalabstract}
\begin{highlights}
\item Research highlight 1
\item Research highlight 2
\end{highlights}
\begin{keyword}
....
....
\end{vquote}
\section{Final print}\label{sec:final}
The authors can format their submission to the page size and margins
of their preferred journal. \file{elsarticle} provides four
class options for the same. But it does not mean that using these
options you can emulate the exact page layout of the final print copy.
\lmrgn=3em
\begin{description}
\item [\texttt{1p}:] $1+$ journals with a text area of
384pt $\times$ 562pt or 13.5cm $\times$ 19.75cm or 5.3in $\times$
7.78in, single column style only.
\item [\texttt{3p}:] $3+$ journals with a text area of 468pt
$\times$ 622pt or 16.45cm $\times$ 21.9cm or 6.5in $\times$
8.6in, single column style.
\item [\texttt{twocolumn}:] should be used along with 3p option if the
journal is $3+$ with the same text area as above, but double column
style.
\item [\texttt{5p}:] $5+$ with text area of 522pt $\times$
682pt or 18.35cm $\times$ 24cm or 7.22in $\times$ 9.45in,
double column style only.
\end{description}
Following pages have the clippings of different parts of
the title page of different journal models typeset in final
format.
Model $1+$ and $3+$ will have the same look and
feel in the typeset copy when presented in this document. That is
also the case with the double column $3+$ and $5+$ journal article
pages. The only difference will be wider text width of
higher models. Therefore we will look at the
different portions of a typical single column journal page and
that of a double column article in the final format.
\begin{center}
\hypertarget{bsc}{}
\hyperlink{sc}{
{\bf [Specimen single column article -- Click here]}
}
\hypertarget{bsc}{}
\hyperlink{dc}{
{\bf [Specimen double column article -- Click here]}
}
\end{center}
\src{}\hypertarget{sc}{}
\deforange{blue!70}
\hyperlink{bsc}{\includeclip{1}{88 120 514 724}{elstest-1p.pdf}}
\deforange{orange}
\src{}\hypertarget{dc}{}
\deforange{blue!70}
\hyperlink{bsc}{\includeclip{1}{27 61 562 758}{elstest-5p.pdf}}
\deforange{orange}
\end{document}
\section{}
\section{Introduction}\label{intro}
Computational Fluid Dynamics (CFD) is a theoretical-method of scientific
and engineering investigation, concerned with the development and
application of a video-camera like tool (a software) which is used
for a unified cause-and-effect based analysis of a fluid-dynamics
as well as heat and mass transfer problem; presented in a recently
published book on CFD by Sharma \cite{Sharma2017}. He proposed a conservation
law based finite volume method for a discrete (independent of continuous)
mathematics based derivation of the system of algebraic equations that
are the governing equations in CFD. The CFD for a multi-fluid flow
is commonly called as Computational Multi-Fluid Dynamics (CMFD) that
involves the application of the conservation laws to each of the fluids
in the multi-fluid system. A key difference between CFD and CMFD
is the lower dimensional fluid-fluid interface that separates two fluids.
In order to track/capture the interface, various CMFD methodologies
are available in the literature. Reliability of any CMFD methodology
depends upon its ability to handle (a) the jump in thermo-physical
properties across the interface and (b) the severe changes in the
topology of the interface. Thus, a CMFD methodology demands a high level
of grid resolution $-$ especially near the interface $-$ to achieve
desired numerical accuracy. However, there must be a trade-off between
the selection of a grid strategy (for better numerical accuracy) and
the associated computational cost/time.
Front Tracking Method (FTM) (Juric and Tryggvason \cite{Juric1996})
is a CMFD method that belongs to the class of Lagrangian framework,
wherein the interface is tracked explicitly by the means of markers. However,
it demands some additional modeling in order to simulate the merger/breakup
of interfaces. Other CMFD methodologies like Volume of Fluid (VOF)
and Level Set Method (LSM) follow the Eulerian framework. In VOF
and LSM, an additional scalar field is defined which helps in capturing
interface implicitly. Volume of Fluid (Hirt and Nicholas \cite{Hirt1981})
is one of the widely adopted multi-fluid methodologies where an interface
is defined by a scalar field based on a volume fraction. Level Set Method (Osher
and Sethian \cite{Osher1988}, Sussman et al. \cite{sussman1994}) is another
interface capturing technique wherein an interface is represented
by a level set function $\phi=0$, where $\phi$ is a scalar field
defined as a signed normal distance. Implementation of surface tension
is very straightforward in LSM as the geometrical parameters can be
obtained directly with the help of the normal distance function field
for $\phi$. Detailed literature survey on level set method based
developments and applications can be found in a recent review-papers
by Sharma \cite{shrma2015} and Gibou et al. \cite{gibou2018}. Broadly,
there are two types of LSMs: Diffuse Interface Level Set Method (DI-LSM)
\cite{sussman1994} and ghost fluid method based Sharp Interface Level
Set method (SI-LSM) \cite{fedkiw1999}. The interfacial force due to surface
tension is modeled as a body-force in the DI-LSM while the SI-LSM
considers the force as the more realistic surface-force acting at
the interface (implemented as an interfacial boundary condition for
pressure-jump across the interface) \cite{shaikh2018}. The SI-LSM as compared to the DI-LSM leads to a substantial reduction in mass error \cite{shaikh2018} $-$ the biggest disadvantage of a LSM. Detrixhe and Aslam \cite{detrixhe2015} introduced an algorithm to obtain a volume fraction field from a level set function, or vice versa, with the second-order accuracy for interface location and first-order accuracy for interface normal. This algorithm can be employed to combine the respective advantages of VOF and LSM.
For most of the multi-fluid flow problems, the fluid-dynamics actions
are concentrated in the vicinity of the lower dimensional fluid-fluid
interface. The interfacial physics demands sufficiently large grid
resolution near the interface for an accurate numerical solution.
An efficient grid strategy in CMFD should generate large grid resolution
near the interfacial region as compared to far-away from the interface.
Based on this consideration, CMFD researchers have worked on the development
and implementation of computationally effective grid strategies such
as stretched/clustered non-uniform grid, nested block grid, and adaptive
mesh. Using the non-uniform grid for FTM, Thomas et al. \cite{thomas2010}
studied thin-film flows during the impact of droplets in an inclined
channel. Furthermore, using the non-uniform grid, a VOF based multi-fluid
computations was presented by several researchers: Richards et al.
\cite{richards1995} studied a jet-breakup problem, Kobayashi et al. \cite{kobayashi2004}
studied formation of emulsion droplet in micro-channels, Yanke et
al. \cite{Yanke2015} studied a electroslag remelting problem, Koukouvinis
et al. \cite{koukouvinis2016} studied bubble collapse and expansion near
the free surface, Waters et al. \cite{waters2017} studied breakup of
turbulent sprays, and Sultana et al. \cite{sultana2017} incorporated
phase change process to study droplet dynamics. Application of
the non-uniform grid for LSM was presented by a few researchers: Jarrahbashi and Sirignano
\cite{Jarrahbashi2014} for simulation of liquid-injection at high pressure,
Montazeri \& Ward \cite{Montezari2014} for proposing a numerical methodology
for generalized body force, and Vilegas et al. \cite{villegas2016,villegas2017}
for simulating leidenfrost effect. Finally, application of the non-uniform
grid for a Coupled Level Set and Volume of Fluid (CLSVOF) method was
presented by Ferrari et al. \cite{ferrari2017} for simulation of micro-scale
multi-phase flows.
\review{Another class of efficient grid strategy based numerical method is Adaptive Mesh Refinement (AMR) \cite{berger1984} which involves dynamic refinement as well as un-refinement of the grid that is based on certain predefined criteria.} The AMR based
VOF method was presented by Popinet \cite{popinet2009} and AMR based LSM
was presented by Sussman et al. \cite{sussman1999} for incompressible
multi-phase flows. Whereas, for compressible multi-phase flow, AMR
based LSM was presented by Nourgaliev and Theofanous \cite{nourgaliev2007}.
Implementation of AMR can be done using Quadtree and Octree data structures (Samet
\cite{samet1989,samet1990}) for 2D and 3D problems, respectively. Brun
et al. \cite{brun2012} used Hash Table instead of Quadtree data
structure with a local LSM \cite{adalsteinsson1995,peng1999}. In VOF framework, Theodorakakos and Bergeles \cite{theodorakakos2004} proposed adaptive mesh refinement of the interfacial cartesian grid by treating it as an unstructured mesh (\emph{i.e.} a computational cell can possess an arbitrary number of faces and neighboring cells). Recently, Antepara et al. \cite{antepara2019} studied the path instability of rising bubbles at high Reynolds number by integrating the conservative level-set method with their earlier AMR framework \cite{antepara2015} for single-phase turbulent flows. \review{Using separate grids for flow solver and interface solver, Herrmann \cite{hermann2008} proposed a Refined Level Set Grid (RLSG) Method with the purpose of simulating two-phase flows with a high-density ratio.} Using twice the number
of grid for the interface as compared to the grid for flow solver, a dual-grid
approach was proposed in our research group for DI-LSM \cite{gada2011}
that was recently extended for the SI-LSM by Shaikh et al. \cite{shaikh2019}.
Summary of the literature review, based on the various types of grid
structure and CMFD methodology, are presented in Table \ref{tab:Summary-of-literature}.
The table shows that although there is some work on adaptive mesh
refinement (AMR) for VOF method and LSM, no such work is found for
Adaptive Mesh \emph{un-Refinement} (AMuR) which is proposed in the
present work. \review{Our AMuR can be considered as a variant of the AMR, with only mesh un-refinement in the AMuR and both refinement and un-refinement of the mesh in the AMR.} The motivation for the proposition of the AMuR as compared
to the already existing AMR is the ease in the implementation of the
AMuR since it allows the usage of commonly used matrix as the \emph{structured}
data structure (with in-built neighboring information) as compared
to the AMR that requires tree-based \emph{unstructured} data structure.
Moreover, as compared to the AMR presented in the Table \ref{tab:Summary-of-literature}
which uses adaptive refinement for both flow solver and interface
solver, the AMuR proposed here considers adaptive unrefinement (of the first level) only
for the interface solver $-$ called as Adaptive interface Mesh un-Refinement
(AiMuR). Since the value of the level set function (representing the
interface) is numerically relevant only up to certain distance away
from the interface, the unrefinement is proposed away from the interface
as merging of the four Cartesian control volumes for level set function.
The motivation is to obtain almost the same accuracy, with a substantial
reduction in the computational time for the solution of level set
equations based interface solver by the AiMuR as compared to uniform/non-uniform Cartesian grid. The objective of this work is to present a detailed \textcolor{black}{CMFD methodology for AiMuR based SI-LSM (section \ref{sec:Concept-of-Semi-Adaptive} and \ref{sec:method}) (on both uniform as well as non-uniform Cartesian grid) and performance study for the AiMuR (section \ref{sec:validation}) (as compared to the results obtained without the unrefinement) on three different two-fluid flow problems: dam break simulation, }breakup of a liquid jet and drop coalescence\textcolor{black}{.}
\begin{table}
\protect\caption{\label{tab:Summary-of-literature}Summary of literature review and the present work based
on the \review{mesh type/algorithm} and computational multi-fluid dynamics (CMFD) methodology. }
\centering{}%
\begin{tabular}{|l|c|c|}
\hline
\multirow{2}{*}{Published Work} & \review{Mesh} & CMFD \tabularnewline
& \review{Type/Algorithm} & Methodology\tabularnewline
\hline
Thomas et al. \cite{thomas2010} & \multirow{2}{*}{Non-uniform grid} & \multirow{2}{*}{VOF}\tabularnewline
\cline{1-1}
Richards et al. \cite{richards1995} & & \tabularnewline
\cline{1-1}
Kobayashi et al. \cite{kobayashi2004} & & \tabularnewline
\cline{1-1}
Yanke et al. \cite{Yanke2015} & & \tabularnewline
\cline{1-1}
Koukouvinis et al. \cite{koukouvinis2016} & & \tabularnewline
\cline{1-1}
Waters et al. \cite{waters2017} & & \tabularnewline
\cline{1-1}
Sultana et al. \cite{sultana2017} & & \tabularnewline
\cline{1-1} \cline{3-3}
Jarrahbashi and Sirignano \cite{Jarrahbashi2014} & & \multirow{2}{*}{LSM}\tabularnewline
\cline{1-1}
Montazeri and Ward \cite{Montezari2014} & & \tabularnewline
\cline{1-1}
Vilegas et al. \cite{villegas2016,villegas2017} & & \tabularnewline
\cline{1-1} \cline{3-3}
Ferrai et al. \cite{ferrari2017} & & CLSVOF\tabularnewline
\hline
Popinet \cite{popinet2009} & \multirow{2}{*}{AMR} & \multirow{2}{*}{VOF}\tabularnewline
\cline{1-1}
Theodorakakos and Bergeles \cite{theodorakakos2004} & & \tabularnewline
\cline{1-1}
\cline{3-3}
Sussman et al. \cite{sussman1999} & & \multirow{2}{*}{LSM}\tabularnewline
\cline{1-1}
Nourgaliev and Theofanous \cite{nourgaliev2007} & & \tabularnewline
\cline{1-1}
Antepara et al. \cite{antepara2019} & & \tabularnewline
\cline{1-2}
Hermann \cite{hermann2008} & RLSG & \tabularnewline
\cline{1-2}
Gada and Sharma \cite{gada2011} and Shaikh et al. \cite{shaikh2019} & DGLSM & \tabularnewline
\cline{1-2}
Present work & AiMuR & \tabularnewline
\hline
\end{tabular}
\end{table}
\section{Ghost Fluid Method based Sharp-Interface Level Set Method}\label{sec3}
In two-phase flows, the interface $\Gamma$ is considered as sharp
curve separating the two disjoints $\left(\Omega\equiv\Omega_{1}\cup\Omega_{2}\right)$
as shown in Fig. \textcolor{black}{\ref{fig:Computational-domain-with}}, with $\phi>0$ in fluid-1 and $\phi<0$ in fluid-2.
For the SI-LSM based simulation of two-phase flow, the incompressible
Navier-Stokes (continuity and momentum) equations (for both the fluids)
are solved for the spatial and temporal variation of the flow field
$-$ with an interfacial boundary condition, implemented using Ghost
Fluid method \cite{fedkiw1999}. The unsteady flow field is used to obtain
the temporal variation of the interface.
\begin{figure}
\begin{centering}
\includegraphics[width=14cm]{Figure_Final/Fig1.pdf}
\par\end{centering}
\protect\caption{\label{fig:Computational-domain-with}($a$) A representative computational
domain along with two-fluid interface and non-uniform grid distribution
and of different types of pressure grid points for the two-fluid
sub-domains ($\Omega_{1}$ and $\Omega_{2}$). Mixing of pressure
grid point (from another fluid sub-domain) during the solution of
pressure Poisson equation for interfacial pressure grid points is
shown for $\Omega_{1}$ in ($b$) and for $\Omega_{2}$ in ($c$). }
\end{figure}
\subsection{\review{Single Fluid Formulation}}
For obtaining a single velocity and pressure field for both the fluids
in a two-fluid flow, a single field formulation based governing equations
and interfacial boundary conditions for SI-LSM are presented in a
recent work from our research group; separately for two-phase flow
without \cite{shaikh2018} and with \cite{shaikh2019} phase change. For
two-phase flow without phase change considered here, the various functions
used in a LSM and the formulation for sharp as well as diffuse interface
LSM are presented in-detail by Shaikh et al. \cite{shaikh2018}; thus,
the formulation is presented concisely in separate subsections below.
For the mathematical formulation, it is assumed that the interface
is massless with zero-thickness, and no-slip in tangential velocity.
Constant material properties are considered, but not equal for each
phase, \emph{i.e.}, the bulk fluids are incompressible. The surface
tension coefficient is assumed to be constant, and its tangential
variation along the interface is neglected. The effects of radiation,
viscous dissipation, and energy contribution due to interface stretching
are neglected.
\subsubsection{Governing Equations for Two-Fluid Flow Properties}\label{sec2.1.1}
Non-dimensional form of the conservation equations for the two-fluid
flow (Navier-Stokes equations) are given as
\noindent \textbf{Volume-Conservation (Continuity) Equation:}
\begin{equation}
\nabla\cdot\mathbf{U}=0,\label{eq:conti}
\end{equation}
\noindent \textbf{Momentum-Conservation Equation:}
\begin{equation}
\frac{\partial\mathbf{U}}{\partial\tau}+\nabla\cdot\left(\mathbf{U}\mathbf{U}\right)=-\frac{\nabla P}{\chi_{i}}+\frac{1}{\chi_{i}Re}\nabla\cdot\left(2\eta_{i}\mathbf{D}\right)-\frac{1}{Fr^{2}}\hat{j},\label{eq:Mom}
\end{equation}
\noindent \textcolor{black}{where rate of deformation tensor, $\mathbf{D}=0.5\left[\nabla\mathbf{U}+\left(\nabla\mathbf{U}\right)^{T}\right]$.
Furthermore, $\chi_{i}$ and $\eta_{i}$ are the non-dimensional density
and viscosity; calculated using a sharp Heaviside function }\cite{shaikh2018}\textcolor{black}{.
Also $\hat{j}$ is the unit vector for gravity ($\hat{j}=<0,-1>$).
}Using characteristic scales as $l_{c}$ for length and $u_{c}$ for
velocity, the non-dimensional spatial as well as temporal coordinates,
non-dimensional flow properties, and non-dimensional governing parameters
(Reynolds number $Re$ and Froude number $Fr$), the non-dimensional variables in the above equations
are defined as
\[
\mathbf{X}=\frac{x}{l_{c}},\,\mathbf{U}=\frac{u}{u_{c}},\,\tau=\frac{tu_{c}}{l_{c}},\: P=\frac{p}{\rho_{1}u_{c}^{2}},\: Re=\frac{\rho_{1}u_{c}l_{c}}{\mu_{1}}\mbox{ and }Fr=\frac{u_{c}}{\sqrt{gl_{c}}}.
\]
For the two-phase as compared to most of the single-phase flow, note
that the above momentum equations consist of gravity force as the
additional force while the force due to surface tension which also
appears for a two-phase flow is incorporated in the SI-LSM as an interfacial
boundary condition during the solution of pressure Poisson equation
(obtained from the above volume conservation equation); presented
below. Also note that the force due to surface tension is considered as
a sharp surface force in the SI-LSM \cite{shaikh2018} while it is modeled
as a volumetric force term (within the thickness of the diffused interface)
in the above momentum equation for the DI-LSM \cite{gada2011}.
\subsubsection{Governing Equations for Two-Fluid Interface}
Physically, the two-fluid interface is advected by the fluid-flow;
obtained by solving the governing equations in the previous subsection.
Mathematically, in a LSM, the unsteady interface advection is represented
by an advection equation for a signed normal distance function representing
the interface, \emph{i.e.}, level set function $\phi$. However, after
the advection, the interface representing $\phi$ no more remains
as a normal distance function and another equation called as reinitialization
equations is solved using the pseudo transient approach. The reinitialization
is essential for an accurate calculation of surface tension, jump
terms, and thermophysical properties. Thus, the governing equations
for the two-fluid interface are given as
\noindent \textbf{Level-Set Advection (Mass-Conservation) Equation}:
\begin{equation}
\frac{\partial\phi}{\partial\tau}+\mathbf{U}_{a}\cdot\nabla\phi=0,\thinspace\thinspace\thinspace\thinspace\thinspace\thinspace\thinspace\label{eq:lsadv}
\end{equation}
where $\mathbf{U}_{a}$ is the advection velocity which is equal to
the bulk-velocity $\mathbf{U}$ (obtained from the solution of the
above volume and momentum conservation equations). The above equation
was derived from a mass conservation equation by Gada and Sharma \cite{gada2009}.
\noindent \textbf{Reinitialization Equation}:
\begin{equation}
\frac{\partial\phi}{\partial\tau_{s}}+S\left(\phi_{o}\right)\widehat{n}\cdot\nabla\phi-S\left(\phi_{o}\right)=0,\label{eq:2.21}
\end{equation}
\noindent where $S\left(\phi_{o}\right)$ is a sign function and $\tau_{s}$
is a pseudo time step. After getting the converged solution of Eq.~(\ref{eq:2.21}),
level set field will again become signed normal distance with respect
to zero level set value. Here, partial differential equation based
reinitialization (Sussman et al. \cite{sussman1994}) is used.
\subsubsection{Interfacial Boundary Conditions}
In a computational fluid dynamics (CFD), the unsteady velocity field
is obtained from the momentum conservation equation (Eq.~(\ref{eq:Mom}))
and the pressure field is left with the volume conservation equation
(Eq.~(\ref{eq:conti})) which does not consist of any pressure term
\cite{Sharma2017}; thus, a predictor-corrector method is used to convert
the volume conservation equation into a pressure Poisson equation
in a pressure projection method. While solving the pressure Poisson
equation and the momentum equation for a two-phase flow in a single
field formulation based SI-LSM, interfacial boundary conditions along
with the boundary conditions for the flow properties at the boundary
of the domain are required. The interfacial BCs involve jump boundary
conditions for pressure and velocity at the interface $\Gamma$; given
as
\begin{eqnarray}
\left[P\right]_{\Gamma} & = & \frac{2}{Re}\left[\eta\right]\hat{N\centerdot}\left(\nabla U\centerdot\hat{N},\nabla V\centerdot\hat{N}\right)+\frac{\kappa}{We},\label{eq:Jump_P_Phase-1}\\
{}[\mathbf{U}]_{\Gamma} & = & 0,\nonumber
\end{eqnarray}
\noindent where the above equation for pressure is obtained by applying
Newton's II law of motion at the interface $\Gamma$ and a detailed
derivation of the pressure-jump BC was presented by Shaikh et al.
\cite{shaikh2018}. The interfacial force balance considers the force
due to surface tension as the \emph{sharp surface-force} which is
balanced with both pressure force and normal viscous force in viscous
flow across the interface\textcolor{blue}{{} }\textcolor{black}{\cite{francois2006}}.
The interfacial boundary condition across the interface
is shown in Fig. \ref{fig:Computational-domain-with}. As shown in
the figure, for pressure, the jump condition notation across the interface
is expressed as\textcolor{black}{{} ${\color{black}{\color{red}{\color{black}[\cdot]_{\Gamma}=\left(\cdot\right)_{1,\Gamma}-\left(\cdot\right)_{2,\Gamma}}}}$};
$\left(\cdot\right)_{1,\Gamma}$ and $\left(\cdot\right)_{2,\Gamma}$
are the value of the flow properties at the interface $\Gamma$ from
the heavier and lighter phase in the $\Omega_{1}$ and $\Omega_{2}$
region, respectively.
\section{Adaptive interface-Mesh un-Refinement}\label{sec:Concept-of-Semi-Adaptive}
\begin{figure}
\begin{centering}
\includegraphics[scale=0.5]{Figure_Final/Fig2.pdf}
\par\end{centering}
\protect\caption{\label{fig:Computational-stencil-with} A representative 2D Cartesian
grid along with the \textit{staggered} grid points for flow-properties
and level set function $\phi$ in a two-fluid problem.}
\end{figure}
\begin{figure}
\begin{centering}
\par\end{centering}
\noindent \begin{centering}
\includegraphics[width=14cm]{Figure_Final/Fig3.pdf}
\par\end{centering}
\protect\caption{\label{fig:(a)-Distribution-of}\review{A representative Cartesian grid for a two-fluid system with an interface: ($a,c$) initial uniform grid at $\tau=0$ for the interface and at all time instants for the flow and ($b,d$) dynamically unrefined grid. Here, ($c$) and ($d$) show the various types of grid points considered to implement the instantaneous interface based dynamic mesh un-refinement. The unrefined interface grid in ($d$) is obtained from the uniform grid for the flow-properties in ($c$) after eliminating ghost-parent and ghost-child level set grid points. Note that a narrow band of the fine grid (at the interface) is shown in ($b$) for representative purpose only and a much wider band is used in the present method for accurate computations.}}
\end{figure}
For the staggered grid used here, the grid points for pressure, velocity
and level set function are shown in Fig.~\ref{fig:Computational-stencil-with}.
For the implementation of the interface-mesh unrefinement, all level
set grid points are tagged as a parent or a child grid point. All parent level set grid points are further tagged as interfacial or interior grid points. Finally, each parent and child grid point is tagged as real or ghost grid point. The various types of level set grid points are shown in
Fig.~\ref{fig:(a)-Distribution-of}. The figure also shows an interface
representing the two-fluid. A representative 2D Cartesian grid is shown in Fig.~\ref{fig:(a)-Distribution-of}($a$)
as a uniform mesh for solving the Navier-Stokes equations (Eq.~(\ref{eq:conti})
and (\ref{eq:Mom})) along with the interfacial boundary conditions
(Eq.~(\ref{eq:Jump_P_Phase-1})); and Fig. \ref{fig:(a)-Distribution-of}($b$)
as the adaptive unrefined interface mesh for solving the level set equations
(Eq.~(\ref{eq:lsadv}) and (\ref{eq:2.21})). The solution of the
respective set of equations results in unsteady flow properties (U,V,
and P) and level set function $\phi$. Fig.~\ref{fig:(a)-Distribution-of}($b$)
shows a merging of the four finer control volumes (CVs) in Fig. \ref{fig:(a)-Distribution-of}($a$) to a coarser control volume, for those CVs which are slightly away
from the interface. This results in the unrefinement of the interface
mesh which is away from the interface and the unrefinement is time-wise adaptive to the position of the interface which evolves with
time $-$ called here as Adaptive interface-Mesh un-Refinement (AiMuR).
The implementation and algorithmic details for the adaptive unrefinement
of the interface mesh (Fig.~\ref{fig:(a)-Distribution-of}($b$)) $-$
from the fixed flow-properties mesh (Fig.~\ref{fig:(a)-Distribution-of}($a$))
$-$ are presented with the help of Fig.~\ref{fig:(a)-Distribution-of}($c$)
and \ref{fig:(a)-Distribution-of}($d$). Fig.~\ref{fig:(a)-Distribution-of}($c$)
shows a tagging of each level set grid point as parent or child, interfacial
or interior, and real or ghost grid points; and Fig.~\ref{fig:(a)-Distribution-of}($d$)
shows only real (not the ghost) grid points that lead to the AiMuR.
The three types of tagging for each level set function grid point
are as follows:
\noindent 1. \textit{Tag as parent or child grid point}: parent if
both the running indices \textit{i} and \textit{j} are even; otherwise,
child.
\noindent 2. \textit{Tag parent grid points as interfacial or interior}:
all parent level set grid points with at least one adjoining neighbor
(east/west/north/south) parent level set grid point in another fluid
are tagged as an interfacial parent grid point. Identification of
the interfacial and non-interfacial parent grid points are done by
considering change in the sign of level set function $-$ interfacial
parent grid point if the product of level set function at parent grid
point $\phi_{P}$ and at any of the adjoining parent neighbor $\phi_{NB}$
is negative ($\phi_{P}\phi_{NB=W,E,S,N}<0$); otherwise, consider
the grid point as interior parent grid point.
\noindent 3. \textit{Tag as ghost or real}: interior as ghost and
interfacial as real, for the parent grid points; whereas, for the
child grid points, the adjoining neighbor (north, south, east, and
west) child grid points of a ghost interior parent grid point are
considered as ghost and all the other child nodes in the domain are
considered as real. Note that the common adjoining child neighbors
of ghost interior parent grid points and real interfacial parent grid
points are considered as real child grid points.
Based on the proposed definition of parent and child level set grid
points and interface configuration shown in Fig.~\ref{fig:(a)-Distribution-of}($c$),
level set function grid points at the intersection of the horizontal strips
and vertical strips (marked in the figure) are the parent level set grid points. Here, words
real and ghost are used in the sense that level set equations are
solved only for real grid points and not for ghost grid points. This
classification of parent and child level set grid points into real
and ghost grid points generates level set grid point distribution
as finer in the interfacial region and coarser in the non-interfacial
region. Implementing the tagging procedure (discussed above) for
level set grid point distribution shown in Fig.~\ref{fig:(a)-Distribution-of}($c$)
and then eliminating the ghost parent and child nodes results in real
grid points distribution as shown in Fig.~\ref{fig:(a)-Distribution-of}($d$).
The above-discussed implementation results in a \textit{single level}
adaptive interface mesh unrefinement. However, the present unstructured
adaptive grid-like distribution is implicitly achieved by the unrefinement
using tagging and without involving any tree data structure. Once
the unrefinement is done, the level set grid will have the same resolution
as that of flow grid in the interfacial region while the level set
grid away from interface will be coarser by the single-level. Limiting
the refined grid close to the interface is justified since the value
of the level set function $\phi$ close to the physically relevant
interface $\phi=0$ is only numerically relevant $-$ $\phi$ values
close to the interface are only involved in the calculation of interfacial
parameters such as fluid properties, curvature, and jump in the flow
properties.
Although the above implementation details for AiMuR are presented in Fig. \ref{fig:(a)-Distribution-of}
for one interfacial cell on each side of the interface, note that
every interfacial parent level set grid point and its three neighbor
parent level set grid points in all the four directions (east/west/north/south)
are considered in the present work for a more accurate CMFD computations.
Thus, the wider interfacial band is considered in the proposed AiMuR since
the one interfacial cell-based AiMuR shown in Fig.~\ref{fig:(a)-Distribution-of}($b$)
leads to an inaccurate solution. Moreover, as commonly used in AMR
\cite{popinet2009,theodorakakos2004} and used here for a more efficient AiMuR, the adaption of the grid is
done after certain number of time steps (instead of after every $\Delta\tau$); $50\Delta\tau$, $150\Delta\tau$, and $15\Delta\tau$ are considered for the dam break simulation, liquid jet breakup, and droplet coalescence problems (presented below), respectively. \review{These time-periods of the unrefinment are obtained after an unrefinment time-period independence study, presented below in subsection~\ref{sub:Unref_freq}.} The periodic grid unrefinement justifies the need for the wider
interfacial band of the finer grid. Further, it is ensured that the interface
does not enter into unrefined region during the above mentioned time
interval of the periodic unrefinement for the three problems considered in the present work.
\section{Numerical Methodology}\label{sec:method}
\subsection{Solution of Volume and Momentum Conservation Equations}
Numerical solution of volume and momentum conservation equations is
obtained by the pressure projection method in the present study. Here,
semi-implicit formulation is adopted wherein the volume conservation
equation is treated implicitly and all the terms of the momentum conservation
equation except advection term are treated implicitly.
Temporal discretization of the corresponding equations (Eq.~(\ref{eq:conti})
and (\ref{eq:Mom})) are given as
\begin{equation}
\nabla\cdot\mathbf{U}_{P}^{n+1}=0,\label{eq:volume conservation}
\end{equation}
\begin{equation}
\frac{\mathbf{U}_{P}^{n+1}-\mathbf{U}_{P}^{n}}{\Delta\tau}+\nabla\cdot(\mathbf{U}_{P}^{n}\mathbf{U}_{P}^{n})=-\frac{\nabla P^{n+1}}{\chi_{i}^{n}}+\frac{1}{\chi_{i}^{n}Re}\nabla\cdot(2\eta_{i}^{n}\mathbf{D}^{n+1})-\frac{1}{Fr^{2}}\hat{j}.\label{eq:6}
\end{equation}
\subsubsection{Semi-Implicit Pressure Projection Method}
In the pressure projection method, velocity field is predicted by
neglecting the pressure term in Eq.~(\ref{eq:6}); given as
\begin{equation}
\frac{\mathbf{U}_{P}^{*}-\mathbf{U}_{P}^{n}}{\Delta\tau}+\nabla\cdot(\mathbf{U}_{P}^{n}\mathbf{U}_{P}^{n})=\frac{1}{\chi_{i}^{n}Re}\nabla\cdot(2\eta_{i}^{n}\mathbf{D}^{*})-\frac{1}{Fr^{2}}\hat{j}.\label{eq:7-1}
\end{equation}
\noindent Using the predicted velocity field $\mathbf{U^{*}}$, new
time level pressure field is obtained by solving a pressure Poisson
equation (obtained from Eq.~(\ref{eq:volume conservation}) using
a predictor-corrector method); given as
\begin{equation}
\nabla\cdot\left(\frac{\nabla P^{n+1}}{\chi_{i}^{n}}\right)=\frac{1}{\Delta\tau}\nabla\cdot\mathbf{U^{*}}.\label{eq:9-1}
\end{equation}
\noindent Finally, by subtracting Eq.~(\ref{eq:7-1}) from Eq.~(\ref{eq:6})
and neglecting the velocity correction in the diffusion terms, continuity
satisfying velocity field at the new time level is obtained as
\begin{equation}
\mathbf{U}_{P}^{n+1}=\mathbf{U}_{P}^{*}-\frac{\nabla P^{n+1}}{\chi_{i}^{n}}\Delta\tau.\label{eq:8}
\end{equation}
\noindent While solving the pressure Poisson equation (Eq.~(\ref{eq:9-1})),
an interfacial jump boundary condition for pressure is used; presented
in the next subsection.
\subsubsection{Implementation of Jump Boundary Condition for Pressure\label{sub:Implementation-of-Jump}}
In a two-fluid system, there will be a lower dimensional mass-less
interface separating different fluids. As shown in Fig.~\ref{fig:Computational-domain-with}($a$),
for each fluid, there will be two types of control volumes: (1) interfacial
and (2) interior. While solving pressure Poisson equation (Eq.~(\ref{eq:9-1}))
for interfacial control volumes, as depicted by the computational
stencil in Fig.~\ref{fig:Computational-domain-with}($b$)-($c$), the resulting
linear algebraic equation involves pressure from the other fluid that
leads to a poor approximation of pressure gradient term across the
interface. This was demonstrated by Liu et al. \cite{liu2000} using
order-of-magnitude analysis.
The poor approximation is avoided by using a pressure jump as an interfacial
boundary condition \cite{liu2000} while solving the pressure Poisson
equation (Eq.~(\ref{eq:9-1})). The interfacial pressure boundary
condition is obtained by incorporating force balance at the interface \cite{shaikh2018};
given as ${(p_{1}-p_{2})-\mathbf{((\hat{n}\cdot\sigma)_{1}-(\hat{n}\cdot\sigma)_{2})\cdot\hat{n}}=-\gamma\mathbf{\nabla\cdot\hat{n}}}$,
here, $p$ is pressure, $\mathbf{\sigma}$ is viscous stress tensor, $\gamma$ is
surface tension coefficient and $\mathbf{\hat{n}}$ is a normal unit vector;
and subscripts 1 and 2 denote fluid-1 and fluid-2, respectively. This
force balance at the interface takes care of the discontinuity in
pressure across the two-fluid interface. Here, a finite volume method
based generalized algebraic formulation of pressure Poisson equation
(along with the interfacial jump boundary condition for pressure),
proposed by Shaikh et al. \cite{shaikh2018}, is used. The generalized
formulation involves an additional source term for the interfacial
control volumes that is zero for the interior control volumes for
pressure.
\begin{center}
\par\end{center}
\subsubsection{Special Treatment for a Non-Uniform Grid}
\begin{figure}
\begin{centering}
\par\end{centering}
\begin{centering}
\includegraphics[width=14cm]{Figure_Final/Fig4.pdf}
\par\end{centering}
\protect\caption{\label{fig:Offset-between-velocity}Offset between the centroid of velocity
control volume and the face of pressure control volume.}
\end{figure}
Although Section \ref{sec:Concept-of-Semi-Adaptive} and Fig.~\ref{fig:(a)-Distribution-of}
presents AiMuR on a uniform grid, the AiMuR and SI-LSM based in-house
code is developed in the present work for both uniform and non-uniform
Cartesian-grid. In this section, additional numerical details for
non-uniform as compared to a uniform grid is presented. The essential
difference in the numerical methodology is due to the staggered grid
that results in a non-coinciding or an offset between the centroid
of a velocity control volume and the associated face-center of the
pressure control volume. This offset is shown in Fig.~\ref{fig:Offset-between-velocity}
for the east face of the non-uniform pressure control volume along
with no such offset for the uniform grid.
The offset for the non-uniform grid results in a distance-based linear
interpolations to compute the predicted velocities at the various
face centers ($U_{e}^{*}$, $U_{w}^{*}$, $V_{n}^{*}$, and $V_{s}^{*}$)
of the pressure control volume from the predicted velocities (Eq.~(\ref{eq:7-1}))
at the centroid of the adjoining velocity control volumes ($U_{P}^{*}$,
$U_{W}^{*}$, $V_{P}^{*}$, and $V_{S}^{*}$); thereafter, the $U_{e}^{*}$,
$U_{w}^{*}$, $V_{n}^{*}$, and $V_{s}^{*}$ are used to calculate
the predicted mass source on the right-hand side of the pressure Poisson
equation (Eq. (\ref{eq:9-1})). Furthermore, after obtaining the correct
velocity field $\mathbf{U}_{P}^{n+1}$ from Eq.~(\ref{eq:8}), the
cell-center velocities are linearly interpolated to compute the velocity
at the face-center of the pressure control volumes ($U_{e}^{n+1}$,
$U_{w}^{n+1}$, $V_{n}^{n+1}$, and $V_{s}^{n+1}$). Finally, the
face-center velocity are interpolated to obtain velocity at the corners of
the pressure control volumes that is used to advect the level set
function field.
\subsection{Solution of Level Set Advection~(Mass-Conservation) Equations}\label{sub:Solution-of-Level}
\begin{figure}
\begin{centering}
\includegraphics[scale=0.65]{Figure_Final/Fig5.pdf}
\par\end{centering}
\protect\caption{\label{fig:Stencil-arrangement-in}Stencil arrangement for $3^{rd}$
order accurate Essentially Non-Oscillatory (ENO) scheme for non-uniformly
distributed grid points.}
\end{figure}
\begin{figure}
\begin{centering}
\includegraphics[scale=0.65]{Figure_Final/Fig6.pdf}
\par\end{centering}
\protect\caption{\label{fig:Ghost-level-set} Interpolation of level set function at
ghost grid point using real level set function grid points.}
\end{figure}
The numerical methodology for the solution of the Navier-Stokes equations
(presented above) uses a physical law based finite volume method based algebraic formulation \cite{Sharma2017} while finite difference method
is used for the discretization of the level set equations (Eq.~(\ref{eq:lsadv})
and (\ref{eq:2.21})). Spatial (advection) term in the level set equations
is discretized using a III-order accurate Essentially Non-Oscillatory
(ENO) scheme (Jiang and Peng \cite{jiang2000}). The temporal discretization
of the level set advection equation is done using a III-order accurate
Runge-Kutta scheme and using a I-order accurate forward difference
for the reinitialization equation. Pseudo time step $\Delta\tau_{s}$
for the temporal term in the reinitialization equation is taken as
0.1 times of minimum grid size.
Although the formulation for the ENO scheme corresponding to a non-uniform
grid is available for the finite volume method in literature \cite{smit2005},
the formulation for finite difference method is presented here with
the help of Fig.~\ref{fig:Stencil-arrangement-in}. The figure shows
a non-uniform spacing based 7-point main-stencil, for implementing the ENO scheme on a non-uniform grid.
The figure also shows that the main stencil is subdivided into two
6-point stencil: left and right biased stencils (LBS and RBS). These
left/right stencils are further subdivided into three 4-point substencils:
left substencil as LBSS1, LBSS2, and LBSS3; and right substencil as
RBSS1, RBSS2, and RBSS3. Fitting a III-order Lagrange interpolation
polynomial in each of these substencils results in a finite difference
representation of the first derivative in the level set advection
equation $-$ presented below for $\phi_{X}$ (representing ${\partial\phi}/{\partial X}$)
at the various LBSS as
\begin{multline}
\phi_{X,i}^{LBSS1}=\phi_{i-3}\left(\frac{X_{i}^{2}-X_{i}X_{i-1}-X_{i}X_{i-2}+X_{i-1}X_{i-2}}{\left(X_{i-3}-X_{i}\right)\left(X_{i-3}-X_{i-2}\right)\left(X_{i-3}-X_{i-1}\right)}\right)\\
+\phi_{i-2}\left(\frac{X_{i}^{2}-X_{i}X_{i-1}-X_{i}X_{i-3}+X_{i-1}X_{i-3}}{\left(X_{i-2}-X_{i-3}\right)\left(X_{i-2}-X_{i-1}\right)\left(X_{i-2}-X_{i}\right)}\right)\\
+\phi_{i-1}\left(\frac{X_{i}^{2}-X_{i}X_{i-2}-X_{i}X_{i-3}+X_{i-2}X_{i-3}}{\left(X_{i-1}-X_{i-3}\right)\left(X_{i-1}-X_{i-2}\right)\left(X_{i-1}-X_{i}\right)}\right)\\
+\phi_{i}\left(\frac{1}{\left(X_{i}-X_{i-3}\right)}+\frac{1}{\left(X_{i}-X_{i-2}\right)}+\frac{1}{\left(X_{i}-X_{i-1}\right)}\right),\label{eq:2.22-2}
\end{multline}
\begin{multline}
\phi_{X,i}^{LBSS2}=\phi_{i-2}\left(\frac{X_{i}^{2}-X_{i}X_{i-1}-X_{i}X_{i+1}+X_{i-1}X_{i+1}}{\left(X_{i-2}-X_{i-1}\right)\left(X_{i-2}-X_{i}\right)\left(X_{i-2}-X_{i+1}\right)}\right)\\
+\phi_{i-1}\left(\frac{X_{i}^{2}-X_{i}X_{i-2}-X_{i}X_{i+1}+X_{i-2}X_{i+1}}{\left(X_{i-1}-X_{i-2}\right)\left(X_{i-1}-X_{i}\right)\left(X_{i-1}-X_{i+1}\right)}\right)\\
+\phi_{i+1}\left(\frac{X_{i}^{2}-X_{i}X_{i-1}-X_{i}X_{i-2}+X_{i-1}X_{i-2}}{\left(X_{i+1}-X_{i}\right)\left(X_{i+1}-X_{i-2}\right)\left(X_{i+1}-X_{i-1}\right)}\right)\\
+\phi_{i}\left(\frac{1}{\left(X_{i}-X_{i-2}\right)}+\frac{1}{\left(X_{i}-X_{i-1}\right)}+\frac{1}{\left(X_{i}-X_{i+1}\right)}\right),\label{eq:2.28-1}
\end{multline}
\begin{multline}
\phi_{X,i}^{LBSS3}=\phi_{i-1}\left(\frac{X_{i}^{2}-X_{i}X_{i+1}-X_{i}X_{i+2}+X_{i+1}X_{i+2}}{\left(X_{i-1}-X_{i}\right)\left(X_{i-1}-X_{i+1}\right)\left(X_{i-1}-X_{i+2}\right)}\right)\\
+\phi_{i+1}\left(\frac{X_{i}^{2}-X_{i}X_{i-1}-X_{i}X_{i+2}+X_{i-1}X_{i+2}}{\left(X_{i+1}-X_{i-1}\right)\left(X_{i+1}-X_{i}\right)\left(X_{i+1}-X_{i+2}\right)}\right)\\
+\phi_{i+2}\left(\frac{X_{i}^{2}-X_{i}X_{i-1}-X_{i}X_{i+1}+X_{i-1}X_{i+1}}{\left(X_{i+2}-X_{i}\right)\left(X_{i+2}-X_{i+1}\right)\left(X_{i+2}-X_{i-1}\right)}\right)\\
+\phi_{i}\left(\frac{1}{\left(X_{i}-X_{i-1}\right)}+\frac{1}{\left(X_{i}-X_{i+1}\right)}+\frac{1}{\left(X_{i}-X_{i+2}\right)}\right),\label{eq:2.29-1}
\end{multline}
From the above values, the $\phi_{X,i}^{LBSS}$ is chosen as
\begin{equation}
\phi_{X,i}^{LBSS}=\begin{cases}
\phi_{X,i}^{LBSS1} & \begin{array}{cc}
if\end{array}\mid B\mid<\mid C\mid\&\mid A-B\mid<\mid B-C\mid\\
\phi_{X,i}^{LBSS3} & \begin{array}{cc}
if\end{array}\mid B\mid>\mid C\mid\&\mid B-C\mid>\mid C-D\mid\\
\phi_{X,i}^{LBSS2} & \text{otherwise},
\end{cases}\label{eq:2.22-1-1}
\end{equation}
where
\[
A=\frac{\phi_{i-3}-\phi_{i-2}}{X_{i-2}-X_{i-3}}+\frac{\phi_{i-1}-\phi_{i-2}}{X_{i-1}-X_{i-2}},\,\,\,\, B=\frac{\phi_{i-2}-\phi_{i-1}}{X_{i-1}-X_{i-2}}+\frac{\phi_{i}-\phi_{i-1}}{X_{i}-X_{i-1}}
\]
\[
C=\frac{\phi_{i-1}-\phi_{i}}{X_{i}-X_{i-1}}+\frac{\phi_{i+1}-\phi_{i}}{X_{i+1}-X_{i}},\,\, \text{and}\,\, D=\frac{\phi_{i}-\phi_{i+1}}{X_{i+1}-X_{i}}+\frac{\phi_{i+2}-\phi_{i+1}}{X_{i+2}-X_{i+1}}.
\]
Similarly, the expression for $\phi_{X,i}^{RBSS}$ can be obtained
and the ENO scheme based discretized form of $\phi_{X,i}$ in the level
set advection equation (Eq.~(\ref{eq:lsadv})) is given as
\begin{equation}
U\frac{\partial\phi}{\partial X}=\text{max}(U,0)\phi_{X,i}^{LBSS}+\text{min}(U,0)\phi_{X,i}^{RBSS}
\end{equation}
For the AiMuR
on a uniform or non-uniform Cartesian-grid, now the implementation details for the above ENO scheme are discussed. \review{For the AiMuR, ghost grid points are considered in the stencil wherever needed while applying the ENO scheme for the real grid points; and are not needed for the interfacial boundary condition since we ensured a sufficiently wider band of the refined grid near the interface.}
This is done to ensure that the weights of neighboring $\phi'$s in Eq.
(\ref{eq:2.22-2}), (\ref{eq:2.28-1}) and (\ref{eq:2.29-1}) are
computed only once (after the generation of uniform or non-uniform
Cartesian-grid) and do not change with time $-$ they are not dynamic.
Values of the level set function at the ghost grid points are computed
by linear interpolation of the adjoining real grid points. This
is shown in Fig.~\ref{fig:Ghost-level-set}, where the arrows show
the neighboring real child point values involved in the interpolation.
In addition to the computation of ENO scheme, these interpolated level
set function values at ghost grid points are utilized when ghost level
set grid points turn into real level set grid points.
\section{Solution Algorithm }
\begin{enumerate}
\item Generate initial configuration of fluid-fluid interface for all the
level set grid points. Initialize pressure and velocity as zero. Calculate
the weights of ENO scheme based on the distribution of level set grid
points.
\item Identify parent as well as child level set grid points (see section
\ref{sec:Concept-of-Semi-Adaptive}). Further, bifurcate them into
real and ghost level set grid points.
\item Calculate the thermo-physical properties using a sharp Heaviside function
\cite{shaikh2018}. Harmonic mean of the thermo-physical properties on
the either side of the interface is considered for interfacial cells.
\item Calculate the advection and diffusion flux (in Eq.~(\ref{eq:7-1}))
considering the continuity in velocity field and in its gradient at
the fluid-fluid interface. Predict the velocity $\mathbf{U^{*}}$
at the new time level by solving Eq.~(\ref{eq:7-1}). Here, III-order
Lin-Lin \textit{total variation diminishing} (TVD) \cite{date2005} scheme
is employed for discretizing the explicit advection term while the
diffusion term is discretized using a central difference scheme.
\item Calculate the mass-source (RHS of Eq.~(\ref{eq:9-1})) by linearly
interpolating predicted velocity $\mathbf{U^{*}}$ at the face-center
of the pressure control volume.
\item Obtain the converged solution of the pressure Poisson equation (Eq.~(\ref{eq:9-1})) using the jump condition by Ghost Fluid Method
(GFM).
\item Calculate the corrected velocity at the new time step (Eq.~(\ref{eq:8})).
Linearly interpolate the corrected velocity at the face-center of
the pressure control volume.
\item Obtain the level set advection velocity $\mathbf{U}_{a}$ at the real
level set grid points using a linear interpolation of the velocity
at the face-center of the pressure control volume. Advect the level
set function field using Eq.~(\ref{eq:lsadv}) for real level set
grid points using the methodology explained in subsection \ref{sub:Solution-of-Level}.
\item Interpolate the advected level set function field at ghost level set
grid points from the real level set grid points (see Fig.~\ref{fig:Ghost-level-set}).
\item Set the level set field as normal signed distance function by solving
level set reinitialization equation (Eq.~\ref{eq:2.21}) for real
level set grid points.
\item Repeat step 9.
\item Go to step 2 until the stopping criterion is met.
\end{enumerate}
\section{Validation and Qualitative Performance Study of A\lowercase{i}M\lowercase{u}R based SI-LSM }\label{sec:validation}
\begin{table}
\protect\caption{\label{tab:Resolution-of-different}Grid size for the five different grid
types: uniform coarse grid ($U_{c}$), non-uniform coarse grid ($NU_{c}$),
non-uniform coarse grid with AiMuR ($NU_{c}^{AiMuR}$), uniform fine grid with AiMuR ($U_{f}^{AiMuR}$) and uniform fine grid ($U_{f}$)
corresponding to the dam break, jet breakup and droplet coalescence problem . }
\begin{centering}
\par\end{centering}
\centering{}%
\begin{tabular}{cccc}
\hline
& DB & JB & DC\tabularnewline
\hline
$U_{c}$, $NU_{c}$, and $NU_{c}^{AiMuR}$ & 100$\times$50 & 35$\times$200 & 100$\times$200\tabularnewline
$U_{f}$ and $U_{f}^{AiMuR}$ & 144$\times$80 & 50$\times$300 & 200$\times$400\tabularnewline
\hline
\end{tabular}
\end{table}
In order to present the validation of the proposed numerical methodology
and performance study, three different types of two-phase flow problems are considered: \textbf{\underline{D}}am-\textbf{\underline{B}}reak
(\textbf{DB}), \textbf{\underline{J}}et-\textbf{\underline{B}}reakup
(\textbf{JB}) and \textbf{\underline{D}}rop-\textbf{\underline{C}}oalescence
(\textbf{DC}). The dominant force is gravity, inertia and capillary force in the DB, JB and DC simulations, respectively. The DB simulation does not involve breakup of interface while the JB and DC problems involve more rigorous interface dynamics with break-up of interface that leads to a droplet formation. Computational setup corresponding to the three problems are shown in Fig.
\ref{fig:Computational-setup-for-3}. A performance study of the proposed AiMuR based SI-LSM is presented here by considering the adaptive unrefinement of the interface mesh on both uniform and non-uniform grid. However, since the result on a non-uniform as compared to the uniform grid is more accurate, the AiMuR on a non-uniform grid is considered on a coarser grid while the AiMuR on a uniform grid is presented on a finer grid; the respective AiMuR based SI-LSM is represented here as $NU_{c}^{AiMuR}$ and $U_{f}^{AiMuR}$. Considering our in-house codes for the novel AiMuR based SI-LSM as well as the traditional SI-LSM, the scope of the present performance study is to compare the relative accuracy of the novel and traditional SI-LSMs (on uniform and non-uniform grid), with the accuracy obtained by comparing with the published experimental and numerical results for the DB, JB and DC problems. The relative accuracy is presented qualitatively in this section and and quantitatively in the next section. The resulting five different grid types of SI-LSM are presented in Table \ref{tab:Resolution-of-different} along with the associated grid size considered in the present simulations. Note that grid size mentioned in Table \ref{tab:Resolution-of-different} for $NU_{c}^{AiMuR}$ and $U_{f}^{AiMuR}$ is without performing unrefinement for the level set function.
For the five grid types ($U_{c}$, $NU_{c}$, $NU_{c}^{AiMuR}$, $U_{f}^{AiMuR}$, and $U_{f}$), the grid resolution of uniform coarse grid $U_{c}$ (Table \ref{tab:Resolution-of-different}) is intentionally
chosen such that, numerical result will not be accurate enough while the finer grid size $U_{f}$ is kept fine enough to produce reliable numerical results. Furthermore, non-uniform
coarse grid ($NU_{c}$) is chosen such that it comprises of same number of control volumes
as that of uniform coarse grid ($U_{c}$). However, grid stretching
in $NU_{c}$ is done such that the grid resolution in interfacial region is comparable to uniform fine grid ($U_{f}$). For grid case $NU_{c}^{AiMuR}$, control
volume distribution for pressure and velocity is same as that for
$NU_{c}$. Nevertheless, mesh unrefinement strategy is incorporated
in $NU_{c}^{AiMuR}$, which creates level set resolution equivalent
to $NU_{c}$ in interfacial region and coarser resolution in non-interfacial
region. Similar discussion is also applicable for grid types $U_{f}$ and $U_{f}^{AiMuR}$. Similar to $NU_{c}$, both $NU_{c}^{AiMuR}$
and $U_{f}^{AiMuR}$ possess grid resolution equivalent to that of $U_{f}$ near the interface.
Based on the characteristic of the grid types selected in present
work, one can predict that computational time for $U_{f}$ will be
maximum among all, which will get reduced after applying mesh unrefinement
($U_{f}^{AiMuR}$). Computational time associated with $U_{c}$ and
$NU_{c}$ should be nearly same, as they have same number of control volumes.
However, it largely depends on the trend of iterations while solving
pressure Poisson equation and also up to some extent on additional
computational operations required for $NU_{c}$ as compared to $U_{c}$. Computational time
for $NU_{c}^{AiMuR}$ should be less than that required by $NU_{c}$.
Difference in computational time for $NU_{c}^{AiMuR}$
($U_{f}^{AiMuR}$) and $NU_{c}$ ($U_{f}$) will depend on the number
of unrefined level set grid points (which implicitly depends on how the interface evolves with time) in $NU_{c}^{AiMuR}$ ($U_{f}^{AiMuR}$). The hypothesised computational time for the various grid types are compared quantitatively in the next section.
\begin{figure}
\begin{centering}
\includegraphics[width=16cm]{Figure_Final/Fig7.pdf}
\par\end{centering}
\protect\caption{\label{fig:Computational-setup-for-3}Computational setup for (a)
Dam break simulation (b) Breakup of a liquid jet and (c) Coalescence
of a stagnant ethanol drop at air-ethanol interface.}
\end{figure}
\subsection{Dam Break Simulation}\label{sub:Dam-Break-Simulation}
\begin{figure}
\begin{centering}
\par\end{centering}
\begin{centering}
\includegraphics[width=16.5cm]{Figure_Final/Fig8.pdf}
\par\end{centering}
\protect\caption{\label{fig:Mesh-distribution-for} Interface (level set) mesh
for ($a$) dam break simulation, ($b$) liquid jet-breakup, and ($c$) drop coalescence
problems. The interface mesh shown in $(a_1)$, $(a_2,b,c)$, and $(a_3)$ is for $NU_{c}$, $NU_{c}^{AiMuR}$, and $U_{f}^{AiMuR}$, respectively. The \textit{adaptive unrefined instantaneous interface mesh} is at $\tau=1.5$ for ($a_2$) and ($a_3$), $\tau=150$ for ($b$), and $\tau=0.55$ for ($c$).}
\end{figure}
\begin{figure
\begin{centering}
\par\end{centering}
\begin{centering}
\includegraphics[width=14.5cm]{Figure_Final/Fig9.pdf}
\par\end{centering}
\protect\caption{\label{fig:Qualitative-and-quantitative}Dam break simulation at $Re=3 \times 10^6$ and $Fr=1$. For the present SI-LSM on the various grid types (Table \ref{tab:Resolution-of-different}), ($a-e$)~instantaneous interface position at three different time instances and ($f$)~comparison of the present numerical and the published experimental \cite{martin1952} result. The stair-stepped lines for $NU_{c}^{AiMuR}$ and $U_{f}^{AiMuR}$ represent the interfacial region (in between the lines) outside which the level set grid points are dynamically unrefined.}
\end{figure}
Computational setup for this problem in Fig.~\ref{fig:Computational-setup-for-3}($a$)
shows a water column that is allowed to collapse under the effect of gravity. For the non-uniform Cartesian grid generation, a grid transformation function \cite{hoffmann2000}
is used that is given as
\begin{equation}
X/Y=L\lambda\left(1+\frac{\text{sinh}\left(\beta\left(\xi-A\right)\right)}{\text{sinh}\left(\beta A\right)}\right),\label{eq:4.2-1}
\end{equation}
where,
\[
A=\frac{\text{ln}\left(\frac{1+\lambda\left(e^{\beta}-1\right)}{1+\lambda\left(e^{-\beta}-1\right)}\right)}{2\beta}.
\]
\noindent The value of different tuning parameters for non-uniform distribution
in X and Y directions are $\beta_{X}=2.5$, $\beta_{Y}=3.1$, $\lambda_{X}=0.466$, and
$\lambda_{Y}=0.066$. Resulting non-uniform grid distribution is shown
in Fig.~\ref{fig:Mesh-distribution-for}($a_{1}$) for $NU_{c}$ and Fig.~\ref{fig:Mesh-distribution-for}($a_{2}$) for $NU_{c}^{AiMuR}$; and Fig.~\ref{fig:Mesh-distribution-for}($a_{3}$) shows adaptive unrefined uniform grid $U_{f}^{AiMuR}$. Note that the adaptive unrefined grid in Fig.~\ref{fig:Mesh-distribution-for}($a_{2},a_{3}$) corresponds to $\tau=1.5$. For instantaneous interface position, Fig.~\ref{fig:Qualitative-and-quantitative}($a$)-($e$) shows excellent agreement between the present results on the various types of SI-LSM on uniform/non-uniform grids (with or without interface mesh unrefinement) except the present result on $U_{c}$. This is also demonstrated for the leading edge distance in Fig.~\ref{fig:Qualitative-and-quantitative}($f$) by comparing with a benchmark experimental results \cite{martin1952}.
\noindent
\subsection{Breakup of a Liquid Jet}\label{sub:Breakup-of-a}
\begin{figure}
\begin{centering}
\par\end{centering}
\begin{centering}
\par\end{centering}
\begin{centering}
\includegraphics[width=12cm]{Figure_Final/Fig10.pdf}
\par\end{centering}
\protect\caption{\label{fig:Qualitative-and-quantitative-1}For jet breakup study at $Re=396$, $We=1.27$, and $Fr=5.44$, comparison of instantaneous interface obtained from $U_{c}$, $NU_{c}$, $NU_{c}^{AiMuR}$,
and $U_{f}^{AiMuR}$ (left) with that obtained from
$U_{f}$ (right) after $(a_{1}-d_{1})$ first jet breakup and $(a_{2}-d_{2})$ second jet breakup at time instances $\tau=80$ and $145$, respectively. Temporal variation
of jet length $L_j$ obtained in the present work is plotted in ($e$) and compared with the published numerical results \cite{lakdawala2014}.}
\end{figure}
Computational setup for this problem is shown in Fig.~\ref{fig:Computational-setup-for-3}($b$), where a lighter liquid is injected (against the gravity) in the heavier liquid with a constant velocity $0.15$ m/s. For the present problem, as long as the surface tension force dominates over the
buoyancy force, the jet will keep on rising. Once buoyancy force exceeds
the surface tension force, a neck forms and a droplet gets detached from the jet. The detached droplet continues to rise
in the heavier stagnant fluid and the jet will regain its original shape.
Number of control volumes employed for the present jet breakup problem is presented in Table \ref{tab:Resolution-of-different}. For
$NU_{c}$ and $NU_{c}^{AiMuR}$, gird clustering is implemented in both radial and axial
direction, that results in almost same grid resolution to that for the fine
uniform grid ($U_{f}$) in the breakup region. Distribution of level
set function grid points after performing unrefinement on a non-uniform
grid is shown in Fig.~\ref{fig:Mesh-distribution-for}($b$) at a time instance $\tau=150$. Results for the interface dynamics corresponding to breakup of two droplets from the inlet jet are shown in Fig.~\ref{fig:Qualitative-and-quantitative-1}. The instantaneous interface at $\tau=80$ and $\tau=145$ in Fig.~\ref{fig:Qualitative-and-quantitative-1}($a$)$-$($d$) shows an excellent agreement between the present results on a coarse non-uniform grid (with and without unrefinement) as compared to the uniform grid. Similar agreement between the results on the various grid types and also with the results reported in Lakdawala
et al. \cite{lakdawala2014} is shown in Fig.~\ref{fig:Qualitative-and-quantitative-1}($e$), for the temporal variation of jet length $L_{j}$; except for the result on uniform coarse grid $U_{c}$, which experiences late breakup of the jet as the interplay
between surface tension and buoyancy force is not captured well because
of insufficient grid cells in radial and axial direction.
\subsection{Coalescence of an Ethanol Droplet}\label{sub:Coalescence-of-an}
\begin{figure}
\begin{centering}
\includegraphics[width=16cm]{Figure_Final/Fig11.pdf}
\par\end{centering}
\protect\caption{\label{fig:Comparison-of-present}For coalescence study of an ethanol droplet (of diameter $1.07$ mm) in air, comparison of the temporal variation of present SI-LSM based numerically obtained instantaneous interface on five different grid types (Table \ref{tab:Resolution-of-different}) with experimental results of Blanchette and Bigioni \cite{blanchette2006}. The time instant marked above (0.53, 1.15, 1.40, 2.62 and 3.57) are in milli-second and the present numerically obtained interface is shown as line contour.}
\end{figure}
\begin{figure}
\begin{centering}
\includegraphics[width=14cm]{Figure_Final/Fig12.pdf}
\par\end{centering}
\protect\caption{\label{fig:Comparison-of-interface}
For coalescence dynamics of an ethanol droplet in air, comparison of temporal variation of instantaneous interface obtained for $U_{c}$, $NU_{c}$, $NU_{c}^{AiMuR}$, and $U_{f}^{AiMuR}$ (left) with that obtained for $U_{f}$ (right).}
\end{figure}
Computational set-up for the coalescence dynamics of an ethanol droplet of diameter $1.07$ mm, surrounded by air, over a pool of ethanol is shown in Fig.~\ref{fig:Computational-setup-for-3}($c$)); and the unrefined non-uniform interface-mesh at $\tau = 0.55$ is shown in Fig.~\ref{fig:Mesh-distribution-for}($c$). Fig.~\ref{fig:Comparison-of-present} shows an excellent agreement between the instantaneous interface obtained on the various grid types and the experimental results reported by Blanchette and Bigioni \cite{blanchette2006}. However, at time instance $3.57$ ms, the present result for $U_{c}$ as compared to the result on other grid types shows a much thicker neck that indicates a delay in the pinch-off and the resulting formation of secondary droplet.
As compared to the time-duration just before the first pinch-off, Fig.~\ref{fig:Comparison-of-interface} shows the temporal variation of the instantaneous interface for a longer time-duration corresponding to the second pinch-off of the secondary droplet. The figure shows that our result for the non-uniform grid with or without unrefinement agrees very well with the result on the finer uniform grid. However, the present result on a coarser uniform grid shows a slight delay in the first pinch-off of the primary droplet and thereafter it does not show the second pinch-off that is seen in the present results on the other grid types.
\review{
\section{Unrefinement Time-Period Independence and Order-of-Accuracy Studies}
\subsection{Unrefinement Time-Period Independence Study}\label{sub:Unref_freq}
\begin{figure}
\begin{centering}
\includegraphics[width=14cm]{Figure_Final/Fig13.pdf}
\par\end{centering}
\protect\caption{\label{fig:adaption_frequency1}
\review{For the droplet coalescence problem, unrefinement time-period independence study of the present AiMuR on a uniform $200 \times 400$ grid: ($a$) variation of \% error and \% increase in computational-time with decreasing number ($n$) of the time-step $\Delta t$ after which the interface-mesh is periodically-unrefined; and ($b_{1}$)-($b_{5}$) instantaneous interface obtained for the different values of $n$. The \% error is for the first pinch-off time reported by Blanchette and Bigioni \cite{blanchette2006}. For ($b_{1}$)-($b_{5}$), the region in-between the red-curves corresponds to the fine-mesh region, with unrefined coarser-mesh outside this region; and the dashed and solid black-lines represent the interface at a time-instant corresponding to the beginning ($\tau_{1}$) and end ($\tau_{2}$) of the associated unrefinement time-period, respectively.}}
\end{figure}
For the present AiMuR, the periodic unrefinement of the interface mesh is done after certain number $n$ of the time-step $\Delta t$ that results in the time-period for the unrefinement as $n\Delta t$ . Thus $n$ is a numerical parameter for the present method that is problem dependent and determined here from an unrefinement time-period independence study; similar to the grid-independence and time-step independence studies commonly used in CFD. The time-period independence study is presented in Fig.~\ref{fig:adaption_frequency1}($a$), for the uniform grid based AiMuR and the droplet-coalascence problem. The figure shows an asymtotic decrease in the error with increasing $n$, with almost no change in the error after $n=15$. Thus, $n=15$, \emph{i.e.}, the periodic-unrefinement after every $15^{th}$ time-step, is chosen for the AiMuR based simulation of the coalascence of an ethanol droplet in air. The figure also shows an almost $20\%$ increase in the computational time as $n$ decreases from $120$ to $15$.
The unrefinement after certain number of time-steps, instead of after every time-step, is due to the fact that the present AiMuR involves a wider band of finer mesh near the interface. The fine-mesh region, along with the interface extreme positions, during the time-interval of the unrefinement is shown in Fig.~\ref{fig:adaption_frequency1}($b_{1}$)-($b_{5}$) for various values of $n$. For the cases with $n=120$ and $60$, the figure shows that the interface moves outside the fine-mesh region during the time period $n\Delta t$ of the unrefinement; thus resulting in the larger error as seen in Fig.~\ref{fig:adaption_frequency1}($a$). The unrefinement time-period independence study ensures that the fluid-fluid interface stays within the fine-mesh region for an accurate solution. Similar unrefinement independence study for the other problems resulted in $n=50$ for the dam break problem and $n=150$ for the liquid jet breakup problem.
\subsection{Order of Accuracy Study}\label{sub:Order}
For a multiphase flow solver, order of accuracy study is widely reported for a problem on decaying oscillations of a capillary wave that has an analytical solution (Prosperetti \cite{prosperetti1981}). Thus, after ensuring the verification of our numerical with the analytical solution, Fig.~\ref{fig:order_of_accuracy1}($a$) presents an order of accuracy study for this problem. The computational setup for this problem can be found in Gerlach et al. \cite{Gerlach2006}; error is defined as $L_{2}$ norm of the difference between time-wise variation of the non-dimensional relative amplitude computed numerically and that obtained analytically. The figure shows that the order of accuracy of our SI-LSM on a uniform grid, with and without AiMuR, is between first and second order; almost same as that seen in the figure for the refined level-set grid method of Hermann \cite{hermann2008}. For a comparative study, the figure also presents the order of accuracy study of seven other numerical methods: front-tracking method \cite{ftm1999}, Gerris flow-solver \cite{popinet2009} (volume-of-fluid implementation with generalised height-function curvature calculation for quadtree and octree discretizations), PROST \cite{Renardy2002} (volume-of-fluid implementation with a parabolic reconstruction of surface tension) and CLSVOF \cite{Sussman2000} (coupled level-set volume-of-fluid formulation) implementations of Gerlach et al.\cite{Gerlach2006}, CSF-VOF \cite{Gueyffier1999} (continuous surface force method based modelling of surface tension in volume-of-fluid framework), and VOF-NIFPA-1 \cite{Ivey2017} (VOF implementation with non-intersecting flux polyhedron advection (NIFPA) scheme for the advection of volume fraction) and Conservative DI \cite{Mirjalili2020} (diffuse-interface) implementations of Mirjalili et al. \cite{Mirjalili2019} . The figure shows that the Gerris, PROST, and CLSVOF are almost second order accurate while the other six multiphase flow solvers (including our SI-LSM) exhibit an order of accuracy between first and second order. It is worth noting from the figure that the present SI-LSM as compared to the other numerical methods is most accurate for the coarser grid resolution of $N=8$ Whereas, on relatively finer grid resolution of $N=64$, it can be seen that our SI-LSM is more accuracte than the front-tracking, CSF-VOF, conservative DI and RLSG.
Order of accuracy study is also presented in Fig.~\ref{fig:order_of_accuracy1}($b$) for the same dam-break simulation (Fig.~\ref{fig:Computational-setup-for-3}($a$)),considering the mass-error since this is the biggest disadvantage of the level set method \cite{shrma2015}. With grid refinement, the convergence of the mass-error (at some particular time-instant) in the figure shows that the present present AiMuR based LSM is somewhere between first and second order accurate; same as concluded from Fig.~\ref{fig:order_of_accuracy1}($a$). Using the physical interpretation of Heaviside function, proposed \cite{gada2009} and later used in the previous work from our reasearch group \cite{gada2011, Lakdawala2015}, the mass error is computed here as
\begin{equation}
\text{\% Mass Error} = 100\times\frac{1}{\tau_{max}}\int_{0}^{\tau_{max}}\frac{\left | \sum_{i,j}H_{i,j}^{\tau}\Delta V_{i,j}-\sum_{i,j}H_{i,j}^{o}\Delta V_{i,j} \right |}{\sum_{i,j}H_{i,j}^{o}\Delta V_{i,j}}d\tau,
\end{equation}
\noindent where, $H_{i,j}^{o}$ is the initial Heaviside function and $H_{i,j}^{\tau}$ is Heaviside function at a particular time instance $\tau$.
\begin{figure}
\begin{centering}
\includegraphics[width=16cm]{Figure_Final/Fig14.pdf}
\par\end{centering}
\protect\caption{\label{fig:order_of_accuracy1}\review{
With increasing grid refinement levels, variation of ($a$) $L_{2}$ norm of the error (between the present/published mumtiphase solvers and analytical solution \cite{prosperetti1981}) for the time-wise variation of the non-dimensional relative amplitude of a damped capillary wave (for $\rho_{1}=\rho_{2}=1$, $\mu_{1}=\mu_{2}=0.064720863$, and Ohnesorge number $Oh=1/\sqrt{3000}$) and (b) mass-error for the $U_{f}^{AiMuR}$ based dam-break simulation.}}
\end{figure}
}
\section{Quantitative Performance Study}\label{sec:performance}
\begin{figure}
\begin{centering}
\par\end{centering}
\begin{centering}
\includegraphics[width=16.5cm]{Figure_Final/Fig15.pdf}
\par\end{centering}
\protect\caption{\label{fig:Performance-curve-for}Variation of the performance parameters (Eq.~(\ref{eq:4.2-222})) for the present novel SI-LSM and traditional SI-LSM on the various grid types (Table \ref{tab:Resolution-of-different}) for $(a)$ dam break, $(b)$ jet breakup, and $(c)$ drop coalescence
problems.}
\end{figure}
\begin{figure}
\begin{centering}
\includegraphics[width=16.5cm]{Figure_Final/Fig16.pdf}
\par\end{centering}
\protect\caption{\label{fig:Temporal-variation-of-1}\review{Temporal variation of AiMuR based
total grid-point reduction (\%) for the level set function on the $(a_1,b_1,c_1)$ non-uniform coarse grid $NU_{c}$ and $(a_2,b_2,c_2)$ uniform fine grid $U_{f}$, for $(a_1,a_2)$ dam break, $(b_1,b_2)$ jet breakup and $(c_1,c_2)$ droplet coalescence problems.}}
\end{figure}
For the three different two-phase problems, the above comparison of the unsteady interface dynamics on the various grid types and also with the published numerical/experimental results clearly demonstrates the superiority of the SI-LSM on the non-uniform grid and unrefinement as compared to that on the uniform grid. Almost similar superiority of the $NU_{c}$, $NU_{c}^{AiMuR}$,
and $U_{f}^{AiMuR}$ as compared to $U_{c}$ was demonstrated qualitatively above and presented quantitatively here.
The quantitative representation of the relative performance considers the \review{total} computational time \review{(including the time required for the interpolation and the inter-grid transfer)} along with the computational accuracy to distinguish the relatively superior performance of $NU_{c}$, $NU_{c}^{AiMuR}$,
and $U_{f}^{AiMuR}$ as compared to $U_{c}$. Thus,
for a quantitative representation, a detailed performance study is carried out by defining two performance parameters: \% Error
Reduction and \% Computational Time Increment; given as \review{ \cite{gada2011,Lakdawala2015,Patil2016,shaikh2019}}
\[
\%\,\, \text{Error}\,\, \text{Reduction}=\left(1-\frac{\text{Error}_{grid-type}}{\text{Error}_{U_{C}}}\right)\times100,
\]
\begin{equation}
\%\,\, \text{Computational}\,\, \text{Time}\,(C.T.)\,\, \text{Increment}=\left(\frac{C.T.{}_{grid-type}}{C.T.{}_{U_{C}}}-1\right)\times100,
\label{eq:4.2-222}
\end{equation}
where a grid-type corresponds to $NU_{c}$, $NU_{c}^{AiMuR}$,
$U_{f}^{AiMuR}$, and $U_{f}$. Further, present performance study is carried
out using coarse uniform grid ($U_{c}$) as a reference grid for all
the problems. In order to calculate the error associated with the present numerical
results on various grid types, as compared to the published experimental/numerical results, certain parameter is selected
in each problem.
The parameter considered for calculating the error of the present SI-LSM corresponds to leading edge distance reported by
Martin and Moyce \cite{martin1952} at time $\tau=2.4$, jet breakup length reported by Lakdawala et al. \cite{lakdawala2014} (after second
breakup) at time $\tau=145$, and first pinch-off time reported by Blanchette
and Bigioni \cite{blanchette2006} for\textbf{ }\textbf{\underline{D}}am-\textbf{\underline{B}}reak (\textbf{DB}),
\textbf{\underline{J}}et-\textbf{\underline{B}}reakup (\textbf{JB})
and \textbf{\underline{D}}rop-\textbf{\underline{C}}oalescence (\textbf{DC})
problems, respectively.
For the three sufficiently different two phase flow problems, the performance parameters (Eq.~(\ref{eq:4.2-222})) for the present novel and traditional SI-LSM on various grid types are shown in Fig.~\ref{fig:Performance-curve-for}.
As discussed in previous subsection, the error reduction in Fig.~\ref{fig:Performance-curve-for} demonstrates a quantitative (in terms of accuracy) evidence of almost same superiority of the $NU_{c}$, $NU_{c}^{AiMuR}$,
and $U_{f}^{AiMuR}$ as compared to $U_{c}$. Whereas, the computational time increment clearly demonstrates the relative superiority of the $NU_{c}$, $NU_{c}^{AiMuR}$,
and $U_{f}^{AiMuR}$, with the least computational time increment by the SI-LSM on $NU_{c}^{AiMuR}$ as compared to that on $NU_{c}$ and $U_{f}^{AiMuR}$. Theoretically,
computational time for grid type $NU_{c}$ should be same as that
for $U_{c}$ (as both of them are having same number of control volumes).
Nevertheless, since $NU_{c}$ as compared to $U_{c}$ requires more iterations
for solving pressure Poisson equation, $NU_{c}$ results in more computational
time. Application of AiMuR on $NU_{c}$ reduces this overhead
in computational time. This is seen in Fig.~\ref{fig:Performance-curve-for}($a_{2},b_{2},$), with a negligible increase in computational time by $NU_{c}^{AiMuR}$ as compared to $U_{c}$. Further, the figure also shows that computational time demanded by $U_{f}$ gets reduced after applying the mesh unrefinement.
After applying AiMuR strategy
on either uniform or non-uniform grid, the reduction in computational time is correlated with AiMuR based total grid-point
reduction (\%) that is shown in Fig.~\ref{fig:Temporal-variation-of-1}. The figure shows that instantaneous value of AiMuR based total grid-point
reduction (\%) for level set function is more than 45\% for the problems studied here. Time-wise increase or decrease of AiMuR based total grid-point reduction
(\%) in Fig.~\ref{fig:Temporal-variation-of-1} also implicitly represents
the dynamics of fluid-fluid interface, \emph{i.e.}, spreading of the fluid-fluid interface in computational domain and AiMuR based total grid-point reduction (\%) are inversely related. In dam break problem, gradual
decrease in AiMuR based total grid-point reduction (\%) is due to
the interface spreading after the collapse of the water column. Similarly,
in jet breakup, initial decrement in total grid-point reduction (\%)
is because of the continuous injection of fluid. After the first breakup,
an increase in total grid-point reduction (\%) is attained as soon as the detached droplet escapes the computational domain, followed by another
decrease-increase cycle. For drop coalescence problem, an increase in
AiMuR based total grid-point reduction (\%) after first pinch off
corresponds to the smaller daughter droplet size. Among all grid combinations,
$NU_{c}^{AiMuR}$ is found to be computationally most efficient since it produces
numerical results of almost same accuracy as that on a fine uniform grid ($U_{f}$)
and requires a computational time almost same as that on coarse uniform grid
($U_{c}$).
\section*{Concluding Remarks}
In the present work, numerical methodology for simulating multi-phase flows on dynamically
unrefined uniform as well as non-uniform level set mesh is proposed,
where unrefinement is carried out away from the interface location.
The dynamic unrefinement is done for the Cartesian interface mesh corresponding to level set function only. Consequently,
higher order schemes based solution of level set equations (advection
and reinitialization) is obtained on almost half of the grid in the
region away from the interface. Further, ENO scheme
with varying weights is used to solve mass conservation equation on
highly stretched non-uniform grids. To demonstrate the numerical accuracy and
computational efficiency of the proposed AiMuR based SI-LSM, performance study
is carried out for three sufficiently different two-phase flow problems: dam break, breakup of a liquid jet and drop coalescence
problems. For a detailed qualitative and quantitative performance study of the proposed adaptive unrefinement based SI-LSM as compared to the traditional SI-LSM, a systematic combinations of various types of SI-LSM and coarse/fine grid size are considered. It is found that the present SI-LSM on a non-uniform coarse grid ($NU_{c}$) demands more computational
time than for the uniform coarse grid ($U_{c}$) with numerical accuracy
almost same as the uniform fine grid ($U_{f}$). After implementing
adaptive interface-mesh unrefinement (AiMuR) on a non-uniform grid ($NU_{c}^{AiMuR}$),
further reduction in computational time is obtained without much compromise
in numerical accuracy. Incorporating AiMuR on a fine uniform grid ($U_{f}^{AiMuR}$)
also produces results of almost same accuracy as that of uniform fine grid but with
less computational time. However, reduction in computational time
by $U_{f}^{AiMuR}$ is not as significant as that of $NU_{c}^{AiMuR}$.
\review{The application of the AMR as well as the AiMuR algorithm generates a time-evolving hierarchical distribution of Cartesian control volumes. The evolution of this hierarchical distribution (successive refinement or un-refinement of control volumes) is governed by the mesh refinement/un-refinement criteria that is based on flow physics as well as interface dynamics for the AMR and only interface dynamics for the AiMuR. However, the implementation details of the novel AiMuR are relatively less complex as compared to the AMR. The AiMuR based LSM is presented here as a proof-of-concept and studies on the performance of AiMuR on more suitable multiphase problems is part of future work.} Application of the present non-uniform and adaptive unrefinement grid strategies will be extended
to two-phase flow involving phase change. Furthermore, performance characteristics of these grid types
will also be studied for three-dimensional multi-processor multi-phase flow simulations as present study is restricted to two dimensional two-phase flows.
\section*{Acknowledgement}
The first author would like to acknowledge the fellowship received from Indian Institute of Technology Bombay as a part of the IRCC Research Internship Award. The support received from the Institute of Technology, Nirma University
$-$ for sending the first author to carry out research at Indian
Institute of Technology Bombay $-$ is gratefully acknowledged.
\bibliographystyle{elsarticle-num}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
When studying and working with the two main functional interpretations, namely the \emph{dialectica} \cite{Avigad(98),Goedel(58)} and the modified realizability \cite{Kreisel(59)} interpretations, one notices a striking similarity in the way the two interpretations behave. For instance, they both interpret $\forall \exists$-statements in precisely the same way, and their soundness (also called adequacy) proofs follow very similar patterns. Yet, for all purpose these are two very different interpretations, validating different principles\footnote{For instance, the dialectica interpretation validates the Markov principle whereas modified realizability does not. On the other hand, modified realizability validates full extensionality whereas the dialectica interpretation does not.}, and having different properties\footnote{For instance, realizability interpretations always have a so-called ``truth" variant, whereas the dialectica interpretation does not.}. Several questions naturally arise. What is the common structure behind these two functional interpretations? How are the different witnesses obtained from a given proof when applying different interpretations related to each other?
It was with these questions in mind that I set out \cite{Oliva(06)} to develop a general framework to unify functional interpretations. This initial work was followed by several other articles \cite{FO(2009A),FO(2012),FO(2011A),GO(2010),Hernest(2008),Oliva(2007A),Oliva(2007),Oliva(2008),Oliva(2009A),Oliva(2009B)} further refining or generalising the original idea. These were mainly done in collaboration with Gilda Ferreira, Jaime Gaspar and Mircea-Dan Hernest. What started as a small modification of the dialectica interpretation to also capture realizability and the Diller-Nahm variant \cite{Diller(74)} ended up as a very general hybrid functional interpretation of intuitionistic affine logic\footnote{Intuitionistic linear logic plus the weakening rule.}, also capturing Stein's family of functional interpretations \cite{Stein(79)}, functional interpretations ``with truth" \cite{GO(2010)}, and bounded functional interpretations \cite{Ferreira(05A),Ferreira(05),Ferreira(06)}.
This article will survey the work mentioned above, singling out what I believe to be the key lessons learnt so far. These are summarised as follows. For details see the corresponding sections and the articles mentioned.
\begin{enumerate}
\item[(\S \ref{newReal})] Modified realizability can also alternatively be presented as a \emph{relation} between potential witnesses and challenges, in a way very similar to the way the dialectica interpretation is presented. This is originally observed in \cite{Oliva(06)} and is key to extending realizability to affine logic \cite{Oliva(2007)}.
\item[(\S \ref{factoring})] Most functional interpretations of \emph{intuitionistic logic} can be factored via \emph{affine logic}. More interestingly, all functional interpretations considered, when extended to affine logic, coincide in the pure fragment, where modalities are absent. This factorisation allows us to clearly see that the only difference between most of the functional interpretations is in the treatment of contraction, which in affine logic is captured by $! A$. Although this was originally done in the setting of \emph{classical} affine logic \cite{Hernest(2008),Oliva(2007A),Oliva(2007),Oliva(2009A)}, it turned out that \emph{intuitionistic} affine logic is not only enough, but the unification becomes much simpler \cite{FO(2009A),FO(2011A),GO(2010)} (albeit at the cost of losing symmetry).
\item[(\S \ref{sec-truth})] When designing the unified functional interpretation of intuitionistic affine logic we were only expecting to be able to capture the classic interpretations such as the dialectica, modified realizability and Diller-Nahm. We were therefore surprised when we discovered \cite{GO(2010)} that even the truth variants of functional interpretations fit in the framework almost effortlessly. Which means that even proof interpretations with truth only differ from their ``non-truth" variants in the treatment of $! A$, but coincide in the treatment of all other connectives.
\item[(\S \ref{hybrid})] Because the bang ($!$) of affine logic is not canonical, one can then effectively combine all the functional interpretations mentioned above, including their truth variants, into single interpretations which we called \emph{hybrid functional interpretations} \cite{Hernest(2008),Oliva(2009B)}. This means, for instance, that in a single proof one can try to make use of both the dialectica interpretation in some parts of the proof and modified realizability in others, combining their strengths to maximum benefit.
\end{enumerate}
We will conclude (\S \ref{future-work}) by listing thirteen open questions which indicate possible interesting directions for further research.
\vspace{2mm}
\noindent {\bf Acknowledgement}. Most of the work presented here has been done in collaboration with Gilda Ferreira, Jaime Gaspar and Mircea-Dan Hernest. I would also like to acknowledge previous work done in this direction on which the current work builds, such as those of Martin Stein \cite{Stein(79),Stein(1980)}, Val\'eria de Paiva \cite{dePaiva(1989A),dePaiva(1989B)}, Masaru Shirahata \cite{Shirahata(2006)} and Andreas Blass \cite{Blass(1992)}. Finally, many thanks to Thomas Powell, Jules Hedges and Gilda Ferreira for several comments and corrections on an earlier version of this paper.
\vspace{2mm}
\noindent {\bf Notation}. We use $X :\equiv A$ to say that $X$ is defined by $A$. We use $A \equiv B$ to mean $A$ and $B$ are syntactically equal.
