content stringlengths 86 994k | meta stringlengths 288 619 |
|---|---|
Can I do this with glTexGen ??? [Archive] - OpenGL Discussion and Help Forums
08-11-2005, 12:50 AM
Hi everybody,
I need to map a texture to a flat surface. The mapping of Texturespace to Objectspace is given by a mathematic formula (follows).
To get the coordinates in the Objectspace to which a point on the texture is mapped is calculated by the following formula:
X= ((1 + A*(sē+tē) + B*(sē+tē)ē ) *s + C ) * D
Y= ((1 + A*(sē+tē) + B*(sē+tē)ē ) *t + E ) * F
X,Y --> coordinates in ObjectSpace
s,t --> coordinates on texture
A,B,C,D,E,F --> constants (given at the beginning, they do not change)
No, donīt get all like :eek: or :confused: , this is actually a pretty easy calculation.
So, if you have a point on the texture, you can easily calculate the coordinates to which it will be mapped on the object.
I havenīt found a way to do it the other way round (coord. on object given, look up point on texture). Iīm not sure if itīs possible at all.
Iīve looked at glTexGen, but it only allows 4 parameters for the calculation. Or is there any other way ?
Thanks in advance. | {"url":"http://www.opengl.org/discussion_boards/archive/index.php/t-142583.html","timestamp":"2014-04-20T06:03:55Z","content_type":null,"content_length":"4884","record_id":"<urn:uuid:b5b7977d-2500-4295-9a64-68fe46a874b8>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00146-ip-10-147-4-33.ec2.internal.warc.gz"} |
Ballistic Sagnac
The Sagnac effect exhibited by two beams of light propagating in opposite directions around a rotating configuration of mirrors was described in a previous article. That analysis was based on the
fact that a pulse of light propagates at the speed c with respect to any standard system of inertial coordinates, independent of the state of motion of the source. One of Sagnac’s motivations for
examining this effect in 1913 was to test whether light really does possess this property – which he associated with wavelike propagation through a medium – or whether light propagates like Newtonian
ballistic particles at a characteristic speed relative to the source. He reasoned that, under the ballistic assumption, there would be no phase shift, so the observed phase shift was presented as a
disproof of the Newtonian ballistic conception of light.
By the way, when referring to the “Newtonian ballistic conception of light”, the word “Newtonian” is intended as a qualifier on the word “ballistic”, not on the phrase “conception of light”. It would
be unfair and inaccurate to suggest that Newton regarded the principles of his mechanical ballistics to be a satisfactory basis for a conception of light. He often seemed to lean toward a corpuscular
theory, but he recognized the difficulties of trying to account for all the phenomena of light if we regard the corpuscles as ordinary matter.
The assertion that Newtonian ballistic particles (in the context of Galilean spacetime) would exhibit no Sagnac effect is trivially true for a perfectly circular path, which might be conceived as the
limit of infinitely many mirrors placed infinitesimally close together around the circumference of a rotating disk. In such a device, the emitter, receiver, and all the mirrors are moving at the
speed v tangentially to the hub, and hence the particles are constantly moving (relative to the hub frame) at the speed c+v in the forward direction and c-v in the rearward direction. Also, the
receiver is moving with the speed v away from each forward-going particle and toward each rearward-going particle, so the “closing speeds” are (c+v)-c and (c-v)+c respectively, both of which equal c.
Each particle begins with the same separation from the receiver, and has the same closing speed, so the two particles will arrive simultaneously.
However, we can also consider a Sagnac device with a non-circular path. For example, suppose we have just three mirrors on a rotating platform, with perfectly elastic particles bouncing off these
surfaces in both directions, as illustrated in the figure below.
Initially the mirrors are at A[0], B[0], and C[0], and they are rotating about the center of the circle in the counter-clockwise direction. We can imagine two perfectly elastic particles emitted from
A[0], one toward B and one toward C, at speeds such that they arrive after an amount of time Dt simultaneously at positions B[1] and C[1] respectively. They are reflected and proceed (in the same
amount of time Dt) to the mirrors at the positions C[2] and B[2] respectively, where they are reflected again, and then both arrive simultaneously back at mirror A at the position A3. The paths are
reversible, so the angles of incidence and reflection are equal. Also, since no work is done on the particles, the energy and hence the speeds of the particles remain constant. Thus with this
arrangement there would be no Sagnac effect. However, the particles are obviously traversing different distances (with respect to the hub frame inertial coordinates), so in order for their arrivals
to be simultaneous they must have different speeds (again, with respect to the hub frame). The question, then, is whether at the points of reflection the speeds of the particles are equal to each
other relative to the rest frame of the local mirror.
To determine this, consider the general polygonal case where consecutive mirrors are separated by an angle of f, and are rotating around the circumference of a disk of radius R with angular speed w
and tangential speed v = wR about the origin of Cartesian coordinates as shown below.
The coordinates of the leading and trailing mirrors are
We require that the speed of each particle must be a fixed number, which we will denote by c (not necessarily signifying the speed of light), relative to the rest frame of the emitter, which we take
to be the mirror at x[0],y[0] in this case. To simplify the calculations, we first transform the coordinates of the leading and trailing mirrors to a system of inertial coordinates with origin at x
[0],y[0] and moving in the positive y direction at the speed v, so that it represents the rest frame of the emitter. The required transformation is
Therefore the transformed coordinates of the leading and trailing mirrors are
The particles are emitted from the origin of the x’,y’ coordinates at time t = 0, and one moves at the speed c to the point x[1]’,y[1]’ at time t = t[1], whereas the other moves at speed c to the
point x[2]’,y[2]’ at time t = t[2]. Thus we have
Inserting the previous expressions for x and y, we get
Expanding and simplifying, these can be written as
We could solve these equations for t[1] and t[2], and then subtract one from the other to give the difference between the travel times from one mirror to the next, but there is no simple closed-form
solution of these equations. As an alternative, suppose the angle wt through which the mirrors rotate during the transit of the particles from one to the next is quite small (i.e., the particles are
moving much faster than the mirrors). In that case we can expand the right hand sides of these equations to give
The first three terms on the right hand sides of these equations are identical, so to this level of approximation the values of t[1] and t[2] are the same, and we can solve the equations up to this
order to give
However, the equations differ in the third order (and all higher odd orders), so the values of t[1] and t[2] are no exactly equal (unless f goes to 0 or p). This implies that, for general polygonal
paths, there actually is a Sagnac effect for Newtonian ballistic particles, but it is of a much smaller order than the usual Sagnac effect for light. To determine the difference in transit times for
the particles in the two directions, we can subtract one of the previous two expansions from the other, to give
Re-arranging terms, and letting t[1 ]+ t[2] be approximated by 2t, and t[1]^3 + t[2]^3 by 2t^3, where “t” is an estimate of both t[1] and t[2], we get
Substituting the approximation for (wt)^2 from equation (2), this becomes
For a complete regular polygonal loop of n mirrors, we set f = 2p/n and then multiply the entire expression by n to give the total difference in travel times for the two particles:
This shows that the lowest order “Sagnac effect” for ballistic particles moving at the speed c in opposite direction around a regular polygonal arrangement of mirrors moving with speed v is fourth
order in v/c. If c is the speed of light and v is many orders of magnitude smaller (as in any realistic Sagnac device), this effect is so small as to be undetectable. On the other hand, since c need
not denote the speed of light, we can impart a much smaller speed to the ballistic particles, so we could achieve any ratio v/c that we like. Of course, the convergence of our series expansion of (1)
depends on the speeds being such that the mirrors move only a small angular distance in the time required for a particle to move from one mirror to the next. Also, our approximation assumes t[1]
differs from t[2] by only a very small amount.
For any fixed values of v and c such that v/c is much smaller than 1, the squared quantity in the numerator is nearly equal to 1, and the overall effect is proportional to
To determine the angle that gives the maximum effect, we differentiate this quantity and set the result to zero, which gives
Multiplying through by 1 + cos(f), and noting that 1 – cos(f)^2 = sin(f)^2, we can then divide through by sin(f)^2 to give 1 + 2cos(f) = 0, and hence cos(f) = -1/2, from which it follows that f = 2p/
3. Therefore, as we would expect, the maximum effect occurs with three mirrors separated by 2p/3.
As an aside, attempts have sometimes been made to reconcile a Newtonian ballistic conception of light with the observed Sagnac effect. (Of course, to entertain any such conception of light, one must
disregard all the experimental and observational evidence that the speed of light in terms of any standard inertial coordinate system is independent of the speed of the source.) One approach is to
argue that reflections of light should be treated differently from emissions of light. Specifically, we might hypothesize that a particle of light always moves at the fixed speed c relative to the
inertial rest frame coordinates of the original source at the moment of emission, even if the particle is reflected off one or more surfaces during its travel. Thus the hypothesis asserts that the
speed of light is independent of the speed of any object that it encounters in a reflective interaction. Even aside from the ad hoc and incoherent nature of this hypothesis, it is obviously not
consistent with Newtonian ballistic principles. It is actually an ether theory (which does indeed yield the observed Sagnac effect), except that instead of positing a single absolute ether, it
assigns a separate ether for each emission event. Of course, if one adopted the electromagnetic world view, it could be argued that all electromagnetic energy is simply participating in reflective
and scattering interactions, even when confined within material object, so we could never know what speed to expect, since we can’t know the state of motion of its original primal source, which
supposedly governs its motion thereafter. One might argue that all light ultimately can be traced back to a single primal emission event, which would imply a single fixed ether theory. Ironically,
the assumption that the speed of light is unaffected by scattering interactions is mutually exclusive with the “extinction” argument that was sometimes advanced by proponents of ballistic theories to
discount astronomical observations (such as de Sitter’s) that show the speed of light is independent of the speed of the source.