\section{A Different View on Realizability}
\label{newReal}
The first obvious difference between modified realizability \cite{Kreisel(59)} and the dialectica interpretation \cite{Goedel(58)} is that the first interprets formulas $A$ as \emph{unary} predicates $\real{\pvec x}{A}$, normally written as ``$\pvec x$ realizes $A$", whereas the dialectica interpretation associates to formulas $A$ \emph{binary} predicates $\dial{\pvec x}{\pvec y}{A}$. Here $\pvec x$ and $\pvec y$ denote tuples of variables $\pvec x = x_1, \ldots, x_n$ and $\pvec y = y_1, \ldots, y_m$, where the length of the tuple and the types of the variables depend on the logical structure of the formula $A$. The two formulas $\real{\pvec x}{A}$ and $\dial{\pvec x}{\pvec y}{A}$ are defined inductively as\footnote{We are using the abbreviation $\pcond{b}{A}{B} :\equiv (b = {\sf true} \to A) \wedge (b = {\sf false} \to B)$. We also use the same macro in the context of affine logic where it stands for $\pcond{b}{A}{B} :\equiv (! (b = {\sf true}) \multimap A) \otimes (! (b = {\sf false}) \multimap B)$. }
\[
{\small
\begin{array}{lcl}
\real{\pvec x, \pvec y}{(A \wedge B)} & :\equiv & \real{\pvec x}{A} \wedge \real{\pvec y}{B} \\[1mm]
\real{\pvec x, \pvec y, b}{(A \vee B)} & :\equiv & \pcond{b}{\real{\pvec x}{A}}{\real{\pvec y}{B}} \\[1mm]
\real{\pvec f}{(A \to B)} & :\equiv & \forall \pvec x (\real{\pvec x}{A} \to \real{\pvec f \pvec x}{B}) \\[1mm]
\real{\pvec x, a}{(\exists z A)} & :\equiv & \real{\pvec x}{(A[a/z])} \\[1mm]
\real{\pvec f}{(\forall z A)} & :\equiv & \forall z \real{\pvec f z}{A}
\end{array}
\quad
\begin{array}{lcl}
\dial{\pvec x,\pvec v}{\pvec y, \pvec w}{(A \wedge B)} & :\equiv & \dial{\pvec x}{\pvec y}{A} \wedge \dial{\pvec v}{\pvec w}{B} \\[1mm]
\dial{\pvec x,\pvec v,b}{\pvec y, \pvec w}{(A \vee B)} & :\equiv & \pcond{b}{\dial{\pvec x}{\pvec y}{A}}{\dial{\pvec v}{\pvec w}{B}} \\[1mm]
\dial{\pvec f, \pvec g}{\pvec x, \pvec w}{(A \to B)} & :\equiv & \dial{\pvec x}{\pvec g \pvec x \pvec w}{A} \to \dial{\pvec f \pvec x}{\pvec w}{B} \\[1mm]
\dial{\pvec x, a}{\pvec y}{(\exists z A)} & :\equiv & \dial{\pvec x}{\pvec y}{(A[a/z])} \\[1mm]
\dial{\pvec f}{\pvec y, a}{(\forall z A)} & :\equiv & \dial{\pvec f a}{\pvec y}{(A[a/z])}.
\end{array}
}
\]
with the base case $\real{\epsilon}{(A_{{\sf at}})} = \dial{\epsilon}{\epsilon}{(A_{{\sf at}})} = A_{{\sf at}}$, for atomic formulas $A_{{\sf at}}$, with $\epsilon$ denoting the empty tuple (henceforth omitted). Note that for tuples of variables $\pvec f = f_1, \ldots, f_n$ and $\pvec x$ we write $\pvec f \pvec x$ for the tuple of terms $f_1 \pvec x, \ldots, f_n \pvec x$. Using these predicates $\real{\pvec x}{A}$ and $\dial{\pvec x}{\pvec y}{A}$ we can define two sets of ``functionals"
\[ A \quad \mapsto \quad \setComp{\pvec x}{\real{\pvec x}{A}} \hspace{2cm} A \quad \mapsto \quad \setComp{\pvec x}{\forall \pvec y \dial{\pvec x}{\pvec y}{A}} \]
which we will refer to as the ``realizability witnesses" and the ``dialectica witnesses". The two functional interpretations, modified realizability and dialectica, can be viewed as algorithms to turn an intuitionistic proof of $A$ into concrete (e.g. higher-order programs) elements of these sets.
The work on unifying different functional interpretations \cite{Oliva(06)} started with the observation that one can also view modified realizability as associating formulas with a \emph{binary} predicate $\rreal{\pvec x}{\pvec y}{A}$ (which I will call ``relational realizability") between two tuples $\pvec x$ and $\pvec y$ in a way very similar to the dialectica interpretation, namely
\begin{equation} \label{relational-realizability}
\begin{array}{lcl}
\rreal{\pvec x, \pvec v}{\pvec y, \pvec w}{(A \wedge B)} & :\equiv & \rreal{\pvec x}{\pvec y}{A} \wedge \rreal{\pvec v}{\pvec w}{B} \\[1mm]
\rreal{\pvec x, \pvec v, b}{\pvec y, \pvec w}{(A \vee B)} & :\equiv & \pcond{b}{\rreal{\pvec x}{\pvec y}{A}}{\rreal{\pvec v}{\pvec w}{B}} \\[1mm]
\rreal{\pvec f}{\pvec x, \pvec w}{(A \to B)} & :\equiv & \forall \pvec y \rreal{\pvec x}{\pvec y}{A} \to \rreal{\pvec f \pvec x}{\pvec w}{B} \\[1mm]
\rreal{\pvec x, a}{\pvec y}{(\exists z A)} & :\equiv & \rreal{\pvec x}{\pvec y}{(A[a/z])} \\[1mm]
\rreal{\pvec f}{\pvec y, a}{(\forall z A)} & :\equiv & \rreal{\pvec f a}{\pvec y}{(A[a/z])}.
\end{array}
\end{equation}
It is easy to show by induction on the formula $A$ that these two different definitions of realizability lead to the same interpretation as the following equivalence is intuitionistically provable:
\begin{equation*}
\real{\pvec x}{A} \quad \Leftrightarrow \quad \forall \pvec y \rreal{\pvec x}{\pvec y}{A}.
\end{equation*}
The relational presentation of realizability, however, makes it absolutely clear that realizability only differs from the dialectica interpretation in the clause for implication $A \to B$. While the realizability interpretation does not attempt to witness the universal quantifier $\forall \pvec y$ in the clause for $A \to B$, the dialectica interpretation witnesses such quantifier via the extra tuple of functionals $\pvec g$.
The two main ideas behind the original \emph{unifying functional interpretation} \cite{Oliva(06)} are the introduction of a common notation $\uInter{A}{\pvec x}{\pvec y}$ for such binary predicates, and a parametrised interpretation of $A \to B$. That is achieved via an abstract formula constructor $\bQuant{\pvec x}{\pvec a}{A}$ that takes a tuple of terms $\pvec a$ and a formula $A$ (with free variables $\pvec x$) and produces a new formula where $\pvec x$ are no longer free. A parametrised functional interpretation can then be given as
\begin{equation} \label{ufi-implication}
\begin{array}{lcl}
\uInter{A \wedge B}{\pvec x, \pvec v}{\pvec y, \pvec w}& :\equiv &
\uInter{A}{\pvec x}{\pvec y} \wedge \uInter{B}{\pvec v}{\pvec w} \\[1mm]
\uInter{A \vee B}{\pvec x, \pvec v, b}{\pvec y, \pvec w} & :\equiv &
\pcond{b}{\uInter{A}{\pvec x}{\pvec y}}{\uInter{B}{\pvec v}{\pvec w}} \\[1mm]
\uInter{A \to B}{\pvec f, \pvec g}{\pvec x, \pvec w} & :\equiv &
\bQuant{\pvec y}{\pvec g \pvec x \pvec w}{\uInter{A}{\pvec x}{\pvec y}} \to \uInter{B}{\pvec f \pvec x}{\pvec w} \\[1mm]
\uInter{\exists z A}{\pvec x, a}{\pvec y} & :\equiv &
\uInter{A[a/z]}{\pvec x}{\pvec y} \\[1mm]
\uInter{\forall z A}{\pvec f}{\pvec y, a} & :\equiv &
\uInter{A[a/z]}{\pvec f a}{\pvec y}.
\end{array}
\end{equation}
Subject to a few conditions (cf. \cite{Oliva(06)}) on $\bQuant{\pvec x}{\pvec a}{A}$, one can then prove a uniform soundness theorem for intuitionistic logic. When the formula constructor is instantiated one obtains the three main functional interpretations as follows:
\begin{equation*}
\begin{array}{c|c}
\bQuant{\pvec x}{\pvec a}{A} & \mbox{{\bf Functional interpretation}} \\[1mm]
\hline \\[-3mm]
A[\pvec a/\pvec x] & \mbox{G\"odel's dialectica interpretation} \\
\forall \pvec x \!\in\! \pvec a \, A & \mbox{Diller-Nahm interpretation} \\
\forall \pvec x A & \mbox{Kreisel modified realizability}
\end{array}
\end{equation*}
In order to show that each of these three interpretations is sound one only needs to check that they satisfy the required conditions mentioned above.
\begin{remark}[Stein family of interpretations] Let $M \in \mathbb{N} \cup \{ \infty \}$. Given a tuple of variables $\pvec x = x_0, \ldots, x_n$ let us denote by $\pvec x^{\geq M}$ the tuple containing only the elements of $\pvec x$ with type level $\geq M$. Similarly we denote by $\pvec x^{< M}$ the tuple containing only the elements of $\pvec x$ with type level $< M$. Note that $\pvec x^{< \infty} = \pvec x$ and $\pvec x^{< 0}$ is the empty tuple. Stein's family of functional interpretations \cite{Stein(79)} also fits in the above framework as we can take for each given $M$
\[ \bQuant{\pvec x}{\pvec a}{A} :\equiv \forall \pvec x^{< M} \forall \pvec x^{\geq M} \!\in\! \pvec a \, A \]
where $\pvec a$ is a set indexed by the pure type $M$, i.e. $\pvec a \colon M \to \rho$ for some type $\rho$. When $M = \infty$ this coincides with modified realizability, whereas with $M = 0$ this is a variant of the Diller-Nahm interpretation that allows for infinite (countable) sets, as $\pvec a \colon \mathbb{N} \to \rho$ ($\mathbb{N}$ is the pure type having type level $0$).
\end{remark}
\section{Factoring Through Affine Logic}
\label{factoring}
Reformulating realizability as a binary predicate as described in Section \ref{newReal} was an important step towards showing that modified realizability and the dialectica interpretation have much more in common than previously imagined. The fact is that they only differ on their handling of witnesses coming from the premise of an implication. But that opens a new question: What is special about the premise of an implication that allows for these different interpretations to exist? A satisfactory answer to this question came from the analysis of functional interpretations via affine logic.
Intuitionistic affine logic (${\rm AL}_i$) is a refinement of intuitionistic logic (${\rm IL}$) where particular attention is paid to the contraction rule \cite{Benton(1993),Girard(87B)}. We call this a \emph{refinement} because the connectives of intuitionistic logic can be recovered from a combination of those from affine logic. This is formally expressed via Girard's translations of intuitionistic logic into linear logic. The two most commonly used are\footnote{The usual clause for $\starT{(A \wedge B)}$ is $\starT{(A \wedge B)} :\equiv \starT{A} \,\&\, \starT{B}$. We can take $\starT{(A \wedge B)} :\equiv \starT{A} \otimes \starT{B}$ instead because we are embedding intuitionistic logic into affine logic (linear logic with the weakening rule).}
\[
\begin{array}{lcl}
\starT{P} & :\equiv & P \\[2mm]
\starT{(A \wedge B)} & :\equiv & \starT{A} \otimes \starT{B} \\[2mm]
\starT{(A \vee B)} & :\equiv & ! \starT{A} \, \oplus \; ! \starT{B} \\[2mm]
\starT{(A \to B)} & :\equiv & ! \starT{A} \multimap \starT{B} \\[2mm]
\starT{(\forall x A)} & :\equiv & \forall x \starT{A} \\[2mm]
\starT{(\exists x A)} & :\equiv & \exists x ! \starT{A}.
\end{array}
\hspace{10mm}
\begin{array}{lcl}
\circT{P} & :\equiv & ! P \\[2mm]
\circT{(A \wedge B)} & :\equiv & \circT{A}\otimes \circT{B} \\[2mm]
\circT{(A \vee B)} & :\equiv & \circT{A} \oplus \circT{B} \\[2mm]
\circT{(A \to B)} & :\equiv & ! (\circT{A} \multimap \circT{B}) \\[2mm]
\circT{(\forall x A)} & :\equiv & ! \forall x \circT{A} \\[2mm]
\circT{(\exists x A)} & :\equiv & \exists x \circT{A}.
\end{array}
\]
The translations are such that if $A$ is provable in ${\rm IL}$ then both $! \starT{A}$ and $\circT{A}$ are provable in ${\rm AL}_i$.
While working on \cite{Oliva(06)}, in the setting of intuitionistic logic, I came across de Paiva's \cite{dePaiva(1989B)} dialectica (and Diller-Nahm) interpretation of \emph{affine logic}. It then occurred to me that one could use the new formulation of realizability discussed in Section \ref{newReal} to extend the \emph{realizabillity} interpretation from intuitionistic logic to affine logic. This was developed and presented in \cite{Oliva(2007A),Oliva(2007)}. The starting point is the functional interpretation of pure affine logic (affine logic without the exponentials). As mentioned in the introduction, we consider the intuitionistic fragment of affine logic:
\begin{equation} \label{basic-inter}
\begin{array}{lcl}
\uInter{A \oplus B}{\pvec x, \pvec v,z}{\pvec y, \pvec w} & :\equiv & \pcond{z}{\uInter{A}{\pvec x}{\pvec y}}{\uInter{B}{\pvec v}{\pvec w}} \\[2mm]
\uInter{A \otimes B}{\pvec x, \pvec v}{\pvec y, \pvec w} & :\equiv & \uInter{A}{\pvec x}{\pvec y} \otimes \uInter{B}{\pvec v}{\pvec w} \\[2mm]
\uInter{A \multimap B}{\pvec f, \pvec g}{\pvec x, \pvec w} & :\equiv & \uInter{A}{\pvec x}{\pvec g \pvec x \pvec w} \multimap \uInter{B}{\pvec f \pvec y}{\pvec w} \\[2mm]
\uInter{\forall z A(z)}{\pvec f}{\pvec y, a} & :\equiv & \uInter{A[a/z]}{\pvec f a}{\pvec y} \\[2mm]
\uInter{\exists z A(z)}{\pvec x, a}{\pvec y} & :\equiv & \uInter{A[a/z]}{\pvec x}{\pvec y}.
\end{array}
\end{equation}
\begin{figure}[t]
\begin{center}
\setlength{\unitlength}{10mm}
\begin{picture}(6.0,3.3)
\thicklines
\put(0.5,2.8){$A$}
\put(0.65,2.65){\vector(0,-1){1.8}}
\put(-0.2,1.7){$\circT{(\cdot)}$}
\put(1.1,2.95){\vector(1,0){3.3}}
\put(1.5,2.5){mod. realizability}
\put(0.5,0.3){$\circT{A}$}
\put(4.5,2.8){$\real{\pvec x}{A}$}
\put(4.65,2.6){\vector(0,-1){1.8}}
\put(5.1,1.7){$\circT{(\cdot)}$}
\put(1.2,0.45){\vector(1,0){3.2}}
\put(2.4,0.7){$\uInter{\cdot}{}{}$}
\put(2.0,0.0){(\ref{basic-inter}) + (\ref{bang-realizability})}
\put(4.5,0.3){$\uInter{\circT{A}}{\pvec x}{} \equiv \circT{(\real{\pvec x}{A})}$}
\end{picture}
\caption{Factoring modified realizability}
\label{factor-realizability}
\end{center}
\end{figure}
What one notices is that the parameter constructor $\bQuant{\pvec x}{\pvec a}{A}$ used to interpret $A \to B$ in (\ref{ufi-implication}) is in fact the interpretation of the affine logic modality $! A$.
So we can extend the basic interpretation (\ref{basic-inter}) to a parametrised interpretation of full intuitionistic affine logic as
\begin{equation} \label{bang-unifying}
\begin{array}{lcl}
\uInter{! A}{\pvec x}{\pvec a} & :\equiv & ! \bQuant{\pvec y}{\pvec a}{\uInter{A}{\pvec x}{\pvec y}}.
\end{array}
\end{equation}
Via the translations $\circT{(\cdot)}$ and $\starT{(\cdot)}$ of ${\rm IL}$ into ${\rm AL}_i$ one can recover the interpretations of intuitionistic logic from those of intuitionistic affine logic as follows. For instance, consider the abbreviation $\bQuant{\pvec x}{\pvec a}{A} :\equiv \forall \pvec x A$, so that (\ref{bang-unifying}) simplifies to
\begin{equation} \label{bang-realizability}
\begin{array}{lcl}
\uInter{! A}{\pvec x}{} & :\equiv & ! \forall \pvec y \uInter{A}{\pvec x}{\pvec y}.
\end{array}
\end{equation}
We call the resulting interpretation a \emph{modified realizability} interpretation of affine logic because the diagram of Figure \ref{factor-realizability} commutes, i.e. given a formula $A$ of intuitionistic logic we can either apply modified realizability directly and translate the result into liner logic, or alternatively, we can first translate $A$ into affine logic, and then apply the interpretation with $\bQuant{\pvec x}{\pvec a}{A} :\equiv \forall \pvec x A$. Both paths result in the \emph{same} formula. Note that we really mean syntactic equality, rather than logical equivalence.
Now, if instead of using the Girard translation $\circT{A}$ we use instead the translation $\starT{A}$ we obtain a different diagram (Figure \ref{factor-relational-realizability}) which also commutes if we take in the upper arrow the \emph{relational} realizability instead.
\begin{figure}[h]
\begin{center}
\setlength{\unitlength}{10mm}
\begin{picture}(6.0,3.3)
\thicklines
\put(0.5,2.8){$A$}
\put(0.65,2.65){\vector(0,-1){1.8}}
\put(-0.2,1.7){$\starT{(\cdot)}$}
\put(1.1,2.95){\vector(1,0){3.3}}
\put(1.5,2.5){rel. realizability}
\put(0.5,0.3){$\starT{A}$}
\put(4.5,2.8){$\rreal{\pvec x}{\pvec y}{A}$}
\put(4.65,2.65){\vector(0,-1){1.8}}
\put(5.1,1.7){$\starT{(\cdot)}$ \quad (cf. Remark \ref{remark-trans-simp} below)}
\put(1.2,0.45){\vector(1,0){3.2}}
\put(2.4,0.7){$\uInter{\cdot}{}{}$}
\put(2.0,0.0){(\ref{basic-inter}) + (\ref{bang-realizability})}
\put(4.5,0.3){$\uInter{\starT{A}}{\pvec x}{\pvec y} \equiv \starT{(\rreal{\pvec x}{\pvec y}{A})}$}
\end{picture}
\caption{Factoring the relational variant of modified realizability}
\label{factor-relational-realizability}
\end{center}
\end{figure}
In other words, the two ways of presenting modified realizability arise from the two possible ways of translating intuitionistic logic into affine logic. In both cases the modified realizability interpretation of \emph{affine logic} is fixed (the lower arrows of Figures \ref{factor-realizability} and \ref{factor-relational-realizability}). That illustrates how affine logic has a more fundamental nature, as it is able to capture precisely the inherent structure of realizability.
Just as we have factored the realizability interpretation through affine logic, we can also do the same for the dialectica interpretation by considering the abbreviation $\bQuant{\pvec x}{\pvec a}{A} :\equiv A[\pvec a/\pvec x]$ leading to the interpretation of $! A$ as
\begin{equation} \label{bang-dialectica}
\begin{array}{lcl}
\uInter{! A}{\pvec x}{\pvec y} & :\equiv & ! \uInter{A}{\pvec x}{\pvec y}.
\end{array}
\end{equation}
Again, we say that (\ref{bang-dialectica}) is a dialectica interpretation of affine logic because it corresponds to the dialectica interpretation of intuitionistic logic as depicted in the commuting diagram of Figure \ref{factor-dialectica}.
\begin{figure}[h]
\begin{center}
\setlength{\unitlength}{10mm}
\begin{picture}(6.0,3.3)
\thicklines
\put(0.5,2.8){$A$}
\put(0.65,2.65){\vector(0,-1){1.8}}
\put(-0.2,1.7){$\starT{(\cdot)}$}
\put(1.1,2.95){\vector(1,0){3.3}}
\put(1.9,2.5){dialectica}
\put(0.5,0.3){$\starT{A}$}
\put(4.5,2.8){$\dial{\pvec x}{\pvec y}{A}$}
\put(4.65,2.65){\vector(0,-1){1.8}}
\put(5.1,1.7){$\starT{(\cdot)}$ \quad (cf. Remark \ref{remark-trans-simp} below)}
\put(1.2,0.45){\vector(1,0){3.2}}
\put(2.4,0.7){$\uInter{\cdot}{}{}$}
\put(2.0,0.0){(\ref{basic-inter}) + (\ref{bang-dialectica})}
\put(4.5,0.3){$\uInter{\starT{A}}{\pvec x}{\pvec y} \equiv \starT{(\dial{\pvec x}{\pvec y}{A})}$}
\end{picture}
\caption{Factoring G\"odel's dialectica interpretation}
\label{factor-dialectica}
\end{center}
\end{figure}
Finally, a Diller-Nahm interpretation of affine logic is obtained by choosing the abbreviation
\[ \bQuant{\pvec x}{\pvec a}{A} :\equiv \forall \pvec x \!\in\! \pvec a \, A, \]
where $\pvec a$ is a tuple of finite sets, and $\pvec x \in \pvec a$ denotes the usual set inclusion. For further details on the factorisation of the main functional interpretations via affine logic see \cite{FO(2009A),FO(2011A)}.
\begin{remark} \label{remark-trans-simp} In the diagrams of Figures \ref{factor-relational-realizability} and \ref{factor-dialectica} we are taking a simplified form of the $\starT{(\cdot)}$-translation, namely, one where the clauses for disjunction and existential quantifier are simply
\[
\begin{array}{lcl}
\starT{(A \vee B)} & :\equiv & \starT{A} \oplus \starT{B} \\[2mm]
\starT{(\exists x A)} & :\equiv & \exists x \starT{A},
\end{array}
\]
i.e. the bang is not used. The reason why we can work with this simpler translation of ${\rm IL}$ into ${\rm AL}_i$ is because we are considering ${\rm AL}_i$ extended with the following two principles
\begin{equation} \label{ufi-extra-principles}
\begin{array}{c}
! A \, \oplus \, ! B \multimap~! (A \oplus B) \\[2mm]
\exists x ! A \multimap~! \exists x A.
\end{array}
\end{equation}
These principles are harmless because they are interpretable by the interpretation $\uInter{A}{\pvec x}{\pvec y}$ for any of the three choices of $\bQuant{\pvec x}{\pvec a}{A}$ above. In general however, the combination of $\uInter{A}{\pvec x}{\pvec y}$ with the translation $\starT{(\cdot)}$ will lead to interpretations of disjunction and existential quantifier as
\begin{equation} \label{ufi-exists}
\begin{array}{lcl}
\uInter{A \vee B}{\pvec x, \pvec v, b}{\pvec y, \pvec w} & :\equiv & \pcond{b}{\bQuant{\pvec y}{\pvec a}{\uInter{A}{\pvec x}{\pvec y}}}{\bQuant{\pvec w}{\pvec c}{\uInter{B}{\pvec v}{\pvec w}}} \\[2mm]
\uInter{\exists z A}{\pvec x, a}{\pvec c} & :\equiv & \bQuant{\pvec y}{\pvec c}{\uInter{A[a/z]}{\pvec x}{\pvec y}}.
\end{array}
\end{equation}
This more general treatment is important for instance in the functional interpretation with truth as discussed in the following section.
\end{remark}
\section{Interpretations with Truth}
\label{sec-truth}
\begin{figure}[t]
\begin{center}
\setlength{\unitlength}{10mm}
\begin{picture}(6.0,3.3)
\thicklines
\put(0.0,2.8){$A$}
\put(0.15,2.65){\vector(0,-1){1.8}}
\put(-0.7,1.7){$\circT{(\cdot)}$}
\put(0.6,2.95){\vector(1,0){4.3}}
\put(1.0,2.5){realizability with truth}
\put(0.0,0.3){$\circT{A}$}
\put(5.0,2.8){$\mrt{\pvec x}{A}$}
\put(5.15,2.65){\vector(0,-1){1.8}}
\put(5.45,1.7){$\circT{(\cdot)}$}
\put(0.7,0.45){\vector(1,0){4.2}}
\put(2.0,0.0){(\ref{basic-inter}) + (\ref{bang-real-truth})}
\put(5.0,0.3){$\uInter{\circT{A}}{\pvec x}{} \equiv \circT{(\mrt{\pvec x}{A})}$}
\end{picture}
\caption{Factoring modified realizability with truth}
\label{factor-realizability-with-truth}
\end{center}
\end{figure}
The soundness of functional interpretations guarantees that from a proof of $A$ a tuple of terms $\pvec t$ can be extracted such that $\uInter{A}{\pvec t}{\pvec y}$. An important issue is that such a tuple $\pvec t$ provides a witness to the statement $\exists \pvec x \forall \pvec y \uInter{A}{\pvec x}{\pvec y}$, but not necessarily a witness to the original theorem $A$. For realizability interpretations some variants have been developed so that a realiser for $\exists z A$ also contains a witness for $z$. These are the so-called q-\emph{realizability} and \emph{realizability with truth} \cite{Grayson(1981),Kleene(45),Troelstra(98)}. In general what we would like is that
\begin{equation} \label{truth-property}
\forall \pvec y \uInter{A}{\pvec x}{\pvec y} \to A
\end{equation}
is derivable without the need for the characterisation principles\footnote{The characterisation principles are the extra logical principles needed to show the equivalence between $A$ and its interpretation $\exists \pvec x \forall \pvec y \uInter{A}{\pvec x}{\pvec y}$.} of the interpretation $\uInter{\cdot}{}{}$, because then we can extract actual witnesses from proofs of existential statements as follows
\[ \vdash \exists z A(z) \qquad \stackrel{\textup{soundness}}{\Rightarrow} \qquad \vdash \uInter{\exists z A(z)}{\pvec t, s}{\pvec y} \qquad \stackrel{(\ref{basic-inter})}{\equiv} \qquad \vdash \uInter{A(s)}{\pvec t}{\pvec y} \qquad \stackrel{(\ref{truth-property})}{\Rightarrow} \qquad \vdash A(s). \]
In joint work with Jaime Gaspar \cite{GO(2010)} we have shown how interpretations with truth arise from a slight modification of the abstract interpretation of $! A$ from (\ref{bang-unifying}) to
\begin{equation} \label{bang-unifying-truth}
\begin{array}{lcl}
\uInter{! A}{\pvec x}{\pvec a} & :\equiv & ! \bQuant{\pvec y}{\pvec a}{\uInter{A}{\pvec x}{\pvec y}} \;\otimes\; ! A.
\end{array}
\end{equation}
For instance, if we take the realizability abbreviation $\bQuant{\pvec y}{\pvec a}{A} :\equiv \forall \pvec y A$ in this case we obtain
\begin{equation} \label{bang-real-truth}
\uInter{! A}{\pvec x}{} :\equiv~! \forall \pvec y \uInter{A}{\pvec x}{\pvec y} \;\otimes\; ! A.
\end{equation}
The composition of this affine logic interpretation with the translation $\circT{(\cdot)}$ gives us precisely the \emph{modified realizability with truth} \cite{Kohlenbach(92A),Kohlenbach(98A),Kohlenbach(2008)}, as described in the diagram of Figure \ref{factor-realizability-with-truth}.
Consider then the q-variant of the relational realizability (\ref{relational-realizability}) where the clauses for disjunction and existential quantification are modified as
\begin{equation} \label{q-relational-realizability}
\begin{array}{lcl}
\qrreal{\pvec x, \pvec v, b}{}{(A \vee B)} & :\equiv & \pcond{b}{(\forall \pvec y \qrreal{\pvec x}{\pvec y}{A} \wedge A)}{(\forall \pvec w \qrreal{\pvec v}{\pvec w}{B} \wedge B)} \\[2mm]
\qrreal{\pvec x, a}{}{(\exists z A)} & :\equiv & \forall \pvec y \qrreal{\pvec x}{\pvec y}{(A[a/z])} \wedge A[a/z].
\end{array}
\end{equation}
The diagram of Figure \ref{factor-q-realizability} shows how such q-realizability corresponds to the $\starT{(\cdot)}$ translation, making use in this particular case of the forgetful translation $\forgetT{(\cdot)}$ of affine logic back into intuitionistic logic instead\footnote{In this case a diagram similar to the ones considered before would not lead to a commuting diagram (not even if logical equivalence is taken instead of syntactic equality). The problem is that whereas $A$ might contain existential quantifiers its interpretation $\qrreal{\pvec x}{\pvec y}{A}$ does not. Hence, formulas which are duplicated in $\uInter{\starT{A}}{\pvec x}{\pvec y}$ because of the $!$ in $\exists x ! A$ are not duplicated in $\starT{(\qrreal{\pvec x}{\pvec y}{A})}$ because the existential quantifiers have disappeared. One way to solve this is presented in \cite{GO(2010)}, but uses logical equivalence. Here we present an alternative solution which is to use the forgetful translation that leads to a commuting diagram with syntactic equality instead. Obviously this is a weaker result than the previous four diagrams, as $\starT{(A^I)} \equiv (\starT{A})^J$ implies $A^I \equiv \forgetT{((\starT{A})^J)}$ but not conversely.}.
\begin{figure}[h]
\begin{center}
\setlength{\unitlength}{10mm}
\begin{picture}(6.0,3.3)
\thicklines
\put(0.0,2.8){$A$}
\put(0.15,2.65){\vector(0,-1){1.8}}
\put(-0.7,1.7){$\starT{(\cdot)}$}
\put(0.6,2.95){\vector(1,0){4.3}}
\put(1.5,2.5){q-realizability}
\put(0.0,0.3){$\starT{A}$}
\put(5.0,2.8){$\qrreal{\pvec x}{\pvec y}{A} \equiv \forgetT{(\uInter{\starT{A}}{\pvec x}{\pvec y})}$}
\put(5.15,0.8){\vector(0,1){1.8}}
\put(5.45,1.7){$\forgetT{(\cdot)}$}
\put(0.7,0.45){\vector(1,0){4.2}}
\put(2.0,0.0){(\ref{basic-inter}) + (\ref{bang-real-truth})}
\put(5.0,0.3){$\uInter{\starT{A}}{\pvec x}{\pvec y}$}
\end{picture}
\caption{Factoring q-realizability}
\label{factor-q-realizability}
\end{center}
\end{figure}
\noindent If one observes that the $\circT{A}$ translation is affine logic equivalent to the ``banged" $\starT{A}$ translation, i.e. $\circT{A} \leftrightarrow~! \starT{A}$, one obtains the following interesting (apparently unobserved) correspondence between realizability with truth and q-realizability
\[ \mrt{\pvec x}{A} \quad \stackrel{{\rm IL}}{\Leftrightarrow} \quad \forall \pvec y \qrreal{\pvec x}{\pvec y}{A} \wedge A. \]
A great benefit of this analysis of truth interpretations via affine logic is that it gave us a handle to define truth variants of other functional interpretations. For instance, contrary to what was thought \cite{Joergensen(2004)}, we can immediately obtain a Diller-Nahm with truth instantiating (\ref{bang-unifying-truth}) as
\[
\uInter{! A}{\pvec x}{\pvec a} :\equiv~! \forall \pvec y \!\in\! \pvec a \, \uInter{A}{\pvec x}{\pvec y} \;\otimes\; ! A.
\]
For more details on the unification of functional interpretations with truth see \cite{GO(2010)}.
\begin{remark} It is essential here that one uses the full $\starT{(\cdot)}$ translation, not the simplification of the previous section (cf. Remark \ref{remark-trans-simp}) as the choice of interpretation (\ref{bang-unifying-truth}) for $! A$, although sound for affine logic, it is not sound for the extra principles (\ref{ufi-extra-principles}).
\end{remark}
\section{Putting it All Together}
\label{hybrid}
The analysis of different functional interpretations via \emph{affine logic} not only provides a setting where the precise differences between the interpretations can be clearly seen, but surprisingly it also allows us to combine multiple interpretations when analysing a single proof. This follows because, as observed by Girard, the bang ($! A$) is not a canonical operator. One can add multiple instances $!' A, !'' A, \ldots$ all with the same four rules without being able to show that any two are provably equivalent. This observation led us \cite{Hernest(2008),Oliva(2009B)} to consider a system of multi-modal affine logic with a different instance of $! A$ for each of the functional interpretations discussed above. For instance, we could add five different variants of $! A$ and interpret each as follows:
\[
\begin{array}{lll}
\uInter{{}!_\text{\rm k} A}{\pvec x}{} & :\equiv~! \forall \pvec y \uInter{A}{\pvec x}{\pvec y} & \text{(Kreisel's modified realizability)} \\[2mm]
\uInter{{}!_\text{\rm d} A}{\pvec x}{\pvec a} & :\equiv~! \forall \pvec y \!\in\! \pvec a \uInter{A}{\pvec x}{\pvec y} & \text{(Diller-Nahm interpretation)} \\[2mm]
\uInter{{}!_\text{\rm g} A}{\pvec x}{\pvec y} & :\equiv~! \uInter{A}{\pvec x}{\pvec y} & \text{(G\"odel's dialectica interpretation)} \\[2mm]
\uInter{{}!_\text{\rm kt} A}{\pvec x}{} & :\equiv~! \forall \pvec y \uInter{A}{\pvec x}{\pvec y} \otimes~! A & \text{(Kreisel's modified realizability with truth)} \\[2mm]
\uInter{{}!_\text{\rm dt} A}{\pvec x}{\pvec a} & :\equiv~! \forall \pvec y \!\in\! \pvec a \uInter{A}{\pvec x}{\pvec y} \otimes~! A \qquad & \text{(Diller-Nahm interpretation with truth)}
\end{array}
\]
This leads to what we have termed \emph{hybrid functional interpretations}. If left completely unrelated, however, it would be difficult to make any practical use of this idea. We can observe, however, that there is a certain partial order between these different modalities, as for instance, a witness for ${}!_\text{\rm k} A$ is clearly also a witness for ${}!_\text{\rm d} A$. Therefore, we can add a rule that allows us to conclude ${}!_\text{\rm d} A$ from ${}!_\text{\rm k} A$, i.e.
\[
\begin{prooftree}
\Gamma \vdash {}!_\text{\rm k} A
\justifies
\Gamma \vdash {}!_\text{\rm d} A
\end{prooftree}
\]
In the diagram of Figure \ref{bang-diagram} we write $!_X$ above $!_Y$ if the interpretation of $!_X A$ implies the interpretation of $!_Y A$. As such, we could say that modified realizability with truth and G\"odel's \emph{dialectica} interpretation are the two ``extreme" interpretations amongst these five. For more details on these hybrid functional interpretations see \cite{GO(2010),Hernest(2008),Oliva(2009B)}.
\begin{figure}[h]
\begin{center}
\setlength{\unitlength}{8mm}
\begin{picture}(4.5,4.5)
\thicklines
\put(1.0,-0.5){${}!_\text{\rm g}$}
\put(1.1,0.0){\line(0,1){0.7}}
\put(1.0,1.0){${}!_\text{\rm d}$}
\put(1.1,1.5){\line(0,1){0.7}}
\put(1.1,1.5){\line(2,1){1.4}}
\put(1.0,2.5){${}!_\text{\rm k}$}
\put(1.1,3.0){\line(2,1){1.4}}
\put(2.5,3.0){\line(0,1){0.7}}
\put(2.4,2.5){${}!_\text{\rm dt}$}
\put(2.4,4.0){${}!_\text{\rm kt}$}
\end{picture}
\end{center}
\label{bang-diagram}
\caption{Ordering between different interpretations of $! A$}
\end{figure}
\section{Directions for Further Work}
\label{future-work}
Let us conclude by outlining a few possible directions for further work. These are either directly related to the unification of functional interpretation or to the actual nature and better understanding of functional interpretations themselves.
\subsection{Functional interpretations with forcing}
The combination of realizability with Cohen's notion of forcing was originally studied by Goodman \cite{Goodman(1978)} who showed it to be an effective way to prove conservation results that cannot apparently be shown by realizability alone. Goodman's work is related to the interpretations with truth (cf. Section \ref{sec-truth}) as forcing is used precisely to recover the truth property (\ref{truth-property}). Although Goodman presented a single combined interpretation, Beeson \cite{Beeson(1979)} showed that Goodman's interpretation can actually be seen as a simple composition of the Kleene number realizability based on Turing machines with oracles followed by an application of forcing. Recently, another variant of realizability, called \emph{learning-based realizability} \cite{Aschieri(2010)}, has been developed providing an extension of realizability to classical arithmetic. Although different from Goodman's, the learning-based realizability has many similar features to Goodman's combination of realizability and forcing. For instance, the learning-based interpretation of formulas is described relative to a \emph{memory}, which can be understood as a forcing condition approximating a non-computable oracle. Ineffective formulas (formulas without computable realisers) can be given an approximating realiser that works only when the memory has the correct information. The main result is that from a proof one can extract an agent that will be able to smartly build an approximation to the memory good enough to eventually produce a correct realiser. Finally, Alexander Miquel \cite{Miquel(2011)} has been working on extending Krivine's classical realizability with forcing, in the context of second-order arithmetic. This raises a few questions:
\begin{itemize}
\item[({\bf Q1})] What underlies the combination of realizability and forcing in general? Can forcing be combined with other functional interpretations, e.g. Diller-Nahm? What benefits could that bring?
\item[({\bf Q2})] As with Goodman's interpretation, could the learning-based realizability be decomposed into a standard realizability interpretation followed by some variant of forcing?
\end{itemize}
\subsection{Bounded-like interpretations}
Very recently \cite{BBS(2012)} variants of modified realizability and the \emph{dialectica} interpretation have been proposed which apply to proofs in \emph{nonstandard arithmetic}. The main feature of the interpretation is to extract from a proof of an existential statement a finite set of candidate witnesses (as in Herbrand's theorem), rather than a precise witness. The authors show that finite sets are the appropriate way to interpret existential \emph{standard} quantifiers, while unrestricted existential quantifiers are interpreted uniformly (as in \cite{Berger(05c)} and \cite{Krivine(2003)}).
Also recently, so-called \emph{bounded} variants of the dialectica and modified realizability interpretations \cite{Ferreira(05A),Ferreira(05),Ferreira(06)} have been proposed which make use of the Howard/Bezem strong majorizability relation but in a more embedded way than Kohlenbach's monotone interpretation. The original motivation was to extend functional interpretations to deal with ineffective principles in analysis such as weak K\"onig's lemma even over weak fragments of analysis. The bounded modified realizability was then extended into a \emph{confined} variant \cite{FO(2008)} which looks both for upper and lower bounds. There are striking similarities between the functional interpretation of non-standard arithmetic and the bounded and confined interpretations, as pointed out in \cite{BBS(2012)}. That raises the question:
\begin{itemize}
\item[({\bf Q3})] What is the common structure behind these \emph{bounded-like} interpretations? In joint work with Gilda Ferreira \cite{FO(2012)} we have extended the unifying framework to deal with the bounded and confined interpretations, but unfortunately, this does not look to be general enough to include the non-standard arithmetic interpretation \cite{BBS(2012)}, as they make crucial use of a new form of functional application.
\end{itemize}
\subsection{Type-free functional interpretations}
We have so far only been discussing Kreisel's version of realizability known as \emph{modified realizability}. The original realizability interpretation, however, due to Kleene \cite{Kleene(45)}, makes use of numbers (codes of Turing machines) as realizers, rather than functionals of higher type. The crucial difference is that not all codes $n$ define a total function $\kleene{n} \colon \mathbb{N} \to \mathbb{N}$. As such, the realizability of an implication $A \to B$ was originally defined as
\[
\begin{array}{lcl}
\kreal{n}{(A \to B)} & :\equiv & \forall k (\kreal{k}{A} \to \defined{\kleene{n}(k)} \wedge \kreal{\kleene{n}(k)}{B}),
\end{array}
\]
so $\kleene{n}$ only needs to be defined on $k$ if $k$ is indeed a realizer\footnote{To appreciate the difference between Kleene number realizability and Kreisel's modified realizability it is enough to point out that the former is sound for the Markov principle whereas the later isn't. In fact, Kreisel developed modified realizability \cite{Kreisel(59)} precisely to show that the Markov principle is independent of intuitionistic arithmetic.} for $A$. Let us refer to Kleene's original notion of realizability as \emph{number realizability}. It is clear that a \emph{relational} variant of number realizability also exists. For instance, the clause for implication would be:
\[
\begin{array}{lcl}
\rkreal{n}{k}{(A \to B)} & :\equiv & \forall m \rkreal{k_0}{m}{A} \to \defined{\kleene{n}(k_0)} \wedge \rkreal{\kleene{n}(k_0)}{k_1}{B}
\end{array}
\]
where $k_0$ and $k_1$ denote the first and second projections inverses of the standard coding $\mathbb{N} \times \mathbb{N} \to \mathbb{N}$.
That raises the following questions:
\begin{itemize}
%
\item[({\bf Q4})] Is there a \emph{number realizability} interpretation of affine logic? By that we mean an interpretation which works on numbers rather than functionals of finite type, and makes use of the fact that realizers might be partial. For instance, that might involve modifying the clause for $A \multimap B$ in (\ref{basic-inter}) as
%
\[
\begin{array}{lcl}
\uInter{A \multimap B}{n}{k} & :\equiv & \uInter{A}{k_0}{\kleene{n_1}(k)} \multimap \uInter{B}{\kleene{n_0}(k_0)}{k_1}.
\end{array}
\]
%
But the question is when should we require that $\kleene{n_0}(k_0)$ and $\kleene{n_1}(k)$ be defined so as to obtain not only a sound interpretation but also possibly interpret new principles that are not interpreted by Kreisel's modified realizability? It seems none of the obvious choices work. But that of course does not rule out more comprehensive changes which could lead to a sound interpretation.
\item[({\bf Q5})] Related to ({\bf Q4}), can one in general show that every natural (e.g.~modular) functional interpretation of intuitionistic logic can be extended to an interpretation of intuitionistic affine logic? And, even if this is not the case, is it always possible to relate functional interpretations in a similar way to the one done in Section \ref{hybrid}, perhaps using different parameters than the interpretation of $! A$?
\item[({\bf Q6})] Is there a ``number variant" of the other aforementioned interpretations? Beeson \cite{Beeson(1978)} has looked at the question for the dialectica interpretation, which he calls a \emph{type-free} dialectica. Beeson points out that there cannot be one for the actual dialectica interpretation, as it requires decidability of quantifier-free formulas whereas statements of the form $\defined{\kleene{n}(k)}$ are not decidable in general. He then suggests a type-free variant of the Diller-Nahm interpretation as
%
\[
\begin{array}{lcl}
\uInter{A \to B}{n}{k} & :\equiv & \defined{\kleene{n_1}(k)} \wedge (\forall i \in \kleene{n_1}(k) \, \uInter{A}{k_0}{i} \to \defined{\kleene{n_0}(k_0)} \wedge \uInter{B}{\kleene{n_0}(k_0)}{k_1}).
\end{array}
\]
%
In other words, he requires the counter-example functions to be total\footnote{I confess to not have been able to completely verify the soundness of Beeson's interpretation. The problem seems to appear in the interpretation of the cut rule ($A \to B$ and $B \to C$ implies $A \to C$) as the ``positive" witnesses for $A \to B$ need not be total, but that is used in building the ``negative" witnesses for $A \to C$, which should be total (cf. \cite{Beeson(1978)} middle of page 221).}, whereas the witnessing functions might be partial. Could this be relaxed? Could this be translated to the setting of affine logic? Would this lead to extra principles that go beyond those interpreted by the typed Diller-Nahm interpretation?
\end{itemize}
\subsection{Short games versus long games}
The use of games between two players to model non-classical logics started with the work of Lorentzen \cite{Felscher(2002)} where formulas were put in correspondence with debates/dialogues so that those provable in intuitionistic logic corresponded to dialogues in which the first player had a winning ``strategy". This idea was refined in the works of Blass \cite{Blass(1992)}, Abramsky \cite{Abramsky(1994)} and several others, and led to complete semantics for fragments of linear logic.
The connections between games and the functional interpretations such as G\"odel's dialectica have been there from the start \cite{Scott(1968)}. In the final section 8 of \cite{Blass(1992)}, Blass discusses at great length how one can view de Paiva's \cite{dePaiva(1989B)} categorical formulation of the Diller-Nahm interpretation of linear logic as arising from Blass' game semantics. Blass' suggestion is that the functional interpretation of linear logic arises by considering short two-move games combined according to his rules but including ``Skolemisation" steps whenever it may be necessary to bring a long game into a two-move game.
\begin{itemize}
\item[({\bf Q7})] I feel that a better understanding of the differences between long games with concrete moves and the short games with higher-order moves is still lacking. Although Blass shows how one can think of the dialectica category as arising from his game semantics, it is well known that \emph{dialectica-like} games are useful to interpret extra principles that go beyond the interpreted logic such as the Markov principle, independence of premise and the axiom of choice. Blass long games, however, capture precisely some fragments of the logic providing a sound and complete semantics.
\item[({\bf Q8})] Related to ({\bf Q7}), can functional interpretations be used to build fully abstract models? Another question that would provide guidance towards this is: How does the functional interpretation of the \emph{propositional} fragment of linear logic relate to other models of linear logic such as proof nets, monoidal closed categories, coherent spaces and phase semantics?
\item[({\bf Q9})] In the context of long games people have been able to fine tune the interpreted logic by restricting the kind of strategies one or both of the players is allowed to play (e.g. innocent \cite{Hyland(2000)}, fair, history-free). Not much in this direction has been done in the setting of functional interpretations, whereby one could consider restrictions on the class of realisers in order to avoid interpreting certain principles. It seems hard, however, to think of any restrictions that would make the interpretation not sound with respect to the axiom of choice, for instance, as its realiser is the identity. But one could consider other restrictions such as linear functionals, functionals of certain complexity, etc.
\item[({\bf Q10})] Using the nomenclature of game theory \cite{Fudenberg(1991)}, the long games considered by Blass and Abramsky are said to be in \emph{extensive form}. Such games can be thought of as trees where each node in the tree is assigned one of the players and terminal nodes determine which player has won. Games in extensive form can be brought into a so-called \emph{normal form}, a matrix specifying for each given pair of strategies for the two players which of the two wins the game if they follow these strategies. Games in normal form can also be thought of as two-move games. The two-move game arising from a functional interpretation is obviously not going to be the same as the normal form of the given strategic Blass/Abramsky game. Two questions arise: What is the relation between these two different two-move games that come for the same logical formula $A$? Moreover, could the functional interpretation way of constructing two-move games have any relevance to game theory?
\end{itemize}
\subsection{Treading between linear and intuitionistic logic}
We have seen that we can better understand and generalise an interpretation of intuitionistic logic by moving to the more general (and finer) setting of affine logic. There are, however, some interesting logics in between linear (no contraction) and intuitionistic (full contraction) logic. For instance, consider the following ``intuitionistic" version of {\L}ukasiewicz logic (${\rm {\L}L}_i$) obtained by adding to affine intuitionistic logic the contraction schema
\begin{equation} \label{weak-contraction}
A \multimap S_B A \otimes K_B A
\end{equation}
where $S_B A :\equiv B \multimap A$ and $K_B A :\equiv (A \multimap B) \multimap B$. Note that (\ref{weak-contraction}) clearly follows from $A \multimap A \otimes A$ since $A$ implies over affine logic both $S_B A$ and $K_B A$. We can obtain ``classical" {\L}ukasiewicz logic (${\rm {\L}L}_c$) by adding the double negation elimination $(A^\perp)^\perp \multimap A$. If we denote by ${\rm CL} =$ classical logic, ${\rm IL} = $ intuitionistic logic, ${\rm AL}_i =$ intuitionistic affine logic, and ${\rm AL}_c =$ classical affine logic, the relation between these six logics is shown in the diagram below, where an arrow from $X$ to $Y$ means that $Y$ is an extension of $X$.
\begin{center}
\setlength{\unitlength}{10mm}
\begin{picture}(8,3)
\thicklines
\put(0.5,0.0){${\rm AL}_i$}
\put(1.2,0.15){\vector(1,0){2.7}}
\put(4.0,0.0){${\rm {\L}L}_i$}
\put(4.7,0.15){\vector(1,0){2.7}}
\put(7.5,0.0){${\rm IL}$}
\put(0.5,2.5){${\rm AL}_c$}
\put(1.1,2.65){\vector(1,0){2.7}}
\put(4.0,2.5){${\rm {\L}L}_c$}
\put(4.7,2.65){\vector(1,0){2.7}}
\put(7.5,2.5){${\rm CL}$}
\put(0.65,0.5){\vector(0,1){1.8}}
\put(4.15,0.5){\vector(0,1){1.8}}
\put(7.65,0.5){\vector(0,1){1.8}}
\end{picture}
\end{center}
\begin{itemize}
\item[({\bf Q11})] Since ${\rm {\L}L}_i$ is a fragment of ${\rm IL}$, obviously any interpretation of ${\rm IL}$ also interprets ${\rm {\L}L}_i$. The question, however, is whether one can make use of the fact that only limited contraction is available in ${\rm {\L}L}_i$ and hence restrict the kind of functionals needed for the interpretation. For instance, which kind of minimal fragment of the simply-typed lambda calculus would be sufficient to provide a \emph{modified realizability} interpretation of ${\rm {\L}L}_i$? This is related to {\bf (Q9)}.
\end{itemize}
\subsection{Endless possibilities?}
The various functional interpretations discussed in Section \ref{hybrid} are only what one could call the ``classic" interpretations. As has been discussed in this Section \ref{future-work}, several other new and fascinating functional interpretations have been discovered recently. Beyond those already mentioned one also has:
\begin{itemize}
\item Kohlenbach's \emph{monotone functional interpretations} \cite{Kohlenbach(A)}. These have been the cornerstone of the successful programme of \emph{proof mining} \cite{Kohlenbach(2008)}. It exploits a powerful combination of G\"odel's original dialectica interpretation with Howard's (or Bezem's) majorizability relation \cite{Bezem(85),Howard(73)}.
\item The \emph{Copenhagen interpretation} \cite{Biering(2008B)}. A variant of the dialectica interpretation where essentially in the interpretation of $A \to B$ the negative witnessing functional is allowed to ``give up" and not return a value. The original idea (apparently due to Martin Hyland) is that monads on types can quite often be lifted into an interpretation of (the comonad) $! A$. The Copenhagen interpretation carries this out for the monad $T X = X + 1$.
\item \emph{Krivine classical realizability} \cite{Krivine(2003)}. Realizability interpretation of classical second order arithmetic, recently extended to countable choice. Krivine's realizability can be viewed as a combination of negative translation with a simpler intuitionistic realizability interpretation \cite{Oliva(2008A)}.
\end{itemize}
We close with some final questions:
\begin{itemize}
\item[({\bf Q12})] Is there a common structure behind all functional interpretations? What would be the appropriate way to define what functional interpretations are in general?
\item[({\bf Q13})] Functional interpretations of classical logic have all been shown to arise from an interpretation of intuitionistic logic combined with a negative translation. Can one show that this is always the case?
\end{itemize}
\bibliographystyle{plain}
|
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"redpajama_set_name": "RedPajamaArXiv"
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| 5,487
|
Super City MOD APK [Unlocked All]
Among them is the superhero of the moment. There is a lot of attention being paid to these phenomena. Films associated with these products are the top-earning films and the most popular movies. It can be said that every video game that features superhero characters attracts a lot of attention. Over one million downloads of Super City (Superhero Sim) have been made on Google Play. You can tell that this game is different from most current popular products just by looking at its graphics. They did not follow common sense but went their own way. If you look closely, you'll realize that.
It is gorgeous even though it does not seem to be lovely. A meticulous and accurate design goes into every detail of the character. It is likely that each character will have distinctive characteristics and their colors will also reflect the famous elements. When you look at your idol, you recognize him immediately. Characters that work particularly well are smooth and fun, even though the style is slightly different. There will be a lot of different combos that each character will be able to manipulate, and each will be suited to the personality of the character.
You can choose among every famous superhero you've ever heard of in Super City (Superhero Sim). Marvel and DC heroes cohabitant one of the world's most special cities, where everyone has some kind of power. It is likely that even evil people will join the most chaotic battle ever fought. What will the winner be? The combat system in Super City will be familiar with combat RPGs. Action games today are very different from this. You can play it on first-generation consoles as if it were an old wrestling game. With that mechanism and graphics like that, players are reminded of old games while simultaneously being transported to a new and modern setting.
Download Super City MOD APK
You can start playing Super City immediately after learning how to download it. The following notes are in order:
Visit our installation guide to learn how to install.
You can check CPU and GPU of Android devices with the CPU-Z application
Moreover, the power of these devices can be customized based on your preferences. It's possible to customize power, equipment, and body stats according to your preferences. This equipment will ensure that your hero is stronger, which is one of the main reasons for their use. However, you will have to wage a lot of battle to get that upgrade. I don't particularly like it. There is a clear representation of the controls on the screen. A joystick is not present on the left side, but rather a 4-way navigation simulator. On the right will make a set of skills denoted by letters You will fight like a superhero if you are able to maximize the effects of these combos. Each person brings a different set of skills to the game so each player will feel something different.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 683
|
{"url":"http:\/\/clay6.com\/qa\/37916\/the-number-of-tangents-that-can-be-drawn-to-two-non-intersecting-circles-is","text":"Home\u00a0\u00a0>>\u00a0\u00a0AIMS\n\n# The number of tangents that can be drawn to two non- intersecting circles is :\n\n$\\begin{array}{1 1}(A)\\;4 \\\\(B)\\;3 \\\\(C)\\;2 \\\\ (D)\\;13 \\end{array}$\n\nThe number of tangents that can be drawn to two non- intersecting circles is 4\nHence A is the correct answer.","date":"2017-08-21 06:39:53","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7667396068572998, \"perplexity\": 358.72660530952214}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-34\/segments\/1502886107720.63\/warc\/CC-MAIN-20170821060924-20170821080924-00378.warc.gz\"}"}
| null | null |
Q: Excel File Error After Download in C# Using NPOI I have an excel file template, and then add dropdown data to excel using C#, everthing is fine in my local machine, i can download it but when i put it in server is always getting error
and actually, this error file still can be used, but its really annoying especially for user
i,m using NPOI for processing this excel file
XSSFWorkbook hssfwb;
string path = Server.MapPath("~/Content/Uploads").ToString() + ConfigurationManager.AppSettings["PathAllocationRuleTemplate"].ToString();
string newpath = Server.MapPath("~/Content/Uploads").ToString() + ConfigurationManager.AppSettings["PathAllocationRule"].ToString();
using (FileStream file = new FileStream(path, FileMode.Open, FileAccess.Read))
{
hssfwb = new XSSFWorkbook(file);
file.Close();
}
> some code for filling data
**downloading part**
using (FileStream file = new FileStream(newpath, FileMode.Create, FileAccess.Write))
{
hssfwb.Write(file);
file.Close();
}
System.Web.HttpResponse response = System.Web.HttpContext.Current.Response;
response.ClearContent();
response.Clear();
response.ContentType = "application/vnd.openxmlformats-officedocument.spreadsheetml.sheet";
response.AddHeader("Content-Disposition", "attachment; filename=Allocation Rule Template.xlsx");
response.TransmitFile(newpath);
response.Buffer = true;
response.Flush();
response.End();
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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| 1,479
|
Atherigona tricolorifolia este o specie de muște din genul Atherigona, familia Muscidae, descrisă de Fan și Liu în anul 1982. Conform Catalogue of Life specia Atherigona tricolorifolia nu are subspecii cunoscute.
Referințe
Atherigona
|
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"redpajama_set_name": "RedPajamaWikipedia"
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| 6,369
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\section{Introduction}
\noindent{\bf {\it 1. Introduction.}} Electric weak links made of materials with strong spin-orbit interactions open a promising
way to achieve spin-dependent transport of electrons.
In the particular case of the Rashba spin-orbit coupling \cite{Rashba}, the interaction can be tuned electrostatically \cite{Nitta,Sato,Beukman}
or mechanically \cite{RS2013, MJ2018}. This coupling obeys time-reversal symmetry which prevents spin splitting of electron transport in two-terminal junctions \cite{bardarson}, in most cases eliminating the possibility to manipulate electronic conduction through Rashba weak links.
Spin-orbit interactions do, however, have an effect on spin-polarized electrons in magnetic materials \cite{datta,sarkar,
RS2014}, and on electrons subjected to
external magnetic fields \cite{lyanda,janine,us,Saarikoski,Shmakov,Nagasawa}.
Here we propose that imposing a {\it time dependence} on the effective magnetic fields induced by the spin-orbit coupling offers another means to destroy time-reversal symmetry of two-terminal junctions. In particular we predict that time-dependent Rashba interactions generate a DC electric current through unbiased junctions.
Coherent electronic transport in response to periodic modulations
of the shape of quantum dots or of other potential parameters of mesoscopic junctions
has been attracting considerable interest
\cite{Altshuler,Avron} following the seminal paper by Thouless \cite{Thouless}, who showed that a slow periodic variation of the potential landscape may yield quantized and non-dissipative particle transport in unbiased junctions--a phenomenon termed ``adiabatic quantum pumping".
Adiabatic pumping of spin currents resulting from periodic modulations of the shape of a spin-orbit coupled junction has been discussed as well \cite{Sharma},
also as a result of temporal modulations of the Rashba interaction \cite{Governale,Avishai,Brosco,MJ2019}. However, the possibility to induce a DC {\em particle current} by such modulations in the absence of a bias voltage was not considered.
\begin{figure}[htp]
\includegraphics[width=8.5cm]{linear_4}
\caption{(Color online.) Illustration of the model system. A quantum dot, represented by a localized energy level, is attached by two weak links lying in the $x-y$ plane to two reservoirs, denoted $L$ and $R$. An AC electric field along
$\hat{\bf z}$, whose amplitude oscillates with frequency $\Omega$, induces a Rashba spin-orbit interaction in the links.
\label{sys}
\end{figure}
DC charge transport driven by time-dependent spin-orbit coupling is an alternative to the pumping of charge caused by tuning periodically the potential landscape of mesoscopic structures. It occurs in
inhomogeneous junctions in which mirror reflection-symmetry is violated. In an unbiased junction no net current flows when the spin-orbit interaction is static, even in an asymmetric device: transport of electrons incident from the two opposite reservoirs is fully equilibrated. In fact, a static spin-orbit coupling, which results in a unitary evolution of the spinor wave-function, does not modify the DC transport. However, unitarity
is destroyed by the time dependence that entails additional reflection processes due to inelastic tunneling. These in general differ
for the two opposite directions in which electrons can be reflected from the junction, leading to uncompensated electronic transport. To elaborate on this general statement we refer to the device illustrated in Fig. \ref{sys}: a quantum dot represented by a single level of energy $\epsilon$ is
connected by spin-orbit coupled weak links to left and right reservoirs. Due to the Aharonov-Casher effect \cite{AC}, the tunneling matrix elements attain unitary-matrix (in spin space) phase factors \cite{Oreg}, denoted below by $V_{L(R)}$ for tunneling through the left (right) link. When these are time dependent, the reflection, say to the left direction\aa{,} is then modified by factors of the form
\begin{align}
\int ^{t}dt' [V^{\dagger}_{L}(t) e^{i(\epsilon -\omega+i\Gamma)(t-t')}V^{}_{L}(t')+{\rm c.c.}]
\ ,
\label{int}
\end{align}
where $\Gamma$ is the width of the resonance formed on the dot (using $\hbar =1$). This form pertains to tunneling from the left lead to the dot, accomplished at time $t'$, followed by a time evolution of the electronic wave-function on the dot during the time interval $t-t'$, and then tunneling back to the left lead at time $t$.
One observes
that in the static case, where $V^{\dagger}_{L}V^{}_{L}=1$, the integral (\ref{int}) yields the usual Breit-Wigner density of states on the dot, $2\Gamma/[(\omega-\epsilon)^{2}+\Gamma^{2}]$. For a
Rashba interaction that varies periodically with frequency $\Omega$,
the reflection comprises multiple inelastic channels with emission and absorption of $n\Omega$ energy quanta, which shift the resonance above and below $\epsilon$. This complex modification of the reflection may differ for the opposite directions of the junction, leading to a net DC current.
Below we show that such a difference can indeed result from the Rashba interaction when the lengths of the two weak links
are not identical.
\noindent{\bf {\it 2. Details of the model.}}
\label{details}
The Rashba interaction in the links is induced by external electric fields, which can be polarized in various ways. Here we focus on the simplest one of a longitudinal field (along the $\hat{\bf z}$ direction), whose amplitude oscillates with frequency $\Omega$ (see Fig. \ref{sys}).
The Aharonov-Casher phase factor multiplying the tunneling amplitude through a link of length $d$ along $\hat{\bf d}$ is then \cite{Aharony,moi}
\begin{align}
\exp[i\varphi^{}_{AC}(t)]=\exp[ik^{}_{\rm so}d\cos (\Omega t)\hat{\bf z}\times\hat{\bf d}\cdot{\mbox{\boldmath{$\sigma$}}}]\ ,
\end{align}
where ${\mbox{\boldmath{$\sigma$}}}=(\sigma^{}_{x},\sigma^{}_{y},\sigma^{}_{z})$ is the vector of the Pauli matrices, and $k_{\rm so}^{}$
is the Rashba coupling.
For the geometry of Fig.~\ref{sys}
the Aharonov-Casher phase factors are
\begin{align}
V^{}_{L(R)}(t)&=\cos[k^{}_{\rm so}d^{}_{L(R)}\cos(\Omega t)]\nonumber\\
&+i
\sin[k^{}_{\rm so}d^{}_{L(R)}\cos(\Omega t)]{\mbox{\boldmath{$\sigma$}}}\cdot\hat{\bf e}^{}_{L(R)}\ ,
\label{linp}
\end{align}
where $d_{L(R)}$ is the length of the link connecting the dot to the left (right) reservoir. For links along the $\hat{\bf x}-$direction (Fig.~\ref{sys}), the effective magnetic fields
created by the Rashba interaction are along $\hat{\bf e}^{}_{L}=-\hat{\bf y}$ and $\hat{\bf e}^{}_{R}=\hat{\bf y}$.
The entire junction
is described by the Hamiltonian
\begin{align}
{\cal H}(t)={\cal H}^{}_{0}+{\cal H}^{}_{\rm tun}(t)\ ,
\end{align}
where the time-independent ${\cal H}^{}_{0}$ pertains to the decoupled system, i.e., two separate reservoirs and a quantum dot,
\begin{align}
{\cal H}^{}_{0}=
\sum_{\sigma}\epsilon d^{\dagger}_{\sigma}d^{}_{\sigma}+\sum_{{\bf k} ,\sigma}\epsilon^{}_{ k}c^{\dagger}_{{\bf k}\sigma}c^{}_{{\bf k}\sigma}+\sum_{{\bf p} ,\sigma}\epsilon^{}_{ p}c^{\dagger}_{{\bf p}\sigma}c^{}_{{\bf p}\sigma}\ .
\label{H0}
\end{align}
The first term in Eq.~(\ref{H0}) describes the decoupled dot, with
$d^{\dagger}_{\sigma}$ ($d^{}_{\sigma}$) being the creation (annihilation) operator of an electron of energy $\epsilon$ in the spin state $|\sigma\rangle$.
The other two terms describe the decoupled electronic reservoirs, assumed to comprise non-polarized free electrons. There, $
c^{\dagger}_{{\bf k}\sigma} $ ($c^{}_{{\bf k}\sigma}$) creates (annihilates) a particle with energy $\epsilon_{k}$ ($\epsilon_p$), momentum ${\bf k}$ (${\bf p}$), and spin $\sigma$
in the left (right) lead. The tunneling Hamiltonian reads
\begin{align}
\label{Htun}
&{\cal H}^{}_{\rm tun}(t)=
\sum_{\alpha=L,R}{\cal H}^{\alpha}_{\rm tun}(t
\\
&=\sum_\alpha J^{}_{L(R)}\sum_{\sigma,\sigma'}\{[V^{}_{L(R)}(t)]^{}_{\sigma\sigma'}
\sum_{{\bf k}({\bf p})}c^{\dagger}_{{\bf k}({\bf p})\sigma}d^{}_{\sigma'}+{\rm H. c. }\}\ .
\nonumber
\end{align}
The tunneling amplitudes, characterized by the energy $J_{L(R)}$, are assumed to be
given by their values at the Fermi energy.
\noindent{\it{3. Currents in the time domain.}}
Within the Keldysh technique \cite{Langreth,Jauho} the particle current, say into the left lead, is conveniently expressed in terms of the Green's function on the dot \cite{Meir} $G_{dd}(t,t')$ (a matrix in spin space),
\begin{align}
I^{}_{L}(t)\equiv
\frac{d}{dt} \sum_{{\bf k}}\sum_{\sigma}&\langle c^{\dagger}_{{\bf k}\sigma}c^{}_{{\bf k}\sigma}\rangle
= \int dt^{}_{1}{\rm Tr} \{\Sigma^{}_{L}(t,t^{}_{1})
G^{}_{dd}(t^{}_{1},t)\nonumber\\
&-G^{}_{dd}(t,t^{}_{1})\Sigma^{}_{L}(t^{}_{1},t)
\}^{<}_{}\ ,
\label{ILA}
\end{align}
where the angular brackets denote quantum averaging. The superscript $<$ indicates the lesser Green's function, and $\Sigma^{}_{L}(t,t')$
is the self energy due to the coupling of the dot to the left reservoir,
\begin{align}
\Sigma^{}_{L}(t,t')=&J^{2}_{L}V^{\dagger}_{L}(t)g^{}_{L}(t,t')V^{}_{L}(t')\ ,
\label{ASEL}
\end{align}
where $g^{}_{L}(t,t')$ is the Green's function of the decoupled left reservoir. Green's functions without a superscript represent all three Keldysh Green's functions, the lesser, and the retarded and advanced ones (marked by the superscripts $r$ and $a$).
The expression in Eq. (\ref{ILA}) can be worked out explicitly in the wide-band limit \cite{Odashima,supplemental}, where the densities of states in each of the reservoirs are approximated by their value on the Fermi surface.
The self energy $\Sigma_{L}^{r(a)}(t,t')$ is then
proportional to the unit matrix in spin space, with
\begin{align}
\Sigma^{r(a)}_{L}(t,t')&=\mp i\Gamma^{}_{L}\delta (t-t')\ ,
\label{rasel}
\end{align}
where
\begin{align}
\Gamma^{}_{L}&=\pi{\cal N}^{}_{L}J^{2}_{L}\ ,
\label{AgamL}
\end{align}
is the (partial) width of the resonance formed on the dot due to the coupling with the left reservoir and ${\cal N}^{}_{L}$ denotes the density of states of the left lead on the Fermi surface. The total width of the resonance on the dot is $\Gamma=\Gamma_{L}+\Gamma_{R}$. The lesser self energy is a matrix in spin space,
\begin{align}
\Sigma^{<}_{L}(t,t')&=2i\Gamma^{}_{L}\int\frac{d\omega}{2\pi}e^{-i\omega(t-t')}f(\omega)V^{\dagger}_{L}(t)V^{}_{L}(t')\ .
\label{AlesSEL}
\end{align}
Here $f(\omega)=\{\exp[\beta(\omega-\mu)]+1\}^{-1}$ is the equilibrium Fermi distribution, with the inverse temperature $\beta$ and the chemical potential $\mu$ being identical for the two reservoirs. [$\Sigma_{R}(t,t')$ is obtained from these expressions by changing $L$ to $R$.]
The explicit expression for $I_{L}(t)$ is found by applying the Langreth rules \cite{Langreth} to Eq. (\ref{ILA}),
\begin{align}
&I^{}_{L}(t)
=2\Gamma^{}_{L}{\rm Tr}\{-iG^{<}_{dd}(t,t) -\int\frac{d\omega}{2\pi}f(\omega)\nonumber\\
&\times
\int^{t}_{}dt^{}_{1}
[e^{-i(\epsilon-\omega+i\Gamma)(t^{}_{1}-t)}V^{\dagger}_{L}(t)V^{}_{L}(t^{}_{1})+{\rm c.c.}]\}\ .
\label{BIL}
\end{align}
The equal-time lesser Green's function $-iG^{<}_{dd}(t,t)$, which yields the occupation of the dot, is
\begin{align}
-iG^{<}_{dd}(t,t)&=\int\frac{d\omega}{\pi}f(\omega)[\Gamma^{}_{L}{\rm w}^{}_{L}(\omega,t
+
\Gamma^{}_{R}{\rm w}^{}_{R}(\omega,t)]\ ,
\label{AG}
\end{align}
where
\begin{align}
&{\rm w}^{}_{L}(\omega,t)=\int^{t}_{}dt^{}_{1}\int ^{t}_{}dt^{}_{2}
e^{-i\omega (t^{}_{1}-t^{}_{2})}\nonumber\\
&\times
e^{-i(\epsilon-i\Gamma)(t-t^{}_{1})}e^{-i(\epsilon+i\Gamma)(t^{}_{2}-t)}
V^{\dagger}_{L}(t^{}_{1})V^{}_{L}(t^{}_{2})\ ,
\label{WA}
\end{align}
with an analogous expression for $w_{R}(\omega,t)$ (more details are given in Ref. \onlinecite{supplemental}). Thus, integrals of the form (\ref{int}) determine the explicit expressions for the current.
Using the expansion \cite{AS}
\begin{align}
e^{i\zeta\cos(\phi)}=\sum_{n=-\infty}^{\infty}i^{n}J^{}_{n}(\zeta)e^{in\phi}\ ,
\end{align}
where $J_{n}(\zeta)$ in the Bessel function of integer order $n$, one finds
(see Ref. \onlinecite{supplemental} for details)
\begin{align}
{\rm w}^{}_{L}(\omega,t)&=\Big
|J^{}_{0}(k^{}_{\rm so}d^{}_{L})D(\omega)\nonumber\\
&+\sum_{n=1}^{\infty}(-1)^{n}_{}J^{}_{2n}(k^{}_{\rm so}d^{}_{L})F^{}_{2n}(\omega,t)\Big |^{2}_{}\nonumber\\
&+
\Big |\sum_{n=0}^{\infty}(-1)^{n}_{}J^{}_{2n+1}(k^{}_{\rm so}d^{}_{L})F^{}_{2n+1}(\omega,t)\Big |^{2}_{}\ ,
\label{ww}
\end{align}
where
\begin{align}
D(\omega)=i/[\omega-\epsilon+i\Gamma]
\end{align}
is the Breit-Wigner resonance on the dot, and
\begin{align}
F^{}_{n}(\omega,t)=D(\omega-n\Omega)e^{in\Omega t}+D(\omega+n\Omega)e^{-in\Omega t}
\end{align}
is an even function of $\Omega$ that contains the contributions of the inelastic processes.
The second term on the right-hand side of Eq. (\ref{BIL}) is found in a similar fashion \cite{supplemental}. The particle current is then
\begin{align}
I^{}_{L}(t)=&4\Gamma^{}_{L}\Gamma^{}_{R}\int \frac{d\omega}{\pi}f(\omega)[{\rm w}^{}_{R}(\omega,t)-{\rm w}^{}_{L}(\omega,t)]\nonumber\\
&-2\Gamma^{}_{L}\int\frac{d\omega}{\pi}f(\omega)\frac{d{\rm w}^{}_{L}(\omega,t)}{dt}\ .
\label{ILC}
\end{align}
One notes that $I^{}_{L}(t)+I^{}_{R}(t)$ [the latter is obtained by interchanging $L$ with $R$ in Eq. (\ref{ILC})] equals the time derivative of $-{\rm Tr}\{iG^{<}_{dd}(t,t)\}$ [Eq. (\ref{AG})] which is the occupation on the dot; i.e., charge is conserved in the junction. Note also that for $\Omega=0$ Eq. (\ref{ww}) becomes w$^{}_{L}(\omega)=[\cos^{2}(k^{}_{\rm so}d^{}_{L})+\sin^{2}(k^{}_{\rm so}d^{}_{L})]|D(\omega)|^{2}_{}=|D(\omega)|^{2}_{}$ which depends neither on the length $d_{L}$ nor on the spin-orbit coupling $k_{\rm so}$. In that case the first term on the right-hand side of Eq. (\ref{ILC}) vanishes, and there is no DC particle flow in an unbiased junction.
\noindent{\it{4. DC electromotive force generated by time-dependent Rashba interaction.}}
The current $I_{L}(t)$ comprises a static term, in addition to the time-dependent one. Obviously the derivative $d{\rm w}_{L}(t)/dt$ depends on time; but ${\rm w}_{L}$ (and similarly ${\rm w}_{R}$) contains a static term, ${\rm w}^{}_{L,{\rm s}}$, which takes a particularly simple form,
\begin{align}
{\rm w}^{}_{L,{\rm s}}(\omega)&=\sum_{n=-\infty}^{\infty}J^{2}_{n}(k^{}_{\rm so}d^{}_{L})|D(\omega-n\Omega)|^{2}
\ ,
\label{wLs}
\end{align}
which is even in $\Omega$.
As a result, the DC particle current through the junction is
\begin{align}
I^{}_{DC}&=\int \frac{d\omega}{\pi}4\Gamma^{}_{L}\Gamma^{}_{R}|D(\omega)|^{2}\nonumber\\
&\times\sum_{n=-\infty}^{\infty}f(\omega+n\Omega)[J^{2}_{n}(k^{}_{\rm so}d^{}_{R})-J^{2}_{n}(k^{}_{\rm so}d^{}_{L})]\ .
\label{Idc}
\end{align}
(The time-dependent parts of the currents can be found in Ref. \onlinecite{supplemental}.)
Figure \ref{IDC} portrays the current {\it vs.} $k^{}_{\rm so}d^{}_R$ at a fixed value of $k^{}_{\rm so}d^{}_L$, as calculated from Eq. (\ref{Idc}) for several values of temperature and $\Omega$. The oscillations, at low temperatures, reflect the oscillatory length-dependence of the effect of the Rashba interaction \cite{Aharony}.
These oscillations disappear gradually as the temperature is raised. At low temperatures and large $\Omega$'s, $I_{DC}$ is dominated by the oscillations of the zeroth and first order Bessel functions.
The appearance of DC electronic charge transport in the absence of a bias voltage across the device is a manifestation of an electromotive force acting in the electric circuit. In our case, the force relies on the electronic spin, and drives the electron\st{s'} flow through a junction subject to a time-dependence spin-orbit interaction. The driving occurs due to the fermionic nature of the electrons which imposes constraints on the inelastic spin-scattering induced by the time-dependent Rashba interaction:
some of the inelastic scattering channels become
partly blocked due to the Pauli principle. This is why the unitarity of spin transmission, which would hold if all inelastic transmission channels would be equally open, is broken \cite{sumrule}.
The peculiar photovoltaic effect discussed above manifests itself in inhomogeneous devices with a well-defined direction of the inhomogeneity along the direction of the current flow. The single-dot tunneling device studied here, in which the reflection asymmetry is generated by the different lengths of the links (in conjunction with the Rashba coupling), is an example of such an inhomogeneity.
\begin{figure}[htp]
\includegraphics[width=5.5cm]{IDCa.pdf}\\
\includegraphics[width=6cm]{IDCb.pdf}
\caption{The particle current $I_{\rm DC}$, normalized to $I^{}_{0}=(4\Gamma^{}_{L}\Gamma^{}_{R})/(\Gamma\pi\hbar)$, calculated from Eq. (\ref{Idc})
as a function of $k^{}_{\rm so}d^{}_{R}$ for $k^{}_{\rm so}d^{}_{L}=1.0$, $\epsilon-\mu=0.5\, \Gamma$; (a) $\Omega =0.5\,\Gamma$,
(b) $\Omega =2.0\,\Gamma$. The increasing dash lengths correspond to $\beta\Gamma$=10.0, 2.0, 1.0, and 0.5.}
\label{IDC}
\end{figure}
One may propose a simple procedure to measure the spin-orbit-induced electromotive force. Suppose that the spin-orbit coupled weak link (which contains the dot) is an element of an {\it open} electric circuit. Then the spin-driven electromotive force would lead to an accumulation of extra charges of opposite signs on the two terminals, and in turn to the building up of a voltage drop across the junction. A steady-state configuration would then emerge, provided that the ohmic current generated by this voltage drop compensates the DC current due to the electromotive force induced by the Rashba interaction.
Thus, a novel photovoltaic effect can be predicted: a microwave field applied to a gate electrode (see Fig. \ref{sys}) induces a voltage drop across the junction.
A simple analytical estimate of the
voltage signal can easily be obtained for a weak Rashba coupling,
$k^{}_{\rm so}d^{}_{L(R)}\ll 1$: In the absence of the spin-orbit interaction, a bias voltage $V$ on the junction gives rise to a DC particle current \cite{Jauho}
\begin{align}
I^{}_{\rm DC}=\frac{4\Gamma^{}_{L}\Gamma^{}_{R}}{\pi\hbar}\frac{eV}{\epsilon^{2}_{0}+\Gamma^{2}}\sim
\frac{4\Gamma^{}_{L}\Gamma^{}_{R}}{\pi\epsilon^{2}_{0}}\frac{eV}{\hbar}\ ,
\label{IDC0}
\end{align}
where $\epsilon_{0}^{}\equiv \epsilon-\mu $ is assumed to be much larger than $\Gamma $ in the last step ($\hbar$ was re-introduced into the expressions for the following estimates).
On the other hand, according to Eq. (\ref{Idc}) at small spin-orbit coupling, the oscillating Rashba interaction generates the zero-temperature particle DC current
\begin{align}
&I^{}_{\rm DC}\Big |^{}_{T=0}=\frac{4\Gamma^{}_{L}\Gamma^{}_{R}}{\pi\hbar\Gamma}\frac{k^{2}_{\rm so}[d^{2}_{L}-d^{2}_{R}]}{2}\\
&\times\Big [\frac{1}{2}\Big (
\arctan\frac{\epsilon^{}_{0}+\Omega}{\Gamma}
+
\arctan\frac{\epsilon^ {}_{0}-\Omega}{\Gamma}\Big )-\arctan\frac{\epsilon^ {}_{0}}{\Gamma}\Big ]
\ ,
\nonumber
\end{align}
which becomes, for $\epsilon^{}_{0}\gg\Gamma$ and $\Omega<\epsilon^{}_{0}$
\begin{align}
&I^{}_{\rm DC}\Big |^{}_{T=0}\sim
\frac{4\Gamma^{}_{L}\Gamma^{}_{R}}{\pi\epsilon^{2}_{0}}k^{2}_{\rm so}[d^{2}_{R}-d^{2}_{L}]\frac{(\hbar\Omega)^{2}}{2\hbar\epsilon^{}_{0}}\ .
\label{IT0}
\end{align}
Thus, the voltage drop $V^{}_{\rm em}$ generated by the electromotive force is
\begin{align}
V^{}_{\rm em}=k^{2}_{\rm so}(d^{2}_{R}-d^{2}_{L})(\hbar\Omega)^{2}/(2e\epsilon^{}_{0})\ .
\end{align}
Similar considerations for the oscillatory length-dependence pertain to the case where the Rashba interaction is induced by mechanical vibrations of the nanowire forming the link \cite{RS2013, MJ2018}.
Our model system could be implemented by, e.g., three in-line, side-gated InAs nanowires \cite{Scherubl}. The left and right nanowires of length $d_{L}$ and $d_{R}$ would serve as weak links and be in tunneling contact with, respectively, the source- and drain electrodes as well as with the short, central nanowire, which would serve as a quantum dot. One of the two gates on either side of the weak links would be excited by a microwave field that creates an AC gate voltage, $V_{ac}\cos(\Omega t)$ \cite{Nowack}, while a static voltage on the the two gates on either side of the quantum dot would be used to tune the energy levels in the dot.
With a distance of $\sim$200 nm between the side gates \cite{Scherubl} a microwave-generated amplitude of $V_{ac} = 1$ V on the side gates would produce a transverse electric field amplitude of $\sim$50 kV/cm in the wires, corresponding to a Rashba parameter $\alpha_R = \hbar^2 k_{\rm so}/m^* \sim 50\, {\rm meV} \cdot$\AA\, \cite{Zunger} and, using $m^* = 0.023 m_e$, a Rashba coupling $k_{\rm so} \sim 2\cdot 10^{-3}\,$(nm)$^{-1}$ in the weak links. Assuming $d_{L} \sim d_{R} \sim 250\,$nm and microwave frequency of $2\pi \times 100\,$ GHz (so that $\hbar \Omega$ is of the order of the energy level $\epsilon_0\sim 1\,$meV [with respect to the chemical potential]) one finds $V_{\rm em}\sim 5\ \mu$V; thus the photovoltaic voltage in response to the microwave field seems to be measurable. Using the same parameter estimates the particle current, Eq. (\ref{IT0}), is $\sim 5\cdot 10^{7}$ s$^{-1}$, corresponding to a charge current $\sim 10$ pA.
\noindent{\it{5. Summary.}}
We have found that the spin-orbit (Rashba) interaction confined to an electric weak link, which -- when static -- has no significant effect on DC transport of two-terminal devices, may act as a source of DC currents
when generated by a periodic electric field. This electric field renders the Rashba interaction time dependent, breaking the unitarity of the spin transmission by generating inelastic transmission channels. We have shown that this loss of unitarity appears as additional contributions to the backscattering [see Eqs. (\ref{int}) and (\ref{WA})]. An estimate of the generated voltage drop in an open circuit suggests that it can be detected experimentally.
The effect we find is due to modifications of the probabilities for electron reflections, which are different for electrons approaching the junction from opposite directions; nonetheless, it is not related to quantum pumping \cite{Thouless}. The origin of the latter are different time-dependent {\em phases} of the instantaneous reflection amplitudes \cite{Avron}, whereas a straightforward calculation of the instantaneous scattering matrix
for the junction illustrated in Fig. \ref{sys}
shows that the reflection amplitudes do not depend on time. This is because $V^{\dagger}_{L}(t)V^{}_{L}(t)=1$ due to the unitarity of the Aharonov-Casher phase factor. In our case, the reflections are modified by Aharonov-Casher phase factors at different times, and necessitate the inclusion of the inelastic dynamics on the dot.
\begin{acknowledgments}
This research was partially supported by the Israel Science Foundation (ISF), by the infrastructure program of Israel Ministry of Science and Technology under contract 3-11173, and by the Pazy Foundation. We acknowledge the hospitality of the PCS at IBS, Daejeon, Korea, and Zhejiang University, Hangzhou, China, where part of this work was supported by
IBS funding number
(IBS-R024-D1).
\end{acknowledgments}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,698
|
\subsection{Network Architecture}
Our representation learning module consists of two fully convolutional networks both based on VGG16 architecture~\cite{VGG16} which we call them as \emph{Collision Net} and \emph{Semantic Net}. Figure~\ref{fig:net_arch} shows our network architecture.
For the Collision Net, we follow~\cite{sadeghi2017cadrl} to pre-train a free-space prediction network.
Collision Net takes in an RGB image $I$ and the output logit of its last convolutional layer provides an $N\times N$ collision map $\phi_{\hat{\theta}_{c}}(I)$ which predicts if an obstacle exists in the distance of 1 meter to the agent in its 2D ego-centric view. In Figure~\ref{fig:net_arch}, $\phi_{\hat{\theta}_{c}}(I)$ is shown as a purple $N \times N$ map.
Our Semantic Net is built and trained based on~\cite{izadinia2018viser}.
We pre-train our Semantic Net on the MS-COCO object categories~\cite{lin2014microsoft} with a weakly supervised object localization setup similar to~\cite{izadinia2018viser}. We use the penultimate layer of the fully convolutional neural network of~\cite{izadinia2018viser} to encode visual semantics in the spatial image space. Semantic Net describes each RGB image input via an $N\times N \times 2048$ map which we denote it as $S(I)$ and is shown by yellow box in Figure ~\ref{fig:net_arch}.
For each goal reaching task, our network takes in a goal image $I^{g}$ that is fixed during the entire episode. At each timestep $t$, the network takes in the current image $I_t$, the previous image $I_{t-1}$ as well as a goal image $I^{g}$. We use our Semantic Net to compute semantic feature representations $S(I^{t})$, $S(I^{t-1})$ and $S(I^{g})$, respectively. To represent the semantic correlation between the goal image and each of the input images in the 2D ego-centric view of the agent, we convolve the semantic visual representation of each input image with that of the goal image $\phi_{\hat{\theta}_{s}}(I,I_g) = S(I)\odot S(I^{g})$. Also, for each pair of consecutive input images $I_t$ and $I_{t-1}$, we compute the optical flow map $\psi(I_t,I_{t-1})$. We then stack the resulted pairs of collision maps $\phi_{\hat{\theta}_{c}}$, semantic correlation maps $\phi_{\hat{\theta}_{s}}$, and optical flow map $\psi$ to generate the visual representation $\Phi_{\hat{\theta}}$ at each timestep $t$. For brevity we omit $I$s from the equation.
\begin{equation}
\label{eq:rep}
\Phi_{\hat{\theta}_{t}} = [\phi_{\hat{\theta}_{c}, t},\phi_{\hat{\theta}_{c}, t-1},\phi_{\hat{\theta}_{s}, t},\phi_{\hat{\theta}_{s}, t-1},\psi_{t,t-1}]
\end{equation}
At each timestep $t$, we feed the observation $o_t = \Phi_{\hat{\theta}_{t}}$ into our policy learning module. Our policy learning module consists of a convolution layer of size $2 \times 2 \times 64$, and a ConvLSTM~\cite{xingjian2015convolutional} unit to incorporate the history. The policy is aimed to learn Q-values corresponding to the $k$ discrete actions.