Another odd variation on the Newtonian ballistic concept of light is based on the premises that (1) our empirical observations of light speed are all based on interference effects rather than direct
timing of propagation, and (2) all interference phenomena have been fundamentally misinterpreted. Needless to say, the first premise (1) is false, because we have both astronomical and terrestrial
observations of the actual arrival times for light emitted from objects moving at different speeds. Nevertheless, dedicated proponents of the ballistic concept are undaunted, and proceed to argue as
if (1) was true, considering only interference-based observations. They argue, for example, that the time for two particles of light to move around a Sagnac device in opposite directions may be
equal, and yet may still yield interference fringes in the receiver. (This is obviously inconsistent with very fundamental attributes of propagating electromagnetic waves, both in classical theory
and in quantum electrodynamics, but, again, the proponents are undaunted.) The idea is that each particle of light possesses its own “phase”, which advances in proportion to the optical path length
that the particle has traversed. Typically this is taken to be length in terms of an absolute space, so it’s as if each particle of light contains an odometer, whose reading corresponds to the phase
of the particle. When two or more particles collide, their effects are added together in accord with their phases. Thus if two particles hitting a receiver have opposite phases, they cancel out
(destructive interference) and have no effect, whereas if they have the same phase their effects are added (constructive interference).
These peculiar hypotheses do indeed yield the observed Sagnac effect, because even though the two particles (moving in opposite directions around the loop) arrive simultaneously, they produce
interference fringes due to the phase differences arising from the different optical path lengths relative to the posited absolute stationary space. However, this conception of light leads to many
difficulties. First, it predicts a non-null result for the Michelson-Morley experiment, because the perpendicular rays of light traverse unequal distances relative to absolute space (assuming the
Earth is moving relative to that space). This is ironic, because one of the original motivations for interest in ballistic theories was their ability to account for the Michelson-Morley experiment.
By modifying the theory to force agreement with the Sagnac effect, we sacrifice agreement with Michelson-Morley. Second, it is at least debatable whether this modified ballistic theory is really a
ballistic theory at all, because it relies on interaction between the light particles and the absolute fixed background to determine the phases of the particles. Thus it is really a hybrid, grafting
a ballistic theory on top of a fixed ether theory. Third, we get two different kinds of frequency for a beam of light, one representing the number of particles per second, and another representing
the rate of phase advance of each particle. In effect, if we consider a closely-spaced sequence of particles, the phase velocity is different from the particle velocity, so a given phase crest must
move from one particle to another. Conversely, we can imagine an ordinary wave in the posited background space, and the only “ballistic” aspect is that we conceptually identify small segments of this
wave as “particles”, which can be said to propagate at any speed we like, since the speed of these partitions has no effect – for a continuous beam of light. The only putative effect would be on the
timing for the beginning and ending of a beam of light, e.g., the speed of the “leading edge” of a phase wave. But of course these timing effects (which are observed to be inconsistent with the
ballistic hypothesis) are precisely what the Newtonian ballistic proponent declines to consider.
Oddly enough, the modern theory of electrodynamics and light, called quantum electrodynamics or QED, could with some plausibility be called a ballistic theory, since it satisfies the defining
condition, i.e., light propagates at the speed c in terms of the standard inertial rest frame coordinates of the source. But it can also be called an ether theory, since it satisfies the defining
condition, i.e., light propagates with a characteristic speed c (relative to a standard inertial coordinate system) independent of the motion of the source. Thus it isn’t surprising that the attempts
to represent light in terms of Newtonian mechanical principles end up being hybrids, because this is unavoidable for a phenomenon that exhibits both particle and wave attributes.
It’s also interesting to note that Feynman’s “sum over paths” formulation of QED bears some resemblance to the Newtonian ballistic concept just described, i.e., we consider each possible path from
emitter to receiver, and each path has an associated phase, proportional to the optical path length. The probability density is then the squared norm of the sum of all the complex amplitudes
(representing the phases). However, there are fundamental differences between QED and the hypothesized Newtonian ballistic theory. For one, the phase of a photon does not advance during transit;
instead, the light path simply represents a mapping from the emitter’s worldline to the receiver’s worldline, and the phase of the emitter is projected to the receiver. The phase depends on the path
length only because a longer path conveys an earlier phase of the emitter. Second, in QED each photon interferes only with itself (if we neglect some higher-order non-linear effects), based on all
the possible paths that it could follow. In contrast, the ballistic theory requires multiple particles to give interference. Thus they could not reproduce the results of Young’s two-slit experiment
when performed with light of such low intensity that only a single particle/photon is registered at a time. QED correctly predicts the observed interference effects in such a case, whereas the
ballistic theory must give no interference at all in this case. For the same reason, any classical ballistic theory is unable to give a satisfactory account for diffraction.
Return to MathPages Main Menu | {"url":"http://mathpages.com/home/kmath443/kmath443.htm","timestamp":"2014-04-21T02:06:08Z","content_type":null,"content_length":"33612","record_id":"<urn:uuid:7738570d-034e-41a4-8825-6e7b75a610b0>","cc-path":"CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00331-ip-10-147-4-33.ec2.internal.warc.gz"} |
Introduction to modular property of affine alegebra and conformal vertex algebra
Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
I wonder how modular property naturally arises in conformal theory. Is it obvious from physical viewpoint?
add comment
up vote 1 Yes -- see Cardy's paper Operator content of two-dimensional conformally invariant theories. In a nutshell, the torus partition function of a conformal theory can be computed using a
down vote transfer matrix in several ways. The equivalence of these different calculations is the modular invariance of the torus partition function.
add comment
Not the answer you're looking for? Browse other questions tagged abstract-algebra or ask your own question. | {"url":"http://mathoverflow.net/questions/16425/introduction-to-modular-property-of-affine-alegebra-and-conformal-vertex-algebr","timestamp":"2014-04-20T04:00:14Z","content_type":null,"content_length":"50282","record_id":"<urn:uuid:82f02520-4f71-4b17-807c-459ce26ab7cc>","cc-path":"CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00134-ip-10-147-4-33.ec2.internal.warc.gz"} |
Graph theory is widely used in computer science, engineering and of course, mathematics. Here, visitors will find links to information about the applications and components of graph theory, as well
as its pioneers.
Wikipedia: Graph Theory
Drawing on the knowledge of the people, Wikipedia presents this site on graph theory. Here, the history, problems, and applications of graph theory are...
more info
Graph Theory with Applications
Written by J.A. Bondy and U.S.R. Murty of the Pierre and Marie Curie University in Paris, this online 270-page textbook presents graph theory and its...
more info
Georgia Tech: Four Color Theorem
Presented by Robin Thomas at the Georgia Institute of Technology, this page describes the four color theorem of graph theory. The page gives a history of the...
more info
Graph Theory Book
From the Graduate Texts in Mathematics series comes this textbook on graph theory by Reinhard Diestel from the University of Hamburg. Topics covered include...
more info
Frank Harary 1921-2005
Written by Desh Ranjan of New Mexico State University, this page remembers Frank Harary, "widely recognized as one of the pioneers of modern graph theory." ...
more info
more featured folders
AMSER is a portal of
educational resources
built specifically for use by those in
Technical Colleges
for anyone to use.
AMSER is funded by the
National Science Foundation
as part of the
National Science Digital Library
, and is being created by a team of project partners led by
Internet Scout
There is a difference between a billion in a America and a billion in Great Britain. In the U.S., a billion equals one thousand million. In Great Britain, a billion equals a million million.
forget your password?
Manage your resources
Save, organize, and share resources that you find.
Subscribe to bulletins
Automatically be notified about new resources that match your interests.
It's easy, fast, and FREE! | {"url":"https://amser.org/index.php?option=com_content&view=article&id=316&Itemid=125","timestamp":"2014-04-21T16:23:10Z","content_type":null,"content_length":"22260","record_id":"<urn:uuid:37a00508-fd95-487e-a808-48abd851aa49>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00056-ip-10-147-4-33.ec2.internal.warc.gz"} |
You are currently browsing the monthly archive for June 2006.
After Italy scored the overtime goal against Australia on Monday, CCTV commentator Huang Jianxiang went beserk, shouting 马尔蒂尼今天生日快乐, happy birthday Maldini, 意大利万岁 long live (literally,
“live 10,000 years”) Italy, and so on. We share the sentiment. He later had to apologize.
At YouTube there is an extended transcript (in English).
By the way, is it Go West by the Pet Shop Boys playing at the end in the background?
Update: as the commenters correctly point out, Go West is by the Village People, and the Pet Shop Boys version is a later cover. Shame on me. To atone, here is the Village People video:
Microsoft Research has developed a tool to measure how butch is a web site. (Via Doug Tygar.) In Theory scores 54% male. It must be all those manly posts about math. (Although I have to agree with
the first comment here.)
When traveling in East Asia, it is easy to make fun of the mistranslated signs and the oddly named stores. (There is, in fact, a whole website devoted to just that: see a few examples here, here and
here, out of several hundreds.)
Anyways, when we use Chinese characters in the West, the joke is on us.
After discussing Szemeredi’s Theorem and the analytical approaches of Roth and Gowers, let’s see some ideas and open problems in the combinatorial approach.
The following result is a good starting point.
Triangle Removal Lemma. For every $\delta >0$ there is a constant $\epsilon(\delta) > 0$ such that if $G$ is an $n$-vertex graph with at most $\epsilon(\delta)n^3$ triangles, then it is possible
to make $G$ triangle-free by removing at most $\delta n^2$ edges.
This result follows easily from the Szemeredi Regularity Lemma, and it is a prototype of several results in the field of property testing.
Indeed, consider the problem of distinguishing triangle-free graphs from graphs that are not even close to being triangle-free. For the purpose of this example, we think of a graph as “close to being
triangle-free” if it can be made triangle-free by removing at most $\delta n^2$ edges, for some small constant $\delta > 0$. Then the Lemma tells us that in a not-even-close graph we have at least $\
epsilon(\delta) n^3$ triangles, and so a sample of $O(1/\epsilon(\delta))$ vertices is likely to contain a triangle. So here is an algorithm for the problem: pick at random $O(1/\epsilon(\delta))$
vertices and see if they induce a triangle. We note that:
• The algorithm satisfies our requirement;
• The running time is a constant independent of $n$ and dependent only on $\delta$;
• this all makes sense only if $1/\epsilon(\delta)$ grows moderately as a function of $1/\delta$.
Let us now see that the Triangle Removal Lemma proves Szemeredi’s Theorem for sequences of length 3. As we discussed earlier, it is enough to prove the Theorem in groups of the type ${\mathbf Z}_N$,
with $N$ prime; we will do better and prove the Theorem in any abelian group. So let $G$ be an abelian group of size $N$, an let $A$ be a subset of $G$ of size $\delta N$. Construct a tri-partite
graph $(X,Y,Z,E)$ where $X,Y,Z$ are sets of vertices, each of size $N$, and each a copy of the group $G$. The set of edges is defined as follows:
1. for $x \in X$ and $y \in Y$, $(x,y)$ is an edge if there is an $a \in A$ such that $x+a=y$
2. for $x \in X$ and $z \in Z$, $(x,z)$ is an edge if there is a $b\in A$ such that $x + b + b = z$
3. for $y \in Y$ and $z \in Z$, $(y,z)$ is an edge if there is a $c \in A$ such that $y+c=z$
Now we notice that if $x,y,z$ is a triangle, then there are $a,b,c$ in $A$ such that (after some cancellations) $a+c = b+b$, which means that $a,b,c$ is an arithmetic progression of length 3 in the
group $G$. In fact, we see that the number of triangles in the graph is precisely $N$ times the number of triples $(a,b,c)$ in arithmetic progression in $A$.
Consider now the $N \cdot |A| = \delta N^2$ triangles corresponding to the “trivial” progressions of the form $a,a,a$. (These are the triangles $x,x+a,x+a+a$.) We can see that these triangles are
edge-disjoint, and so in order just to remove such triangles we have to remove from the graph at least $\delta N^2$ edges. So the Triangle Removal Lemma implies that there are at least $\epsilon(\
delta)N^3$ triangles in the graph, and so at least $\epsilon(\delta)N^2$ triples in arithmetic progression in $A$. If $N > \delta/\epsilon(\delta)$, then some of those arithmetic progressions must be
non-trivial, and we have the length-3 case of Szemeredi’s theorem.
We see that both for the “property testing” application and for the Szemeredi Theorem application it is important to have good quantitative bounds on $\epsilon(\delta)$. We know that, in Szemeredi’s
theorem, $N$ must be super-polynomial in $1/\delta$, and so, in the Triangle Removal Lemma, $1/\epsilon(\delta)$ must be super-polynomial in $1/\delta$.
The known bounds, however, are quite unreasonable: we only know how to bound $1/\epsilon(\delta)$ by a tower of exponentials whose height is $poly(1/\delta)$. Unfortunately, such unreasonable bounds
are unavoidable in any proof of the Triangle Removal Lemma based on Szemeredi’s Regularity Lemma. This is because, as proved by Gowers, such tower-of-exponentials bounds are necessary in the
Regularity Lemma.
Can we find a different proof of the Triangle Removal Lemma that has only a singly- or doubly-exponential $\epsilon(\delta)$? That would be wonderful, both for property testing (because the proof
would probably apply to other sub-graph homomorphism problems) and for additive combinatorics. Over the last year, I have found at least three such proofs. Unfortunately they were all fatally flawed.
Or, is there a more-than-exponential lower bound for the Triangle Removal Lemma? This would also be a major result: it would show that several results in property testing for dense graphs have no
hope of being practical, and that there is a “separation” between the quantitative version of Szemeredi’s Theorem provable with analytical methods versus what can be proved with the above reduction.
Besides, it’s not often that we have super-exponential lower bounds for natural problems, with Gowers’s result being a rare exception.
By the way, what about Szemeredi’s Theorem for longer sequences? For sequences of length $k$ one needs a “$k$-clique removal lemma” for $(k-1)$-uniform hypergraphs, which in turn can be derived from
the proper generalization of the Regularity Lemma to hypergraphs. This turns out to be quite complicated, and it has been accomplished only very recently in independent work by Nagle, Rödl and
Schacht; and by Gowers. An alternative proof has been given by Tao. The interested reader can find more in expository paper by Gowers and Tao.
What about Szemeredi’s own proof? It does use the Regularity Lemma, which was conceived and proved specifically for this application, and it involves a reduction to a graph-theoretic problem. I have
to admit that I don’t know much else.
The Strings 2006 conference is under way in Beijing, and yesterday Field Medalist Yau Shing-Tung gave a popular talk on the Poincare conjecture. Yau’s talk was preceded by taped remarks by Richard
Hamilton. A transcript of Hamilton’s remarks is here, the People’s Daily article is here and a first-hand account is here.
The 30th Frameline film festival is under way. It can exist, and be such a big production, thanks to the contributions of the Frameline members and to the major sponsors. In addition, each screening
has its own sponsor. The movie I saw today was sponsored by … Canada!
No kidding.
This is not an isolated act of kindness. The Frameline programmer who introduced the movie said that, over time, the Canadian government has contributed more than the US federal government to the
I have two things to say: (1) foreign aid to needy countries is very noble; (2) I blame the electoral college.
Found today in a fortune cookie:
At 20 years of age the will reigns; at 30 the wit; at 40 the judgement.
Scott complains that “art snobs” want to have it both ways: to assert that the beauty of art is an aesthetic experience, a gut feeling, and, at the same time, that certain tastes are more valid than
others. What is this, do they think that their guts are better than ours? That’s certainly not how we do things in complexity theory. Or is it?
When we talk about the “beauty” of a theorem or of a proof, we rarely refer to the literal statement of the theorem, much less to the fact that the proof is correct.
The beauty of a theorem is typically found in the way it fits into the bigger fabric of a theory, how it is explained by, and how it explains, other results. The statement of a theorem can feel
comforting, surprising, or even unsettling, or worrisome. In a proof, we appreciate economy, a way of getting to the point in what feels like the “right” way, an unexpected use of techniques, a quick
turn and a surprising ending.
If we think of, say, Reingold’s proof that L=SL, we (meaning, I and some other people) appreciate the statement for being a major milestone in the program of derandomization, and we appreciate the
proof for the simplicity of its structure and for the cleverness of the way its technical tools are used.
Although, in the end, it is a matter of taste to see that the statement is important and that the proof is beautiful, I don’t think that the taste of the expert in the area is equally valid as the
taste of the non-expert who says, oh this is an algorithm for connectivity that runs in n^100 time and it does not even work on directed graphs?
(I am so delighted to have a discussion where one can take the notion of mathematical beauty for granted, and then use it to argue about artistic beauty.)
This wouldn’t be a non-technical In Theory post without an unnecessary personal story, so let me conclude with my experience with modern dance.
At one point, a few years ago, I was taken to see several modern dance performances. My first experience was not unlike Woody Allen’s in Small Time Crooks. While the sound system was playing annoying
and discordant sounds, people on stage were moving around in what looked like a random way. I was convinced that the nearly sold-out audience at Zellerbach (it’s a big theater) was there simply to
feel good about themeselves and nobody could really like that stuff. There was something that puzzled me, however: at one point, everybody laughed, presumably because something (intentionally) funny
happened in the choreography. Everybody got it (except me, of course), so perhaps there was something going on in those random movements, after all. After a few more shows, the experience started to
feel less agonizing, and I started to notice that I would like some segments better than others, and that this would agree with what others thought. Finally, one night, I laughed out when a dancer
did something really funny on stage, and so did the rest of the audience. Aha, the brainwashing had succeeded! I left the theater feeling good about myself… No, wait, this is so not the point I
wanted to make…
I can’t decide if this is funny or racist. (From Gizoogle.)
My latest post on Szemeredi’s theorem was long and rambling, mostly because I had no idea what I was talking about. There are, however, a couple of neat questions, and I am afraid they got lost in
the rambling, so let me state them again.
1. It is either known or probably derivable from known proof techniques that
If f:{0,1}^n -> {0,1} has agreement 1/2+eps with a degree-k polynomial, then there is an affine subspace V of {0,1}^n, of dimension n/c, and a linear function L, such that f and L have
agreement 1/2 + eps’ when restricted to V. Here c=c(k) is a constant that depends only on k and eps’=eps’(eps,k) is a constant that depends only on eps and on k.
This is somewhat surprising, even if you look at the special case of a function f that is a polynomial (as opposed to being correlated with a polynomial).
Is there a simple proof of this result? Is the result true if you replace “subspace” by “restriction”? (Meaning, you are only allowed to fix all but a constant fraction of the variables.)
Shouldn’t this be useful in complexity theory somewhere?
[Update 7/14/06: the degree-2 case has indeed a very simple proof. A more general result is proved here, in section 7. For higher degree, the result is actually false, in the sense that it is
impossible to find a subspace of dimension constant*n. Avi Wigderson and I have found a counterexample already for degree 3, and Ben Green has sharpened our lower bound. The best one can do for
degree-k polynomials is to find a subspace of dimension about n^(1/(k-1)).]
2. If f has agreement 1/2+eps with a linear function L in a subspace V of dimension n-t, then there is a linear function L’ such that f and L’ agree on a fraction at least 1/2+eps/2^t of all of
This is fairly easy to see.
3. This is a fascinating challenge: find an simple proof (or any proof that fits in fewer than, say, 20 pages) that if f:{0,1}^n->{-1,1} has dimension-k Gowers uniformity at least eps, then there is
a linear subspace V of dimension n/c and a linear function L, such that f and L have agreement at least 1/2+eps’ on V. (Where c=c(k) and eps’=eps’(eps,k).)
Chances are that such a proof could be turned into a simpler proof of Gowers’s quantitative version of Szemeredi’s theorem. (A proof of the above result for boolean functions can probably be
“translated back” from Gowers’s paper, and it would probably be at least 50-60 pages. As I understand it, such a proof would first argue that f is correlated with a polynomial in a large
subspace, and then proceed with (1) above. I wonder: can one prove such a statement without mentioning polynomials at all?)
4. Unfortunately the conclusion cannot be strenghtened to “… there is a linear subspace V of dimension n-o(n)…”. Consider
f(x[1],…,x[1]):= x[1]*x[2]+…+ x[n-1]*x[n] mod 2
Its dimension-3 Gowers uniformity is 1, but, if you could find a subspace V of dimension n-o(n) on which f agrees with a linear function on a 1/2+eps’ fraction of inputs, then you could also find
a linear function that agrees with f on a 1/2+eps/2^o(n) fraction of inputs. But we know that no linear function agrees with f on more than a 1/2+1/2^n/2 fraction of inputs.