\subsection{Direct Policy Transfer to the Real World}
Our Semantic Net incorporates robust visual features trained on rich semantic object categories and is capable of producing correlation map between the visual goal and the robot observation. Our simple mechanism for computing the visual correlation between the goal and the observation is the crux of our network for modeling domain invariant stimuli $\phi_{\hat{\theta}_{s}}$. This stimuli is directly fed to our policy network so that the agent can learn generalizable policies that can be directly transferred to the real world.
At the test time, we are able to use the same network for querying our visual servoing policy with semantic object categories. To do that, we mask the last layer of the Semantic Net with the category id $l$ to produce $S_l(I)$ and use it in lieu of the correlation map $\widehat{\phi_{\hat{\theta}_{s}}}(I,l) = S_l(I) $ which will be fed into our policy module. Given the fact that our Semantic Net is trained with real images and is robust to noisy samples~\cite{izadinia2018viser}, our approach for computing the semantic correlation map as an input to the policy network provides domain invariant representations which we will empirically show to work well in real world scenarios. In addition to that, our Collision Net is also domain invariant as it is pre-trained via domain randomization technique~\cite{sadeghi2017cadrl}.
\subsection{Object Reaching via Deep RL}
We consider a goal conditioned agent interacting with an environment in discrete timesteps. Starting from a random policy the agent is trained to choose actions towards getting closer to a goal. The goal is defined by cropping out the image patch around the goal object as seen at the initial state and is denote by $I^g$. At each timestep $t$, the agent receives an observation $o_t$, takes an action $a_t$ from a set of $k$ discrete actions $\{a^1,a^2,...,a^k\}$ and obtains a scalar reward $R_t$. Each action corresponds to a rotation angle using which a continuous motion vector is computed to move the agent forward in the 3D environment. The motion vector has constant velocity for all the actions. By following its policy $\pi_\theta$, the agent produces a sequence of state-action pairs $\tau=\{s_t,a_t\}^{T-1}_{t=0}$ after $T$ steps. The goal of the agent is to maximize the expected sum of discounted future rewards with a discounting factor $\gamma\in[0,1]$:
\begin{figure*}[t]
\centering
\includegraphics[width=\textwidth]{sem_goal_real.pdf}
\vspace{-0.35in}
\caption{\small{Real world experiment for reaching semantic goals of toilet, teddy bear, chair and suitcase. The sequences show the robot view captured by head mounted monocular camera. DIViS can generalize to reach semantic goal objects in the real world.}}
\label{real_exp_qual_sem}
\vspace{-0.15in}
\end{figure*}
\vspace{-.14 in}
\begin{equation}
\label{eq:qfunc}
Q(s_t,a) = R(s_t,a) + E_{\tau \sim \pi_\theta}[\sum_{t'=t+1}^{T}\gamma^{t'-t} R(s_{t'}, a_{t'})]
\end{equation}
\vspace{-.1 in}
\vspace{.07 in}
\noindent{\bf Dense Multi-Step Monte Carlo Rollouts:}
We perform multi-step Monte Carlo policy evaluation~\cite{sutton1998reinforcement} for all possible $K$ actions at each state visited during an episode to generate dense rollouts. This enables us to train a deep network to make long-horizon dense predictions. Starting the agent from an initial state we generate dense rollouts with maximum length of $T$. For each state along the trajectory $\tau$, the dense rollouts are generated by performing $K-1$ additional rollouts corresponding to the actions $\{a^i\}_{i=1,a^i\neq a_t}^K$ which are not selected according to the agent's current policy $a_t \sim \pi_\theta$.
Figure~\ref{fig:net_arch}, demonstrates our dense Monte Carlo rollouts along a trajectory. The agent moves forward based on $\pi_\theta$. However, policy evaluations are computed for all possible actions that can be taken in each state. We evaluate the return of each action $a$ according to Equation~\ref{eq:qfunc}.
Therefore, for each state along the trajectories, we compute $\mathbb{Q}_{s_t} =\{Q(s_t,a^i)\}_{i=1}^{K}$ that densely encapsulates $Q$ values that quantify the expected sum of future rewards for each of the possible actions $a^i$. This policy evaluation provides us with a dataset of trajectories of the form:
\begin{equation}
\label{eq:trj}
(s_0,\mathbb{Q}_{s_0},a_0,...,s_{T-1},\mathbb{Q}_{s_{T-1}},a_{T-1})
\end{equation}
If at any point during the episode or at any of the Monte Carlo branches, the agent collides with any of the objects in the scene the corresponding rollout branch will be terminated.
\vspace{.07 in}
\noindent{\bf Batch RL: } During training, we use batch RL~\cite{lange2012batch}, where we generate dense rollouts with Monte Carlo return estimates as explained above. Starting with a random policy, during each batch the agent explores the space by following its current policy to produce rollouts that will be used to update the policy. For each of the training tasks, we collect dense Monte Carlo rollouts multiple times each with a randomized rendering setup. During training, we collect samples from all our environments and learn a single policy over all different reaching tasks simultaneously. This enforces the agent to learn the common shared aspect between various tasks (i.e. to reach different goals) and acquire generalization capability to unseen test scenarios rather than memorizing a single task seen at the training time.
\vspace{.07 in}
\noindent{\bf Reactive Policy: } The \emph{reactive} agent starts from a random policy and does not save history from its past observations. The state at each timestep is described by the observation $s_t=o_t$. The visual observation $o_t$ at timestep $t$ is represented by $[\phi_{\hat{\theta}_{c}, t},\phi_{\hat{\theta}_{s}, t}]$ and $(o_t,\mathbb{Q}_{o_t})$ pairs are used to update the policy.
\vspace{.07 in}
\noindent{\bf Recurrent Policy: }
Starting from a random policy, the agent learns a recurrent policy using a sequence of observations. The recurrent policy uses the entire history of the observation, action pairs to describe the state $s_t = (o_1,a_1,...,a_{t-1},o_t)$. Each observation along the trajectory is represented by $\Phi_{\hat{\theta}_{t}}$ according to Equation~\ref{eq:rep}. Given the sequential nature of the problem, we use dense trajectories described in Equation~\ref{eq:trj} and we model the policy $\pi$ using a ConvLSTM unit. Intuitively, the history of past observations and actions will be captured in the hidden state of ConvLSTM.
\vspace{.07 in}
\noindent{\bf Reward Function: }
For the task of collision-free goal reaching, the agent should traverse a trajectory that decreases its distance to the goal object while avoiding obstacles. This implies two objectives that should be reflected in the reward function: (1) Collision avoidance: We define the collision reward function as $R_c = \min(1,\frac{d_o - r}{\tau_d - r}) $ to penalize the agent for colliding with various objects in the environment. Here, $r$ is the vehicle radius, $d_o$ denotes distance to the closest obstacle, and $\tau_d$ is a distance threshold.
(2) Progressing towards goal: The agent is rewarded whenever it makes progress towards the goal. Considering $d_t$ as the distance of the agent to the goal and $d_{init}$ as the initial distance of the agent to the goal, our progress reward function is defined as $R_g = \max(0,1-\frac{\min(d_{t},d_{init})}{d_{init}})$. The total reward is $R = R_c + R_g$.
\begin{figure*}[t]
\centering
\includegraphics[width=.99\textwidth]{im_goal_real.pdf}
\vspace{-0.12in}
\caption{\small{Real world experiments for reaching a goal in the robots view identified with a goal image. The first and second columns show the goal image and the third person view of the robot respectively. The image sequence show the input RGB images. Our goal reaching policy can generalize to diverse goals and can successfully avoid collisions in real world situations.}}
\label{real_exp_qual_im}
\vspace{-0.15in}
\end{figure*}
\section{Introduction}
\input{intro.tex}
\section{Related Work}
\input{related.tex}
\section{Diverse Collision Free Goal Reaching}
\input{sim}
\section{Domain Invariant Visual Servoing}
\label{sec:approach}
\input{approach}
\section{Experimental Results}
\label{sec:result}
\input{exp.tex}
\section{Discussion}
\label{sec:conclusion}
\input{con.tex}
\vspace{0.05in}
\noindent{\bf Acknowledgment}
This work was made possible by NVIDIA support through a Graduate Research Fellowship to Fereshteh Sadeghi as well as support from Google. We would like to thank Pieter Abbeel for insightful discussions and Maya Cakmak for providing Turtlebot2 at UW for real world experiments.
{\small
\bibliographystyle{ieee}
\subsection{Real-World Evaluations}
\label{sec:realexp}
We use two different mobile robot platforms, TurtleBot2 and Waffle Pi (TurtleBot3), equipped with different monocular cameras (Astra and Raspberry Pi camera) to capture RGB sensory data used as input to our network shown in Figure~\ref{fig:net_arch}.
We compare various settings of training DIViS entirely in our domain randomized simulator and without any further fine-tuning or adaptation. Our goal is to answer the following key questions: (1) How well DIViS generalizes to real world settings while no real robot navigation data is used at training time? (2) How well does our approach transfer real world object-level semantics into the policy that is entirely trained in simulation? (3) How effective is our proposed recurrent policy compared to a reactive policy that is trained with similar pre-trained visual features? What is our performance compared to a conventional approach that visually matches the goal with current camera view? We study answer to these questions in the context of quantitative and qualitative real-world experiments.
\subsubsection{Quantitative Real World Experiments}
Our quantitative real world evaluation consists of two different setups for collision-free goal-reaching (a) Goal Image: reaching a visual goal as specified by a
user selecting an image patch from the initial robot view. (b) Semantic object: Reaching a semantic object category such as \emph{chair}, \emph{teddy bear}, etc. that is inside the initial robot view.
\vspace{.06 in}
\noindent{\bf Generalizing to real world: } Table~\ref{tab:all_real_exp}, shows that our policy is robust to visually diverse inputs. Our Semantic Net and Collision Net and policy can directly transfer to real world for reaching image goals while avoiding obstacles obtaining an average success rate of 82.35\% in goal image and 79.24\% in semantic object scenarios using two different real robot platforms.
\vspace{.06 in}
\noindent{\bf Generalizing to semantic objects:} Our experiments outlined in Table~\ref{tab:all_real_exp} and Table~\ref{tab:all_real_exp_cmpr} show that our policy can successfully generalize to reach semantic object categories with an average success rate of $79.24\%$ (over 53 trials) although it has not been directly trained for this task. Since our Semantic Net (explained in section~\ref{sec:approach}) is capable of localizing various object categories, it can provide the visual semantic correlation map for our policy network resulting in high generalization capability.
\vspace{.06 in}
\noindent{\bf Ablation and comparison with baseline:}
We compare the performance of DIViS to its reactive version explained in Section~\ref{sec:approach} as well as a Visual goal matching policy that mimics a conventional visual servoing baseline as explained in Section~\ref{sec:simexp_quant}.
To compare each method against DIViS, we run same scenarios with same goal and same initial robot pose. Each section in Table~\ref{tab:all_real_exp_cmpr}, compares the methods over similar scenarios.
A successful policy should be capable of making turns to avoid obstacles while keeping track of the target object that can go out of the monocular view of the robot in sub-trajectories. Table~\ref{tab:all_real_exp_cmpr} outlines that DIViS has the highest success rate in all setups. Whilethe reactive policy can avoid obstacles it fails reaching the goal when it looses track of the objects at turns. Visual goal matching collides with obstacles more frequently as it greedily moves towards the object without considering the path clearance. Having saved the memory of past observations via a recurrent policy, DIViS is able to keep track of the goal object when it gets out of the view and makes better decisions to avoid obstacles.
\begin{table}[t]
\begin{small}
\begin{center}
\small
\caption{\small{DIViS success rate using two real robot platforms. \label{tab:all_real_exp}} \vspace{-.05in}}
\renewcommand*{\arraystretch}{0.9}
\begin{tabular}[10pt]{lcccc}
\toprule
{Robot}& \multicolumn{2}{c}{Goal Image } & \multicolumn{2}{c}{Semantic Object} \\\cline{2-5}
&{success rate} & {\#trials} & {success rate} & {\#trials} \\
\midrule
{WafflePi} & {82.35\%} & {17} & {85.18\%} & {27} \\
{TurtleBot2} & {81.81\%} & {22} & {73.07\%} & {26} \\
\midrule
{Total} & {82.35\%} & {39} & {79.24\%} & {53} \\
\bottomrule
\vspace{-.4in}
\end{tabular}
\end{center}
\end{small}
\end{table}
\begin{table*}[t]
\begin{small}
\begin{center}
\small
\caption{\small{Comparing DIViS to baselines in reaching diverse goals in real world}\label{tab:all_real_exp_cmpr}\vspace{-.05in}}
\renewcommand*{\arraystretch}{0.9}
\begin{tabular}[10pt]{lcc|cc|c}
\toprule
& \multicolumn{2}{c}{Goal Image } & \multicolumn{2}{c}{Semantic object} & \multicolumn{1}{c}{Total} \\
&{success rate} & {\#trials} & {success rate} & {\#trials} & {success rate} \\
\midrule
{DIViS(ours)} & {{\bf 83.78\%}} & {37} & {{\bf 75.6\%}} & {41} & {{\bf 79.48\%}}\\
{DIViS-reactive(ours)} & {54.04\%} & {} & {43.9\%} & {} & {48.71\%}\\
\midrule
{DIViS(ours)} & {{\bf 82.35\%}} & {17} & {{\bf 85.18\%}} & {27} & {{\bf 84.1\%}}\\
{Visual Goal Matching} & {35.29\%} & {} & {18.51\%} & {} & {25.0\%}\\
\midrule
{DIViS(ours)} & {{\bf 86.66\%}} & {15} & {{\bf 80.0\%}} & {15} & {{\bf 83.33\%}}\\
{DIViS-reactive(ours)} & {53.0\%} & {} & {53.53\%} & {} & {53.53\%}\\
{Visual Goal Matching} & {40.0\%} & {} & {20.0\%} & {} & {30.0\%}\\
\bottomrule
\vspace{-.4in}
\end{tabular}
\end{center}
\end{small}
\end{table*}
\vspace{.05 in}
\noindent{\bf Comparison to ~\cite{pathak2018zero} for visual goal reaching:} Amongst prior navigation works, the most related paper to our work is~\cite{pathak2018zero} which servos to visual goals and is tested on a Turtlebot2 on 8 different scenarios in a single environment.~\cite{pathak2018zero} does not deal with simulation to real transfer and does not support navigating to semantic object categories . We tested our approach on 92 different scenarios conducted on 20 real world environments with substantially different appearance, furniture layouts and lighting conditions including outdoors. In total, we gained a success rate of 82.35\% in ``Goal image'' scenarios averaged over 39 trials.
\subsubsection{Qualitative Real World Experiments}
Figure~\ref{fig:teddy_expample} visualizes the performance of DIViS in a real wold ``semantic goal'' scenario where the goal is to reach the ``teddy bear''. This example demonstrates the importance of incorporating both object semantics and free space reasoning in choosing best actions to find a collision-free path in order to reach the goal object. First row in Figure~\ref{fig:teddy_expample} shows the RGB images observed by the robot and the second row shows the object localization score map for the ``teddy bear'' as obtained by our Semantic Net. Red arrows in the third row of Figure~\ref{fig:teddy_expample} show the action direction chosen by visual goal matching policy which only incorporates semantic object understanding. Green arrows show the action directions chosen by DIViS. While visual goal matching guides the robot to get close to the goal object, it does not have any mechanism to avoid obstacles and thus fails by colliding into other room furniture. On the other hand, DIViS maintains a collision-free path by choosing actions that both involve object semantics and free space reasoning. During traversal, DIViS may decide to take turns in order to avoid obstacles. This can result in loosing the sight of object for several steps. Being capable of maintaining a short memory, DIViS can turn back to the goal object after avoiding the obstacle.
More qualitative examples of DIViS for \emph{goal image} and \emph{semantic object} such as ``toilet'', ``teddy bear'', ``chair'' and ``suitcase'' are provided in Figure~\ref{real_exp_qual_im} and Figure~\ref{real_exp_qual_sem}, respectively. As demonstrated, DIViS can generalize to various real-world scenarios including diverse set of image goals, diverse object categories and and different environments with various indoor and outdoor layout and lighting. Please check supplementary videos at \href{https://fsadeghi.github.io/DIViS}{https://fsadeghi.github.io/DIViS} for more examples of the DIViS performance on two real robot platforms as well as results in our simulation environment.
\begin{figure*}[t]
\centering
\includegraphics[width=\linewidth]{our_traj_vis.pdf}
\vspace{-0.25in}
\caption{
\label{fig:Qualitative results}
\small{Qualitative results on several complex test scenarios. In each scenario the trajectory taken by the agent is overlaid on the map (right) and several frames along the path are shown (left). To avoid collisions, the agent needs to take turns that often takes the goal object out of its view and traverse walkable areas for achieving the visually indicated goal in diverse scenarios.}}
\vspace{-0.15in}
\end{figure*}
\subsection{Simulation Evaluation}
\label{sec:simexp}
To generate simulation test scenarios, we sample free spaces in the environments uniformly at random to select the initial location and camera orientation of the agent. Therefore, the distance to the goal object and the initial view points change from one scenario to another. To further diversify the test scenarios and test the generalization capability, we do simulation randomization (also known as domain randomization)~\cite{sadeghi2017cadrl} in each test scenario using textures that were unseen during the training time. During the course of each trial, if distance of the agent to any of the scene objects other than the goal object becomes less than the agents radius~(i.e.~$\sim 16cm$) a collision event is registered and the trial is terminated.
\subsubsection{Quantitative Simulation Experiments}
\label{sec:simexp_quant}
For the evaluation criteria, we report \emph{success rate} which is the percentage of times that the agent successfully reaches the visually indicated object. If distance of the agent with the goal object is less than ~$30cm$, it is registered as success. We report the average success rate over a total of 700 different scenarios involving $65$ distinct goal objects collected from train( 380 scenarios) and novel test (320 scenario) environments .
We compare DIViS (full model with recurrent policy and use of optical flow) against several alternative approaches explained below. Quantitative comparisons are summarized in Table~\ref{tab:sim_quant}.
\noindent{\bf Random Policy:} At each step, the agent selects one of the $k$ actions uniformly at random.
\vspace{.07 in}
\noindent{\bf Visual Goal Matching:} This baseline models a greedy policy that follows an oracle rule of following the path with highest visual similarity to the goal and mimics conventional image-based visual servoing techniques to find the best matching visual features with the goal. Note that this policy uses a high-level prior knowledge about the underlying task while our agent s trained via RL does not have access to such knowledge and instead should learn a policy from scratch without any priors. Visual Goal Matching selects one of the $k$ actions based on the spatial location of the maximum visual matching score of the visual goal and the current observation. To be fair, we use exact same Semantic Net pre-trained features used in our network to compute the correlation map.
\vspace{.07 in}
\noindent{\bf Visual Goal Matching with Collision Avoidance:}. This baseline combines prior sim2real collision avoidance method of~\cite{sadeghi2017cadrl} with conventional visual servoing for following the path with highest visual match to the goal and lowest chance of collision. We incorporate our predicted collision maps to extend Visual Goal Matching policy for better collision avoidance. Using our Collision Net and Semantic Net, we compute the spatial free space map and semantic correlation map for each observation. We sum up these two maps and obtain a single spatial score map that highlights the action directions with highest visual correlation and lowest chance of collision.
The agent selects one of the $k$ actions based on the spatial location with highest total score. To be fair, we use the exact same pre-trained features of Collision Net and Semantic Net in our network for this policy.
\vspace{.07 in}
\noindent{\bf DIViS-Reactive policy:} The agent selects the best action based on the maximum Q-value produced by the reactive policy explained in Section~\ref{sec:approach}.
\vspace{.07 in}
\noindent{\bf DIViS-Recurrent:} The agent selects the best action based on the maximum Q-value produced by our recurrent policy without incorporating optical flow $\psi$ explained in Section~\ref{sec:approach}.
\vspace{.07 in}
\noindent{\bf DIViS-Recurrent with flow:} Our full model that select the best action based on the maximum Q-value produced by our network that also uses the optical flow between each two consecutive observations as explained in Section~\ref{sec:approach} and Equation~\ref{eq:rep}.
Table~\ref{tab:sim_quant}, compares the success rates between different approaches. The highest performance is obtained by our recurrent policy and the best results are obtained when optical flow$\psi$ is also incorporated. Interestingly, naive combination of collision prediction probabilities with visual goal matching results in lower performance than only using visual goal matching. This is because the collision avoidance tends to select actions that navigate the agent to spaces with smallest probability of collision. However, in order to reach goals the agent should be able to take narrow paths in confined spaces which might not have the lowest collision probability. Given the results obtained in this experiment, we used our recurrent policy with optical flow during our real-world experiments in Section~\ref{sec:realexp}.
\subsubsection{Qualitative Simulation Experiments}
We qualitatively evaluate the performance and behavior of the best policy i.e. DIViS (with recurrent policy and optical flow) in a number of complex test scenarios. Figure~\ref{fig:Qualitative results} demonstrates several of such examples.
In each scenario, the trajectory taken by the agent is overlaid on the top view of map for visualization. The initial and final position of the agent are shown by a red and a blue dot, respectively. During these scenarios, the agent needs to take actions which may increase its distance to the goal but will result in avoiding obstacles. However, the agent recovers by taking turns around the obstacles and successfully reaches the goal object.
\begin{table}[t]
\begin{small}
\begin{center}
\caption{\small Success rate in simulation. \label{tab:sim_quant}\vspace{-.05in}}
\begin{tabular}{l|cc}
\toprule
{Method} & {Seen Env.} & {Unseen Env.}\\
\midrule
{DIViS-Recurrent w/flow (ours)} & \bf{87.6} & \bf{81.6}\\
{DIViS-Recurrent (ours)} & 82.1 & 75.3\\
{DIViS-Reactive (ours)} & 76.3 & 69.7\\
{Visual Goal Matching} & 56.3 & 54.4\\
{Visual Goal Matching w/ collis.} & 48.9 & 47.8\\
{Random policy} & 23.4 & 22.2\\
\bottomrule
\end{tabular}
\end{center}
\end{small}
\vspace{-.3in}
\end{table}
|
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| 5,050
|
{"url":"http:\/\/www.math.uni-bonn.de\/veranstaltung\/ywhapde2016\/abstracts\/westermann?language=en","text":"# Young Women in Harmonic Analysis and PDE\n\n## December 2-4, 2016\n\n### Laura Westermann (University of D\u00fcsseldorf)\n\n#### Optimal Sobolev Regularity for Laplace and Stokes Operator on Wegde Type Domains subject to Navier Slip Boundary Conditions\n\nThe aim of this talk is to show for $1 < p < \\infty$ the $W^{2,p}$-Sobolev regularity for Laplace and Stokes operator in the $L^p$-space on two-dimensional wedge type domains subject to Navier slip boundary conditions. Introducing polar coordinates and applying the Euler transformation, we transform the elliptic problem of the Laplace operator from wedge type domains to a layer domain. The resulting operator on a layer is described by the sum of two linear closed operators. The proof of the $W^{2,p}$-Sobolev regularity requires a subtle spectral analysis of these two operators. This then allows for applying elements of $H^\\infty$-calculus and a consequence of the Kalton-Weis theorem to prove invertibility of the full operator on the layer domain. Thanks to this result and after back transformation to wedge type domains, we are able to prove the well-posedness of the Stokes equations. The topic of the talk is content of [1], [2].\n\nReferences\n\n[1] J. Saal, L. Westermann. Optimal Sobolev Regularity for the Stokes Operator subject to Navier Slip on two dimensional Wedges. In preparation.\n[2] L. Westermann. Optimal Regularity for Laplace and Stokes Equation on Polygonal Domains. Master\u2019s thesis, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, 2016.","date":"2018-01-23 07:59:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6662129759788513, \"perplexity\": 1030.2305248865423}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-05\/segments\/1516084891791.95\/warc\/CC-MAIN-20180123072105-20180123092105-00176.warc.gz\"}"}
| null | null |
Iatrogenesi (dal greco iatròs, medico e γένεσις, dalla radice γεν- di γίγνομαι nascere; ciò che è causato dal medico o dalla medicina) indica patologie, effetti collaterali o complicanze dovute a farmaci o a trattamenti medici in generale, risultati errati.
Da un punto di vista sociologico esistono tre forme di iatrogenesi: clinica, sociale e culturale.
La iatrogenesi si riferisce il più delle volte alle conseguenze negative delle azioni dei medici, ma può essere riferita anche a errori attribuibili a psicologi, terapeuti, farmacisti, infermieri, dentisti e così via.
Storia
Fin dai tempi di Ippocrate è noto il potenziale effetto dannoso delle cure mediche.
Il vecchio detto "Primum non nocere" è un'importante condizione dell'etica medica, e le sofferenze o la morte causate intenzionalmente o tramite errori evitabili o negligenza sono punite in molte società.
Lo sviluppo della medicina nel ventesimo secolo ha permesso, soprattutto grazie alla scoperta degli antisettici, dell'anestesia e degli antibiotici di ridurre fortemente la mortalità iatrogenica.
Cause della iatrogenesi
Esistono diverse cause di iatrogenesi:
Errori medici
Negligenza o procedure difettose
Interazione tra i farmaci prescritti
Effetti collaterali dei farmaci prescritti
Sottostima degli effetti negativi dovuti alla somministrazione di farmaci
Abuso di farmaci che inducono resistenza ai trattamenti antibiotici
Trattamenti non testati o non rispondenti alla specifica connotazione genetica del paziente
Diagnosi parziali
Infezioni ospedaliere
Sperimentazioni mediche
Condizioni di iatrogenesi non derivano sempre da errori medici, come possono essere gli errori chirurgici o la prescrizione di una terapia errata. Infatti a volte sono iatrogeni gli effetti non voluti di alcuni trattamenti medici, come la "terapia radiante" o la chemioterapia, dovuti all'aggressività degli agenti terapeutici che possono portare a perdita dei capelli, anemia, vomito, nausea, danni cerebrali (come nel caso della somministrazione di neurolettici senza episodi di psicosi, mania o schizofrenia), ecc. La perdita di funzioni dovute all'asportazione di un organo è altresì considerata causa di iatrogenesi, ad esempio il diabete scatenato dall'asportazione del pancreas.
Un caso raro, ma comunque da considerare è quello in cui il farmacista, incapace di decifrare la prescrizione medica anche soltanto perché scritta in maniera non comprensibile, dispensa al paziente un farmaco errato che ne aggrava le condizioni.
Causa molto comune di iatrogenesi è l'interazione tra farmaci; talvolta un medico non verifica tutti i farmaci che il paziente sta assumendo e ne prescrive altri che possono potenziarne o indebolirne l'effetto, o scatenare reazioni allergiche o inaspettate.
Ulteriore causa di iatrogenesi può essere considerata la resistenza dei batteri alla somministrazione di antibiotici, dovuta fondamentalmente a due fattori: un'eccessiva prescrizione di antibiotici da parte dei medici anche quando non indispensabili e l'abitudine dei pazienti a interrompere la terapia una volta apparentemente ristabilitisi, anziché prolungarla fino alla completa eradicazione dell'agente patogeno.
Trattamenti radicali o non testati sono un'altra causa di malattia o morte iatrogena. È il caso di quei tipi di approcci medici "disperati" che erano usati soprattutto in passato, come la lobotomia, la terapia elettro-convulsivante (meglio nota come elettroshock) o la colostomia.
Un termine collegato sovente a iatrogenesi è "ospedaliera". Si tratta di tutte quelle patologie che il malato riporta in seguito alla degenza ospedaliera, caso tipico le infezioni. Le cause più comuni di infezioni ospedaliere sono da attribuire ad aghi e altri strumenti chirurgici non sterilizzati, o il mancato uso dei guanti per eseguire procedure mediche o dentistiche.
Esiste una vasta documentazione di epatiti B e C causate da chirurghi e dentisti.
Una recente causa di terribile iatrogenesi fu l'epidemia del virus Ebola in Sudan e Zaire, dove il riutilizzo sistematico di aghi e siringhe non sterilizzati causò centinaia di vittime.
Iatrogenesi a cascata
Per iatrogenesi a cascata si intende una serie di effetti sulla salute del paziente causati da interventi medici volti a risolvere i precedenti infruttuosi tentativi di guarigione.
Esempio reale quello di un paziente con una severa forma di artrite. In un primo tempo la terapia cortisonica fu efficace, ma l'assunzione prolungata del farmaco causò il primo effetto a cascata: l'insorgere del diabete. Il diabete aumentò la suscettibilità del paziente verso le infezioni, attivando una tubercolosi polmonare latente. Il trattamento cortisonico fu sospeso e sostituito da terapia con corticotropina, la quale provocò insufficienza renale e osteoporosi, con dolorose fratture spontanee. Seguirono un'insufficienza multiorgano e, inevitabilmente, la morte.
Incidenza e importanza
Negli Stati Uniti il monitoraggio di questo fenomeno è molto accurato: la iatrogenesi è la terza causa di morte dopo l'infarto e il cancro.
In Italia si stima che ogni anno circa 15.000 pazienti presentino denunce contro i medici.
In Italia, come in altri paesi, la legislazione prevede che il paziente dia il suo consenso per ogni pratica medica alla quale debba essere sottoposto. Pertanto al chirurgo (come a ogni specialista) è richiesto di informare in modo chiaro ed esauriente il paziente del perché verrà sottoposta all'intervento, di spiegargli in modo comprensibile anche i dettagli tecnici, le aspettative e gli esiti dell'intervento e soprattutto di soffermarsi e dare risalto (come molta giurisprudenza sottolinea) ai rischi e alle complicanze cui può andare incontro. Solo così sarà considerato valido il consenso informato.
Tuttavia accade che ogni evento negativo (reale o vissuto come tale dal paziente spesso deluso nelle sue aspettative) connesso all'intervento viene inevitabilmente ricondotto a una malpractice (episodio di malasanità) e quindi considerato iatrogeno. E tutto ciò costituisce un problema che in alcuni paesi, come gli USA, ha già profondamente stravolto il rapporto tra paziente, medico e istituti di assicurazione, fino ad arrivare al paradosso della cosiddetta "medicina difensiva", cioè quella condizione in cui il medico viene portato a considerare il paziente un problema in quanto tale, facendosi influenzare nelle scelte terapeutiche dai timori di rivalsa economica, alterando quindi la base stessa del corretto rapporto medico-paziente.
Note
Bibliografia
Ivan Illich, Nemesi medica. L'espropriazione della salute, ed. Red, 2005
Voci correlate
Discinesia tardiva
Disfunzione Sessuale Post-SSRI
Bioetica
Disease-mongering
Medicina
Mortalità evitabile
Prevenzione quaternaria
Trattamento sanitario obbligatorio
Neurolettici
Danno morale
Danno esistenziale
Collegamenti esterni
Terapie
Patologia
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Each restaurant has export object as default export with these keys:
- `id` - restaurant ID, should be unique
- `name` - restaurant name
- `endOfOrders` - object defining time of end of orders `{ hour: <number>, minute: <number> }` or `null`
- `isNotifiable` - whether kitchen ninja can send notification about arrived/not arrived food
- `isOrder` - function that checks, whether message is order for this restaurant or not
- `getMenuLink` (optional) - function that returns link to current menu
- `getMenu` (optional) - function that returns actual menu
- `help` - text of help
- `getOrdersCounter` - function that returns new orders counter - object with two methods: `add(text)` and `view()`
- `add(text)` - if `text` represents valid order, function stores order details and return `true`, otherwise returns `false`
- `view()` - function returns HTML with actual status of ordered food
|
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Asthenomacrurus is een geslacht van straalvinnige vissen uit de familie van rattenstaarten (Macrouridae).
Soorten
Asthenomacrurus fragilis (Garman, 1899)
Asthenomacrurus victoris Sazonov & Shcherbachev, 1982
Rattenstaarten
|
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\section{Introduction}
Most solar-type stars reside in binaries \citep{duq91}, yet their formation is
not well understood. It is generally accepted
that most stars form in groups rather than in isolation \citep{ada01}. Intriguingly,
the multiplicity of young stars in many regions seems to be systematically higher
than that of their
main-sequence counterparts \citep[e.g.][and references therein]{mat00}. The
reason for this multiplicity overabundance is not entirely understood, although
two principal scenarios have been proposed.
One is that the multiplicity fraction is sensitive to the initial conditions of
the star formation process. That would imply that different regions show a
variety of multiplicity properties, and indeed, there seems to be some evidence
for the multiplicity fraction being anticorrelated with the stellar density of
the region \citep{pat01}.
Another possibility is that young stars start out with a high fraction of multiples
that subsequently are disrupted due to dynamical evolution \citep[e.g.][]{rei00}.
Star-forming regions
are generally too dispersed for binaries to be disrupted by interactions between
members. The alternative is that many stars form not just in binaries, but in
unstable higher-order multiples that get disrupted with time, as indeed suggested by
numerical simulations \citep{bat02,del04}. For a recent review on the current
status of the field, see \citet{duc06}.
The nearby (97\,pc), young \citep[6--8\,Myr,][and references therein]{jil05}
$\eta$\,Chamaeleontis cluster was
found by the X-rays emitted from its members, as revealed by \textit{ROSAT},
together with their common space motion, as revealed by \textit{Hipparcos} \citep{mam99}.
The cluster is mainly populated by late-type stars (K3-M6, see Table~\ref{t:targets}),
and shows no evidence for extinction \citep{mam00}. These properties all contribute
to make the cluster an excellent laboratory for investigating brown dwarf (BD) and
planet formation, and their evolution \citep[e.g.][]{son04,luh04a,hai05,lyo06,jay06}.
In particular, using adaptive optics (AO) systems on large telescopes, it is
possible to reach high contrast-ratio sensitivities close in, to detect any
wide ($>$0\farcs5) companion down to planetary masses.
In a previous high-resolution survey using speckle interferometry and AO
on 2.2--3.6\,m telescopes, \citet{koh02} searched 13 members for companions
($\eta$\,Cha~1--12 and 15, see Table~\ref{t:targets}). They found two resolved
binaries, $\eta$\,Cha~1 and $\eta$\,Cha~9,
and one suspected unresolved binary, $\eta$\,Cha~12.
$\eta$\,Cha~12 has also been suspected to be binary due to its
elevation in color-magnitude diagrams \citep{law01,luh04b}.
In the present paper we report on a deep AO search for faint companions to 17
confirmed members of the $\eta$\,Cha cluster. \S\,\ref{s:obs}
details the observations. \S\,\ref{s:analysis} describes analysis and
results, including how astrometry and photometry were performed, how
the Strehl ratio was measured and the contrast sensitivity estimated.
In \S\,\ref{s:discuss} we discuss the companion candidates and constrain
the orbit of the previously observed 0\farcs2
binary $\eta$\,Cha~1 (Fig.~\ref{f:ec01}).
We then go on to determine limits on the companion probability, use
this to discuss the apparent deficit of binaries in the $\eta$\,Cha
cluster, and estimate the likelihood of binaries being disrupted by
stellar encounters. \S\,\ref{s:conclusions} contains an enumerated list
of conclusions.
In the Appendices, we first derive the (time-averaged) probability distribution
for the projected separation of a binary, given its semi-major axis. We
then continue with some useful properties of multiplicity statistics, in particular
how to estimate binomial confidence intervals, and how to test if two outcomes
are derived from the same binomial distribution.
\section{Observations}
\label{s:obs}
\begin{deluxetable*}{clcccccl}
\tabletypesize{\scriptsize}
\tablewidth{0pt}
\tablecaption{\label{t:targets}Targets observed in the $\eta$~Chamaeleontis cluster}
\tablehead{
\colhead{$\eta$\,Cha\tablenotemark{a}} &
\colhead{Name} &
\colhead{$\alpha_{\mathrm{J}2000.0}$} &
\colhead{$\delta_{\mathrm{J}2000.0}$} &
\colhead{$J$} &
\colhead{$H$} &
\colhead{$K_s$} &
\colhead{SpT}
}
\startdata
\phn1 & EG\,Cha & 08:36:56.24 & -78:56:45.5 & \phn8.155\,$\pm$\,0.019 & \phn7.498\,$\pm$\,0.049 & \phn7.338\,$\pm$\,0.021 & K4 \\
\phn2 & $\eta$\,Cha & 08:41:19.48 & -78:57:48.1 & \phn5.688\,$\pm$\,0.019 & \phn5.721\,$\pm$\,0.040 & \phn5.718\,$\pm$\,0.018 & B8 \\
\phn3 & EH\,Cha & 08:41:37.03 & -79:03:30.4 & 10.349\,$\pm$\,0.023 & \phn9.647\,$\pm$\,0.022 & \phn9.415\,$\pm$\,0.019 & M3 \\
\phn4 & EI\,Cha & 08:42:23.72 & -79:04:03.0 & \phn9.535\,$\pm$\,0.024 & \phn8.779\,$\pm$\,0.061 & \phn8.615\,$\pm$\,0.019 & K7 \\
\phn5 & EK\,Cha & 08:42:27.11 & -78:57:47.9 & 10.777\,$\pm$\,0.023 & 10.099\,$\pm$\,0.021 & \phn9.855\,$\pm$\,0.021 & M5 \\
\phn6 & EL\,Cha & 08:42:38.80 & -78:54:42.8 & 10.232\,$\pm$\,0.027 & \phn9.584\,$\pm$\,0.023 & \phn9.290\,$\pm$\,0.021 & M2 \\
\phn7 & EM\,Cha & 08:43:07.24 & -79:04:52.5 & \phn8.420\,$\pm$\,0.024 & \phn7.758\,$\pm$\,0.034 & \phn7.635\,$\pm$\,0.033 & K3 \\
\phn8 & RS\,Cha & 08:43:12.23 & -79:04:12.3 & \phn5.994\,$\pm$\,0.030 & \phn5.877\,$\pm$\,0.038 & \phn5.852\,$\pm$\,0.034 & A7 \\
\phn9 & EN\,Cha & 08:44:16.38 & -78:59:08.1 & 10.260\,$\pm$\,0.026 & \phn9.668\,$\pm$\,0.026 & \phn9.335\,$\pm$\,0.024 & M4 \\
10 & EO\,Cha & 08:44:31.88 & -78:46:31.2 & \phn9.653\,$\pm$\,0.023 & \phn8.919\,$\pm$\,0.063 & \phn8.732\,$\pm$\,0.021 & K7 \\
11 & EP\,Cha & 08:47:01.66 & -78:59:34.5 & \phn8.729\,$\pm$\,0.020 & \phn8.025\,$\pm$\,0.055 & \phn7.655\,$\pm$\,0.038 & K4 \\
12 & EQ\,Cha & 08:47:56.77 & -78:54:53.2 & \phn9.323\,$\pm$\,0.024 & \phn8.683\,$\pm$\,0.082 & \phn8.410\,$\pm$\,0.031 & M1 \\
13 & HD\,75505 & 08:41:44.72 & -79:02:53.1 & \phn7.059\,$\pm$\,0.026 & \phn6.987\,$\pm$\,0.036 & \phn6.928\,$\pm$\,0.023 & A1V \\
15 & ECHA\,J0843.3-7905 & 08:43:18.58 & -79:05:18.2 & 10.505\,$\pm$\,0.026 & \phn9.834\,$\pm$\,0.021 & \phn9.431\,$\pm$\,0.023 & M4 \\
16 & ECHA\,J0844.2-7833 & 08:44:09.15 & -78:33:45.7 & 12.505\,$\pm$\,0.024 & 11.976\,$\pm$\,0.022 & 11.618\,$\pm$\,0.024 & M5 \\
17 & ECHA\,J0838.9-7916 & 08:38:51.50 & -79:16:13.7 & 11.275\,$\pm$\,0.023 & 10.721\,$\pm$\,0.022 & 10.428\,$\pm$\,0.023 & M5 \\
18 & ECHA\,J0836.2-7908 & 08:36:10.73 & -79:08:18.4 & 11.849\,$\pm$\,0.024 & 11.277\,$\pm$\,0.026 & 10.945\,$\pm$\,0.021 & M5.5
\enddata
\tablecomments{Coordinates and IR magnitudes are from the 2MASS All Sky Data Release.
The spectral types are from \citet{mam99} for 1--12, \citet{hou75} for 13, \citet{law02} for 15,
and \citet{son04} for 16--18.}
\tablenotetext{a}{Numbers 1--12 coincide with the RECX numbers introduced by \cite{mam99},
and 1--18 with \cite{luh04b}. Their number 14 (``USNO Anon 1'') was not observed.}
\end{deluxetable*}
\begin{deluxetable}{lclrr}
\tablewidth{0pt}
\tabletypesize{\scriptsize}
\tablecaption{\label{t:obslog}Observation log}
\tablehead{
\colhead{} &
\colhead{} &
\colhead{} &
\colhead{DIT} &
\colhead{Total} \\
\colhead{$\eta$\,Cha\tablenotemark{a}} &
\colhead{UT Date} &
\colhead{Instrument\tablenotemark{b}} &
\colhead{(s)} &
\colhead{(min)}
}
\startdata
\phn1 & 2004-04-03 & VIS $H$ cor. & 3 & 19 \\
\phn2 & 2004-04-04 & VIS $H$ cor. & 3 & 15 \\
\phn3 & 2004-04-02 & N90C10 $J$ & 20 & 13 \\
\phn3 & 2002-10-20 & VIS $H$ & 0.6 & 15 \\
\phn3 & 2002-10-21 & VIS $H$ & 0.6 & 14 \\
\phn3 & 2004-04-02 & N90C10 $K_s$ & 20 & 27 \\
\phn4\,B & 2004-04-22 & ISAAC $H$ spec. & 200 & 40 \\
\phn4 & 2002-11-17 & VIS $H$ ND & 1.5 & 0.7 \\
\phn4 & 2002-11-17 & VIS $H$ & 0.34 & 13 \\
\phn5 & 2003-01-17 & N20C80 $H$ & 0.5 & 20 \\
\phn5 & 2003-01-21 & N20C80 $H$ & 0.5 & 14 \\
\phn5 & 2003-02-17 & N20C80 $H$ & 0.5 & 6 \\
\phn5 & 2003-02-19 & N20C80 $H$ & 0.5 & 13 \\
\phn6 & 2003-01-18 & VIS $H$ ND & 5 & 1.6 \\
\phn6 & 2003-01-18 & VIS $H$ & 0.35 & 21 \\
\phn7 & 2004-04-04 & VIS $H$ cor. & 20 & 20 \\
\phn8 & 2004-04-04 & VIS $H$ cor. & 3 & 14 \\
\phn9 & 2004-04-02 & N90C10 $J$ & 8 & 13 \\
\phn9 & 2003-01-21 & VIS $H$ ND & 6 & 2 \\
\phn9 & 2003-01-21 & VIS $H$ & 0.35 & 13 \\
\phn9 & 2004-04-02 & N90C10 $K_s$ & 16 & 27 \\
\phn9\,Aab & 2004-04-03 & N90C10 $H$ spec.& 120 & 40 \\
\phn9\,B & 2004-04-22 & ISAAC $H$ spec. & 200 & 47 \\
10 & 2003-01-22 & VIS $H$ ND & 1.5 & 0.5 \\
10 & 2003-01-22 & VIS $H$ & 0.35 & 13 \\
10\,B & 2004-04-24 & ISAAC $H$ spec. & 200 & 60 \\
11 & 2003-01-22 & VIS $H$ ND & 1.2 & 0.4 \\
11 & 2003-01-22 & VIS $H$ & 0.35 & 13 \\
12 & 2003-01-22 & VIS $H$ ND & 1.5 & 0.5 \\
12 & 2003-01-22 & VIS $H$ & 0.35 & 13 \\
13 & 2004-04-03 & VIS $H$ cor. & 10 & 12 \\
15 & 2004-04-02 & N90C10 $J$ & 16 & 27 \\
15 & 2003-01-21 & VIS $H$ ND & 6 & 4 \\
15 & 2003-01-21 & VIS $H$ & 0.35 & 11 \\
15 & 2003-01-22 & VIS $H$ & 0.35 & 11 \\
15 & 2004-04-02 & N90C10 $K_s$ & 16 & 26 \\
15\,C & 2004-04-22 & ISAAC $H$ spec. & 200 & 40 \\
16 & 2004-04-02 & N90C10 $H$ & 80 & 36 \\
17 & 2004-04-03 & N90C10 $H$ & 10 & 33 \\
18 & 2004-04-02 & N90C10 $H$ & 30 & 33
\enddata
\tablenotetext{a}{\ Letters refer to the companion candidate
observed in addition to the primary.}
\tablenotetext{b}{For NACO observations, VIS, N20C80 and N90C10 correspond
to the used WFS, $J$, $H$, and $K_s$ are the used filters, ND means neutral density
filter, cor.\ coronographic observations, and spec.\ spectroscopy. All ISAAC
observation were made in the same mode (see \S\,\ref{s:obs}).}
\end{deluxetable}
\begin{figure}
\includegraphics[width=\hsize,clip=true]{f1.eps}
\caption{\label{f:ec01}The close 0\farcs2 binary $\eta$\,Cha~1 observed with a
semi-transparent coronographic mask, and a likely background object 9\arcsec\ away
(\S\,\ref{s:companions}).
The orientation and scale are shown by the two 1\arcsec\ perpendicular axes..}
\end{figure}
\begin{figure}
\includegraphics[width=\hsize,clip=true]{f2.eps}
\caption{\label{f:ec0912}Close-ups of the tight binaries $\eta$\,Cha~9 (left) and
$\eta$\,Cha~12 (right). The box sizes are 1\arcsec\ on a side. $\eta$\,Cha~9 is a well
resolved 0\farcs2 binary, while $\eta$\,Cha~12 is unresolved. From the asymmetric
profile, we infer that the $\eta$\,Cha~12 separation is $\sim$0\farcs04
(\S\,\ref{s:astrophot}). North is up, and east is to the left.}
\end{figure}
We have observed 17 confirmed members of the $\eta$\,Cha cluster with
high-resolution AO imaging and follow-up spectroscopy of companion candidates.
Table~\ref{t:targets} summarizes the observed target parameters and assigns a
running target identification number used in this paper.
Imaging data were obtained in service mode with the AO system NACO
on the 8.2\,m VLT Yepun at ESO (Cerro Paranal, Chile), during two different
semesters (2002/2003 and 2004). Spectroscopic follow-up observations were obtained
in service mode during 2004 using NACO and ISAAC (on VLT Antu).
For imaging with NACO, we used the high-resolution lens, giving
a pixel scale of 13.26\,mas\,pix$^{-1}$\ and the field of view
13\farcs6$\times$13\farcs6. The full-width half maximums (FWHMs) of the diffraction
limited point-spread functions (PSFs) of the setup in our used
photometric bands $J$ (1.27\,$\mu$m), $H$ (1.66\,$\mu$m), and $K_s$ (2.18\,$\mu$m)
are 32\,mas, 42\,mas, and 56\,mas, respectively.
In the first semester, we obtained an extra exposure with a 5~mag neutral
density filter for the stars we expected would saturate the array during
the minimum exposure time of 0.3454\,s.
In the second semester, we instead made use of the new semi-transparent
coronographic mask for the brightest targets, that reduces the light
within 0\farcs35 radius. We measured the contrast between the inside and outside
of the mask to be $6.0\pm0.1$~mag in $H$ and $6.3\pm0.1$~mag in $K_s$, by observing
a binary with and without the coronographic plate. This is consistent with results
found by the NACO instrument team (N.~Ageorges, private communication).
We used either the visual wave front sensor (WFS) mode VIS,
or the infrared WFS modes N20C80 or N90C10, that direct 20\%
or 90\% of the IR light to the WFS, and the rest to the
science camera CONICA.
The zenith seeing in the $V$-band was better than 0\farcs6 in general, though the
targets, due to their low declination of -78\degr, were observed at the relatively
high air mass of 1.5--2.0.
Three examples of obtained images are show in
Figs.~\ref{f:ec01}\,\&\,\ref{f:ec0912}.
For spectroscopy with NACO, we used Grism~3 with the S27 lens, the N90C10
WFS, and a 0\farcs086$\times$40\arcsec\ slit that produces an $H$-band spectrum
from 1.44\,$\mu$m to 1.72\,$\mu$m at spectral resolution $R\sim1500$
and pixel scale 27\,mas\,pix$^{-1} \times$ 3.4\,\AA\,pix$^{-1}$.
For spectroscopy with ISAAC, we used the SWS1-LR mode with the $SH$ filter,
and a 1\arcsec$\times$120\arcsec\ slit that produces an $H$-band spectrum
from 1.48\,$\mu$m to 1.80\,$\mu$m at spectral resolution $R\sim500$
and pixel scale 0\farcs148\,mas\,pix$^{-1} \times$ 4.1\,\AA\,pix$^{-1}$.
The basic reduction was done in a standard way, making use of the
reduction pipeline in the case of ISAAC. The sky was estimated
from the jittered observations and subtracted from all frames, which were
subsequently corrected for cosmic rays and flat fielded. Since the coronographic
mask is in a fixed position on the array, half of the integration time was spent
with the source chopped out of the field. For the spectroscopic observations,
the slit was put over both primary and companion candidate, and then jittered
along the slit. To decompose the spectra of two stars on the slit, we extracted
the spectra by fitting two-component Moffat functions \citep{mof69} to the
spatial profiles. The wavelength calibration made use of Ar lamp spectra obtained
during daytime. To correct for atmospheric absorption lines, an early type
(B2--B5) telluric standard star was observed each night, at a similar airmass (within 0.2)
to the target. The science spectra were then divided by the telluric standard spectra,
multiplied by standard star models, and normalized. Unfortunately, the telluric line
correction proved to not be entirely reliable, most probably due to the high airmass
($\sim$2) at which the observations were made.
The use of AO and a narrow slit makes the calibration of NACO spectra
difficult. For example, the PSF, and therefore slit loss, varies
with wavelength. In the NACO $H$-band spectra of the resolved $\eta$\,Cha~9 binary we
noticed the spectral shape to be somewhat steeper than the ISAAC $H$-band spectrum
we have for the unresolved binary. Since the observations were made at high airmass,
we suspect this
difference might be due to additional wavelength-dependent slit losses, caused by
atmospheric differential refraction. To test this hypothesis we computed the
expected atmospheric dispersion using the refraction index from \citet{pec72},
and the standard dispersion equation (e.g., equation~3 in \citealt{roe02}),
giving the expected dispersion of 50\,mas between 1.5\,$\mu$m and 1.7\,$\mu$m,
which is a fair fraction of the 86\,mas slitwidth. Projected on the slit orientation,
the computed offset increases from 25\,mas to 34\,mas during the 10 exposures of
$\eta$\,Cha~9, while at the same time the observed spectral slope gets steeper by
$\sim$15\%, indicating that differential refraction may indeed be significant. The
telluric standard was observed with the slit at the parallactic angle, and was thus not
affected by differential refraction.
These wavelength-dependent slit losses are of no consequence for the present observations,
since we are interested in the spectral difference between the two components, but they
might be of importance for future observations using VLT/NACO at high airmass.
Table~\ref{t:obslog} presents the observing log, with epochs, instrumentation,
exposure time, and total integration time on source for each target.
\section{Analysis and results}
\label{s:analysis}
\subsection{Astrometry and photometry of sources in the field}
\label{s:astrophot}
\begin{deluxetable}{ccccc}
\tablewidth{0pt}
\tablecaption{\label{t:comp}Confirmed companions}
\tablehead{
\colhead{$\eta$\,Cha} &
\colhead{Sep (\arcsec)} &
\colhead{PA\tablenotemark{a} (\degr)} &
\colhead{Band} &
\colhead{FR\tablenotemark{b}}
}
\startdata
1 & 0.192\,$\pm$\,0.002 & 354.0\,$\pm$\,0.3 & $H$ & \phn1.15\,$\pm$\,0.02 \\
9 & 0.204\,$\pm$\,0.003 & 195.7\,$\pm$\,0.5 & $J$ & \phn1.03\,$\pm$\,0.04 \\
9 & 0.207\,$\pm$\,0.003 & 195.8\,$\pm$\,0.5 & $H$ & \phn0.96\,$\pm$\,0.04 \\
9 & 0.209\,$\pm$\,0.003 & 196.4\,$\pm$\,0.5 & $K_s$ & \phn1.05\,$\pm$\,0.04 \\
12\tablenotemark{c} & 0.040\,$\pm$\,0.010 & 28\,$\pm$\,4 & $H$ & \phn\phn1.0\,$\pm$\,0.1
\enddata
\tablenotetext{a}{The position angle is measured from north to east. There is an additional systematic error of $\sim1\degr$.}
\tablenotetext{b}{The flux ratio A/B.}
\tablenotetext{c}{$\eta$\,Cha\,12 is unresolved, see \S\,\ref{s:astrophot}.}
\end{deluxetable}
\begin{deluxetable}{ccccc}
\tablewidth{0pt}
\tablecaption{\label{t:bg}Likely chance alignment objects}
\tablehead{
\colhead{$\eta$\,Cha} &
\colhead{Sep (\arcsec)} &
\colhead{PA\tablenotemark{a} (\degr)} &
\colhead{Band} &
\colhead{Mag\tablenotemark{b}}
}
\startdata
\phn\phm{$^c$}1\tablenotemark{c} & 8.610\,$\pm$\,0.018 & \phn13.8\,$\pm$\,0.2 & $H$\phn & 11.5\,$\pm$\,1.0 \\
\phn2 & 7.997\,$\pm$\,0.020 & 263.6\,$\pm$\,0.2 & $H$\phn & 19.8\,$\pm$\,0.5 \\
\phn3 & 2.084\,$\pm$\,0.005 & 106.5\,$\pm$\,0.3 & $J$\phn & 17.0\,$\pm$\,0.5 \\
\phn3 & 2.034\,$\pm$\,0.005 & 106.6\,$\pm$\,0.3 & $H$\phn & 16.3\,$\pm$\,0.2 \\
\phn3 & 2.082\,$\pm$\,0.005 & 106.1\,$\pm$\,0.3 & $K_s$ & 15.9\,$\pm$\,0.2 \\
\phn\phm{$^i$}4\tablenotemark{d} & 7.352\,$\pm$\,0.018 & 273.3\,$\pm$\,0.2 & $H$\phn & 13.9\,$\pm$\,0.3 \\
\phn7 & 5.611\,$\pm$\,0.016 & 344.2\,$\pm$\,0.2 & $H$\phn & 15.9\,$\pm$\,1.0 \\
\phn8 & 9.443\,$\pm$\,0.023 & \phn30.8\,$\pm$\,0.2 & $H$\phn & 17.4\,$\pm$\,1.0 \\
\phn\phm{$^e$}9\tablenotemark{e} & 3.582\,$\pm$\,0.010 & 141.7\,$\pm$\,0.3 & $J$\phn & 15.6\,$\pm$\,0.2 \\
\phn\phm{$^e$}9\tablenotemark{e} & 3.526\,$\pm$\,0.010 & 142.2\,$\pm$\,0.3 & $H$\phn & 15.3\,$\pm$\,0.1 \\
\phn\phm{$^e$}9\tablenotemark{e} & 3.568\,$\pm$\,0.010 & 141.8\,$\pm$\,0.3 & $K_s$ & 15.1\,$\pm$\,0.1 \\
10 & 9.895\,$\pm$\,0.026 & \phn62.5\,$\pm$\,0.2 & $H$\phn & 16.6\,$\pm$\,0.5 \\
\phm{$^i$}15\tablenotemark{f} & 2.707\,$\pm$\,0.040 & \phn73.4\,$\pm$\,0.8 & $J$\phn & 18.0\,$\pm$\,0.5 \\
15 & 2.726\,$\pm$\,0.008 & \phn72.1\,$\pm$\,0.3 & $H$\phn & 17.5\,$\pm$\,0.2 \\
\phm{$^i$}15\tablenotemark{f} & 2.752\,$\pm$\,0.040 & \phn72.7\,$\pm$\,0.8 & $K_s$ & 17.3\,$\pm$\,0.5 \\
\phm{$^g$}15\tablenotemark{g} & 6.370\,$\pm$\,0.017 & 209.4\,$\pm$\,0.2 & $J$\phn & 13.8\,$\pm$\,0.4 \\
15 & 6.352\,$\pm$\,0.017 & 210.0\,$\pm$\,0.2 & $H$\phn & 13.6\,$\pm$\,0.2
\enddata
\tablenotetext{a}{The position angle is measured from north to east. There is an additional systematic error of $\sim1\degr$.}
\tablenotetext{b}{Apparent magnitudes were derived from Table~\ref{t:targets}.}
\tablenotetext{c}{The astrometry was measured relative to the photocenter of the inner binary. This object
is listed in 2MASS with $J=11.70\pm0.06$, $H=11.12\pm0.08$, and $K=11.06\pm0.06$, and in DENIS with
$I = 12.43\pm0.03$.}
\tablenotetext{d}{This object
is listed in 2MASS as having $J=14.48\pm0.23$, $H=13.81\pm0.32$, and $K=13.72\pm0.12$.}
\tablenotetext{e}{The astrometry was measured relative to the south component B of the inner binary.}
\tablenotetext{f}{Marginal detection}
\tablenotetext{g}{Object located at edge of array.}
\end{deluxetable}
For observations where multiple sources were well separated in the field, we
measured the pixel positions on the array by making use of the \texttt{iraf}
routine \texttt{imexamine}. To determine the relative precision of the astrometry
we measured the separation between the tight, but well resolved, binary $\eta$\,Cha~1
for 10 different consecutive frames. The standard deviation was found to be about
0.12 pixels, or $\sigma_{\mathrm{std}} = 1.6$\,mas. In addition, there is a systematic
image scale uncertainty of $\sigma_{\mathrm{scl}} \sim 0.01$\,mas\,pix$^{-1}$, so the
estimated total separation error $\sigma_{\mathrm{sep}}$ depends on the separation $s$ as
$\sigma_{\mathrm{sep}}(s) = [(\sigma_{\mathrm{scl}}s)^2 + \sigma_{\mathrm{std}}^2]^{1/2}$. For
some of the fainter sources, $\sigma_{\mathrm{std}}$ would be larger by a factor of several,
due to poor centering.
The relative position angle error $\sigma_{\mathrm{PA}}$ was computed from
$\sigma_{\mathrm{std}}$ by scaling the error with separation, i.e.\ $\sigma_{\mathrm{PA}}(s) =
\arctan(\sigma_{\mathrm{std}} s^{-1}) \approx \sigma_{\mathrm{std}} s^{-1}$\,rad.
The position angle error is generally dominated by the systematic error of $\sim 1\degr$, due to the
uncertain orientation of the array. The astrometry is summarized in Table~\ref{t:comp}\,\&\,\ref{t:bg}.
Photometric measurements of AO data are complicated by the spatially
varying PSF. To estimate the level of anisoplanatism, we measured the PSF
for the targets with multiple sources in the field. The FWHM
of the PSF core (and thus the Strehl ratio) was found to be strongly dependent
on the distance to the primary WFS. Out to a few arcseconds, the
variation is less than 10\%, but at larger separations ($\ga$7\arcsec)
the Strehl ratio can decrease by as much as a factor of 10. Part of the reason for this
strong anisoplanatism may be that the stars were all observed at relatively high
airmass ($\eta$\,Cha never rises below an airmass of 1.5 from Cerro Paranal).
Because of the dependence of the PSF on separation, sources separated
$\ga$4\arcsec\ from the primary have poorly constrained photometry. For those
well-separated sources, we used a large aperture of 100 pixel radius for both the
primary and secondary, if it was bright enough; otherwise
we fit a Gaussian to the PSF core and computed the integrated flux under the
Gaussian. Since the Strehl ratio is so low for the sources at large separation from
the WFS star, their PSFs are reasonably well approximated by Gaussians. By using the
Gauss-fitting procedure also on the bright wide companions, we found the two
methods to be consistent within 0.3\,mag, which is the quoted error. As a second
consistency check we used the relatively
bright source 7\arcsec\ from $\eta$\,Cha~4, catalogued as $H = 13.81 \pm 0.32$
by 2MASS, in agreement with our estimated $H = 13.9 \pm 0.3$.
For the
close-in companions, where the PSF is roughly constant, we used aperture
photometry with a radius of 4 pixels, and subtracted the background halo from
the primary by measuring its brightness at the same separation but opposite
position angle. The photometry is much more robust in this case. The error
of the measured flux ratios is estimated by finding the consistency of
multiple (consecutive) observations of the same target.
As the binary $\eta$\,Cha~12 is unresolved (Fig.~\ref{f:ec0912}), it requires
special attention.
We assume that the PSF core of the observation is circularly symmetric,
as is the case for the other observed central PSFs, and that the elongation to the north
east is the result of an equal mass binary. The position angle is then estimated
from the position angle of an elliptical Gaussian fit, and the separation from
the FWHM of the fit along and across the major axis, by computing their
difference.
\subsection{Strehl ratios\label{s:strehl}}
The Strehl ratio $S$ is defined as the ratio between the observed peak intensity
$P_{\mathrm{obs}}$ of the PSF, and the theoretical peak intensity
$P_{\mathrm{ideal}}$ of an idealized telescope (no distortion of wavefront,
no obstructions) of the same aperture observing the same star,
$S \equiv P_{\mathrm{obs}} / P_{\mathrm{ideal}}$. Instead of computing
$P_{\mathrm{ideal}}$ for each observation, we estimated the ratio
$R_{\mathrm{ideal}} = P_{\mathrm{ideal}} / A_{\mathrm{ideal}}$, where
$A_{\mathrm{ideal}}$ is the flux (integrated intensity), that only depends
on telescope aperture and wavelength. For an 8.2\,m telescope we computed
$R_J$ = 772\,arcsec$^{-2}$, $R_H$ = 452\,arcsec$^{-2}$, and $R_{K_s}$ = 263\,arcsec$^{-2}$,
for $J$, $H$, and $K_s$, respectively.
We then estimated similar ratios
$R_{\mathrm{obs}} = P_{\mathrm{obs}} / A_{\mathrm{obs}}$ for the observations, and
determined the Strehl ratio as $S = R_{\mathrm{obs}} / R_{\mathrm{ideal}}$. The
peak intensity of the observed profile was found
by fitting a circular Gaussian function to the PSF core, and the integrated
intensity by summing up all pixels within a circular aperture of 2\arcsec\ radius.
The estimated Strehl ratios are shown in Figs.~\ref{f:contrast1}\,\&\,\ref{f:contrast2},
except for the coronographic observations where we could not determine $R_{\mathrm{obs}}$ reliably,
due to the presence of the mask. Because the coronographic targets are bright, and observed
under similar conditions, we expect the Strehl ratios to be at the high end ($>$15\,\%).
The lower the Strehl ratio, the larger fraction of the stellar flux that is diluted into the
seeing disc. Even down to Strehl ratios of a few percent, however, there usually is a
diffraction-limited core of the PSF. This means that searches for point sources (such as
stars) are greatly aided by AO even at low Strehl ratios, while searches for extended
structures (such as circumstellar material) are critically dependent on high Strehl
ratios.
\subsection{Contrast sensitivities}
\label{s:contrast}
\begin{figure*}
\includegraphics[width=\hsize,clip=true]{f3.eps}
\caption{\label{f:contrast1}See the caption of Fig.~\ref{f:contrast2}.}
\end{figure*}
\begin{figure*}
\includegraphics[width=\hsize,clip=true]{f4.eps}
\caption{\label{f:contrast2} Sensitivity to companions as a function of
separation, determined as described in \S\,\ref{s:contrast}. The photometric
band and magnitude is given in each panel, as well as the measured Strehl ratio
(except for the coronographics observations, see \S\,\ref{s:strehl}). Left vertical axes
show the contrast sensitivity, while the right axes show the absolute
sensitivity. The bottom horizontal axes show the angular separation
and the upper axes the corresponding projected separation at the
$\eta$\,Cha cluster distance of 97\,pc. The diffraction limit and
the semitransparent coronographic mask radius are shown as vertical
dashed lines. The two horizontal dashed lines depict the star/brown
dwarf (0.08\,M$_{\sun}$: $J=12.5$, $H=12.0$, and $K=11.8$) and brown dwarf/planetary
mass (15\,M$_{\mathrm{J}}$: $J=15.0$, $H=14.6$, and $K=14.2$) boundaries for the \citet{bar03}
evolutionary models at age 8\,Myr and distance 97\,pc.}
\end{figure*}
In order to estimate the sensitivity to companions as a function
of separation, we used the following procedure:
\begin{enumerate}
\item For every pixel $j$ in the detector, compute the distance $r_j$ to the
determined center of the primary.
\item \label{en:affine} Choose two radii $R_0$ and $R_1$ and fit an affine function
$f(r) = a_0 + a_1r$, where $a_0$ and $a_1$ are fitting constants,
to the intensity $I_j$ of all pixels $j$ with $r_j \in [R_0,R_1]$.
Reject pixels more than 3$\sigma$ from the fit.
\item Compute the standard deviation of the fit residuals,
$\sigma_{\mathrm{pix}}(R) = \mathrm{StdDev}[I_j - f(r_j)]$, where
$R$ is the mean of all $r_j \in [R_0,R_1]$.
\item Measure the FWHM of the primary PSF, and the number
of pixels $N_{\mathrm{PSF}}$ and integrated flux $F_{\mathrm{PSF}}$
within that area.
\item The derived 5$\sigma$ contrast sensitivity is then estimated to be
\begin{equation}
\Sigma(R) = -2.5 \log_{10}\left[ \frac{5\sigma_{\mathrm{pix}}(R)
\sqrt{N_{\mathrm{PSF}}}}{F_{\mathrm{PSF}}}\right]\,\mathrm{mag}.
\end{equation}
\end{enumerate}
The \textit{absolute} sensitivity is obtained by adding the primary magnitude
to $\Sigma(R)$. The function $f(r)$ in step~\ref{en:affine} is fit to remove
the radial gradient in the pixel intensities, that is due to the PSF. We confirmed
that this procedure accurately estimates our achieved sensitivity by artificially
placing intensity scaled PSFs at various separations. Since we limit the
search to within 5\arcsec, we do not correct for anisoplanatism (see \S\,\ref{s:astrophot}).
For the semi-transparent coronographic observations, we made use of the
measured suppression ratio in $H$ ($6.0\pm0.1$~mag, \S\,\ref{s:obs}).
In the case of $\eta$\,Cha\,9, which is a tight 0\farcs2
binary, we computed the contrast sensitivity from the center of
light of the two stars, and estimated $N_{\mathrm{PSF}}$ and
$F_{\mathrm{PSF}}$ as the average and sum, respectively, of
both stars. The iso-intensity curves from the combined pair
are elliptical rather than circular symmetric close to the
stars, which is the reason the contrast sensitivity is estimated
only at $\ge0\farcs2$ from the common center.
The contrast sensitivities for all observations are presented in
Figs.~\ref{f:contrast1}\,\&\,\ref{f:contrast2}.
\subsection{Spectra of companion candidates}
\label{s:spectra}
\begin{figure}
\includegraphics[width=\hsize,clip=true]{f5.eps}
\epsscale{0.8}
\caption{\label{f:isaac}ISAAC spectra of the primaries and companion
candidates of $\eta$\,Cha 4, 9, 10, and 15, denoted in the figure.
The spectra have been normalized and offset in steps of 0.25. The
lowest spectrum shows the telluric atmospheric extinction, also
normalized and offset to 0. All of these companion candidates are
likely background objects (\S\,\ref{s:companions}).}
\end{figure}
\begin{figure}
\includegraphics[width=\hsize,clip=true]{f6.eps}
\epsscale{1.0}
\caption{\label{f:nacospec} Resolved NACO spectra of the inner
0\farcs2 $\eta$\,Cha~9 binary, normalized and offset by 0.25
from each other. The spectra are virtually identical. The scale
has been chosen so that the flux scale / wavelength scale ratio is the same as
in Fig.~\ref{f:isaac}.}
\end{figure}
The obtained ISAAC $H$-band spectra of the primaries and companion
candidates of the systems $\eta$\,Cha 4, 9, 10 and 15
are shown in Fig.~\ref{f:isaac}. Since the correction for telluric
lines was poor due to high airmass, a plot of the extinction is
also shown in Fig.~\ref{f:isaac}.
The NACO $H$-band spectrum of the inner 0\farcs2 binary of $\eta$\,Cha~9
is shown in Fig.~\ref{f:nacospec}.
\section{Discussion}
\label{s:discuss}
\subsection{Companion candidates}
\label{s:companions}
The $\eta$\,Cha cluster is only 22\degr\ from the Galactic plane,
so the probability of chance alignment stars in the
13\farcs6$\times$13\farcs6 field of view is non-negligible. From the 2MASS
All-Sky Data Release we find that the density of stars brighter than $H\sim16$
is $\sim10^{-3}$\,arcsec$^{-2}$, that statistically would produce
about $3 \pm 2$ chance alignments in our 17 fields, consistent with the total
number of companion candidates (5) with $H<16$ in our sample. Since
the observations are generally much more sensitive than this, we expect
even more faint background stars. We have unfortunately no access to
a deeper NIR survey of the region to find the local star
density, but a general conclusion is that potentially \textit{all} of
the 10 new companion candidates found (Table~\ref{t:bg}) could be chance
alignments.
For four of the candidates (near $\eta$\,Cha 4, 9, 10, and 6\farcs4 from $\eta$\,Cha~15)
we have NIR ISAAC $H$-band spectra. If these companion candidates had been members of
the $\eta$\,Cha cluster, their age ($\sim$8\,Myr) and
luminosity (from Table~\ref{t:bg} and the distance 97\,pc) would have implied
very low-mass objects with atmospheres cooler than 2500\,K \citep{bar03},
corresponding to spectral types later than M8.5 \citep{kir99,luh03}.
This is clearly not the case,
as the ISAAC spectra reveal all companion candidates to
have spectral types equal to, or earlier than, their primaries
(Fig.~\ref{f:isaac}). In particular, there is no evidence for water
depression that should be visible at $\sim$\,1.5$\,\mu$m for spectral
types later than M5 \citep{cus05}. We thus conclude that these companion
candidates most likely are background stars, and not associated
with the $\eta$\,Cha cluster.
For the companion candidate near $\eta$\,Cha~3, we have two epochs of data separated
by 1.25\,yr that show a relative position difference of
$(\Delta\alpha,\Delta\delta)$ = $(48\pm7,-14\pm7)$\,mas, implying a relative proper motion
of $(\mu_{\alpha},\mu_{\delta}) = (38\pm6,-11\pm6)$\,mas\,yr$^{-1}$. A common proper
motion is thus ruled out with $>5\sigma$-significance, while the relative proper motion
is roughly consistent with the companion
candidate being a background star, since the proper motion of the $\eta$\,Cha cluster
is $(\mu_{\alpha},\mu_{\delta}) = (-30.0\pm0.3,27.8\pm0.3)$\,mas\,yr$^{-1}$ \citep{mam00}.
The inner companion candidate of $\eta$\,Cha~3 also has two epochs of data, but unfortunately
the positional precision is not sufficient to significantly constrain the relative proper motion.
The non-membership status of the star is instead revealed by its NIR colors; a $H=17.5$ $\eta$\,Cha
member should have had $J-K \sim 3$ rather than $J-K = 0.7\pm0.7$.
The companion near candidate $\eta$\,Cha~1 is separated and bright enough to have 2MASS and DENIS photometry
(Table~\ref{t:bg}). We reject this as a physical companion, since the observed $I-(J,H,K)$
colors are $\sim$1\,mag fainter than expected from the \citet{bar98} models, even when allowing for
variability due to the epoch difference between 2MASS and DENIS.
The remaining 3 companion candidate stars (near $\eta$\,Cha 2, 7, and 8)
have only single epoch $H$-band imaging, and therefore no direct way of
ruling them out as physical companions. They are all quite distant from the system
primary ($>5.6\arcsec \sim 540$\,AU) and faint ($H\ga16$), however, and therefore
likely chance alignments.
We conclude that, among the 17 $\eta$\,Cha members surveyed, there are no detected companions with
projected separations 20--500\,AU.
\subsection{Orbit of $\eta$\,Cha~1}
\label{s:orbit}
\citet{koh02} used multi-epoch observations of $\eta$\,Cha~1 between
1996-03-29 and 2001-12-10 to compute a preliminary orbit, estimating
a dynamical mass. With the additional data point from 2004-04-03, we
can constrain the orbit further (see Fig.~\ref{f:orbit}). In particular, among
the two preferred orbits with periods of 43\,yr and 151\,yr found in
\citet{koh02}, the longer orbit is clearly favoured by our data. To possibly
find a better orbital solution, we developed a simple orbit-fitting code that
works as follows:
\begin{enumerate}
\item For a given orbit $k$, compute the positions $(s^{k}_i,\phi^{k}_i)$
on sky for the dates of the observations, where $s^{k}_i$ is the separation
of orbit $k$ and observation $i$, and $\phi^{k}_i$ the corresponding position angle.
\item Compute the square sum $\chi^2$ of the differences between the positions
$(s^{k}_i,\phi^{k}_i)$ from the assumed orbit, and the observed positions
$(s^{\mathrm{obs}}_i,\phi^{\mathrm{obs}}_i)$:
\begin{displaymath}
\chi^2(k) = \sum_{i=1}^N \left[ \left(\frac{s^{k}_i - s^{\mathrm{obs}}_i}{\sigma_{s,i}}\right)^2
+ \left(\frac{\phi^{k}_i - \phi^{\mathrm{obs}}_i}{\sigma_{\phi,i}}\right)^2 \right],
\end{displaymath}
where $\sigma_{s,i}$ is the error in separation and $\sigma_{\phi,i}$ the error in
position angle (including estimated systematic errors).
\item Find the orbit $k$ that minimizes $\chi^2(k)$.
\end{enumerate}
\begin{figure}
\center{\includegraphics[width=\hsize,clip=true]{f7.eps}}
\caption{\label{f:orbit}Relative astrometry between the two components of
$\eta$\,Cha~1. The crosses show the measured separations, with the
right-most data point coming from this paper and the others from \citet{koh02}. The
1$\sigma$ positional errors are indicated by the size of the crosses.
The dashed and dash-dotted curves are the orbit solutions found by
\citet[see their Table~4]{koh02}, with periods of 150.8\,yr and 42.5\,yr,
respectively. The unbroken line is the unphysical 93\,yr period orbit
fit mentioned in \S\,\ref{s:orbit}. The small circles denote the positions in the orbits
that correspond to the dates of the observations.
}
\end{figure}
The reason for using polar coordinates is that the position angle normally
introduces a larger error than the separation, due to uncertainties in detector orientation.
While the 151\,yr orbit of \citet{koh02} produces a good fit (Fig.~\ref{f:orbit}), we find a multitude of
very different orbits that produce equally good or better fits. In particular,
there is a general solution degeneracy such that extremely eccentric orbits
at high inclinations produce good fits (but with an unrealisticly high system
mass). An example is given in Fig.~\ref{f:orbit}, where the unbroken line shows an orbit
with a period of 93\,yr and semi-major axis 0\farcs416, corresponding to the
system mass of 7.6\,M$_{\sun}$ at the distance of 97\,pc. Our conclusion is
that the orbit has to be followed for a longer time span before useful limits
on the dynamical mass can be made. Alternatively, spatially resolved radial
velocity measurements would add valuable constraints.
\subsection{Limits on companion probability}
\label{s:limits}
The contrast sensitivity estimates from \S\,\ref{s:contrast} can
be used to put limits on the number of likely companions. The basic approach
is to assume that companions of stars are assigned by a stochastic
process such that any given star system will have a companion with
probability $p$, called the multiplicity (or binary) probability.
The observed systems are then seen as a sample of
this stochastic variable. Even if we knew with complete certainty
that the 17 systems of $\eta$\,Cha had no wide stellar companions, there
would still be a 5\% chance that this outcome would have been produced
with $p = 0.16$; thus, the 95\% confidence upper limit for $p$
would have been $0.16$.
Before we can do the proper statistics, however, we need to correct
for the observational biases. That is, given that there is a companion,
would we have detected it?
Let $p$ be the probability that a star has a companion, and $q_j$ the
probability that a companion would have been detected in system $j$, given
that there had indeed been a companion there. Then the probability
that a companion is not detected in system $j$ is $1 - p q_j$, and the
probability that no companions are detected in $N$ systems enumerated
from 1 to $N$ is
\begin{equation}
\label{e:upper}
\Phi(p) = \prod_{j=1}^N (1 - p q_j).
\end{equation}
With a confidence set we mean the set of $p$ such that
$\Phi(p) \le 1 - \alpha$, where $\alpha$ is the chosen confidence,
typically $\alpha = 95\%$. As $\Phi(p)$ is a monotonously decreasing
function of $p$, the confidence set becomes an interval
$[0,p_{\alpha}]$, where we call $p_{\alpha}$ the $\alpha$-confidence
upper limit on $p$.
\begin{figure*}
\includegraphics[width=\hsize,clip=true]{f8.eps}
\caption{\label{f:sep}
The 95\% confidence upper limits on the probability
of companions. The left panel shows the upper limits for companions of
specific contrasts to the primary, as a function of separation from the
star. The dashed lines (colored blue in electronic edition) show the
sensitivity limits to mass ratios $q = M_{\mathrm{comp}}/M_{\mathrm{prim}}$,
while the unbroken lines (colored red) show the limits for flux-ratios
$\Delta H$. The right panel displays the absolute sensitivity,
where the dashed lines (colored blue) show sensitivity to companion
masses, and the unbroken lines (colored red) show the sensitivity to
apparent $H$-band magnitudes. The dashed horizontal line
shows the 95\% confidence upper limit that would have been obtained statistically
for our sample of 17 systems, had the detection sensitivity been 100\%. The
increased upper limits at separations $>$2\farcs5 is due to part of the field
being outside the array.
}
\end{figure*}
To derive $p_{\alpha}$ we need to know $q_j$ for all observed systems.
For a given magnitude and separation from the star, this becomes straightforward
using the contrast sensitivity estimates from \S\,\ref{s:contrast}. If the
brightness is above the sensitivity limit at the
given separation in system $j$, $q_j = 1$; else $q_j = 0$.
Equation~\ref{e:upper} thus reduces to $\Phi(p) = (1 - p)^n$, where $n$ is the
number of systems where detection would have been possible. This implies
$p_{\alpha} = 1 - (1 - \alpha)^{1/n}$. Because $p_{\alpha}$ thus only
depends on the discrete $n$, $p_{\alpha}$ will also be discrete, as
shown in Fig.~\ref{f:sep}.
In the left panel of Fig.~\ref{f:sep} we derive 95\% upper
limits on the probability of
companions of specific flux ratios to the primary, as a function of
separation. To derive limits on the companion probability for specific
mass ratios $q$, we assume primary masses from \citet{lyo04b}, and use
evolutionary models from \citet{bar03} to translate companion mass to an
$H$-band magnitude, assuming the age 8\,Myr, distance 97\,pc and solar metallicity.
In the right panel of Fig.~\ref{f:sep} we instead display limits on the absolute
sensitivity to companions of different $H$-band magnitudes and masses.
From a physical point of view, rather than knowing the companion probability
as a function of observed (projected) separation, it is more interesting to
find the probability as a function of semi-major axis. To do that we need to
know the probability $q_j$ to find a companion, given that it has a specific
semi-major axis. Our ability to detect a companion will depend on its
projected distance to the primary, which in turn depends on viewing
geometry and orbital phase (for eccentric orbits). In the Appendix, we
compute the projected separation probability distribution for a
companion of semi-major axis $a$. Assuming a random orientation, we derive
the distribution
analytically for circular orbits (\S\,\ref{s:circular}), and use a numerical
approach in the case of eccentric orbits with an eccentricity distribution
$f(e)=2e$ (motivated by both theory and observations; see
\S\,\ref{s:elliptical}). The probability $q_j$ is then
the probability that the companion is located at
a detectable distance from the binary. Assuming that the sensitivity increases
monotonously as a function of separation, this equals the
probability that the companion is outside the ``detection separation'' $d$
-- i.e.\
\begin{equation}
\label{e:qj}
q_j = \int_{d/a}^{\infty} f_S(s)\,\mathrm{d}s = 1 - F_S(d/a),
\end{equation}
where $f_S(s)$ is the projected separation probability density distribution
found in the Appendix and shown in Fig.~\ref{f:prob}, and $F_S(s)$ is the corresponding
probability distribution. Since the projected
separation can be arbitrary small for any semi-major axis, we always have
that $F_S(d/a) > 0$ for $d/a > 0$, and thus $q_j < 1$. Once we know $q_j$,
equation~\ref{e:upper} is used to compute 95\% upper limits on the probability
of companions. For the coronographic observations, the mask is at a fixed
position only $h=2\farcs5$ from the edge of the detector; we therefore introduce
the additional correction factor $g(s) = 1 - \pi^{-1}\arccos(h/s)$ (for
$s > h$) into the integral of equation~\ref{e:qj}, where $g(s)$ is the probability that a
companion at separation $s$ is in the field of view.
\begin{figure*}
\includegraphics[width=\hsize,clip=true]{f9.eps}
\caption{\label{f:major}
Same as in Fig.~\ref{f:sep}, except that the sensitivity limits are displayed
as a function of semi-major axes, assuming the eccentricity
probability density distribution $f(e) = 2e$.}
\end{figure*}
In Fig.~\ref{f:major} we show the 95\% upper limits in the same way as in Fig.~\ref{f:sep},
but as a function of the semi-major axes.
\subsection{Deficit of wide binaries}
\label{s:deficiency}
It is remarkable that, despite our high sensitivity, the \emph{widest} binary
detected in the $\eta$\,Cha cluster is only
0\farcs21, corresponding to the projected distance of 20\,AU. This lack of wide binaries
was already noted by \cite{koh02}, albeit with smaller statistics and less sensitive measurements.
Outside 20\,AU, we would have found any stellar
companion (of mass $>$0.07\,M$_{\odot}$; see Fig.~\ref{f:sep}). The fact that
we do not detect any wide binaries among the 17 members implies that
the wide ($>30$\,AU) binary probability $w_{\eta\,\mathrm{Cha}}$ with 1$\sigma$
confidence is lower than $p_{1\sigma}$=0.07, and with 95\% confidence is lower
than $p_{95\%}$=0.18 (Fig.~\ref{f:major}). This stands in stark contrast to the other
nearby, young (of the similar age 8\,Myr) TW~Hydrae association (TWA),
where 11 out of the member stars TWA~1--19 are
binaries with separations $\ga 30$\,AU \citep{bra03}, corresponding to a wide
binary probability
of $w_{\mathrm{TWA}}=0.58^{+0.13}_{-0.14}$, clearly different from what
we find in $\eta$\,Cha.
This difference cannot be due to detection sensitivity differences; all the
companions in TWA would have easily been detected in the $\eta$\,Cha cluster
by this survey. The difference cannot be explained by small number statistics
either, as the statistical likelihood that the $\eta$\,Cha cluster
and TWA have binary frequencies drawn from the same distribution is less than
$2\times10^{-4}$ (see the Appendix).
There is certainly no deficiency of \emph{close} binaries ($< 30$\,AU) in the
$\eta$\,Cha cluster \citep{lyo04b}. If anything, there might be a small
over-abundance, compared to TWA, but the statistics are inconclusive.
One may speculate on the cause for such a difference in the wide binary
population between the $\eta$\,Cha cluster and the TWA. One notable difference is that
the $\eta$\,Cha cluster is much denser than the TWA. Could it be that wide binaries are
dynamically disrupted in the $\eta$\,Cha cluster? To investigate this possibility we
estimate the timescale for a binary to undergo a strong encounter with another
star in the cluster. From \citet[equation~7]{iva05}, we have that this timescale is
\begin{eqnarray}
\label{e:colltime}
\tau_{\mathrm{coll}} = 1.7 \times 10^{8}\,\mathrm{yr} \times
\eta^2 k^{-2} n_5^{-1}\frac{\langle M \rangle^2}{M_1^2M_2^2} \nonumber\\
\times \left(1 + \eta \frac{2}{k}\frac{M_1 + M_2 +
\langle M \rangle}{M_1 M_2} \langle M \rangle \right)^{-1},
\end{eqnarray}
where $\eta$ is the hardness of a binary, $k \simeq 2$, $n_5$ is the number
density of star systems in units of $10^5$\,pc$^{-3}$, $\langle M \rangle$
is the mean mass per star system in units of M$_{\sun}$, and $M_1$ and $M_2$ are
the masses of the binary components, also in units of M$_{\sun}$. The hardness
of a binary is defined as
\begin{equation}
\eta = \frac{M_1 M_2}{\langle M \rangle \sigma^2 a} G \mathrm{M}_{\sun},
\end{equation}
where $G$ is the gravitational constant, $a$ is the binary separation,
and $\sigma$ is the velocity dispersion
of the cluster. Binaries with $\eta < 1$ are termed soft, and those with
$\eta > 1$ hard. In general, soft binaries are disrupted by strong encounters,
while hard binaries may survive. In the $\eta$\,Cha cluster, we have the cumulative
mass 16.6\,M$_{\sun}$ distributed over 17 systems \citep{lyo04b},
giving $\langle M \rangle = 1.0$.