Recent Comments
• student on This story has a moral
• Not a Troll on This story has a moral
• Jim Hefferon on This story has a moral | {"url":"http://lucatrevisan.wordpress.com/2006/06/","timestamp":"2014-04-20T06:19:31Z","content_type":null,"content_length":"75087","record_id":"<urn:uuid:2118f752-4780-40bc-b24c-fa47e968187f>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00401-ip-10-147-4-33.ec2.internal.warc.gz"} |
seq/parametricity properties/free theorems and a proposal/question
Tyson Whitehead twhitehead at gmail.com
Fri Mar 18 17:23:42 CET 2011
On March 18, 2011 11:12:44 Max Bolingbroke wrote:
> On 18 March 2011 14:54, Tyson Whitehead <twhitehead at gmail.com> wrote:
> > map f . map g = map (f . g)
> >
> > should be derivable from the type of map "(a -> b) -> [a] -> [b]"
> I don't think this is true as stated. Consider:
> map f [] = []
> map f [x] = [f x]
> map f (x:y:zs) = f x : map zs
> Your proposed property is violated though we have the appropriate
> type. IIRC I think what is true is that
> map f . map' g = map' (f . g)
> For any map' :: (a -> b) -> [a] -> [b]
You are correct. You don't actually get the "map f . map g = map (f . g)"
relationship without looking at the definition of map (which, as you point out,
could be otherwise doing things like dropping elements).
Ignoring my bad example though, the key, though still is that without seq, the
only operations that polymorphic functions can invoke that peer inside their
universally quantified arguments are those passed to them.
This guarantee gives compilers more freedom in manipulating expressions
(through free theorems and, as Simon pointed out, more eta-expansion).
Cheers! -Tyson
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 490 bytes
Desc: This is a digitally signed message part.
URL: <http://www.haskell.org/pipermail/libraries/attachments/20110318/2595c35d/attachment.pgp>
More information about the Libraries mailing list | {"url":"http://www.haskell.org/pipermail/libraries/2011-March/016053.html","timestamp":"2014-04-19T03:09:44Z","content_type":null,"content_length":"4601","record_id":"<urn:uuid:3bb47b6a-3174-4b01-8818-a06a6e24cea3>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00620-ip-10-147-4-33.ec2.internal.warc.gz"} |
A Provable Time and Space Efficient Implementation of NESL
Guy E. Blelloch and John Greiner
International Conference on Functional Programming, May 1996.
Abstract: In this paper we prove time and space bounds for the implementation of the programming language NESL on various parallel machine models. NESL is a sugared typed lambda-calculus with a set
of array primitives and an explicit parallel map over arrays. Our results extend previous work on provable implementation bounds for functional languages by considering space and by including arrays.
For modeling the cost of NESL we augment a standard call-by-value operational semantics to return two cost measures: a DAG representing the sequential dependences in the computation, and a measure of
the space taken by a sequential implementation. We show that a NESL program with w work (nodes in the DAG), d depth (levels in the DAG), and s sequential space can be implemented on a p processor
butterfly network, hypercube, or CRCW PRAM using O(w/p + d log p) time and O(s + d p log p) reachable space. For programs with sufficient parallelism these bounds are optimal in that they give linear
speedup and use space within a constant factor of the sequential space.
Note that this online version corrects some typographical errors, mostly in Figure 8.
@inproceedings {BLELLOCH96nesl,
author = "Guy~E. Blelloch and John Greiner",
title = "A Provable Time and Space Efficient Implementation of NESL",
booktitle = "ACM SIGPLAN International Conference on Functional Programming",
year = 1996,
month = may,
pages = "213--225"} | {"url":"http://www.cs.cmu.edu/afs/cs.cmu.edu/project/scandal/public/papers/icfp96-nesl.html","timestamp":"2014-04-17T07:41:50Z","content_type":null,"content_length":"2216","record_id":"<urn:uuid:078bfc88-3b0f-41eb-9d74-aac39d822531>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00601-ip-10-147-4-33.ec2.internal.warc.gz"} |
Summary: 21-700 Mathematical Logic II
Spring 2011 MWF 11:30 WEH 7201
Professor Andrews
Department of Mathematical Sciences
Office: WEH 7216
email: andrews@cmu.edu or pa01@andrew.cmu.edu
Phones: 412-268-2554 (office), 412-767-5564 (home)
Usual office hours:
Web site
Peter B. Andrews, An Introduction to Mathematical Logic and Type Theory: To Truth
Through Proof, Second Edition, Kluwer Academic Publishers, now published by Springer, 2002.
Please tell me about any misprints you notice, or suggestions about the next edition you wish
to make.
This semester we will cover Chapters 5 - 7. The lectures will correspond closely to the material
in the book. You are expected to read the material in the book corresponding to the material
covered in class. The purpose of the lectures is to help you understand and thoroughly absorb this
material, so you are always encouraged to ask questions during lectures.
Computer assignments | {"url":"http://www.osti.gov/eprints/topicpages/documents/record/255/1654584.html","timestamp":"2014-04-20T13:44:19Z","content_type":null,"content_length":"8037","record_id":"<urn:uuid:d2e693f1-f953-4b38-b605-4e11b89852bf>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00368-ip-10-147-4-33.ec2.internal.warc.gz"} |
FOM: Re: Arithmetic/Geometry
Vladimir Sazonov sazonov at logic.botik.ru
Sat Oct 17 03:52:10 EDT 1998
I mistakely sent (on Fri, 16 Oct 1998 19:15) the following
posting only to Harvey Friedman personally. Now I am sanding
it also to fom.
Harvey Friedman wrote:
> I think
> making some distinctions would help get to the bottom of the disagreement,
> if there is any.
> Consider the following four:
> 1. Arithmetic as motivated by casual considerations of physical reality.
> 1'. Arithmetic taken as statements about physical reality.
> 2. Geometry as motivated by casual considerations of physical reality.
> 2'. Geometry taken as statements about physical reality.
> Mathematicians are generally concerned only with items 1 and 2. They focus
> successfully on 1 and 2 because of the startling fact that everything they
> want to know is based on only such casual considerations, and the great
> power of deductive reasoning. The main point is that for 1 and 2, physical
> experimentation seems completely useless and irrelevant.
Completely useless and irrelevant?
I agree only that once a formal system is fixed mathematician
(if he is indeed a mathematician) should deduce theorems in this
system using physical and any other consideration *only* as
motivations or a help for the intuition to find a proof.
However, when a formal system arise it may be based on physical
experiments or anything else. The best example is geometry!
Is this correct interpretation of your point of view? At least,
after making these notes I see (almost) no contradiction with you
and will follow below to this interpretation of 1. and 2.
Both 1. and 2. are based on "casual" considerations of
physical reality and, I would add, different such considerations
may lead, in principle, to different versions of 1. and 2.
For the clarity I should say that I personally am interested
mostly in *various* forms of 1. (and 2., which is actually
sufficiently elaborated if not take into account influence of
other possible forms of 1.) because these are *mathematical*
subjects. 2'. (and 1'.?) are rather physical subjects (or
subjects of experimental "computational" mathematics?) and
should be investigated by corresponding experimental methods
in close cooperation with appropriate mathematical formalisms.
Although, even
> this point is subtly misleading or incorrect. The running of computer
> programs can be viewed as a kind of physical experimentation, which is now
> a common way of establishing new results in 1 and 2. However, it is also
> "clear" that such results are always deductive consequences of the basic 1
> and 2, but the deductions are themselves too large to be obtained by humans
> without resorting to the "physical experimentation of actual computing." I
> could follow this line of thought further, to good effect, but I will stop
> here. E.g., how do I know that this physical experimentation can be
> "replaced" by deductions? That involves a whole host of issues such as "why
> should I believe a computer?" In any case, it seems inconceivable that
> physical experimentation - in the broadest possible sense - is ever going
> to falsify results in 1 and 2.
Yes, of course!! If a *formal* proof is written on a paper
nothing can make it incorrect with respect to fixed axioms and
proof rules. But experiments or general physical considerations
may suggest us to change "the rules of game", i.e. axioms and
proof rules to get some more appropriate formalism (as an
*instrument* of knowledge).
> One can follow this train of thought, back
> and forth, with a determined sceptic - like Wittgenstein(?)(!) - and
> generate state of the art f.o.m.
> As far as 2' is concerned, it has become part of the folklore of physics
> that this kind of geometry is affected by physical experimentation and
> observation, and their is an underlying objective reality to this. I think
> that the situation in contemporary physics is so conceptually murky - with
> such things as quantum mechanics, string theory, etc. - that the content
> and status of 2' is rather unclear. For example, in light of modern
> thinking in physics, what exact meaning, operationally and otherwise, can
> really be assigned to such questions as "is the parallel postulate true?"
> "is space indivisible?" I have my doubts about the meaningfullness and/or
> objectivity of this sort of thing.
Does not this mean that mathematics suggests to physics
fundamental concepts of finite/infinite, discrete/continuous
which are not sufficiently appropriate to its contemporary
needs? It seems that if we will continue to stay on our
*traditional* fundamental concepts without any attempt of
variations to find more *realistic* versions then mathematics
may loose some of its positions in science.
Just one example. The astro-physical fact that the number of
electrons in our Universe is < 2^1000 is usually interpreted
according to traditional mathematics, as that the Universe is
finite so that seemingly it is meaningful considering the
*exact* number of all electrons. This seems to be very
non-plausible conclusion. I understand the situation quite
differently. The Universe is infinite, but bounded (by 2^1000).
Compare with the case of standard natural numbers imbedded into
a nonstandard model M and bounded by a nonstandart m\in M. What
does it mean the nonstandard cardinality (in the sense of M) of
the set of all standard numbers? Is it meaningful and < m?
Analogously, 2^1000 serves rather as "non-standard number" for
feasible numbers (playing the role of standard ones) by which
(i.e. by feasible numbers) we probably could count electrons or
some other "objects" of our Universe. There is no biggest
feasible number, and the Universe is, "therefore" infinite.
> And for 1', I don't see people even considering it. However, one could
> interpret 1' to involve something like this: Is the axiom of successor
> true? Another way one may want to put this is: are there infinitely many
> physical objects? Of course, I don't know what a physical object is, and
> that seems also to be very murky right now. Spinoff for f.o.m.: study
> arithmetic without the axiom of successor.
Could you be a bit more explicit? Do you mean to postulate
existence of a biggest number (note that in some my posting I
discussed on such a \Box-arithmetic or []-arithmetic), or what?
By the way, such a studying arithmetic with changed axiom(s) of
successor as well as any reasonable arithmetics of feasible
numbers is of course a subject of 1., *rather than* of 1'. We take
only *some* aspects of reality, formalize them by some appropriate
axioms and proof rules and then work as in the ordinary mathematics:
infere theorems by using considerations from the reality *only*
as motivations or a help for the intuition to find a proof.
Do you agree?
> I don't want to say more about
> this right now, except that this also leads to some specific state of the
> art projects in f.o.m.
> Now there are profoundly interesting similarities and difference and
> relationships between 1 and 2. A lot of this quickly leads to unexplored
> state of the art f.o.m. if systematically pursued. But before going further
> into this on the fom, I'll stop here and see whether people in this thread
> find it useful to cast the issues in this general framework. In particular,
> in the light of this framework, what precisely is the disagreement about?
Say, my disagreement with Neil Tennant concerns
"1. Arithmetic as motivated by casual considerations of physical
This is also my point of view on arithmetic (and on its possible
reasonable variations), but Tennant, on the contrary, mysteriously
believes in "absolutely true" arithmetic which arose completely
independently of our reality.
Vladimir Sazonov
-- | Tel. +7-08535-98945 (Inst.),
Computer Logic Lab., | Tel. +7-08535-98953 (Inst.),
Program Systems Institute, | Tel. +7-08535-98365 (home),
Russian Acad. of Sci. | Fax. +7-08535-20566
Pereslavl-Zalessky, | e-mail: sazonov at logic.botik.ru
152140, RUSSIA | http://www.botik.ru/~logic/SAZONOV/
More information about the FOM mailing list | {"url":"http://www.cs.nyu.edu/pipermail/fom/1998-October/002369.html","timestamp":"2014-04-20T18:48:10Z","content_type":null,"content_length":"11139","record_id":"<urn:uuid:6aa78a92-b6a2-45be-8156-3cacb70e62e5>","cc-path":"CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00442-ip-10-147-4-33.ec2.internal.warc.gz"} |
Krull rings and determinantal invariants
up vote 8 down vote favorite
During another attempt to come to grips with Hillman's excellent book Algebraic Invariants of Links, I am having difficulty figuring out why Krull rings are the setting for Chapter 3- the natural
setting for determinantal invariants, such as the Alexander polynomial and Franz-Reidemeister torsion. What is an example of a non-noetherian or non-factorial Krull ring which might conceivably be
useful in low-dimensional topology?
In fact, I have a simpler, more general question:
What are examples of non-noetherian Krull rings, or non-factorial Krull rings, which are actually used in mathematics?
In particular, how does the condition for a ring to be Krull manifest itself in terms of the geometry or topology of something, as opposed to some other class such as Grothendieck's "excellent
rings"? In another direction, does something good happen for K-theory over Krull rings? Are Krull rings somehow natural objects to take determinants in?
ac.commutative-algebra knot-theory 3-manifolds examples
+1 for a question with commutative algebra and knot theory tag! – Hailong Dao Apr 14 '10 at 18:05
add comment
Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.
Browse other questions tagged ac.commutative-algebra knot-theory 3-manifolds examples or ask your own question. | {"url":"http://mathoverflow.net/questions/21349/krull-rings-and-determinantal-invariants","timestamp":"2014-04-18T10:59:03Z","content_type":null,"content_length":"48458","record_id":"<urn:uuid:a1b1889c-1fb3-48f3-a2ac-78b517e23797>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00004-ip-10-147-4-33.ec2.internal.warc.gz"} |
Mensa Math/Logic Problems...How to Solve? - New Logic/Math PuzzlesMensa Math/Logic Problems...How to Solve? - New Logic/Math PuzzlesMensa Math/Logic Problems...How to Solve? - New Logic/Math Puzzles
I am unable to find similar problems or solutions online, so I thought I'd ask here...I'd really appreciate it if you all could help me learn how to solve these types of problems, so please include
the correct reasoning process and solution, if you don't mind.
Thanks in advance! | {"url":"http://brainden.com/forum/index.php/topic/16597-mensa-mathlogic-problemshow-to-solve/","timestamp":"2014-04-24T22:43:18Z","content_type":null,"content_length":"100730","record_id":"<urn:uuid:2487ac0e-821e-4e41-bc96-e5553ba02abc>","cc-path":"CC-MAIN-2014-15/segments/1398223206770.7/warc/CC-MAIN-20140423032006-00165-ip-10-147-4-33.ec2.internal.warc.gz"} |
Portability GHC
Stability highly unstable
Maintainer Stephen Tetley <stephen.tetley@gmail.com>
Anchor points on shapes, bounding boxes, etc.
Anchors are addressable positions, an examplary use is taking anchors on node shapes to get the start and end points for connectors in a network (graph) diagram.
** WARNING ** - The API here needs some thought as to a good balance of the type classes - in a nutshell "are corners better than cardinals". Originally I tried to follow how I understand the TikZ
anchors to work, but this is perhaps not ideal for dividing into type-classes.
class CenterAnchor t whereSource
Fractional u => CenterAnchor (BoundingBox u)
class CardinalAnchor t whereSource
Cardinal (compass) positions on an object.
Note - in TikZ cardinal anchors are not necessarily at the equivalent radial position, for instance reactangle north-east is the top-right corner whether or not this is incident at 45deg.
Wumpus generally follows the TikZ convention.
Fractional u => CardinalAnchor (BoundingBox u)
class CardinalAnchor2 t whereSource
Secondary group of cardinal (compass) positions on an object.
It seems possible that for some objects defining the primary compass points (north, south,...) will be straight-forward whereas defining the secondary compass points may be problematic, hence the
compass points are split into two classes.
Fractional u => CardinalAnchor2 (BoundingBox u)
class RadialAnchor t whereSource
Anchor on a border that can be addressed by an angle.
The angle is counter-clockwise from the right-horizontal, i.e. 0 is east.
class TopCornerAnchor t whereSource
Anchors at the top left and right corners of a shape.
For some shapes (Rectangle) the TikZ convention appears to be have cardinals as the corner anchors, but this doesn't seem to be uniform. Wumpus will need to reconsider anchors at some point...
class SideMidpointAnchor t whereSource
Anchors in the center of a side.
Sides are addressable by index. Following TikZ, side 1 is expected to be the top of the shape. If the shape has an apex instead of a side then side 1 is expected to be the first side left of the
Implementations are also expected to modulo the side number, rather than throw an out-of-bounds error.
Extended anchor points
projectAnchor :: (Real u, Floating u, u ~ DUnit t, CenterAnchor t) => (t -> Point2 u) -> u -> t -> Point2 uSource
projectAnchor : extract_func * dist * object -> Point
Derive a anchor by projecting a line from the center of an object through the intermediate anchor (produced by the extraction function). The final answer point is located along the projected line at
the supplied distance dist.
E.g. take the north of a rectangle and project it 10 units further on:
projectAnchor north 10 my_rect
If the distance is zero the answer with be whatever point the the extraction function produces.
If the distance is negative the answer will be along the projection line, between the center and the intermediate anchor.
If the distance is positive the anchor will be extend outwards from the intermediate anchor. | {"url":"http://hackage.haskell.org/package/wumpus-basic-0.16.0/docs/Wumpus-Basic-Kernel-Base-Anchors.html","timestamp":"2014-04-23T21:12:12Z","content_type":null,"content_length":"26038","record_id":"<urn:uuid:abbe35b6-51db-4db4-9850-0feddb67de07>","cc-path":"CC-MAIN-2014-15/segments/1398223203422.8/warc/CC-MAIN-20140423032003-00412-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
Find the simple interest if $1,000 is invested for 1 year at 6%.
• one year ago
• one year ago
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/4fb5c3d0e4b05565342ba719","timestamp":"2014-04-17T19:04:05Z","content_type":null,"content_length":"34640","record_id":"<urn:uuid:d4246ace-fa43-4055-bbe3-31df8b17a3b3>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00167-ip-10-147-4-33.ec2.internal.warc.gz"} |
About "Purplemath - Your Algebra Resource"
Description: Algebra modules provide lessons, practical tips, hints, worked examples, and point out common mistakes in basic triangle length (trigonometry) values, calculators (what model to buy),
canceling units, domain and range, exponents, factoring quadratics, function notation, functions, graphing, induction proofs, intercepts, percent of increase/decrease/markup/markdown, piecewise
functions, radicals (square roots), scientific notation, slope and graphing, slope and y-intercept, slope of a straight line, solving inequalities (three methods), straight-line equations,
translation of word problems (distance problems, investment problems, mixture problems, and work problems), variables, and the vertical line test. Homework guidelines list examples, with commentary,
of acceptable and unacceptable solutions. Also, an online study skills survey, and links to others' algebra sites. | {"url":"http://mathforum.org/library/view/12529.html","timestamp":"2014-04-17T02:07:09Z","content_type":null,"content_length":"6294","record_id":"<urn:uuid:f633a047-035f-4509-a14e-53fa5b135f7d>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00275-ip-10-147-4-33.ec2.internal.warc.gz"} |
The IBM Research/NYU/Columbia Theory Day
External sponsorship by: Google
Friday, December 8, 2006
Courant Institute of Mathematical Sciences
New York University
251 Mercer Street, Auditorium 109
New York, NY
9:30 - 10:00 Coffee and bagels
10:00 - 10:55 Dr. Julia Chuzhoy (Institute for Advanced Study)
Cut Problems in Graphs: Algorithms and Complexity
10:55 - 11:05 Short Break
11:05 - 12:00 Prof. Dan Boneh (Stanford University)
Queries on Encrypted Data
12:00 - 2:00 Lunch break
2:00 - 2:55 Prof. Michel Goemans (MIT)
Minimum Bounded Degree Spanning Trees
2:55 - 3:15 Coffee break
3:15 - 4:10 Dr. Jonathan Kelner (Institute for Advanced Study and MIT)
A Randomized Polynomial-Time Simplex Algorithm for Linear Programming
For directions, please see: http://www.cims.nyu.edu/direct.html For additional directions, please see: http://cs.nyu.edu/csweb/Location/directions.html To subscribe to our mailing list, follow
instructions at: http://www.cs.nyu.edu/mailman/listinfo/theory-ny
Yevgeniy Dodis dodis@cs.nyu.edu
TalRabin talr@watson.ibm.com
Baruch Schieber sbar@watson.ibm.com
Rocco Serverdio rocco@cs.columbia.edu
The organizers also thank Google Labs for their generous support.