There are presently no accurate radial velocities published for the $\eta$\,Cha
members. However, from the estimated age of the cluster ($\sim$8\,Myr) and
observed effective radius ($\sim0.2$\,pc), we infer that the cluster most likely is
gravitationally bound. The present escape velocity is namely
$v_{\mathrm{esc}} = (2GM/R)^{1/2} \sim 0.75$\,km\,s$^{-1}$, assuming $M$ = 13\,M$_{\sun}$
within $R = 0.2$\,pc \citep{lyo04b}, which gives a crossing time of merely 0.3\,Myr,
enough to traverse the cluster core 25 times during its lifetime, while the relaxation
time is only a few times the crossing time \citep[chapter 4]{bin87}. We
therefore assume $\sigma = v_{\mathrm{esc}}/2 = 0.37$\,km\,s$^{-1}$, in accordance
with the virial theorem, implying that the condition for a binary to
be soft in the $\eta$\,Cha cluster is $a > 1600$\,AU $\gg 30$\,AU for the typical masses
$M_1 = M_2 = 0.5$.
Moreover, for the $\eta$\,Cha cluster $n_5 \sim 3\times10^{-3}$, and the collision timescale
for $\eta=1$ binaries is thus $\tau_{\mathrm{coll}}\sim26$\,Gyr, i.e.\ 3000 times
longer than the lifetime of the system. That dynamical interactions between binaries
in the present configuration of the cluster should be responsible for the lack of
wide ($>$30\,AU) binaries, consequently seems highly unlikely.
Since both the $\eta$\,Cha cluster and TWA are of similar age, the remaining
explanation is that the difference in multiplicity properties were imprinted during
the formation phase, as a result of different initial conditions. Either the groups
formed with different multiplicity properties, or the properties
dynamically evolved very early on, when the stars were possibly much closer together.
There seems to be a general trend that denser groups have smaller wide binary
frequencies than sparser regions; the sparse regions Taurus, Ophiuchus and
Chamaeleon \citep{duc99}, and MBM~12 \citep{bra03} all have high wide binary
frequencies, while the denser regions Trapezium \citep{pet98}, and NGC~2024, 2068, and
2071 \citep{pad97}, have low wide binary frequencies.
Solar-type main-sequence stars
in the solar neighborhood have a binary probability of $\sim$0.45
\citep[and references therein]{lei93}, with half being wide
\citep{duq91}, and thus $w_{\mathrm{MS}}=0.23$, which is right in between
$w_{\eta\,\mathrm{Cha}}$ and $w_{\mathrm{TWA}}$.
It is therefore not clear from the wide binary statistics alone if sparse
or dense star formation is the dominant mode -- possibly both contribute
equally. What is clear is that models of cluster formation and early evolution
probably are essential to explain multiplicity properties
\citep[e.g.][]{bat02,del04,goo06}.
\section{Conclusions}
\label{s:conclusions}
We summarize our conclusions as follows:
\begin{enumerate}
\item We found no new companions to stars in the $\eta$\,Cha
cluster, despite being sensitive down to the star/BD limit outside
0\farcs3 (30\,AU) and down to the BD/planet limit outside 0\farcs5
(50\,AU).
\item We have constrained the orbit of $\eta$\,Cha\,1 further, but are unable
to usefully constrain a dynamical mass. Resolved radial velocities of the
two components, or a longer astrometric time baseline, are required for an
accurate mass estimate.
\item The 95\,\% upper limit for the wide ($>$30\,AU) binary probability $w_{\eta\,\mathrm{Cha}}$
in $\eta$\,Cha is $p_{95\%}$=0.18. This contrasts to the wide binary
probability $w_{\mathrm{TWA}}=0.58^{+0.13}_{-0.14}$ of TWA. The
likelihood that $w_{\eta\,\mathrm{Cha}} = w_{\mathrm{TWA}}$ is less than
$2\times10^{-4}$.
\item Multiplicity properties depend on the initial conditions of the
formation environment.
\end{enumerate}
\acknowledgments
We acknowledge the outstanding support by the ESO user support department,
in particular Sabine Mengel and Danuta Dobrzycka. We also thank Nancy Ageorges
for help in determining the contrast of the semi-transparent mask.
We are grateful to Marten van Kerkwijk, Natasha Ivanova and Serge Correia for
valuable discussion.
This research was supported by an NSERC grant and an SAO subcontract for the
Keck Nuller project to RJ.
We made extensive use of NASA's Astrophysics Data System
Bibliographic Services, and the SIMBAD database and VizieR catalogue access tool,
operated at CDS, Strasbourg, France. We used
data products from the Two Micron All Sky Survey and the DENIS consortium.
\textit{Facilities:} \facility{VLT:Yepun (NACO)}, \facility{VLT:Antu (ISAAC)}.
\begin{appendix}
\section{Probability distributions for projected binary separations}
This appendix concerns the computation of probability distributions
of the observed projected separation between the two components of a
binary system, given that the semi-major axis is known. Here we use
the semi-major axis $a$ of the companion orbit \emph{relative to the primary}.
If the mass of the companion is a significant fraction of the primary,
this will be different from the semi-major axis $a_{\mathrm{com}}$ of
the companion orbit relative to the center of mass. The relation is
$a = (M_{\mathrm{comp}} / M_{\mathrm{prim}} + 1) a_{\mathrm{com}}$,
where $M_{\mathrm{comp}}$ and $M_{\mathrm{prim}}$ are the masses of the
companion and primary, respectively. The derived probability distributions
below are easily scaled to $a_{\mathrm{com}}$ in case of specific
mass-ratio systems.
\subsection{Companions in circular orbits}
\label{s:circular}
To compute the
probability distribution for the projected separation of a companion, we
need to make the assumption that the orbit is observed from a uniformly
distributed direction; that is, any viewing direction is equally probable.
To generate a stochastic vector with a direction
uniformly distributed over the unit sphere is a less trivial problem
than one might naively expect. One cannot simply use a uniform distribution of
spherical coordinates, since this would bias the vectors too much towards the
poles; and one cannot simply use uniformly distributed Cartesian coordinates,
since this would bias the directions towards the corners. Instead, a stochastic
vector $\mathbf{d}=(x,y,z)$ uniformly distributed over the unit sphere may be
generated as
\begin{eqnarray*}
x &=& \sqrt{1-z^2}\cos\phi \\
y &=& \sqrt{1-z^2}\sin\phi \\
z &\in& U(-1,1),
\end{eqnarray*}
where $X \in U(a,b)$ means that $X$ is a stochastic variable uniformly
distributed between $a$ and $b$, and $\phi \in U(0,2\pi)$. This is a corollary
from a theorem by Archimedes, that states that a lateral area of a section cut
out of a sphere by two parallel planes equals $A = 2 \pi R h$, where
$R$ is the radius of the sphere and $h$ is the distance between the planes.
With $\mathbf{R}$ being the radius vector from the star to the companion,
$R$ its length and $\mathbf{d}$ the unit
viewing direction vector, the projected distance between the star and the
planet onto a plane perpendicular to the viewing direction will be
$s = \sqrt{R^2 - (\mathbf{R \bullet d})^2}$.
Since $\mathbf{d}$ is uniformly distributed on the unit sphere, we can (without
loss of generality) let $\mathbf{R} = R \mathbf{e}_\mathrm{z}$, where $\mathbf{e}_\mathrm{z}$ is the
unit vector along the z-axis. The scalar product becomes
$\mathbf{R \bullet d} = R d_\mathrm{z}$, where $d_\mathrm{z}$ is the z-component
of the direction vector $\mathbf{d}$. That is, the scalar product is only dependent
on the z-component of the direction vector:
\begin{equation}
\label{e:projection}
s = R \sqrt{1 - d_\mathrm{z}^2}.
\end{equation}
The probability distribution for the corresponding stochastic variable
$S = \sqrt{1 - D^2}$, where $D \in U(0,1)$, becomes $F_S(s) = 1 - \sqrt{1 - s^2}$,
and the probability density distribution $f_S(s) = \mathrm{d}F_S(s)/\mathrm{d}s = s/\sqrt{1 - s^2}$.
\begin{figure}
\center{\includegraphics[width=\hsize,clip=true]{f10.eps}}
\caption{\label{f:prob}The left panel shows the probability density distribution
for the projected separation of a companion to a star, in units of its semi-major axis. Two
cases are plotted, one where the orbits are assumed to be circular (solid line),
and one where the eccentricity density distribution is assumed to be $f(e)=2e$
(crosses). The projected separation distribution is computed exactly for
circular orbits, and by a monte carlo approach for the eccentric orbits. The
dashed line is an approximate fit, as outlined in \S\,\ref{s:elliptical}. The
right panel shows the corresponding probability distribution, i.e.\ the integral over the
probability density.
}
\end{figure}
These distributions thus describe the projected separation $s$, in units of the orbital radius,
of a companion in a circular orbit around a star (Fig.~\ref{f:prob}).
\subsection{Companions in elliptical orbits}
\label{s:elliptical}
To derive the projected separation distribution for elliptical orbits is slightly more
complicated than for circular motion, since the radial distance
between the star and its companion is non-linear in time. We also have to
make an additional assumption on the eccentricity distribution. We still do
not have to bother with the orbital elements concerning a specific orientation
of an orbit however, since we already have assumed that the viewing direction is
random.
The mean anomaly $M$ of an elliptical orbit is defined to be linearly increasing
with time \citep[Chapter 29]{mee91}. Its relation to the eccentric anomaly $E$, that is used
to compute the actual position of the companion, is defined by the Kepler equation
$E = M + e\sin E$, where $e$ is the eccentricity of the orbit. Since the
Kepler equation is transcendental it cannot be solved algebraically, which
complicates the analysis. We therefore derive the probability density distribution
using the following monte carlo approach instead.
\begin{enumerate}
\item Let the mean anomaly $M \in U(0,2\pi)$.
\item Get the eccentricity $e$ from some pre-defined distribution $f(e)$.
\item Solve Kepler's equation numerically and compute the
eccentric anomaly $E(M)$.
\item Compute the instantaneous distance between star and companion,
$R = 1 - e\cos E$.
\item Let the projection term $d_{\mathrm{z}} \in U(-1,1)$,
in line with equation~\ref{e:projection}, and compute the projected
separation $s = R \sqrt{1 - d_\mathrm{z}^2}$.
\end{enumerate}
The choice of eccentricity distribution is important for the resulting
probability density distribution.
Theoretical considerations \citep{amb37} predict
the distribution $f(e) = 2e$, where $e \in [0,1]$, which is reasonably
confirmed by observations of long-period binaries
\citep[$>$1000~days;][]{duq91}. To generate a stochastic variable with
$f(e) = 2e$, we let $e = X^{1/2}$, where $X \in U(0,1)$.
The result from a simulation of $10^8$ binaries is shown in Fig.~\ref{f:prob}. The
probability density distribution is well approximated, although not perfectly,
by the function
\begin{equation}
f_S(s) = \frac{\pi}{4}\sin\left(\frac{\pi}{2}s\right),
\end{equation}
where $s \in [0,2]$, which is over plotted in Fig.~\ref{f:prob}.
The corresponding probability distribution
is
\begin{equation}
F_S(s) = \frac{1}{2} \left[1 - \cos\left(\frac{\pi}{2}s\right)\right].
\end{equation}
A stochastic variable $S$ with this distribution can be generated
from $X \in U(0,1)$ by setting $S = 2 \pi^{-1} \arccos(1-2X)$, that might prove
useful for future completeness studies.
\section{Multiplicity statistics}
Statistical estimates of multiplicity frequencies are often limited by small
sample numbers, where approximate methods using assumptions of Poisson or
normal statistics become insufficient. Instead, more accurate estimates can
be obtained by explicit use of binomial statistics. The multiplicities of $N$
systems of a stellar association are viewed as outcomes $x_i$ of a binomially
distributed stochastic variable $X \in Bin(1,p)$, where $p$ is the multiplicity
probability for any specific system. $x_i = 1$ if system $i$ is multiple, and $x_i = 0$
if not. The number of multiple systems is then $k = \sum_i x_i$, which in itself
can be seen as the outcome of a binomially distributed stochastic variable
$K \in Bin(N,p)$.
The goal is to constrain $p$ from a given set $\{x_i\}$, assuming all $x_i$
are drawn from the same distribution. Here we summarize results from two
outstanding problems, how to constrain the multiplicity probability $p$ by a
confidence interval, and how to decide if two sets $\{x_i\}$ and $\{y_i\}$ are
outcomes of the same binomial distribution.
\subsection{Binomial confidence intervals}
The well-known maximum-likelihood estimator of $p$ is $\hat{p} = \sum_i x_i/N$, but
to compute an accurate variance of this estimator is much more difficult. The most
widely used way of computing the standard deviation of $\hat{p}$ is by using the
so-called \textit{Wald} method, that has the simple form
$\sigma = (\hat{p}(1-\hat{p})/N)^{1/2}$. The Wald standard deviation
produces very poor approximations whenever $p$ is close to 0 or 1, however, and
its usage is generally not recommended \citep{bro01}. The problem of computing
accurate confidence intervals for the binomial distribution is not a new one,
and there exist a plenitude of literature on the subject (see \citealt{bro01}
for a review of methods). A robust ``exact'' method guaranteed to produce intervals with
confidence of \textit{at least} $\alpha$ was proposed by \citet{clo34}. If $K \in Bin(N,p)$,
the probability that an outcome is $k$ is
$P(k~\mathrm{of}~N) = {N\choose k} p^k(1-p)^{N-k}$, and the probability that $k < n \le N$ is
$P(k < n~\mathrm{of}~N) = \sum_{k=0}^{n-1} P(k~\mathrm{of}~N)$. For any given significance
$\alpha$ and specific outcome $k$, the Clopper-Pearson method consists of finding the interval
$(p_{\mathrm{min}},p_{\mathrm{max}})$ such that if $p \ge p_{\mathrm{min}}$, then
$P(j < k~\mathrm{of}~N) \le (1-\alpha)/2$, and if $p \le p_{\mathrm{max}}$, then
$P(j > k~\mathrm{of}~N) \le (1-\alpha)/2$. By solving for the equalities, we get
\begin{eqnarray}
\sum_{j=0}^{k} {N\choose j} p_{\mathrm{min}}^j(1-p_{\mathrm{min}})^{N-j} &=& \frac{1-\alpha}{2} \label{e:pmin}\\
\sum_{j=0}^{k-1}{N\choose j} p_{\mathrm{max}}^j(1-p_{\mathrm{max}})^{N-j} &=& \frac{1 + \alpha}{2}, \label{e:pmax}
\end{eqnarray}
where we have used that $P(j > k~\mathrm{of}~N) = 1 - P(j < k+1~\mathrm{of}~N)$. The equations
\ref{e:pmin} \& \ref{e:pmax} are normally best solved numerically.\footnote{An applet
to compute binomial confidence intervals is available at \url{http://statpages.org/confint.html}}
In the degenerate case where
$k=0$ or $k=N$, the confidence interval becomes one-sided, and the equations
\ref{e:pmin} \& \ref{e:pmax} are easily solved analytically
(e.g., equation \ref{e:upper} in \S\,\ref{s:limits}).
\subsection{Comparing binomial distributions}
Let $k_A$ out of $N_A$ systems in association $A$ be multiple, and $k_B$ out of $N_B$
systems in association $B$. The question that naturally arises is, is the multiplicity
probability $p_A$ of system $A$ similar to $p_B$ of system $B$? As in the case
of binomial confidence intervals, there are several tests available in the literature
(see \citealt{sto90} for a review). A conservative ``exact'' hypothesis test is
based on \citet{fis35}, where the hypothesis that $p_A = p_B$ is tested: Let
$h(k_A,k_B,N_A,N_B) = {N_A\choose k_A} {N_B\choose k_B} / {N_A+N_B\choose k_A+k_B}$
and $I[\mathit{expression}]$ be the indicator function that is 1 if $\mathit{expression}$
is true, and 0 otherwise. Then the test function is
\begin{equation}
T = \sum_{x=\max(0,k_A+k_B-n_B)}^{\min(n_A,k_A+k_B)} h(x,k_A+k_B-x,n_A,n_B) \times I\left[h(x,k_A+k_B-x,n_A,n_B) \le
h(k_A,k_B,n_A,n_B)\right],
\end{equation}
and the hypothesis is rejected if $T \le \alpha$, where $\alpha$ is the significance of the test. As an
example, if $k_A = 0$, $N_A = 17$, $k_B = 11$, and $N_B = 19$, then $T = 1.46\times10^{-4}$, which is
the quoted likelihood that the wide binary probability is equal in $\eta$\,Cha and TWA (\S\,\ref{s:deficiency}).
\end{appendix}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,686
|
In cryptography and computer security, self-signed certificates are public key certificates that are not issued by a certificate authority (CA). These self-signed certificates are easy to make and do not cost money. However, they do not provide any trust value.
For instance, if a website owner uses a self-signed certificate to provide HTTPS services, people who visit that website cannot be certain that they are connected to their intended destination. For all they know, a malicious third-party could be redirecting the connection using another self-signed certificate bearing the same holder name. The connection is still encrypted, but does not necessarily lead to its intended target. In comparison, a certificate signed by a trusted CA prevents this attack because the user's web browser separately validates the certificate against the issuing CA. The attacker's certificate fails this validation.
Self-signed certificates, however, have their own limited uses. They have full trust value when the issuer and the sole user are the same entity. For example, the Encrypting File System on Microsoft Windows issues a self-signed certificate on behalf of the encrypting user and uses it to transparently decrypt data on the fly. Another example is the root certificate, which is a form of self-signed certificate.
Benefits
Self-signed certificates can be created for free, using a wide variety of tools including OpenSSL, Java's keytool, Adobe Reader, wolfSSL and Apple's Keychain. They are easy to customize; e.g, they can have larger key sizes or hold additional metadata. Their use doesn't involve the problems of trusting third parties that may improperly sign certificates. Self-signed certificate transactions usually present a far smaller attack surface by eliminating both the complex certificate chain validation, and CA revocation checks like CRL and OCSP.
Trust issues
In a CA-based PKI system, parties engaged in secure communication must trust a CA, i.e. place the CA certificates in a whitelist of trusted certificates. Developers of web browsers may use procedures specified by the CA/Browser Forum to whitelist well-known, public certificate authorities. Individual groups and companies may whitelist additional, private CA certificates. The trust issues of an entity accepting a new self-signed certificate are similar to the issues of an entity trusting the addition of a new CA certificate. The parties in a self-signed PKI must establish trust with each other (using procedures outside the PKI), and confirm the accurate transfer of public keys e.g. compare the certificate's cryptographic hash out of band.
There are many subtle differences between CA signed and self-signed certificates, especially in the amount of trust that can be placed in the security assertions of the certificate. Some CAs can verify the identity of the person to whom they issue a certificate; for example the US military issues their Common Access Cards in person, with multiple forms of other ID. The CA can attest identity values like these by including them in the signed certificate. The entity that validates the certificate can trust the information in that certificate, to the same extent that they trust the CA that signed it (and by implication, the security procedures the CA used to verify the attested information).
With a self-signed certificate by contrast, trust of the values in the certificate are more complicated because the entity possesses the signing key, and can always generate a new certificate with different values. For example, the validity dates of a self-signed certificate might not be trusted because the entity could always create and sign a new certificate that contained a valid date range.
The values in a self-signed certificate can only be trusted when the values were verified out-of-band during the acceptance of the certificate, and there is a method to verify the self-signed certificate has not changed after it was trusted. For example, the procedure of trusting a self-signed certificate includes a manual verification of validity dates, and a hash of the certificate is incorporated into the white list. When the certificate is presented for an entity to validate, they first verify the hash of the certificate matches the reference hash in the white-list, and if they match (indicating the self-signed certificate is the same as the one that was formally trusted) then the certificate's validity dates can be trusted. Special treatment of X.509 certificate fields for self-signed certificate can be found in RFC 3280.
Revocation of self-signed certificates differs from CA-signed certificates. By nature, no entity (CA or others) can revoke a self-signed certificate. But one could invalidate a self-signed CA by removing it from the trust whitelist.
Uses
Self-signed certificates have limited uses, e.g. in the cases where the issuer and the sole user are the same entity. For example, the Encrypting File System on Microsoft Windows issues a self-signed certificate on behalf of a user account to transparently encrypt and decrypt files on the fly. Another example is root certificate, which is a form of self-signed certificate.
See also
X.509, the standard describing the most widely used format for storing certificates
Let's Encrypt, a certificate authority which provides free domain-validated certificates
References
Public key infrastructure
Key management
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,619
|
https://www.ourmidland.com/news/article/200-butterflies-to-be-released-at-Dow-Diamond-6969352.php
200 butterflies to be released at Dow Diamond honoring cancer survivorship
Published 7:31 am EDT, Monday, June 11, 2012
Cancer survivors, caregivers and their family members will be honored during a special Cancer Survivors Day event during the Great Lakes Loons game on Wednesday at Dow Diamond in Midland.
Sponsored by MidMichigan Medical Center-Midland, the celebration will take place in conjunction with the 7:05 p.m. Loons home game against the Dayton Dragons and will feature a pre-game ceremony with the Loons first ever butterfly release at Dow Diamond.
Oncology Services Director Joan Herbert, Pharm.D., asks community members to celebrate cancer survivorship during the game by wearing purple to the game and observing the butterfly release.
"The butterfly release will create a lasting memory for all survivors, family members and friends as they watch hundreds of butterflies go aloft in the Dow Diamond for the first time," Herbert said. "We at MidMichigan Health understand the challenges of cancer diagnosis and treatment, and we are hosting this event as a way of honoring everyone who has faced a cancer journey."
Along with the butterfly release, the pre-game ceremony will include an awards presentation by the American Cancer Society, Great Lakes Division, Inc., to MidMichigan Health for the Five Star Investor and Community Investor awards, the first pitch by Amy Livsey-Sommer, STAR certified provider and manager of Rehabilitation Services at MidMichigan Medical Center-Midland, and a moment of silence for those who have lost their battle with cancer.
During the game, MidMichigan Health, Cancer Services and the American Cancer Society will have exhibits on the Dow Diamond concourse with information about cancer topics. Cancer survivors in attendance should stop by the Cancer Services table on the concourse for a special gift.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,204
|
Q: Firebase - Angularfire2 subscribe wait for response to return value I have a problem with the asynchronous operations of Angularfire2. I want to create a new resource in my Firebase database but first I want to check if exists a resource with the same name and return a message to the front-end.
The problem is that I can't return the message into the subscribe method. VS throws this error:
Severity Code Description Project File Line Suppression State
Error TS2355 (TS) A function whose declared type is neither 'void' nor 'any' must return a value.
This is my function code:
createInstance(instanceName: string): string {
this.databaseService.getList('/Events/' + instanceName).subscribe(
result => {
var message;
if (result.length === 0)
{
this.databaseService.update('/Events/' + instanceName + '/Configuration', myObject);
message = "Instance created";
}
else
{
message = "Instance already exists";
}
return message;
});
}
A: The function you are running is asynchronous, hence you subscribe to the response in order to get informed when the operation has completed.
Your function however, runs synchronously, so it gets executed and returns before the database fetches the data, that happens later.
So the error you're getting is because your function is not actually returning anything, but it's declared as returning a string, which you only get later in time.
One solution is to declare you function as an Observable, like the database service you're using, and consume it asynchronously.
For example:
// extra import you'll need
import { Observable } from 'rxjs';
createInstance(instanceName: string): Observable<string> {
return Observable.create(observer => {
this.databaseService.getList('/Events/' + instanceName).subscribe(result => {
if (result.length === 0) {
this.databaseService.update('/Events/' + instanceName + '/Configuration', myObject);
observer.next('Instance created');
} else {
observer.next('Instance already exists');
}
observer.complete();
});
});
}
And you consume it like this:
createInstance('test').subscribe(message => {
// here you go
});
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,434
|
import numpy as np
import pandas as pd
from collections import deque
from pytz import timezone
window_days = 28 # window length in minutes
window_minutes = window_days*390 # window length in minutes; each trading day has 390 minutes
def initialize(context):
context.max_notional = 100000
context.min_notional = -100000
context.stocks = [sid(14516), sid(14517)]
context.evec = [0.943, -0.822]
context.unit_shares = 20
context.tickers = [int(str(e).split(' ')[0].strip("Security(")) for e in context.stocks]
context.prices = pd.DataFrame({ k : pd.Series() for k in context.tickers } )
context.previous_datetime = None
context.new_day = None
set_commission(commission.PerShare(cost=0.00))
def handle_data(context, data):
# skip tic if any orders are open or any stocks did not trade
for stock in context.stocks:
if bool(get_open_orders(stock)) or data[stock].datetime < get_datetime():
return
current_datetime = get_datetime().astimezone(timezone('US/Eastern'))
# detect new trading day
if context.previous_datetime is None or current_datetime.day != context.previous_datetime.day:
context.new_day = True
context.previous_datetime = current_datetime
#log.info("len price: {lp}, window: {window}".format(lp = len(context.prices), window = window_days))
if len(context.prices)<window_days and context.new_day:
context.previous_datetime = get_datetime().astimezone(timezone('US/Eastern'))
if intradingwindow_check(context):
newRow = pd.DataFrame({k:float(data[s].price) for k,s in zip(context.tickers, context.stocks) },index=[0])
context.prices = context.prices.append(newRow, ignore_index = True)
context.new_day = False
else:
if intradingwindow_check(context) and context.new_day:
#context.new_day = False
comb_price_past_window = np.zeros(len(context.prices))
for ii,k in enumerate(context.tickers):
comb_price_past_window += context.evec[ii]*context.prices[k]
meanPrice = np.mean(comb_price_past_window); stdPrice = np.std(comb_price_past_window)
comb_price = sum([e*data[s].price for e,s in zip(context.evec, context.stocks)])
h = (comb_price - meanPrice)/stdPrice
current_amount = []; cash_spent = [];
for ii, stock in enumerate(context.stocks):
current_position = context.portfolio.positions[stock].amount
new_position = context.unit_shares * (-h) * context.evec[ii]
current_amount.append(new_position)
cash_spent.append((new_position - current_position)*data[stock].price)
order(stock, new_position - current_position)
context.new_day = False
#log.info("ordered!")
notionals = []
for ii,stock in enumerate(context.stocks):
#notionals.append((context.portfolio.positions[stock].amount*data[stock].price)/context.portfolio.starting_cash)
notionals.append((context.portfolio.positions[stock].amount*data[stock].price)/context.portfolio.starting_cash)
log.info("h = {h}, comb_price = {comb_price}, notionals = {notionals}, total = {tot}, price0 = {p0}, price1 = {p1}, cash = {cash}, amount = {amount}, new_cash = {nc}".\
format(h = h, comb_price = comb_price, notionals = notionals, \
tot = context.portfolio.positions_value + context.portfolio.cash, p0 = data[context.stocks[0]].price, \
p1 = data[context.stocks[1]].price, cash = context.portfolio.cash, amount = current_amount, \
nc = context.portfolio.cash - sum(cash_spent)))
newRow = pd.DataFrame({k:float(data[s].price) for k,s in zip(context.tickers, context.stocks) },index=[0])
context.prices = context.prices.append(newRow, ignore_index = True)
context.prices = context.prices[1:len(context.prices)]
record(h = h, mPri = meanPrice)
record(comb_price = comb_price)
record(not0 = notionals[0], not1 = notionals[1])
#if not context.new_day:
# log.info("time = {time}, cash = {cash}".format(cash = context.portfolio.cash, time = current_datetime))
#record(price0 = data[context.stocks[0]].price*abs(context.evec[0]), price1 = data[context.stocks[1]].price*abs(context.evec[1]))
#record(price0 = data[context.stocks[0]].price, price1 = data[context.stocks[1]].price)
#record(port = context.portfolio.positions_value, cash = context.portfolio.cash)
def intradingwindow_check(context):
# Converts all time-zones into US EST to avoid confusion
loc_dt = get_datetime().astimezone(timezone('US/Eastern'))
# if loc_dt.hour > 10 and loc_dt.hour < 15:
if loc_dt.hour == 15 and loc_dt.minute > 0:
return True
else:
return False
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,147
|
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Speaking at Eleventy Meetup Next Week (03/24/2022)
Hosting an Alexa Skill on Pipedream (03/17/2022)
Building Table Sorting and Pagination in JavaScript (03/14/2022)
Including RSS Content in your Eleventy Site (03/08/2022)
Working with Algolia's Crawler (03/04/2022)
Testing out the new Pipedream to Get Trance Releases (02/22/2022)
Another Early Look - Netlify Graph (02/17/2022)
Adding QR Codes to Your Jamstack Site (02/11/2022)
Turning a Microsoft ToDo List Into a Public JSON Feed with Pipedream (02/09/2022)
Using the Microsoft Computer Vision API with Python (02/08/2022)
An Early Look at Netlify Scheduled Functions (02/04/2022)
A Google Static Maps Eleventy Plugin (02/02/2022)
Using a Google Photos Album in your Eleventy Site with Pipedream (01/28/2022)
Accessing Google Photos with Pipedream (01/26/2022)
Searching the New York Times with Python (01/22/2022)
A Guide to Building a Blog in Eleventy (01/19/2022)
Review: Make 7 Apps With Vue 2 (01/16/2022)
Building my First Idle Clicker Game in Vue.js (01/13/2022)
Working with Front Matter in Python (01/06/2022)
Building a File Search Script in Python (01/03/2022)
year++ (01/02/2022)
Python for My Last Post of the Year... (12/24/2021)
Using Google Analytics 4 for Blog Stats (12/17/2021)
Running Netlify Dev and Eleventy Two or More Times At Once (12/10/2021)
Fun (Scary?) Webcam Demo (12/08/2021)
Eleventy 1.0 - The Serverless Plugin (12/04/2021)
Review: Captain Code: Unleash Your Coding Superpower with Python (11/22/2021)
Congratulating Yourself with Pipedream and Microsoft To Do (11/13/2021)
Eleventy 1.0 - Global Data via Plugins Example (11/07/2021)
Eleventy 1.0 - New Option for Global Data (11/02/2021)
Welcome to RaymondCamden.com 2022 (10/21/2021)
Eleventy 1.0 - Dynamic Ignores (10/15/2021)
Adding PDF Output Support to Eleventy (10/13/2021)
Eleventy Hack/Tip/Possibly Bad Idea - Dynamic Theme Testing (10/11/2021)
Eleventy 1.0 - Upgrading Experience (10/08/2021)
Eleventy 1.0 - New Output Options (10/07/2021)
Eleventy 1.0 Beta! (10/06/2021)
Building the PlacePlaceHolder Service with Pipedream (09/28/2021)
Creating a (Manual) Related Posts Feature in Eleventy (09/24/2021)
Supporting Multiple Authors in an Eleventy Blog - Follow-Up (09/19/2021)
Building an App with the StackOverflow API (09/16/2021)
Making Monsters Fight for Fun and Profit (minus the profit) (09/06/2021)
Using PDFs with the Jamstack - Building a Document Viewer (08/30/2021)
Using Liquid Blocks in Eleventy Layouts (08/19/2021)
More Work on Algolia and My Blog (08/11/2021)
Uploading Multiple Files with Fetch (08/08/2021)
Check out Begin (08/06/2021)
An Adobe PDF Embed Plugin for Eleventy (08/02/2021)
Page Level URL Fetching with Eleventy (07/30/2021)
Integrating Eleventy with GitHub Flat Data (07/14/2021)
Creating an Additive Capture Shortcode in Eleventy (07/12/2021)
Graphing Movie Rating Distribution For No Good Reason (07/09/2021)
Using Pipedream to Proxy Other APIs (06/30/2021)
Dynamic Short URLs with Eleventy (06/22/2021)
Using PDFs with the Jamstack - Adding Search with Text Extraction (06/18/2021)
Quick Tip - Using Pipedream to Monitor my Algolia Index (06/16/2021)
Using Lunr with Eleventy via Netlify Serverless Functions - Part Two (06/06/2021)
Using Lunr with Eleventy via Netlify Serverless Functions (06/02/2021)
Recreating Breaking Bad Credits with JavaScript (and a bit of CSS) (05/31/2021)
Quick Netlify Tip for Redirects (05/24/2021)
Building a Choose Your Own Adventure site with Eleventy (05/16/2021)
Updating (and Supporting) URL Parameters with Vue.js (05/08/2021)
Adding an Email Subscription to Your Jamstack Site (05/01/2021)
Crickets and Other Things (04/28/2021)
Building a Database Driven Eleventy Site (04/15/2021)
Proof of Concept - Dynamically Filtering a Large Select (04/12/2021)
Load a PDF Embed when Visible (04/09/2021)
Building a Simple Image Gallery with Eleventy (04/07/2021)
Quick Tips for Eleventy and Vercel (03/27/2021)
How I Write Content Here... (03/24/2021)
Using PDFs with the Jamstack - Now with Thumbnails (03/16/2021)
Hello (Again), Adobe! (03/15/2021)
Adding Filtering to my Vue.js Table Sorting and Pagination Demo (03/11/2021)
Saying Goodbye to HERE (03/05/2021)
Using the Adobe PDF Tools API to Generate Thumbnails (03/02/2021)
Using PDFs with the Jamstack (02/25/2021)
Keeping Count of User Visits (02/23/2021)
Integrating Navigation Search with Lunr and Eleventy (02/22/2021)
Using the PDF Embed API with Vue.js (02/17/2021)
Exporting Disqus Comments and Adding Them to Eleventy (02/11/2021)
Quick Hack for Reveal.js Presentations (01/29/2021)
Highly Analytics - A Review (01/28/2021)
Using Pre-Built Lunr Indexes with Eleventy (01/22/2021)
Accessing Eleventy Data on the Client Side (01/18/2021)
A Vue Component for Handling Loading State (01/15/2021)
Remembering (and Restoring) a Route with Vue Router (01/12/2021)
Identifying Pictures via SMS with Pipedream, Twilio, and Microsoft Cognitive Services (01/07/2021)
Building Generic Workflows in Pipedream (01/03/2021)
2020 Can Kiss My... (12/26/2020)
Vue Quick Shot - Downloading Data as a File (12/15/2020)
Adding Google Calendar to Your Jamstack - with Pipedream (12/08/2020)
Building a Web App Powered by Google Forms and Sheets (11/20/2020)
Vue Quick Shot - Preventing Multiple Form Submissions (11/17/2020)
The Jamstack Book - Early Access Release (11/12/2020)
Adding a Warning for Old Posts to Your Jamstack Site (11/09/2020)
Adding Your Netlify Build Status to Your Site (11/04/2020)
Selecting Random Posts in Eleventy (10/26/2020)
Review: Learning Progressive Web Apps by John Wargo (10/21/2020)
Vue Quick Shot - Warn Before Leaving a Form (10/15/2020)
Another Netlify Analytics Hack - Stats Per URL (10/08/2020)
Tracking Posts by Week in Eleventy (09/30/2020)
Vue Quick Shot - Uploading a File (09/20/2020)
Hooking Up FaunaDB to Eleventy (09/15/2020)
Vue Quick Shot - Form Field Character Counters (09/14/2020)
Building a Traffic-Based Workflow in Pipedream (09/06/2020)
Vue Quick Shot - Fullscreen API (09/04/2020)
Vue Quick Shot - Using Page Visibility (09/03/2020)
An Experiment with Vue Components (08/28/2020)
Supporting Multiple Authors in an Eleventy Blog (08/24/2020)
Designing Random Encounters for my Vue RPG (08/19/2020)
Migrating from Node and Express to the Jamstack - Part 3 (08/16/2020)
Migrating from Filters in Vue 3 (08/13/2020)
Hiding Future Content with Eleventy (08/07/2020)
Sharing Your Movies with Pipedream and Letterboxd (08/04/2020)
Building a Twitter Scheduling System with Pipedream and Google Sheets (07/28/2020)
Making Monsters with JavaScript (07/19/2020)
Testing Vue.js Application Files That Aren't Components (07/17/2020)
Review: The Bard's Tale IV (07/12/2020)
Building a Vue Application with Serverless on Netlify (07/07/2020)
How to Enable your Jamstack Site to have a "Rain Day" (07/06/2020)
Adding Algolia Search to Eleventy and Netlify - Part Two (07/01/2020)
Adding Algolia Search to Eleventy and Netlify (06/24/2020)
Determining Food Popularity By Location (06/23/2020)
Testing Netlify's Proxy Support for API Hiding (06/10/2020)
Building a Dual Selects Control in Vue.js (06/08/2020)
Enhancing Your Netlify Build Notifications (05/29/2020)
Integrating Google Analytics with Eleventy (05/21/2020)
Updating my Reddit Workflow with Pipedream (05/19/2020)
Integrating Netlify Analytics and Eleventy (05/18/2020)
Let's Make Everyone a Queen! (05/15/2020)
Want to Learn Vue.js? (05/14/2020)
Notes on Upgrades to WSL2 (And Why You Should) (05/08/2020)
Looking at Pipedream's Event Sources (05/07/2020)
Modifying Prism's Copy Plugin (05/05/2020)
Playing with QuickChart and Vue.js (05/03/2020)
My Tech Stack (So Far) in 2020 (04/29/2020)
Building a Google Sheets Twitter Bot with Pipedream (04/27/2020)
Building a Reddit Workflow with Pipedream (04/20/2020)
Processing Email Sentiment with Pipedream (04/15/2020)
Creating Both HTML and API with Pipedream (04/14/2020)
What are Red Flags to Me as a Developer? (04/13/2020)
How Pipedream Got Me Excited About SQL Again (04/11/2020)
MadLibs with Vue.js (04/08/2020)
Using State in Pipedream Workflows (04/04/2020)
Quick Tip on Using Vue with Eleventy (04/03/2020)
Building a Twitter Bot in Pipedream (04/02/2020)
A Look at Pipedream (03/28/2020)
Implementing Google Custom Search Engine's JSON API in the JAMStack (03/22/2020)
Tips for Giving Remote Presentations (03/10/2020)
Vue Quick Shot - Links, Links, and More Links (03/06/2020)
Vue Quick Shot - Image Upload Previews (03/05/2020)
Vue Quick Shot - Copy to the Clipboard (03/04/2020)
Vue Quick Shot - Using a Loading Message (03/04/2020)
A Voicemail Assistant with Vue and RingCentral (03/02/2020)
Vue Quick Shot - Disabling a Submit Button While Waiting for an Ajax Call (03/02/2020)
RaymondCamden.com now powered by Eleventy! (02/27/2020)
Working with RingCentral Webhooks (02/26/2020)
Sending SMS Messages for Form Data with RingCentral and Netlify (02/25/2020)
Adding a SMS Alert for Netlify Builds with RingCentral (02/22/2020)
Adding Another Template Language to Eleventy (02/19/2020)
Ionicons in Vue.js (02/17/2020)
Adding Text Linting to Eleventy (02/10/2020)
Checking (and Upgrading) Template Engines in Eleventy (02/07/2020)
Adding a Last Edited Field to Eleventy (02/06/2020)
Building Table Sorting and Pagination in Vue.js - with Async Data (02/01/2020)
Vue and Form Fields (01/27/2020)
The Last Damn Vue ToDo App (01/19/2020)
Some Notes on Building Blogs with Gridsome (01/12/2020)
Yet Another Damn ToDo App in Vue.js (01/08/2020)
Another Damn ToDo App in Vue.js (01/03/2020)
Goodbye 2019, Hello 2020 (12/31/2019)
Another Vue Game Demo - Hangman (12/26/2019)
A Non-Spoiler Review of The Rise of Skywalker (12/20/2019)
Building Sudoku in Vue.js - Part 2 (12/19/2019)
Using Bearer for Easier OAuth and API Calls (12/11/2019)
Sunday Quick Hack - Eliza in Vue.js (12/08/2019)
Sanitizing HTML in Vue.js (11/26/2019)
Adding Google Calendar to your JAMStack (11/18/2019)
Serverless JAMStack AndCats Demo (11/14/2019)
Building a Custom Sound Board with Vue and IndexedDB (11/12/2019)
Adding Search to your Eleventy Static Site with Lunr (10/20/2019)
Using IndexedDB with Vue.js (10/16/2019)
Why I'm Digging Eleventy (10/12/2019)
Building a Netlify Stats Viewer in Vue.js (10/05/2019)
Using OAuth and Vue.js to Build an Untappd Stats Page (09/28/2019)
Sending a Notification to Alexa when Netlify Builds Your Site (09/20/2019)
An iTunes Audio Enabled Search Built in Vue.js (09/18/2019)
A National Parks Service API Demo with Vue.js (09/09/2019)
A Look at Zeit's Zero Config and Serverless Platform (09/06/2019)
Using Geolocation with Vue.js (09/01/2019)
Starting My New Role at HERE! (08/24/2019)
Sailing the Seas with Vue - My Take on Taipan (08/19/2019)
My Thoughts on Documentation (08/14/2019)
Working with the Keyboard in your Vue App (08/12/2019)
Drag and Drop File Upload in Vue.js (08/08/2019)
Book Review: Progressive Web Apps (08/06/2019)
Creating a One Click Visual Studio Code Snippet to Wrap Content (08/02/2019)
Playing with Vue and Vuex - Lemonade Stand (08/01/2019)
Multiple Ways of API Integration in your JAMStack (07/25/2019)
Quick Netlify Dev Tip for Complex Static Sites (07/15/2019)
Netlify Analytics - An Initial Look (07/12/2019)
Replacing a Dynamic Regex Match with the Same Number of Spaces (07/05/2019)
Random Pictures of Beauty with Azure Functions and the NPS (07/01/2019)
My Podcast on Views with Vue (06/28/2019)
Vue Components FTW - vue-country-flag (06/21/2019)
Two Tips for NativeScript and Vue Development on the Playground (06/19/2019)
Reading Image Sizes and Dimensions with Vue.js (06/13/2019)
Using NativeScript and Vue.js to Turn Your Friends into Cats (06/11/2019)
Using the MailChimp API with Netlify Serverless Functions (05/29/2019)
FusionReactor and Your ColdFusion Queries (05/25/2019)
Reading Client-Side Files for Validation with Vue.js (05/21/2019)
Using HTML Form Validation without a Form (Kinda) (05/15/2019)
Building a Plex Server Duration Search with Vue.js (05/14/2019)
Handling Errors in Vue.js (05/01/2019)
Working with Audio in NativeScript - Part Two (04/30/2019)
Working with Audio in NativeScript - Part One (04/25/2019)
Vue Components FTW - VGauge (and a love letter to CodeSandbox) (04/19/2019)
Blocking Web Sites from Prompting for Notifications (04/17/2019)
Getting Location in NativeScript - Part 2 (04/14/2019)
Getting Location in NativeScript (04/10/2019)
Adding Visual Feedback to an Alexa Skill (04/01/2019)
Finding (and Fixing) Your Slow ColdFusion Pages with FusionReactor (03/25/2019)
Getting Started with FusionReactor (for ColdFusion Devs) (03/19/2019)
An Example of Nuxt.js with a Custom Generator (03/12/2019)
Assets and Stuff from My Vue.js Presentations (03/09/2019)
What is $nextTick in Vue and When You Need It (02/22/2019)
Vue Components FTW - vue-pure-lightbox (02/20/2019)
Book Review: Learning GraphQL (02/15/2019)
Vue Components FTW - Toasted (02/06/2019)
Using Netlify's Build Process for Somewhat Static Data (01/22/2019)
Adding Emotional Tone Analysis to Your Contact Form (01/18/2019)
Customized Form Handling on Netlify with Serverless Functions (01/15/2019)
Adding Serverless Functions to Your Netlify Static Site (01/08/2019)
Creating a Live Time Duration Component in Vue.js (01/07/2019)
Adding Automated Text Linting to My Blog (12/28/2018)
Using Alexa to Mess with Your Kids, Because Why Not? (12/13/2018)
Adding Ice Bear to Alexa, Because Why Not? (11/28/2018)
Review of NativeScripting's Vue Intro Course (11/26/2018)
Working with the Camera in a NativeScript Vue App (11/15/2018)
A Review of My Arcade1Up Machine (11/09/2018)
Using NativeScript DataForm with Vue.js - Some Tips (11/07/2018)
Using Azure Functions and the Marvel API to Visualize Character History (11/04/2018)
Working with Dynamic Components in Vue.js (10/31/2018)
I Built a NativeScript/Vue.js App and You Won't Believe What Happened Next... (10/25/2018)
Creating a Slide Show for Pinterest Boards in Vue.js (10/09/2018)
Storing (and Retrieving) Photos in IndexedDB (10/05/2018)
A Quick Look at Stitch (09/19/2018)
My Next Online Presentation - Serverless with Webtask (09/12/2018)
My First Azure Function App - Twitter Image Displayer (09/09/2018)
An Update (08/29/2018)
HTTP Stuff with Azure Functions (and more) (08/20/2018)
Node.js for the Non-Node.js Developer (08/10/2018)
Adding Your YouTube Videos to Your Static Site on Netlify (08/08/2018)
Testing Local Development with Azure Functions (08/03/2018)
Adding Your YouTube Videos to Your Static Site with Vue.js (08/01/2018)
Building a Stats Page for Jekyll Blogs (07/21/2018)
Quick Note on Azure Functions Returns and Results (07/16/2018)
My (Rough) Start with Azure Functions (07/06/2018)
Summer Plans - Looking at Azure Functions (07/02/2018)
My First Stab at a Grammar Extension for VS Code (06/18/2018)
Transforming JSON Data into an API with Serverless (06/15/2018)
Getting Notifications for New GitHub Project Releases (06/13/2018)
My Vue.js Course is Coming Soon! (06/11/2018)
Keeping Up with Browser Updates (06/07/2018)
RIP ColdFusion Bloggers (05/22/2018)
Text Sentiment Analysis IoT Demo (05/21/2018)
Deploying a VuePress Site to Netlify (05/16/2018)
Adding a Recent Content Component to VuePress (05/09/2018)
Next Event - Modern Development with the JAMStack (04/30/2018)
Getting Up to Speed with Vue.js (04/20/2018)
An Example of the Async Clipboard API with Vue.js (04/19/2018)
TIL - Pushing Node Apps to Azure with Visual Studio Code (04/18/2018)
Missed VueConfUS? Watch (Parts) Online! (04/16/2018)
Datalists with Vue.js (04/12/2018)
Serverless IoT for Enterprise Light Bulb Demos (04/11/2018)
Adding reCaptcha with a Serverless Form Processor (04/06/2018)
TIL - Vue.js and Non-Prop Attributes (04/03/2018)
Building Three Common Form Interfaces in Vue.js (04/02/2018)
Reminder on File Inputs, JavaScript, and Read Access (03/29/2018)
Links for Learning Webtask (03/28/2018)
Building a Customizable Weather App in Vue - 2 (03/27/2018)
Remotely Interesting (03/23/2018)
Slides and Assets from JazzCon PWA Talk (03/22/2018)
Building a Customizable Weather App in Vue.js (03/19/2018)
Adding Referrer Protection to Webtasks (03/19/2018)
Building a Text-Based Adventure in Vue.js (3) (03/13/2018)
Building a Serverless Form Handler with Auth0 Webtasks - Express Style (03/07/2018)
Learn JavaScript Fundamentals at KnowJS (03/06/2018)
Building a Serverless Form Handler with Auth0 Webtasks (03/02/2018)
An Example of Ajax Searching with Vue.js (03/01/2018)
Building an HTML5 Comic Book Reader - in 2018 (02/28/2018)
An Introduction to Webtask (02/27/2018)
Getting Happy with Vue.js (02/26/2018)
Hello Auth0 Extend! (02/26/2018)
Slides and Assets from My OpenWhisk Talk (02/24/2018)
Slides and Assets from My Vue.js Talk (02/23/2018)
New PWA Series (02/21/2018)
Happy 15 (02/15/2018)
Building a Text-Based Adventure in Vue.js (02/14/2018)
Leaving Big Blue (02/12/2018)
Installing Jekyll on Windows (02/12/2018)
Building Table Sorting and Pagination in Vue.js (02/08/2018)
Pointing a Raygun at Your Site (02/03/2018)
Better Support for Scheduled Actions with OpenWhisk and IBM Cloud Functions (02/01/2018)
A Multi-Step Form in Vue.js (01/29/2018)
Building a Progressive Color Thief (01/25/2018)
A Few Tips on Debugging OpenWhisk Functions with VS Code (01/23/2018)
Building a Quiz with Vue.js (01/22/2018)
An Example of Vue.js DevTools (01/18/2018)
Using DevTools to Scrape Web Content (01/17/2018)
Generating Random Cure Song Titles with Markov Chain (01/16/2018)
Nuxt and Server-Side/Static Vue.js Sites (01/15/2018)
My New Lynda Course - Building APIs with LoopBack (01/10/2018)
Building an OpenWhisk Activation Poll with Node, Vue.js and Vuetify (01/09/2018)
Another Example of Vue.js and Vuex - an API Wrapper (01/05/2018)
Vue.js Version of My Random Comic Book Viewer (12/29/2017)
My 2017 and My Plans for 2018 (12/26/2017)
Favorite Media of 2017 (12/24/2017)
Using JSON Web Tokens with Serverless OpenWhisk (12/22/2017)
An Example of Vuex and State Management for Vue.js (12/20/2017)
Building an Image Placeholder Component for Vue.js (12/18/2017)
Review: The Last Jedi (12/15/2017)
New IBM Composer Feature - Additional Action Logging (12/12/2017)
Adding Referrer Protection to OpenWhisk Actions (12/11/2017)
An Example of Form Validation with Vue.js (12/07/2017)
Quick Example of Apache Cordova and Vue.js (12/06/2017)
Building Related Selects with Vue.js (12/05/2017)
Advent of Code 2017 (12/04/2017)
Last Update, Honest, to My Vue.js INeedIt Demo (11/28/2017)
Yet Another Update to my INeedIt Vue.js App (11/24/2017)
Thank You! (11/23/2017)
Serverless Try/Catch/Finally with IBM Composer (11/22/2017)
Update to my Vue.js INeedIt Demo (11/21/2017)
Two Quick OpenWhisk/IBM Cloud Functions Updates (11/20/2017)
Another Vue.js Demo - INeedIt (11/16/2017)
Working with Routes in Vue.js (11/12/2017)
A Great Tutorial for Webpack (11/07/2017)
Read My (Free) Book on Apache OpenWhisk (11/05/2017)
My NCDevCon Progressive Web App Talk (10/31/2017)
OOO (10/27/2017)
Calling Multiple Serverless Actions and Retaining Values with IBM Composer (10/25/2017)
IBM Watson OpenWhisk Actions (10/24/2017)
Migrating a Static Site from Harp to Jekyll (10/23/2017)
Upgrading Serverless Superman to IBM Composer (10/20/2017)
Copying to Clipboard with Windows Subsystem for Linux (10/19/2017)
Building Your First Serverless Composition with IBM Cloud Functions (10/18/2017)
DevTools Tips for Progressive Web Apps (10/17/2017)
Review: Building Progressive Web Apps (10/16/2017)
Some Progressive Web App Tips (10/13/2017)
Turning My No Man's Sky App Into a PWA (10/12/2017)
Serverless Composition with IBM Cloud Functions (10/09/2017)
Facebook Chatbots with OpenWhisk (10/09/2017)
Rebuilding a Flex Mobile App as an Alexa Skill (10/04/2017)
Reading a Text File on OpenWhisk (10/02/2017)
Calling a PowerShell Script from WSL (09/25/2017)
Quick Note on CFLib (09/21/2017)
Run Visual Studio Code Insiders from WSL (09/20/2017)
Microsoft's Edge Web Summit 2017 (09/17/2017)
Quick Web Dev Tip Everyone Knows (09/13/2017)
Very Cool Update for the OpenWhisk CLI (09/11/2017)
Another Vue Example - Image Recognition Service Tester (09/05/2017)
Update to My Image Recognition Service Tester - Amazon Rekognition Support (09/04/2017)
An Example of Sessions with Amazon Alexa Skills (09/01/2017)
Building a No Man's Sky Utility with Node and Vue.js (08/31/2017)
Quick OpenWhisk Utility - Activation Reporting (08/29/2017)
Dynamically Documenting OpenWhisk Packages (08/25/2017)
Why I Hated (and Now Love) Arrow Functions (08/25/2017)
Serverless iCal Parsing (08/24/2017)
An OpenWhisk Package for Alexa Verification (08/18/2017)
Migrating from a Node App to Serverless (08/14/2017)
Career Advice for a New Web Dev (08/09/2017)
Quick Example of Vue.js (08/07/2017)
Working with the Forwarder Action in OpenWhisk (08/05/2017)
Working with Action Metadata in OpenWhisk (08/04/2017)
Serverless BASIC (08/01/2017)
Geolocation Emulation in Chrome (and others) (07/31/2017)
Online Presentation - Developing in JavaScript in 2017 (07/31/2017)
Some Notes on Windows 10 and Ubuntu (07/28/2017)
Serverless for Vampires (07/27/2017)
Using Postman with OpenWhisk (07/24/2017)
Great Reminder of Persistence in Serverless (07/18/2017)
Creating a Serverless Meetup API Wrapper (07/17/2017)
Handling SMS with OpenWhisk, IBM Watson and Twilio - an Update (07/07/2017)
Google Analytics and RSS Report - Version 2 (07/06/2017)
Important Note for OpenWhisk Developers (07/05/2017)
Designing an OpenWhisk Action for Web Action Support - Take Two (07/03/2017)
Handling SMS with OpenWhisk, IBM Watson, and Twilio (06/29/2017)
An OpenWhisk Monitor/Alert POC (06/27/2017)
Another Form Processor Option - LiveForm (06/23/2017)
Update on My Random Comic Book Character API (06/21/2017)
Enabling API Management for Serverless with OpenWhisk (06/20/2017)
Serverless Demo - Random Comic Book Character via Comic Vine API (06/19/2017)
Monitoring OpenWhisk Activity (06/16/2017)
Testing Multiple Image Recognition Services at Once (06/15/2017)
Using a Generic CORS Enabler in OpenWhisk (06/12/2017)
Uploading Files to an OpenWhisk Action (06/09/2017)
Recording and Assets for OpenWhisk Serverless Presentation (06/08/2017)
Quick OpenWhisk Debugging Example (06/05/2017)
Integrating OpenWhisk with Your Node Application (06/02/2017)
TIL about Datalist and Display Limits (06/01/2017)
Updating NodeJS on Windows - Some Tips (05/31/2017)
Handling Errors in OpenWhisk Sequences with a Combinator (05/26/2017)
OpenWhisk Webinar and Presentations for June (05/23/2017)
Building the Serverless Superman (05/19/2017)
My First Lynda Course - Learning Ionic (05/19/2017)
Creating a JSON Feed for Hugo (05/18/2017)
Using URL Paths in OpenWhisk Web Actions (05/17/2017)
My Own OpenWhisk Stat Tool (05/15/2017)
Some thoughts on HoloLens (and the new Surface Laptop) (05/12/2017)
Enabling CORS for an OpenWhisk Action (05/09/2017)
Launching Today - Serverless Weekly (05/05/2017)
New Book: Mobile App Development with Ionic 2 (05/04/2017)
Building Your Own Serverless Search Engine with OpenWhisk (05/02/2017)
OpenWhisk Sequences as Input/Output Providers (05/01/2017)
Bound Packages, OpenWhisk, and Web Actions (04/28/2017)
An Example of How I Dig Into Your Code (04/27/2017)
Using Device Motion on the Web (04/25/2017)
Updating Your OpenWhisk CLI (04/25/2017)
Integrating HTML Templating with OpenWhisk Web Actions (04/21/2017)
Artificially Delaying Providers with Observable.Delay (04/19/2017)
Enabling CORS for an OpenWhisk Web Action (04/18/2017)
OpenWhisk, Serverless, and Security - a POC (04/17/2017)
PSA for New Web Developers - Don't Use file:// (04/14/2017)
A Tip for Zipped Actions and Packages in OpenWhisk (04/13/2017)
FusionReactor - Still the Best for ColdFusion (04/12/2017)
From Actions to Sequences to Services (04/07/2017)
Extracting One (or more) Pages from a PDF (04/06/2017)
OpenWhisk Sequences and Errors (04/04/2017)
Quick Notes on OpenWhisk Packages and Defaults (04/03/2017)
Another OpenWhisk Alexa Skill - Death Clock (03/31/2017)
Check out PaveAI for Analytics (03/23/2017)
Using IBM Watson Tone Analyzer in OpenWhisk (03/22/2017)
Some Thoughts on Static Sites and Security (03/21/2017)
My OpenWhisk Alexa Skill is Live! (03/20/2017)
Creating Alexa Skills with OpenWhisk - Part Two (03/17/2017)
A Twitter Package for OpenWhisk (03/15/2017)
Quick console script for O'Reilly Authors (03/14/2017)
An Introduction to Creating Alexa Skills with OpenWhisk (03/09/2017)
New Option for Android Testing - Genymotion on Demand (03/09/2017)
A tip for testing Alexa Skills (03/08/2017)
Working with Static Sites - Final Release! (03/07/2017)
Designing an OpenWhisk Action for Web Action Support (03/02/2017)
An Example of a Static Site with a Dynamic Calendar (02/25/2017)
Another OpenWhisk Cron Example - the Blog Nag (02/21/2017)
VS Code Extensions: mssql and vscode-database (02/17/2017)
Building a Form Handler Service in OpenWhisk - Part Two (02/15/2017)
Collecting 911 Data with OpenWhisk Cron Triggers (02/14/2017)
More Thoughts on Leveling Up (02/10/2017)
Serverless and Persistence (02/09/2017)
Using Social Login with Passport and Node (02/08/2017)
VS Code Extensions: Output Colorizer (02/06/2017)
Working with OpenWhisk Triggers (02/02/2017)
The Apache OpenWhisk Slack (02/01/2017)
Using Packages in OpenWhisk (01/31/2017)
Some Guidance for Blogging (01/31/2017)
Further Down the Windows Train... (01/30/2017)
Talking to your Bot on OpenWhisk (01/26/2017)
Building a Form Handler Service in OpenWhisk (01/25/2017)
New Camera Hotness from Chrome (01/24/2017)
LoopBack now has a CLI! (01/23/2017)
Working with IonicDB (01/19/2017)
All My Friends Are Superheroes (01/18/2017)
Creating Zipped Actions in OpenWhisk (01/10/2017)
Quick Tip for Testing OpenWhisk Actions Locally (01/09/2017)
A Survey for CFML Users (Past and Present) (01/08/2017)
An Example of an OpenWhisk Sequence (01/06/2017)
An example of the Ionic 2 Menu Component (01/05/2017)
Getting Started with OpenWhisk (01/03/2017)
Building a Serverless API Proxy with OpenWhisk (01/02/2017)
Advent of Code - Day 15 to 20 (12/30/2016)
Favorite Media in 2016 (12/26/2016)
Going Serverless with OpenWhisk (12/23/2016)
Integrating Intl with Ionic (12/22/2016)
Having trouble emulating iOS with Cordova/Ionic? (12/21/2016)
LoopBack 3.0 Released (12/21/2016)
My Entirely Not-Biased Review of Rogue One (12/18/2016)
Advent of Code - Day 13 and 14 (12/16/2016)
Advent of Code - Day 9 to 12 (12/13/2016)
Working with Ionic Native - Contact Fixer (12/12/2016)
Advent of Code - Day 8 (12/10/2016)
Updates to Client Storage for the Browser (12/08/2016)
Advent of Code - Day 6 and 7 (12/08/2016)
Begin the Advent of Code! (12/01/2016)
A Simple Stats Script for Hugo (12/01/2016)
Scraping a web page in Node with Cheerio (11/30/2016)
Online Pug Testing Tool (11/18/2016)
A Social Example of Ionic Auth (11/17/2016)
November is National Adoption Month (11/14/2016)
Speaking on Static Sites at Ortus Developer Week (11/11/2016)
Some Advice for a Web Developer Learning New Skills (11/09/2016)
Quick LoopBack Tip - Using the Client Folder for your Static Directory (11/08/2016)
An example of the Ionic Auth service with Ionic 2 (11/04/2016)
Building a Simple Form Handler Service in Node (10/31/2016)
Final(ish) Thoughts on the Microsoft Surface (as well as Apple) (10/28/2016)
Article: Building Node-based APIs with the LoopBack Framework (10/26/2016)
Ionic Example: Slides (10/24/2016)
Using HTML Form Validation in Pure JavaScript (10/19/2016)
Quick DevTools Tip - what is still trying to load? (10/17/2016)
The Microsoft Surface Book - Part Three (10/16/2016)
Working with SOAP in a Node App (10/12/2016)
I've switched RaymondCamden.com to Netlify (10/10/2016)
I've fallen in love with The Flash (10/08/2016)
NativeScript 2.3 Launch Webinar (10/06/2016)
TIL - Form fields and invalid values (10/04/2016)
The Microsoft Surface Book - Part Two (10/03/2016)
Some quick NativeScript tips (09/28/2016)
The Microsoft Surface Book - Part One (09/26/2016)
Recording - What they didn't tell you about Cordova (09/26/2016)
Chrome Network Emulation and Change Events (09/15/2016)
Reminder on using Ionic for the Web (09/13/2016)
Fixing "Browser Has Stopped" Errors in the Android Simulator (09/13/2016)
Bringing Dynamic Back (Presentation) (09/12/2016)
Looping Audio in a Cordova App (09/09/2016)
Adding opacity to a background image in reveal.js (09/06/2016)
Review: No Man's Sky (09/04/2016)
Pagination and IndexedDB (09/02/2016)
My NodeSummit LoopBack Presentation (08/31/2016)
Using CommandBox for Lucee (08/30/2016)
Looking for RIAForge? (08/26/2016)
Working with the Disqus API - Deeper Stats (2) (08/25/2016)
Working with Ionic Native - Shake, Rattle, and Roll (Follow Up) (08/22/2016)
Working with the Disqus API - Deeper Stats (08/19/2016)
Working with the Disqus API - Comment Count (08/18/2016)
Working with Ionic Native - Using Secure Storage (08/16/2016)
Victory! (08/15/2016)
Some Tips for Conferences (08/12/2016)
How Many Days Since the Last JavaScript Framework? (08/11/2016)
Quick tip for installing Bash on Windows 10 (08/11/2016)
Need a Test SMTP Server? (08/09/2016)
My Blog Tech Stack (08/05/2016)
Excellent overview of Static Sites (08/04/2016)
Working with Ionic Native - Using the Diagnostics Plugin (08/02/2016)
Checking (and updating) your Ionic Native install (08/01/2016)
My next book - Working with Static Sites (07/21/2016)
"Apache Cordova in Action" 50% off Monday (07/17/2016)
Scraping URLs from a Sitemap File (07/16/2016)
Fighting against a content stealer on Blogger (07/15/2016)
Deciding what client-side storage system to use (07/08/2016)
Working with Ionic Native - Shake, Rattle, and Roll (07/07/2016)
New POC - DailyReddit (07/05/2016)
An Ionic 1 and 2 app side by side (06/30/2016)
No back button in your Ionic header? (06/29/2016)
Linking to PDFs in Cordova apps (06/26/2016)
Some quick tips for Passport (06/23/2016)
Ionic 2 Weather Application (06/17/2016)
Assets and slides from my JS Templating Presentation (06/16/2016)
Very cool browser extension - Wappalyzer (06/13/2016)
An example of Nexmo's Communications API (06/09/2016)
Introduction to API Connect Webinar (06/08/2016)
Capturing camera/picture data without PhoneGap - An Update (06/03/2016)
Adding (Limited) Pagination to Hugo (05/31/2016)
Working on my NativeScript RSS Application (05/27/2016)
Building an AJAX-based form for Formspree (05/25/2016)
A simple RSS reader in NativeScript (05/23/2016)
Thoughts on NativeScript 2.0 (05/16/2016)
Is it ever appropriate to hide an async process behind a sync one? (05/13/2016)
Uploading multiple files at once - with Fetch (05/10/2016)
Uploading multiple files at once - for Cordova (05/06/2016)
Uploading multiple files at once with Ajax and XHR2 (05/05/2016)
Disabling Forms Disabling Autocomplete (05/04/2016)
LoopBack, StrongLoop, and API Connect - how in the heck do they relate? (04/27/2016)
Speaking at Gluecon 2016 - Want a discount code? (04/27/2016)
An example of virtualScroll and Infinite Scroll in Ionic 2 (04/25/2016)
GET vs POST for Ajax Requests (04/21/2016)
How I added https to my blog (04/15/2016)
Rogue One Teaser Released (04/07/2016)
Articles on TDN and StrongLoop.com (04/06/2016)
Basic Node performance monitoring with Node Application Metrics (04/04/2016)
Introduction to LoopBack Presentation (03/31/2016)
Webinar Tips for Presenters (03/31/2016)
jQuery Mobile Web Development Essentials - Third Edition (03/29/2016)
Testing the New Ionic User Service (03/28/2016)
Getting Images from a Twitter Account (03/25/2016)
The Cordova Browser Platform (03/22/2016)
DS9 Rewatch Complete (03/20/2016)
Recording for Browser Tools Presentation (03/18/2016)
JSONPath for parsing JSON (03/15/2016)
Webinar next week on Browser Dev Tools (03/09/2016)
How I added search to my static blog (03/07/2016)
Ionic Services enter Beta (03/04/2016)
Starting a new role at IBM - StrongLoop Evangelist (03/03/2016)
Adding an API to a static site (03/01/2016)
Using the Onymos Media Component (03/01/2016)
Performing sentiment analysis of Twitter data (02/25/2016)
Building a Twitter bot to display random comic book covers (02/22/2016)
Creating an unread count for a static site (02/18/2016)
My PhoneGap Day 2016 Presentation (02/17/2016)
Adobe ColdFusion 2016 Released (02/16/2016)
Missing DevNexus (02/15/2016)
Displaying Google Street View images (02/13/2016)
Time for Ionic 2 (02/11/2016)
HTML Escaper Visual Studio Code Extension (02/10/2016)
Speaking at DevNexus 2016 (02/05/2016)
Playing with StrongLoop - Building a Blog - Part Three (02/03/2016)
Article on Improving Your JavaScript Skills (02/01/2016)
Visual Studio Code extension for Cordova (01/29/2016)
Survey Results for Rebecca Murphey's Learning JavaScript Survey (01/26/2016)
Apache Cordova SplashScreen Change (01/25/2016)
Dynamic Subjects with Formspree (01/22/2016)
Speaking at PhoneGap Day (01/21/2016)
What happens when you screw up an Ionic Deployment? (01/20/2016)
DefinitelyTyped project for IBM MobileFirst and Hybrid Mobile Apps (01/19/2016)
Time for Angular 2? (01/18/2016)
Working with Hugo on RaymondCamden.com (01/16/2016)
Going from static to dynamic with Ionic Creator (01/11/2016)
Playing with StrongLoop - Building a Blog - Part Two (01/07/2016)
Seeding data for a StrongLoop app (01/06/2016)
My first O'Reilly Book: Client-Side Data Storage (01/06/2016)
Playing with StrongLoop - Building a Blog - Part One (01/05/2016)
Speaking on Ionic in NYC Next Week (01/04/2016)
Another year, another Wordpress issue (01/02/2016)
Doing some testing... (01/02/2016)
Books I Read in 2015 (12/23/2015)
My Year (12/22/2015)
Article: A Review of JavaScript Error Monitoring Services (12/21/2015)
Is your Ionic View title not updating? (12/18/2015)
Review: Star Wars - The Force Awakens (12/18/2015)
A quick example of the Ionic Loading Widget (12/17/2015)
My first extension for Visual Studio Code - CSSLint (12/16/2015)
Deals on my Cordova book and JavaScript videos (12/16/2015)
Using Ionic Creator with MobileFirst 7.1 (12/15/2015)
Parsing RSS Feeds in JavaScript - Options (12/08/2015)
Feeling bored? Want to hurt your brain a bit? Play the Advent of Code (12/07/2015)
Review: Destiny and Star Wars Battlefront (12/05/2015)
Swift goes open source, and loads of new resources (12/04/2015)
Ionic/Cordova Demo: Where did I take that picture? (12/03/2015)
Book Review: Ionic Cookbook (12/02/2015)
Adobe loses its (web) edge... (12/01/2015)
How to tell if a Cordova application is running in the simulator (11/30/2015)
Where I want to go with Node next... (11/30/2015)
Happy Thanksgiving! (11/26/2015)
Important update for Apache Cordova and Android (11/25/2015)
HarpJS GUI in Beta (11/24/2015)
TIL - Autocomplete and forms (11/23/2015)
Using the Meetup API in Client-Side Applications (11/20/2015)
CFLib converted to Harp and on Surge (11/19/2015)
Using Authorization Tokens for IBM Watson services (11/13/2015)
Working with the Clipboard in Cordova apps (11/11/2015)
Article: Advanced Image Editing in the Browser (11/11/2015)
Demo of the Ionic Resources command (11/10/2015)
Cordova, iOS, and Orientation - wondering why it is locked? (11/09/2015)
Cordova Demo - Apple TV HD Video Viewer (11/05/2015)
Checking for platform and plugin updates in your Cordova project (11/04/2015)
In defense of the Reset button... (11/03/2015)
Quick Tip - Ionic apps and touch events (11/02/2015)
Building a hybrid mobile app? Avoid using CDNs for your libraries (10/30/2015)
StrongLoop, Ionic, and IBM Bluemix (10/29/2015)
A quick look at debugging Node.js with StrongLoop and Visual Studio Code (10/28/2015)
"Apache Cordova in Action" final edition released! (10/27/2015)
NodeSchool for IBM Bluemix and Node.js (10/27/2015)
Status of RIAForge (10/25/2015)
Getting an error running a Cordova project to iOS? (10/23/2015)
Quick tip for Cordova and the Browser platform - Setting a custom port (10/22/2015)
Working with StrongLoop (Part Four) - Locking down the API (10/21/2015)
Building my own iPhone Availability Web App (10/20/2015)
The New TFA Trailer (10/19/2015)
Working with StrongLoop (Part Three) (10/15/2015)
Adding localization to your Ionic application with IBM Bluemix (10/14/2015)
Working with StrongLoop (Part Two) (10/13/2015)
Important note for targeting iOS Emulators in Cordova (10/13/2015)
Working with StrongLoop (Part One) (10/12/2015)
Article: A Review of ContentTools – a Rich Content Editor (10/09/2015)
Testing Ionic Push Webhooks with IBM Bluemix (10/07/2015)
Learn about Ionic at Appcamp (10/02/2015)
Some cool things in Lucee (10/01/2015)
Proof of Concept: Validating an HTML Snippet in a Form (10/01/2015)
Ionic 1.6.5 and updates to Services (09/30/2015)
New ColdFusion docs (and some tips for handling it) (09/29/2015)
Speaking on Ionic Services at Ionic-SF (09/29/2015)
Switching platforms with Ionic Serve (09/27/2015)
Assets from my NCDevCon Preso (09/27/2015)
New book on Static Sites Generators (09/25/2015)
"Beginning JavaScript" (09/23/2015)
Another Cordova Mashup - Pixelatize (09/22/2015)
Finally! A good (darn good) Star Wars book (09/20/2015)
Integrating the Calendar into your Ionic App (09/18/2015)
Creating a custom display for Google's Analytics Embed Library (09/17/2015)
Ionic Example: ion-slide-box (09/16/2015)
Want to learn about client-side storage? (09/15/2015)
Working with Directories and HarpJS (09/11/2015)
Node 4 and libsass issues? (09/09/2015)
Working around Ionic's cached views (09/07/2015)
Is it time to stop using ColdFusion for remote APIs? (09/04/2015)
New MobileFirst Slack! (09/04/2015)
Speaking on Cordova, Ionic, and MobileFirst/Bluemix in Manilla (09/03/2015)
Recording of my ORA Static Site Presentation (09/02/2015)
Looking for mobile developers who want to test something cool... (09/02/2015)
Ripple is Reborn (Again!) (09/02/2015)
Calling remote services from Ionic Serve (09/01/2015)
Upcoming Ionic/Bluemix Presentations in Asia (08/31/2015)
Upcoming Presentation: Static site generators: Why use them and how they work (08/25/2015)
Using Generators with Harp (08/24/2015)
Chrome, console, and URLs - watch out (08/20/2015)
Speaking Down Under Next Week (08/20/2015)
Developing Ionic Apps with MobileFirst 7.1 (08/19/2015)
Developing Hybrid Mobile Apps with IBM MobileFirst 7.1 (08/18/2015)
Coming Soon: The Ionic Market (08/17/2015)
Getting Started with Mobile Development and IBM MobileFirst 7.1 (08/17/2015)
A quick Pokemon demo, because, Pokemon (08/15/2015)
IBM MobileFirst 7.1 Released (08/14/2015)
Processing multiple simultaneous uploads with Cordova (08/10/2015)
More information on restoring Ionic projects (08/06/2015)
A real world app with IBM Bluemix, Node, Cordova, and Ionic (08/05/2015)
Review: REST Web APIs: The Book (08/02/2015)
Cordova/Ionic Sample App: My Sound Board (07/30/2015)
SauceDB: Writing data back (07/29/2015)
Recording and saving audio in Cordova applications (07/27/2015)
SauceDB - Handling the Sauce view (07/24/2015)
Some initial thoughts on building desktop apps with Ionic and Electron (07/23/2015)
Using JavaScript to integrate with the EventBrite API (07/22/2015)
SauceDB - Building the back end with IBM Bluemix (07/20/2015)
Review: "Build an HTML5 Game" (07/19/2015)
Using JavaScript, IndexedDB to cheat at WordBrain (07/17/2015)
Safari and HTTP Caching (07/16/2015)
Article: Merging Dynamic and Static Sites (07/16/2015)
SauceDB - Working on the front end (07/15/2015)
FYI - Cordova events must be run after deviceReady (07/15/2015)
Quick Tip: Navigating in Ionic without History (07/14/2015)
New Demo Project: SauceDB (07/14/2015)
Review: Dave vs the Monsters (07/12/2015)
Combining client-side social login and server-side authorization with Cordova and Node (07/10/2015)
Using friendlier URLs for a HarpJS Static Site (07/08/2015)
Using the Google Analytics Embed API to Build a Dashboard (07/07/2015)
Recording from Static Sites Presentation (07/06/2015)
Using Angular and a Content Security Policy? Watch out for this... (07/03/2015)
Ionic Push example supporting State Changes (07/02/2015)
Happy 20th, ColdFusion (07/02/2015)
Online presentation - Working with Static Sites (06/25/2015)
Keyboard Tip for the iOS Simulator (06/24/2015)
Working with Ionic, Box, and IBM MobileFirst (06/24/2015)
An update to my RSS Reader built with Ionic (06/22/2015)
Presentation: Leveling Up at JavaScript (06/16/2015)
Vacation Notice (06/10/2015)
Quick example of the Google Analytics Embed API (06/10/2015)
Using Cloud Code, Mobile Application Security, Node.js and Bluemix (06/09/2015)
Speaking at Ionic Dallas next month (06/09/2015)
Google Analytics and RSS Report (06/08/2015)
Cordova Sample: Capture and Display Video (06/05/2015)
My first video course for O'Reilly - JavaScript Templating (06/05/2015)
Online presentation next week - How to Become An "Intermediate" JavaScript Programmer (06/04/2015)
A look at New Relic Browser (05/30/2015)
Finding the owner of a file with ColdFusion (05/29/2015)
Best Voice Recognition Fail(?) Ever... (05/27/2015)
Using the Marvel API with IBM Watson (05/26/2015)
Important information about Cordova 5 (05/25/2015)
Getting initial console messages you missed with remote debug (05/21/2015)
Looking at the JavaScript API in Hybrid MobileFirst Apps (2) (05/19/2015)
Working with the new PhoneGap/Cordova ContentSync Plugin (05/19/2015)
Tracking and notifying geolocation status with Ionic (05/18/2015)
Fascinating cftry/cfcatch/cfoutput bug with ColdFusion (05/18/2015)
A simple Cordova task runner for Visual Studio Code (05/17/2015)
Suggestions for Database Syncing with PhoneGap/Cordova (05/15/2015)
My speaker's self post-mortem (05/14/2015)
Sorry for not responding... (05/14/2015)
Ionic hits 1.0 (05/12/2015)
Fluent 2015 (05/11/2015)
Online ColdFusion Meetup Back in Action (05/11/2015)
IBM and Ionic (05/08/2015)
Working with MP3s, ID3, and PhoneGap/Cordova - Adding IBM MobileFirst (05/06/2015)
Article: The Epic, Awesome & Supremely Useful Data Attribute (05/05/2015)
Working with MP3s, ID3, and PhoneGap/Cordova (3) (05/01/2015)
PhoneGap CLI and Templates (05/01/2015)
My Cordova book is on sale again (04/30/2015)
Working with MP3s, ID3, and PhoneGap/Cordova (04/29/2015)
Can't find Cordova plugin docs? (04/29/2015)
Looking at the JavaScript API in Hybrid MobileFirst Apps (04/28/2015)
Testing Camera Quality Settings and PhoneGap/Cordova (04/27/2015)
Connecting PouchDB to Cloudant on IBM Bluemix (04/24/2015)
IndexedDB and Limits - IE (04/24/2015)
Want to learn about Ionic? (04/23/2015)
Big updates to Apache Cordova (04/21/2015)
Crazy cool Chrome extension (and how to dig into the source) (04/21/2015)
Ionic adds a new State feature (04/20/2015)
Some games to pick up (04/19/2015)
IndexedDB and Limits (04/17/2015)
The Second Star Wars Teaser (04/16/2015)
Speaking on Ionic next week at FluentConf (04/15/2015)
ColdFusion Updates Released Today (04/14/2015)
Blowing up LocalStorage (or what happens when you exceed quota) (04/14/2015)
Chaining multiple Cordova File Transfers with ngCordova (04/13/2015)
Front-End Interview Questions – Part 5 (04/10/2015)
Using MobileFirst HTTP Adapters with an Ionic Application (04/08/2015)
Form analytics with Formatic (04/07/2015)
Cool ColdFusion site on Kickstarter (04/07/2015)
Some tips for writing JavaScript adapters for IBM MobileFirst (04/06/2015)
Strategies for dealing with multiple Ajax calls (04/03/2015)
Using MobileFirst SQL Adapters with an Ionic Application (04/02/2015)
Using Remote Logging with Ionic and IBM MobileFirst (03/31/2015)
An early look at Ionic Push (03/31/2015)
Working with IBM MobileFirst and Ionic - a follow up (03/30/2015)
Tip: Viewing Network Requests with the Safari Debugger (03/27/2015)
Using Grunt to Automate MobileFirst/Hybrid Builds (03/26/2015)
Reminder - Having a tool doesn't mean you always use that tool... (03/25/2015)
Working with IBM MobileFirst and Ionic - Bootstrapping (03/24/2015)
Having trouble with splash screens, Cordova, and Android? (03/24/2015)
Learning Cordova's config.xml? Check out this online tool (03/23/2015)
Working with IBM MobileFirst and the Ionic Framework (03/23/2015)
OS X Yosemite Tip - Maximizing Windows (03/22/2015)
Avoid Ratchet for PhoneGap/Cordova development (03/21/2015)
Creating simple comparative bars with JavaScript and CSS (03/19/2015)
Ionic Serve's Lab option (03/16/2015)
Quick Handlebars tip concerning precompilation (03/14/2015)
Testing MetaCert's Security API Service (03/13/2015)
Selecting multiple images in a PhoneGap/Cordova app (03/12/2015)
Example of Ionic's Updating Feature (03/11/2015)
Check out "Ten Apps in Ten Weeks" (03/10/2015)
Working with the Bluemix Personality Insights Service (03/10/2015)
Need to test a service that doesn't use CORS? There's a plugin for that. (03/09/2015)
My early access Cordova book is half off today! (03/08/2015)
Warning about Ionic Live Reload and the PhoneGap Developer App (03/08/2015)
Warning a user before they leave a form (03/06/2015)
My experience working with Jekyll (03/05/2015)
Hosting static sites with Surge (03/04/2015)
Brackets Tip: Specifying one linter (the right way) (03/03/2015)
Cordova CLI Updated (03/03/2015)
Hosting Node.js apps on Bluemix (03/02/2015)
Sunday OT: Rise of the Runelords (03/01/2015)
Quick Cordova tip - Preventing multiple sounds at once (02/27/2015)
Reminder - You don't need AppCache for PhoneGap/Cordova (02/25/2015)
Migrating servers on Google Compute Engine (02/24/2015)
Brian Rinaldi on Static Sites (02/24/2015)
POC - Determining the "Health" of your GitHub Repos (02/23/2015)
Static site hosting on Google Cloud (02/22/2015)
Using the MobileFirst Mobile Browser Simulator (02/20/2015)
My experiences with Google Compute Engine (02/19/2015)
Apache Cordova in Action MEAP Updated (02/18/2015)
Traffic on ColdFusion Bloggers (02/18/2015)
Reminder - Get this blog via email (02/17/2015)
Adding keyboard navigation to a client-side application (02/16/2015)
Working with hybrid applications and IBM MobileFirst (02/16/2015)
Interesting error reporting difference in Chrome and Firefox (02/14/2015)
A few examples of "tag as script" in ColdFusion 11 (02/11/2015)
Reminder - stop using the old CFC-based tags in ColdFusion 11 (02/10/2015)
Possible Cordova FileSystem Resource (02/10/2015)
Using the new Bluemix Visual Recognition service in Cordova (02/06/2015)
Can't run ColdFusion Builder 3 on OS X? Read This. (02/03/2015)
Missing orders, Prime membership, Cloud music, etc with Amazon? (02/02/2015)
Lucee, new fork of Railo, has launched (02/01/2015)
Thank you, Jack Wilber (01/30/2015)
Latest Firefox adds Storage to Developer Tools (01/29/2015)
Suggestions for learning JSON? (01/29/2015)
An example of application specific scheduled tasks in ColdFusion (01/27/2015)
Front-End Interview Questions - Part 2 (01/27/2015)
ColdFusion Builder 3 Updated (the right way) (01/26/2015)
ColdFusion Bloggers migrated to Node.js (01/26/2015)
Front-End Interview Questions (01/22/2015)
Drag and Drop on File Inputs in HTML (01/21/2015)
PhoneGap/Cordova Tip: Working with files under www and Android (01/21/2015)
Alt-History on TV - The Man in the High Castle (01/18/2015)
Lame, client-side 404 handling with Amazon S3 (01/17/2015)
New Year, New Job (01/16/2015)
Know WordPress? Need some advice. (01/13/2015)
PhoneGap Online/Offline Tip (2) (01/13/2015)
ColdFusion Builder 3 Updated (and I bet you didn't know...) (01/12/2015)
Dropdown to Ajax call to ColdFusion example (01/09/2015)
Article: A Case Study in JavaScript Code Improvement (01/08/2015)
Check out Happy Metrix (again) (01/06/2015)
CFLib moves to Node.js (01/05/2015)
Using Grunt and Jasmine and having issues with XHR? Read this. (01/02/2015)
My 2014 (12/30/2014)
Looking to learn Node and Express? (12/29/2014)
My 2014 Book List (12/27/2014)
Avoid the minified AngularJS library in development (12/26/2014)
Creating Spreadsheets with ColdFusion without headers (12/24/2014)
Cordova Demo - Viewing all Contacts (12/23/2014)
Introduction to jQuery (12/19/2014)
Get jQuery Mobile Web Development Essentials for Five Dollars! (12/18/2014)
Viewport and Cordova Tip (12/18/2014)
AppFog and MongoDB 2 Configuration (12/17/2014)
Online presentation tonight on ColdFusion 11 (12/16/2014)
A quick message for the ColdFusion community (12/15/2014)
cfwddx doesn't work in script - FYI (12/15/2014)
ColdFusion, CFHTTP, and java.io.ByteArrayOutputStream (12/12/2014)
Cordova Example - Sending SMS Messages (12/11/2014)
Really useful Chrome Dev Tools tip (12/10/2014)
Oops, RSS issue (12/10/2014)
ColdFusion updated, and some notes about query caching (12/09/2014)
My Cordova/PhoneGap Developer Setup (Fall 2014) (12/08/2014)
Quick review of SumAll.com (12/07/2014)
Update on migration and Disqus Thread Migration tool (12/04/2014)
Welcome to the 2015 RaymondCamden.com (12/03/2014)
HTML5 (or HTML in general) book recommendations? (12/01/2014)
Selecting a random record from an IndexedDB Object Store (11/30/2014)
Star Wars Teaser (11/28/2014)
Disqus update (and BlogCFC export script) (11/26/2014)
Early Access to My Next Book - Apache Cordova in Action (11/25/2014)
Status of Disqus updates, and a tool for URL migration (11/23/2014)
Check out FormKeep, another option for static sites (11/21/2014)
ColdFusion Startup Issue with Hostname (11/21/2014)
Blog Migration Update (11/20/2014)
Determining installed plugins at runtime for Cordova and PhoneGap applications (11/19/2014)
Using the autodivider feature in jQuery Mobile (take two) (11/18/2014)
Looking for Suggestions: Best Conferences for Mobile/Web Development (11/18/2014)
Cordova's copy-from tip (11/14/2014)
Test with Extract (11/13/2014)
Any WordPress users familiar with BlogCFC? (11/13/2014)
Hello world! (11/13/2014)
ColdFusion Example: Using jQuery UI Accordion with a ColdFusion query (11/12/2014)
Good post on Cordova, PhoneGap, and versioning (11/10/2014)
Random code I'm sharing for no good reason (11/09/2014)
Cordova and Asset Downloads (11/07/2014)
List auto-dividers in Ionic (11/06/2014)
Cordova Example: Writing to a file (11/05/2014)
Syncing Brackets extensions across multiple machines (11/04/2014)
Using PhoneGap Build? Check out the new support forum (11/03/2014)
self.getFamily().addOne().addOne() (11/01/2014)
My Modern Web Conference presentation is now available online (10/29/2014)
Beautiful (10/24/2014)
Yesterday (10/23/2014)
OOO for a bit so why not say hi to each other? (10/16/2014)
Thoughts on Integrating Ionic into an Existing Application (10/16/2014)
Nunjucks templating by Mozilla (10/15/2014)
Delaying an Edge Animate asset until visible - Part 6 (10/14/2014)
My review of Ionic's Visual Application Builder (10/10/2014)
Cordova, the Camera plugin, AngularJS, and Ninja Cats. (10/10/2014)
Another bug with queryExecute - Threads (10/09/2014)
Bug with queryExecute - use with caution (10/09/2014)
Timing out users by role in a ColdFusion Application (10/08/2014)
Cordova and Large Asset Downloads - An Abstract (10/07/2014)
CreativeSDK (really) Launches (10/06/2014)
ColdFusion Jedi is no more... (10/06/2014)
Figuring out what version of Cordova created a project (10/03/2014)
Ionic has a CDN (use with caution) (10/02/2014)
UX question, handling notifications (10/02/2014)
Cordova, Plugins, and Determining What Supports What (10/01/2014)
The Future of cfObjective. (09/29/2014)
Syncing Edge Animate with Window Scroll (09/29/2014)
Another IndexedDB Bug - Possibly (09/26/2014)
IndexedDB on iOS 8 - Broken Bad (09/25/2014)
Browser as a platform for your PhoneGap/Cordova apps (09/24/2014)
Safari Remote Debug and IndexedDB (09/24/2014)
Tip: Using Ionic - without Ionic (09/23/2014)
Simple photo filters with VintageJS and Cordova (09/23/2014)
ColdFusion 11 Updated, and my (non)appearance at the ColdFusion Summit (09/22/2014)
Datalist support in Mobile Chrome (09/18/2014)
ColdFusion's ArrayEach and Struct JSON Serialization (09/17/2014)
Using the New York Times API to Chart Occurrences in Headlines (09/15/2014)
Video: My top features of ColdFusion 11 (09/14/2014)
Video: Building Hybrid Applications with Ionic (09/13/2014)
Having issues sending a Cordova app to an iOS device? Seeing lldb? (09/11/2014)
CommandBox CLI and Package Manager for ColdFusion (09/11/2014)
Ionic Framework and CLI updated (09/10/2014)
What is the optimal environment for trying Ionic? (09/09/2014)
Proof of Concept: Live HTML checking for a textarea (09/08/2014)
RSS Reader Cordova demo updated with Ionic (09/05/2014)
Bug with ColdFusion 11's Elvis Operator (09/04/2014)
Ionic 1.2.0 Released (09/04/2014)
Speaking at NCDevCon 2014 (09/03/2014)
Datalist version of Country Dropdown (08/27/2014)
Chrome 37 has landed - but what exactly changed? (08/27/2014)
Did you do this? (08/25/2014)
My weekend experiment - PebbleJS (08/24/2014)
IndexedDB - On the move... (08/22/2014)
Project Parfait moves to Creative Cloud (08/21/2014)
Follow up to ColdFusion Axis2 Web Service Issue (08/21/2014)
Ionic releases an easier path to Cordova / Android development (08/19/2014)
PhoneGap/Cordova Example - Getting File Metadata (and an update to the FAQ) (08/18/2014)
Ionic and Cordova's DeviceReady - My Solution (08/16/2014)
Eventbrite API Demos (08/15/2014)
Review: Code School's JavaScript Best Practices (08/13/2014)
Presentation tonight on Apache Cordova (08/12/2014)
Centering a Google Map on America (08/09/2014)
Avoid Zero (or super short) Application Timeouts (08/08/2014)
Keep your DOM from shifting around... (08/05/2014)
MockData CFC Released (08/04/2014)
How to make a phone call via GMail (08/01/2014)
Read Holly's guide to the iOS Status Bar (07/31/2014)
Linting your ColdFusion code (07/31/2014)
Check out CodeSchool's Angular course (07/29/2014)
My perspective of working with the Ionic Framework (07/28/2014)
Sunday OT - Wolfenstein: The New Order (07/27/2014)
Updated/Relaunched site - Popular Followers (07/24/2014)
An example of Cordova's Camera PopoverOptions (07/23/2014)
PhoneGap Day US and EU Announced (07/22/2014)
Targeting a device type with Cordova Emulate (07/21/2014)
ColdFusion, isValid, Email and new TLDs (07/21/2014)
Soundings Update (07/16/2014)
Cordova Sample: Reading a text file (07/15/2014)
Yet another Cordova/PhoneGap Debugging Tip (07/15/2014)
Verified plugins site for Cordova applications (07/14/2014)
First release of Cordova Brackets extension (07/11/2014)
Issue with CFINDEX (07/11/2014)
Unexpected behavior with Axis2 web services in ColdFusion (07/10/2014)
Video example: collection-repeat performance in Ionic (07/10/2014)
Cordova Plugins update, and new Contacts demo (07/09/2014)
Proof of Concept Cordova integration with Brackets (07/08/2014)
Article: Static Site Engine Battle Royale (07/07/2014)
Sunday OT - Video Game Reviews (07/06/2014)
GapDebug, a new mobile debugging tool (07/02/2014)
Cordova Sample: Check for a file and download if it isn't there (07/01/2014)
Article on Fenix Web Server (06/30/2014)
Add "Search Export" to ColdFusion Builder 3 (06/26/2014)
XCode "forgets" frameworks and bundles after a restart (06/25/2014)
PhoneGap/Cordova File System questions (06/23/2014)
Cordova Media API Example (06/23/2014)
Using the Gamepad API (06/20/2014)
iOS Simulator not refreshing with Cordova (PhoneGap)? Read this. (06/20/2014)
ColdFusion UI The Right Way - HTML version (06/19/2014)
Why I took that ObjectiveC training... (06/18/2014)
Building a Car Safety Inspection Finder (the good, ugly, and more ugly) (06/17/2014)
Issue with ColdFusion JavaSettings and ReloadOnChange (06/16/2014)
My NCDevCon presentation: Practical HTML5 (06/12/2014)
Important Update for ColdFusion Builder 3 Users (06/11/2014)
Date Fields, JavaScript, and the things that make me go crazy... (06/10/2014)
ColdFusion Trusted Cache and Deleted Files (06/09/2014)
ColdFusion Developer Security Guide (06/06/2014)
Quick FYI: XHR, Cross Domain Requests, and Sessions (06/05/2014)
ngCordova Released (06/04/2014)
ColdFusion Summit 2014 - Call for Speakers (06/03/2014)
White paper on Hybrid Mobile Apps (06/02/2014)
Related selects with multiple options (05/30/2014)
Update your bookmarks for the ColdFusion Docs (05/28/2014)
Cordova 3.5 and the "What's Next" Guide (05/27/2014)
Browser slowdown? SVN failing? Read this. (05/25/2014)
PhoneGap Tip: Temporarily changing orientation for video in a portrait only application (05/24/2014)
Important note about ColdFusion 11 and CFHTTP (05/22/2014)
Remember tabindex? (05/21/2014)
Example of Password Protected Zips in ColdFusion 11 (05/20/2014)
Sunday OT - New Games (05/18/2014)
Quick FYI - JSHint for CFBuilder (05/17/2014)
ColdFusion 11 Lockdown Guide (05/15/2014)
Article: Working with Intl (05/13/2014)
Downloading ColdFusion Documentation (05/12/2014)
ColdFusion UI The Right Way - An Update (and Thanks) (05/12/2014)
Sunday OT - STTNG Rewatch Complete! (05/11/2014)
ColdFusion 11's new Struct format for JSON (and how to use it in ColdFusion 10) (05/08/2014)
Mimicking the GMail Delayed Message Load UX (05/07/2014)
Using Project Templates in ColdFusion Builder 3 (05/05/2014)
Intergral folks are (still) hiring! (05/02/2014)
A Warning - The White Screen of Death with ColdFusion Builder 3 (05/01/2014)
What is the "best" form to return different types of data? (04/29/2014)
ColdFusion 11 and ColdFusion Builder 3 Released (04/29/2014)
Article: Expose Yourself with ngrok (04/28/2014)
"Table View" Extension for ColdFusion Builder (04/25/2014)
Keeping up with Cordova and PhoneGap (04/24/2014)
Logs from Open PhoneGap Session (04/23/2014)
Project Parfait - PSD Introspection in the Browser (04/22/2014)
PhoneGap Developer App (04/21/2014)
Recording: Debugging Mobile Applications Presentation (04/18/2014)
Another Weekly to Sign Up For... (04/18/2014)
Article: HTML out of the Browser (04/17/2014)
Open PhoneGap/Cordova Session next week (04/16/2014)
Example of Async Linting support in Brackets Sprint 38 (04/15/2014)
Google Hangout - Debugging Mobile Web/Cordova Apps - A Quick Review (04/15/2014)
Multi-File Uploads and Multiple Selects (Part 2) (04/14/2014)
Results of PhoneGap Survey (04/11/2014)
Update to my JavaScript Behance API (04/11/2014)
Recording and demos from my ColdFusion 11 presentation (04/10/2014)
getSafeHTML and ColdFusion 11 (04/09/2014)
Upcoming ColdFusion E-Seminars (04/09/2014)
This is not the function you are looking for (04/08/2014)
Interesting addition to ColdFusion 11 (and an example of it in ColdFusion 10) (04/07/2014)
Quick survey on PhoneGap/Cordova versions (04/07/2014)
Dynamically Creating CSV Files on the Client (04/03/2014)
Adding an Absolutely Positioned Header to Reveal.js (04/01/2014)
Dash integration for Brackets (03/31/2014)
Check out Dash (03/30/2014)
AngularJS Tip - Avoid Multiple Variables in ng-src (03/29/2014)
ColdFusion Example: Upload a zip of images for processing (03/28/2014)
PhoneGap for the Enterprise (03/25/2014)
My first native iOS app - Death Clock (03/25/2014)
Intergral folks are hiring! (03/25/2014)
Sunday Quickie - Bookmarklet to Fix Forms that Disable autocomplete (03/23/2014)
I survived Big Nerd Ranch training (03/22/2014)
Example of a JavaScript Disqus Recent Comment Widget (03/21/2014)
This server... (03/20/2014)
Brackets Sprint 37 and Upcoming Hackathon (03/18/2014)
Attending cfObjective? Check out Into The Box (03/17/2014)
Very odd CFDOCUMENT Bug (03/16/2014)
CodeCanyon and ColdFusion (03/14/2014)
This blog... (03/14/2014)
Reprint: What in the heck is JSONP and why would you use it? (03/12/2014)
ColdFusion, Random Numbers, and Time (03/11/2014)
Remember DevelopRIA? (03/10/2014)
Barcode Scanner sample, and new repo for Cordova examples (03/05/2014)
My ColdFusion Bugs - visualized (02/28/2014)
Interesting discovery with CasperJS, jQuery, and transitions (02/28/2014)
Nested Layouts in HarpJS (02/27/2014)
Creating Next/Previous Links in HarpJS (02/26/2014)
Comic Cover Muzei (02/26/2014)
ColdFusion and Form Fields with the Same Name (02/25/2014)
Creating a data backup of a WebSQL database (02/24/2014)
Recommendation: The Merchant Princes series by Charles Stross (02/23/2014)
Cordova 3.4.0 Released (02/21/2014)
Recording and Assets from my Harp.js Presentation (02/21/2014)
Friday Puzzler: Rolling the die... (02/21/2014)
Google+ Sign-In and ColdFusion (02/20/2014)
Video: Debugging with Firefox DevTools (02/20/2014)
ColdFusion Splendor/Thunder Public Betas (02/19/2014)
ColdFusion UI Project Update (02/19/2014)
Somewhat lame iOS Cordova debugging tip (02/17/2014)
Cordova File System - Important Update (02/17/2014)
Adding a dynamic calendar to HarpJS (02/14/2014)
Two Harp.js Recipes: Limiting a list of blog entries by count and by date (02/13/2014)
Presenting on Harp.js next week (02/12/2014)
Mimicking fixNewLine in ColdFusion Script (02/10/2014)
Small warning to folks writing Brackets extensions (02/08/2014)
AngularJS IndexedDB Demo (02/07/2014)
Some tips for working with PDF Forms and ColdFusion (02/06/2014)
Simple Trick - Adding a Play Indicator to the Browser Tab (02/04/2014)
Article: Creating Brackets Extensions (02/03/2014)
Examples of the Marvel API (02/02/2014)
Check out Proxxi (01/31/2014)
Modifying the PhoneGap Template in 3.3 (and higher) (01/31/2014)
Smart Quotes Strike Again (01/30/2014)
Topic Undefined - Episode 7 (01/29/2014)
Updated ColdFusion OAuth Code (01/28/2014)
Proof of Concept - Dashboard for Google Analytics (01/24/2014)
I'm not going to tell you to stop using ColdFusion UI tags anymore... (01/23/2014)
Quick Ripple Tip - Detecting Ripple (01/22/2014)
Experience converting a dynamic site to static with HarpJS (01/21/2014)
Edge Animate 3.0 (01/21/2014)
Some quick HarpJS Tips (01/20/2014)
Speaking in San Francisco next week - Mobile+Web DevCon (01/20/2014)
Warning about ColdFusion 10 and ORM Logging (01/17/2014)
Installing and Using Ripple for Cordova Development (A Video) (01/17/2014)
Interesting discovery - Chrome and Storage (01/16/2014)
Creative Cloud Update Today (01/16/2014)
Brackets Tip: Using Live Preview as a Web Server (01/15/2014)
Adobe Edge Reflow - Preview 7 (01/15/2014)
Article: An Overview of Mobile Debugging Techniques – Part Two (01/14/2014)
AngularJS Doesn't Suck! (01/14/2014)
HTML5 Input Patterns and Invalid Regex (01/13/2014)
Question for readers: Site Map of a ColdFusion site? (01/10/2014)
Remove EXIF data with ColdFusion (01/06/2014)
2013 Survey Results (01/05/2014)
Did You Know: Searching for PhoneGap/Cordova Plugins (01/03/2014)
Apache Cordova 3.3 and Remote Debugging for Android (01/02/2014)
Some HarpJS experiments involving categories (01/02/2014)
My 2014 Resolutions (01/01/2014)
My personal little JavaScript WTF (12/31/2013)
My 2013 Reading List (12/30/2013)
Top Ten Entries for 2013 (12/29/2013)
Article: Working with IndexedDB - Part 3 (12/26/2013)
A PhoneGap Discussion around files, API calls, and security (12/23/2013)
Sunday OT: The Last of Us (12/22/2013)
Brackets Sprint 35 Released (12/20/2013)
Dev Tools Tip - Preserving network logs on leaving a page (12/19/2013)
Quick note about HTML5 Form validity and browser differences (12/19/2013)
Help me help you... (12/18/2013)
Using the autodivider feature in jQuery Mobile (12/17/2013)
New Brackets Extension - Canalyzer! (12/16/2013)
Article: Moving to Static and Keeping Your Toys (12/16/2013)
Meanwhile, over in IndexedDB land... (12/13/2013)
jQuery UI Video Course (12/13/2013)
TryCF.com (12/12/2013)
This works... and it freaks me out (12/11/2013)
Quick Sample: Appending URL data to a Form post with JavaScript (12/11/2013)
Click (like crazy) for Toys for Tots (12/10/2013)
Article: An Overview of Mobile Debugging Techniques – Part One (12/10/2013)
What the heck is (index) in Chrome Dev Tools? (12/09/2013)
Building a Quiz Manager for jQuery Mobile (12/05/2013)
Flash Professional CC adds HTML5 Canvas Support (12/03/2013)
I wish I had linted before... (12/02/2013)
Happy Thanksgiving - and what I'm thankful for... (11/28/2013)
Slow posting, responding for a while (11/13/2013)
ColdFusion Security Update (11/13/2013)
Building a Contact Form with Parse and Mailgun (11/12/2013)
The Online ColdFusion Meetup is back (11/11/2013)
The Sunday OT: My Favorite Video Game Commercials (11/10/2013)
Nettuts Article: Deeper into Brackets (11/08/2013)
Using Grunt to automatically build your PhoneGap/Cordova projects (11/07/2013)
Want help with Snap.svg? (And a few more examples...) (11/06/2013)
Ripple is Reborn! (11/05/2013)
ExpressWorks (building on NodeSchool) (11/05/2013)
Android, Photo Gallery Widget, and "Unable to Save Cropped Photo" (11/04/2013)
Seeing two geolocation prompts in a PhoneGap/Cordova application? (11/02/2013)
HTMLHint extension for Brackets (11/01/2013)
Check out nodeschool.io (11/01/2013)
Using ColdFusion UI tags and many bound controls (10/29/2013)
ColdFusion Documentation Wiki (10/29/2013)
What broke my event handler? (10/28/2013)
Snap.svg demo - Census Data (10/28/2013)
ColdFusion Summit 2013 (10/26/2013)
Solr presentation assets, and a note on DisMax searching (10/24/2013)
Introducing Snap.svg (10/23/2013)
Moving from dynamic to static with Harp (10/22/2013)
Article: Working with IndexedDB - Part Two (10/21/2013)
Drag and drop image matching search at Behance (10/18/2013)
Second draft - JavaScript Library for Behance Integration (10/17/2013)
cfObjective 2014 Call for Speakers (and my proposed sessions) (10/16/2013)
First draft - JavaScript Library for Behance Integration (10/16/2013)
File-based Indexes with ColdFusion - a quick tip (10/15/2013)
Back to the Edge Recording (10/13/2013)
Back to the Edge - Meeting Reminder (10/10/2013)
Custom Y-Axis Labels in ColdFusion Charting (10/09/2013)
Article: New Linting API (10/07/2013)
Working with binary data in a Brackets Extension (10/07/2013)
Brackets Extension: HTMLEscaper (10/02/2013)
PhoneGap Build and PhoneGap 3.0 (10/01/2013)
Multi-File Uploads and Multiple Selects (10/01/2013)
Webinar - Back to the Edge (09/30/2013)
Sunday OT: Review of Epic Spell Wars (09/29/2013)
I know what Brackets is missing... (09/27/2013)
jQuery Mobile Web Development Essentials, Second Edition (09/26/2013)
CSS Regions and Edge Tooling (09/24/2013)
Download the PhoneGap Refcard (09/23/2013)
My videos (and others) from NCDevCon (09/22/2013)
CSS Animation Workshop (09/19/2013)
Playing with the Details/Summary Tag (09/17/2013)
Edge Code Update (09/17/2013)
PhoneGap Day Video on Parse.com (09/16/2013)
Create Now SF is this Thursday! (09/16/2013)
Minor formatting change here for comments (09/15/2013)
Article: Working with IndexedDB (09/13/2013)
Review of Modulus for Node.js Hosting (09/11/2013)
Attend NCDevCon! (09/10/2013)
Adding a file display list to a multi-file upload HTML control (09/10/2013)
Photoshop launches new Generator feature (09/09/2013)
A quick test of Prism.js (09/07/2013)
Working with Plugins in PhoneGap 3.0 (09/06/2013)
How do you check (and update) your PhoneGap version in 3.0? (09/05/2013)
Working with jQuery Mobile Panels (09/05/2013)
Come discuss PhoneGap 3 (09/04/2013)
Implementing custom JSON serialization for your CFCs (09/04/2013)
No more job openings... (09/03/2013)
Create Now Tour coming to North America (09/03/2013)
Some tips for using Brackets and Theseus (08/28/2013)
Like Brackets? Help support it at the Linux Journal Readers Choice Awards (08/28/2013)
Another Node Experiment: AndKittens (08/27/2013)
Over 5000! (Almost...) (08/26/2013)
PSA: CF Live (08/26/2013)
Review: Effective JavaScript (08/25/2013)
Brick by Mozilla (08/23/2013)
FusionReactor 5 Released (08/22/2013)
Two more Windows Phone/PhoneGap Tips (08/21/2013)
Node.js Quickie - checking the current domain name (08/21/2013)
Node Weekly Launching (08/20/2013)
More ways to be a hero with Edge Animate (08/19/2013)
Using Drawing Tools and Maps to Find Data (08/19/2013)
Using Topcoat and Brackets? Check out these Snippets (08/16/2013)
Friday Puzzler: Get off your butt and learn your browser tools! (08/16/2013)
JavaScript Errors and the Firefox Console (08/16/2013)
Using the PhoneGap CLI on Windows? Watch out for this bug. (08/15/2013)
Updating PhoneGap Databases (08/14/2013)
Using the Directory-serving middleware in Express (08/11/2013)
Sunday OT: Best 2600 Video Ever (08/11/2013)
Google Maps and Markers Update (08/09/2013)
Sharing ColdFusion WebSockets among different applications (08/08/2013)
Article: Going Live With Node (08/05/2013)
Sunday OT: New Who (08/04/2013)
Authored Content, Episode 29 (08/02/2013)
PhoneGap 3.0 FAQ (08/01/2013)
First impressions of Leap Motion (07/31/2013)
Welcome to the Nielsen Family - and 1960 (07/30/2013)
Check out Happy Metrix (07/27/2013)
Friday Puzzler: How to get to there from here... (07/26/2013)
Modifying the PhoneGap Template in 3.0 (07/24/2013)
ColdFusion Job Opening - SiteVision - Roanoke, VA - Telecommute (07/23/2013)
Better example of PhoneGap, Parse, and uploading files (07/23/2013)
Article: Introduction to Express (07/22/2013)
PhoneGap 3.0 Released - Things You Should Know (07/19/2013)
Speaking at PhoneGap Day 2013 (07/17/2013)
CajunIpsum - Because - Um - Yeah! (07/16/2013)
Upcoming Event: HTML5 Testing with Rebecca Hauck (07/15/2013)
What is the impact of enabling CLOB/BLOB for a ColdFusion DSN? (07/12/2013)
Quick note for Parse and JavaScript Users (07/10/2013)
Big update for ColdFusion 10, and Security Fix (07/09/2013)
Want a copy of Object-Oriented Programming in ColdFusion? (07/08/2013)
Firefox OS Announcement (07/02/2013)
ColdFusion Job Opening - University of Maryland, College Park, MD (07/01/2013)
My first RefCard for DZone is available - Getting Started with PhoneGap (07/01/2013)
ColdFusion Job Opening - SignUpGenius.com (06/28/2013)
Brackets, Edge Code, and MAX 2013 (06/26/2013)
Trying something new - my new podcast with Brian Rinaldi (06/26/2013)
Node lessons learned painfully (or why my site crashed) (06/24/2013)
Book Review: Third-Party JavaScript (06/23/2013)
Great questions about client-side development from a server-side developer (06/20/2013)
The official, real launch of JavaScriptCookbook (06/20/2013)
Edge Inspect Brackets/Edge Code extension open sourced (06/19/2013)
Edge Reflow CC (06/18/2013)
Creative Cloud is Here (06/18/2013)
ColdFusion Job Opening - State College, PA (06/17/2013)
Recording + Assets from PhoneGap Presentation (06/17/2013)
Another Sunday morning mega-video game review (06/16/2013)
More on my JavaScriptCookbook Node project (06/14/2013)
Looking for ColdFusion support in Brackets? (06/14/2013)
Using Errorception with PhoneGap (06/13/2013)
Have some Ramen with your ColdFusion (06/12/2013)
Vote and Suggest Topics for the CF Summit (06/12/2013)
Edge Code CC and Edge Inspect Integration (06/11/2013)
New Project: JavaScript Cookbook (06/10/2013)
IndexedDB and Date Example (06/06/2013)
Have a published PhoneGap app? Try the Windows Phone Porting Challenge (06/03/2013)
Looking for comments about pictures, orientation, and ColdFusion (06/03/2013)
Speaking at ColdBox Developer Week 2 (06/02/2013)
Two more MAX Videos: Cutting-Edge HTML and Debugging Your Web Apps (05/31/2013)
Check out the Kuler app (05/30/2013)
Assets from my TechWed Preso (05/29/2013)
Using the Page Visibility API with Edge Animate (05/29/2013)
PhoneGap Day 2013 (05/28/2013)
Using the Page Visibility API (05/28/2013)
Review: Instant Wijmo Widgets How-To (05/27/2013)
PhoneGap Online/Offline Tip (05/24/2013)
Video Tutorial: Installing the Ripple Emulator for PhoneGap Development (05/23/2013)
OSX Outlook keeps asking for a password (05/22/2013)
The Future of the Web (05/22/2013)
Infinite Scroll Example with ColdFusion (05/21/2013)
ColdFusion Summit Announced (05/20/2013)
Capturing camera/picture data without PhoneGap (05/20/2013)
Converting a list of dates into a shorter, combined list (05/19/2013)
Note to folks attending cfObjective and attending my sessions (05/16/2013)
ColdFusion Job Opening - healthendevours.com (05/15/2013)
Forms not working on your ColdFusion server? Size matters. (05/14/2013)
Hear me wax poetic on Nerd Radio (05/13/2013)
JavaScript Design Patterns - The Revealing Module Pattern (05/13/2013)
Missed MAX 2013? How to catch up... (05/10/2013)
MAX Session: Advanced PhoneGap Build (05/09/2013)
How I'd sell unit testing... (05/08/2013)
Update to my Edge Inspect Viewer (05/07/2013)
Coolest Unboxing Ever (05/06/2013)
Visual comparisons of PhoneGap Notification UIs (05/05/2013)
Recording and Assets from my PhoneGap Presentation (05/02/2013)
Using the Progress event in PhoneGap file transfers (05/01/2013)
Do you remember the ColdFusion Cookbook? (05/01/2013)
Check out Brackets Sprint 24 (04/30/2013)
Code School Kicks Butt (04/28/2013)
Auto-escaping code blocks in Reveal.js (04/25/2013)
New Brackets extension - JSDownloader (04/24/2013)
Note about PhoneGap Build and Splash Screens (04/23/2013)
Presenting on PhoneGap Next Week (04/23/2013)
Article Posted (Again) : Building a Google Maps Application with Updating Markers (04/22/2013)
Article Posted: My Favorite Features in ColdFusion 10 (04/19/2013)
Another reason to attend MAX - Hack on Brackets and PhoneGap (04/18/2013)
ColdFusion and OAuth Part 3 - Google (04/17/2013)
ColdFusion Job Opening - Columbia, MD -Telecommute (04/17/2013)
Proof of Concept - Connecting a Node app with Brackets (04/16/2013)
Review: Learning JavaScript Design Patterns (04/14/2013)
Join me at Adobe MAX (04/12/2013)
New project: Service Data Format Library (04/10/2013)
Some recent ColdFusion ORM Pain (04/09/2013)
Check out Flippin' Awesome! (04/08/2013)
How long ago was 1973? (04/08/2013)
Quick Code Sample - Add your Behance portfolio to your web site (04/05/2013)
ColdFusion Web Application Construction Kit 10 (04/04/2013)
ColdFusion and OAuth Part 2 - LinkedIn (04/03/2013)
Delaying an Edge Animate asset until visible (04/03/2013)
Recording from my PhoneGap Build Ask a Pro Session (04/02/2013)
Remember this special little rule about ColdFusion Components (04/02/2013)
ColdFusion Job Opening - St. Louis, MO (04/02/2013)
ColdFusion and OAuth Part 1 - Facebook (04/01/2013)
ColdFusion Job Opening - JB Anacostia-Bolling, D.C. (JBAB) (04/01/2013)
Friday Puzzler: Sort Type (03/29/2013)
Google Analytics and PhoneGap (03/28/2013)
Startup Weekend New Orleans (03/27/2013)
Brackets Sprint 22 - The Awesomer (03/27/2013)
"Ask a Pro" presentation this Friday (03/26/2013)
Sunday OT Post: Tomb Raider (03/24/2013)
JavaScript Design Patterns - The Module Pattern (03/22/2013)
New online material for Chrome DevTools (03/21/2013)
Want to try the next version of ColdFusion? (03/20/2013)
ColdFusion Job Opening - NexOne, Inc (03/20/2013)
JavaScript Design Patterns - My Crazy Plan (03/19/2013)
Building "Robust" PhoneGap Applications (03/18/2013)
ColdFusion Job Opening - Background Investigation Bureau (03/17/2013)
ColdFusion on AWS (03/14/2013)
Free ColdFusion 10 and jQuery Mobile Tutorial (03/12/2013)
ColdFusion Job Opening - Brandeis University (03/12/2013)
Date/Time issue with CFINDEX and SOLR (03/11/2013)
LocalStorage Monitor Updated (03/11/2013)
ColdFusion Job Opening - Uhlig (03/07/2013)
Testing PhoneGap, Parse, and Push? Read This (03/07/2013)
Programmatically clearing ColdFusion's Trusted Cache By Time (03/06/2013)
Speaking Engagements for March, 2013 (03/05/2013)
Simple Reverse Geocoding Example (03/05/2013)
PhoneGap Sample - Diary (Database and Camera support) (03/04/2013)
Friday Puzzler: Color Rotator (03/01/2013)
My IndexedDB recording, and a few notes (02/28/2013)
Quick Tip - Make Apache's Directory Indexes look nicer on mobile (02/27/2013)
ColdFusion Updates Today (02/27/2013)
A highly unusual ColdFusion arguments error (02/26/2013)
While learning JavaScript and CSS, spend some time with HTML (02/25/2013)
Welcome to RaymondCamden.com (2013) (02/25/2013)
Presentation: Browser Tools for Debugging (02/22/2013)
Integrating Parse.com on the Server (02/22/2013)
Upcoming E-Seminar on FusionReactor and ColdFusion (02/21/2013)
Another Lafayette Job - Game Programming Teacher (02/20/2013)
Some examples of Android PhoneGap Config Settings (02/19/2013)
Local Job Opportunity: After Effects Designer - Louisiana (02/18/2013)
Google Map/Directions Mashup (02/18/2013)
Edge Reflow and Edge Inspect get engaged for Valentine's Day (02/14/2013)
Big new releases today - including Reflow (02/14/2013)
Getting a quota error with Google and you've barely touched your limit? (02/13/2013)
Ten Years Ago Today... (02/12/2013)
Quick example of Chrome JavaScript Hot Swapping (02/11/2013)
jQuery Example: Related, hidden selects (02/08/2013)
PhoneGap 2.4.0 Released (02/08/2013)
Job Opening - Duquesne Light (02/07/2013)
Using Ripple for PhoneGap Development (02/06/2013)
Playing with SVG and JavaScript (02/05/2013)
Choose Your Own Application (02/05/2013)
OpenDeviceLab.com (02/04/2013)
Speaking Engagements in February (02/04/2013)
Advice for a Server to Client Side Developer (02/01/2013)
Latest presentations and materials (01/31/2013)
A walkthrough of some basic jQuery help (01/28/2013)
Job Opening - Multiple (01/25/2013)
Tip for PhoneGap Users - Modify the WWW template (01/24/2013)
TechLive Presentation - HTML5 Storage (01/24/2013)
W3Conf (San Francisco February 21-23) (01/23/2013)
Using ColdFusion to check available disk space (01/22/2013)
Did you know - Safari Remote Debugging and PhoneGap (01/21/2013)
FYI - iOS, JavaScript, and inactive tabs (01/20/2013)
Old School CFCHART Tip (01/18/2013)
Transcripts from Open PhoneGap Session (01/17/2013)
Quick Tip: Running WebSQL commands in Chrome Dev Tools (01/16/2013)
PhoneGap Sample - Shake to Roll (01/15/2013)
Adobe Developer Connection - Email signup (01/14/2013)
Sunday OT Post: Yes, I know it isn't Sunday... (01/14/2013)
Chrome Extension for Microdata (01/11/2013)
Win a free copy of the PhoneGap Mobile Application Development Cookbook (01/10/2013)
CFImage and paths with spaces (01/09/2013)
New Lafayette Meetup - Louisiana Hackathons & Jams (01/06/2013)
ColdFusion Job Opening - Luther Consulting, LLC (01/04/2013)
Adobe Developer Connection in 2012 (01/04/2013)
ColdFusion Quickie - Turning a set of XML nodes into a string. (01/03/2013)
Speaking Engagements in January (01/02/2013)
First doc sprint in Europe for WebPlatform.org (01/02/2013)
Most-viewed blog entries of 2012 (thanks Charlie!) (12/29/2012)
Enough presentations to last you till next year... (12/28/2012)
For your post-Christmas hangover, another CanIUse Mashup (12/26/2012)
Newsletters You Need (12/21/2012)
ColdFusion News (12/19/2012)
W3C and the HTML5 Spec (12/18/2012)
An example of history management in the browser (12/17/2012)
New Site: Adobe TechLive (12/17/2012)
Another proof of concept - MockData (12/13/2012)
ColdFusion Job Opening - Western New England University (12/12/2012)
New Chrome Extension - Kittenify (12/11/2012)
ColdFusion Platform Survey (12/11/2012)
Sunday OT Post: Transformative Media (12/09/2012)
ColdFusion Job Opening - Clear Capital (12/08/2012)
ColdFusion Job Opening - Job Opening at NC State University (12/06/2012)
ColdFusion 10 REST and Self-Documentation (12/06/2012)
Interesting Links (12/05/2012)
Recording and assets from my ColdFusion 10 REST Presentation (12/05/2012)
Dynamically skipping animations in Edge Animate (12/04/2012)
Book Review: The Cross Browser Handbook (12/04/2012)
Simple Google Maps demo with Custom Markers - Followup (12/03/2012)
Presenting tomorrow on ColdFusion 10 and REST (12/03/2012)
Simple Google Maps demo with Custom Markers (12/01/2012)
Coming soon (like tomorrow) - 24 ways (11/30/2012)
Friday Puzzler: Split the Bill (11/30/2012)
Web Job Opening in God's Country (AKA Lafayette) (11/28/2012)
Reading Microdata Elements in Chrome (11/26/2012)
ContentBox Holiday Contest (11/26/2012)
Sunday Mega Video Game Review (11/25/2012)
ColdFusion Job Opening - Infinite Web Design (11/20/2012)
HTML5 Hacks Released (11/19/2012)
CFHOUR requesting donations for Hurricane Sandy victims (11/19/2012)
Testing Globalization Support in PhoneGap 2.2 (11/15/2012)
POC: Integrating a Chrome Extension with Adobe Edge Animate (11/14/2012)
Want to learn more about the Edge Tools? (11/14/2012)
Dynamically loading a style sheet based on weather conditions (11/12/2012)
Want another option to learn PhoneGap? (11/08/2012)
Released: Learn CF in a Week (11/08/2012)
Data-driven Edge Animate projects (11/07/2012)
Proof of Concept - An Edge Inspect Screenshot Viewer (11/06/2012)
Sending data to the server with HTTP? Size matters (11/05/2012)
Bored today? Do a quick survey! (11/04/2012)
Friday Puzzler: Sieve of Eratosthenes (11/02/2012)
Some tips for working with Data Import Handlers in ColdFusion 10 (11/01/2012)
Adding Parse.com User support to your PhoneGap application (10/31/2012)
ColdFusion Job Opening - Catholic University (10/29/2012)
The movies that scared the crap out of me... (10/28/2012)
Building a Parse.com Enabled PhoneGap App - Part 5 (10/24/2012)
Curious about Edge Inspect? (10/24/2012)
Broken Promises of HTML5 - by Christian Heilmann (10/23/2012)
Stop using jQuery!! (all the time...) (10/23/2012)
Simple POC - Dynamically select an element from a list and skip the last chosen (10/22/2012)
CFCAMP 2012 (10/22/2012)
Adding mouse click navigation to Reveal.js (10/20/2012)
CFML Weekly Launches (10/19/2012)
Enable CORS for ColdFusion Services (10/17/2012)
Third Update to ColdFusion 10 Released (10/16/2012)
Experiment - Build your own stock market AI (10/15/2012)
Displaying iCal data in PhoneGap? (10/12/2012)
Going to Germany for CFCAMP - but more importantly - what do I eat? (10/12/2012)
PhoneGap, Parse.com, and Push Notifications (10/10/2012)
My DZone Interview - Embrace the Epic Nerdness (10/09/2012)
Neat little ColdFusion 10 REST Trick (10/05/2012)
ColdFusion 10 WebSockets, Selectors, and canSendMessage (10/04/2012)
Missed NCDevCon? Watch the entire thing online now - in your underwear (10/03/2012)
Upcoming Test the Web Forward Hackathons (10/02/2012)
Brackets Extension for CanIUse (10/01/2012)
Some Brackets Extension Tips (10/01/2012)
WebGL: Up and Running (09/30/2012)
NCDevCon Resources (09/30/2012)
ColdFusion WebSocket Tip - saving custom client metadata (09/28/2012)
Two ColdFusion 10 WebSocket Experiments (09/25/2012)
Adobe and Create the Web - Round up so far (09/24/2012)
Join us tomorrow for the Create the Web livestream (09/23/2012)
Tales from the Trenches - Swapping Libraries (09/22/2012)
ColdFusion Job Opening - Lincoln Investment Planning, Inc (09/21/2012)
Numeric HTML fields, keyboards, and zip codes (09/20/2012)
ColdFusion Job Opening - Sales Development Services (09/19/2012)
Looking for a Face.com API replacement? Try ReKognition. (09/18/2012)
Example of a Parse.com JavaScript application with offline support (09/14/2012)
Microsoft WebMatrix - a quick review (09/13/2012)
Updating my CanIUse Mashup with LocalStorage (09/12/2012)
Stealing a Post - How to Ask Me a Question (09/12/2012)
ColdFusion Security Hotfix (09/11/2012)
Video of my HTML5 Storage presentation (09/10/2012)
Update to my Node Blog Engine (09/09/2012)
HDC12 Presentation and Demo Assets (09/07/2012)
SOT: Review of my Everdark Quest (09/06/2012)
Using ColdFusion's Autosuggest? Check your query size (09/04/2012)
Mashups of CanIUse.com data (09/04/2012)
Two ColdFusion links for you... (08/31/2012)
A PhoneGap Build API wrapper in Node (08/31/2012)
Job Shadow Interview (08/30/2012)
Thoughts on Node.js and Express (08/29/2012)
PhoneGap Open Session Transcript (08/28/2012)
Reminder - Open Session on PhoneGap Tomorrow! (08/27/2012)
Example of M3U Support for CFMEDIAPLAYER (08/27/2012)
First release of ColdFire for Chrome (08/24/2012)
PhoneGap Build adds Hydration (08/23/2012)
Proof of Concept - Build a download feature for IndexedDB (08/23/2012)
Two speaking engagements in Omaha (08/23/2012)
Small little Adobe Brackets tweak - remove Smart Indent (08/22/2012)
Adobe announces the Create the Web Tour (08/21/2012)
ColdFusion Job Openings - Phoenix, AZ and Maryland (08/21/2012)
New site - PopularFollowers.com (08/20/2012)
ColdFusion Job Opening - inLEAGUE (08/20/2012)
PhoneGap RSS Reader - Part 5 (08/17/2012)
Open Session on PhoneGap Development (08/16/2012)
getAllTheTexts - simple Apache Tika wrapper (08/16/2012)
Push reveal.js notes into the console (08/15/2012)
Another ColdFusion 10 Closures Post (08/14/2012)
Searching for array elements in IndexedDB (08/10/2012)
Critical Android/PhoneGap issue (08/09/2012)
Resources from my RIACon presentations (08/08/2012)
Charting demos from the RIACon Keynote (08/07/2012)
What tags does your browser support? (2012) (08/06/2012)
WebSocket example with keyword highlighting (08/06/2012)
How to update the Panel DOM in a Chrome Extension Panel (08/03/2012)
Editing notification settings for Twitter on Android (08/03/2012)
Using jQuery to load HTML and filter it by N selectors (08/02/2012)
Got a new Chrome? Got a joystick? Check out the Gamepad API (08/01/2012)
Best of ColdFusion 10 Contest - The Winners! (08/01/2012)
Recording from Web+Mobile DevCon Presentation (07/30/2012)
Example of form validation in a jQuery Mobile Application (07/30/2012)
Guest Blog Post: Shipping a populated SQLite DB with PhoneGap (07/27/2012)
How I debugged a Flash-based uploader issue (07/26/2012)
Good example of practical microdata (07/25/2012)
ColdFusion Job Opening - Fairfax County Schools (07/24/2012)
Adding a background image to a reveal.js presentation (07/23/2012)
Preventing navigation to a page in jQuery Mobile (07/19/2012)
Guest Blog Post: Solr in a multi-instance setup (07/17/2012)
Firefox bug(?) with DOM Manipulation (07/17/2012)
Speaking at Mobile + Web Devcon (07/16/2012)
How to add a panel to Chrome Dev Tools (07/15/2012)
LocalStorage Example: Storing previous searches (07/13/2012)
Video from PhoneGap presentation (07/13/2012)
Windows 7 version of PhoneGap/Cordova (07/12/2012)
What a Klout Perk looks like (07/12/2012)
Slides and code from my Nashville presentation (07/11/2012)
Quick tip for getting Adobe Shadow working in certain Wi-Fi environments (07/10/2012)
Article posted to HTML5Rocks - Databinding UI Elements with IndexedDB (07/09/2012)
Speaking in Nashville on PhoneGap and Web Debugging (07/08/2012)
Simple JavaScript number format function, and an example of Jasmine (07/06/2012)
Adobe hosted online ColdFusion presentations (07/05/2012)
The Online ColdFusion Meetup Returns (07/04/2012)
ColdFusion page timeouts and scheduled tasks (07/03/2012)
Proof of Concept - Updating news items dynamically (07/02/2012)
ColdBox Developer Week (07/01/2012)
PhoneGap 1.9 Released (06/29/2012)
Slides and code from presentation at jQuery Conference (06/28/2012)
Best of ColdFusion 10: MightySpec (06/27/2012)
Dynamically changing jQuery Mobile Buttons (06/26/2012)
Say hello to Brackets (06/25/2012)
Quick Note: PhoneGap Build issue (06/25/2012)
Review: Railsea (06/24/2012)
ColdFusion and Pagination - Six Years Later (06/22/2012)
Ask a Jedi: ColdFusion WebSockets and Subchannels (06/22/2012)
Update to my Server-Based Login PhoneGap Demo (06/21/2012)
Best of ColdFusion 10: CFShoutout (06/20/2012)
ColdFusion 10 Missing Feature - Form Fields and Arrays (06/19/2012)
Example of a dynamic HTML5 datalist control (06/14/2012)
ColdFusion 9.0.2 has one CF10 tidbit (06/13/2012)
Posted my first Brackets Extension - CSSLint (06/12/2012)
Issues with IndexedDB and Chrome (06/12/2012)
ColdFusion Developer Week Recordings (06/11/2012)
Spoiler Talk on Prometheus (06/09/2012)
Example of authentication and ColdFusion 10 WebSockets (2) (06/08/2012)
New Chrome Extension: Diablo 3 Server Checker (06/07/2012)
Quick tip for debugging Chrome Extensions (06/06/2012)
Recording and Assets from WebSockets Presentation (06/06/2012)
Case sensitivity and ColdFusion 10 WebSockets (06/05/2012)
ColdFusion Developer Week is here! (06/04/2012)
Examples of authentication and ColdFusion 10 WebSockets (06/01/2012)
There is a new ColdFusion Builder, right? (05/31/2012)
Best of ColdFusion 10: PDF Protector (05/31/2012)
Example of adding menu support to a PhoneGap Application (05/30/2012)
Seeing the light at the end of the Node (05/30/2012)
New ColdFusion Builder Extension: GistCreator (05/29/2012)
Building an HTML5 Comic Book Reader (05/29/2012)
Sunday Review: Comics I Read (05/27/2012)
Taking ColdFusion Closures all the way to 11 (05/25/2012)
Example of getUserMedia and CSS Filters (05/25/2012)
Best of ColdFusion 10: HTML Email Utility (05/24/2012)
Context Menu Example with jQuery Mobile (05/23/2012)
ColdFusion Developer Week (and graphics) (05/23/2012)
Notes on the ColdFusion 10 EULA (05/22/2012)
Creating watermarked images in PhoneGap (05/22/2012)
Nifty little trick with fileRead and ColdFusion 10 (05/21/2012)
cfObjective 2012 (05/20/2012)
E-Seminar on Slatwall next week (05/18/2012)
Slides, code, from my HTML5 Presentation (05/17/2012)
Important note on availability of ColdFusion 9 (05/17/2012)
Some thoughts on organizing a large jQuery Mobile project (05/16/2012)
ColdFusion 10 Released (05/14/2012)
Adding "Filter as you type" support to IndexedDB (05/14/2012)
Example of invokeAndPublish with WebSockets and ColdFusion 10 (05/11/2012)
Using CFC data with Handlebars (05/11/2012)
Setting up console debugging for PhoneGap and Android (05/10/2012)
Recording, slides, and code from my WebSockets presentation (05/09/2012)
Transcripts from PhoneGap Session (05/08/2012)
Very cool BOF at cfObjective (05/08/2012)
Converting a dynamic web site to a PhoneGap application (05/05/2012)
jQuery Mobile Web Development Essentials - Released (05/04/2012)
Presenting on ColdFusion 10 and WebSockets (05/03/2012)
This is why Adobe Shadow rocks (05/02/2012)
Example of Intents with PhoneGap (05/01/2012)
ADC: Real-world example of the HTML5 FileSystem API (05/01/2012)
Second issue of Appliness Launches (04/30/2012)
"Full" sample of IndexedDB in action (04/30/2012)
Sunday Review: Kingdoms of Amalur (04/29/2012)
Scotch on the Rocks ColdFusion Tour (04/28/2012)
Sample of IndexedDB with Autogenerating Keys (04/26/2012)
How to handle setup logic with IndexedDB (04/25/2012)
What the heck is Application ''? (04/25/2012)
Products Are Hard, May 1 in San Francisco (04/24/2012)
ColdFusion Builder 2.0.1 Extension Updates (04/21/2012)
What do you look for before joining a team? (04/20/2012)
Demo of Handlebars, and why you should consider a templating engine (04/19/2012)
Job Posting: Council for Logistics Research, Inc. (04/18/2012)
Dynamically replacing Gists with raw content for jQuery Mobile (04/14/2012)
jQuery Mobile 1.1 Released (04/13/2012)
Tracking application usage with PhoneGap (04/13/2012)
PhoneGap hits 1.6 (04/11/2012)
Security Profile Admin Extension for ColdFusion 10 (04/11/2012)
ColdFusion Job Opening - Goodville Mutual (04/09/2012)
Face detection with getUserMedia (04/06/2012)
jsoup adds jQuery-like parsing in Java (04/06/2012)
Using jQuery to conditionally load requests (04/05/2012)
Reminder - Best of ColdFusion 10 Contest! (04/05/2012)
Chrome Dev Tools and WebSQL (04/04/2012)
Adding database synchronization to your PhoneGap project (04/03/2012)
Open Discussion - Learning a scripting language (04/02/2012)
Two new PhoneGap videos for your enjoyment (04/02/2012)
Reminder - Use the proper jQuery Mobile event handler (04/01/2012)
ColdFusion Job Opening - Football Nation (03/29/2012)
Revealing ColdFusion exceptions hidden by try/catch (03/29/2012)
How I cheated Mozilla's new HTML5 Game (03/28/2012)
Adobe launches Appliness (03/28/2012)
Simple date math to get the Sunday for a given date (03/27/2012)
Example of Autocomplete in jQuery Mobile (03/27/2012)
Open Discussion - Additional methods in Application.cfc (03/26/2012)
ColdFusion Job Opening - Greater Media Charlotte (03/24/2012)
HTML5 Form Validation with Style (03/23/2012)
DevNexus Presentation Assets (03/21/2012)
HTML5 Form Validation - The Constraint Validation API (03/19/2012)
Please read this plea for help from a reader (03/18/2012)
A look at HTML5 Form Validation (03/16/2012)
Slides, code, and recording from my PhoneGap Presentation (03/14/2012)
Adding click support in ColdFusion 10 Charting (03/14/2012)
Security hotfix available for ColdFusion (03/13/2012)
Simple JavaScript template system at WhichElement (03/13/2012)
ColdFusion Job Opening - Senior ColdFusion Developer (03/12/2012)
Rough guide to building Android PhoneGap apps from the command line (03/12/2012)
Coming soon... (03/10/2012)
PhoneGap's File API (03/09/2012)
Avoid ColdFusion Scope Names as Arguments (03/08/2012)
Adobe Shadow (03/07/2012)
RIACon 2012 - Call for Speakers, Change of Venue (03/06/2012)
ColdFusion 10 presentation slides and code (03/06/2012)
ColdFusion 10 Web Socket Demo - Whiteboard (03/05/2012)
Some thoughts on Windows Phone (and Windows 8 in general) (03/05/2012)
Web Sockets with server side logic (2) (03/02/2012)
Interesting PhoneGap/Android crash (03/01/2012)
Introduction to ColdFusion 10 - Next Tuesday (03/01/2012)
Web Sockets with server side logic (02/29/2012)
Best of Adobe ColdFusion 10 (Beta) Contest (02/29/2012)
Working with HTML5's multiple file upload support (02/28/2012)
ColdFusion 10 Image Updates (02/28/2012)
How to add MySQL time zone tables on Windows (02/27/2012)
ColdFusion Job Opening - Top of Mind Networks (02/27/2012)
ColdFusion 10 - Admin Audit Log (02/27/2012)
Changes to defaults in ColdFusion 10 (02/26/2012)
Server Downtime / ColdFusion 10 demos (02/25/2012)
Getting URL parameters in a jQuery Mobile page (02/24/2012)
ColdFusion 10 Beta Hosting (02/24/2012)
Your security lesson for the day - Console is the MCP (02/23/2012)
ColdFusion 10 Web Socket JavaScript APIs (02/23/2012)
ColdFusion Job Opening - Air Methods Corporation, Englewood CO (02/22/2012)
jQuery Mobile Cookbook call for authors (02/22/2012)
Determining the HTTP request method in ColdFusion (02/22/2012)
ColdFusion 10 Web Socket Demos (02/20/2012)
ColdFusion 10 Demo Dump (02/18/2012)
ColdFusion 10 and ColdFusion Builder 2.0.1 Public Betas (02/17/2012)
Quick demo of accessing XML data with jQuery (02/16/2012)
Adding Internationalization/Localization Support to Web Applications (02/15/2012)
Tell MS Word to stop pasting in styles (02/14/2012)
Make your Android PhoneGap app less scary (02/13/2012)
Shortening a string by removing text in the middle (02/11/2012)
Adobe eSeminar on ColdFusion and Monitoring (02/08/2012)
ColdFusion offer from Intergral (02/07/2012)
Job Opening for ColdFusion Developer at Arizona State University (02/04/2012)
Job Opening for Sr. ColdFusion Developer in CA/ San Fernando Valley (02/03/2012)
Update to my highlight/fadeout example - now with CSS hotness (02/03/2012)
Creating a highlight/fadeout text effect on a tag cloud (02/02/2012)
Generate a tag cloud from an RSS feed with ColdFusion (02/01/2012)
Reminder - Adobe Cookbooks (02/01/2012)
RIACon 2012 (01/30/2012)
Bad use of tablet space - an example (01/30/2012)
Searching across all resources in Chrome (01/27/2012)
A look at JavaScript Form Validation (01/27/2012)
A database utility class for PhoneGap (01/26/2012)
New Adobe Inspire Magazine out (with an article by yours truly...) (01/25/2012)
ColdFusion Position at Adobe (01/24/2012)
Detecting invalid HTML with JavaScript (01/23/2012)
ColdFusion Koans (01/23/2012)
Two CFGRID Examples: Related grids and updating checkboxes (01/22/2012)
Downloading files to a PhoneGap application - Part 2 (01/20/2012)
ColdFusion opportunity at the Catholic University of America (01/19/2012)
Quick tip - using cfthrow as a reminder (01/18/2012)
CF101: Adding an API to your site (01/18/2012)
(Still) Looking for a ColdFusion job? (01/17/2012)
What do you need to get for mobile development? (01/16/2012)
Demo of Color Palettes and PhoneGap (01/13/2012)
Working with the battery in a PhoneGap application (01/13/2012)
How to get your ColdFusion Builder 2 Serial (01/12/2012)
ColdFusion Zeus POTW: queryNew/queryAddRow (01/11/2012)
Using a server, or session storage, to persist form values (01/10/2012)
Important ADC article on ColdFusion and Security (01/09/2012)
Example of callback URL support in ColdFusion Builder (01/09/2012)
E-Seminar on Tuesday - RIAForge (01/09/2012)
Some thoughts from the mobile workshop yesterday... (01/08/2012)
Job Posting: Simpleview, inc (01/07/2012)
Code+Slides from jQuery Mobile Presentation (01/07/2012)
Working with dates and SQLite in PhoneGap (01/06/2012)
ColdFusion Zeus POTW - XPath/XLST Updates (01/05/2012)
Converting XML to JSON - My exploration into madness... (01/04/2012)
Looking for a ColdFusion job? (01/04/2012)
Parse.com - dynamic data storage for mobile (01/03/2012)
Speaking in San Francisco this weekend (01/03/2012)
Creating a fade/toggle/change effect in jQuery (01/02/2012)
How I debug JavaScript issues (12/30/2011)
The future of BlogCFC (12/29/2011)
Business logic in a PhoneGap app (12/27/2011)
Zeus on the ColdFusion Meetup (12/26/2011)
Using DDX and CFPDF to set the initial page for a PDF (12/23/2011)
jQuery Mobile course available on Udemy (12/23/2011)
ColdFusion Zeus POTW - Extra edition again... (12/22/2011)
ColdFusion + jQuery example (12/21/2011)
ColdFusion Zeus POTW - Extra edition... (12/20/2011)
Suggestions for learning mobile development? (12/20/2011)
ColdFusion Zeus POTW: CallStack (12/19/2011)
Two followup jQuery Mobile questions (12/15/2011)
Recording and Slides from jQuery Mobile presentation (12/15/2011)
Updating buttons in jQuery Mobile (12/14/2011)
Presenting on jQuery Mobile - online - for free (12/12/2011)
Proof of Concept - Working with Remote PDF Data (12/10/2011)
Yes, you're in the right place (12/09/2011)
Working with Google and OAuth2 (12/06/2011)
PhoneGap and constants (12/05/2011)
ColdFusion Zeus POTW: Application Metadata (12/05/2011)
Adding voice-based search to a PhoneGap app (12/02/2011)
Friday Puzzler: Pi - it's what's for dinner (12/02/2011)
Check out GeoNames (11/30/2011)
ColdFusion, Solr, and Title Searches - an FYI (11/30/2011)
My first AngularJS application (11/29/2011)
Work with ColdBox and win a Kindle Fire! (11/28/2011)
ColdFusion Sample - Using CFZIP (Again) (11/27/2011)
ColdFusion Sample - Using CFZIP (11/26/2011)
Happy Thanksgiving (11/24/2011)
Note from a .Net programmer getting into ColdFusion (11/23/2011)
Demo of a multi-step form in jQuery Mobile (Part 2) (11/22/2011)
Book Review: Web Development Recipes (11/22/2011)
Building a Twitter Search that highlights important tweets (11/21/2011)
Some PhoneGap samples (11/20/2011)
Demo of a multi-step form in jQuery Mobile (11/18/2011)
jQuery Mobile Released! (11/18/2011)
Working with Scoreoid's Game API (11/17/2011)
Some Canvas Experiments (11/16/2011)
Motorola's App Testing Program (11/15/2011)
ColdFusion Zeus POTW: Total and Free Disk Space (11/15/2011)
How to give dynamic driving directions to your customers (11/14/2011)
ColdFusion's JSON Prefix feature - more than AJAX (11/13/2011)
Cool Edge example (11/11/2011)
Friday Puzzler: The Quest for Foo (11/11/2011)
Ask a Jedi: Sharing a shopping cart between multiple (related) sites (11/10/2011)
Example of server-based login with PhoneGap (11/10/2011)
Using the Chrome JavaScript Debugger (11/09/2011)
Adobe TV Video - Debugging Tips for ColdFusion (11/08/2011)
Handling JSON with prefixes in jQuery and jQueryUI (11/08/2011)
Face.com API released (11/07/2011)
Open Discussion - Separate content versus CSS for mobile sites (11/07/2011)
Latest Mobile app - WTFRU (11/04/2011)
PhoneGap Orientation Example (11/04/2011)
HTML5 Data Attribute Example (11/03/2011)
PhoneGap file upload to ColdFusion (11/02/2011)
Mobile app show and tell on Friday (11/02/2011)
What I want from an App Store (as a developer) (11/01/2011)
jQuery Mobile Reference Guide (11/01/2011)
ColdFusion Zeus POTW: Cookie via Script (10/31/2011)
Using jQuery to create a dynamic time countdown (10/30/2011)
Intro to jQuery slides + code (10/28/2011)
Example of Flex/AIR - Greg's Toolkit (10/28/2011)
Quick survey for ColdFusion Users (10/27/2011)
Attending my ColdFusion session at RIAUnleashed? (10/26/2011)
ColdFusion Ad Server updated (10/25/2011)
Responding to tab changes with CFLAYOUT (10/25/2011)
Add server uptime to the ColdFusion Administrator (10/24/2011)
FusionAnalytics Released (Finally!) (10/24/2011)
Review: Dead Island (10/23/2011)
Updating Death Clock for Flex 4.6 (10/21/2011)
Quick Example - Parsing USGS Earthquake Data (10/21/2011)
Example of PhoneGap's Database Support (10/20/2011)
Pakt running "jQuery Month" (10/20/2011)
Example of console debugging with Weinre and PhoneGap (10/19/2011)
Two new ColdFusion Resources (10/19/2011)
Enabling automatic back buttons in jQuery Mobile (10/18/2011)
Speaking tomorrow at the Cleveland Adobe User Group (10/18/2011)
Postmark release free Spam API (10/17/2011)
ColdFusion Zeus POTW: CFINCLUDE Improvement (10/17/2011)
Is this a bug with ColdFusion Spreadsheet functionality? (10/14/2011)
Friday Puzzler: The Days of The Week (10/14/2011)
Determining the ColdFusion Default, and Max, Session timeouts with code (10/13/2011)
Recording, slides, and code from my Flex and ColdFusion Presentation (10/13/2011)
First test of PhoneGap Plugins (10/12/2011)
PhoneGap RSS Reader (10/11/2011)
Playing with PhoneGap? Make your projects even easier (10/11/2011)
Experiment with Mobile Adsense (10/10/2011)
"My Database View" ColdFusion Builder Extension (10/09/2011)
Commenting (via Disqus) returns to CFLib (10/09/2011)
LESS Tester (10/07/2011)
E-Seminar on Tuesday - Flex and ColdFusion (10/07/2011)
MAX 2011 (10/07/2011)
My MAX Preso - the future of ColdFusion (10/04/2011)
Playing with PhoneGap? Try the Mega Demo (10/04/2011)
Lafayette Mobile Jump Start (10/01/2011)
ColdFusion Sample - Multi-Step Forms (09/30/2011)
Quick video demo of using Flash Builder to inspect remote data results (09/27/2011)
Why is my Ajax not working? (09/26/2011)
Quick tip for Android users - change your user agent (09/25/2011)
Tracking application usage with Flex Mobile (09/24/2011)
Simple Canvas Experiment (09/23/2011)
Friday Puzzler: Family Tree Simulation (09/23/2011)
Couple of Adobe AIR announcements, and a reminder... (09/21/2011)
Slides, code, etc from my NCDevCon Presentations (09/18/2011)
ColdFusion 9.0.1 CHF 2 Released (09/16/2011)
Generating EML files with ColdFusion (09/16/2011)
Google+ API Released (09/15/2011)
My first Chrome Extension (09/15/2011)
Detect window close/reload versus exit (09/14/2011)
Slides, code, recording, beer, from my ColdFusion Components presentation (09/13/2011)
Get cookie metadata in ColdFusion (09/13/2011)
Live response to email verification - Ajax based proof of concept (09/12/2011)
Using Local Storage to keep a draft of form data (09/11/2011)
Quick example of script-based FTP operations (09/10/2011)
ColdFusion/Solr Slides and Recording (09/09/2011)
Flex for Mobile - VPN? Secure connections? (09/07/2011)
Galleon Forums 2.5.0 (09/07/2011)
Adobe AIR 3.0 Release Candidate - Huge News (09/06/2011)
Check out Adaptive Images (09/06/2011)
Reminder - there is more to the CGI scope than what the dump shows (09/03/2011)
Crazy Flex, Mobile, ColdFusion, BlazeDS experiment (09/02/2011)
Finally tried a NoSQL server... and it's kinda cool (09/02/2011)
Using ColdFusion and Ajax to check for an existing database record (with jQuery) (09/01/2011)
Using ColdFusion and Ajax to check for an existing database record (08/31/2011)
ColdFusion and Professional Grade Tools (08/31/2011)
Spock sneak peak / geolocation example (08/30/2011)
New content for Adobe Developer Connection (08/29/2011)
Note to self about Server-Sent Events (08/29/2011)
Latest Nook App - TBS Horoscope (08/28/2011)
Quick tip with cfpop and debugging (08/27/2011)
Making jQuery Mobile templates even easier - with ColdFusion (08/26/2011)
query, dump, query, dump - is this better? (08/25/2011)
FusionReactor Update (08/25/2011)
Even more ColdFusion sessions... (08/24/2011)
Using a background with a Flex Mobile project (08/24/2011)
Adobe ColdFusion Developer Week (08/23/2011)
jQuery Quickie - Noticing ctrl/shift keyboard events (08/23/2011)
Ask a Jedi: Printing data by column in ColdFusion (08/22/2011)
Indexing PDFs with Solr? Read this tip. (08/22/2011)
Finding dates in a string using ColdFusion (08/20/2011)
Thoughts on developing for the Nook (08/19/2011)
Next presentation - ColdFusion and Solr (08/19/2011)
Flex Mobile Chat Session on Thursday (08/17/2011)
Application Report - ColdFusion Admin Extension example (08/15/2011)
Muse available on Adobe Labs (08/15/2011)
Revisiting an old blog entry - how ColdFusion can help save your business (08/14/2011)
Support for Collection, Index, and Search operations in Script-Based CFCs (08/13/2011)
ColdFusion Sample - Turning a form input into a PDF for email (08/12/2011)
Script based query issue to watch out for (and a fix!) (08/12/2011)
cfcache user? Watch out for this mistake! (08/11/2011)
AIR 3 Beta updated (08/10/2011)
Speaking at NCDevCon (08/09/2011)
Updating my ColdFusion HTML presentation to use jQuery (08/08/2011)
cfpresentation and HTML slides (08/08/2011)
Quick demo of jQuery and Google Maps (08/06/2011)
jQuery Mobile Beta 2 released (and a small demo) (08/04/2011)
My "Don't try this at home" experiment with jQuery UI (08/02/2011)
Query of Query bug involving numbers (08/01/2011)
How I got started in ColdFusion (08/01/2011)
RIAForge update, and a reminder about ColdFusion debugging (07/29/2011)
ColdFusion Unconference - Final Schedule (07/29/2011)
Flex Mobile and ColdFusion Sessions (07/28/2011)
ColdFusion Sample - Searching a RSS Feed for Keywords (07/28/2011)
New ColdFusion site - FaqMe (07/27/2011)
How are Facebook and Google+ creating link previews? (07/26/2011)
Don't make your mobile site a prison (07/25/2011)
Great quote on ColdFusion (07/25/2011)
jQuery Mobile - adding Local Storage (07/13/2011)
Adobe AIR 3 and Flash Player 11 hit Labs (and Sony news!) (07/13/2011)
These are REALLY big pictures of my eyes (07/13/2011)
One more (I swear this is it) follow up to my CFSpreadSheet Example (07/12/2011)
Quick followup to my CFSpreadSheet Samples (07/11/2011)
Sunday Reviews: Strange vocabulary and killer robots (07/10/2011)
Some thoughts on working with CFCs remotely (07/08/2011)
Online CFMeetup celebrating it's 200th meeting (07/07/2011)
Yes - you can develop Flash apps for iOS on Windows! (07/06/2011)
Another regex - simple formatting for comments (07/06/2011)
Quick little regex example - Youtube video from URL (07/05/2011)
Components for script-based search, index, and collection (07/04/2011)
Initial list of speakers and sessions for the ColdFusion Unconference (07/03/2011)
DateDiff and Wholeness (07/01/2011)
Change in debugging with CFCs in ColdFusion 9 (06/30/2011)
Interested in AIR development for the Nook? (06/29/2011)
jQuery Mobile Quick Start and new jQuery class (06/29/2011)
Presentation tonight: Introduction to jQuery Mobile (06/29/2011)
Initiative to improve ColdFusion docs (06/28/2011)
Need to scan ColdFusion code? Try the analyzer (06/28/2011)
Ask a Jedi: Hack for percentage based CFCHART (06/27/2011)
Working with Adobe AIR and Dreamweaver CS 5.5 (06/26/2011)
Flex Mobile/ColdFusion Example - Art Search (06/25/2011)
This weeks winner for the "Bug you will never run into a million years" award (06/24/2011)
jQuery Mobile First Look (06/24/2011)
Slides, code, and recording from my Flex Mobile/ColdFusion presentation (06/24/2011)
Some thoughts on presenting (06/23/2011)
Presenting tomorrow: Flex 4.5 and ColdFusion (06/22/2011)
Using ColdFusion 9's Caching Feature? Watch your keys (06/22/2011)
Deep dive into CFCs and Requests (06/21/2011)
I'm joining Adobe (06/20/2011)
Updates to Flash Builder for iOS and Blackberry (06/20/2011)
Take a look at Angular (06/19/2011)
Talk to me about Green Lantern (non-spoiler) (06/18/2011)
Handling/Testing of Emails in a ColdFusion App (06/17/2011)
FullCalendar jQuery Plugin (06/17/2011)
Best way to handle history autocomplete in a form? (06/16/2011)
Update to CFLib (and a quick trip to the past...) (06/15/2011)
Example of using Chrome Dev tools to solve Ajax issues (06/15/2011)
Can you manually run your ColdFusion's onServerStart CFC? (06/14/2011)
A few simple (and harmless) ColdFusion mistakes (06/13/2011)
ColdFusion Sample - Building a daily scheduled report (06/12/2011)
Two Eclipse search tips (06/09/2011)
Speaking at MAX 2011 - What's Next in ColdFusion (06/07/2011)
Wrapping a call to the Twitter user lookup API with ColdFusion (06/07/2011)
ColdFusion Unconference 2011 call for Speakers (06/06/2011)
Saving images from an RSS feed with ColdFusion (06/06/2011)
ColdFusion Sample - Reading a RSS Feed (06/05/2011)
ColdFusion Spreadsheet Bug with Formulas (06/03/2011)
Real time textual analysis via OpenAmplify (06/02/2011)
Meet the "Zeus" at RIACon (06/02/2011)
ColdFusion Sample - Create an Excel File (06/01/2011)
ColdFusion Sample - Upload and Parse an Excel File (05/31/2011)
Adding Login/Registration to a Flex Mobile project (05/29/2011)
When is it proper to try/catch versus global exception handling? (05/26/2011)
Flex 4.5 List control springing to top? (05/26/2011)
INeedIt - in the market (05/25/2011)
Adobe Developer Week 2011 (05/25/2011)
Extracting bookmarks from a PDF with ColdFusion (05/24/2011)
Adding a real time component to your Flex application (05/23/2011)
jQuery Quickie: On form change update a div (05/23/2011)
Few quick reviews (05/22/2011)
Working with Google Maps in Flex Mobile (05/21/2011)
Short and sweet good news - ColdFusion Unconference is on (05/20/2011)
My Flex Mobile/DPI issue - solved! (05/20/2011)
cfchart and non-American locales (05/19/2011)
When not to use cfcontent (05/18/2011)
INeedIt - Addressing text size issues (05/17/2011)
What's an expert ColdFusion developer? (05/17/2011)
Why (and how) to lock file operations in ColdFusion (05/16/2011)
New DZone reference for ColdFusion Builder 2 (05/16/2011)
Best way to learn JavaScript? (05/15/2011)
INeedIt - Simple Flex Mobile example (05/14/2011)
ColdFusion Builder 2 - View bug (05/13/2011)
Code from the keynote - the Jersey Shore Collection (05/12/2011)
cfObjective Bound (05/11/2011)
Using ColdFusion to add simple content formatting to user input (05/10/2011)
Interesting issue with reserved function names inside CFCs (05/09/2011)
Thoughts on the Xoom and Playbook (05/08/2011)
jQuery Mobile, Phonegap, and remote Ajax calls (05/06/2011)
Soundings 4.0 - Ready for testing (05/06/2011)
Anyone playing with iText and ColdFusion? (05/06/2011)
Related selects in jQuery - an example (05/05/2011)
Mobile developer? Check out Dreamweaver CS 5.5 (05/04/2011)
Getting file information in ColdFusion Builder (or Eclipse in general) (05/04/2011)
Update to CFLib Extension (05/03/2011)
Where is the documentation for ColdFusion Builder 2? (05/03/2011)
Official release of ColdFusion Builder 2, Creative Suite 5.5, Flash Builder 4.5 (05/03/2011)
Dynamic debug templates in ColdFusion? (04/29/2011)
How do jQuery, jQuery UI, and jQuery Mobile fit together? (04/29/2011)
Bug with CFFEED and iTunes podcasting metadata (04/28/2011)
CS5.5 and jQuery Mobile presentations tomorrow (04/27/2011)
ColdFusion Builder 2 adds a Free Edition (04/27/2011)
Bring the Misery Hammer down on your trolls (04/26/2011)
In Cali this weekend? Check out the Flash Camp (04/26/2011)
Video encoding with Zencoder (04/26/2011)
Null, Entities, and CFDUMP (04/25/2011)
Examples of ColdFusion 9 Script Support (04/25/2011)
Issue with callback URLs and ColdFusion Builder 2 Extensions (04/24/2011)
ColdFusion Quickie: Splitting data into columns (04/23/2011)
Good example of a jQuery demo with two rewrites (04/22/2011)
this.datasource versus this.ormsettings.datasource (04/21/2011)
Script based version of CFWDDX (04/21/2011)
Interesting JSON issue to look out for - and a cffileupload bug (04/19/2011)
jQuery Mobile + Google Analytics proof of concept (04/19/2011)
My first jQuery Conference (04/18/2011)
Slides, code from my jQuery Mobile presentation (04/16/2011)
Working with RARs in ColdFusion - Why I did it... (04/14/2011)
Simple introduction to Google Maps Part 2 - Markers (04/13/2011)
Interesting Internet Explorer/Ajax/ColdFusion issue (04/13/2011)
Programmatically select a row in CFGRID (04/12/2011)
Spot the error - it may not be what you think (04/12/2011)
Looking for comments - CFCs for Exceptions (04/11/2011)
Did you know - previousCriteria and cfsearch (04/10/2011)
Stupid experiments with Google Static Maps and ColdFusion Image functions (04/07/2011)
Slides, Recording, Code for my HTML 5 Presentation (04/07/2011)
Workarounds for things not supported in ColdFusion Script (04/07/2011)
Collapsible content and Ajax loading with jQuery Mobile (04/05/2011)
Speaking at the cfObjective Keynote (04/05/2011)
ColdFusion Quickie: Finding all the credit card numbers in a string (04/04/2011)
Presentation on Thursday: A Gentle Introduction to HTML5 (04/04/2011)
Example of jQuery Mobile site using authentication - first round (04/03/2011)
CFC, returnForm, JSON, and content-type (04/02/2011)
Help with a frustrating jQuery UI Tabs issue (04/01/2011)
Joining Apple as Developer Insight/Creative/Knowledge Evangelist (04/01/2011)
jQuery Mobile Alpha 4 Released (plus jQuery core update!) (03/31/2011)
How do you play video on an Android device? (03/31/2011)
ColdFusion Builder Extensions and Long Processes (03/30/2011)
Persistence with ColdFusion Builder Extensions (03/29/2011)
Detecting mobile, and providing a way out (03/28/2011)
Review: Homefront and Bad Company 2 (03/27/2011)
Another experiment in jQuery Mobile swipe navigation (03/26/2011)
Friday Puzzler: Joe's Car Wash and the Cheap Employee Problem (03/25/2011)
Exploring CFDUMP, AKA an Ode to Dump (03/24/2011)
Ask a Jedi: jQuery and ColdFusion 7 (03/24/2011)
New ColdFusion Security resource (03/23/2011)
Thoughts on PhoneGap (03/23/2011)
Creating category specific RSS feeds (03/22/2011)
Quick advice for handling the ColdFusion haters (03/21/2011)
jQuery Blog Aggregator - jQueryBloggers.com (03/20/2011)
Source code for ColdFusionBloggers (03/18/2011)
Mobile version of ColdFusion Bloggers updated (03/18/2011)
builderUtil - tool for extension developers (03/17/2011)
Table not found error when you know it exists? Check your triggers (03/16/2011)
Speaking at the jQuery Conference (03/16/2011)
Outputting a ColdFusion query dynamically (03/15/2011)
Using CAPTCHA in ColdFusion with reload powered by jQuery (03/14/2011)
Using swipe gestures for navigation in jQuery Mobile (03/14/2011)
Building an offline capable mobile web site with jQuery Mobile (03/12/2011)
Better handling of missing files with your web application (03/11/2011)
Frustrating issues with Firefox and offline manifests (03/10/2011)
The right (and wrong) way to package a ColdFusion Builder extension (03/10/2011)
Flex aggregator updated... (03/09/2011)
Adding driving directions to a jQuery Mobile web site (03/09/2011)
ColdFusion Builder extensions - Assigning multiple handlers to one file (03/07/2011)
ColdFusion Security Resources (03/07/2011)
jQuery Mobile presentation (03/04/2011)
Video on ColdFusion Builder 2 Extension Enhancements (03/03/2011)
ColdFusion X Writeup (03/03/2011)
New public bug base launched (03/02/2011)
Stormy weather.... ColdFusion Builder 2 on Labs (03/02/2011)
Ask a Jedi: Hard coded values - how to handle? (03/01/2011)
cfcache and errors (02/28/2011)
CFBloggers, CFLib updates (02/27/2011)
jQuery Mobile Example - Paged Search Results (02/25/2011)
RIACon Announced (02/25/2011)
Parts of the ColdFusion Server Scope are read only (02/24/2011)
Example of categories and Solr searching (02/24/2011)
Your blog needs... (02/23/2011)
Reminder - there is a maximum number of network connections in your browser (02/23/2011)
ColdFusion: Counting to a number and repeating (02/22/2011)
ColdFusion 9 ORM error: String index out of range: 0 (02/21/2011)
Working with RARs in ColdFusion (02/21/2011)
Did I stutter? (02/20/2011)
National Broadband Map (jQuery Demo) (02/17/2011)
When using ANT to write to the file system, specify a file (02/17/2011)
What tags does your browser support? (02/17/2011)
Offtopic (and NSFW) blog post - Dead Island Trailer (02/16/2011)
ColdFusion, INI files, and comments (02/16/2011)
Simple introduction to Google Maps (02/15/2011)
Ask a Jedi: Strategies for minimizing/customizing resources loaded by a template (02/15/2011)
cfdump ER you may want to vote for (02/14/2011)
Adobe releases FormsCentral (02/14/2011)
Ask a Jedi: SQL showing up in Verity indexes (02/12/2011)
Adding Google Streetview to ColdFusion CFMAP (02/11/2011)
Two quick Application.cfc questions (02/11/2011)
New blog for Adobe/jQuery Partnership (02/10/2011)
ColdFusion S3 Issue with Folders (02/10/2011)
No (MS)Access for you... (02/09/2011)
Updating an HTML/Adobe AIR Application Title (02/09/2011)
Comparing different ways of writing out large amounts of data (02/08/2011)
Security Bulletin for ColdFusion (02/08/2011)
Panel Reminder - 11AM CST (02/08/2011)
ColdFusion S3 Implementation bug with metadata and ACLs (02/07/2011)
When does ColdFusion's Trim function not trim? (02/07/2011)
Using jQuery to search against different types of content (3) (02/06/2011)
Open Connect room today at 4CST (02/04/2011)
CFPanel next week: Why Server Side Developers Should Consider jQuery (02/03/2011)
Working with Base64 representations of strings in ColdFusion (02/02/2011)
Automatically storing changes in a form (02/01/2011)
Using jQuery to search against different types of content (02/01/2011)
jQuery 1.5 Released (01/31/2011)
Getting additional machine information in ColdFusion (01/30/2011)
Ask a Jedi: Concerns about CFGRID performance (01/29/2011)
My InsideRIA Archive (01/28/2011)
Proud to be an Adobe Community Professional for 2011 (01/28/2011)
Yet another charting option - Highcharts (01/27/2011)
ColdFusion and Unscoped Variables (01/26/2011)
Update to my Pie chart with lots of data post (01/26/2011)
Results of ColdFusion's XMLSearch functions are references (01/25/2011)
Ask a Jedi: ColdFusion Pie chart with lots of data (01/24/2011)
Quick thanks (01/24/2011)
Picking randomly but not from the last few choices (01/22/2011)
My biggest regret (in code) (01/21/2011)
Quick Regex example - matching multiple things at once (01/20/2011)
RIAForge Update (01/19/2011)
Personalizing a login form with jQuery and ColdFusion (01/19/2011)
Slides, code from HTML5 Preso (01/19/2011)
Next ColdFusion Panel announced (01/18/2011)
Galleon updated - getTempDirectory issue (01/18/2011)
New (and very annoying) Chrome behavior - blocking access to your own pages (01/13/2011)
jQuery quickie: Reading the contents of form fields in an iframe (01/13/2011)
Diagnosing a CFHTTP issue - peer not authenticated (01/12/2011)
ColdFusion UDFs for Google URL Shortening service (01/10/2011)
jQuery based example of simple shopping cart UI (01/10/2011)
RIAForge Status (looking for help Apache/SVN) (01/09/2011)
ColdFusion Portal updated (01/07/2011)
My Vizio support experience (Updated with a positive outcome!) (01/06/2011)
Creating map previews with jQuery and Google's Static Map API (01/05/2011)
Quick follow up to Modal Dialog Editing post with jQuery and ColdFusion (01/04/2011)
Searching multiple ColdFusion SOLR Collections at once (01/04/2011)
Two ColdFusion Builder videos posted by Adobe (01/04/2011)
A special message from RIAForge's new director of public relations... (01/03/2011)
Ask a Jedi: Example of modal dialog editing with jQuery (01/02/2011)
Calling wrapped ColdFusion custom tags within CFIF blocks (12/30/2010)
ColdFusion Regex example - finding URLs in CSS (12/29/2010)
Providing context help for drop downs with jQuery (12/28/2010)
Merry Christmas (12/24/2010)
Open Discussion - Organizing 19000 Queries (12/22/2010)
Review: WireframeSketcher (12/21/2010)
Thoughts on Tron Legacy (12/20/2010)
ColdFusion Quickie - Adding an average to a line chart (12/20/2010)
Disabling CFC auto documentation (12/20/2010)
Hey you - yes you - I need your feedback (12/18/2010)
ColdFusion driven jqPlot charts (12/17/2010)
Looking for work? FirstComp hiring.. (12/16/2010)
Blackberry version of Hangman (12/16/2010)
Using ReplaceList and null replacements (12/15/2010)
Review: JavaScript Patterns (12/14/2010)
Automating, and customizing, your Android applications (12/14/2010)
Uber Panel Recording URL (12/13/2010)
Review: NOOKcolor (12/10/2010)
Using ColdFusion to find the RSS URL from a web site (12/09/2010)
Ask a Jedi: How to approach moving logic into objects (12/09/2010)
Simple RSS Reader built in AIR for Mobile (12/08/2010)
cfObjective Call for Speakers is open (12/08/2010)
Meeting URL for the Uber Panel (12/07/2010)
Using argumentCollection with AJAX calls - about ajaxProxy (12/07/2010)
Ask a Jedi: Using ehcache with stored procs in ColdFusion (12/06/2010)