Cut Problems in Graphs: Algorithms and Complexity
Dr. Julia Chuzhoy
Institute for Advanced Study
Cut problems are fundamental to combinatorial optimization, and they naturally arise as intermediate problems in algorithm design. The study of cut problems is inherently connected to the dual notion
of flows. In particular, starting with the celebrated max flow-min cut theorem, flow-cut gaps have been extensively studied and are the basis for many graph partitioning and routing algorithms.
In this talk we will investigate several well-known cut problems in graphs, including multicut and sparsest cut. We will survey some existing algorithmic techniques and present some recent hardness
of approximation results. In particular, we will show that the flow-cut gap in directed graphs can be as large as polynomial. This is in sharp contrast with the undirected graphs, where the gap is
known to be only logarithmic.
Queries on Encrypted Data
Prof. Dan Boneh
Stanford University
We will survey a number of recent results on answering queries on encrypted data. For example, we will present a recent system supporting comparison queries --- given a ciphertext C=E[m] and a secret
key d_i, one can test if m>i, but learn no other information about m. More general systems can support conjunctive and subset queries. We will show that encryption schemes supporting queries on
encrypted data lead to efficient traitor tracing systems and are closely related to other classic problems in cryptography. Our constructions are mostly based on bilinear maps in groups of composite
This is joint work with Brent Waters. The talk will be self contained.
Minimum Bounded Degree Spanning Trees
Prof. Michel Goemans
The minimum spanning tree is one the most fundamental combinatorial optimization problems, and its efficient solution makes it of wide applicability in a variety of areas, including network design,
routing, communication and clustering. In this talk, I will consider the variant under the additional restriction that all degrees of the spanning tree must be at most a given value $k$. The main
result I will describe is that one can efficiently find a spanning tree of maximum degree at most $k+2$ whose cost is at most the cost of the optimum spanning tree of maximum degree $k$. This is
almost best possible, as the problem of just deciding whether a graph has a spanning tree of maximum degree $k$ is NP-complete.
The approach uses a sequence of simple algebraic, polyhedral and combinatorial arguments. It illustrates many techniques and ideas in combinatorial optimization as it involves polyhedral
characterizations, uncrossing, matroid intersection, and graph orientations (or packing of spanning trees). Little prior knowledge will be assumed; just a willingness to learn...
The result generalizes to the setting where every vertex has upper and lower bounds on its degree. It also gives a better understanding for relaxations of related problems, including the symmetric
and asymmetric traveling salesman problems.
A Randomized Polynomial-Time Simplex Algorithm for Linear Programming
Dr. Jonathan Kelner
Institute for Advanced Study and MIT
In this talk, I shall present the first randomized polynomial-time simplex algorithm for linear programming. Like the other known polynomial-time algorithms for linear programming, its running time
depends polynomially on the number of bits used to represent its input. We begin by reducing the input linear program to a special form in which we merely need to certify boundedness. As boundedness
does not depend upon the right-hand-side vector, we run the shadow-vertex simplex method with a random right-hand-side vector. Thus, we do not need to bound the diameter of the original polytope. Our
analysis rests on a geometric statement of independent interest: given a polytope Ax <= b in isotropic position, if one makes a polynomially small perturbation to b then the number of edges of the
projection of the perturbed polytope onto a random 2-dimensional subspace is expected to be polynomial.
This is joint work with Daniel Spielman.
| contact webmaster@cs.nyu.edu | {"url":"http://cs.nyu.edu/web/Calendar/colloquium/fall06/dec08.html","timestamp":"2014-04-20T03:15:08Z","content_type":null,"content_length":"14038","record_id":"<urn:uuid:015eb49a-a6ff-401a-b9ab-5ea04108afa5>","cc-path":"CC-MAIN-2014-15/segments/1398223202548.14/warc/CC-MAIN-20140423032002-00364-ip-10-147-4-33.ec2.internal.warc.gz"} |
Bimmerfest - BMW Forums - View Single Post - Pen and Pencil Lease Payment Calculation
07-30-2006, 02:56 PM
Registered User
Location: Twin Cities, MN
Originally Posted by Greg220
This is the best ED lease calculation tool I have seen so far, thank you for sharing it!
I have only two questions:
- what exactly does cell A39 mean ["Difference in MF - $ amt over 24 mos (if used .00007 multiplier)] and why is it a negative number if dealer's MF markup is 0?
- cell D20 ("Total Paid at Signing") includes the 1st lease payment (D19). However cell D8 says "Total of Lease Pmts (not incl. 1st pmt, nor 2nd that BMW pays)". So, if BMW pays the 1st and 2nd
payments, why is it included in D19 and D20?
Glad you are finding it helpful!
Re: A39 - that was a cell I had added because our dealer insisted that we only get .00005 per extra deposit, rather than .00007, so in our calcs we were looking at the money we would lose by getting
only .00005 off instead of .00007 as dealer profit. (Basically, with 7 MSD's and nothing for dealer profit, we were getting an MF of .00176, so I took the difference between that and what the dealer
was offering to figure out dealer profit.) I have updated the sheet by removing that cell and inserting cell A38 to show the $ profit resulting from the dealer markup of MF (just nominal $ over the
length of the lease). Let me know if that helps and/or makes sense to do it that way.
Re: D20 - Looks like my wording was confusing. For D7, I meant that it did not include the first payment that you paid at signing, nor the second payment that you will not pay at all b/c BMW pays it.
The first payment is included in D8 so I wanted to be clear I had not included it in D7 and therefore double counted it. And the second payment is not included in either one since you don't pay it at
all. I updated the sheet to slightly change the wording in D7. Hope that helps!
I'll try to keep checking in here to see if there are any other issues.
To turpiwa and EvilM3 - not sure if you are refering to my spreadsheet, but if you are --
I recommend taking the spreadsheet with you on a laptop and getting the dealer to account for every single number that goes into it. That is what I did, and how I got this spreadsheet to where it is
- when I was done going over each number with the finance person, she and I had exactly the same numbers input and were getting the exact same numbers on the back end. (She was using the BMWFS
system, so it should be the same everywhere.) Also double check how taxes are handled - I did this lease in Minnesota, which requires the dealer to pay the taxes up front, though many people spread
it out in the payments (we chose to pay it up front). Assuming you know how taxes are handled by your dealer, and you have the right calculation for taxes, everything else in this spreadsheet should
give you the same numbers the dealer has, assuming they are telling you everything. | {"url":"http://www.bimmerfest.com/forums/showpost.php?p=1839338&postcount=56","timestamp":"2014-04-21T16:26:47Z","content_type":null,"content_length":"21200","record_id":"<urn:uuid:24fd544f-63ab-4a00-a678-38e210a14d3e>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00618-ip-10-147-4-33.ec2.internal.warc.gz"} |
How Do You Graph These?
Post reply
How Do You Graph These?
2. (0, -4) and (-4/3, 0)
3. (0, -5) (- 15/4, 0)
5. (2, 4) (2, 6)
6. (0, -2) (-2, 0)
What do these look like once they're graphed? I've tried a bunch and keep getting it wrong. Help me!!
By the way, there should be 2 lines once graphed. Each 2 point sets are for one line.
I'm just here to get some help with an online math course I'm taking.
Re: How Do You Graph These?
hi SlowlyFading,
Have a look at the diagram below.
I've 'colour-coded' them to make it easier to see which is which.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Re: How Do You Graph These?
Why are they all on one graph?
I'm just here to get some help with an online math course I'm taking.
Re: How Do You Graph These?
Why are they all on one graph?
Strictly speaking, my diagram shows four graphs on a single set of axes.
And I did this to save time.
If you need four separate answers, just make 4 separate diagrams.
But sometimes, you need to put two or more lines onto a single set of axes, so you can see where they cross.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Re: How Do You Graph These?
There needs to be two lines on each graph, once graphed. *Each 2 point sets* are for one line. So for #2, (0, -4) is for one line and the other point set is for another line. That's one graph.
I'm just here to get some help with an online math course I'm taking.
Re: How Do You Graph These?
I'm confused about what you want.
2. (0, -4) and (-4/3, 0)
That is two points so I showed them in red on my diagram with a line joining them.
3. (0, -5) (- 15/4, 0)
That's another two points, shown this time in blue, with a line joining them.
Perhaps you need to post the actual question wording that went with these coordinates.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Re: How Do You Graph These?
Okay, I'm going to try to explain it better.
My lesson is about liner equations, which states, "A system of linear equations is two or more linear equations that are solved at the same time. To solve a system of linear equations by graphing, we
graph the equations on one coordinate plane. The solution is the point where the lines cross."
So, the line doesn't need to join them together. The graph needs two lines, not one line joining the coordinates. So, using the coordinates from #2; the graph needs to lines, one line from (0, -4)
and another from (-4/3, 0). Not one line made from joining both coordinates.
Hopefully, this clarifies. By the way, I'm not sure if the lines will cross each other on every graph. It's okay if they're not..
I'm just here to get some help with an online math course I'm taking.
Re: How Do You Graph These?
Hi SlowlyFading;
the graph needs to lines, one line from (0, -4) and another from (-4/3, 0)
Takes two points to determine a line. There are bajillions of lines that go through (0,-4).
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
Re: How Do You Graph These?
hi SlowlyFading,
I understand the theory of systems of linear equations.
What I want is the exact wording of the questions you have been set.
It is not possible to draw a single line where only one point is given.
When you know two points, you can join them with a line.
Then if you have another two points, you can join them with another line.
Then you can look to see where the lines cross.
I have decided to assume that Q2 and Q3 are meant to be taken as such a system.