Quck Review: Spider-Man Shattered Dimensions (12/05/2010)
Monitor your ColdFusion server... Zelda style (12/04/2010)
Reminder - Uber Panel of ColdFusion Awesomeness (12/03/2010)
Using jQuery to mimic the NYT's new paragraph linking (12/03/2010)
Quick Test - Script Based UDFs (12/02/2010)
ColdFusion Quickie: Tell if a file is being run as a custom tag (12/02/2010)
Testing HTML/AIR support for HTML5 controls (12/02/2010)
AndroidGator.com (12/01/2010)
Quick jQuery Tip - Removing default search text (12/01/2010)
Doozy of a bug to watch out for - ColdFusion ORM, logging, and TailView (12/01/2010)
Ask a Jedi: Automatically selecting certain values with ColdFusion Ajax-bound controls (11/30/2010)
Simple mobile directory browser built with AIR (11/30/2010)
Ask a Jedi: Prevent ColdFusion from deleting log files (11/29/2010)
Broken CFC outline in ColdFusion Builder? Check your HTML (11/29/2010)
What I install (and why) (11/28/2010)
Announcing - The End of the Year ColdFusion Panel of Uber Awesomeness (11/23/2010)
Best alternative to cfcontent for large files? (11/23/2010)
Gracefully handling form posts and session timeouts in ColdFusion (11/22/2010)
Small "policy" change for this blog (11/22/2010)
The end of the ColdFusion Open Source Update (11/22/2010)
Want a copy of ColdFusion Builder? (11/19/2010)
Time to check out the Playbook (11/18/2010)
cfObjective - Call for Topics (11/18/2010)
Open Discussion - Mobile Application Security (11/18/2010)
Very cool Model-Glue/Firebug extension (11/17/2010)
Adding real time suggestions for search with ColdFusion, Solr, and jQuery (11/17/2010)
Ask a Jedi: Stop hiding a ColdFusion error (11/16/2010)
Two ColdFusion/Solr questions (11/15/2010)
Source code plus initial impressions of Android marketplace (11/15/2010)
Determining the original case of form fields in ColdFusion (11/12/2010)
Slides, code from ColdFusion/Solr presentation (11/12/2010)
Just found this - JSLint (11/10/2010)
Install (or update) the Adobe AIR Launchpad (11/09/2010)
Working with a ColdFusion Query in jQuery (11/09/2010)
Food for thought - 10 Beginner Tips from the PHP Masters (11/08/2010)
Two ColdFusion/Solr issues I discovered (11/08/2010)
Review: Transformers - War for Cybertron (11/07/2010)
Quickie AIR for Mobile Geolocation Example (11/05/2010)
ColdFusion 9 Certification announced (11/05/2010)
Ask a Jedi: Preventing logins from other machines (11/05/2010)
First draft of a ColdFusion Spider (11/04/2010)
Using ColdFusion Builder's debugger for Flex and Ajax (11/04/2010)
Rolling your own JSON in ColdFusion? Be careful with returnFormat (11/03/2010)
Best JSON option for folks not running ColdFusion 9 (11/03/2010)
Windows 7 - Lost the notification area (11/03/2010)
Building a simple ColdFusion Token/Template System (11/02/2010)
Interested in Adobe AIR development for Devices? (11/02/2010)
Using argumentCollection with AJAX calls to ColdFusion Components (11/01/2010)
ColdFusion Unconference - 2010 (11/01/2010)
Five minutes to your first mobile AIR Application (11/01/2010)
My first jQuery Mobile experiment (10/30/2010)
MAX 2010 Videos (10/29/2010)
Slides from my MAX presentation: Best Practices of the Modern ColdFusion Developer (10/29/2010)
Ask a Jedi: How do you get just the string value using XPath in ColdFusion? (10/29/2010)
ColdFusion Builder 2 "Storm" - Sneak Peak (10/27/2010)
MAX Day Two (10/26/2010)
ColdFusion Unconference - Schedule Change (10/26/2010)
MAX Day One (10/25/2010)
Simple Example: Sound effects for an HTML/Adobe AIR Application (10/24/2010)
What is the best jQuery Dump option? (10/22/2010)
My First Android Application (10/21/2010)
Determining the version of an HTML-based AIR Application (10/21/2010)
SpoolMail Updated (10/21/2010)
Update to my ColdFusion Mail Throttler (10/20/2010)
Warning about cfgrid bug (10/20/2010)
Using JavaScript to update the browser window title when the user is away (10/19/2010)
A week till MAX - a week till the ColdFusion Unconference (10/18/2010)
Adobe AIR Game - Hamurabi (10/17/2010)
Diagnosing an error - Form entries are incomplete or invalid. (10/15/2010)
Proof of Concept - Throttling automatic emails in ColdFusion (10/14/2010)
Trusted Cache and the VFS (10/14/2010)
Why aren't you using Trusted Cache? (10/13/2010)
Review: Halo: Reach (10/10/2010)
BlogCFC 5.9.7 Released (10/08/2010)
Quick Tip - Restarting ColdFusion at an interval (10/08/2010)
Ask a Jedi: Localization issue with ColdFusion's Datefield control (10/07/2010)
Can't dump? Try a fake dump. (10/06/2010)
Followup to jQuery experiment - autoshortener as a plugin (10/06/2010)
ColdFusion Forums at Adobe (10/05/2010)
Simple jQuery experiment - automatically shortening a long list (10/05/2010)
Another CFLOG/JSON Tip (10/04/2010)
Centering a map when you don't know where to center it (10/02/2010)
Proof of Concept - Turning HTML into an Image (10/01/2010)
Dealing with remote resources in ColdFusion and HTML/JS (10/01/2010)
Quick list of high profile ColdFusion sites (09/30/2010)
Take a look at OpenAmplify (09/29/2010)
Doing Adobe AIR development with HTML? Join this group! (09/28/2010)
Listing your Twitter followers by popularity (using 50 lines of ColdFusion) (09/24/2010)
Null Pointer Error with HQL? Check for this... (09/24/2010)
Galleon 2.4 (09/23/2010)
Presenting next week in Omaha (09/22/2010)
Ask a Jedi: Dealing with messy RSS (09/21/2010)
RIAForge Milestone (09/20/2010)
ColdFusion Cookbook Recipe Drive (09/20/2010)
Building a simple Alert system with Adobe AIR and ColdFusion (09/19/2010)
High Ascii strikes again (with CFMAP) (09/18/2010)
Followup to CFGRID MultiRow Post (09/16/2010)
Handling session timeouts in Ajax applications - Follow up (09/15/2010)
Ask a Jedi: Children custom tags reading data from their parents (09/15/2010)
Adobe Developer Connection - Finding old articles and sending feedback (09/14/2010)
Guest Post: Apple Push Notifications From ColdFusion in Ten Minutes or Less (09/13/2010)
Quick XML tip - inserting HTML into an XML object (09/13/2010)
New ColdFusion Builder Extension - jsonview (09/11/2010)
Baby steps towards impossible (09/10/2010)
Friday Puzzler: Show me the money (09/10/2010)
Example of handling session time outs in an Ajax application (09/08/2010)
Adding support for automated tweets with OAuth (09/07/2010)
Ask a Jedi: Caching "constant" structures? (09/07/2010)
Adobe AIR and Microphone Support (09/03/2010)
Update to my 911 Viewer (09/03/2010)
ColdFusion's Multi File uploader is impacted by debugging (09/01/2010)
Cumulative Hotfix for 901 Released (08/31/2010)
Speaking at RIAUnleashed (08/31/2010)
Small formatting issue with emails sent via ColdFusion 9 Mail.cfc (08/28/2010)
CF901 CFGRID's new multirowselect feature (08/28/2010)
ColdFusion Unconference - Sessions Announced (08/27/2010)
Select boxes that limit other select boxes (08/26/2010)
Is HTMLEditFormat enough? (08/26/2010)
ColdFusion Administrator bug with mappings (08/24/2010)
Can a web action fire off an AIR event? (08/23/2010)
Win a copy of ColdFusion Builder and support a great cause (08/23/2010)
ColdFusion Quickie - Leaving an include (08/23/2010)
HTML-based AIR Applications can do video (08/20/2010)
Quick question for Galleon users (08/20/2010)
Please stop using Flash Forms (08/19/2010)
HTML/Adobe AIR Application Diversion Three - Add ActionScript to your HTML (08/17/2010)
Opportunity to learn about Git (08/16/2010)
Second example of an HTML-powered AIR application (08/15/2010)
Adding timezone detection for Adobe Groups (08/14/2010)
Limiting individual file sizes in the Ajax based uploader in ColdFusion 9 (08/13/2010)
Share Your (Code) Pride (08/13/2010)
Recording from Adobe AIR/HTML/jQuery/ColdFusion Presentation (08/12/2010)
Cool Adobe resource for Chrome users (08/11/2010)
Yet one more YQL demo - Term extraction from CFBloggers (08/11/2010)
Lighthouse Pro adds stored filters (08/11/2010)
ColdFusion Security Hotfix Released (08/10/2010)
Ask a Jedi: Modify cfchart to remove commas from y-axis (08/10/2010)
Missed me at CFUNITED? Catch my presentation this week (08/09/2010)
ColdFusion Unconference Update (08/07/2010)
HTML/Adobe AIR Application Diversion Two - Data Layout (08/06/2010)
Online ColdFusion docs updated for CF901 (08/06/2010)
HTML/Adobe AIR Application Diversion One - User Login (08/05/2010)
First example of an HTML-powered AIR Application (08/04/2010)
Video of CFUN Presentation on Adobe AIR HTML Applications (08/04/2010)
Building your first HTML/Adobe AIR Application - Using Aptana (08/03/2010)
Nice Lighthouse Pro update (08/03/2010)
Building your first HTML/Adobe AIR Application (07/31/2010)
Some ColdFusionBloggers.org Guidelines (07/30/2010)
Slides + Code from CFUNITED10 (07/29/2010)
Announcing CFAM - ColdFusion Administrator Mobile (07/28/2010)
Interesting bug to watch out for involving cfqueryparam and sql (07/27/2010)
Three ways to sign URLs for Amazon Web Services (07/27/2010)
jQTouch Notes (07/25/2010)
CF901: Changes to the multi file uploader (07/22/2010)
Not happy with the CF901 JSON Changes? (07/21/2010)
Custom grid renderers with CFGRID (2) (07/20/2010)
CF901: Logging enhancements (07/20/2010)
CF901: Solr is (once again) the bomb (07/19/2010)
Ask a Jedi: Foreign text over CFDIV (07/19/2010)
Show me a better way: Inserting date/time strings into SQLite via HTML and Adobe AIR (07/17/2010)
Example of Ajax-based address verification with ColdFusion and jQuery (07/16/2010)
Odd ColdFusion Ajax binding error? (07/15/2010)
CF901: Guide to Amazon S3 support in ColdFusion 9.0.1 (07/15/2010)
CF901: File upload support in cfscript (07/14/2010)
CF901: CFDump Update (07/13/2010)
ColdFusion 9.0.1 Released (07/13/2010)
Ask a Jedi: Disabling form submission when using ColdFusion Ajax Binding (07/10/2010)
Quick example of jQuery Templates (07/09/2010)
Another simple jQuery/ColdFusion example (07/09/2010)
Getting Started with ColdFusion Security (07/08/2010)
Ask a Jedi: Questions on the VFS (07/07/2010)
Proof of Concept - Remembering preferences in ColdFusion Builder Extensions (07/06/2010)
Adding print support to ColdFusion Builder Extensions (07/02/2010)
Recording, slides and bits from todays presentation on CFBuilder (07/01/2010)
Hackin' the MAX Scheduler (06/30/2010)
Flash Remoting, onCFCRequest Issue (06/30/2010)
Presentation tomorrow: Building CFBuilder Extensions (06/30/2010)
CFUNITED T-Shirt Contest! (06/29/2010)
CF101: Splitting a string into parts using ColdFusion (06/29/2010)
Generate Random Data CFBuilder Extension (06/28/2010)
Tour de ColdFusion Beta (06/28/2010)
Building the map view for Adobe Groups (06/22/2010)
New ColdFusion Ref Card from DZone (06/22/2010)
MAX Sessions posted (06/22/2010)
How to use one remote method in Flex for multiple "clients" (06/21/2010)
Survey on the Future of ColdFusion (06/21/2010)
RIAForge Restored (06/21/2010)
RIAForge Downtime (06/20/2010)
Quick Eclipse Tip - "Refresh the file and stop fracking bugging me" (06/19/2010)
Scary little CFFEED Bug (06/18/2010)
Settings cookies (with expiration, etc) in CFScript (06/17/2010)
ORM Scanner Extension (06/17/2010)
Quick example of RSS URL checking with jQuery and ColdFusion (06/16/2010)
Review: Object-Oriented JavaScript (06/15/2010)
Spell checking in ColdFusion? (06/14/2010)
Ask a Jedi: Using links to select tabs in jQuery UI Tabs (06/11/2010)
Recording and Slides from SQLite presentation (06/11/2010)
Adobe AIR 2 + Flash Player 10.1 Released (06/10/2010)
Presentation tomorrow: Beginning SQLite Database Development for AIR (06/09/2010)
Quick look at Visustin (06/09/2010)
Google Storage for Devs - how compatible with S3? (06/08/2010)
ColdFusion 9.0.1 Sneak (06/08/2010)
Interesting change with listToArray from ColdFusion 8 to 9 (06/04/2010)
Automating watermarking of images with ColdFusion (06/04/2010)
Ask a Jedi: Composite, Dynamic Views in Model-Glue? (06/02/2010)
Linking dynamic content to Wikipedia (06/01/2010)
Scotch on the Rocks 2010 (and other random ramblings) (05/30/2010)
Very cool trick - CFBuilder extensions and Firebug Lite (05/27/2010)
Turning a form into a multistep process with jQuery (05/26/2010)
Two CFBuilder Extensions (05/25/2010)
Scotch on the Rocks Preso and Files (05/24/2010)
Example of jQuery loading form fields (05/24/2010)
Two new ColdFusion 9.0.1 Gems (05/24/2010)
Congrats to Akbar and the AppCore Creator (05/22/2010)
Ask a Jedi: Dynamic math? (05/21/2010)
CFBuilder Contest: Final Thoughts... (05/20/2010)
SciFi BOF @ CFUNITED (05/20/2010)
First update to ColdFusion Builder Released (05/20/2010)
Ask a Jedi: Using ColdFusion Image functions and ImageUtils to create dynamic banners (05/19/2010)
Important BlogCFC update - thanks to ProCheckup (05/19/2010)
CFBuilder Contest: Gilt (05/18/2010)
Attending my second SOTR presentation next week? Read this. (05/18/2010)
jQuery Autocomplete and HTML (05/17/2010)
Bug with local scope, cfthread, and ColdFusion 9 (05/13/2010)
CFBuilder Contest: AppCore Creator (05/12/2010)
New ColdFusion Security Bulletin (05/11/2010)
Good news on the ORM front (05/11/2010)
ColdFusion Builder Extension Developer Group (05/10/2010)
Galleon ColdFusion Forums 2.3.1 (05/10/2010)
Simple jQuery/ColdFusion form example (05/08/2010)
Sometimes it's the small mistakes... (2) (05/08/2010)
CFBuilder Contest: Base64 Image Converter (05/07/2010)
Help me pick a PC... (05/07/2010)
ColdFusion 9, Caching, IP_ADD_MEMBERSHIP Error (05/06/2010)
CFBuilder Contest: Pastebin (05/05/2010)
Ask a Jedi: Dynamic Updates for CFMEDIAPLAYER (05/05/2010)
Help (05/04/2010)
Best Photoshop Content Aware Demo Ever (05/04/2010)
CFBuilder Contest: Squeezer (05/04/2010)
Ask a Jedi: When do you catch errors? (05/03/2010)
Simple jQuery/ColdFusion data loading example (05/01/2010)
Eclipse Tip - Whitespace characters visible when they are turned off (04/30/2010)
Get WACKed (04/30/2010)
Last day for entries in the ColdFusion Builder Contest (04/30/2010)
Can you search a CFGRID? (04/29/2010)
Stupid jQuery Trick - HTML Preview (04/28/2010)
Interesting arraySet Behavior (04/28/2010)
Contact Form Issue (04/27/2010)
Linking Two (or more) jQuery Autocompletes (04/27/2010)
An experiment in combining JavaScript and CSS Requests (04/26/2010)
FYI on ColdFusion Bloggers (04/23/2010)
cfObjective Code and Slides - SQLite and AIR (04/22/2010)
ColdFusion 9.0.1 Sneaks (04/22/2010)
Ouch - this cookie bug has teeth (04/20/2010)
Model-Glue Question - Helpers calling helpers (04/20/2010)
New files in Flash Builder and code hinting/coloring (04/18/2010)
Reminder - Get your entries in for the ColdFusion Builder Contest (04/16/2010)
MAX 2010 Call for Speakers (04/14/2010)
Ask a Jedi: Passing values to ColdFusion's MessageBox (04/14/2010)
Adobe Groups is now ColdFusion (04/13/2010)
Playing with jQuery UI's Autocomplete Control (04/12/2010)
jQuery Quickie: Using a checkbox to enable/disable a row of checkboxes (04/10/2010)
My thoughts on Apple (04/09/2010)
ColdFusion 9 without OpenOffice (04/09/2010)
Some morbid ColdFusion Birthday fun (04/08/2010)
SVNStalker POC (04/07/2010)
Ask a Jedi: Getting the legend from CFCHART (04/07/2010)
ColdFusion 9 fixes arrayIsDefined (04/06/2010)
Detecting CFINCLUDE versus Custom Tag (04/02/2010)
A new path (04/01/2010)
Processing forms with duplicate field names (03/31/2010)
Quick example - updating stuff with CFSLIDER (03/30/2010)
Galleon and Lighthouse Pro updates (03/29/2010)
Adding a preview to CFFILEUPLOAD (03/29/2010)
Tips for folks new to CFBuilder and the Eclipse Platform (03/26/2010)
Friday ColdFusion Contest (03/26/2010)
Yet another CFMAP Demo - Bird Report App (03/25/2010)
ORMScanner CFBuilder Extension (03/24/2010)
Using jQuery to post an array to a ColdFusion Component (03/23/2010)
Three useful ColdFusion Builder links (03/22/2010)
ColdFusion Builder Contest (03/22/2010)
ColdFusion Builder Has Arrived! (03/21/2010)
Video demo of GoogleGeocode (03/20/2010)
Using jQuery to convert text into form fields (2) (03/19/2010)
Quick Review: Clean Code by Robert Martin (03/19/2010)
ColdFusion Quickie - Run something no more than once every N minutes (03/18/2010)
Full ColdFusion Builder Tour Listing (03/18/2010)
How do you do X in CFScript? (03/17/2010)
Ask a Jedi: Click a CFMAP to get Longitude/Latitude (03/16/2010)
JavaScript Tip - Auto Capitalizing (03/16/2010)
Simple CFML Trick - Add logging to ColdFusion Administrator (03/15/2010)
NCDevCon - Looking for speakers on ColdFusion Basics (03/15/2010)
ColdFusion Builder Reference via DZone (03/15/2010)
Coloring CFCHART Dynamically (03/12/2010)
ColdFusion Builder - References (03/12/2010)
ColdFusion Builder - Refactoring (03/10/2010)
ColdFusion Builder - Code Assist for Scoped Variables (03/09/2010)
Ajax Image Uploads (with Previews) (03/08/2010)
Speaking at Scotch on the Rocks 2010 (03/08/2010)
ColdFusion 9 Multifile Uploader - Complete Example (03/05/2010)
Quick Demo - KML and CFMAP (03/03/2010)
Interesting issue with ORM, Model-Glue, and Exceptions (03/02/2010)
ColdFusion Builder Tip - Internal Web Browser (03/01/2010)
Framework One Sample Application - QBall (02/27/2010)
Exploring ColdFusion Builder's Services Browser (02/26/2010)
Doing translations with Twitter (using ColdFusion, jQuery, and AIR) (02/25/2010)
Small ColdFusion Admin Bug (DSN Form and Timeouts) (02/25/2010)
ColdFusion 9 Performance Brief (02/24/2010)
Tweak ColdFusion Builder's Outline Mode (02/23/2010)
Change ColdFusion Builder's Icon (02/22/2010)
CHF Warning - Impacts MXUnit (02/20/2010)
Cumulative Hot Fix for ColdFusion 9 Released (02/20/2010)
Video: Using ColdFusion Builder's SQL Editor (02/19/2010)
Quick Tip: Adding a bookmark to a PDF when it has none (02/19/2010)
ColdFusion Security Bulletin - impacts version 7 through 9 (02/18/2010)
Watch out for "Disable CFC Type Check" (02/18/2010)
A Simple Class Scheduling/Conflict Handler built with ColdFusion and jQuery (02/18/2010)
Modifying a search to enable OR/AND style matches (02/15/2010)
Example of iPhone Geolocation with jQuery (02/12/2010)
Dynamic Dummy Generator (02/12/2010)
Attending CFUNITED? Vote for topics! (02/12/2010)
Two (More) iPhone development tips (also involves ColdFusion Components) (02/11/2010)
Latest update on the CFML Advisory Committee (02/10/2010)
Get 10 more pixels of coding space with CFBuilder (02/10/2010)
Totally useless ActionScript drawing tests (02/10/2010)
Ask a Jedi: Handling a recurring billing date (02/09/2010)
Another ColdFusion Builder Extension example (02/09/2010)
ORM Entity not available? Check your logs (02/08/2010)
Repeat - ColdFusion 9 does NOT remove the need to var scope! (02/08/2010)
AIR 2.0 and Flash 10.1 Betas (02/08/2010)
Looking for ideas on ORM Optimization (Post Launch) (02/05/2010)
Google's Static Map API (02/04/2010)
Cropping to the center of an image (02/03/2010)
Translating from Roman to Decimal Numbers with ColdFusion (02/02/2010)
Example of pagination with jQuery and ColdFusion with "External Buttons" (02/01/2010)
Best of ColdFusion 9 Contest: And the winners are... (01/29/2010)
ColdFusion 9 Security Bulletin (01/29/2010)
Get BIRT-y with Flash and Flex (01/29/2010)
Trouble downloading from RIAForge? Read this (01/29/2010)
One example of dealing with JSON deserialization issues (01/28/2010)
Quick example of table sorting with ColdFusion and jQuery (01/28/2010)
Bug with CFDUMP/output, impacts XML/JSON services (01/27/2010)
The last ColdFusion Builder Extension you will install (01/27/2010)
Some criticisms on Solr in ColdFusion 9 (01/26/2010)
Ask a Jedi: Adding additional text to a CFCHART (01/25/2010)
ColdFusion Quickie: Simple way to cache by arguments passed to a method (01/23/2010)
Getting Component Metadata via CF Builder Extension (01/22/2010)
Be careful with ColdFusion 9's isNull (01/21/2010)
Best of CF9: MuralBuilder (01/21/2010)
Follow up to CFMAP/jQuery/911 Demo (01/20/2010)
Looping over an array with XML objects - CF8 versus CF9 (01/20/2010)
Ask a Jedi: What is Cause and RootCause in ColdFusion exceptions? (01/20/2010)
Proof of Concept 911 Viewer (01/19/2010)
Meet your new Adobe Community Professionals (01/18/2010)
Proof of Concept - CFMAP with Driving Directions (01/18/2010)
Best of CF9: MailClient (01/17/2010)
jQuery 1.4 is Born... (01/14/2010)
Ask a Jedi: Cycling through Charts (01/13/2010)
Best of CF9: Collyba (01/12/2010)
Proof of Concept CFBuilder Extension: convertToCFSCRIPT (01/11/2010)
Review: Need for Speed: Shift (01/09/2010)
Example of ColdFusion 9 Cache Reporting (01/08/2010)
Interesting ColdFusion Ajax Issue(Bug?) (01/08/2010)
Best of CF9: MultiMail (01/07/2010)
Speaking at cfObjective 2010 (01/06/2010)
Change to Scheduled Tasks page in ColdFusion 9 (01/06/2010)
jQuery Quickie: Highlighting a table row after selecting a checkbox (2) (01/05/2010)
Sometimes it's the small mistakes... (01/01/2010)
Model-Glue Documentation Updates (12/31/2009)
Two Oh Oh Nine (12/31/2009)
Best of CF9: Application.cfc Script Template (12/30/2009)
Looking for router/hub advice (12/29/2009)
Best of CF9: Hyrule (12/28/2009)
Changes to an existing ORM entity are automatically persisted. (12/28/2009)
CFMAP and Centering (12/27/2009)
Two great ColdFusion Builder tips (12/24/2009)
UDF to crop and highlight a block of text (12/23/2009)
Tip: cfsavecontent and cfinclude within script based CFCs (12/22/2009)
12 Days of Christmas - Yahoo Style - 2009 (12/22/2009)
Best of CF9: easyImages (12/21/2009)
RIAForge Update - SVN Files/Changelists (12/21/2009)
Looking for help with a bad query (12/21/2009)
Coffee talk about Avatar (12/20/2009)
Best of CF9: PostIt (12/19/2009)
ColdFusion Builder Forums (12/18/2009)
Determining which component called a method in a parent class (12/18/2009)
ColdFusion Builder - Beta 3 Released (12/17/2009)
Best of CF9: Document Repository (12/16/2009)
Having trouble with too many map markers and CFMAP? (12/15/2009)
ColdFusion as a Service Examples - HTML/jQuery (12/15/2009)
RIAForge Updates (12/14/2009)
Using ColdFusion Ajax libraries on a remote server (12/14/2009)
Simple proof of concept - UML Generator (12/14/2009)
Best of CF9: cf_ext_navbar (12/13/2009)
New docs for script functions based on CFCs (12/13/2009)
Working with Dynamic Map Markers in ColdFusion 9 (12/12/2009)
Warning about a Model-Glue Issue (12/11/2009)
Why I use a framework... (12/11/2009)
Best of CF9: CFDungeon (12/10/2009)
Best of CF9: School Directory (12/09/2009)
Quick Tip: Dealing with Freaky Facebook Form Fields (12/09/2009)
Best of CF9: GView (12/08/2009)
Ask a Jedi: Adding Print support for CFMAP (12/08/2009)
ColdFusion 9 ORM Tip - Count related entities (12/08/2009)
Best of CF9: spreadEdit (12/07/2009)
Using DUMP/TOP with ORM CFCs (12/07/2009)
ColdFusion Chart Quickie - Title w/o Border (12/06/2009)
ColdFusion as a Service Examples - Images (12/05/2009)
Flex/AS3 support in TextMate (12/04/2009)
Cumulative Hot Fix 4 for 8.0.1 (12/03/2009)
Getting ORM Stats via the Session and Factory (12/01/2009)
Quick example of posting videos to Brightcove (12/01/2009)
Simple example of processing a form in FW/1 (11/30/2009)
Review: The City & The City (11/29/2009)
Framework One (11/28/2009)
Looking for (mainly) non-American testers for RIAForge (11/27/2009)
Quick Tip - Treating a ColdFusion Query like a Structure (11/25/2009)
Quick TailView Tip (11/25/2009)
Last Reminder - Best of ColdFusion 9 Contest (11/24/2009)
Learning ColdFusion as a Service (11/23/2009)
Ask a Jedi: ColdFusion Autosuggest on 2 Columns (11/22/2009)
Quick example of jQuery/ColdFusion 9 multifile uploader (11/20/2009)
Friday Contest - Time for the smack down (11/20/2009)
Recording for Intro to ColdFusion 9 ORM (11/19/2009)
Quick Tip - CFLOG and JSON (11/19/2009)
New comments policy (11/19/2009)
jQuery Quickie: Highlighting a table row after selecting a checkbox (11/18/2009)
Talking about ColdFusion 9 and ORM Tomorrow (11/18/2009)
Ask a Jedi: Round robin display of data (11/17/2009)
Looking For: Writing ColdFusion in Visual Studio (11/17/2009)
AIR 2.0 Released to Labs (11/17/2009)
"Pretty Dates" with jQuery (ColdFusion example) (11/16/2009)
Home from RIAUnleashed (11/15/2009)
Some notes on CFFILE/UploadAll (11/14/2009)
Exploring CFaaS Presentation (11/13/2009)
Call for Speakers: CFUNITED and cfObjective (11/13/2009)
ColdFusion 9 developer? Grab the 8.0.1 release notes! (11/11/2009)
Important notes about ColdFusion 9's new multi file uploader (11/11/2009)
Very cool ColdFusion 9 Video (11/11/2009)
jQuery/CFDebugging One-Liner (11/10/2009)
Demo of CFWINDOW and jQuery Date Picker (11/10/2009)
Reminder - Best of ColdFusion 9 Contest (11/09/2009)
ColdFusion/ORM Example - Filtering with a many to many (11/07/2009)
Friday Contest: You are CF Dude (11/06/2009)
Ask a Jedi: Name conflicts on file rename/move (11/06/2009)
ColdSpring Presentation - Slides and Code (11/05/2009)
Demo: Using jQuery and perserving UI state (11/05/2009)
Checking for updates to tags/functions in ColdFusion 9 (11/04/2009)
Interesting CFDUMP Bug (11/04/2009)
ColdSpring Presentation (Warning - Rough Draft) (11/04/2009)
BlogCFC 5.9.5 Released (with video) (11/03/2009)
Adobe offering Flex training for ColdFusion developers (11/03/2009)
Fixing the CFFORM Mask/Scroll problem (11/02/2009)
ColdFusion Administrator Extension - Searcher (11/01/2009)
Quick ColdFusion Builder Tip - Make it recognize HBMXML Files (10/31/2009)
Some basic Solr/Verity Differences (10/30/2009)
Ask a Jedi: Add a "Show All" button to CFGRID (10/29/2009)
Building an AIR Spy Application (10/27/2009)
Broken (cf)windows? (10/27/2009)
Ask a Jedi: Formatting times client side (10/27/2009)
Quick ColdFusion/jQuery Google Ajax Language Example (10/26/2009)
Review: Halo 3: ODST (10/25/2009)
Ask a Jedi: ColdFusion Ajax example of retrieving fields of data (3) (10/23/2009)
Announcement: Best of ColdFusion 9 Contest (10/23/2009)
Ask a Jedi: Using HQL versus other ORM Functions (10/21/2009)
Quick example of Diff within the ColdFusion Server Manager (10/21/2009)
Update to FusionReactor (10/20/2009)
From the Obvious Department: Read the Release Notes (10/20/2009)
Quick example - jQuery code to add confirmations to links (10/19/2009)
BFusion/BFlex Conference (10/19/2009)
ColdFusion 9 JSON Bug (10/19/2009)
Ask a Jedi: ColdFusion Ajax example of retrieving fields of data (10/18/2009)
Warning to Ajax users in ColdFusion 9 (10/15/2009)
Ask a Jedi: Counting words in a textarea (10/14/2009)
Help spread the word - post a ColdFusion Cookbook entry and win ColdFusion 9 (10/13/2009)
Ask a Jedi: Documentation on VFS Support (10/12/2009)
Ask a Jedi: CFASSOCIATE Example (10/09/2009)
Google group for ColdFusion ORM Discussion (10/09/2009)
Goodbye MAX 2009 (10/08/2009)
Recorded version of my MAX ColdFusion ORM Presentation (10/08/2009)
MAX 2009 Day 2 (10/07/2009)
ColdFusion 9 ORM does not respect security settings on the DSN (10/07/2009)
Very important updates to ColdFusion 9 Licensing (10/06/2009)
MAX Day 1 (10/05/2009)
My official Out of Office notice - I'm MAX Bound (10/02/2009)
Take a look at jQuery Flot (10/02/2009)
Friday Challenge - Rolling it Old School, or mine is bigger than yours... (10/02/2009)
This works... but don't do it. (10/01/2009)
Ask a Jedi: ColdFusion support for CALS Tables (10/01/2009)
Two Cool Adobe MAX Updates (09/30/2009)
jQuery/AIR Quickie - YQL Tester (09/29/2009)
Gotches with Queries in Script (09/29/2009)
Ask a Jedi followup - updating multiple records at once (09/28/2009)
Quick Example - Locking in ColdFusion 9 (09/25/2009)
New Adobe Cookbooks (09/25/2009)
ColdFusion/jQuery/Yahoo Example (09/24/2009)
CFYahoo Updated (09/24/2009)
Hooking up ColdFusion and SQLite (09/24/2009)
Splitting up your ColdSpring.xml file in a Model-Glue Application (09/23/2009)
Odd jQuery/Keypress/AIR Issue (09/23/2009)
Ask a Jedi: Unblocking user accounts after failed logins (09/22/2009)
Interesting issue with CFC Lookup (09/21/2009)
How Galleon was Hacked (09/21/2009)
Review: Fuel (XBox 360) (09/20/2009)
Have you seen this? XBox 360 freeze on some games only (09/19/2009)
Using jQuery to convert text into form fields (09/18/2009)
Important Galleon Updates (09/18/2009)
Interesting tidbits on ColdFusion Exceptions (09/17/2009)
Building a Twitter Report in ColdFusion (Part 2) (09/16/2009)
Ask a Jedi: Why does package access not work with interface? (09/15/2009)
WebCharts3D Editor in Eclipse (09/14/2009)
Building a Twitter Report in ColdFusion (09/14/2009)
Ask a Jedi: Sorting files numerically that begin with strings (09/12/2009)
Delicious little problem with Application.cfc (09/11/2009)
Friday Puzzler - Twitter style (with an actual prize this time!) (09/11/2009)
Yahoo Query Language (09/10/2009)
Some thoughts on ColdFusion 9 ORM and Persistent CFCs (09/09/2009)
Speaking at RIA Unleashed, and help me get a PS3 Slim. (09/09/2009)
Ask a Jedi: Fingering the bad web service (09/08/2009)
Win a ColdFusion Dude Camera (09/08/2009)
Registration open for cfObjective(ANZ) (09/07/2009)
ColdFusion Charting - Y Axis Titles and Dashed Lines (09/06/2009)
Increasing the canvas size of an image (09/04/2009)
Making Subclipse recognize a project checked out from Subversion (09/03/2009)
Cumulative Hot Fix 3 did NOT include security updates (09/03/2009)
Quick warning/tip to ColdFusion Builder Extension writers (and note on varScoper fix) (09/02/2009)
Ask a Jedi: How do I convert JSON to XML? (09/02/2009)
Stupid ColdFusion Syntax Trick (09/01/2009)
Cumulative Hot Fix 3 for ColdFusion 8.0.1 (09/01/2009)
createUUID speeded up in ColdFusion 9 (08/31/2009)
SlideSix News (08/31/2009)
ColdFusion Builder Tip - Finding a file (08/31/2009)
Another example of the QofQ Bug (08/28/2009)
Ask a Jedi: Impact of whitespace and script based CFCs (08/26/2009)
Using ColdFusion 9's new FileSeek (08/21/2009)
Followup on ColdFusion 9/Solr Post (08/21/2009)
Speaking on the ColdFusion Panel Tomorrow (08/20/2009)
Simple ColdFusion 9 ORM/Solr Example (08/20/2009)
ColdFusion Quickie - Scan and Report on Exception Logs (08/19/2009)
onServerStart and handling a bad startup (08/19/2009)
Problem with Scatter graphs in ColdFusion (08/19/2009)
Cool (and undocumented) ColdFusion 9 Feature (08/18/2009)
CFUNITED 09 - Review (08/18/2009)
Subtle little query caching performance issue (08/17/2009)
Application.cfc lookup order change in ColdFusion 9 (08/16/2009)
My evil jQuery Plugin (08/15/2009)
CFUNITED Demo Derby Code (08/15/2009)
Simple ColdFusion 9 ORM Paging Demo (08/14/2009)
CFUNITED Presentations - jQuery, Application.cfc, and Charting (08/14/2009)
MAXROWS Attribute - Not as good as I thought (08/12/2009)
Interesting CFQUERY Bug (08/11/2009)
South Korea closing out international adoption (08/11/2009)
My Mile High OOO Notice for CFUNITED (08/11/2009)
Model-Glue 3 Released (08/10/2009)
Quick Ajax Debugging Tip (08/10/2009)
Tell me you don't dream like this (08/10/2009)
Watch out for this CFLOGIN Bug (08/07/2009)
Friday Challenge: Cut and Randomize a Picture (08/07/2009)
More useless ColdFusion maze code (08/06/2009)
CFUNITED Mobile (08/06/2009)
Ask a Jedi: CFDOCUMENT and formatting (08/05/2009)
CFUNITED Next Week! (08/05/2009)
Nice ColdFusion 9 Admin Change - Settings Summary (08/03/2009)
Quick example of serving up cached XML (with CF8 and CF9) (08/03/2009)
ColdFusion 9 Virtual File System for your Application (08/02/2009)
Update to VarScoper ColdFusion Builder Extension (08/01/2009)
Hi, my name is... (08/01/2009)
Small update to CF9 ORM CMS Demo (07/30/2009)
My experience with Adobe Wave (07/28/2009)
Very simple, very ugly, CMS built with ColdFusion 9 (07/25/2009)
Feeling charitable? Help out Families Helping Families (07/24/2009)
No CFADMIN access means no logging, right? (07/24/2009)
Ask a Jedi: Dynamic binds with cfdiv? (07/24/2009)
Galleon ColdFusion 9 fix, and pagination UI update (07/23/2009)
Generating mazes in ColdFusion (07/23/2009)
Blog going bye bye... (07/22/2009)
MAX 2009 Augmented Reality demo (07/22/2009)
ColdFusion Panel Launched (07/22/2009)
Couple of new ColdFusion conferences coming up... (07/22/2009)
Does my mailbox need a stimulant? (07/21/2009)
ColdFusion 9 and Caching Enhancements (2) (07/21/2009)
Followup to Google/RIAForge Post (07/20/2009)
Playing with cfProgressBar (07/20/2009)
RIAForge Update, and awesome example of ColdFusion/Google Integration (07/19/2009)
QuickSort in ColdFusion, with a ColdFusion 9 example as well (07/19/2009)
ColdFusion 9 and Caching Enhancements (07/18/2009)
Review: Harry Potter and the Half Blood Prince (07/17/2009)
ColdFusion Builder and Outline Mode (07/17/2009)
Question from Reader: ColdFusion and Licensing Schemes (07/17/2009)
Important Model-Glue note, and CanvasWiki update (07/16/2009)
ColdFusion 9 and CFFEED (07/15/2009)
No, not ColdFusion 9, not BlogCFC 6, but new update to BlogCFC 5 (07/15/2009)
Intro to jQuery Presentation (07/15/2009)
Error resizing a JPG with ColdFusion? (07/15/2009)
ColdFusion 9 Videos (07/14/2009)
ColdFusion 9 adds SpoolMail (Kinda...) (07/14/2009)
jQuery Presentation Tonight (07/14/2009)
CFaaS Demo - Dead Bike (07/13/2009)
ColdFusion 9's new Application variables (07/13/2009)
ColdFusion 9 fixes onRequest, adds onCFCRequest (07/13/2009)
My first ColdFusion 9 scoop - disable server side validation (07/12/2009)
Adobe releases public beta of ColdFusion 9 and ColdFusion Builder (07/12/2009)
Links (07/12/2009)
Are we falling behind? (07/10/2009)
Ask a Jedi: Elegant way of handling errors with cfQueryParam? (07/10/2009)
Oh snap - special CFMEETUP on ColdFusion 9 and ColdFusion Builder (07/09/2009)
Quick example of ExternalInterface, communicating between Flex and JavaScript (07/09/2009)
Hot Fix for FCK Issue (07/08/2009)
Forcing ColdFusion to recognize changes made to data used for Ajax bindings (07/08/2009)
Link - Reporting ColdFusion Security Issues (07/08/2009)
StructSort Example (07/06/2009)
Adobe response to recent FCK Issue (07/06/2009)
Review: Red Faction Guerrilla (XBOX 360) (07/04/2009)
Did you know Adobe had a Product Security Incident Response blog? (07/04/2009)
ColdFusion Security Issue - FCKEditor (07/03/2009)
Converting ColdFusion data for jQuery Plugins - An example (07/02/2009)
Query of query issue with where clause/joins (07/02/2009)
Quick example of Java via ColdFusion - Reading FLV Metadata (07/01/2009)
Important RIAForge Updates (06/30/2009)
Are you aware of the MIME/File Upload Security Issue? (06/30/2009)
Ask a Jedi: CFAJAXPROXY and Managing Callbacks (06/29/2009)
MAX 2009 ColdFusion Unconference - Call for Speakers/Comments (06/29/2009)
ColdFusion Portal Update (06/28/2009)
iPhone 3GS - So far, so good (06/28/2009)
LighthousePro 2.6 (06/27/2009)
Finding the username in an AIR app, and a quick binding tip (06/27/2009)
Interesting ColdFusion POST to PHP Issue (06/26/2009)
Calling a function... did you really call it? (06/25/2009)
Ask a Jedi: onMissingTemplate in ColdFusion 7? (06/25/2009)
Specifying tag attributes in a structure (06/21/2009)
Quick Frameworks Tip (06/19/2009)
Quick ColdFusion Builder Extension Demo (06/19/2009)
Follow up on creating ATOM Feeds with RSS (06/19/2009)
Fascinating issue with createTimeSpan (06/18/2009)
Centaur and Bolt are... (06/18/2009)
CFThread Example - Creating and merging PDFs (06/17/2009)
Will you go 3 oh? (06/17/2009)
Flex Question: How do I render a grid row differently based on data? (06/16/2009)
Please Read: Help Tim Buntel and Flex 4 (06/16/2009)
Sneak preview of CFLib via Bolt (06/15/2009)
New version of Lighthouse Pro - Need Testers (06/14/2009)
Incrementing with ++ (06/12/2009)
Follow up - Flash Builder 4, ColdFusion CFCs, and AIR (06/12/2009)
ColdFusion Quickie - Generating JavaScript from CFML (06/11/2009)
Tomorrow on the Online Meetup - Adobe ColdFusion Eclipse Extensions (06/10/2009)
ColdFusion Quickie - Moving a file to a day-based folder (06/10/2009)
Simple example of accessing ColdFusion data with Flex (now with Flash Builder 4) (06/08/2009)
Converting the color space of an image for PDF consumption (06/08/2009)
My waste of time this weekend - playing with Yahoo Maps and jQuery (06/07/2009)
jQuery Tabs and Google Maps (06/05/2009)
Working with XML in ColdFusion - Struct versus XML functions (06/04/2009)
Is this too much? (Change to Contact form) (06/04/2009)
Simple example of accessing ColdFusion data with Flex (06/03/2009)
CFHOUR() Feels(Needs) Your Pain (06/02/2009)
Ask a Jedi: Building a ColdFusion site to support dynamic subdomains (06/01/2009)
Flex4/FlashBuilder4/Flash Catalyst Links (06/01/2009)
Flash Builder 4 and Flash Catalyst hit Labs (05/31/2009)
What's that on RIAForge? (05/31/2009)
Generating Speech with ColdFusion and Java (05/28/2009)
2 Quick ColdFusion 8 RichText Editor Tips (05/27/2009)
'Formal' release of ColdFusion Cross OS Guide (05/27/2009)
School's Out (05/27/2009)
User Submitted Tip: Refreshing a CFDIV bound to a CFC (05/26/2009)
Ask a Jedi: Embedding FlashPaper on a page (05/26/2009)
Using ColdFusion to determine the distance between two addresses (05/25/2009)
CFUG Netherlands (05/24/2009)
Is this surveillance overkill? (05/22/2009)
Preventing resizes in CFGRID Columns (05/22/2009)
Adobe Community Achievement Awards Announced (05/21/2009)
CFTHREAD with a loading message (05/20/2009)
Figuring out how many mails are in a POP account (05/20/2009)
New ADC Article: Using Dreamweaver, InContext Editing, and Spry to build a dynamic site (05/19/2009)
MAX 2009 Site Updated (05/19/2009)
ColdFusion Cookbook Update (05/18/2009)
CFTHREAD - When to join? (05/18/2009)
CFTHREAD, Names, and Commas (05/18/2009)
Notes from the cfObjective Keynote (05/15/2009)
Simple CFCHART/jQuery Demo (05/15/2009)
Small project updates (05/14/2009)
(Possible?) Answer to slow image resizes in ColdFusion 8 (05/14/2009)
Model-Glue 3 News (05/12/2009)
CFAJAXPROXY and Extended CFCs (05/11/2009)
Got ColdFire? (05/11/2009)
More playtime with Flex, AIR, ColdFusion, and Flex Messaging (05/10/2009)
Review: Star Trek (05/08/2009)
Liked GameOne? Want to learn more about BlazeDS/ColdFusion/Flex/AIR? (05/08/2009)
Using a Remote JSONP ColdFusion Service to Send Mail (05/07/2009)
Transfer Presentation, Files, Recording URL (05/07/2009)
Transfer Meeting - Online - 3 Hours. Be there or be a PHP developer! (05/07/2009)
My (Early) Review of the Kindle (05/06/2009)
Are you a friend of ColdFusion? (Facebook Friend that is...) (05/06/2009)
Cross Operating System ColdFusion Development Guide (First Draft) (05/05/2009)
Using Application.cfc for headers and footers and still want to use Ajax? (05/04/2009)
Review: Learning jQuery 1.3 (05/03/2009)
Another RIAForge Milestone (05/02/2009)
I Heart Amazon Referrals (05/01/2009)
ColdFusion and Pass by Reference versus Value (05/01/2009)
Blocking ColdFusion Debugging for AJAX Requests (04/30/2009)
Interestng CFHTTP issue (04/30/2009)
Quick Example - Using Ajax for a Slow Process (04/29/2009)
Scotch on the Road 2009 (04/29/2009)
If I use ColdFusion, I don't have to worry about data types, right? (04/28/2009)
What is your favorite Java class to use with ColdFusion? (04/27/2009)
Code and Design of Gameone (04/26/2009)
Quick sanity check... (04/24/2009)
Handling additional (non charted) values in CFCHART? (04/24/2009)
ColdFusion 8 - Automatic Thumbnail/Preview Demo (04/23/2009)
GameOne Released (04/22/2009)
Ask a Jedi: Using ColdFusion to detect a Proxy Server (04/21/2009)
Important Note for ColdFusion 8 Ajax Developers (04/20/2009)
Full Sail University uses ColdFusion in Web Design and Development Program (04/20/2009)
Have you installed BlazeDS with ColdFusion? (04/19/2009)
ColdFusion Admin checks JVM Path (04/18/2009)
Food for thought - method to block non-Ajax requests (04/17/2009)
My first jQuery/AIR Application: Selecter Tester (04/16/2009)
On doors closing (and hopefully opening) (04/16/2009)
Did you know you could verify DSNs with ColdFusion code? (04/15/2009)
FusionDebug for Railo 3.1 Open Source (04/14/2009)
Ask a Jedi: Catching type exceptions in cfargument (04/13/2009)
Using ColdFusion to get the end of a file (04/12/2009)
Follow up to CFGRID post, interesting queryConvertForGrid Behavior (04/11/2009)
Friday Puzzler - Fractions (04/10/2009)
CFUnited Express Atlanta - Next Week (04/09/2009)
Ask a Jedi: Noticing an empty CFGRID (04/09/2009)
Using Wrap() in a PDF (04/08/2009)
ColdFusion, jQuery and Search Example (04/08/2009)
jQuery 101 Presentation (04/07/2009)
500th (and more) ColdFusion project released at RIAForge (04/06/2009)
CFCHARTs with Custom Markers (04/03/2009)
Two quickies - Cache Clearer Admin Extension and CFCHART Doc Typo (04/02/2009)
Foundeo releases ColdFusion Web Application Firewall (04/02/2009)
Skipping labels in a ColdFusion Chart (04/02/2009)
Small (very small) ColdFusion 9 leak (04/01/2009)
A new month, a new beginning... (04/01/2009)
CFUNITED Manager's Guide, Early Bird Pricing Ends Today! (03/31/2009)
Help spread the word about Ulitzer/Con-Sys (03/30/2009)
Ask a Jedi: CFCHART and Scaling to Decimal Points (03/30/2009)
ColdFusion Logs to RSS (with a quick sidetrack into zombies) (03/28/2009)
Interesting CFCHART Trick (03/27/2009)
Call for Help: Web shops using ColdFusion (03/27/2009)
Using jQuery to validate the sum of form fields (2) (03/27/2009)
CFUNITED 09 - Early Bird Ending Soon... (03/26/2009)
Using jQuery to validate the sum of form fields (03/26/2009)
CFLib Submissions (03/25/2009)
Ask a Jedi: How secure are the username/password values of a ColdFusion Scheduled Task? (03/24/2009)
Simple example of a Form post to ColdFusion with jQuery - Login (03/24/2009)
Want to learn ColdFusion (again)? (03/23/2009)
InsideRIA Links for March 8-21, 2009 (03/21/2009)
Friday Puzzler - Gold baby, pure gold... (03/20/2009)
Simple example of a Form post to ColdFusion with jQuery (03/20/2009)
Quick Transfer Tip (03/19/2009)
Want to learn ColdFusion? (03/18/2009)
More sessions announced for CFUNITED... (03/18/2009)
Simple example of loading a ColdFusion query with jQuery (03/17/2009)
Multi-file search and replace in Eclipse (03/16/2009)
Today is Fail Day... (Looking for MySQL, Vista, whatever else help) (03/15/2009)
Sites moving.. (03/14/2009)
Friday Puzzler - Helping the Model-Glue Team (03/13/2009)
Presentation files (and thanks) (03/12/2009)
Presenting today: The Art of AJAX Development Using ColdFusion at the Online Meetup (03/12/2009)
Writing a JSONP service in ColdFusion (03/11/2009)
Flex Builder Question - Not seeing files during AIR export (03/11/2009)
How To: ColdFusion Chart with No Numbers (03/09/2009)
When does it make sense to cache ColdFusion code? (03/08/2009)
InsideRIA Links for March 2-7, 2009 (03/07/2009)
Ask a Jedi: Showing the values on a chart (03/06/2009)
jQuery UI 1.7 Released (03/06/2009)
Open Question: Women speakers at conferences? (03/05/2009)
CFUNITED 09 - New speakers announced (03/04/2009)
Ask a Jedi: New to ColdFusion, why use cfform, cfdiv, cftable? (03/04/2009)
Holy Smokes - MAX 2009 Call for Speakers (03/03/2009)
Riddle me this, OSX Firefox Users (03/03/2009)
Groovy version of code to get an Amazon S3 Download URL (03/03/2009)
Yet another ADC article on Dreamweaver: Creating a Spry XML data set (03/02/2009)
CFBL - A Year Later (03/02/2009)
Latest Broadchoice Workspace now has a free edition (02/28/2009)
Ask a Jedi: ColdFusion's version of .Net's IsPostBack (02/27/2009)
Google Analytics and Ajax (02/26/2009)
jQuery Progress Bar (with ColdFusion) (02/26/2009)
Do you test under cfsetting? (02/26/2009)
jQuery Sortable with ColdFusion (02/25/2009)
Metadata properties for CFFEED - Atom (02/25/2009)
Out of Office notice - getting fat on Tuesday (02/24/2009)
Question for Readers: Flex alignment with textarea controls (02/23/2009)
Using jQuery to add form fields - with validation (02/22/2009)
jQuery Thickbox and ColdFusion Dynamic Image Resizing - With Bookmarks (02/20/2009)
Ask a Jedi: Showing Every Nth Record (02/20/2009)
GoogleDocs CFC (02/19/2009)
Using jQuery to add form fields (02/19/2009)
Officer Roseland offers a unique take on 'Stimulus Package' (02/18/2009)
jQuery Thickbox and ColdFusion Dynamic Image Resizing (02/17/2009)
ColdFusion LiveDocs Updated (02/16/2009)
jQuery Form Validation with Selects (02/16/2009)
Use Google Analytics and Ajax? Remember to update your code (02/15/2009)
Ask a Jedi: Career advice for a ColdFusion Developer? (02/14/2009)
ColdFusion added to Adobe Community Help (02/13/2009)
Ask a Jedi: Using ColdFusion Ajax to set Client Variables (02/12/2009)
An Introduction to jQuery and Form Validation (3) (02/12/2009)
Determining the location of ColdFusion's log files (02/11/2009)
Ask a Jedi: jQuery or ColdFusion 8 Ajax? Or both? (02/11/2009)
Ask a Jedi: Updating multiple records at once (02/10/2009)
An Introduction to jQuery and Form Validation (02/09/2009)
Open Question: ColdFusion and Reports? (02/09/2009)
Ready2Run Open BlueDragon and Web Services (02/07/2009)
ColdFusion and SugarCRM Intergration (02/07/2009)
New ColdFusion/Bolt Product Manager (02/06/2009)
Working with Office Metadata (02/06/2009)
CFML Advisory Committee Update (02/06/2009)
Reading Office documents with ColdFusion (2) (02/05/2009)
Reading Office documents with ColdFusion (02/04/2009)
How to report a security problem with ColdFusion (or any other Adobe product)? (02/03/2009)
This is ColdFusion - this is ColdFusion 100% in Script, on Bolt... (02/03/2009)
Using jQuery and ColdFusion to create an auto-link for definition application (2) (02/03/2009)
Reader Survey Results (02/02/2009)
Creating a Dialog with jQuery UI (2) (02/02/2009)
Creating a Dialog with jQuery UI (02/01/2009)
Using jQuery and ColdFusion to create an auto-link for definition application (01/31/2009)
CF-Talk Status (01/29/2009)
CFBloggers.org/Twitter Issue (Another Simple Mistake!) (01/27/2009)
Update to CFPDF/Password Issue (no unicorns this time) (01/27/2009)
Article on Spry HTML Datasets and DWCS4 (01/26/2009)
Using ColdFusion to estimate the number of seconds a user spends on a page (01/26/2009)
Is the Sys-CON at it again? (01/26/2009)
ColdFire 1.3 (01/25/2009)
New XBox Experience and Video Streaming Problem (01/25/2009)
How to remove a password from a PDF using ColdFusion (01/23/2009)
Horror fan? Horror addict? (01/22/2009)
Ask a Jedi: Sending a dynamic PDF via email (01/22/2009)
Why you should, and should not, break encapsulation in methods (01/22/2009)
Ask a Jedi: Run a callback on every ColdFusion.navigate/AjaxLink (01/20/2009)
Reminder - MAX Sessions on AdobeTV (01/19/2009)
Cross-Post: ColdFusion survey on the cloud (01/19/2009)
Mixing client side dynamic forms with dynamic ColdFusion form processing (01/18/2009)
Making a "sticky" CFWINDOW (01/17/2009)
Launching CFWINDOW with a Dynamic Location (01/16/2009)
Please Help (01/16/2009)
cfchart and cfimage - useless experiment (01/15/2009)
Ask a Jedi: Emailing CFCHART (01/14/2009)
Ask a Jedi: Dynamic expires with an image via ColdFusion (01/13/2009)
Speaking at NYCFUG Tomorrow Night (01/12/2009)
Hal's next OO Class - February 23 (01/12/2009)
Ask a Jedi: RSS Reader with CFGRID? (01/12/2009)
Project Updates (and a small little security fix) (01/11/2009)
Update ColdFusionBloggers Feed (01/10/2009)
An odd cfdiv issue (01/09/2009)
Ask a Jedi: cfdiv, cfform, cflayout and selecting tabs - also a new bug? (01/09/2009)
ColdFusion 8 Ajax and History Management (01/08/2009)
They podcast over there (01/08/2009)
Cool use of CFPOD (01/07/2009)
2008 @ ColdFusionBloggers.org (01/07/2009)
Be careful with CFCHART (01/07/2009)
Survey Reminder (01/07/2009)
If I'm going to use Eclipse for ColdFusion development, what packages do I need? (01/06/2009)
Handling CFDIV's resizes (01/06/2009)
Having issues with your BlazeDS/Flex app? Try changing the display-name (01/05/2009)
Don't forget to validate those checkboxes/radio buttons/multi selects/etc (01/05/2009)
This is where your hot sauce comes from... (01/02/2009)
structClear and Sessions - Still bad? (01/02/2009)
Ask a Jedi: cflogout, session variables, and the back button (01/01/2009)
My New Years Resolutions (01/01/2009)
Happy New Year! (12/31/2008)
Broadchoice Workspace reviewed on Refreshing Apps (12/31/2008)
Using CF8 Ajax features to solve the 'pick one of thousands' issue (2) (12/31/2008)
Ratings added to CFLib (12/30/2008)
Uberpanel podcast from MAX now available (12/30/2008)
Readers - your time for revenge is here... (12/29/2008)
What was "THE" game for you this year? (12/27/2008)
Transfer Caching and Performance Features (12/27/2008)
Using CF8 Ajax features to solve the 'pick one of thousands' issue (12/25/2008)
Merry Christmas, Hanukkah, Kwanzaa, Yule, Festivus, or Whatever (12/24/2008)
First round of CFUNITED 09 Talks Released (12/23/2008)
ColdFire Updated/Call for Help (12/23/2008)
First batch of Dreamweaver/ColdFusion articles up @ Adobe (12/22/2008)
Watch those fonts (12/22/2008)
Ask a Jedi: Removing Pagination from CFGRID (12/21/2008)
Quick Updates (12/19/2008)
Spry Tip - Paged Datasets, Filters, and Row Numbering (12/18/2008)
Early Christmas related excuse to test a jQuery Plugin (12/17/2008)
Ask the Jedi: Counting characters and lines with Spry (12/17/2008)
ColdFusion.navigate works with non-CF generated UI items (12/16/2008)
Ask a Jedi: Mixing ColdFusion 8 binding with jQuery (12/16/2008)
Soundings 3 - Preview and Live Demo (12/15/2008)
Please read and comment: More Flex? (12/15/2008)
Ask a Jedi: Simple ColdFusion 8 Ajax Pagination (12/14/2008)
Take the OO Quiz - and prepare to be humbled... (12/12/2008)
Ask a Jedi: Doing a trim with Spry (12/12/2008)
Ask the Crowd: Documentation (12/11/2008)
Global warming is a sham! (12/11/2008)
Ask a Jedi: Checking Spry data for duplicates (and Spry 1.7 News) (12/10/2008)
Ask a Jedi: Example of onMissingTemplate to handle dynamic city/state pages (12/09/2008)
Ask a Jedi: Issue with layoutarea and cflocation (12/09/2008)
Working with Transfer's Event Model (12/08/2008)
Ask a Jedi: Where to use Transfer? (12/08/2008)
Spry, SWFs, and an interesting HTML 5 Tidbit (12/07/2008)
Question for Mac users, and coolest video you will see all month... (12/06/2008)
My solution to the Friday Puzzle (12/06/2008)
Friday Puzzler: Quick Stats (12/05/2008)
Ask a Jedi: Showing error details on a dev machine (12/04/2008)
CFUNITED Topic Survey Open (12/04/2008)
You will use cfqueryparam... or else! (12/03/2008)
ColdFusion Tidbit - How does CF show the lines where your error occured? (12/03/2008)
Quick note on what I did to RIAForge (12/03/2008)
Quick RIAForge Notice of Downtime (12/02/2008)
Ask a Jedi: Running code on Tab change with ColdFusion 8 Tabs (12/01/2008)
Ask a Jedi: Getting file permissions (11/30/2008)
Getting form data from cflayout based tabs (11/28/2008)
Another Hack Job - Update to classic.cfm debug template (11/26/2008)
The (Far) Future of ColdFusion (11/26/2008)
Decorating Eye for the Transfer Guy (11/25/2008)
MAX Presentation Slides and Files (11/25/2008)
Yes, Virginia, there are queries in Transfer (11/24/2008)
MAX Videos to be available... to all (11/24/2008)
Is MAX over yet? (11/24/2008)
Friday Insanity (11/21/2008)
Article at InfoQ published: Debunking Common Myths about ColdFusion (11/19/2008)
MAX Sneak Peaks (11/19/2008)
MAX Day Two - Brazillian BBQ is Evil (11/19/2008)
MAX Keynote Liveblog - Day 2 (11/18/2008)
Bolt - ColdFusion IDE (11/18/2008)
MAX Day One - and why Brian Rinaldi is my hero (11/18/2008)
ColdFusion in the Cloud (11/17/2008)
New on Adobe Labs (11/17/2008)
MAX Keynote Liveblog (11/17/2008)
And so it begins - first MAX Announcements (11/17/2008)
Safe and Sound in the Big City (11/16/2008)
Less than 10 hours to take off... (11/15/2008)
Getting Some with Transfer (11/14/2008)
Broadchoice Workspace in da House... (11/14/2008)
Guide to ColdFusion Administrator Extensions (11/13/2008)
Ask a Jedi: Showing new content to a user? (11/13/2008)
Managing Relationships with Transfer (3) (11/12/2008)
CFUNITED 09 Dates, Regisitration Open (11/12/2008)
YouTubeCFC update and the most insane API you will see today... (11/12/2008)
Ask a Jedi: Two Y Axis for ColdFusion Charts (11/11/2008)
When did Dreamweaver add this? (11/11/2008)
ColdFusion Camp (Germany) (11/10/2008)
MAX Birds of a Feather Sessions Posted (11/08/2008)
Ask a Jedi: Handling Changes (11/08/2008)
Managing relationships with Transfer (or the ORM meets Dr. Phil) (11/07/2008)
Ask a Jedi: CFLOGIN and duplicate logins? (11/07/2008)
Building CRUD with Transfer (2) (11/06/2008)
Nice new Flex based viewer on SlideSix (11/06/2008)
ColdFusion Unconference firming up @ MAX (11/06/2008)
Building CRUD with Transfer (11/05/2008)
Attribute validation error with CFTEXTAREA (11/05/2008)
Setting up my Transfer Application (11/04/2008)
ColdFusin 9 + AIR Session @ MAX (11/04/2008)
Vote (11/04/2008)
ColdFusion and Transfer (And that 3 letter "O" word) (11/03/2008)
YouTubeCFC and update to the CFHTTP Tag (11/03/2008)
ColdFusion 8 Autosuggest bug to watch out for (11/03/2008)
ColdFusion 8 Image Resize options (11/01/2008)
cf_happyHalloween (10/31/2008)
New ORM Related session @ MAX (10/30/2008)
MTV Music (Yes, it has an API) (10/28/2008)
Handling a slow process in a Model-Glue (or other MVC) application (10/27/2008)
Speaking of Model-Glue (and other Frameworks)... (10/27/2008)
Model-Glue Survey (10/27/2008)
Want to see something really scary? (10/26/2008)
Lighthouse Pro 2.5.001 (10/25/2008)
PIcture: Our Lady of the Ghouls (10/24/2008)
Cool CFCHART Tip - Background Ranges (10/23/2008)
Ask a Jedi:Using cfdirectory and a form to delete files (10/22/2008)
Today's Weird JavaScript Issue (10/22/2008)
CFUNIITED 09: Call for Topics (10/21/2008)
Looking For: "Enterprise" ColdFusion 8 Ajax Applications (10/21/2008)
ColdFusion 8 Posters (10/21/2008)
Ask a Jedi: Tieing together multiple UDFs (10/20/2008)
My OT funny/not so funny story from this weekend (10/20/2008)
Ask a Jedi: Find available UDFs (10/18/2008)
Lighthouse Pro 2.5 Out the Door (Kuler, YouTube News too...) (10/17/2008)
Transfer 1.1 is Out (10/17/2008)
Ask a Jedi: Formatting large numbers (10/16/2008)
Ask a Jedi: Detect JavaScript with ColdFusion? (10/15/2008)
Ask a Jedi: Working with ColdFusion's Debug Query Display and CFQUERYPARAM (10/15/2008)
Ask a Jedi: Advice on building a remote API? (10/14/2008)
SpoolMail, ColdFire Updates (10/14/2008)
Translation via Google (10/13/2008)
Transfer Survey (10/13/2008)
Broadchoice Beta - Soon! (10/10/2008)
Two iPhone development tips, and jQuery to the rescue (10/09/2008)
Ask a Jedi: UDFs in Custom Tags (10/07/2008)
Interesting CFFEED Issue with Spaces (10/07/2008)
Quick tweak added to ColdFusionBloggers.org (10/07/2008)
Kristen Schofield's Short RIA Survey (10/06/2008)
Ask a Jedi: Finding where a variable is defined (10/06/2008)
Review: Star Wars - The Force Unleashed (10/05/2008)
Simple auto-reload ColdFusion 8 Ajax Demo (10/03/2008)
Soundings 2.1 (10/03/2008)
Speaking at CF_Underground 2008 (10/02/2008)
Ask a Jedi: ColdFusion datefield/change question (10/01/2008)
iPhone Simulator? Try the SDK (10/01/2008)
Custom rounding in ColdFusion (09/30/2008)
ID this Plane (09/29/2008)
More on the Ajax changes to Lighthouse Pro (09/29/2008)
Lighthouse Pro 2.5 (Beta) (09/28/2008)
Ask a Jedi: Another CFWINDOW Example (09/26/2008)
More clues about CF9 (09/26/2008)
Using ColdFusion to help with my son's homework (09/25/2008)
Ask a Jedi: Why is one UDF faster than another? Variables? (09/24/2008)
Transfer Query - From Phrase to AND Search (09/23/2008)
A Quick Thank You (09/22/2008)
Ask a Jedi: Functions and dynamic arguments (09/22/2008)
Review: Burnout Paradise (Regained) (09/21/2008)
Quick CFGRID Tip - disable sorting (09/19/2008)
Ask a Jedi: Abstract date ranges and search (09/18/2008)
Google Calendar/Contacts update (09/17/2008)
Quick AIR Tip - including an icon with your application (09/17/2008)
Ask a Jedi: Handling nulls in a chart (09/17/2008)
Help a coder get to MAX, get a little Sith love... (09/16/2008)
ColdFusion Quickie - Last 12 Months (09/16/2008)
ColdFire 1.2.89.89 (09/15/2008)
Help a reader decide on SQL Server versus MySQL (09/15/2008)
Triple Related Selects (and interesting CFDIV trick) (09/14/2008)
Review: V: The Second Generation (09/14/2008)
Ask a Jedi: Tracking views when using an Ajax-front end (09/12/2008)
So why do I have insurance again? (09/12/2008)
ColdFusion Puzzler - Inspect It! (09/12/2008)
IMified Relaunches (09/11/2008)
Too early to show your CF9 love? I think not! (09/11/2008)
Few quick notes (BlogCFC, TV, and a Textmate query) (09/10/2008)
Ask a Jedi: Dynamically updating line items on a form (09/10/2008)
Railo 3 Released (09/10/2008)
Ask a Jedi: Handling errors in ColdFusion Ajax applications (09/08/2008)
Want a peek? (09/07/2008)
Configuring the date mask for ColdFusion Logs (09/07/2008)
Google Contacts Wrapper (09/06/2008)
Ask a Jedi: Embedding ColdFusion-based code on another server (09/05/2008)
Subclipse and Unable to load default SVN client (09/05/2008)
ColdFusion Ajax leading zeros issue (09/04/2008)
By the power of LUS... (09/04/2008)
No hurricane will stop my blog - Details on Free ColdFusion for Education (09/02/2008)
Gustav Update (08/31/2008)
CFFEED - You have failed me for the last time. (08/29/2008)
Ask a Jedi: Problem with CFGRID and Edit Action (08/29/2008)
Spry, Detail Regions, and hiding content until a click (08/28/2008)
Tracking the storm (with ColdFusion!) (08/28/2008)
Death is a giant, brightly-covered slug heading your way.... (08/27/2008)
Minor updates (08/26/2008)
Using a CFC to drive content to cftooltip (08/26/2008)
Bug with Ajax HTML Grid and File Upload Forms (08/25/2008)
Review: Clone Wars - It didn't suck! (08/24/2008)
Ask a Jedi: Making use of ColdSpring/Model-Glue and Remote Proxies (08/22/2008)
Code, slide, and recordings from yesterday's presentations (08/22/2008)
Reminder - BFusion and BFlex (08/21/2008)
Eclipse trick (08/21/2008)
Yet another post on cffeed and columnMap (08/21/2008)
Two Presentations Tomorrow (08/20/2008)
Ask a Jedi: Creating a list of product options (08/20/2008)
360|Flex Recordings posted to AMP (and cool AIR fact) (08/19/2008)
ColdFusion Ajax Bindings - Form Fields only? (08/19/2008)
ColdFusion Unconference Update - The Uber Panel (08/18/2008)
ColdFusion Ajax Grid - and POST (08/18/2008)
Ask a Jedi: Controlling the size of bars in cfchart (08/17/2008)
Pardon me while I have a brain cramp (or three) (08/16/2008)
Ask a Jedi: UDFs versus CFCs (08/14/2008)
Interview (08/14/2008)
Getting page orientation and size from PDFs (08/12/2008)
Day 100 from the ColdFusion war front (or, what's going on with RIAForge) (08/12/2008)
About time - Cockfighting ending in LA (08/11/2008)
Review: Soulcalibur IV (XBOX 360) (08/10/2008)
SpoolMail update (08/09/2008)
Quote of the Day: From Ben Forta (08/08/2008)
Ask a Jedi: Validating a set of form fields as a date (08/08/2008)
My Wife Kicks Butt... (08/07/2008)
Ask a Jedi: Handling legend clicks in CFCHART (08/07/2008)
Speaking at Online ColdFusion Meetup, on August 21, on something (08/07/2008)
Be sure to check out ArgumentCollection (08/06/2008)
GoogleCal Update (08/06/2008)
Ajax-based CFGRID and IE issue (08/05/2008)
Book Review: Flex 3 in Action (08/05/2008)
The Dark Side of the iPhone? (08/04/2008)
Welcome Brian! (08/04/2008)
Transfer 1.1 Out (08/04/2008)
Ask a Jedi: Two quick ColdFusion Component questions (08/04/2008)
Ask a Jedi: Using query data in cflayoutarea (08/01/2008)
Interesting issue with ColdFusion's AJAX features and large strings (07/31/2008)
ColdFusion MAX Unconference Update (07/31/2008)
Google Analytics AIR update (07/31/2008)
Ask a Jedi: Learning cfscript? (07/30/2008)
Ask a Jedi: Doing arithmetic with Spry data (07/30/2008)
What? Folks aren't using cfqueryparam? (07/29/2008)
Ask a Jedi: Moving to UNIX, but didn't plan for it. Now what? (07/28/2008)
I survived! (Mostly) (07/28/2008)
Welcome Joe! (07/24/2008)
Goodbye for a while (and some quick media reviews...) (07/20/2008)
Quick Note on Glenda Vigoreaux (07/19/2008)
Flying the not-so-friendly skies (07/17/2008)
Software Updates (before I go - go) (07/17/2008)
Update from the CFML Advisory Group (07/16/2008)
Vimeo ColdFusion wrapper (07/16/2008)
Quick Tip: What to do when your error handling isn't working? (07/15/2008)
Follow ColdFusion Bloggers on Twitter (07/14/2008)
Lemonade Stand - The Results Are In (07/14/2008)
Non-Flash ColdFusion charts are still interactive (07/13/2008)
Ask a Jedi: Application.cfc, Application variables, and CFLOCK (07/13/2008)
iPhone 2.0 Apps - my thoughts so far (07/12/2008)
iAftermath - and how ColdFusion held up (07/12/2008)
Contest Delay (07/11/2008)
So far iPhone 2.0 is.... DOA (07/11/2008)
Friday Puzzler final checkin (07/11/2008)
Another RIAForge update, and some good examples of my mistakes (07/10/2008)
Ask a Jedi: Using CFTREE for Navigation (2) (07/10/2008)
Presentation tonight to the Connecticut CF User Group (07/09/2008)
A tip concerning Model-Glue and Google AdSense (07/08/2008)
Friday Puzzler (a bit early...) (07/07/2008)
jQuery API Browser - Another cool AIR Example (07/07/2008)
Railo 3 and the Cluster Scope (07/07/2008)
Review: World War Z (07/06/2008)
Ask a Jedi: Sorting a 2D Array (07/05/2008)
Happy July 4th! (07/04/2008)
Got cookies? (in your logs) (07/03/2008)
Ask a Jedi: Trouble with ColdFusion.Ajax.SubmitForm (07/03/2008)
Overriding returnFormat at runtime (07/03/2008)
My last post on Adobe Certification (07/02/2008)
New ColdFusion Book Ships (07/02/2008)
Ask a Jedi: Issue with datefield and mask (07/02/2008)
IE issue with AjaxProxy (07/01/2008)
Bribery for the ColdFusion Cookbook (and looking for a grunt or two) (07/01/2008)
Does your form validation need to be less strict? (06/30/2008)
ColdFusion Bloggers code update (06/30/2008)
ColdFire update for latest Firebug (06/30/2008)
Ask a Jedi: jQuery versus Spry... (06/28/2008)
Second beta of Railo 3 out (06/27/2008)
Announcing the ColdFusion Unconference at MAX (06/26/2008)
Ask a Jedi: Question on DBA's and their plans to ruin our lives... (06/26/2008)
MAX Website up, Sessions Listed (including mine) (06/25/2008)
Ask a Jedi: Followup on Certification (06/25/2008)
Ask a Jedi: Complex security possible in ColdFusion? (06/23/2008)
Ask a Jedi: Mixing ColdFusion Ajax and CFCALENDAR (06/23/2008)
Sunday Mega Media Review (06/22/2008)
ColdFusion 8 Ajax Browser Support (06/21/2008)
Ask a Jedi: URL Rewriting example (06/21/2008)
CFUNITED - Internals of the Adobe ColdFusion Server (06/20/2008)
Seeker updated to support Word docs and Excel files (06/20/2008)
Clearing individual files/folders from ColdFusion template's cache (06/19/2008)
Files/Slides from CFUNITED Presentations (06/19/2008)
The coolest thing I've seen at CFUNITED (06/19/2008)
SciFi BOF Members - Post Here (06/18/2008)
SciFi BOF Location (06/18/2008)
CFUNITED 08 Opening Keynote (06/18/2008)
Mr. Camden goes to Washington (06/17/2008)
CFDevcon - Coming to an England near you... (06/16/2008)
CFConversations - First podcast available now (06/16/2008)
Ask a Jedi: Problem using onMissingMethod inside a CFC (06/13/2008)
Transfer deep relationship/order bug (06/13/2008)
RIAForge is now officially the mac-daddy (06/12/2008)
Firebug Tip - When Ajax Calls Go Bad... (06/12/2008)
Ask a Jedi: ColdFusion Search Engine Safe URLs versus URL Rewriting (06/12/2008)
Model-Glue 3 - Custom Event Types - Want that in XML? (06/11/2008)
Ask a Jedi: Paging within cfsearch? (06/11/2008)
Seeker update (06/11/2008)
Quick correction about my new CFUNITED Preso (06/10/2008)
ColdFusion 8, DIV, "Loading" graphic issue (06/10/2008)
More on CFLib update (Transfer specifics) (06/10/2008)
CFLib 2008 (06/09/2008)
CFFILE/Upload Issue I ran into (06/09/2008)
Transfer 1.0 is Gold (in more ways than one) (06/08/2008)
Uber Friday OS Report (06/06/2008)
Ask a Jedi: CFWINDOW for Messaging? (06/06/2008)
Waiting for CFUNITED (06/06/2008)
Use cgi.server_name? Be careful (06/05/2008)
Recording/Code from Last Nights CF8/Ajax Meeting (06/05/2008)
I'm a bit late to the party, but big announcement from Railo (06/05/2008)
RIAForge Crash and Burn (06/04/2008)
Bonehead Custom Tag mistake (06/04/2008)
CFUNITED Survey (06/04/2008)
Ask a Jedi: Two jQuery and ColdFusion questions (06/04/2008)
Open Letter to Adobe on Certification (06/03/2008)
Another Seeker Update (06/03/2008)
Be careful with returnFormat and JSON (06/03/2008)
Presenting to New Zealand CFUG (06/02/2008)
Changing the size of a footer in CFDOCUMENT (06/02/2008)
Seeker code update (06/02/2008)
Small updates (Share, Lighthouse Pro) (05/30/2008)
Ask a Jedi: Getting the SQL from a Query (05/30/2008)
SlideShareCFC Wrapper (05/30/2008)
Another option for trimming text in ColdFusion (05/29/2008)
Comparing centuries of dates (05/29/2008)
MAX 2008 Registration opens (05/28/2008)
Ask a Jedi: Best way to trim text (05/28/2008)
Ask a Jedi: Best way to handle feed stats (05/27/2008)
Complex data in an auto-suggest (05/27/2008)
CFFEED and Date Values (05/24/2008)
BlogCFC and Galleon updates (05/22/2008)
VarScoper Tool (05/22/2008)
Charlie Arehart and CF911 (05/21/2008)
WebManiacs ColdFusion Images Presentation (Lecture/Hands On) (05/20/2008)
ColdFusion Image Processing - Shrinking an image, but not the canvas (05/20/2008)
Broadchoice Web Platform Released (05/19/2008)
Did you know a hot fix for ColdFusion was released this week? (05/17/2008)
The other returnFormat - plain (05/16/2008)
Ask a Jedi: Add an edit button to a ColdFusion 8 Ajax Grid (05/16/2008)
Two ColdFusion Server Monitoring Tips (05/15/2008)
Who Uses ColdFusion? (05/15/2008)
RIAForge Status (05/15/2008)
Model-Glue 3 - Example of Formats (05/14/2008)
New ColdFusion 8 Book (05/14/2008)
Adobe Connect failure on the Mac - apologies to the Connecticut UG (05/13/2008)
Playing with jQuery - ColdFusionBloggers.org Update (05/13/2008)
Ask a Jedi: Complete Spry CRUD Example (05/13/2008)
Speaking at Connecticut ColdFusion Users Group (05/13/2008)
Link - SES URLs in Model-Glue 3 (05/12/2008)
The last book you will ever read (05/11/2008)
Model-Glue 3 - Example of Custom Event Types (05/09/2008)
There is only one Spry... (05/09/2008)
Proposals for ColdFusion 9 - From the Enemy's Camp (05/09/2008)
CFLOG and Permissions (05/08/2008)
Ask a Jedi: Getting the current directory (05/08/2008)
Quick CFBL update and a minor LighthousePro update (05/07/2008)
Running Model-Glue 3 on a box with Model-Glue 2 (05/07/2008)
Ask a Jedi: Multiple templates and Model-Glue (05/07/2008)
Adobe Developer Week recordings (05/06/2008)
I'm not a programmer (05/05/2008)
cfObjective Slides/Code (05/04/2008)
2 quick links (one tech, one music) (05/03/2008)
(Short) Review: Iron Man (05/02/2008)
Model-Glue 3 - The New Frakin' Awesomeness (05/02/2008)
Another hint on ColdFusion 9? (05/02/2008)
Adobe announces public bug/enhancement database for ColdFusion (05/02/2008)
cfObjective Keynote: News on Centaur (CF9) (05/02/2008)
Ask a Jedi: Why would I use cfhtmlhead? (05/02/2008)
New month, new job. I've joined Broadchoice (05/01/2008)
Ask a Jedi - Why isn't my session expired when I logout? (05/01/2008)
Project updates (04/30/2008)
Recording URL and Slides from CF/OS Presentation (04/30/2008)
Ask a Jedi: Does ColdFusion have a htmlfoot tag? (04/30/2008)
Ask a Jedi: Copy session values from one application to another (04/29/2008)
Presentation tonight on ColdFusion and Open Source (04/29/2008)
LighthousePro Updated (04/28/2008)
Reader looking for UK-based (or related) Reseller (04/28/2008)
Transfer 1.0 RC is Out (04/28/2008)
Small Canvas update (04/25/2008)
ColdFusion/SlideShare integration tip (04/25/2008)
Ask a Jedi: Caching Stored Procedures (04/25/2008)
Galleon 2.013 Released (04/24/2008)
Real men write their own forms (or do they?) (04/24/2008)
Ask a Jedi: Using JSON in older versions of ColdFusion (04/24/2008)
cfObjective Blog Posts (City Related) (04/23/2008)
Ask a Jedi: Handling RSS feeds with custom data (04/23/2008)
What makes a code diva? (04/22/2008)
Ask a Jedi: Query naming inside a CFC - best practice? (04/22/2008)
Ask a Jedi: Extending ColdFusion's auto-complete feature (04/21/2008)
Check out varScoper (04/21/2008)
YouTube CFC Updated (04/19/2008)
Review: Rock Band (04/19/2008)
Ask a Jedi: Question about learning frameworks (and other things) (04/18/2008)
CFCACHE and the Fall of Rome (04/17/2008)
Ask a Jedi: Two CFGRID Questions (04/17/2008)
Ask a Jedi: Creating lowercased cookies in ColdFusion (04/16/2008)
My current least favorite Mac 'feature' (04/16/2008)
First draft of new YouTube API (04/15/2008)
How can I move my Flex app into multiple layers? (04/15/2008)
imageUtils gets some Tiff love (04/15/2008)
Ask a Jedi: What is the proper way to handle session/cgi variables in CFCs? (04/15/2008)
Inteviewed by Greg Cerveny (04/14/2008)
WebCharts and ColdFusion (04/14/2008)
Ask a Jedi: Flash, ColdFusion and FIle Uploads (04/10/2008)
Designers for CFLib wanted (04/10/2008)
Model-Glue 3 Preview (04/10/2008)
ColdFusion 8.0.1 change to CFEXECUTE (04/09/2008)
Open BlueDragon Steering Committee (04/08/2008)
ColdFire Update (04/08/2008)
I hit level 35 today (IRL) (04/08/2008)
Free Exchange Testing (04/07/2008)
XML forms and CFIMAGE (04/07/2008)
RIA Dev Shed Review (and Files) (04/07/2008)
Ask a Jedi: Is my site slow because of Ajax or something else? (04/07/2008)
Update to pdfUtils Component (04/04/2008)
ColdFusion 8.0.1 - Easier to add PDF Watermarks (04/04/2008)
CFFEED Fixes in 8.0.1 (04/04/2008)
ColdFusion 8.0.1 is out the door! (04/03/2008)
ColdFusion 8.0.1 adds pizazz to implicit array/struct creation (04/03/2008)
Changes to attributeCollection in 8.0.1 (04/03/2008)
The Jedi Punts - Need IE testers (04/02/2008)
Galleon ColdFusion Forums update (04/01/2008)
Work for the NFL! (ColdFusion Job, and no, not an April Fool's joke) (04/01/2008)
Old School Ray (04/01/2008)
Forget web development, I'm becoming a gold farmer (04/01/2008)
Misleading docs for isUserInAnyRole (03/31/2008)
Ask a Jedi: Sending emails out over time. (03/31/2008)
ColdFusion Bloggers Update (03/30/2008)
These are not the search results you are lookin for... (03/30/2008)
Quick and Dirty ColdFusion 8 CAPTCHA Guide (03/29/2008)
Ask a Jedi: CFIMAGE performance concerns (03/28/2008)
Searching CFDocs (03/28/2008)
I'm an idiot for not using... (03/27/2008)
Photoshop Express Example (03/27/2008)
Photoshop Express Launches (03/27/2008)
One AIR annoyance (03/27/2008)
TimeTracker updated (again!) (03/26/2008)
Quick RIAForge Update (03/26/2008)
TimeTracker Updated - Dealing with long strings in Flex DataGrids (03/26/2008)
Ask a Jedi: MVC too much work? (03/26/2008)
Time Tracker AIR Application Updated (03/25/2008)
Quick BlueDragon/Galleon Tip (03/25/2008)
cf.Objective Birds of a Feather Sessions (03/24/2008)
Ask a Jedi: Question on Application based CFCs (03/24/2008)
TimeTracker Updated, and how I did date filtering in SQLite/AIR (03/24/2008)
BACFUG Spry Preso Files (03/23/2008)
You know your plane is safe when it's running Linux... (03/21/2008)
is your framework up to date? (03/20/2008)
CFBL - Week 10 - The End (03/20/2008)
Adobe Developer Week (03/19/2008)
Ask a Jedi: Ajax-bound requests and onRequest (03/19/2008)
ColdFusion Biggest Loser Reminder (03/19/2008)
Ask a Jedi: So what happens when you don't var scope? (03/18/2008)
Facebook API Book (03/18/2008)
Ask a Jedi: CFC Scope Question (03/18/2008)
Files from last weeks Images presentation (03/17/2008)
Interesting ColdFusion 8, Auto-Suggest issue to watch for (03/17/2008)
Book Review: The Intellectual Devotional: American History (03/15/2008)
Lighthouse Pro 2.4.3 (03/14/2008)
Ask a Jedi: ColdFusion 8 Licensing Question (03/14/2008)
CFBL Update - Week 9 (03/14/2008)
Ask a Jedi: ColdFusion 8 Ajax Features and JavaScript Detection (03/13/2008)
Ask a Jedi: List question (03/12/2008)
Presenting tomorrow, and next week (03/12/2008)
Ask a Jedi: Having CFCHART Links in a new window (03/11/2008)
Coffee Talk: New Atlanta Announcement (03/11/2008)
Ask a Jedi: Spry, Database, and XML Question (03/10/2008)
Ask a Jedi: Development question - built in JRun web server versus IIS (03/10/2008)
Top 100 Sci-Fi Books (03/09/2008)
Someone tell me what this odd TV issue is (03/08/2008)
Suggest a topic for CFUNTED 08, and win a pass! (03/07/2008)
Cross-Domain AJAX calls using ColdFusion (03/07/2008)
ColdFusion wins DDJ Award (03/06/2008)
Ask a Jedi: Block access to an include files (03/06/2008)
Spry, Dates, and how we will make you conform.... (03/05/2008)
It's ok - we want you to lie to us... (03/05/2008)
Ask a Jedi: Check for file existence before upload (03/04/2008)
Speaking at BACFUG (03/04/2008)
Adding an ADD button for cfgrid - Part Deux (03/03/2008)
Adding an ADD button for cfgrid (03/03/2008)
ImageUtils updated (03/01/2008)
Semi-Pro, All Bad (02/29/2008)
Ask a Jedi: No cookie for you! (02/29/2008)
Even more YouTube... (02/29/2008)
My 30 seconds on ColdFusion (02/29/2008)
Quick and dirty CAPTCHA Guide - for ColdFusion 8 (02/28/2008)
ScopeCache on RIAForge (02/28/2008)
Can you do file uploads with ColdFusion 8's Ajax features? (02/27/2008)
CFBL Update - Week 7 - The "Numbers Lie" Edition (02/27/2008)
Ask a Jedi: Converting a set of static method calls to dynamic calls (02/26/2008)
Ask a Jedi: Where did Loci come from in Lighthouse Pro? (02/26/2008)
Galleon update (02/26/2008)
Ask a Jedi: Flex released - where do I go next? (02/25/2008)
Spry 1.6.1 Released (02/25/2008)
AIR Support? (02/25/2008)
Flex 3, AIR Released (02/24/2008)
Quick review of the Facebook platform (02/23/2008)
Interview as a Mac convert for the Digital Media Dude (02/22/2008)
Ask a Jedi: Creating RSS Feeds on the Fly from Semi-Dynamic Sites (02/22/2008)
The Friday "How dumb was I" post (02/22/2008)
How would you replicate CFIMPERSONATE? (02/21/2008)
Simple math tricks with ColdFusion 8 Ajax tags (02/21/2008)
Ask a Jedi: Remote access blocked by a host? (02/21/2008)
Spry update on the way (02/20/2008)
CFBL Update - Week 6 - The "Getting There" Edition (02/19/2008)
Article on Developer Center (02/19/2008)
Ask a Jedi: Delaying CFMENU (02/19/2008)
ColdFusion site, BabyPlays.com, featured on the Today show (02/19/2008)
Ask a Jedi: Why isn't my cferror working? (02/18/2008)
Small update to LighthousePro (02/18/2008)
Review: Burnout Paradise (Lost) (02/16/2008)
Ask a Jedi: Another Chart Question (02/15/2008)
Ask a Jedi: Question about CFC Security (02/14/2008)
CFBL Update - Week 5 - Half-Way to SkinnyVille Edition (02/14/2008)
Ask a Jedi: Requiring an API key for web services (02/14/2008)
Thank you to the NYCFUG (02/14/2008)
Five years old today (warning, fluff post) (02/12/2008)
Careers in Usability? (02/11/2008)
Quick Google Analytics Tip (02/11/2008)
Ask a Jedi: Issue with cfdocument and name (02/11/2008)
I Heart New York (02/11/2008)
Watch out for this CFFORM issue (02/10/2008)
ImageUtils launched at RIAForge (02/09/2008)
ColdFusion 8 is bringing the web counter back! (02/08/2008)
Another Charting Option - JFreeChart (02/08/2008)
Stupid CFCHART Trick of the Week (02/08/2008)
Ask a Jedi: Custom Tags, OnRequestStart, UDFs, and Antimatter Engines (02/07/2008)
CFBL Update - Week 4 - The "Show me your numbers" Mardi Gras Edition (02/07/2008)
Ask a Jedi: CFCHART Question (02/07/2008)
Important ColdFire security update (02/06/2008)
Happy Mardi Gras Recovery Day (02/06/2008)
Ask a Jedi: Dealing with session variables and multiple windows (02/06/2008)
CFBL Week 4 Numbers - Resend (02/06/2008)
This week... (02/04/2008)
Word of the Day: Query Anxiety (02/01/2008)
Ask a Jedi: AjaxProxy and working with CFCs (02/01/2008)
Ask a Jedi: Another CF8 Ajax question - Running code when stuff loads (01/31/2008)
Lost premiers tonight (01/31/2008)
Speaking at February New York CFUG Meeting (01/30/2008)
Ask a Jedi: AjaxProxy example (01/30/2008)
RIAForge back up (and note on what I screwed up) (01/30/2008)
OSX, multiple monitors, and mouse issues (01/29/2008)
Ask a Jedi: Moving the label of a pie chart to the right (01/29/2008)
ColdFusion Zone at DZone (01/29/2008)
Chasing down a whitespace issue (01/28/2008)
Ask a Jedi: CFIMPORT, Application.cfc, and custom tags (01/26/2008)
Ask a Jedi/Stump the Chump: CFDOCUMENT PDFs with Forms (01/25/2008)
Fight the (Spam) Power (01/24/2008)
Ask a Jedi: Remembering a search (01/24/2008)
RIAForge hits 400 (01/23/2008)
Ask a Jedi: Seeing a SOAP Request that ColdFusion sent (01/23/2008)
Are you No Name? (01/23/2008)
Ask a Jedi: Resources for selling ColdFusion? (01/23/2008)
Ask a Jedi: AjaxProxy and Application Scoped CFCs (01/22/2008)
Me (Too) and Gmail (01/22/2008)
BlogCFC, Custom tags and applications (01/21/2008)
InsideRIA Launches (01/21/2008)
Ask a Jedi: Getting started with SVN (01/21/2008)
Cloverfield is... (01/20/2008)
Review: SimCity DS (01/19/2008)
Coolest CFCHART Trick Ever (01/18/2008)
Friday Challenge - Build the End of the World (01/18/2008)
Ask a Jedi: Making large PDFs with CFDOCUMENT (01/17/2008)
Ask a Jedi: Formatting a year to just 08? (01/17/2008)
ColdFusion 8 Image functions and text size (01/16/2008)
Ask a Jedi: A onSessionEnd Question/Example (01/16/2008)
Ask a Jedi: Contact Form questions (01/15/2008)
CFBL Initial Stats (01/15/2008)
The Circle is Now Complete - CFWACK B3 in the house... (01/14/2008)
Another Adobe ColdFusion Survey (01/14/2008)
Wildly off topic - Hey you, fatso! (01/14/2008)
Fun little feed parsing issue to watch out for - new lines! (01/14/2008)
BlogCFC, ColdFire Updates (01/14/2008)
Ask a Jedi: Mixing cfform validation and ajax-based functions (01/11/2008)
Time Tracker AIR Update, and what I learned about label functions and optional args in Flex (01/11/2008)
Ask a Jedi: One login, multiple applications (01/11/2008)
Two SQLite tool recommendations (01/10/2008)
Working with Flex, AIR, and SQL (2) (01/09/2008)
Ask a Jedi: Multiple questions on Application startup and templating (01/09/2008)
Hey DevWebPro, aggregate this! (01/08/2008)
Ask a Jedi: Development versus Staging servers (01/08/2008)
Ask a Jedi: Getting stuff from the Ajax Tree, hack of Forta's File Browser Example (01/08/2008)
In Memory: Jacqueline Camden (01/07/2008)
Stump the Chump - Applying JRun Updaters to ColdFusion (01/07/2008)
ColdFusion IDE Survey (01/07/2008)
Flex 3 / AIR Pre-release tour (01/07/2008)
Ask a Jedi: Getting a bit fancier with a layout custom tag (01/06/2008)
Another charting option: XML/SWF Charts (01/04/2008)
Ask a Jedi: Flexible string comparisons (01/03/2008)
Top entries from 2007, and word count fun (01/03/2008)
RIAForge back up (01/03/2008)
Ask a Jedi: Where in the heck is this PATH variable coming from? (01/02/2008)
CFUNITED and the Early Bird Discount (01/02/2008)
Ask a Jedi: "Object of type class.lang.Boolean cannot be used as an array" (01/02/2008)
Happy New Year, and my thoughts on last and this year (01/01/2008)
Working with Flex, AIR, and SQL (12/31/2007)
End of Year RIAForge Stats (12/31/2007)
I've encrypted my CFML templates and lost the originals, now what? (12/28/2007)
Executing JavaScript functions from within ColdFusion 8 containers (12/27/2007)
Implicit array/struct and function calls (12/27/2007)
Merry Christmas! (12/25/2007)
Review: Puzzle Quest: Challenge of the Warlords (12/24/2007)
Out of office this week (12/23/2007)
Additional (Free!) chapters from CFWACK posted (12/23/2007)
Ask a Jedi: Handling print format when using custom tags (12/22/2007)
CFeMmy Winners Announced (12/21/2007)
Parsing an IIS log file in ColdFusion (12/20/2007)
Speaking at cf.Objective (12/20/2007)
Linux Flex Builder Alpha Released (12/19/2007)
Ask a Jedi: Getting a list of application names in ColdFusion (12/19/2007)
Flex 3/AIR version of CFLib demo (12/19/2007)
ColdFusion Relative Time Script UDF (12/19/2007)
Ask a Jedi: Migrating from static XML to CF for Spry development (12/18/2007)
2007 CFeMmys Open (12/18/2007)
CFLib gets a dose of fresh air... (12/18/2007)
Important Spry/AIR Resource (12/17/2007)
Model-Glue Cookbook (12/17/2007)
Spry Validation: Textarea (12/17/2007)
Blue Man Group Review (12/16/2007)
12 Days of Christmas - Yahoo Style (12/14/2007)
Enabling features in ColdFusion's Rich Text Editor (12/14/2007)
Friday Challenge - Christmas Style (12/14/2007)
When does it make sense to "mess" with your search engine? (12/13/2007)
Labs updates Flex, AIR, and release BlazeDS (12/13/2007)
More on Thermo (12/12/2007)
OS X CD ripper recommendation? (12/12/2007)
Speaking at WebManiacs (12/12/2007)
Video on Thermo (12/12/2007)
CFeMmy Nominations (12/12/2007)
iPhone version of ColdFusionBloggers.org (12/11/2007)
Look what Todd did... (12/11/2007)
The new, Fetch version of ColdFusion Debugging (with Flair) (12/11/2007)
Dealing with ColdFusion Binds and JavaScripts (12/11/2007)
Update your bookmarks please (12/10/2007)
Google's Charting API (12/10/2007)
Lighthouse Pro Update (12/10/2007)
My quickie iPhone/iPod Touch Review (12/09/2007)
Google Docs CFC (12/08/2007)
Quick example of the Google Docs API (12/07/2007)
Friday Challenge - Compare Directories (12/07/2007)
Ask a Jedi: Building a JavaScript Widget with ColdFusion (12/07/2007)
Review: Mass Effect (12/06/2007)
ServerMonitor API Example (12/06/2007)
Tapper, Nimer and Digital Primates join up (12/05/2007)
The Complete Guide to Adding Error Handling to Your ColdFusion Application (12/05/2007)
Late night XBLA question (12/04/2007)
Ask a Jedi: Setting focus to a field inside cflayout - possible? (12/04/2007)
Ask a Jedi: Randomizing the display of a query (12/04/2007)
PDF issue with ColdFusion Cookbook (12/03/2007)
Interesting display bug with CF8 HTML Grid (12/03/2007)
Ask a Jedi: Using Robust Exception Information on a shared host (12/03/2007)
I'll be a good citizen (soon) (12/03/2007)
The Wisdom of Chuck (11/30/2007)
RIAForge Schedular Mystery Solved (Mostly) (11/30/2007)
BlogCFC Export/Import Code (11/30/2007)
And then there was one... (11/29/2007)
ColdFusion 8 and Ajax-Based Login (11/29/2007)
Ask a Jedi: When does a session start? (11/29/2007)
Using CFDBINFO and CFZIP for quick database backups (11/28/2007)
Firefox 3 and Firebug (11/28/2007)
Why do HTMLEditFormat and HTMLCodeFormat take a version? (11/27/2007)
Ask a Jedi: How do you set the remote IPs for ColdFusion Developer Edition? (11/27/2007)
Why must cfexecute be closed? (11/27/2007)
CFWACK URLs for Code, Errata (11/27/2007)
Yellow Shipping CFC (11/26/2007)
Sending in my first XBox360 (11/25/2007)
Spry's URL Helper Utilities (11/25/2007)
Cool entry on mixing Spry tabs with HTML Panels (11/24/2007)
(Unofficial) Lighthouse Pro for Sybase (11/21/2007)
Interesting WDDX Bug with nulls (11/21/2007)
Today's waste of time: WOW Commercials (11/21/2007)
Quick (and simple) Tip 2: Zipping old files (11/20/2007)
Quick (and simple) Tip: Deleting old files (11/20/2007)
Request beta access for 64bit/Leopard Updates (11/20/2007)
Scheduler issue with RIAForge (11/20/2007)
BlogCFC, Galleon Updates (11/19/2007)
My cheesy non-database ColdFusion Code for Model-Glue.com (11/19/2007)
List of Model-Glue sites launched (11/19/2007)
Multiple Emails from RIAForge (Yes, I know) (11/19/2007)
Ask a Jedi: ColdFusion 8 and Ext (11/17/2007)
Why isn't ColdFusion Free and Open Source? (11/16/2007)
Ask a Jedi: Dynamic evaluation (11/16/2007)
Avoid use of scope names for argument names (11/15/2007)
AIR gets a logo (11/15/2007)
Interview with High School ColdFusion Teacher (11/15/2007)
ColdFusion 8 Cumalitive Hot Fix 2 Out (11/14/2007)
Ask a Jedi: Mixing CFLAYOUT and PDF/Flash (11/14/2007)
ColdFusion/DotNet question for my readers (11/13/2007)
ColdFusion based application featured at Apple (11/13/2007)
Followup to XML Post (11/13/2007)
When is XML not XML? (11/12/2007)
My Leopard Report - The Good, the Bad, and the Ugly (11/12/2007)
Reviews: Call of Duty 4 and Guitar Hero 3 (11/11/2007)
ColdFusionCommunity.org Launches (11/10/2007)
Recording URLs and Downloads (11/09/2007)
Application.cfc Methods and Example Uses (11/09/2007)
Ask a Jedi: Moving to ColdFusion (11/08/2007)
Adobe releases JRun Updater (11/08/2007)
Multiple Presentations Today (11/08/2007)
Official word on ColdFusion and Leopard (11/07/2007)
Another OS X Question (11/07/2007)
Ask a Jedi: Getting all the link labels from a string in ColdFusion (11/07/2007)
Kristen Schofield is now blogging (11/07/2007)
Spry's HTML Panel (2) (11/06/2007)
Checkout the Stroz on DevNet: Using ColdFusion 8 with Microsoft Exchange Server (11/05/2007)
Application.CFC Template Update (11/05/2007)
Model-Glue's new Flex Integration (11/05/2007)
Spry's HTML Panel (11/04/2007)
Review: The Sunrise Lands (11/03/2007)
Create a RSS Feed out of your Share Files (11/02/2007)
Ask a Jedi: How do I insert Spry data into a ColdFusion variable? (11/02/2007)
Friday quickie - Example of simple caching of RSS Items (11/02/2007)
Happy November, Happy National Adoption Month (11/01/2007)
Ask a Jedi: How do you start an Adobe User Group? (11/01/2007)
Ask a Jedi: Why isn't my form reloading the whole page? (10/31/2007)
Application.CFC Code Review (10/31/2007)
Lucene, Share, and SpoolMail Updates (10/30/2007)
10,000 Downloads - Do I get a gold watch? (10/30/2007)
DirectoryWatcher and ColdFusion Image Manipulation Example (10/29/2007)
Non-Leopard OSX ColdFusion install issue to watch for (10/29/2007)
New Layout (10/28/2007)
ColdFusion 8 + Leopard (10/28/2007)
Spry's Confirmation Validation (10/26/2007)
Happy Leopard Day (10/26/2007)
Quick test post (10/25/2007)
ImageScaleToFit goes both ways (10/25/2007)
ImageScaleToFit Bug (10/25/2007)
Lucene Update (10/24/2007)
Spry adds support for CSV and TSV datasets (10/23/2007)
Using spry:hover, spry:even, and spry:odd all together (10/22/2007)
WSDL is not documentation! (10/22/2007)
Flex 3 Jedi? Help seed the cookbook! (10/22/2007)
Spry's Password Validation (10/21/2007)
Minor update to Galleon (10/21/2007)
Playing with form validation in Spry (10/20/2007)
Ask a Jedi: Loading a Page with CFCALENDAR (10/19/2007)
Ask a Jedi: Restricting CFAJAXProxy to certain methods (10/18/2007)
Cool Spry Tip (10/18/2007)
Presentation Tonight: Spry and ColdFusion (10/18/2007)
ColdFusion Administrator Extension - Verity Searcher (10/17/2007)
Share API Updated (10/17/2007)
ColdFusionBloggers adds Ping (10/17/2007)
Another OS X Question - All my apps go to the netherworld... (10/16/2007)
Caching CFCONTENT (10/16/2007)
RIAForge DNS (10/16/2007)
Doing HTTP Conditional Gets in ColdFusion (10/15/2007)
Ask a Jedi: Using Sleep ok? (10/15/2007)
Flex Aggregator Launches: All Your Flex Are Belong To Us (10/15/2007)
BioShock versus Halo 3 (10/13/2007)
Update #3: Galleon 2 (10/12/2007)
Update #2: BlogCFC 5.9 (10/12/2007)
Update #1: toXML (10/12/2007)
File Upload Guide (10/12/2007)
ColdFusion and Verity Tip - Getting results found when paging (10/11/2007)
ColdFusion eSeminar Series (10/11/2007)
ColdFusion Code Beautifiers? (10/11/2007)
Simple ColdFusion 8 Drop Shadow Example (10/10/2007)
xkcd - Web Comic (10/10/2007)
ColdFusion Account Managers (10/09/2007)
ColdFusion Developer Center at Yahoo (For real this time) (10/09/2007)
License Report at RIAForge (10/08/2007)
Ask a Jedi: How can you timeout a session in an Ajax-based application? (10/08/2007)
Warning to Adium/iTunes users (10/08/2007)
First version of Share CFC Released (10/06/2007)
Friday Worthless Post (10/05/2007)
Ask a Jedi - Issue with single quotes in a query (10/05/2007)
Quick tip - using ColdFusion.navigate instead of bindings (10/04/2007)
Code from ColdFusion Boot Camp, and Tip about ColdFusion 8 and JSON (10/03/2007)
Dailyrazor hosted sites down (10/03/2007)
ColdFusion Sneak Peak (10/02/2007)
ColdFusion 9's code name is... (10/02/2007)
MAX Keynote Notes - Day 2 (10/02/2007)
MAX Keynote Notes Day 2 - Part Deux (10/02/2007)
ColdFire Guide (10/02/2007)
It's funny who you can meet at MAX... (10/01/2007)
MAX Keynote Notes (10/01/2007)
Spry 1.6 Released (10/01/2007)
More new releases on Labs (10/01/2007)
ColdFusion Lucene Test (09/30/2007)
My obligatory "Off to MAX" Post (09/29/2007)
Adobe Developer Connection Launches (09/29/2007)
ColdFusion 8, MySQL, HostMySite, and NPEs (09/28/2007)
Changing the text of a CFWINDOW (09/28/2007)
CFThread Demo with Status Messages (09/27/2007)
Galleon 2 ready for testing (Release Candidate) (09/26/2007)
Ask a Jedi: CFThread Questions (09/26/2007)
Looking for wireless suggestions (09/26/2007)
Quickie Code Review (09/25/2007)
ColdFire 1.0 Released (09/25/2007)
What shouldn't you be doing in ColdFusion? (09/24/2007)
Ask a Jedi: Finding an value in an array of structures (09/23/2007)
Firefox 2.0.0.7 - DOA? (09/21/2007)
Fixing the Facebook Problem, and why one ColdFusion feature needs to die... (09/21/2007)
Ask a Jedi: Can you run a tag in "end" mode inside a CFIF? (09/21/2007)
Database Explorer Updated (09/21/2007)
The Friday "I like to link" Post (09/21/2007)
The book is here!! (09/20/2007)
A use for structFind! (09/20/2007)
Quick and Dirty JSON/Query Example (09/20/2007)
MAX BOF list posted - CFC Session is on again (09/19/2007)
Quick CFEclipse/Frameworks Explorer Tip (09/19/2007)
Pablo Vos on ColdFusion and PHP/ASP (09/19/2007)
MAX Attendance Record! (09/18/2007)
The End of the World (09/18/2007)
CFFEED Tip - Structure versus Query (09/18/2007)
Using Sitemaps with Verity (09/17/2007)
CFSnippets.org Launches (09/17/2007)
Geek the Tube Forums moved... (09/17/2007)
CFCATCH accepts any attribute? (09/16/2007)
Logo for ColdFusion - CFImage Demo (09/14/2007)
Serving up CFIMages via Image Tags (and a Non-CF Friday contest!) (09/14/2007)
Mean People Suck (09/13/2007)
CFCDev Mailing List (09/13/2007)
Working with funky XML in ColdFusion (09/13/2007)
CS3 doesn't like me - can anyone help? (09/13/2007)
My kul CFC (Kuler API CFC) (09/12/2007)
NPEs, onRequest, and other mysteries of the universe... (09/12/2007)
Presenting to Detroit CFUG Tonight (09/12/2007)
2 new projects up at RIAForge (09/11/2007)
CFWACK 8 Volume 1 Site and Forums (and sample chapters!) (09/11/2007)
Slow page report - Doing it with ColdFusion 8 (09/11/2007)
Important Message for CFDJ Subscribers (09/11/2007)
First ColdFusion 8 Cumulative Hot Fix Released (09/10/2007)
Bug with JavaScript bind and textareas (09/10/2007)
Web Development Tip - Always provide directions... (09/10/2007)
ColdFusion mapping names and conflicts (09/10/2007)
Galleon 2 Update (09/09/2007)
Sys-Con announces end of CFDJ (09/09/2007)
Shall we play a game? (09/08/2007)
Site launched - TipBin.com (09/07/2007)
ColdFusion 8 Tip - Reading the top (or another slice) of a file (09/07/2007)
Thunderbird Tip: Rewrap (09/06/2007)
JSON/Paging Fix for Spry (09/06/2007)
And I'm back... (09/06/2007)
Exporting from CFGRID (09/04/2007)
OOO Notice (09/04/2007)
ColdFusion custom tag for layout example (09/03/2007)
Ding dong the WACK is dead... (09/01/2007)
Updating a drop down based on an HTML Grid Selection (08/31/2007)
Ask a Jedi: Display value of file upload field (08/31/2007)
Slideshow with Flair (08/31/2007)
New ColdFusion web site: learncf.com (08/31/2007)
Adding "virtual" data to a Zip with ColdFusion (08/30/2007)
Using component as a variable type (08/30/2007)
Simple image slide show built in ColdFusion 8 (08/29/2007)
Holy RIAForge Milestone, Batman! (08/29/2007)
Cool feature in CFPRESENTATION (08/29/2007)
Excellent ColdFusion/Ajax Demo by James Edmunds (08/28/2007)
Ajaxian publishing ColdFusion/Ajax articles (08/28/2007)
Avoid those "hidden" features (08/28/2007)
Can you send flushed content to ColdFusion 8 Ajax UI containers? (08/27/2007)
Speaking at CFUNITED Express in Chicago (08/27/2007)
Speaker recommendations? (08/27/2007)
Friday Challenge - Reorder a CFC File (08/24/2007)
FeedBurner CFC (08/24/2007)
Calling want-to-be artists - Galleon Logo (08/24/2007)
Jason Delmore of Adobe blogging (08/23/2007)
CFWACK TOC (08/23/2007)
YouTube CFC Update and a Demo Site (08/22/2007)
Metadata properties for CFFEED (08/22/2007)
YouTube API CFC (08/21/2007)
Getting the space available on a hard drive (partition) (08/21/2007)
Mark Drew's Model-Glue Tips (08/21/2007)
Custom grid renderers with CFGRID (08/20/2007)
Interesting little bug with query columns (08/20/2007)
Adobe ColdFusion Extensions and CFEclipse (08/20/2007)
Update to ColdFusion Eclipse Plugins (08/17/2007)
Got?CFM Released 1000th Site (08/17/2007)
Ask a Jedi: Becoming a Jedi? (08/17/2007)
Cool little CFPOD Trick (08/17/2007)
Updates to ColdFusionBloggers (08/16/2007)
Quick note on Google for Domains (and other misc personal/boring stuff) (08/16/2007)
Ajax Presentation Recording and Files (08/15/2007)
Presentation to Hartford, CT Adobe User Group Tonight (08/15/2007)
What has changed (tag/function-wise) in ColdFusion 8? (08/15/2007)
Using ColdFusion 8 to perform an "Auto Save" (08/15/2007)
ColdFusion Ajax Debugger Ignores CFSETTING (08/15/2007)
Database Explorer - ColdFusion 8 Sample Application (08/14/2007)
ColdFusion 8's Ajax debug works nicely with Spry (08/14/2007)
Help promote ColdFusion (and win some cool crap) (08/13/2007)
Bug to watch out for with CFFEED (08/13/2007)
Ask a Jedi: Structure as an Argument (08/13/2007)
Email alerts added to ColdFusionBloggers (08/13/2007)
Hiding meta information in ColdFusion 8's CFDUMP (08/12/2007)
This Movie Is Not Yet Rated and C.S.A. (08/12/2007)
Another Flash Launches Tonight (08/10/2007)
Yes, Virginia, you can put HTML into a CFGRID (08/10/2007)
Friday Joke - Share your best geek one liner (08/10/2007)
Reacting to grid row selection (08/09/2007)
Mysterious method added to your CFCs - where does it come from? (08/09/2007)
Do you want to be in pictures?? (08/09/2007)
Recording from ColdFusion 8 Image Presentation (08/09/2007)
MAX Early Bird ends tonight (Not!) (08/08/2007)
Amazon shows new WACKs (08/08/2007)
Speaking tonight at Boston CFUG on CFIMAGE (08/08/2007)
Preselecting a tab via the URL in ColdFusion 8 (08/08/2007)
Miss a day? Catch up with ColdFusionBloggers.org (08/07/2007)
Selecting default items using ColdFusion 8's AJAX Controls (08/07/2007)
More on VerifyClient - ColdFusion 8 Ajax Security Feature (08/07/2007)
The power we wield... (08/06/2007)
Don't forget that CFCONTENT tag when working with Spry (08/06/2007)
Finally reading some book about a kid wizard - maybe you've heard of it? (08/06/2007)
Warning about onMissingMethod (08/05/2007)
Reminder about forms and ColdFusion 8 Ajax Containers (08/05/2007)
Dreamweaver Help Needed (08/04/2007)
Soundings 2 Released - Shock the Monkey (08/03/2007)
Simple "FIlter as you type" ColdFusion 8 Demo (08/03/2007)
Another simple update to ColdFusionBloggers.org - Logging Search Change (08/03/2007)
Sad day for the sousaphone (08/02/2007)
Counting Word Instances in a String (08/02/2007)
Slick image cropping demo by Todd Sharp (08/02/2007)
Correction to earlier ColdFusionBloggers.org post and a warning about removing HTML (08/01/2007)
Quick - look at the dumb mistake on ColdFusionBloggers.org (08/01/2007)
Sam's list of ColdFusion One-Liners (08/01/2007)
Update to ColdFusionBloggers.org, and a general Thank You! (07/31/2007)
ColdFusion 8 Ajax Security Features (07/31/2007)
Using CFTREE for Navigation (07/31/2007)
Another followup to my Alerts post (07/31/2007)
ColdFusion 8: Working with PDFs (Part 8) (07/30/2007)
Reminder for ColdFusionBloggers.org testers (07/30/2007)
Quick thanks to Aquafold (07/30/2007)
ColdFusion 8 Eclipse Extensions now available separately! (07/30/2007)
ColdFusion 8 - Help spread the word (07/30/2007)
ColdFusion 8 Launches! (07/30/2007)
Livedocs gone? (07/29/2007)
Columnmap "Gotcha" with CFFEED (07/29/2007)
Update to ColdFusionBloggers.org (07/29/2007)
More on ColdFusion 8 Server Alerts (07/27/2007)
Ajax Technology Center (07/27/2007)
Update to ColdFusionBloggers.org: Ajax-based Contact Form (07/27/2007)
Using the CFTHREAD Scope (07/27/2007)
Important Update for BlogCFC Users (07/26/2007)
Getting a page from a PDF Document in ColdFusion 8 (07/26/2007)
ColdFire Updated - Supports Variable (07/26/2007)
Reading text from a PDF in ColdFusion 8 (07/25/2007)
Server Monitor Alerts in ColdFusion 8 (07/25/2007)
Using CFDIV for Paging (ColdFusionBloggers.org Update) (07/24/2007)
Todd gets the funk on with Spry and ColdFusion 8 (07/24/2007)
Another "Gotcha" with cfform tags and cfdiv (07/24/2007)
ModelGlue Tip: ViewState's getAll() (07/23/2007)
A "Gotcha" with Auto Suggestions in ColdFusion 8 (07/23/2007)
Update to ColdFusionBloggers - and a description of my process change (07/22/2007)
Site back up (again) (07/22/2007)
Fun way to break attributeCollection in ColdFusion 8 (07/21/2007)
Model-Glue List of Sites (07/21/2007)
AutoSuggest Example (07/20/2007)
onMissingTemplate Example (07/20/2007)
Change that email address please (07/20/2007)
Building an "auto refresh" div with ColdFusion 8 (07/19/2007)
My little project - ColdFusionBloggers.org (07/19/2007)
Back up... (07/19/2007)
Ask a Jedi: Preventing direct access to a CFC (07/19/2007)
Ask a Jedi: Working with IFrames, JavaScript, and how ColdFusion 8 makes life easier (07/18/2007)
Another "ColdFusion 8 is so super fast" Post (07/17/2007)
Interesting change to CFCONTENT in Scorpio (07/16/2007)
Clearing your SnipEx Cache - and CFLib SnipEx Update (07/16/2007)
ColdFusion Bootcamp at MAX (07/13/2007)
Knowing when to call it a day... (07/13/2007)
ColdFusion 8: Working with PDFs - A Problem (07/12/2007)
ColdFusion 8: Image Rotate Tip (07/12/2007)
You want some RIAForge source? You got some RIAForge source! (07/11/2007)
Remember LINDEX? ColdFusion integration with Lucene (07/11/2007)
Snipex Code Released - CFLib Available in Eclipse (07/11/2007)
Soundings 2 Update / Request for Logo (07/11/2007)
Helping orphans in Iraq (07/10/2007)
Happy Birthday, ColdFusion (07/10/2007)
Interesting blog post on ColdFusion and OO (07/09/2007)
Real life Var scope screw up (07/09/2007)
Boeing 787 Launches (07/09/2007)
Ask a Jedi: Components and the Init Method (07/07/2007)
RIAForge Move Begun (07/06/2007)
Soundings 2 Preview Release (07/06/2007)
RIAForge Notice! (07/06/2007)
ColdFusion 8 - Return Format for ColdFusion Components (07/05/2007)
CFEclipse adds Eclipse 3.3 Support (07/04/2007)
Ask a Jedi: Problem with Autosuggest (07/04/2007)
Review: Transformers (07/03/2007)
MAX BOF Announcement (07/03/2007)
Update to LighthousePro/JSON/Spry Post (07/03/2007)
Ask a Jedi: Listing all var scoped variables (07/03/2007)
Error with queryNew and query of queries (07/02/2007)
Girly man geek helps jock get on MTV (07/02/2007)
Case Study - Moving to Spry 1.5 and JSON for Lighthouse Pro (07/02/2007)
Undocumented change to GetHTTPRequestData in ColdFusion 8 (07/01/2007)
Aptana adds Spry support (07/01/2007)
Back from CFUNITED (06/30/2007)
Windows Live Writer and BlogCFC (06/29/2007)
Spam list reminder (06/29/2007)
Security Presentation Materials (06/29/2007)
Modifying the ColdFusion 8 Administrator Menu (06/28/2007)
ColdFusion 8: Pausing Scheduled Tasks (06/28/2007)
Source code from today's presentations (make that yesterday) (06/27/2007)
Event Gateways are in ColdFusion Standard 8 (06/27/2007)
CFUNITED Keynote Notes (06/27/2007)
Off to CFUNITED! (And a few random notes...) (06/26/2007)
Model-Glue 2 is Here! (06/26/2007)
Birds of a Feather @ CFUNITED (06/26/2007)
Two ColdFusion 8 Documentation Resources (06/25/2007)
Useless Trivia Post - ColdFusion and the Government (06/25/2007)
Review: I Am Legend (06/25/2007)
New Spry Preview: Tooltips (06/23/2007)
Simple AIR Demo - Yahoo Traffic (06/22/2007)
Dunk Me (Seriously) (06/22/2007)
Find the bug.... (06/22/2007)
Registering for MAX? Use me! (06/22/2007)
Quick example of CFTHREAD - and a warning (06/21/2007)
ColdFusion 8's Server Monitor and Performance (06/21/2007)
CFMenu CSS Hacking with Daniel Budde II (06/21/2007)
ColdFusion Meetup Presentation - Mark Drew and CFEclipse (06/21/2007)
Happy Release Day (06/20/2007)
Sessions posted for MAX 2007 - Speaking at MAX (06/20/2007)
Has MX left the party? (06/20/2007)
ColdFusion 8: AJAX UI Windows (06/20/2007)
File System versus Database Argument (06/19/2007)
ColdFusion Position in Lafayette, LA (06/19/2007)
Winner of ColdFusion Newbie Contest (06/19/2007)
ColdFusion 8: Getting the value of AJAX-ified controls (06/19/2007)
ColdFusion 8: AJAX UI Menus (06/18/2007)
Happy Father's Day (06/17/2007)
ColdFusion 8: Getting the autonumber insert ID (06/15/2007)
Warning about the ColdFusion Admin API and CFLOGON (06/15/2007)
ColdFusion Newbie Contest - Wrap Up (06/15/2007)
ColdFusion 8: Server Monitor API (06/14/2007)
One more item for the ColdFusion Security Checklist - AJAX Debugging (06/14/2007)
ColdFusion Newbie Contest - Entry 10 (06/14/2007)
User Group Manangers Meeting (06/13/2007)
ColdFusion 8: URL Thumbnails (06/13/2007)
ColdFusion Newbie Contest - Entry 9 (06/13/2007)
CFUnited Europe Announced (06/13/2007)
RIAForge Milestone (Again!), and time for 'What will happen to Ray on this trip' (06/12/2007)
Aptana adds AIR Support (06/12/2007)
Ask a Jedi: Tracking Users (06/12/2007)
ColdFusion 8: AJAX UI Pods (06/11/2007)
Preachin' the VAR Scope Gospell (06/11/2007)
Aggregator CFC updated, hosted, and named (06/11/2007)
AIR and Flex 3 Betas Launch Tonight (06/10/2007)
HP Printer and the Tone of Death (06/10/2007)
ColdFusion 8: AJAX UI Vertical and Horizontal Boxes (06/08/2007)
Ask a Jedi: Using the Server Scope (06/08/2007)
Diagnose an OS X Slowdown (06/08/2007)
ColdFusion 8 Aggregator CFC - First Release (06/08/2007)
ColdFusion 8: AJAX UI Tabs (06/07/2007)
It is here - Yahoo launches ColdFusion Developer Center (06/07/2007)
Automatically pushing to a new URL, and how ColdFusion 8 makes this a bit simpler (06/07/2007)
ColdFusion 8 Dictionary for CFEclipse (06/07/2007)
ColdFusion 8: Admin API and Trusted Cache (06/07/2007)
ColdFusion 8: AJAX UI Layouts (06/06/2007)
Jericho Returns (06/06/2007)
ColdFusionJedi.com lives (hopefully) (06/06/2007)
Quick note - blog going into "read only" mode. (06/06/2007)
ColdFusion 8: Update to Aggregator UDF (06/06/2007)
ColdFusion 8: RSS Aggregator UDF (06/05/2007)
Ask a Jedi: What day is Wednesday? (06/05/2007)
ColdFusion 8: New Looping Constructs (06/05/2007)
Site Updates + Random Notes (06/04/2007)
ColdFusion 8: Dumping a Query in ColdFusion 8 (06/04/2007)
Mark Drew announces SnipEx (06/04/2007)
Installing Windows on a Dell machine with SATA? Check this tip... (06/04/2007)
ColdFusion 8: A "Tip" For You... (06/03/2007)
ColdFusion 8: Additions to Roles Based Security (06/03/2007)
ColdFusion 8: Built-in Support for MySQL 4/5 (06/02/2007)
ColdFusion 8: QueryConvertForGrid (06/01/2007)
Windows Server ISO with SATA Drivers slipstreamed in... (06/01/2007)
ColdFusion 8: Dumping gets even better (06/01/2007)
Model-Glue 2 - When will it get here? (05/31/2007)
ColdFusion 8: Demo of CFGRID, Ajax binding, and CFWINDOW (05/31/2007)
BlogCFC and ColdFusion 8 (05/31/2007)
ColdFusion 8: Handling missing CFM files (05/31/2007)
ColdFusion 8: Log Viewer added to Eclipse Plugins (05/30/2007)
HostMySite offering free ColdFusion 8 hosting (for testing purposes) (05/30/2007)
ColdFusion 8: Checking the size of an image (05/30/2007)
ColdFusion 8: Checking to see if a file upload is an image (05/29/2007)
Adobe releases public release candidate of ColdFusion 8 - AKA Scorpio (05/29/2007)
Stop downloading MP3s... (05/29/2007)
Next Online ColdFusion Usergroup Meeting (05/29/2007)
Drink Coffee (05/29/2007)
Harlan AdServer Updated (05/28/2007)
Ask a Jedi: Moving existing application code into Model-Glue (05/27/2007)
Forta's Response to the Computerworld Article (05/26/2007)
Computerworld Journalist and the Death of ColdFusion (05/24/2007)
Lost for May 24 - The WTF Edition (05/23/2007)
Warning to Spry folks upgrading to 1.5 (05/23/2007)
RSS data for projects in RIAForge via Yahoo Pipes (05/23/2007)
Watch out for the reserved event values in Model-Glue (05/22/2007)
Autosuggest in Spry - Working with ColdFusion (05/22/2007)
Potential Jericho Closure (05/21/2007)
Travelling to Vegas - Start the pool now... (05/20/2007)
Review: Island in the Sea of Time (Series) (05/19/2007)
Spry, Apollo, and Remote XML Sources (05/19/2007)
Autosuggest in Spry (05/18/2007)
BlogCFC 5.8 Released (05/18/2007)
ColdFusion Security Reminder - Read me now (05/18/2007)
Friday Puzzler - A short one, I swear! (05/18/2007)
Online ColdFusion Meetup - Today! (And CFJUG news...) (05/17/2007)
Lost for May 16 - "...blow them all up to Hell" (05/16/2007)
History of ColdFusion Slide (05/16/2007)
Jericho needs an exit interview (05/16/2007)
Flex/ColdFusion case sensitivity gotcha (05/16/2007)
Newbie Contest Entries (05/16/2007)
Ask a Jedi: Client and Session Storage Questions (05/15/2007)
Macs are cool too... (05/15/2007)
Contest Deadline Today! (05/15/2007)
Coolest. Windows. Feature. Ever. (05/15/2007)
Model-Glue Listserv Notice (05/14/2007)
Presentation from Frameworks Conference Posted (05/14/2007)
Dynamic arguments and attributes in ColdFusion (05/14/2007)
Contest Reminder (05/13/2007)
Battlestar Galactica to continue... (05/12/2007)
Lighthouse Pro 2.4 Released (ColdFusion Bugtracker) (05/12/2007)
Looping over a ColdFusion Array (In ColdFusion 8) (05/11/2007)
Ask a Jedi: Password protecting CFIDE (05/11/2007)
All Mac All Day (or in another words - my thoughts on moving to the Mac full time) (05/10/2007)
Spry up on Livedocs (05/10/2007)
Variable Type Gotchas - ColdFusion Arrays and Boolean Functions (05/10/2007)
Lost for May 9 - "His name is Jacob" (05/09/2007)
Variable Type Gotchas - ColdFusion Arrays and Missing Indexes (05/09/2007)
Critical update for Canvas (ColdFusion Wiki) users (05/08/2007)
Next CF Meetup Meeting - CFUNITED Preview with Charlie Arehart (05/08/2007)
Ask a Jedi: Learning CFScript (05/08/2007)
Ask a Jedi: Sizing a window with ColdFusion (05/07/2007)
cfObjective in Review (05/07/2007)
Ben announces improvements to LCDS (Flex Data Services) Integration (05/06/2007)
Ben announces ColdFusion Debugger for Eclipse (05/06/2007)
Ben announces ColdFusion AJAX Wizard for Eclipse (05/06/2007)
cfObjective - Jason Delmore: Scorpio: 1337 (05/06/2007)
Tip for CFEclipse/CF Frameworks Explorer (05/06/2007)
Framework explorer ready for CFEclipse (05/06/2007)
cfObjective - Filtering and Sorting Data in Flex 2 by Scott Stroz (05/05/2007)
cfObjective - Dynamic Spry Widgets with Coldfusion by Andrew Powell. (05/05/2007)
cfObjective - Mark Drew and CFEclipse (05/04/2007)
Stepping up as Community Manager for Model-Glue (05/04/2007)
Model-Glue and AJAX Presentation (05/04/2007)
cfObjective - Mark Mandel and Transfer ORM (Object Relational Mapping) (05/04/2007)
Cock fighting in Louisiana on the way out... (05/04/2007)
cfObjective - Scorpio Keynote by Jason Delmore, Product Manager for CF. (05/04/2007)
Yes, I did make it, kinda... (05/04/2007)
On my way to CF Objective (05/03/2007)
Variable Type Gotchas - ColdFusion Lists and Empty Elements (05/02/2007)
Lots of Scorpio (ColdFusion 8) News (05/02/2007)
How do you handle libraries of code for your organization? (05/02/2007)
Variable Type Gotchas - ColdFusion List Delimeters (05/02/2007)
Happy happy - joy joy - New Mac on the Way (05/01/2007)
CFJUG Recording and Materials (05/01/2007)
toXML Component Updated (04/30/2007)
CFJUG Meeting Tonight - ColdFusion Variable Datatypes (04/30/2007)
Dealing with cookie-less sessions (04/29/2007)
Want some Joost? (04/27/2007)
Friday Puzzler - Listing all posibilities of a set (04/27/2007)
Mac Mozy in open beta (04/26/2007)
RIAForge hits 200! (04/26/2007)
Can I do it in a CFC? (04/26/2007)
Where to find a ColdFusion Job (04/26/2007)
Flex Going Open Source (04/26/2007)
Where I am (and why I'm still behind) (04/25/2007)
Online ColdFusion Meetup very active this week with 3 meetings (04/25/2007)
Mozy is a life saver (04/25/2007)
Changing ColdFusion settings per application - New Scorpio Feature Announced (04/24/2007)
Where the heck am I? (04/24/2007)
What I did this weekend... (04/23/2007)
Heroes Returns Tonight (04/23/2007)
Two Reminders - Next CFJUG Meeting and ColdFusion Contest (04/23/2007)
Ask a Jedi: Controlling where ColdFusion looks to run a custom tag (04/23/2007)
Watch out for overly vague cfcatch statements (04/20/2007)
New Revision of ColdFusion Web Application Construction Kit - Now with 3 times the goodness! (04/19/2007)
Apollo Recording (04/19/2007)
Why you will never read my blog again... (04/19/2007)
Ask a Jedi: How much is too much when it comes to the Application scope? (04/18/2007)
Helping spread the word - Contributions for Virginia Tech (04/18/2007)
Two Apollo Notes (And no, this isn't a BSG post) (04/17/2007)
Quick example of cleaning up Verity results (04/17/2007)
ColdFusion Query to Flex DataGrid (04/17/2007)
ColdFusion Newbie Contest Announced - Monster Maker (04/16/2007)
CFJUG meeting scheduled (04/16/2007)
Ask a Jedi: cfinvoke and createObject (04/15/2007)
Friday Puzzler : Lines, your days are numbered... (04/13/2007)
Recording from ColdFusion Meetup (04/13/2007)
Recording from last nights presentation (04/12/2007)
Duplicate Application name issue (04/12/2007)
Lost review for April 11 (04/11/2007)
Reminder - ColdFusion Meetup Tomorrow (04/11/2007)
Reminder - Presentation to Toronto UG Tonight (04/11/2007)
Recommend a good UPS? (04/10/2007)
Something to remember when working with inline components in Flex (04/10/2007)
And now for something very important... (04/08/2007)
Using AJAX and Server Side Search (2) (04/07/2007)
Using AJAX and Server Side Search (04/07/2007)
Friday Puzzler - Getting Bob Fired (04/06/2007)
Presenting to Toronto UG (04/05/2007)
Update Firebug. Like now. (04/05/2007)
Ted Patrick publishes a list of top Flex Firms (04/05/2007)
ColdFire/Lighthouse Updates (04/04/2007)
Ask a Jedi: Updating data and refreshing with Spry (04/04/2007)
Did you know about the Log Viewer Filter? (04/03/2007)
JSEclipse Updated (04/03/2007)
Model-Glue code to avoid (04/03/2007)
Why I love my insurance company (Mega) (04/03/2007)
Interesting CFTIMER Behavior (04/02/2007)
Apollo Screensaver Post (04/02/2007)
New pricing plans for my products (04/01/2007)
My second HTML based Apollo application (03/30/2007)
Friday Puzzler - Getting even with Bob (03/30/2007)
ColdFusion MX 7.0.2 Cumulative Hot Fix 2 (03/30/2007)
Building an HTML based Apollo Application (03/29/2007)
Followup to last Model-Glue article - checking for the existence of a value (03/29/2007)
Late night link/question/Star Trek reflections (03/28/2007)
XBox 360 Elite (03/28/2007)
Changes to the ColdFusion Online Meetup group (03/28/2007)
Interesting Model-Glue "Feature" to watch out for (03/27/2007)
Next CFJUG Title (No Date) (03/27/2007)
Building a simple "Days Till" code block in ColdFusion (03/27/2007)
Off to Las Vegas (03/25/2007)
Apollo isn't just Flash/Flex (03/23/2007)
RIAForge updated to include wikis (03/23/2007)
ColdFire's SizeSplit function (and the dumb mistake I made) (03/23/2007)
Getting the columns of a Spry Dataset (03/23/2007)
Model-Glue tip - Watch out for renamed events (03/22/2007)
More new ColdFusion 8 Goodness (03/22/2007)
Public beta of ColdFusion 8 and New Features mentioned at WebDU (03/22/2007)
My cf.Objective() Fusion Authority Interview Is Up (03/22/2007)
Critical ColdFire Update (03/21/2007)
Apollo videos from Apollo Camp (03/21/2007)
Update to my Apollo regex checker (03/21/2007)
Another quick Apollo App (03/21/2007)
Quick Application.cfc Review (03/21/2007)
Spry 1.5's new "Session Expired" Support (03/20/2007)
The Magic of 1 (03/20/2007)
Interview at cfFrameworks (03/20/2007)
Need ColdFire testers (03/20/2007)
Edge article by Brian Rinaldi (03/19/2007)
My first Apollo app (03/19/2007)
Apollo added to RIAForge (03/19/2007)
Apollo on Labs (03/18/2007)
Few Sunday Notes (03/18/2007)
Free Apollo book available on Labs (03/17/2007)
Ask a Jedi: Ordering Verity results by filename (03/16/2007)
Lighthouse Pro 2.3 Released (03/16/2007)
How to tell if a header has been set in ColdFusion (03/16/2007)
Spry 1.5 Preview (03/15/2007)
Uploading multiple files in Flex as one "unit" (03/15/2007)
Counting Sessions with Application.cfc (03/15/2007)
Pre-conference classes for CFUNITED Posted (03/15/2007)
Lost Review for March 14, 2007 (03/15/2007)
Louisiana stands alone (03/14/2007)
Quick example of JSON versus XML (03/14/2007)
Links taking forever to load (03/14/2007)
ColdFire is Hot (03/13/2007)
Is it cold in here or is it just me? ColdFire RC1 Released (03/13/2007)
Tracking data views accurately (03/13/2007)
New Yorkers don't speak like us... (03/12/2007)
Counting Sessions with Application.cfm (03/12/2007)
Announcing ColdFire (03/09/2007)
Trip report and review of CFUNITED/Express (03/09/2007)
On the way to New York (almost) (03/07/2007)
Alagad is hiring (03/06/2007)
Yahoo's Search SDK Updated (And guess what new language is included?) (03/05/2007)
Another Lighthouse (03/05/2007)
Generating XML from a CFC? Watch out for whitespace (03/05/2007)
Do you have to use a remote source for Spry datasets? (03/02/2007)
Useless but cool link: Steampunk Star Wars (03/02/2007)
Recording/Files from Last Night's Presentation (03/01/2007)
MAX 2007 Announced (02/28/2007)
ColdFusion 101: Building a contact form with dynamic TO addresses (02/28/2007)
Presention on Spry tonight to Auckland ColdFusion User Group (02/28/2007)
FlexLib lauches (02/28/2007)
State of the Forge Report (02/28/2007)
The People's Toolbox adding ColdFusion - Victory! (02/28/2007)
Are you going to CF Objective? (02/27/2007)
Make this the last year someone doesn't know what ColdFusion is! (02/27/2007)
Spry demo - check for a valid URL (02/26/2007)
Canvas 2 Beta Refresh (02/26/2007)
Model-Glue Tip - Marking an event private (02/26/2007)
Lost Planet Review (02/24/2007)
Followup on last factory/galleon post (02/24/2007)
Spry and Server Side Paging (02/23/2007)
Speaking at CFUnited Express - NYC (02/23/2007)
Four Years and Counting... (02/23/2007)
Baby steps in Factory Land (right over the edge of a cliff...) (02/22/2007)
Yahoo is now officially the cool kid on the blog (02/22/2007)
Help spread the word at the People's Toolbox (02/22/2007)
Lost is one step away... (02/21/2007)
Scorpio User Group Tour Announced (02/21/2007)
How does RIAForge support the project URLs? (02/20/2007)
(Mostly) Out of Office - Happy Mardi Gras! (02/20/2007)
Baby steps in factory land (again) (02/19/2007)
Why don't bookmarks display in Adobe Reader 8? (02/19/2007)
Simple guide to switching to CFQUERYPARAM (02/18/2007)
Would this make sense in ColdFusion? (02/16/2007)
Flex Chart Gotcha (02/16/2007)
Fixing a Windows Audio Issue (02/16/2007)
Conference (02/16/2007)
FusionDebug 2 Released (02/15/2007)
Generating URL Thumbnails with ColdFusion and Girafa (02/15/2007)
Cool DZone Script - Send JavaScript errors via CFMail (02/15/2007)
Matt Woodward's Mac Guide (02/15/2007)
Presention to Auckland CF (02/14/2007)
RIAForge back up... (02/14/2007)
Frameworks Conference Speaker Feedback (02/14/2007)
Taking another step forward with Fusebox - Configuration (02/13/2007)
Another CF Search Engine (02/13/2007)
Baby steps in factory land (02/10/2007)
Code to Avoid: cfoutput over a query with one row (02/09/2007)
Returning XML in ColdFusion for AJAX (02/08/2007)
Ask a Jedi: Is it worthwhile to learn everything about ColdFusion immediately? (02/08/2007)
Newest member of the family (02/07/2007)
How do you report bugs in Fusebox (and Model-Glue)? (02/07/2007)
Flash Forms are the New Layer Tag (02/07/2007)
Continuing my Fusebox study (02/07/2007)
Lost is Found Tonight (02/07/2007)
CFEclipse TV (02/06/2007)
Removing an error flag from a form field in Flex (02/06/2007)
Installing Fusebox (02/05/2007)
Frameworks Conference - Final Thoughts (02/05/2007)
Louisiana - leading the country in cock fights (02/05/2007)
You guys sure like to talk a lot... (02/04/2007)
Fusebox 5.1 Released (02/03/2007)
Frameworks code/slides (02/03/2007)
Spry blog active again (02/03/2007)
Frameworks Conference: Designing Framework-Agnostic Models with CFCs - Brian Kotek (02/02/2007)
Frameworks Conference: Leveraging ColdSpring To Make Better Applications - Kurt Wiersma (02/02/2007)
Frameworks Conference: Intro to Object Factories - Rob Gonda (02/02/2007)
Frameworks Conference: CFCs ARE the Framework, by Steve Nelson (02/01/2007)
Frameworks Conference: Introduction to Fusebox 5, by Adam Lehman (02/01/2007)
Cool Spry Extension (02/01/2007)
Made it to DC (Mostly Safe) (01/31/2007)
Off to the Frameworks Conference (01/31/2007)
Update to RIAForge Today (and a little secret) (01/30/2007)
ColdFusion 101: Building a Calendar (3) (01/30/2007)
Doing form Post in Spry (2) (01/29/2007)
Quick and dirty debugging tip for Flex/ColdFusion (01/29/2007)
Google Geocode CFC (01/26/2007)
this.Developer Persona (01/26/2007)
This is NOT customer service (01/26/2007)
CFEclipse 1.3 Released (01/26/2007)
CFLib downtime and movement... (01/25/2007)
Quick error handling tip for Model-Glue (01/25/2007)
MySQL Tip - Finding total rows for a query that uses Limit (01/24/2007)
Help create Flex 3 (01/24/2007)
It's a Revolution, Really! (01/23/2007)
Flex Datagrids - not for simple arrays (01/23/2007)
Pssst - hey buddy - wanna test ColdFusion 8? (01/22/2007)
Did you know CFEclipse had a File View? (01/22/2007)
Flex date gotcha (01/22/2007)
Followup to FlashVars in Flex Articles (01/22/2007)
LighthousePro 2.2 Released (01/21/2007)
More on the JavaScript bug I had - and how it relates to Spry (01/21/2007)
Setting the disabled property of a form field (help needed) (01/21/2007)
Friday Night Links (01/19/2007)
Flex/ColdFusion Mystery with a very simple answer (01/19/2007)
New ColdFusion Site:Answers.org(01/19/2007)
This weeks presentations posted (01/19/2007)
What is it? (01/18/2007)
Can you do Flex "Wrappers" like you can with ColdFusion? (01/18/2007)
Presentation to the Scottish CFUG today a 2PM CST (Cool Standard Time) (01/18/2007)
CFLib hits 1000 (01/18/2007)
Ask a Jedi: Frames and Model-Glue (01/17/2007)
Adding an XMLList back to an XML object in Flex/ActionScript 3 (01/17/2007)
RDS and Line Numbers in Eclipse (01/17/2007)
CFJUG Meeting Tonight - ColdFusion Security Checklist (01/17/2007)
Another Flex conference announced - FlexManiacs (01/16/2007)
Want to attend 360Flex? Better hurry (01/16/2007)
Handling this error: The tag does not allow the attribute(s) RESULT. (01/16/2007)
The Flex Show - A Flex Podcast (01/16/2007)
Using CFMAIL's server attribute to store additional information (01/15/2007)
Doing a form POST in Spry (01/14/2007)
Eclipse 3.2, RDS, and OSX (01/14/2007)
Heading back to the bayou (01/12/2007)
ColdFusion Security Patch Released (01/10/2007)
Two Presentations Next Week (01/09/2007)
Children of Men - More than worth your money (and time) (01/07/2007)
Alert can still lock browsers - why? (01/07/2007)
XBox Live Gamercard API in ColdFusion (01/06/2007)
Where the heck is InvalidTag coming from? (01/05/2007)
More on the Flex 2.0.1 (01/05/2007)
Update for ColdFusion UPS Package (01/05/2007)
AJAX and ColdFusion - Help spread the word (01/05/2007)
Flex Builder 2.0.1 (and yes, support for the Mac) is here! (01/05/2007)
Testing with Spry (01/04/2007)
Watch out for functions that return booleans (01/04/2007)
Various updates to a few products (01/04/2007)
So - ya want your Flex Builder for the Mac? (01/03/2007)
Searching Spry Data Sets (01/03/2007)
Quick tips on Spry's new PagedView feature (01/02/2007)
Next CFJUG: January 17 / Security Part 2 (01/02/2007)
Did you know - Flex and ID3 tags (01/02/2007)
Saving data in case of brower crashes (01/01/2007)
Happy New Year! (Well, in 11 hours...) (12/31/2006)
Codec packages for Mac (12/29/2006)
Canvas 2 Beta (12/29/2006)
Replacing colors in an image with ColdFusion - Anyone know how? (12/28/2006)
Ask a Jedi: Organizing user uploads (12/28/2006)
Warning to XBox 360 users about Windows Media Player 11 (12/27/2006)
Custom columns in Spry (12/27/2006)
What did Santa bring you? (12/25/2006)
ColdFusion UPS Package Updated (12/23/2006)
My (Kinda) Farewell (12/22/2006)
New Spry Code: Paged Datasets (12/22/2006)
Ask a Jedi: Figuring out how many rows of data to use with Spry (12/22/2006)
2006 ColdFusion Blog of the Year (12/22/2006)
Canvas Logo (12/21/2006)
Another presentation tip (12/21/2006)
CFUNITED Express (12/20/2006)
Session metrics with Application.cfc (2) (12/20/2006)
The new oddness (and evenness) of Spry 1.4 (12/19/2006)
Session metrics with Application.cfc (12/19/2006)
Flex Cookbook (12/18/2006)
Spry 1.4: Tabs (12/18/2006)
CFUPS in the Wild... (12/18/2006)
Three more features of Spry 1.4: removeClassName, addClassName, getNodeText (12/17/2006)
Spry 1.4: Spry.utils.updateContent (12/17/2006)
Spry 1.4: documentToObject makes XML handling easy (12/17/2006)
Two more gems from Adobe Labs (12/16/2006)
Two Spry tips (12/15/2006)
Spry 1.4 Released (Really), oh and I survived. (12/15/2006)
Out of Office Today (12/15/2006)
Spry 1.4 Released! (12/14/2006)
Lamest command line tool ever (12/14/2006)
Simple Chat in Spry (12/14/2006)
Using CFLOGIN for Authentication of REST Based Queries (12/13/2006)
Problem with Video DVDs under XP (12/13/2006)
ColdFusion UPS Package Released (12/12/2006)
First draft of UPS Package Released (12/12/2006)
WindowShade Flex Component (12/12/2006)
What can Brown do for me? How about a provide an easy to use service? (12/11/2006)
FlashVars in Flex (12/11/2006)
ColdFusion handling of Subversion events (12/09/2006)
JavaScript - Opening a new window with little to no chrome (12/08/2006)
Friday Puzzler - Santas Got (API) Issues (12/08/2006)
BlogCFC and SpoolMail Updated (12/07/2006)
MySQL administration via ColdFusion (12/07/2006)
So - why did we build a web version again? (12/06/2006)
360 Flex (San Jose March 5-7) (12/06/2006)
SpoolLockTimeoutException (12/06/2006)
Flash Forms and ParagraphFormat (12/05/2006)
How to do a "Your download will begin..." type page. (12/05/2006)
RSSWatcher Back (12/05/2006)
Handling remote errors in Flex 2 (12/04/2006)
Announcement - Throwing my hat in the ring... (12/04/2006)
Finding out what an object is in Flex 2 (12/04/2006)
Simple Error Templates (12/04/2006)
Microsoft's Cross Browser Testing "Solution" (12/01/2006)
Don't count on form field's maxlength property (12/01/2006)
Friday Puzzle - Welcome to Santa's IT Department (12/01/2006)
Position of CFERROR Matters (11/30/2006)
RIAForge - 100 Project Mark (11/30/2006)
RSSWatcher Down... (11/29/2006)
ColdFusion Customer List (11/29/2006)
A Loading page with CFFLUSH and JavaScript (11/29/2006)
CFLOGIN, How do I love thee... (11/27/2006)
Gravatar Caching Service (11/26/2006)
Last build of my Flex 2/ColdFusion Security Homework (11/25/2006)
Two Model-Glue 2 backwards compatability issues to watch out for (11/25/2006)
Next build of my Flex 2/ColdFusion Security Homework (11/24/2006)
Geek versus Jock Update (11/24/2006)
Modified version of Zoids custom combo box to allow preselected value (11/22/2006)
Check out Zoid's custom Flex component example (11/22/2006)
Second revision of my Flex homework (11/22/2006)
CFLib.org is back (11/21/2006)
First stab at my Flex homework (11/21/2006)
Handling broken images in Flex 2 (11/21/2006)
My Thanksgiving Flex Homework (11/21/2006)
On the air again (11/21/2006)
Important Notice about My Site Network (11/20/2006)
Sunday Poll: Did you Wii or PS3? (11/19/2006)
Return of the Friday Puzzler: Build a Regex Tester (11/17/2006)
Sitemap Generator (11/16/2006)
Spry Presentation Recording (11/16/2006)
Vertigo - Not your average comic (11/15/2006)
Flex Search Engine (11/15/2006)
Spry Photo Gallery Demo (11/15/2006)
Presenting on Spry tomorrow (the world is invited) (11/14/2006)
SQL Server Profiler (11/14/2006)
Quick and dirty CAPTCHA Guide (11/14/2006)
Adding your own links in the ColdFusion Administrator (11/13/2006)
Example of a custom cache in a ColdFusion Component (11/13/2006)
The Saints are Coming (11/12/2006)
ColdFusion Yahoo Package Updated (11/11/2006)
Sponsored Post: ReviewMe Review (11/10/2006)
Making lemonade with Flex (11/10/2006)
CFSpry updated, and presentation next week (11/10/2006)
Small (In other words - obvious) Flex Builder 2 Tip (11/10/2006)
Discount code for Frameworks Conference (11/10/2006)
Speaking at Frameworks Conference (11/09/2006)
Wrapping up the last contest (11/09/2006)
Lost review for November 8 (11/08/2006)
More Regex - MySQL's Regular Expression Support (11/08/2006)
Regex Coach (11/07/2006)
Model-Glue Short URLs on the Cheap (11/07/2006)
Top 10 Signs You Have an Insecure Web App (11/07/2006)
Geek the Tube (11/06/2006)
CFC Flex Explorer (11/06/2006)
Handling unknown events in Model-Glue (11/05/2006)
Galleon ColdFusion Forums: Version 1.7 (11/03/2006)
ColdFusion/Spry Kit Proof of Concept (11/02/2006)
xmlFormat and Microsoft's Funky Characters (11/02/2006)
Is your site secure? (11/02/2006)
Lost Review for 11-1-06 (11/02/2006)
Spry built-in variables for Datasets (11/01/2006)
CFJUG Meeting Cancelled (11/01/2006)
BlogCFC now supports Contribute + Big Yahoo Package Updates (11/01/2006)
Did I break a mirror? (10/31/2006)
ColdFusion WebSphere Portal Toolkit Released (10/31/2006)
Happy Halloween! And what is on your soundtrack today? (10/31/2006)
Thanks LG! (10/30/2006)
CFJUG October Meeting (10/29/2006)
Try Flex (no, really, go ahead and try it) (10/29/2006)
Yes, I made it (10/27/2006)
The travel curse continues... (10/26/2006)
Notes from MAX Keynote (Day 3) (10/26/2006)
Lost Review for October 25, 2006 (10/26/2006)
Firefox 2 and Intel Mac (10/25/2006)
Notes from the MAX Keynote (Day 2) (10/25/2006)
Flex Builder 2 for the Mac (10/25/2006)
ColdFusion 8 Image Support (10/24/2006)
Server monitoring with ColdFusion (10/24/2006)
ColdFusion .Net Integration (10/24/2006)
Known ColdFusion 8/Scorpio Facts (10/24/2006)
Custom Google Search Engines (10/24/2006)
MAX Keynote Review (Edited 12:12 PM) (10/24/2006)
I'm here (and the travel curse continues...) (10/23/2006)
MAX Flickr Group (10/22/2006)
Out next week (10/22/2006)
Spry Updated (10/20/2006)
How ColdFusion can save your business! (10/20/2006)
ColdFusion Components MAX BOF Scheduled (10/20/2006)
Last CFJUG Recording Available (10/19/2006)
Flash 9 for Linux (10/19/2006)
Oh look - IE7 is released (10/18/2006)
Did you know about the ColdFusion Cookbook? (10/18/2006)
CFJUG Repeat meeting (10/18/2006)
Announcing RIAForge (10/18/2006)
Yahoo Package Updated (10/17/2006)
How do I actually use a UDF? (10/17/2006)
Good tutorial on making an RSS Feed with ColdFusion (10/16/2006)
ColdFusion Yahoo Package - Third Release (10/15/2006)
Using ColdFusion's DirectoryWatcher Gateway (10/13/2006)
All the cool kids are going to MAX - are you? (10/13/2006)
ColdFusion Yahoo Package - Second Release (10/12/2006)
Small update to Lighthouse Pro (10/12/2006)
CFJUG October Meeting/Last Recording (10/12/2006)
Fun little AJAX/Internet Explorer issue (with cool Spry fix!) (10/11/2006)
ColdFusion Yahoo Package - Initial Release (10/11/2006)
CF Security Advisory: Patch available for ColdFusion MX 7 local privilege escalation (10/10/2006)
A perfect ColdFusion-centric host would have... (10/10/2006)
cf.Objective() 2007 - Be there or be trapezoidal (10/10/2006)
Preselecting data with Spry (10/09/2006)
CFJUG Recording/Files (10/09/2006)
Quick note on BlogCFC (10/08/2006)
GoogleCal Updated (1.3) (10/08/2006)
ColdFusion Drag Race at MAXUP/MAX (10/08/2006)
Dynamic BlogCFC Instances (10/07/2006)
Battlestar Galactica Season 3 (10/07/2006)
I survived! (10/05/2006)
Lost review for October 4, 2006 (10/04/2006)
I'm out of here (no thanks to Enterprise) (09/30/2006)
Yahoo Traffic API with ColdFusion and Flex 2 (09/29/2006)
Good article on Flex2 and ColdFusion Integration (09/29/2006)
GoogleCal beta (09/28/2006)
Yahoo Traffic API ColdFusion Example (09/28/2006)
Yahoo Weather API ColdFusion Example (09/27/2006)
Round three against the jock (09/27/2006)
Good custom tag examples (09/27/2006)
ColdFusion Jedi User Group Meeting Tonight (09/27/2006)
GoogleCal Updated (09/26/2006)
CFUNITED Videos Available (09/26/2006)
Yahoo Answers API Example (09/26/2006)
CFC Birds of a Feather on again (09/25/2006)
Followup to Yahoo Search API Post (09/25/2006)
What's going on this week (09/25/2006)
Yahoo Search API (09/24/2006)
CFUnderground 8 (09/23/2006)
Help me with Google (09/22/2006)
Friday's Random Media Post (09/22/2006)
Restricting logins after unsuccessful attempts (09/21/2006)
Flex 2 class in SF needs one more student (09/21/2006)
CFDEVCON - Calling all UK ColdFusion Devs (09/21/2006)
Reminder: Presentation next week (09/20/2006)
Using JavaScript to warn a user about a session timeout (09/20/2006)
Quick note on contacting me (09/20/2006)
Thunderbird Spam suggestions (09/19/2006)
New Quick References (09/19/2006)
Two project updates (Lighthouse Pro/toXML/Canvas) (09/18/2006)
BlogCFC/Flex article up at Adobe's Developer Center (09/18/2006)
Per request debugging in Model-Glue (09/18/2006)
Great quote (09/17/2006)
The news lied to me! (09/17/2006)
Name these books (09/15/2006)
Friday Puzzler: Automatic CFC Method Tester (09/15/2006)
Using ColdFusion's Asynchronous Gateway - 3 (09/14/2006)
Interesting use of onRequestEnd (09/14/2006)
Presentation Tonight (09/14/2006)
Updated CFTHREAD/CFJOIN POC from Adobe (09/13/2006)
Apple enters movie business (yawn) (09/12/2006)
Question on Instant Messenger Gateway (09/12/2006)
This Week (09/11/2006)
A few random 9/11 Thoughts (09/11/2006)
Community track at MAX - MAXUP (09/09/2006)
Dharma Revealed? (09/08/2006)
Nimer's Log Viewer (09/08/2006)
Spry Error Callback Example (09/07/2006)
Using ColdFusion's Asynchronous Gateway (09/07/2006)
Thanks for "Ship of Gold" (09/07/2006)
Where do I report a bug with an Adobe product? (09/06/2006)
Next "virtual" user group meeting scheduled - Building a Security System (09/05/2006)
Return Types in Application.cfc (09/05/2006)
Job titles and salary are a security issue? (09/03/2006)
Mini Cooper is the only car not covered by lemon law (and other fun facts) (09/02/2006)
ColdFusion Quick Reference Sheet (09/01/2006)
Ask a Jedi: Getting a job and code samples (09/01/2006)
Application.cfc Presentation Files + Recording URL + Next Meeting (09/01/2006)
Want to know everything? (09/01/2006)
Flex 2 front end for BlogCFC (08/31/2006)
What's up with my Mini Cooper? (08/31/2006)
Eclipse Tip: Go Into (08/30/2006)
Help an ex-coworker (08/30/2006)
Application.cfc Presentation URL (08/30/2006)
Advanced ColdFusion Contest Entry 2: BruteForce (08/29/2006)
Ask a Jedi: Does using a framework reduce your portability? (08/29/2006)
Reminder on Application.cfc Presentation (08/28/2006)
Flex for CFers (08/28/2006)
The Half Million Dollar Video Game Bill (08/26/2006)
Spry Example: Check if user exists (08/25/2006)
Another Adobe ColdFusion Blogger (08/25/2006)
Ask a Jedi: Learning by doing (08/25/2006)
Quick note on the contest (08/25/2006)
Tip: Convert line feeds for files with Flip (08/24/2006)
Pluto Kicked Out (08/24/2006)
Even more Flex news (08/24/2006)
FlexTV (08/24/2006)
Ask a Jedi: Dealing with an incredibly slow query (08/23/2006)
Canvas 1.5 Released (08/23/2006)
Ask a Jedi: Sending users back after a logon (08/22/2006)
Using AJAX with Model-Glue (08/22/2006)
TEOTWAWKI (A good Monday post) (08/21/2006)
Reminder on CFLOGON and Web Based Security (08/19/2006)
Busting Frames (08/18/2006)
Friday Puzzler: Mail Alerts (08/18/2006)
ColdFusion Custom Tag Tips (08/17/2006)
Prey Review (XBox 360) (08/17/2006)
Harlan Ad Server Updated (08/16/2006)
Hey, stop talking already (08/16/2006)
Application.cfc Presentation Scheduled (08/16/2006)
ColdFusion 101: Picking a random image (2) (08/16/2006)
Application.cfc Presentation (08/15/2006)
ColdFusion 101: Picking a random image or rotating over each one (08/15/2006)
ColdFusion Portal (2) (08/14/2006)
ColdFusion Portal (08/14/2006)
Multi-File Upload with Flex and ColdFusion (08/13/2006)
Back to the Big Easy (08/13/2006)
FusionDebug Released (08/11/2006)
Advanced ColdFusion Contest Entry 1: CodeCop (08/11/2006)
CanvasWiki Updated (Version 1.4.1) (08/10/2006)
Flash Player 9 for Intel Macs (08/10/2006)
You know you're an old techie when... (08/10/2006)
Flex Templating (08/10/2006)
Ask a Jedi: CFCs and Cross Referencing Tables (08/10/2006)
CanvasWiki Updated (Version 1.4) (08/09/2006)
Yet Another Mini Cooper Update (08/09/2006)
Ask a Jedi: cfupdate versus cfquery (08/09/2006)
MAX Awards (08/09/2006)
The new 3.5 JDBC Drivers and ColdFusion (08/08/2006)
Ask a Jedi: Application.cfm, subdirectories, and paths (08/08/2006)
New Site: KidGamers.org (08/07/2006)
Ask a Jedi: Turning a site off (08/07/2006)
My XMLProxy.cfm (08/04/2006)
Real World Flex Seminar (08/04/2006)
Friday Puzzler: ColdFusion Trivia (08/04/2006)
Breaking rules (08/03/2006)
ColdFusion 101: Day of the Week Formatting (08/03/2006)
Dreamweaver Help (08/02/2006)
If Spry Do This... (08/01/2006)
Contest Deadline is Today! (08/01/2006)
Who dropped the mountain on my blog? (07/31/2006)
CFCDev (No, seriously, it's working now. I swear!) (07/31/2006)
Mail updates (07/31/2006)
Generating One-Time URLs with ColdFusion (07/30/2006)
Building an AJAX Based RSS Pod (07/28/2006)
Friday Puzzler: ADT - Can you stand the excitement? (07/28/2006)
Two Spry Questions (07/28/2006)
Last Contest Reminder (07/28/2006)
Spry Presentation Recording/Zip (07/27/2006)
Installing ColdFusion on Intel Macs Guide (07/27/2006)
Spry Presentation Tonight (07/26/2006)
Loading widgets galore (07/26/2006)
ColdFusion Whitespace Options (07/26/2006)
CFCDev Status (07/25/2006)
Review: Sin City, Monster House (07/25/2006)
Quickie Flex2/ColdFusion Application (07/24/2006)
(Non-Adobe) Spry Patches Page (07/24/2006)
Quickie ColdFusion Image Viewer (07/24/2006)
Mail Services for Blogs, Forums, RSSWatcher (and anything I forgot) (07/23/2006)
Fast Track to ColdFusion (07/23/2006)
CFCDev is Dead (For Now) - Thank MailEnable (07/23/2006)
And we're back (hopefully) - along with another Lost post (07/23/2006)
CFTHREAD/CFJOIN Proof of Concept (07/21/2006)
Minor Updates to Galleon/BlogCFC (07/21/2006)
Friday Puzzler: All Fish Must Die! (07/21/2006)
You know you're a geek when... (07/20/2006)
Var Scoping Tool (07/20/2006)
Model-Glue Tip: Watch those event values! (07/20/2006)
BSG Versus Lost (07/19/2006)
I dub thee.... Idiot Bait (07/19/2006)
Caching options in ColdFusion (07/19/2006)
Big stuff planned for Lost? (07/18/2006)
Model-Glue Unity and Generic Database Messages (07/18/2006)
Minor Update to Galleon Forums (07/18/2006)
Blogbeat No More... (07/17/2006)
Ask a Jedi: Is CreateObject slow? (07/17/2006)
Superman was amazing (07/16/2006)
You can be a star! (Until the copyright notices fly...) (07/15/2006)
Return of the Friday Puzzler (07/14/2006)
New features in Spry (07/14/2006)
SpoolMail Updated - Version 1.0.3 (07/13/2006)
ToXML Update (07/13/2006)
Sending Data with Spry (07/12/2006)
Galleon ColdFusion Forums Updated (07/12/2006)
Are you reading Stake Five? (07/12/2006)
Ask a Jedi: Layout in Application.cfc (07/12/2006)
Fusion-Reactor and FusionDebug (07/11/2006)
Spry Resources (07/11/2006)
CFCs and the Base Component (07/11/2006)
Lost is solved (07/11/2006)
Coolest. Video. Ever. (07/10/2006)
ColdFusion and Short Circuit Boolean Evaluation (07/10/2006)
MAX Info Released! (07/10/2006)
Self Defense in High School (07/10/2006)
Reading MP3 ID3 tags with ColdFusion (2) (07/09/2006)
Upcoming Speaking Engagements (07/07/2006)
Another security item to check... (07/07/2006)
Getting the RDS extensions for CFEclipse (07/06/2006)
CFCDev Up (Kinda) (07/06/2006)
CFCDev Down (07/06/2006)
Your mother writes code so bad.... (07/06/2006)
Galleon ColdFusion Forums Beta (07/06/2006)
DS Lite Review (07/05/2006)
Reminder on structs and bracket notation (07/05/2006)
BlogCFC and GoogleSpell Integration (07/04/2006)
Debug template information in the order of process (07/03/2006)
Ask a Jedi: Getting your scope on (07/03/2006)
ToXML CFC - Converting data types to XML (07/02/2006)
Verity Presentation, Spry Notes, and Final Farewall (06/30/2006)
More than meets the eye (06/30/2006)
Correction on RDS for CFE Support (06/30/2006)
RDS Support for CFEclipse (06/30/2006)
Fusion Authority Quarterly Update Launches (06/30/2006)
CFUNITED Review: ColdFusion Application Security (06/29/2006)
CFUNITED Review: Testing ColdFusion Applications (06/29/2006)
A few presentation tips (06/29/2006)
CFC Presentation Posted (06/28/2006)
CFUNITED Review: Managing CF Components w/ Factories (06/28/2006)
CFUNITED Reviews (06/28/2006)
Flex 2, ColdFusion 7.02 Released, Flash 9 (06/28/2006)
Hello from (Wet) CFUNITED (06/27/2006)
This blog, this week (06/26/2006)
Ask a Jedi: Setting up a home environment (06/26/2006)
CFEclipse 1.3 Beta (06/24/2006)
Minor Update to Lighthouse Pro (06/24/2006)
Newbies can share too! (06/24/2006)
Spry Demo: CFLib (06/23/2006)
Lighthouse Pro 2.0.4 Released (and the story of the Sithlord's Eye) (06/22/2006)
Spry Demo Updated (06/22/2006)
Review: Fusion-Reactor 2 (Beta) (06/21/2006)
Ask a Jedi: Wrapping List Elements in ColdFusion (06/21/2006)
Ask a Jedi: Two Application.CFC Questions (and a request) (06/20/2006)
Ask a Jedi: Bilingual Sites (06/19/2006)
Moving from SQL Server to MySQL (06/17/2006)
Mac and Mini Update (06/16/2006)
Yes, you can cock fight, but you can't play GTA (06/16/2006)
Good article on computer languages and being practical (06/16/2006)
Friday Puzzler: Finding a meeting time (06/16/2006)
ColdFusion Security Checklist (06/16/2006)
Ask a Jedi: Coding for Review (06/15/2006)
Tip: Remove some, but not all, HTML (06/15/2006)
CanvasWiki Updated (06/15/2006)
Model-Glue 2 Beta 1 Available (06/14/2006)
Top 10 PHP Vulnerbalities (and why ColdFusion developers need to care) (06/14/2006)
Macbook Pro and Firefox tip (06/13/2006)
ColdFusion Cookbook hits 100! (06/13/2006)
Another Spry demo (06/13/2006)
Reading MP3 ID3 tags with ColdFusion (06/13/2006)
Good use of PDF (06/12/2006)
Advanced ColdFusion Contest Announced (06/11/2006)
Spry updated to version 1.1 (06/09/2006)
Ask a Jedi: In CFCs, why would I use extends? Why would I use init()? (06/09/2006)
Initial MAX info (and yes, I'm back from Detroit) (06/09/2006)
Another night in Detroit, and some thoughts on Compuware (06/07/2006)
Creating a Mailing List in ColdFusion (Part 5) (06/06/2006)
BlogCFC to Wordpress Tool (06/06/2006)
I'm in Detroit, now where is Robocop? (06/05/2006)
Out of Office - Detroit (06/04/2006)
Mini Update (06/03/2006)
Model-Glue: What is reserved in the view state? (06/02/2006)
I heart Spry (06/02/2006)
Ask a Jedi: ColdFusion Calendar (06/02/2006)
Friday Puzzler: Self-Print Challenge (06/02/2006)
Model-Glue is back - get your glue on! (06/01/2006)
Ask a Jedi: If I do my own checking, do I still need cfqueryparam? (06/01/2006)
Bash me (and others!) (06/01/2006)
Model-Glue.com is down (05/31/2006)
Ask a Jedi: Scheduled tasks and username/passwords (05/31/2006)
Ask a Jedi: Pros and Cons of Flash Forms (05/31/2006)
onError, cfabort, and the Final Answer (05/30/2006)
Ask a Jedi: Get the size of a folder (pre-CF7) (05/30/2006)
Ask a Jedi: Encapsulation 101 (05/30/2006)
Do you monitor your site feedback? (05/30/2006)
Ask a Jedi: Backing up DSNs (05/29/2006)
A few more days with the Mac (05/28/2006)
Pandora, a music lovers treat (05/26/2006)
Ask a Jedi: Smaller Dumps (05/26/2006)
Two Adobe Resources (05/25/2006)
Model-Glue Presentation Recording (05/25/2006)
A quick thanks (05/25/2006)
Lost review for May 24, 2006 (05/24/2006)
Let's go to the movies... (05/24/2006)
550 New BlogCFC Installs (05/24/2006)
Reminder - Model-Glue Presentation tonight (05/24/2006)
Flex 2 Class (05/23/2006)
Ask a Jedi: Saving a Dump for Later (05/23/2006)
Macbook Pro in da house... (05/22/2006)
Anyone used the lemon law? (05/21/2006)
CFLib Testers Needed (05/20/2006)
Ask a Jedi: Getting SQL from a query (05/20/2006)
Ionic's ISAPI Rewrite Filter (05/19/2006)
BlogCFC Update (05/19/2006)
Friday Puzzler: The tag popularity contest (05/19/2006)
Round two goes to the nerd (05/18/2006)
Presentation on Model-Glue next week (05/18/2006)
And now for a question from me: Thunderbird and Exchange meeting invites (05/18/2006)
Deployment options? (05/17/2006)
I love Louisiana, but... (05/17/2006)
New Google service: Google Notebook (05/17/2006)
Model-Glue Updates (05/16/2006)
I heart apple. (05/16/2006)
Ask a Jedi: CFQueryParam and MaxLength (05/15/2006)
I could be crazy... (05/15/2006)
BlogCFC v5: The circle is now complete... (05/12/2006)
cfmail and cfoutput (05/12/2006)
Friday Puzzler: Can you find it? (05/12/2006)
Flex 2 Demo: Taipan (05/11/2006)
Ask a Jedi: UDFs and CFCs (05/11/2006)
Styling with Flex Update (05/10/2006)
How NOT to do a game demo (05/09/2006)
Ask a Jedi: Stylin' with Flex (05/09/2006)
CFLib Flex demo updated (05/09/2006)
Flex 2 Beta 3 Released (05/08/2006)
Spammers love me! (05/08/2006)
Ask a Jedi: The Request Scope - not just for breakfast anymore! (05/08/2006)
What are you doing on this Sunday afternoon? (05/07/2006)
BlogCFC Beta 2 Released (05/06/2006)
Random musings (only the first one is important) (05/05/2006)
Friday Puzzler: Math in English (05/05/2006)
Ask a Jedi: Handling a custom sort order update (05/05/2006)
Ask a Jedi: Cached cfinvoke and web services (05/05/2006)
ColdFusion Developer Frappr Map (05/04/2006)
Lost review for May 3 (05/03/2006)
ColdFusion and Subversion (05/03/2006)
Adobe needs testers for new JRun (05/02/2006)
Ask a Jedi: Error thowing and cfthrow (05/02/2006)
Why can't stats be in English? (05/01/2006)
Could media companies finally be getting it? (05/01/2006)
Time for a change... (05/01/2006)
Team Macromedia are ACEs.... (05/01/2006)
BlogCFC 5 Beta Announced (04/28/2006)
Slow page report (04/28/2006)
Friday Puzzler: You can take this data and chart it! (04/28/2006)
BSG spin off in the works (and a quick note) (04/27/2006)
ColdFusion and Pagination - Part 2 (04/26/2006)
Adobe's Active Content Fix (04/25/2006)
ABC launching web based game on Lost, AKA Crack for Geeks (04/24/2006)
ColdFusion and Pagination (04/24/2006)
Advanced ColdFusion Contest Winner (04/21/2006)
Friday Puzzler: My URL is smarter than your URL... (04/21/2006)
GoogleCalendar.cfc Version 1 (04/20/2006)
Ask a Jedi: Is Form more secure than URL? (04/20/2006)
Lighthouse Pro Updated (04/20/2006)
Google Calendar API Released (04/20/2006)
Coping with LWS (Lost Withdrawel Syndrome) (04/19/2006)
Ask a Jedi: Sharing variables between different ColdFusion applications (04/19/2006)
Subscriber bug fixed (04/18/2006)
Ask a Jedi: Pair Counting (04/18/2006)
RSSWatcher.com (04/18/2006)
Cell Hell, or how I'm going to pay the Dummy Tax (04/17/2006)
Ask a Jedi: Getting CFC method names (04/17/2006)
Bug(04/15/2006)
Kameo Review (04/15/2006)
"My backpack, gots jets, I'm Boba, the Fett" (04/14/2006)
Friday Puzzler (04/14/2006)
Subscriber Update (04/13/2006)
BlogCFC5 Update (04/13/2006)
Ask a Jedi: Model-Glue and UDF Libraries (04/13/2006)
Google Calendar - Soon to come: Google Electricity, Google Internet, Google God, and Google Air (04/13/2006)
Happy Anniversary to me (and my wife) (04/13/2006)
Ask a Jedi: Verity and file modification dates (04/12/2006)
One more reason to drop Norton like a radioactive hot potato (04/12/2006)
Protect Little Johnny, but don't take away my NASCAR! (04/11/2006)
Quick FAQs on my applications (04/11/2006)
Ask a Jedi: What do I need to know to learn ColdFusion? (04/11/2006)
Soundings ColdFusion Survey Application Updated (04/10/2006)
Bye bye Experts-Exchange (04/10/2006)
Model-Glue 1.1 Released (04/10/2006)
Building your first Model-Glue application - The Final Battle (04/09/2006)
Happy birthday to me... (04/08/2006)
BlogCFC 5 development starts... (04/07/2006)
Friday Puzzler: First steps to the NSA... (04/07/2006)
I fought the meme and the meme won... (04/06/2006)
Building your first Model-Glue application (part 10) (04/06/2006)
Lost Review for April 5 (04/05/2006)
Reminder on TrackBack Spam List (04/05/2006)
Ask a Jedi: cfinvoke versus createObject (04/05/2006)
Verity: 1, Me: -1705 (04/05/2006)
Another Canvas Update (04/04/2006)
Ask a Jedi: Where do you get help for ActionScript in Flash Forms? (04/04/2006)
Building your first Model-Glue application (part 9) (04/03/2006)
Canvas ColdFusion Wiki Updated (04/03/2006)
CFC scopes updated (04/03/2006)
I give up... (04/01/2006)
Ask a Jedi: CFC Resources? (03/31/2006)
MGDoc, a Model-Glue documentor (03/30/2006)
Review: Elder Scrolls IV: Oblivion (03/30/2006)
Soundings ColdFusion Survey Update - 1.5.1 (03/30/2006)
New CF/Flex Resource (03/30/2006)
LOST Review for March 29th (03/29/2006)
Contest Extension (03/29/2006)
Mindseye is hiring (again) (03/28/2006)
Ask a Jedi: Why (cf)throw? (03/27/2006)
(Yet Another) Waste of time... (03/27/2006)
(Yet Another) Variable Scoping Warning (03/26/2006)
Model-Glue note on events and redirects (03/25/2006)
Soundings ColdFusion Survey Updated (Yet again) (03/24/2006)
Ask a Jedi: Multiple DSNs in ColdFusion Applications (03/23/2006)
Lost Review (3/22) (03/22/2006)
Get "Lost" Tonight (03/22/2006)
Ask a Jedi: Debugging Application.cfc Issues (03/22/2006)
Dude, where's my RDS? (03/21/2006)
RDS support in Eclipse (03/21/2006)
CFLive Presentation (03/16/2006)
Network Help (03/16/2006)
Even more slower than normal... (03/15/2006)
CFLive Meeting (03/15/2006)
New article on DevNet (03/13/2006)
Ask a Jedi: Leaving Application.cfc (03/13/2006)
Another warning about CFCs (03/11/2006)
Ask a Jedi: Using ColdFusion to serve files (03/10/2006)
Star Wars Link: See where the Falcon was built... (03/10/2006)
Mach II port of Canvas Wiki (03/09/2006)
Reminder on duping CFCs... (03/08/2006)
Blogbeat - Blog Stats Review (03/07/2006)
Ask a Jedi: ColdFusion Hosting Plans (03/07/2006)
Is it EVER ok to not screw over a company? (03/05/2006)
Thank you / OOO Notice (03/04/2006)
Model-Glue, Internet Explorer, and File Downloads (03/03/2006)
ACME 3rd Edition Released! (03/03/2006)
QuickPoll CFC Updated (03/02/2006)
ColdFusion MX 7.0.1 Cumulative Hot Fix 2 Released (03/02/2006)
MMORPGs - The next level? (03/02/2006)
CFCDev List Update (03/02/2006)
CFCDev List Status (03/01/2006)
LOST Review - 3/1 (03/01/2006)
BlogCFC Trackback Spam List Exposed! (03/01/2006)
Happy Canvas Day (CanvasWiki Released!) (03/01/2006)
Happy Mardi Gras! (02/28/2006)
Even more LOST Theories... (02/27/2006)
Out of Office (02/27/2006)
Flex2 Lighthouse Pro Interface (02/26/2006)
Calendar Pod Fix for BlogCFC (02/24/2006)
ColdFusion Open Source Success Stories (02/24/2006)
Ask a Jedi: How long should a query take to run? (02/23/2006)
Advanced Contest Clarifications (02/23/2006)
Advanced Contest Announced! (02/22/2006)
Ask a Jedi: QueryAddColumn/QuerySetCell Question (02/22/2006)
Ask a Jedi: Flash Detection (02/21/2006)
Reader Survey (02/21/2006)
New Project: QuickPoll (02/21/2006)
Open Source ColdFusion List (02/20/2006)
Ask a Jedi: Flash Forms and Acting on Drop Downs (02/20/2006)
Interesting Verity Bug (02/19/2006)
Book Review: Stephen King's "Cell" (02/19/2006)
Cool BlogCFC Pod (02/17/2006)
Ugh - Not another CFLOGIN error? (02/17/2006)
Model-Glue issue with redirects (02/16/2006)
Ask a Jedi: Arguments in a CFC/UDF (02/16/2006)
Take a stroll down the ColdFusion Site past... (02/15/2006)
ColdFusion and Security (02/15/2006)
Can we NOT wag the dog today? (02/15/2006)
Ask a Jedi: Ordering CFPOP Data (02/15/2006)
Users want the control (02/14/2006)
Ask a Jedi: Multiple questions, few answers... (02/14/2006)
New aggregator on the scene (02/13/2006)
Props to Jake (02/13/2006)
Ask a Jedi: Time of last Verity update (02/13/2006)
Soundings ColdFusion Survey Updated (02/11/2006)
CFCHART and the Case of the Disappearing Labels (02/10/2006)
cf.Objective() - March 11 and 12th (02/10/2006)
I'd tell you, but then I'd have to kill you... (02/10/2006)
Guides Pod Added (02/10/2006)
What in the heck am I doing? (02/09/2006)
LOST Review (2/8/06) (02/08/2006)
Ask a Jedi: Variable Scopes in CFCs (02/08/2006)
Yet another Lighthouse Pro update... (02/08/2006)
This Skype thing may take off... (02/08/2006)
Ask a Jedi: Checking the Query String (02/08/2006)
Laptop Recommendations (02/08/2006)
Review: Dies the Fire by S. M. Stirling (02/07/2006)
Lighthouse Pro Updated - Now with Creationism! (02/07/2006)
Ask a Jedi: Dumping a Recursive Directory List (02/06/2006)
Ask a Jedi: Multi-purpose CFC Functions (02/06/2006)
BlogCFC and PostgreSQL 8 (02/05/2006)
Good post on the cookbook (02/03/2006)
Norton and Short Cuts (02/03/2006)
Cookbook Milestone! (02/02/2006)
Ask a Jedi: Writing for both ColdFusion 6 and 7 (02/01/2006)
IE7 Beta 2 Ready (01/31/2006)
Reminder - Speaking at Boston CFUG on Friday (01/31/2006)
Lighthouse Pro ColdFusion Bug Tracker - Version 2.0.1 Released (01/31/2006)
Ask a Jedi: Help in preserving user input (01/30/2006)
Online Training Recommendations (01/28/2006)
Harlan ColdFusion Ad Server Updated (01/27/2006)
Ask a Jedi: Send email on long running process (01/27/2006)
LOST Whispers (01/27/2006)
Waste of Time: James T. Kirk Facts (01/26/2006)
Ask a Jedi: Using Cookies for Client Management (01/26/2006)
LOST Review for 1/25 (Spoilers) (01/26/2006)
Two Coldfusion Cookbook Questions (01/26/2006)
Speaking in Boston! (01/25/2006)
Interesting (Real world) Security Issue (01/25/2006)
New Blog on the Block: Building Blocks (01/25/2006)
A Farewell to Arm(s) (01/24/2006)
ColdFusion Cookbook Fixed (01/24/2006)
Regex boundries go both ways (01/24/2006)
Cookbook Update (01/24/2006)
SpoolMail Updated - Version 1 (01/23/2006)
Ask a Jedi: Executing Dynamic ColdFusion (01/23/2006)
MySQL Crash Course Review (01/23/2006)
BlogCFC Updated (01/22/2006)
BlogCFC Security Issue for Apache Users (01/22/2006)
BlogCFC Security Holes (01/22/2006)
Like the ColdFusion Cookbook? Bored? (01/21/2006)
Harlan Ad Server Released! (01/21/2006)
Wounded Horse Report (01/20/2006)
Can't connect Apache and CF due to previous connection? (01/19/2006)
Ask a Jedi: Var Scoping Queries (01/19/2006)
BlogCFC Questions (01/18/2006)
Thank you, thank you, and thank you... (01/18/2006)
Model-Glue Sample - Cookbook (01/18/2006)
Ask a Jedi: AJAX and ColdFusion (01/18/2006)
Grabbing the Bull by the Horn(s) (01/17/2006)
If I was a horse, they would shoot me... (01/17/2006)
Yet another project - announcing SpoolMail (01/16/2006)
More XBox 360 (01/16/2006)
Model-Glue mistake my "friend" made... (01/15/2006)
Starfish ColdFusion Profiler Updater (01/13/2006)
Lighthouse Pro 6.1/Oracle Updated (01/13/2006)
LOST Theories (Spoiler Warning) (01/12/2006)
Ask a Jedi: CFINCLUDE versus CFMODULE (01/11/2006)
ColdFusion Cookbook Email Fixed (01/11/2006)
Initial 360 Review (01/11/2006)
BlogCFC Updated.... 1000 Times (01/10/2006)
And now for a message from Adobe... (01/10/2006)
Cookbook/Blog Updates (01/10/2006)
Ask a Jedi: Filtering Verity Data (01/10/2006)
The Battlestar has returned (01/09/2006)
Get Cooking with ColdFusion... (01/06/2006)
Work with that Model-Glue Guy... (01/06/2006)
And now to make you REALLY hate me... (01/05/2006)
Model-Glue, SES URLs, and Event Redirection (01/05/2006)
Ask a Jedi: Admin Interface for XML Docs (01/05/2006)
Ask a Jedi: Using onError to Mail the Error (01/04/2006)
The ColdFusion Cookbook is on it's way... (01/03/2006)
Coldfusion MX7 Cookbook (01/01/2006)