The diagram below then shows what answer you would get.
If that is not what the questions ask, you will have to give the exact wording of the questions.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Re: How Do You Graph These?
It says, "Graph the following using the given points using the system of linear equations."
The ones I can't get are:
2. (0, -4) and (-4/3, 0)
3. (0, -5) and (- 15/4, 0)
5. (2, 4) and (2, 6)
6. (0, -2) and (-2, 0)
And under each problem would be a graph where I draw my lines.
I'm just here to get some help with an online math course I'm taking.
Re: How Do You Graph These?
Well one point is not enough to fix a line. (see latest diagram)
So what I did in post 2 is the best I can offer for this. Sorry.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Re: How Do You Graph These?
Hi SlowlyFading!
The quote says "Graph the following using the given points using the system of linear equations."
This instruction is poorly worded. I've taught algebra for over 40 years but I can't understand what
this is asking. Perhaps if it comes from a book and the book has had several examples using this
terminology one could figure out what is being asked.
As mentioned in the previous posts it take TWO points to determine a straight line. Then it takes
TWO such lines to determine a system of equations and a point of crossing (if they cross. Distinct
parallel lines do not cross.)
I would think that since the question says "using the system of linear equations" that one would have
to first get the equations for the two lines (like #2 and #3 together). Then one could solve for the
exact point where they cross. Often it is difficult to get better than just an approximation to the
point where they cross since the point may involve fractions or decimals: difficult to figure out from
a drawn graph. If using a graphing calculator then one can zoom in to get better approximations.
Also one doesn't need the system of equations to just graph the lines. The system is needed to
get an accurate point of intersection.
May you be much blessed in your mathematical endeavors!
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
Re: How Do You Graph These?
Oh, shame on me. You guys were right (of course).
Okay, I found the other points, "the given points" are points I have to find. I made an error in thinking I already had them all it it was confusing me greatly.
HOPEFULLY! This works better. Sorry about my screw up guys..
2. (0, -4) (-4/3, 0) and (1, -1) (2, -2)
3. (0, -5)(- 15/4, 0) and
y = x + 2
m = 1
b = 2
5. (2, 4) (3, 6) and (2, 1) (I can't find the other point for some reason, grr..) The equation the point needs to be found from is x + y = 3.
6. I found m = 1/3 b =-1 from x = 3 - 3y
(0, -2) and (-2, 0)
Sorry for my mistakes. I hope this works better! Thanks for all the help!
I'm just here to get some help with an online math course I'm taking.
Re: How Do You Graph These?
Arrrhhh! At last the question makes sense.
Q2 shown in red.
Q3 shown in blue
Q5. shown in green.
You have asked about x + y = 3 before because I remember making a diagram for this.
You just need the x and y numbers to add up to a total of 3. eg. (3,0) (2,1) (1,2) (0,3)
Q6 shown in purple.
I plotted the b point (0,-1) and then used the gradient ... 3 across 1 up, to make more points.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Re: How Do You Graph These?
Hi Bob!
Nice graphs! What program are you using to get those?
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
Re: How Do You Graph These?
hi noelevans,
It's called Geometer's Sketchpad.
It's not free like Geogebra, but has some excellent features.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Re: How Do You Graph These?
That's exactly what I needed! Thanks a million.
I'm just here to get some help with an online math course I'm taking.
Re: How Do You Graph These?
Thanks, Bob
I'll check into it and probably some free ones too.
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
Post reply | {"url":"http://www.mathisfunforum.com/viewtopic.php?pid=228587","timestamp":"2014-04-17T12:49:09Z","content_type":null,"content_length":"36289","record_id":"<urn:uuid:d5a57ad9-d967-4b8b-84f9-0c5bb25e26ff>","cc-path":"CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00385-ip-10-147-4-33.ec2.internal.warc.gz"} |
History of fundamental solutions
up vote 15 down vote favorite
I have a few questions on the history of PDE.
1. Who first wrote down the formula for the solution of the Cauchy problem for the heat equation involving the heat kernel? I have seen it called Poisson's formula. If it is true Poisson has a
formula for each of the heat, wave, and Laplace equations.
2. Who is the discoverer of the analogous formula for the wave equation in 2 and 3 dimensions? I have seen they were called both Kirchhoff's formula and Poisson's formula.
3. Is there a book to look up such questions? I have Dieudonne's History of functional analysis, but it does not have much on PDEs other than the Laplace equation.
ho.history-overview ap.analysis-of-pdes
1 I would have a look at Jahnke (ed.): A history of analysis, ams.org/bookstore-getitem/item=hmath-24 The answer may not be there, but it is a good source and you will find the right references. –
András Bátkai Aug 31 '11 at 7:46
1 For question 3: I don't know of any comprehensive book on the history of PDEs. It is such a diverse subject. The best way I think is to ask some experts about what historical texts/papers may have
citations to the original papers, and start doing a literature search based on that. Another resource is the Springer EOM. It doesn't always have the primary (in terms of historical primacy)
references, but it usually provides enough citation information that digging down a few levels you can probably find the "first" paper. – Willie Wong Aug 31 '11 at 12:05
1 For question 1, it is not inconceivable that Poisson had a formula for the solution of the heat equation. After all, one of the treatises which he didn't quit finish writing at the time of his
death is a mathematical theory of heat. One should also note that he and Fourier are contemporaries. – Willie Wong Aug 31 '11 at 12:31
add comment
3 Answers
active oldest votes
Question 2 is getting clearer now. My sources are Parseval's article from 1800, Poisson's memoire from 1819, Hadamard's Lectures on Cauchy's Problem in Linear Partial Differential Equations
(1923), and Baker and Copson's The Mathematical Theory of Huygens' Principle (1939).
On page 133 of the afore-mentioned memoire, Poisson gives the 3-dimensional formula
$$ u(x,t) = t M_{x,t}u_0 + \partial_t (t M_{x,t}u_1); \qquad u_0(x) := u(x,0), \quad u_1(x) := \partial_tu(x,0), $$
where $M_{x,t}g$ is the average of $g$ (defined in $\mathbb{R}^3$) over the sphere centred at $x$ of radius $t$. Then he goes on to prove it, and by the method of descent, derives several
special cases, including the 1 and 2 dimensional formulas. So the 3D case is due to Poisson.
Later in 1882, Kirchhoff published a more general formula expressing $u(x,t)$ in terms of the values, the normal and time derivatives of $u$ over an arbitrary closed surface containing $x$,
up vote 7 therefore mathematically justifying the Huygens principle. The analogue of Kirchhoff's 1882 formula for 2 dimensions was published by Volterra in 1894. These developments were closely
down vote related to the discoveries of fundamental solutions of the Helmholtz equation in 3 dimensions by Helmholtz in 1859, and for 2 dimensions by Weber in 1869.
As for who was the first to discover the 2 dimensional analogue of Poisson's 1819 formula, when he coins the term "method of descent", Hadamard notes
Creating a phrase for an idea which is merely childish and has been used since the very first steps of the theory is, I must confess, rather ambitious;
and cites Parseval's afore-mentioned article of 1800, Poisson's memoir of 1819, and Duhem's book from 1891. After giving the 2D formula on page 141 of his memoir, Poisson cites Parseval's
article, and says something like "Parseval previously integrated this equation but in a less simple way". Parseval seems to give the formula on page 519 of his article, but I don't
understand sufficiently to say the formula is complete. In particular there seem to be no explicit formulas for the quantities Q and Q'. So the 2D case can be said due to Parseval-Poisson.
2 Ah, so the method of spherical means is due to Poisson! That is going into my reference database. Awesome detective work there. – Willie Wong Sep 3 '11 at 15:21
1 Your answer probably also answers the case for the heat equation! On page 143 he starts to treat the Heat equation. The equation on the bottom of page 145 is the heat kernel! – Willie
Wong Sep 3 '11 at 15:35
1 One last remark: I just skimmed through Poisson's memoire. There is no mention in the text of any inhomogeneous equations. He only considered, as far as I can tell, homogeneous second
order PDEs with constant coefficients. In particular there is no mention of Duhamel's/Huygens' principles. Is Kirchhoff actually the first one to deal with the inhomogeneous terms? (For
the inhomogeneous heat equation, I think Duhamel was the first to extend the solution from the homogeneous case.) – Willie Wong Sep 3 '11 at 15:44
1 Your link to Parseval's "article" looks like it is actually a book by Lacroix? (Though it is stated that the method is due to Parseval.) On page 528 of the book, amazingly we also can
find the solution to the homogeneous wave equation via Fourier transform. – Willie Wong Sep 3 '11 at 16:00
About inhomogeneous case, it appears Kirchhoff was the first. And about the Lacroix's book, my understanding was that the book is essentially a collection of material written by many
different people on Lacroix's request. – timur Sep 3 '11 at 22:32
show 2 more comments
Concerning question 2: Lars Garding credits G.Tedone, in a 1898 paper in the first volume of (the third series of) Annali di Matematica, for the general solution formula for the wave
up vote 5 equation. Also Hadamard calls it Tedone's formula.
down vote
I don't read German well, and Italian not at all, but I think depending on what exact form of the formula one is interested in, a case can be made for either Kirchoff or Tedone.