Ask a Jedi: ColdFusion Frameworks (01/01/2006)
Session Tracking a Security Risk? (12/31/2005)
Another Day - Another Lighthouse Pro Build (12/30/2005)
NSA Invokes the Power of Cookies (12/29/2005)
Lighthouse Pro Updates... (12/29/2005)
24 Doesn't Need to be 24 (12/28/2005)
Lighthouse Pro ColdFusion Bug Tracker - Version 2 (12/28/2005)
Ask a Jedi: Keeping it Together... (12/26/2005)
Fighting the Impossible Fight (2) (12/25/2005)
Did You Know: Looping with ColdFusion Custom Tags (12/23/2005)
2005 in Review (for my blog!) (12/23/2005)
Fighting the Impossible Fight (Again) (12/23/2005)
Ask a Jedi: Returning Two Resultsets (12/23/2005)
Lighthouse Pro 2.0 Beta (12/22/2005)
More on Lafayette Fiber Battle (12/22/2005)
Question for Lighthouse Pro Users (12/21/2005)
One More BlogCFC Bug Fix (12/21/2005)
Mindseye is Hiring - Flash/Flex (12/21/2005)
BellSouth - Thanks for the Suit! (12/20/2005)
(Yet Another) Minor BlogCFC Update (12/20/2005)
Music for Throwing Muses Fans... (12/20/2005)
Dev Center Article on First Contest (12/20/2005)
Stump the Chump: Rounding Errors in ColdFusion (12/19/2005)
Soundings ColdFusion Survey Update (12/19/2005)
Regex Help (12/17/2005)
CFUNITED Topics Revealed (12/17/2005)
BlogCFC (ColdFusion Blog) 4.0.2 Released (12/16/2005)
Ask a Jedi: Encrypting ColdFusion Templates (12/16/2005)
Ask a Jedi: Different Session Timeouts (12/16/2005)
Intermediate Contest Winner! (12/15/2005)
Review of Midway Arcade Cabinet (12/14/2005)
Ask a Jedi: Handling a Dead Database (12/14/2005)
Mute that Browser! (12/13/2005)
Intermediate Contest Entry 11 (12/12/2005)
Ask a Jedi: ColdFusion Debugging (12/12/2005)
Ask a Jedi: Configuring Multiple BlogCFC Installs (12/12/2005)
The XBox is in the house... (12/10/2005)
Ask a Jedi: Current User Error with Admin API (12/09/2005)
Ask a Jedi: Searching Encrypted Values (12/09/2005)
XBox Service - Wow (12/08/2005)
MPAA and Censorship (12/08/2005)
MP3 Downloading - Where is the crime? (12/08/2005)
Ask a Jedi: Application.cfc versus Application.cfm (12/07/2005)
Intermediate Contest Entry 9 (12/07/2005)
New Flex Site: FidelityLabs.com (12/07/2005)
Ask a Jedi: Flash Forms and PreserveData (12/07/2005)
Ask a Jedi: CFC and Array Results (12/06/2005)
Santa 2005 (12/06/2005)
Starfish ColdFusion Profiler Updated (12/03/2005)
XBox 360 - Friend to your local power company... (12/02/2005)
Lighthouse Pro (ColdFusion Bug Tracker) Updated (12/02/2005)
Cool Errors: Dating Trouble (12/01/2005)
Ask a Jedi: Problem with CFC Caching (12/01/2005)
Lost Spoilers (11/30/2005)
Random Book Reviews (11/30/2005)
RIA Wireframing (11/30/2005)
BlogCFC 4.0.1 (11/28/2005)
Ask a Jedi: Refreshing Application Variables (11/28/2005)
Ask a Jedi: ColdFusion Hosts (11/27/2005)
Arcade Game at Target (11/27/2005)
Ask a Jedi: Variables versus Var in a CFC (11/25/2005)
My XBox has gone to that great game graveyard in the sky... (11/23/2005)
Ask a Jedi: Reloading a Page with Flash Forms (11/22/2005)
Interesting TrackBack Spam(?) (11/22/2005)
XBox 360 - Did you buy one? (11/22/2005)
Minor BlogCFC Update (and call for help) (11/22/2005)
Soundings Updated (11/22/2005)
Hybrids Rock (11/21/2005)
Ask a Jedi: What Source Control Do You Use? (11/20/2005)
BlogCFC Bug with MySQL/Access (11/20/2005)
Intermedia Contest Entry 3 (11/18/2005)
Update to First Entry (11/16/2005)
Help New Orleans (11/16/2005)
Contest Guidelines, and General Thoughts (11/16/2005)
Contest Delay (and Thank You) (11/15/2005)
Adding "BlogCFC" Pages (11/14/2005)
Ask a Jedi: Caching LDAP Results (11/14/2005)
Morbid Question for Tech Workers (11/11/2005)
Yet Even More Fixes... (11/11/2005)
And Ten Minutes Later... First Bug Fix! (11/10/2005)
BlogCFC 4 Released (11/10/2005)
Ask a Jedi Clarification (11/09/2005)
ColdFusion 101: Days Till (11/09/2005)
ACME Guide - Really - Get It (11/09/2005)
Ask a Jedi: What's up with "CFIDE"? (And some cool Allaire history to boot!) (11/08/2005)
Update to CFC Adapter/Model-Glue Issue (11/08/2005)
Ask a Jedi: Caching CFC Instances (11/08/2005)
Warning to ModelGlue/CFC Adapter Users (11/07/2005)
Ask a Jedi: CFPARAM versus IsDefined (11/07/2005)
Ask a Jedi: CFC Results to PDF/Flash Paper (11/05/2005)
When it rains - and watch out for the Russians... (11/04/2005)
Ask a Jedi: Dynamic Selected Tab and Flash Form Recompiling (11/03/2005)
ColdFusion 101: Dates can be just numbers (11/03/2005)
Ask a Jedi: Whacking the CFC (11/03/2005)
CFAbort Still Firing onError (11/02/2005)
Oops - Soundings Update (11/02/2005)
Canvas ColdFusion Wiki (11/02/2005)
Ask a Jedi: Working with One Row from a Query (11/02/2005)
Lighthouse Pro, Soundings, Blog Beta Updated (11/02/2005)
Lighthouse Pro ColdFusion Bug Tracker Updated (11/01/2005)
ColdFusion Programmers Don't Share... (NOT) (11/01/2005)
ColdFusion Podcast Explosion (11/01/2005)
Ask a Jedi: Excluding Folders from Verity (11/01/2005)
Lighthouse Pro - Free for All (10/31/2005)
Intermediate ColdFusion Contest! (10/30/2005)
CFCDev List Back Up (10/29/2005)
CFCDev Users - Read (2) (10/29/2005)
CFCDev Users - PLEASE READ (10/29/2005)
And now for something really important... (10/28/2005)
Ask a Jedi: Excluding Pages from Application.cfm/cfc (10/27/2005)
Ask a Jedi: Dealing with Recursion (10/27/2005)
CFMX 7 and Super Fixes (10/27/2005)
Ask a Jedi: Executing Code in OnRequestEnd after an Abort (10/27/2005)
Call to BlogCFC Users (10/26/2005)
BlogCFC 4 Beta (10/26/2005)
rssWatcher Updated (10/25/2005)
Migrating from Blogger to BlogCFC (10/25/2005)
ColdFusion Contest Winner (10/25/2005)
Starfish ColdFusion Debugger Version 0 Released (10/24/2005)
Ask a Jedi: Validating Numbers in a Flash Form Grid (10/24/2005)
ColdFusion Contest - Final Entries (10/24/2005)
Ask a Jedi: Apache Virtual Hosts and Remoting (10/23/2005)
You Need TV (Really) (10/23/2005)
MAX Files (10/22/2005)
Ask a Jedi: Understanding Dereferencing Bug (10/21/2005)
Flex 2 List? (10/20/2005)
Goodbye MAX, and One More Thing... (10/19/2005)
Followup to Sys-Con Issue (10/19/2005)
Should I Be Honored or Offended? (10/18/2005)
MAX: Next Generation Flex: Infrastructure and Logic, Or - How NOT Be a Good Audience Member (10/18/2005)
MAX: Debugging Flex Applications (10/18/2005)
MAX: Day 2 Keynote (10/18/2005)
MAX: Keynote Review (10/17/2005)
MAX: Advanced ColdFusion MX 7 Printing and Reporting (10/17/2005)
MAX Day 0 Report (10/16/2005)
Ask a Jedi: Using UDFs with an Application.cfc Framework (10/16/2005)
On My Way! (10/16/2005)
Ask a Jedi: Building a Template System in ColdFusion (10/14/2005)
Ask a Jedi: Various Quickies... (10/13/2005)
Slow posting and Random TV Topics (10/12/2005)
ColdFusion Contest Entry Examined - Part 5 (10/12/2005)
Flex, Secured Web Services Tip (10/10/2005)
Ask a Jedi: ColdFusion Administration (10/10/2005)
Soundings Updated (Again 3) (10/09/2005)
IIS6 Bug with CFLOCATION (10/08/2005)
Soundings Updated (Again) (10/08/2005)
Soundings Bug - Very Important! (10/07/2005)
Ask a Jedi: MySQL Dumping (10/06/2005)
Flex Announcement (10/06/2005)
Ask a Jedi: Learning CFCs and ColdFusion Wikis... (10/05/2005)
CFC Debugging (10/04/2005)
ColdFusion Contest Entry Examined (10/04/2005)
Modifying Exception Templates in CFMX 7.0.1 (10/04/2005)
Ask a Jedi: Yahoo RSS Feeds and Images (10/03/2005)
Rita Pictures (09/30/2005)
Ask a Jedi: Warning about the End of a Session (09/30/2005)
Ask a Jedi: Determining Country from IP (09/29/2005)
A Thank You To My Supporters (09/29/2005)
Galleon Forums Fix Fix (09/29/2005)
Two Nice Fixes in ColdFusion 7.0.1 (09/28/2005)
Galleon Forums Updated (09/28/2005)
Ask a Jedi: CFGRID Question and Asynchronous Processes in ColdFusion (09/28/2005)
BlogCFC Refreshed (09/28/2005)
Have a ColdFusion Job? Need a ColdFusion Job? (09/27/2005)
BlogCFC Subscribers and Stats (09/27/2005)
Ask a Jedi: Twisted Query (09/27/2005)
Reminder - ColdFusion Contest for Beginners (09/27/2005)
Ask a Jedi: ColdFusion and XML Attributes (09/26/2005)
Ask a Jedi: Installing ColdFusion on OSX (09/26/2005)
Rita Update - The Aftermath (09/25/2005)
Rita Update 11:47 PM (09/23/2005)
Rita Update 9:45 PM (09/23/2005)
Ask a Jedi: Dynamic Images and Deletes (09/23/2005)
Help Me Get More Free Junk (09/23/2005)
Potential Down Time (Part 2) (09/22/2005)
BlogCFC Alpha 2 Launched (09/22/2005)
CFC BOF at MAX (09/22/2005)
A few BlogCFC Notes (09/22/2005)
Galleon Issue with BlueDragon (09/21/2005)
TV: Lost is Found (09/21/2005)
Ask a Jedi: Flash Form Custom Validation (09/20/2005)
ColdFusion 101: Take your blankety-blank darn freaking text elsewhere! (09/20/2005)
Contest: Shall We Play a Game? (09/20/2005)
Ask a Jedi: Two Application.cfc Questions (09/19/2005)
ACME Guide - Get It (09/19/2005)
Ask a Jedi: Dumping ColdFusion Variables (09/19/2005)
Ask a Jedi: Arrays of Objects (09/17/2005)
Free Stuff Is Cool... (A BlogCFC Story) (09/16/2005)
Ask a Jedi: My Application.cfc PDF (09/16/2005)
Galleon ColdFusion Forums 1.5 Released (09/16/2005)
Eliza - Because I wanted to waste time! (09/16/2005)
It's a Revolution! No, Really! (09/16/2005)
Holy Smokes - I'm a Banner?!? (09/15/2005)
Two Cool Event Gateway Articles by Forta (09/15/2005)
Google Sitemap support for BlogCFC (09/15/2005)
Macrochat Recording and Downloads (09/14/2005)
Looking for a roommate at MAX? (09/14/2005)
Ask a Jedi: ColdFusion Forums (09/14/2005)
ScriptProtect "Gotcha" (09/14/2005)
Reminder - Macrochat TODAY! (09/14/2005)
Book Review: Perdido Street Station by China Miéville (09/13/2005)
Ask a Jedi: Debugging with Flash Forms (09/13/2005)
Ask a Jedi: Can I keep a Flash Form item disabled until I'm ready? (09/13/2005)
Oops! Blog go BOOM! (09/13/2005)
Ask a Jedi: Opening a new window from a Flash Form (09/12/2005)
Thanks Google (09/12/2005)
Ask a Jedi: Working with Excel (09/12/2005)
Reminder - Macrochat on Wednesday (09/12/2005)
Galleon ColdFusion Forums Updated (2) (09/10/2005)
Poison Ivy: 2, Ray: 0 (09/09/2005)
Ask a Jedi: Moving items up and down... (09/09/2005)
Bug in BlogCFC 3.9 (09/08/2005)
ColdFusion 101: Config Files A-Go-Go Part 3: Wrap Up (09/08/2005)
Dell Heaven? (09/07/2005)
Ask a Jedi: Multiple Questions (09/07/2005)
Plants: 1, Raymond: 0, and more musings on Dell Hell... (09/06/2005)
Special Invite to Tech Workers in Lafayette (09/05/2005)
ColdFusion 101: Looping over Months (09/05/2005)
The Dell Hell Saga Continues... (09/02/2005)
ColdFusion 101: Config Files A-Go-Go Part 2: XML Files (09/02/2005)
New Site (Well, Updated Site) Launched: Aspen/Snowmass (09/02/2005)
CentraSoft Helping Katrina Victims (09/02/2005)
Welcome Blog Herald Readers, and Ask a Jedi Status (09/02/2005)
How bad can it get? Bad. (09/01/2005)
ColdFusion 101: Building a Calendar (08/31/2005)
Attention BlogCFC Users and Subscribers to this Blog (08/31/2005)
Ask a Jedi: ColdFusion Components and Validation (08/30/2005)
Yet Another Galleon ColdFusion Forums Update, and ColdFusion Tip (08/30/2005)
Flash 8 and Firefox Problems? (08/30/2005)
Cool UDF: cfcToPrinter (08/30/2005)
Macrochat on Validating Input Parameters (08/30/2005)
Galleon ColdFusion Forums Updated (Minor Bug Fixes) (08/29/2005)
ColdFusion 101: Sorting Directory Paths in ColdFusion (08/29/2005)
Katrina Update (08/29/2005)
Hey, MTV Plays Music! (Who Knew?) (08/28/2005)
Potential Downtime (08/28/2005)
ColdFusion 101: Config Files A-Go-Go (08/26/2005)
Comments Please... (08/26/2005)
More Dell Hell (08/26/2005)
BlogCFC 4.0 Update (08/25/2005)
New Depeche Mode Single: Precious (08/25/2005)
New Blog: The Adoption News (08/24/2005)
"Vile" Forms (08/24/2005)
Is a "Thank You" too much to ask for? (08/24/2005)
Dell Hell: The Finale... (08/24/2005)
Ask a Jedi: XML Forms, CFSELECT, and Value Issues (08/24/2005)
Sessions Expiring and Too Many Cookies (08/23/2005)
Ask a Jedi: Using Multiple Categories with Verity in ColdFusion MX 7 (08/23/2005)
Another Mindseye Site of the Day (08/22/2005)
SFU: Everyone's Waiting (08/22/2005)
Verity Tip: How to "hide" content from anonymous users... (08/22/2005)
Minor BlogCFC Update (08/22/2005)
Google Adsense Secrets Review (08/19/2005)
CFLib Spam (08/19/2005)
Need for Speed: Underground Rivals PSP Review (08/18/2005)
Verity Tip: THESAURUS Searching (08/18/2005)
Sorry for the CFLib Email... (08/18/2005)
Ask a Jedi: ColdFusion and PGP (08/18/2005)
Ask a Jedi: Accessing Application Variables set in Application.cfc (08/18/2005)
A Thank You (to someone...) (08/17/2005)
Verity Macrochat Presentation Zip (08/17/2005)
Macrochat Recording (08/17/2005)
Even Jedis Make Dumb Mistakes... CFHTTP, Timeouts, and RSSWatcher (08/17/2005)
Macrochat Today! (08/17/2005)
CFLib/My Blog/RSSWatcher/Etc Downtime... (08/17/2005)
Verity Technote : Indexing Limit (08/16/2005)
Gotta Love that Typeless ColdFusion Goodness! (08/16/2005)
Mac Goodness (08/15/2005)
Model-Glue CFLib Update - Opinions Wanted (08/15/2005)
Away for the Weekend... (08/13/2005)
Ask a Jedi: CFLOCK in CFSCRIPT? (08/12/2005)
BlogCFC 3.9 Released / BlogCFC 4.0 Specs (08/12/2005)
Dell Update Inifinity... (08/12/2005)
Ask a Jedi: Error Handling w/o Robust Exception Information (08/11/2005)
Flash Forms and Flash Paper (08/11/2005)
New Music - Saint Etienne (08/11/2005)
Model-Glue CFlib Update (08/11/2005)
Ask a Jedi: Can I Use a PDF in a Flash Form? (08/11/2005)
Ask a Jedi: ColdFusion Memory Scoped Variables and Clusters (08/10/2005)
The Macs are Coming! The Macs are Coming! (08/10/2005)
Ask a Jedi: Changing a ColdFusion Flash Form "Page" Based on Drop Downs (08/09/2005)
Galleon ColdFusion Forums 1.3.7 Released (08/09/2005)
Announcement: Verity for Fast Text Searching Macrochat (08/09/2005)
ColdFusion Flash Forms File Upload Example (08/09/2005)
Ask a Jedi: Caching Results from ColdFusion Tags (08/09/2005)
Ask a Jedi: Abstracting ColdFusion Queries (08/08/2005)
Luke Skywalker: "Because there is good in him...." (08/08/2005)
BlogCFC 3.9 Beta (08/08/2005)
Ask a Jedi: Enhancing the Flash Form Grid (2) (08/07/2005)
Ask a Jedi: Enhancing the Flash Form Grid (08/06/2005)
Reminder - Accepting ColdFusion and Development Questions (08/06/2005)
Dell Update Number 2,432,940 (08/06/2005)
My Day In H(D)ell (08/05/2005)
Using ColdFusion Scheduler With Files Based on Dates (08/05/2005)
Verity ColdFusion TechNote: Indexing a Verity collection fails with a Path not found error (08/05/2005)
One of Those Days - and Another Dell Horror Story (08/05/2005)
Even More On URL Rewriting (08/04/2005)
Model-Glue Version of CFLib: Version 0 (08/04/2005)
New Site: Atlas Venture (08/03/2005)
Galleon 1.3.6 Released (08/03/2005)
BlogCFC Users - Google Sitemap Support (08/03/2005)
Working with SES URLs Follow Up (08/03/2005)
Ask a Jedi: Working with SES URLs and ColdFusion (08/02/2005)
Don't Try This At Home: CFBASIC (08/02/2005)
Web Stats Recommendations? (08/02/2005)
Totally Useless Post: Half-Life 2 is Amazing (08/01/2005)
Ask a Jedi: Ramping Up to CFMX N+1 (08/01/2005)
More Model-Glue Rumblings... Layouts within Layouts (08/01/2005)
ColdFusion CFERROR Bug (07/31/2005)
ColdFusion Function IsValid Bug (07/31/2005)
Galleon Review (07/30/2005)
Attention Readers (07/29/2005)
For Acadiana Folks Only: LafayetteTech (07/29/2005)
Ask a Jedi: How do I learn Model-Glue? (07/29/2005)
Ask a Jedi: Can you use string functions along with WDDX and JavaScript? (07/28/2005)
Ask a Jedi: What version of the JRE is bundled with CFMX? (07/27/2005)
Ask a Jedi: Can I bind an image to a cell in cfgrid? (07/27/2005)
Ask a Jedi (07/26/2005)
Model-Glue FAQs (07/25/2005)
CFUNITED Feedback Forms (07/24/2005)
Embedded CFCHART in Flash Forms - Part 3 (07/23/2005)
Xbox Review: Halo 2 (07/23/2005)
How NOT To Do Directory Security (07/22/2005)
Blog 3.8 Released (07/22/2005)
DRK12 Released (07/21/2005)
PSP Review: Untold Legends (07/21/2005)
Holy crap XML is cool... (07/21/2005)
Embedded CFCHART in Flash Forms Part Deux! (07/21/2005)
BlogCFC Quick Fix for Titles with Quotes (07/21/2005)
Ray's Adventures in Model-Glue Land (07/21/2005)
Working with MailEnable and ColdFusion (07/20/2005)
Embedded CFCHART in Flash Forms (07/19/2005)
KTML Tip - Getting the Latest Version (07/19/2005)
Not Enough Pink Shoes (07/18/2005)
Lafayette got Slashdotted... (07/18/2005)
Go ahead and offend me, I can take it! (07/15/2005)
Go ahead and DRM the monitor... (07/15/2005)
IIS, SES URLs, and "Check for file existence..." (07/14/2005)
More CFMX Error Modifications (07/14/2005)
BlogCFC 3.8 RC Released (07/12/2005)
Help CF Help You... (07/12/2005)
BlogCFC 3.8 Beta News (07/12/2005)
Macrochat Archive Live on Devnet (07/12/2005)
Query of Queries and Bracket Matching (07/11/2005)
Flash, HTML, and the Non-breaking Space. (07/11/2005)
I'm Home! (07/09/2005)
CFUNITED05 Presentations (07/01/2005)
Blog BOF and "Power Users" (07/01/2005)
Reminder - Out of Office for a while... (06/30/2005)
CFUNITED - Thursday Report 1 (06/30/2005)
Now for something REALY important... (06/30/2005)
CFUNITED Update (06/30/2005)
Verity Session Update Part 2 (06/29/2005)
Verity Session Update (06/29/2005)
I'm Cursed (06/28/2005)
Woohoo! Delay Number Two (06/28/2005)
Woohoo! Delay Number One! (06/28/2005)
Out of Office Notice... (06/27/2005)
BlogCFC Beta Released (06/24/2005)
Question for BlogCFC Users (06/23/2005)
Verity Tip (06/23/2005)
Important BlogCFC Update (06/23/2005)
Addicted to UPS (06/23/2005)
License Issue (06/23/2005)
New Blog: CFChart (06/23/2005)
CFC BOF @ MAX (06/21/2005)
Speaking at MAX 2005 (06/21/2005)
Help CFEclipse (06/17/2005)
Verity Tip - Checking for a Key (06/17/2005)
CF Update Page... Updated (06/16/2005)
Not Politics - A ColdFusion Image Tip (06/16/2005)
Yes, I can lock you up forever... (06/15/2005)
Updaters versus Hot Fixes (06/14/2005)
Verity Doc Note (06/14/2005)
Beta is NOT the End... (06/13/2005)
BlogCFC Tip (06/07/2005)
Macromedia and Eclipse - Where's the Fusion? (06/06/2005)
RSS Issue in BlogCFC (06/01/2005)
As free as I want you to be... (05/31/2005)
Lots of Randon Notes Not Pertaining to CF In Any Way... (05/31/2005)
Another BlogCFC Update (05/27/2005)
BlogCFC / BD / Access Warning (05/27/2005)
2 Bugs Fixed with this Blog (and a note for SimpleContentEditor users!) (05/27/2005)
BlogCFC Quick Fix (05/26/2005)
CFLib / RSSWatcher / CFCZone / This Box (05/26/2005)
Lord of the Dance (05/25/2005)
iCal CFC Part 2 (05/25/2005)
SimpleContentEditor Updated (05/25/2005)
iCal CFC (05/25/2005)
String parsing with quotes (05/24/2005)
I have an enemy? (05/23/2005)
Simple Content Editor (05/22/2005)
New Custom Tag: Simple Content Editor (05/20/2005)
Musical Baton Meme (05/19/2005)
Episode 3 Review (05/19/2005)
Interesting Flash Remoting Issue (05/18/2005)
Soundings Released (05/18/2005)
Happy "Gotcha" Day (05/17/2005)
CFMX7 Verity/Category Bug (05/17/2005)
These are the voyages... (05/14/2005)
License Exceptions and CFChart (05/11/2005)
RSS.cfc Update (05/10/2005)
Random Notes... (05/06/2005)
Greetings (05/06/2005)
Out of Office Notice (05/01/2005)
Lighthouse Pro Bug Fixes (04/28/2005)
DRK11 Launched (04/28/2005)
Advanced ColdFusion MX 7 Application Development Shipping (04/26/2005)
Future Geeks of America - Unite! (04/26/2005)
IE7 Question (04/26/2005)
Galleon Warning / Notice about CFLOGIN (04/25/2005)
Verity and Titles (04/25/2005)
Links to Share (04/24/2005)
Mute the Browser Part Deux (04/24/2005)
Mute the Darn Browser (04/22/2005)
Urgent Message to CF Developers - CF Can Crash! (04/22/2005)
Light Side or Dark Side - Help me choose... (04/20/2005)
Adobe and Macromedia (04/19/2005)
Clone Wars (04/19/2005)
TechSouth (04/19/2005)
BlogCFC Fix Released (04/18/2005)
Installing Flex with ColdFusion (04/18/2005)
Now THAT Is an Error Message (04/13/2005)
Not a Review of Gran Turismo 4 (04/11/2005)
CFC Methods Calling CFC Methods (04/08/2005)
Happy Birthday to Me! (04/08/2005)
Don't Buy.com (04/07/2005)
Galleon 1.3 Released (04/06/2005)
Minor Update (Again) (04/05/2005)
DRM is the new Microsoft... (04/05/2005)
Minor Update (04/05/2005)
Did You Know: Arrays of Components (03/31/2005)
Is it October yet? (03/31/2005)
Small CFLib Fix (03/31/2005)
Slushy Part 3: Return of the Label (03/30/2005)
Slushy Part 2: The Order Strikes Back (03/30/2005)
First CFMX7 Site: Celebrities For Charity (03/30/2005)
Thanks for KOTOR2 (03/30/2005)
Slushy! (03/30/2005)
RSSWatcher Update (03/29/2005)
Reminder on BlogCFC 3.6.X (03/28/2005)
PSP Review (03/28/2005)
Thunderbird/Norton Post #4903 (03/24/2005)
It's Here! CFMX7 WACK! (03/24/2005)
Working on Two Bugs (03/24/2005)
Thanks! (03/18/2005)
Design this Blog (03/18/2005)
Cool BlogCFC Use (03/17/2005)
New Article in CFDJ (03/17/2005)
Important Note for CFDJ Contest (03/17/2005)
Aligning Buttons in CFForm (03/17/2005)
Update to Old Marvel Post (03/14/2005)
Bug Fixing - Ignore (03/11/2005)
Time to Brag... (03/11/2005)
New Star Wars Trailer on OC Tonight! (03/10/2005)
Bug with onSessionEnd (03/10/2005)
Opinions Wanted: RSS.cfc (03/07/2005)
Working with Required Checkboxes in CFFORM (03/07/2005)
Speaking at NOMMUG (03/07/2005)
CFForm Tip (03/07/2005)
One More Thunderbird Issue (03/04/2005)
Fun with Google Maps (03/02/2005)
Always var scope! Always!! Except... (03/02/2005)
RSS for Stats (03/02/2005)
URL Validation - Rant Mode (03/02/2005)
You think cable is safe? (03/01/2005)
CFLib Notice (02/28/2005)
Issue with CFGRID in Flash Forms (02/25/2005)
Issue with empty strings and Flash Forms (02/25/2005)
Still aren't watching Battlestar Galactica? (02/25/2005)
Update to Application.CFC Reference (02/24/2005)
Application.CFC Reference (02/23/2005)
You don't buy the software (part 2) (02/23/2005)
New Beck Single (02/22/2005)
CFUNITED! (02/22/2005)
You don't buy the software, you buy the license. (02/21/2005)
Warning to Thunderbird and Norton Users (02/20/2005)
Good Copyright Article (02/17/2005)
As promised - new ScopeCache Download (02/16/2005)
Query Metadata in CFMX7 (02/16/2005)
Recorded Macrochat (02/16/2005)
CFMX 7: IsValid() (02/11/2005)
Reminder on MacroChat (02/10/2005)
Validating "Pages" in CFFORM (2) (02/09/2005)
Sunbird (02/09/2005)
Aspensnowmass is Macromedia Site of the Day (02/08/2005)
Validating "Pages" in CFFORM (02/07/2005)
CFForm Tips (3) (02/07/2005)
CFForm Tips (02/07/2005)
Warning About Flash Forms (02/07/2005)
Warning About Application Events (02/07/2005)
Security and UDF Names in CFMX 7 (02/07/2005)
CFMX 7 - Favorite Features / Things You Should Note (02/06/2005)
ColdFusion MX 7 is Here! (02/06/2005)
Question for CFLib Users (02/04/2005)
Minor Galleon Update (02/03/2005)
GMail Invites (02/03/2005)
Why did I do that? (02/02/2005)
Galleon Announcement (01/31/2005)
No, you can't lock them up and throw away the key... (01/31/2005)
Nice Flash Animation - Radiohead Video (01/28/2005)
RSSWatcher Moving... (01/26/2005)
Server Issues Fixed (Really!) (01/23/2005)
More on Server Issues (01/21/2005)
Warning about Camdenfamily.com/CFLib.org (01/19/2005)
New Blog Address: (01/17/2005)
CFLib (and camdenfamily) Downtime (01/16/2005)
Battlestar Galactica (01/15/2005)
Hal Helms' Occasional Newsletter (01/14/2005)
Captivate Review (01/13/2005)
My Macrochat (01/10/2005)
RSS.cfc Updated (01/06/2005)
CFLib in 2005 (and 2004) (01/05/2005)
Who's Your Daddy? (01/03/2005)
Bug with isSimpleValue Part 2 (12/28/2004)
Bug with IsSimpleValue (12/27/2004)
Multiple IIS Sites on XP Pro (12/27/2004)
Random Christmas Link (12/23/2004)
CFEclipse Tips 1 and 2 (12/23/2004)
How (Not) To Do a Presentation (12/21/2004)
CFEclipse Week (12/21/2004)
Tutorial Contest (12/20/2004)
rss.cfc: Version 0.1 (12/16/2004)
Let's try that again... (12/13/2004)
Random Notes (12/10/2004)
Upcoming Lighthouse Updates (12/03/2004)
More from My.Yahoo (12/02/2004)
Cox DVR Hint (11/30/2004)
Morpheus @ Yahoo No More (11/28/2004)
Blog Stats (11/19/2004)
Leading 0s and Excel (11/16/2004)
I want it! I want it! (11/15/2004)
Converter for CFXML_Blog to BlogCFC (11/15/2004)
CFLib Comments Disabled (11/15/2004)
Marvel Sues Game Studios (11/12/2004)
Did You Know: CFLib and CFS/HS+ (11/10/2004)
Watch that white space! (11/10/2004)
Client Variable Tip (11/08/2004)
CFC Blackstone Update (11/08/2004)
MAX Round Up (11/08/2004)
New Star Wars Teaser Released (11/06/2004)
HS+ Users and Win XP SP2 (11/06/2004)
MAX: Creating Richer and More Maintainable Sites with CSS (11/04/2004)
More MAX Notes (from Wednesday) (11/03/2004)
More MAX Notes (11/02/2004)
MAX Reports (11/02/2004)
Nintendo Apologizes... (10/29/2004)
Special day yesterday... (10/27/2004)
Soundings Conference (10/26/2004)
DRK9 Released (10/26/2004)
MAX, Community Suite, Etc. (10/26/2004)
Update to MX Migration Issue (10/25/2004)
Issue Migrating to CFMX (10/20/2004)
CFDJ Call for Articles Again (10/19/2004)
FreeIpods Update (10/18/2004)
Blog Fix Released (10/15/2004)
Random (Unimportant) Notes (10/15/2004)
Blog 3.5.2 Released (10/14/2004)
Warning about CFLOGIN (10/13/2004)
Reminder About My Blog (10/11/2004)
National Republican Senatorial Committee: Did you get the survey? (10/05/2004)
DecimalFormat Issue (10/05/2004)
Interesting CFINVOKE Trick (10/05/2004)
Check out Newsbrew (10/04/2004)
Reminder about Roles in CFFUNCTION (10/03/2004)
Corfield's Article on BlogCFC (09/27/2004)
Boston Bound (09/26/2004)
Mail Attack (09/26/2004)
CFLib Shirts (09/23/2004)
Get Lost (09/23/2004)
Second Part to RSS Watch Article Launches (09/22/2004)
CFDUMP and CSS (09/20/2004)
Atom Parsing (09/20/2004)
I Love My Cable Company (Really) (09/18/2004)
CFML History (09/17/2004)
Star Wars Goodies (09/17/2004)
CFC Birds of a Feather is On! (09/15/2004)
BlogCFC and Blackstone (09/09/2004)
Blog 3.5.1 Update (09/09/2004)
CFMX Admin Password Issue (09/07/2004)
Aspensnowmass Launched (09/07/2004)
Another good fix in the Updater... (08/26/2004)
CFLogin/Session Bug Fixed (08/26/2004)
CFMX 6.1 Update Released (08/25/2004)
rssWatcher Launched (08/24/2004)
Latest Article on DevNet (08/22/2004)
Outlook Lookout (08/20/2004)
OT Blatant Greed (08/18/2004)
Working with Sessions and CFLOGIN (08/12/2004)
TechNote on CFLOGIN (08/12/2004)
HS+ Snippets and CFMODULE Workaround (08/10/2004)
Sorry so quiet... (08/09/2004)
Batman Begins Trailer (07/29/2004)
Wolves of the Calla (07/29/2004)
Revenge of the Sith (07/26/2004)
Mindseye Seeking CF Developer (07/26/2004)
Blog CFC Conference (07/26/2004)
I'm not getting old - the Net is getting smaller... (07/21/2004)
Looking for a job? (07/20/2004)
Two New Element Sites (07/20/2004)
Blog 3.5 Available for Testing (07/16/2004)
MAX 2004 CFC BOF (07/15/2004)
Blog 3.5 Update (07/13/2004)
Wierd Little Flash Remoting Bug (07/12/2004)
isDebugMode Reminder (07/12/2004)
Another Element Site: www.irobot.com (07/12/2004)
Administrative Note - New Pod for My Tools (07/09/2004)
CFDJ Writers Needed (07/07/2004)
Question for Blog CFC Users (06/30/2004)
CFUN Notes (06/27/2004)
CFUN Presentation (and apology) (06/26/2004)
New Job (Same Company) (06/21/2004)
Speaking at MAX (06/18/2004)
Vacation! (06/18/2004)
Firefox 0.9 Released (with the same old bug, yea!) (06/16/2004)
Managing Projects (06/14/2004)
Death Wish for a Printer (06/11/2004)
Mute for Browsers (06/09/2004)
iTunes SDK (06/08/2004)
CF Mapping Crazyness (06/03/2004)
Uploading Encrypted Documents (06/02/2004)
Finished Star Wars: KOTOR (06/01/2004)
Draft 2 (05/29/2004)
CF Tags and CFOUTPUT (05/28/2004)
CFCHART Mystery (05/28/2004)
Manually Setting Execution Mode (05/28/2004)
Dumping CFCATCH (05/27/2004)
Return of the Draft? (05/27/2004)
Ain't It a Slow Server (05/25/2004)
A WDDX Bug (05/24/2004)
New Blackstone Blog (05/24/2004)
Star Wars Episode 3 Title Announced (05/20/2004)
Updated Zip for Article (05/18/2004)
My New Devnet Article (05/17/2004)
Question for CF/Apache Users (05/14/2004)
Listen to This... (05/13/2004)
Interesting Little CF Bug... (05/13/2004)
Speaking in Boston Next Week (05/13/2004)
CFC Bug (05/07/2004)
Another Duplicate Update (05/06/2004)
Macromedia Community Week (and other stuff...) (05/04/2004)
Out of Town (04/27/2004)
Jedi vs. the Web Services, Final Round (04/26/2004)
Jedi vs. the Web Services, Round Four (04/26/2004)
Jedi vs. the Web Services, Round Three (04/25/2004)
Jedi vs. the Web Services, Round Two (04/24/2004)
Lighthouse Users - Notice... (04/23/2004)
Web Services / Virtual Host Issue (04/23/2004)
FTC and the Difference Between Email and Email Clients (04/14/2004)
This is the way the world ends... (04/13/2004)
Starting/Stopping CF from HS+/CFStudio (04/12/2004)
My CFUN Interview (04/12/2004)
Happy Birthday to Me! (and other random notes) (04/08/2004)
-sigh- Another Duplicate Bug (04/01/2004)
New laptop and coupon codes (04/01/2004)
Out of Office/In the Office (03/29/2004)
Vinyl Data (03/25/2004)
Odd Issue w/ CFQueryParam (03/24/2004)
HS+ Issue w/ Large Files (03/19/2004)
CFC Issue w/ Arguments (03/19/2004)
Lighthouse Bug Tracker 1.1 Released (03/18/2004)
Lighthouse Bug Tracker - Free (03/16/2004)
Session is Invalid Bug (and Fix) (03/12/2004)
Duplicate Bug Fix! (03/11/2004)
Rethrow in cfscript? (03/09/2004)
CFLib.org Update (03/03/2004)
Tech Note: Using CFCs as Datatypes with Web Services (03/02/2004)
Update to DumpF (02/27/2004)
Another Puzzle Solved with CF (02/26/2004)
Happy (Belated) Mardi Gras! (02/26/2004)
Exporting SQL Server Data to a Script (02/26/2004)
Duplicate Bug (02/18/2004)
CFLib Milestone (02/18/2004)
Blog 3 Officially Released (02/17/2004)
Interesting Quote (02/16/2004)
Latest CFDJ Article (02/12/2004)
CFC Issue to Watch Out For... (02/09/2004)
Blog 3.0 RC Is Here! (02/01/2004)
Payflow Link Warning (01/27/2004)
Reminder - Topic Specific RSS Feeds (01/27/2004)
Woohoo, my new (mini) toy... (01/25/2004)
Code Breaking with CF (01/21/2004)
Sending both HTML and Plain Text Emails in One Shot (01/21/2004)
CFLib Downtime Note (01/21/2004)
Star Wars Game: Battle of Endor (01/19/2004)
Old CF Bug Fixed / single quote issue in complex string functions... (01/15/2004)
So where the heck is 3.0? (01/13/2004)
ScopeCache (01/08/2004)
CFLib Bug Fixed (01/07/2004)
UDF Bug to Watch Out For - Part 2! (01/06/2004)
UDF Bug to Watch Out For... (01/05/2004)
year++; (12/31/2003)
Blog Spam? (12/23/2003)
Random Boring Stuff (12/22/2003)
HS+/CFS Bug (12/19/2003)
adRotator (12/18/2003)
Yet Another Blog Update (12/15/2003)
Macromedia Advisory Groups (12/12/2003)
Working with C# and HomeSite+ (12/11/2003)
Custom Tag: SlideShow (12/11/2003)
Another CFPOP Issue (12/11/2003)
Encrypting URL Values (12/09/2003)
So, how was your weekend? (12/08/2003)
Struct Keys and Case (12/05/2003)
Interesting Structure Reference Issue (12/04/2003)
More CFPOP Issues (12/04/2003)
My new toy: Nomad Jukebox Zen Xtra (12/02/2003)
Copy-crazy (12/02/2003)
One more blog update: (11/29/2003)
New feature at CFLIB (11/28/2003)
structKeyList Order (11/26/2003)
IPod's Dirty Little Secret (11/25/2003)
Unsupported Locale Error w/ CFPOP (11/25/2003)
When good kids meet Santa... (11/25/2003)
MAX Roundup + Random Notes (11/24/2003)
Sneak Peek Info (11/20/2003)
MAX Update (General notes) (11/20/2003)
MAX Bloggers (11/19/2003)
MAX Notes from Keynote 1 (11/19/2003)
MAX Bound.... Maybe (11/17/2003)
CFDJ Ideas (11/17/2003)
CFC Issue with Output Attribute (11/13/2003)
Blog 3 Beta Updated (11/13/2003)
CFMX 6.1 Issues (11/11/2003)
Blog 3.0 Beta Released (11/07/2003)
More HS+ Goodness (11/07/2003)
HS+, Color Coding, and ASPX (11/06/2003)
DW Article and HS+ Tip (11/06/2003)
MX Bug + Blog Update (11/06/2003)
Asp.Net and Queries (11/04/2003)
CF Lists and Delimiters (11/04/2003)
CFC Geeks of a Feather is ON! (11/04/2003)
Amazon's Dirty Little Secret (11/04/2003)
Central Focus (11/03/2003)
Spectra 1.5.3 Released (11/02/2003)
Happy Halloween and Other Random Notes (10/31/2003)
getMetaData Bug (10/29/2003)
There is a First Time for Everything. (10/27/2003)
CF Bug plus the polls... (10/27/2003)
DRK5 Released! (10/24/2003)
structFindValue/structFindKey (10/22/2003)
Movie Movie (10/21/2003)
Old Gamers don't die, they just get a new life... (10/20/2003)
More HS/Studio Extensions (10/20/2003)
CFDJ October Article (10/16/2003)
CFC "Geeks of a Feather" at MAX (10/14/2003)
Blog 3.0 Alpha (10/13/2003)
Windows Explorer (10/09/2003)
structSort (10/07/2003)
Changes due to Eolas (10/07/2003)
We've come so far... (10/06/2003)
The Other Side... (10/03/2003)
Overflow Numbers (10/02/2003)
Odd Issue with cfcontent, cfsetting, and wrapper tags... (10/02/2003)
Error checking... again (10/01/2003)
Oracle CLOBs, MX 6.1, and the Macromedia Forums (09/30/2003)
Apache Virtual Hosts and CF (09/26/2003)
Macromedia Central Beta Released (09/25/2003)
Top Ten Tips for CFCs (09/25/2003)
Favorite HS+/CFS Tools (09/25/2003)
Returning a CFC from a CFC Method (09/22/2003)
Wake Up and Smell the IDE (09/22/2003)
CF Technote on CFC/UDF Names (09/22/2003)
Sell Out! (09/13/2003)
By Ref/By Value (09/12/2003)
MX Developer's Journal (09/11/2003)
CFC Development Meeting (09/10/2003)
Flush Your DNS (09/09/2003)
Issue with CF Server Side Validation (09/09/2003)
min()/max() (09/05/2003)
The Sandman comes again... (09/05/2003)
structGet() (09/03/2003)
Global MMUG Meeting Today (09/03/2003)
Updated Site: Aspensnowmass.com (09/02/2003)
Var statements in cfscript (08/21/2003)
Star Wars in the Snow (08/19/2003)
Start/End Mode and Custom Tags (08/18/2003)
Things just get more interesting... (08/17/2003)
So where was I... (08/14/2003)
Lack of Updates... (08/12/2003)
My Love/Hate Relationship with Mozilla (08/08/2003)
Random Tidbits (08/08/2003)
GetSessions() (08/07/2003)
Using CF Tags in CFSCRIPT (08/05/2003)
Rant Mode On... (08/05/2003)
Tag Editors (08/05/2003)
Updated Tech Notes (08/05/2003)
ColdFusion MX 6.1 (08/04/2003)
FileZilla (08/04/2003)
Polls Added (08/04/2003)
Telemarketers - How do I hate thee... let me count the ways... (07/29/2003)
WAP Support (07/29/2003)
Buymusic.com - Explain this to me... (07/28/2003)
Random Studio/HS+ Tidbits (07/28/2003)
ANN: BlogDev SourceForge (07/25/2003)
CF Hosting (07/25/2003)
OT: "Gotcha" Day (07/25/2003)
Blog Zip Updated (07/23/2003)
Slashdot Article on OSS and Governments (07/22/2003)
Functions in Functions? (07/22/2003)
Size of a SQL Server DB (07/21/2003)
Timing Code (07/16/2003)
CFC Method/UDF Gotcha (07/16/2003)
CFUN-03 Presentations (07/15/2003)
One More Bug Fix (07/15/2003)
Question: How to handle CFCs and initialization? (07/15/2003)
Blog Update (07/14/2003)
Testing SSL and IIS (07/14/2003)
Stress Out Your Web Sites (07/10/2003)
VTML - Language of Masochists (07/09/2003)
Another Update (07/08/2003)
Bulletproof Websites (07/08/2003)
Queries and Bracket Notation (07/07/2003)
Major Blog Update (07/05/2003)
Blog Issue and CFCs Under Load (07/03/2003)
Add Comments Broken (07/02/2003)
Script and Tag Based UDFs and Whitespace (07/02/2003)
CFPARAM Issue + Blog Updated (07/02/2003)
Blog Update + QueryParam Bug (07/01/2003)
I'm Back - and Random Other Notes (06/30/2003)
Internet Killed the Radio (06/19/2003)
CFUN-03 and Vacation (06/19/2003)
DSN and MX Restart Problems (06/19/2003)
Unicode and SQL Server (06/17/2003)
Caching in IIS (06/17/2003)
Blog Update, Minor Notes (06/16/2003)
Exclusive Lock and Single Creation (06/12/2003)
DumpF - Filtering the Dump tag (06/11/2003)
New Site: Celebrities for Charity (06/10/2003)
The Visitors are Your Friends (06/10/2003)
Advanced Securty and MX (06/09/2003)
Blog CFC Updated (06/06/2003)
ColdFusion Studio is NOT Dead! (06/05/2003)
Reminder: List Functions and Delimiters (06/03/2003)
ColdFusion MX Issues (06/03/2003)
Blog Updated (06/02/2003)
A Question for Blog Authors and Readers: Discussions (06/02/2003)
A Tool for Every Need... (06/02/2003)
ColdFusion Red Sky Info (06/02/2003)
Today's Rant: Out of Office Replies (06/02/2003)
PLP Tag Updated (06/02/2003)
PLP Custom Tag Released (05/31/2003)
Mozilla 1.4 Release Candidate 1 Released (05/30/2003)
Blog Updated 2 - Part 2 (05/23/2003)
Blog Updated 2 (05/22/2003)
Minor Blog Update - Major One Soon (05/22/2003)
Question for Blog Readers and Authors (05/22/2003)
MX on the Rocks Presentation Posted (05/19/2003)
CFLib.org RSS Feed (05/16/2003)
Important Blog Error Fixed (05/16/2003)
MX on the Rocks Presentation (05/16/2003)
CFC and Recursion (05/16/2003)
CFC Goodness (05/15/2003)
Blog Updated and Reminder about MX on the Rocks (05/13/2003)
Interesting Observation about DRM (05/09/2003)
CFLogin and Application Names (05/08/2003)
Moz 1.3.1 and 1.4 Beta (05/08/2003)
Interview with Jeremy Allaire (05/08/2003)
Dynamic Datasources in MX (05/05/2003)
Quick Tip: When to Use Pound Signs (05/02/2003)
My first ASP Site: Sciflex (05/02/2003)
Bug Fix in Blog Client (05/01/2003)
HP and Ink Catridges Expiration (04/30/2003)
SpeedComparison (04/30/2003)
Custom Tag Caching (04/30/2003)
Something to Check Out: CFUnit Testing Components (04/29/2003)
2 Upcoming Speaking Engagements (04/28/2003)
What's Up with the Blog (04/28/2003)
Spectrasource Admin - No More! (04/28/2003)
Interesting Behavior with Arguments (04/28/2003)
CF and Network Shares (04/23/2003)
DRK 3 Released (04/22/2003)
Type and CFCs (04/21/2003)
Mozilla - View Source Bug (04/15/2003)
Gone for a While, and Blog News (04/04/2003)
Royale? (03/28/2003)
CFCHART and Display Adapters (03/26/2003)
2 Simple Security Steps (03/25/2003)
Session Tracker (03/25/2003)
Useful Hint for Dealing with Tomcat Issues (03/21/2003)
Interesting Struct Error (03/20/2003)
More on CVS Keyword Substitution (03/20/2003)
CF MX Updater 3 Released (03/19/2003)
CVS - How do I love thee... (03/19/2003)
Blog Updated... Again (03/19/2003)
Blog Updated (3) (03/13/2003)
Blog Updated (Part 2) (03/12/2003)
Blog Code Updated (03/12/2003)
cfloginuser and getAuthUser() (03/11/2003)
returnType Part 2 (03/10/2003)
returnType, CFCs, and Structs (03/10/2003)
CFFLUSH and IE (03/07/2003)
CFMODULE and Application.cfm (03/07/2003)
Importing Data w/ Enterprise Manager (03/05/2003)
MX on the Rocks (02/27/2003)
Special Arguments in component and function tags. (02/26/2003)
Two Errors to Look Out for... (02/24/2003)
Misconceptions abou the CFMODULE tag (02/19/2003)
CGI variables and isDefined (02/18/2003)
Blog CFC (02/13/2003)
Determining if an array element exists... (02/12/2003)
Welcome... (02/12/2003)
|
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| 8,732
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Erminów – dawna gromada, czyli najmniejsza jednostka podziału terytorialnego Polskiej Rzeczypospolitej Ludowej w latach 1954–1972.
Gromady, z gromadzkimi radami narodowymi (GRN) jako organami władzy najniższego stopnia na wsi, funkcjonowały od reformy reorganizującej administrację wiejską przeprowadzonej jesienią 1954 do momentu ich zniesienia z dniem 1 stycznia 1973, tym samym wypierając organizację gminną w latach 1954–1972.
Gromadę Erminów z siedzibą GRN w Erminowie utworzono – jako jedną z 8759 gromad na obszarze Polski – w powiecie sochaczewskim w woj. warszawskim, na mocy uchwały nr VI/10/4/54 WRN w Warszawie z dnia 5 października 1954. W skład jednostki weszły obszary dotychczasowych gromad Antoniew i Dachowa ze zniesionej gminy Kozłów Biskupi oraz obszary dotychczasowych gromad Bronisławy, Erminów i Konstantynów, ponadto wieś Bogumiłe Towarzystwo, wieś Złoty Potok Towarzystwo i Parcele Szwarocin z dotychczasowej gromady Szwarocin, Parcele Ćmiszew z dotychczasowej gromady Ćmiszew oraz wieś Józin Ćmiszewski (enklawa położona w dotychczasowej gromadze Ćmiszew) z dotychczasowej gromady Józin ze zniesionej gminy Rybno w tymże powiecie. Dla gromady ustalono 11 członków gromadzkiej rady narodowej.
31 grudnia 1959 z gromady Erminów wyłączono (a) wieś Antoniew, włączając ją do gromady Zakrzew oraz (b) wieś Dachowa, włączając ją do gromady Kąty w tymże powiecie, po czym gromadę Erminów zniesiono a jej (pozostały) obszar włączono do gromady Rybno tamże.
Przypisy
Erminozzxw
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{
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Бузенхаузен () — коммуна в Германии, в земле Рейнланд-Пфальц.
Входит в состав района Альтенкирхен-Вестервальд. Подчиняется управлению Альтенкирхен. Население составляет 321 человек (на 31 декабря 2010 года). Занимает площадь 3,02 км². Официальный код — 07 1 32 017.
Коммуна подразделяется на 2 сельских округа.
Примечания
Ссылки
Официальная страница
Города Рейнланд-Пфальца
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{"url":"http:\/\/tex.stackexchange.com\/questions\/40060\/problem-with-listings-ext","text":"# Problem with listings-ext [closed]\n\nI am using listings-ext on Ubuntu 11.10 (with LyX) and listings.cfg defines the style colored-code - which I also use in the LaTeX preamble:\n\n\\usepackage[style=colored-code]{listings-ext}\n\n\nBut whenever I try to compile the document - into DVI or PDF I get this:\n\n \\newcommand\n{\\lstdef}[3]{%\n,colored-code\\$\nThis may cause errors in the sequel.\n\n\nAnd a message saying \"Package Listings Error: style colored-code undefined\".\n\nHow can I fix this?\n\nThis is what listings.cfg has:\n\n\\lstdefinestyle{colored-code}{\nbackgroundcolor=\\color{yellow!10},%\nbasicstyle=\\footnotesize\\ttfamily,%\nidentifierstyle=\\color{black},%\nkeywordstyle=\\color{blue},%\nstringstyle=\\color{teal},%\n}\n\n-\n\n## closed as too localized by Werner, Seamus, percusse, Marco Daniel, Claudio FiandrinoAug 18 '12 at 13:11\n\nThis question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.\n\nIs it possible to edit your post and include listings.cfg? Or at least just the part where it defines colored-code? \u2013\u00a0 Werner Jan 4 '12 at 18:39\nHave done so now \u2013\u00a0 adrianmcmenamin Jan 4 '12 at 18:49\nIs your listings.cfg any different from what is posted in @someonr's \"answer\"? \u2013\u00a0 Werner Jan 4 '12 at 18:56\nSince you've solved your problem which stemmed from two different listings.cfg, I think this may be too localized. \u2013\u00a0 Werner Jan 4 '12 at 19:08\n\nI just tried:\n\n\\documentclass[a4paper, 11pt]{article}\n\n\\usepackage[style=colored-code]{listings-ext}\n\n\\begin{document}\ntest\n\\end{document}\n\n\nwith the example listings.cfg:\n\n\\ProvidesFile{listings.cfg}%\n[2009\/08\/23 v1.0 listings configuration of listings-ext]\n\n\\RequirePackage{xcolor}\n\n\\def\\lstlanguagefiles{lstlang1.sty,lstlang2.sty,lstlang3.sty}\n\\lstset{defaultdialect=[ANSI]C,\ndefaultdialect=[ISO]C++,\ndefaultdialect=[95]Fortran,\ndefaultdialect=Java,\ndefaultdialect=[LaTeX]TeX,\nframe=tlb,\nresetmargins=false,\n}\n\\lstdefinestyle{colored-code}{\nbackgroundcolor=\\color{yellow!10},%\nbasicstyle=\\footnotesize\\ttfamily,%\nidentifierstyle=\\color{black},%\nkeywordstyle=\\color{blue},%\nstringstyle=\\color{teal},%\n}\n\\lstdefinestyle{bw-code}{\nbasicstyle=\\small\\fontfamily{lmtt}\\fontseries{m}\\fontshape{n}\\selectfont,\n% instead of lmtt one should use ul9 (luximono) for boldface characters\nkeywordstyle=\\small\\fontfamily{lmtt}\\fontseries{b}\\fontshape{n}\\selectfont,\nstringstyle\n\n=\\small\\fontfamily{lmtt}\\fontseries{m}\\fontshape{it}\\selectfont,\n}\n\n\nand it is all compiling without errors. I think your listings.cfg is wrong.\n\n-\nYeah this is no real answer, but it would be too long for a comment, and should be able to help the question author to find the error. \u2013\u00a0 someonr Jan 4 '12 at 18:45\nI think I have the answer - seems to be a packaging error with Ubuntu: two conflicting listings.cfg files are supplied - one is an unadorned one, which doesn't have the colored-code style and one is supplied by listings-ext which does. I edited the unadorned one to add in the additional styles and it works now. I will try to find out where the conflict is in Ubuntu (if that is where it comes from) and post a bug on their bugzilla. Thanks for the help and time though - it's when you suggested I post the contents of the listings.cfg that I noticed their appeared to be two of them. \u2013\u00a0 adrianmcmenamin Jan 4 '12 at 18:58","date":"2015-04-19 04:52:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8506672978401184, \"perplexity\": 2274.61708697083}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-18\/segments\/1429246637445.19\/warc\/CC-MAIN-20150417045717-00101-ip-10-235-10-82.ec2.internal.warc.gz\"}"}
| null | null |
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{
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| 4,656
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Undergrad Program
Grad Program
Why CU Geography?
Undergraduate Certificates
Arctic Studies Certificate
The Department of Geography offers an interdisciplinary undergraduate certificate in arctic studies, in collaboration with the Program in Nordic Studies (SCAN), the Program in Russian Studies (RUSS), the International Affairs Program (IAFS), the Department of Environmental Studies (ENVS), the Department of Anthropology (ANTH), the Department of Ethnic Studies (ETHN) and the research entities of the Cooperative Institute for Research in Environmental Sciences (CIRES), the National Snow and Ice Data Center (NSIDC) and the Institute of Arctic and Alpine Research (INSTAAR).
Certificate Intent
This certificate prepares students to address pressing environmental, political and cultural issues in the far north. A laboratory for studying the effects of global climate change, the arctic region spans three continents, with territories in Canada, Greenland (Denmark), Finland, Iceland, Norway, Sweden, Russia and the United States. Its population exhibits considerable ethnic, linguistic, and sociopolitical diversity, and contains numerous indigenous peoples. Issues as critical as nationalism, territorial rights and law, security, economic development and resource technology place the arctic at the center of global, regional and national interests. Further, the region's natural and social characteristics have inspired influential and enduring expressive culture—produced by locals and outsiders—from antiquity to the present.
These features make study of the arctic ideal for students pursuing careers in international politics and diplomacy, indigenous rights, environmental science and climate change, humanistic scholarship or creative work. Students pursuing the Arctic Studies certificate may be eligible for a paid internship at the CIRES National Snow and Ice Data Center. Contact Mistia Zuckerman if interested.
The primary contact for the Arctic Studies certificate is Distinguished Professor Mark Serreze.
For more information, see Program Requirements and Contact Info.
GIS Certificate
Geographic Information Scientists (GIScientists) have an ongoing concern with the collection, analysis and display of high precision spatial data. The Department of Geography (GEOG) and the Department of Computer Science (CSCI) are offering a joint undergraduate certificate in GIS and Computational Science. The program draws upon faculty expertise in both departments, providing interdisciplinary training in spatial data analysis and computation, both of which characterize GIS in most career paths. Computational geospatial skills are in high demand on campus and in local, regional and national job markets such as government employment, industry or consulting careers, and graduate school. The certificate is available for all majors and may be of particular interest for students in other earth science disciplines and social science disciplines. Non-matriculated students may enroll at CU through Continuing Education and once admitted, may apply for the certificate.
The undergraduate certificate in GIS and Computational Science will teach students to identify, analyze and understand spatial patterns, with an emphasis on computation and analytical problem solving. Required coursework in GIS, basic statistics, and basic programming, coupled with advanced electives in GIScience will give students the computational knowledge and skills to tackle society's important and pressing environmental problems. The interdisciplinary nature of the certificate introduces students to the special characteristics (scale dependence, spatial autocorrelation) that complicate spatial data analysis, and offers additional programming skills relative to the basic GIS concentration. The computational emphasis will also increase students' competitive edge in the job market and when applying to graduate school.
The primary contact for the GIS Certificate is Sarah Kelly.
For more information, see: Program Requirements and Contact Info
Hydrology Certificate
Geography provides a Certificate Program in Hydrology and Water Resources, designed for students who are either Geography majors or minors and who wish to specialize in hydrology- related themes. Course requirements are designed to provide students wishing to pursue the field of hydrology and other water-related resources beyond the undergraduate degree (graduate school, government employment, consulting jobs) with a broad-based background in this discipline. Upon completion of the required courses and graduation from the Geography Department, students receive a signed certificate of completion.
Certificate Intent:
The primary goal is to provide students with a well-rounded and broad-based background in hydrology. Secondly, we will provide advising for students interested in pursuing hydrology beyond the undergraduate degree. Upon completion of the required courses and graduation from the Geography department, students will receive a certificate signed by Professors Peter Blanken and Katherine Lininger.
The hydrology certificate program is for students who have a major or minor in Geography.
Required Classes for a Hydrology Certificate in Geography
Environmental Systems: Landscapes and Water: GEOG1011
Environmental Systems: Climate and Vegetation: GEOG 1001
Introduction to Hydrology GEOG3511
Statistics: including but not limited to: GEOG3023, APPM4570, BCOR1020, ECON3818, PSYC3101, SOCY2061, SOCY4061
Human dimensions of water: GEOG4501, GEOG4110 World Water Today & Tomorrow
Climate and/or Meteorology: One upper division course GEOG3301, GEOG3601, GEOG4211, GEOG4231, GEOG4271, GEOG4331, ATOC3300, ATOC3600, ENVS3600
Hydrogeology (Groundwater) GEOL3030 or similar course
TWO senior-level hydrology classes from the following list:
Geomorphology GEOG4241, GEOL4291
Fluvial Geomorphology GEOG4251
Snow Hydrology GEOG4321
Watershed Biogeochemistry GEOG4311
World Water Today & Tomorrow GEOG4110
Mountain Hydrology Seminar
Biometeorology GEOG4201
Glaciers and Permafrost GEOG4120, GEOG4261
Wetlands (special topics GEOG course)
Any course in Limnology, Stream Ecology, Aquatic Ecology
Contact Peter Blanken, or Katherine Lininger if you wish to discuss specific courses not listed here that may be acceptable substitutes for the classes listed above.
Course Recommendation
There is no course sequencing. Courses can be taken in any order. However, we strongly suggest that Introduction to Hydrology and Statistics be taken before the senior-level courses.
Lower Division Science Courses. Students who are trying to position themselves for a career in hydrology or related disciplines are encouraged to take lower division courses in mathematics, physics, and chemistry. However, these courses are not required either as prerequistes for the courses or for the hydrology certificate.
Geography Major & Minor
Environment-Society Track
GIS Track
Human Geography Track
Physical Geography Track
General Geography Major
General Geography Major (before Fall 2016)
Undergraduate Geography Major Requirements
What can I do with a Geography degree?
Full Listing of Courses
Featured Course Descriptions
How to Search for Classes
Academic Expectations
Tutoring and Academic Resources
Spring 2022 Course Announcements
Spring 2022 Course Schedule
Lost? Guggenheim Building Layout
GUGG 110, 260 UCB
Boulder, CO 80309-0260
cugeography@colorado.edu
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By admin on 8 December, 2018 in Art, Fun, Kate and Stephen with 0 Comments
By Melissa Tubbs
Private Lives, the last play of the Cloverdale Playhouse's 2018 season, is a fascinating experiment. The play suggests a hypothesis about what might happen if you were trapped an audience in a room with four loathsome screaming monsters for two hours.
The four monsters are all themselves trapped in webs of relationships with one another, but the audience is contained in proximity. As the lives of the characters unravel, the members of the audience may begin to wonder about their own lives. Where did things all go so wrong? Or at least, that's one thing the audience might wonder if they weren't so busy laughing at the banter that cuts across the interactions of these (mostly) drunk and (entirely) insufferable characters.
"Private Lives" is about the shallow and vapid lives of four exceptionally wealthy people in 1930s Britain. It's The Great Gatsby, if Nick and Daisy and Gatsby were all replaced by clones of Tom Buchanan — racist and shallow, vain and impulsive, oblivious to world events and the suffering of anyone around them. They don't even pay attention to the maid, as she suffers from an illness.
It's possible that the play exists as a social technology to make audiences resent rich people, in which case it is a timely and potentially revolutionary piece of art. The performance opens with two sets of couples, each admiring a distant yacht, bobbing in the water from the balcony of their luxury hotel rooms. This object lust leads to the real thing, and a range of other disturbing passions, including domestic violence, and several kisses that rub uncomfortably up against modern ideas of affirmative consent.
All four characters are entirely self-centered and horrible. As such, it's hard to commend any individual performer, but it's worth noting that the sum total of this ensemble's performance might be enough to cause someone to forswear brandy, if not love itself. As always, the Playhouse sets are really nice, and it was cool to see the total change between acts. Some folks worked really hard on this, and it shows.
But it was the subject matter, more than the design, that had us talking after the show. Five years before Noel Coward wrote Private Lives, F. Scott Fitzgerald published The Great Gatsby. That staple of high school English classrooms skewers Jazz Age narcissism and wealth inequality by contrasting the kind, literary nobility of Nick Caraway with the debauchery of Gatsby and his wealthy cronies. The text includes dark and mysterious portents about how Gatsby acquired his wealth, and whether his obsession over Daisy is a moral failing. Coward's work is much shorter than Fitzgerald's novel, and maybe that's one reason that it lacks Gatsby's nuance.
In any case, Private Lives has no such complexity. It's two couples, simultaneously on honeymoons, each self-pitying and tiresome. And once you get tired, strap in, because these are pretty much the only characters you meet for the entire play. And they pace around. And they scream at each other. And they laugh and cry and make up and scream some more.
There are jokes. Many of these, including the repartee that wraps around them, seem to be foundational character sketches for modern antagonistic relationships. If you've ever seen a Tracy and Hepburn movie, here is some of your key source material. But these relationships, boozy and impulsive, may be a little raw for the mid-century heyday of the "screwball comedy."
It's interesting that this play was included in the Playhouse's 2018 season of "Game Changers," which we applauded greatly when it was announced. We were excited about some edgy material, and by and large this season has fulfilled our expectations. It's really challenged us to think about the purposes and possibility of theater. Rosencrantz and Guildenstern are Dead was one of the best performances we'd seen anywhere, ever. And we love that the Playhouse takes risks and tries to bring us challenging material.
This final offering was just a little harder than most, and maybe that's the point of it. In a post here last week, Playhouse Artistic Director Sarah Thornton said that Coward's work provided a kind of escapism similar to what reality TV offers today. But we're not sure that's true. Reality TV, like its older cousin, professional wrestling, has good guys and bad guys. Sure, they may swap around regularly, but there are still generally people to root for and against. Private Lives offers no such comfort or respite. Instead, you're left sitting uncomfortably in your seat trying to decide how to feel when no sides merit sympathy.
And maybe, close to a hundred years after this play was written, there's something very modern about this unsparing look at the beastly human condition. You don't have to have a particular partisan bent to recognize that every day we're deluged by relentless waves of what passes for information designed to wring out our most primal emotions. We're supposed to take sides; we're supposed to have someone to root for. But Private Lives denies us even that. Maybe this is why so many of the laugh lines land. Uncertainty finds provisional grounding in humor, while that lasts, at the same time that we find a way to interact with such uncomfortable material.
Private Lives is a play for the Trump era. It relies on the tensile strength that binds empty banter to lives without responsibility – again and again, until you're exhausted. The characters here disdain old-fashioned ideas like kindness and virtue, which makes modern pundits lamenting the lack of civility seem a little bit even more nostalgic and obsolete. Rich people tangle up with each other, indulge impulse and base desire, and prattle on while the hired help sneezes in the background. It's brutal, but it's real.
Kate and Stephen are Midtown residents with two cats, a dog, ten fish, a garden, an old house and a sense of adventure. They write about life in Midtown here and about life in Montgomery at their blog Lost in Montgomery.
Tags: Cloverdale Playhouse, featured, Kate and Stephen, Noel Coward, Private Lives
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{
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| 9,332
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Воробйовський () — селище у Новосибірському районі Новосибірської області Російської Федерації.
Входить до складу муніципального утворення Кудряшовська сільрада. Населення становить 19 осіб (2010).
Історія
Згідно із законом від 2 червня 2004 року органом місцевого самоврядування є Кудряшовська сільрада. У селищі за даними на 2007 рік відсутня соціальна інфраструктура.
Населення
Примітки
Населені пункти Новосибірського району
Селища Новосибірської області
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{
"redpajama_set_name": "RedPajamaWikipedia"
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| 1,056
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Q: InputText not sending new values I have a simple inputText in which I set default value by getting it from an object. After I edit inputTexts value, I push a button, which calls save method in bean. I would expect that inputText would understand that I changed its value and would change objects value as I edit it. As it turns out, I get old value, not the new (edited one) in the bean.
Maybe you have any ideas what could be the main cause of this issue?
Here is my inputText:
<h:inputText value="#{associationBean.counterTypeView.name}"
id="ctpName" maxlength="100"
validatorMessage="#{msg['classifier.nameRequire']}">
<f:validateRequired />
<rich:validator />
</h:inputText>
A: Insert <a4j:ajax execute="@this"/> inside your inputText control like this
<h:inputText value="#{associationBean.counterTypeView.name}"
id="ctpName"
maxlength="100"
validatorMessage="#{msg['classifier.nameRequire']}">
<f:validateRequired />
<rich:validator />
<a4j:ajax execute="@this" />
</h:inputText>
A: you can use JSF ajax inside the h:inputText tag like this
<h:inputText value="#{associationBean.counterTypeView.name}"
id="ctpName"
maxlength="100"
validatorMessage="#{msg['classifier.nameRequire']}">
<f:validateRequired />
<rich:validator />
<f:ajax event="blur"/>
</h:inputText>
This is, on blur event of Input Text the Ajax will be called and your new data will be saved in the specified bean
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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| 8,191
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The complexity of a simple app has made it possible for any musician to create a song right in the comfort of their own home that sounds as amazing as something recorded in a full-fledged studio.
There are several multi track recorders in the app store, but Meteor Multitrack by 4 Pockets Audio is my favorite. This multitrack recorder has effects, midi recording capabilities and more, offering in-app purchases to help you build your studio. They've even added specialty apps such as a vocal doubler just because I requested it. If you use Meteor and need an effect added, just email me. I'll contact them on your behalf. Of course, for us to record music, we also require other apps such as Drums XD, iFretless Bass, Amplitube and Sampletank, but Meteor is in the top five.
I LOVE vocal effects and IK Multimedia's VocaLive has a special place in my heart. This app features stomp box style pedals you can mix and match to create your own vocal sound with the ability to save all your combinations. The effects are fully programmable with as many features as a stand alone hardware vocal processor.
It is much more in depth than their EZ Voice App (Android), which is still a cool app for beginners.
Finally, TC Helicon released a version of their live effects from processors like VoiceLive and the VoiceTone Singles! I was super excited to get this app. It is a simple preset app to meet your needs. Not being a "looping" musicians, VoiceRack Effects serves me better than an app like VoiceJam Studio. And I can use it live in place of toting around my VoiceLive processor. This is THE perfect app for singers who have not ventured into purchasing a hardware vocal processor but would like to get their feet wet and learn about vocal effects. If you would like to "tweak" some effects, you can also purchase their VoiceJam app (not VoiceJam Studio) which has in-app purchased for their VoiceTone C1 and R1 pedals (pitch correction and reverb). Wow, digital versions of their amazing pedals at a fraction of the price. I'm sold!
I was a huge fan of 80s funk/rap bands like Newcleus and Midnight Star so the Voice Synth app by Qneo meets my needs for the out of this world vocal effects sounds.
Now, I'm not typically the person who will use extreme vocal effects for tones like grit, since I'm a grit machine, but for those robotic sounds, Voice Synth is the app!
Although not a "music" app, Movie Pro is actually one of my tops apps and every singer needs it. It is perfect to record your performances. I've actually used this app to record hundreds of vocal training video and I use it for Scott and I to record vocal performances.
Use this app to film your rehearsals and gigs to post to YouTube and share your musical experiences, as well as to record your vocal practice for self-critiquing your progress.
So, welcome to the age of app engineering! Technology has changed so much in a matter of decade that you can now how to power of a multitrack recorder on your iPad, even more powerful than any home recording DAW on any PC back in 2005.
How do I know? My songwriting partner, Scott Stith and I record our songs on iPads using a variety of apps for multi-track recording, vocal and music effects, guitar cabinets, drums, bass, piano and synths, and more.
Singer's Trainer and Multitool – it's a "digital vocal coach" for vocal coaches and students alike with a variety of vocal training tools such as a tuner, metronome, stop watch, pitch wheel, vocal scale generator and more. There's even a "glass shattering" game which improves intonation, for all of his MythBusters fans. Jaime said that his app has truly changed how he teaches voice (he uses it for all his lessons) and keeps him on his toes for his own vocal routines. If you need a vocal coach in your pocket, download Tuned XD to your iPhone!
|
{
"redpajama_set_name": "RedPajamaC4"
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| 7,068
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Peter Martin: Why is the Tax Office sitting on your refund cheque?
Why is the Tax Office sitting on your refund cheque?
Waiting for a tax refund that just wont come? It could be because you are known to the Child Support Agency.
The Tax office has revealed that since Australia Day it's been sitting on refund cheques for thousands of parents known to the Child Support Agency because of a problem its computers have had communicating with the Agency's.
Although it has been able to pay out the money but hasn't in case the CSA wanted it to withhold some.
"Normally before issuing a refund to someone known to CSA we check to see if the CSA needs us to deduct money," said Tax Office Assistant Commissioner Jenny Reid. "We might owe someone $100 but the CSA might want us to take out $20 for them to hand to the other parent."
"Since we turned on our new computer over the Australia Day weekend it hasn't been easy for the two to systems to talk to each other... So we have been withholding all the refund cheques for taxpayers of interest to the CSA."
The good news is the Tax Office believes the technical issues have been fixed. Those refunds should start flowing on Tuesday.
But a much greater number of returns, around one million, have been caught up in backlog that began at Christmas when the Tax Office turned off its old computers, some several decades old, in order to transfer data to the new system which was turned on on Australia Day.
In an update posted on the ATO website late Thursday Second Commissioner David Butler explains that rather than shrinking the backlog grew because of a second problem involving printers.
"On March 9 we discovered a problem with the data in some notices of assessment which had been printed but not sent to taxpayers," he says. "Unfortunately this meant we could not send anything for printing and posting until we fixed the problem. It took us longer than expected and we recommenced sending notices of assessments to be printed and posted on Monday 22 March."
The backlog of one million has shrunk to 366,000, about 150,000 of which would normally be running through the system at any one time.
"We know some people have experienced delays and frustration," the update says.
"Unfortunately, the size of the systems we deal with means they are incredibly complex. Also, given the importance of the tax and superannuation systems to Australia, we need to ensure the reliability of our processes. We appreciate the patience and support people have shown us."
Mr Butler has promised to pay interest interest on overdue refunds, saying that is normal procedure.
"Interest will be paid on all late refunds after the 30th day. People do not need to ask for it, we will calculate it and pay it with the delayed refund," Mr Butler said.
|
{
"redpajama_set_name": "RedPajamaC4"
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| 8,536
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2008 Nissan Frontier Fuse Diagram - nissan frontier 2008 main fuse box block circuit breaker diagram nissan frontier 2001 fuse box block circuit breaker nissan frontier 2006 fuse box block circuit breaker diagram nissan gtr 2009 interior fuse box block circuit breaker diagram 2000 nissan frontier tail light wiring diagram this is images about 2000 nissan frontier tail light wiring diagram posted by peggy g brown in 2000 category on jan 09 2019 you can also find other images like wiring diagram parts diagram replacement parts electrical diagram repair manuals engine diagram engine scheme wiring harness fuse box vacuum diagram timing belt timing chain nissan 200sx 1997 interior fuse box block circuit breaker diagram nissan skyline r 33 2003 engine fuse box block circuit breaker diagram nissan quest 2008 main engine fuse box block circuit breaker diagram nissan frontier 2008 main fuse box block circuit breaker diagram reply greg.
lane february 22 2008 at 7 03 pm hello first off thank you for this free service i have a 1997 nissan king cab the last year befor they started calling then frontiers you have 98 and up of course my luck just need the color code wiring diagram i printed off the 98 frontier version going to check if maybe they kept them the same thanks for your attempt to find it for me the nissan frontier is a mid size truck models that have been made since 2010 have a focus on safety features read more nissan reviews to learn about other models this pany is not yet span class news dt aug 25 2018 span nbsp 0183 32 you are a nissan tech so perhaps you can answer this the car is a 2006 sentra 1 8s issue large cooling fan us passenger s side fan also listed by you as left side left side of what nissan alternator problems fix nissan alternator problems shops report that nissan alternator problems can sometimes.
be traced to an intermittent in the plug that goes into the voltage regulator in nissan power window problems fix nissan power window problems nissan has issued a service bulletin to address nissan power window problems where the power windows may not work properly after the vehicle s battery has been disconnected or a window fuse blows span class news dt may 30 2015 span nbsp 0183 32 if you replaced the fuses with good ones the only other thing i would think might be the fusible link but that is more of a fuse to keep the voltage regulator from frying the battery 06 dodge ram 1500 wiring diagram this is images about 06 dodge ram 1500 wiring diagram posted by cassandra w thomas in 06 category on jan 11 2019 you can also find other images like wiring diagram parts diagram replacement parts electrical diagram repair manuals engine diagram engine scheme wiring harness fuse box vacuum.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,060
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Mozambican revolution, no. 11 (1964 Oct.)
their attainment of Independence, Justice and Dignity.
The victory of the Mozambican people, from now on can be foreseen. They are defending a just cause against Portuguese colonialism
and fascism, and in their struggle they have the support of all the
democratic forces in the world."
(From "Le Peuple" - Algiers,
10th September 1964)
" Declaration of Djoudi, ambassador of the Democratic and Popular Republic of Algeria in the U.R. of Tanganyika and Zanzibar
" At the announcement of the beginning of the armed struggle in
Mozambique, brother Djoudi, Ambassador of the Democratic and Popular
Republic of Algeria in U.R. of Tanganyika and Zanzibar, and Responsible for military action in the Committee of Coordination for the Liberation of Africa (Committee of Nine) which is an organization set
up by the OAU to aid the anti-colonialist movements - made the following statement to " REVOLUTION AFRICAINE M:
" The announcement of the beginning of the armed revolution in
Mozambique brings great joy and satisfaction to us; however, it was
not a surprise to the Committee. In fact, since its creatin, the
Committee has always given moral and material support to the Mozambique Liberation Front UH-USLIMO). On the other hand, it is not a secret
that our Mozambican brothers have been trained in the techniques of
the revolutionary struggle by the government of the Democratic and
Popular Republic of Algeria, for a long time.
Faced with the stubborness of Portugal and the refusal of the
Portuguese colonialists to recognize■the sacred right of Liberty
and Dignity of the Mozambican people, faced with Salazarfs refusal
to find a peaceful solution by replying the people's peaceful demands
with massacres and exactions, the use of force was inevitable.
The Committee of Nino is convinced that the result cannot be
anything else but the victory of the Mozambican people over the
retrograde Portuguese colonialism. "
( From "REVOLUTION AFRICAINE",
17-10.1964)
Title Mozambican revolution, no. 11 (1964 Oct.)
Description Contents: Editorial (p. 1); Proclamation to the Mozambican people (p. 2); Communique (p. 4); Algeria and the Mozambican Revolution (p. 6).
Full text their attainment of Independence, Justice and Dignity. The victory of the Mozambican people, from now on can be foreseen. They are defending a just cause against Portuguese colonialism and fascism, and in their struggle they have the support of all the democratic forces in the world." (From "Le Peuple" - Algiers, 10th September 1964) " Declaration of Djoudi, ambassador of the Democratic and Popular Republic of Algeria in the U.R. of Tanganyika and Zanzibar " At the announcement of the beginning of the armed struggle in Mozambique, brother Djoudi, Ambassador of the Democratic and Popular Republic of Algeria in U.R. of Tanganyika and Zanzibar, and Responsible for military action in the Committee of Coordination for the Liberation of Africa (Committee of Nine) which is an organization set up by the OAU to aid the anti-colonialist movements - made the following statement to " REVOLUTION AFRICAINE M: " The announcement of the beginning of the armed revolution in Mozambique brings great joy and satisfaction to us; however, it was not a surprise to the Committee. In fact, since its creatin, the Committee has always given moral and material support to the Mozambique Liberation Front UH-USLIMO). On the other hand, it is not a secret that our Mozambican brothers have been trained in the techniques of the revolutionary struggle by the government of the Democratic and Popular Republic of Algeria, for a long time. Faced with the stubborness of Portugal and the refusal of the Portuguese colonialists to recognize■the sacred right of Liberty and Dignity of the Mozambican people, faced with Salazarfs refusal to find a peaceful solution by replying the people's peaceful demands with massacres and exactions, the use of force was inevitable. The Committee of Nino is convinced that the result cannot be anything else but the victory of the Mozambican people over the retrograde Portuguese colonialism. " ( From "REVOLUTION AFRICAINE", 17-10.1964)
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 360
|
Q: if $d'(x_1, x_2)=\min(1, d(x_1, x_2))$, is $d'$ a metric on $X$? I'm given the problem:
If $d'(x_1, x_2)=\min(1, d(x_1, x_2))$, is $d'$ a metric on $X$?
I'm stuck in the triangular inequality. Since we have to show that
$$ d'(x_1, x_3) \leq d'(x_1, x_2) + d'(x_2, x_3) $$
there is a case in which I'm confused:
*
*If $\min(1, d(x_1, x_3))$ is $1$, and $\min(1, d(x_1, x_2))$ and $\min(1, d(x_2, x_3))$ are $d(x_1, x_2)$ and $d(x_2, x_3)$ respectively. What if the values of $d(x_1, x_2)$ and $d(x_2, x_3)$ are less than $0.5$ and there sum isn't $1$ or greater than $1$?
I don't know if I am thinking the right way or there is some mistake in it. Please help me with this problem!
A: You're almost done.
Just remember that
$1=d'(x_1,x_3) \leq d(x_1,x_3) \leq d(x_1,x_2) + d(x_2,x_3)$.
It's very important that you make sure that you have used every hypothesis in a exercice. Otherwise, something is likely missing in your proof or you've proved a more general statement which is unlikely.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,213
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