1 Kirchoff's paper is at least as early as 1882: emis.de/cgi-bin/JFM-item?14.0829.02 While I haven't been able to find Tedone's 1889 paper (it is not in ZBMath or MathSciNet), but I could
find a 1896 paper of Tedone's, which the Reviewer claims to provide a "more general formula then the Huygen's principle of Kirchhoff" emis.de/cgi-bin/JFM-item?27.0702.02 – Willie Wong
Aug 31 '11 at 10:52
1 The association with Poisson, however, I am pretty sure is because that the time-independent case of the wave equation reduces to the Poisson equation, and formally the time-independent
reduction of the Kirchhoff formula gives the same as the Poisson integral. Insofar as the name "Kirchhoff" is concerned, there may also be a citation to the correct paper of Kirchhoff in
Sobolev's paper of 1933, but I can't find a copy handy to check. Sobolev's paper is zentralblatt-math.org/zmath/en/advanced/?q=an:0008.20805 – Willie Wong Aug 31 '11 at 11:15
1 Ah, the Annali paper is actually from 1898. @Piero: I hope you don't mind me correcting that and giving the ZBMath link. – Willie Wong Aug 31 '11 at 12:01
1 @timur: of course it depens what you mean by 'derive'. You can write the solution using Fourier transform, so the fundamental solution is just the Fourier transform of say $cos(t∣\xi∣∣)
$, which can be computed via complex analytic methods. By the way, I believed you were asking about the higher dimensional case; I was so convinced that Kirchhoff solved the 3D case that
it did not occur to me you might be asking for that case. – Piero D'Ancona Aug 31 '11 at 17:28
1 On the other hand, ... Hadamard attributes the 3D case to Poisson 1819, and it seems what Kirchhoff did was the inhomogeneous case. Now I am in the the same state I started. – timur Sep
2 '11 at 12:09
show 4 more comments
This is an update on Question 1. As Willie observed, in his 1819 memoir Poisson studies not only the wave equation but also the heat equation from page 143 on, and reaches the heat kernel on
page 145. However, amazingly, in Fourier's original memoir where he derived the heat equation and gave a convincing case for the importance of trigonometric series, the heat kernel appears on
page 454 for 1D, on page 475 for 1D in the usual form as presented today, and on page 479 for 3D. Fourier's memoir was published in 1822 after a long delay, and it is said that the memoir is
essentially Fourier's 1811 work that won a mathematical prize, which was in turn a continuation of his work presented in 1807, and summarized by Poisson in 1808. That said, even more
amazingly, a new player appears in the story. After giving the 1D heat kernel on page 454, Fourier says something like
up vote This integral, which contains an arbitrary function, was not known when we started our research on the theory of heat, which were presented at the Institute of France in December 1807. It
2 down was given by Mr. Laplace, in volume VI of des Mémoires de l'école polytechnique, and we have only applied his results here.
Poisson also mentions Laplace on page 148, and says that his 3D result was a straightforward extension of Laplace's formula. I found volume 6 of Journal de l'école polytechnique but there is
nothing by Laplace, and moreover the journal is from 1806. I wondered if des Mémoires is different than Journal, but skimmed through Fourier's book to find that on page 513 he cites Laplace
again, but now says volume 8. Then volume 8 it is! It is published in 1809, and the heat kernel appears on its page 241!
add comment
Not the answer you're looking for? Browse other questions tagged ho.history-overview ap.analysis-of-pdes or ask your own question. | {"url":"http://mathoverflow.net/questions/74136/history-of-fundamental-solutions/74142","timestamp":"2014-04-21T09:49:46Z","content_type":null,"content_length":"82853","record_id":"<urn:uuid:24934762-24b5-4f7b-98ef-26fe5dc47cd1>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00255-ip-10-147-4-33.ec2.internal.warc.gz"} |
Requirements for the Doctoral Program in ACO
Course Requirements
The Coordinating Committee for the Ph.D. program in Algorithms, Combinatorics and Optimization has established the following core curriculum. This curriculum is designed to provide students with
significant flexibility in choosing courses, while simultaneously ensuring a solid grounding in the fundamentals of ACO. (Students entering the program prior to Fall 1997 may choose instead to follow
the previous requirements.) More information on specific courses can be found in the home departments: CS, TSB, and Math.
The course requirements for the ACO doctoral program consist of 10 course semesters (counting minis as 1/2 semester): 3 semesters in Mathematics, 3 in Computer Science, and 3 in TSB, plus a semester
of Probability Theory.
CORE COURSE (required of all students):
Discrete Math (21-701)
2 of the following, at least 1 of which must be a starred option:
*Algebra (21-610)
*Real Analysis and Lebesgue Integration (21-620 and 21-621)
Numerical Analysis (21-660)
Methods of Optimization (21-690)
Computer Science:
CORE COURSE (required of all students):
Algorithms (15-750)
2 of the following:
Artificial Intelligence (15-780)
Computer Systems (15-740)
Programming Languages (15-711)
Software Systems (15-712)
Complexity Theory (15-855)
Security and Cryptography (15-827)
Theory of Performance Modeling (15-849)
Algorithms in the Real World (15-853)
Machine Learning Theory (15-859B)
or any course in the 15-85x numbering (upper-level algorithms/theory)
CORE COURSES (required of all students):
One mini: Theory and Algorithms for LP
One mini: Graph theory
One mini: Integer programming
3 minis to be taken from:
Networks and Matchings
Advanced Integer Programming
Convex Polytopes
Advanced Linear Programming
Dynamic Programming
Nonlinear programming
Optimal Control Theory
Approximation Algorithms
Topics in Polyhedral Combinatorics
Packing and Covering
Computational Molecular Biology
Network Design Algorithms
Special Topics in OR
Students are also required to take one of the following courses in Probability Theory:
Probability and Combinatorics (15-8xx)
Probability Theory (21-780)
Probability Theory and Stochastic Processes I (36-753)
In addition, there is a qualifying examination covering the fundamentals of the program; The exam syllabus will take account of the choices of electives made by the particular set of students taking
the exam. This examination will be given at the beginning of the student's fourth semester. Students are expected to have satisfied all course requirements by the end of the sixth semester.
In the event that a student has already mastered the material covered by a required course when entering the program, another course may be substituted with approval from the student's advisor in
consultation with the ACO Coordinating Committee.
Research Requirements
During their residence at Carnegie Mellon, students in the Ph.D. program in Algorithms, Combinatorics and Optimization are expected to participate in the weekly ACO research seminar. Students are
also expected to take advanced courses in the area of their research in addition to the course requirements listed above.
At the end of the third semester (if not earlier), students should choose a faculty member to supervise their research and dissertation. Throughout this period, they will be subject to an annual
review by the ACO faculty. The ACO faculty will judge whether the thesis work is proceeding satisfactorily. Approximately a year before the expected graduation date, students must make a thesis
proposal before a thesis committee, composed of the advisor and two or more faculty members of the student's choosing. The final transition point is the thesis defense, which is presented before the
same committee.
To graduate, students will need some teaching experience, and all students must demonstrate programming skills. (For every student, a faculty member, approved by the student's advisor, would attest
that the student has adequately demonstrated programming skills.)
Back to the ACO home page | {"url":"http://www.cs.cmu.edu/~ACO/reqs.html","timestamp":"2014-04-21T09:48:55Z","content_type":null,"content_length":"5744","record_id":"<urn:uuid:13525bb4-5801-4ce9-9a9c-dac92606299e>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00438-ip-10-147-4-33.ec2.internal.warc.gz"} |
Wen Ching Li Awarded the 2010 Chern Prize in Mathematics
Main Content
20 January 2011 —
Wen Ching (Winnie) Li, a professor of mathematics at Penn State University, has been awarded the 2010 Chern Prize in Mathematics by the International Congress of Chinese Mathematicians for her
outstanding contributions to the field. Established in 2001 in honor of Professor Shing-Shen Chern, one of the greatest geometers and Chinese mathematicians of the twentieth century, the Chern Prize
in Mathematics is presented every three years to mathematicians of Chinese descent who have made exceptional contributions to mathematical research or to public service activities in support of
Li's research focuses on number theory. She studies the theory of automorphic forms and applications of number theory to coding theory and spectral graph theory. In particular, she has applied her
research results in automorphic forms and number theory to construct efficient communication networks called Ramanujan graphs and Ramanujan complexes. Her thesis work on the theory of modular forms
was cited in Andrew Wiles' historical paper in which the 350-year-old unsolved problem -- "Fermat's Last Theorem" -- was proven. In recent years, Li has revitalized the research on a field of
mathematics known as arithmetic of modular forms for noncongruence subgroups.
In addition to her position as professor of mathematics at Penn State, since 2009, Li has been the director of the Taiwan's National Center of Theoretical Sciences -- established by the National
Science Council (NSC) and recognized internationally as a major influence on current mathematical research. Her previous awards and honors include a NSC Distinguished Visiting Chair and a Mathematics
Adjunct Professorship at National Tsing Hua University, Taiwan, from 2009 to 2011; a Mary Lister McCammon Teaching Award in 2008 from Penn State's Department of Mathematics; a Distinguished Visiting
Professorship at National Tsinghua University, Taiwan, in 1999; and an Alfred P. Sloan Fellowship from 1981 to 1983. Li has held numerous other visiting professorships at universities in the United
States and throughout Europe and Asia. In addition, Li has served as editor for several mathematical journals including the Journal of Combinatorics and Number Theory, the International Journal of
Number Theory, Transactions of the American Mathematical Society, and Proceedings of the American Mathematical Society. She has given numerous invited lectures at institutions in the United States
and abroad. In 2011, she will be the honored speaker for the Distinguished Women in Math Lecture Series at the University of Texas at Austin, as well as the Oliver Atkin Memorial Lecture speaker at
the University of Illinois at Chicago.
Before joining the Penn State faculty in 1979, Li was an assistant professor at the University of Illinois at Chicago, a member at the Institute for Advanced Study at Princeton, and a Benjamin Peirce
Assistant Professor at Harvard University.
In 1974, Li received a Ph.D. degree from the University of California at Berkeley. She earned a B.S. degree at National Taiwan University in 1970.
[ K V ]
Document Actions | {"url":"http://science.psu.edu/news-and-events/2011-news/Li1-2011","timestamp":"2014-04-18T13:43:11Z","content_type":null,"content_length":"46955","record_id":"<urn:uuid:96974c92-bcdc-49c4-abec-88c40900db2a>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00298-ip-10-147-4-33.ec2.internal.warc.gz"} |
Einstein's Sphere
Einstein's Sphere
Everyone should read a book called "RELATIVITY: A Simple Explanation that Anyone Can Understand" by Albert Einstein. No one understood the subject better than Einstein himself. He used methods, like
imaginary time, that have been abandoned by today's "relativity" books. In paperback this book is also much less expensive than the heavy book the college forced you to buy! In his writings, Einstein
even mentioned changing the speed of light.
In Chapter 31 Einstein attempts to imagine an entire Universe! Like Pythagoras 2500 years before, Einstein is motivated by a search for harmony. He follows what would be called the Cosmological
Principle: The Universe looks the same no matter what direction one looks, and every bit resembles every other bit. He rejects a flat Universe, for his General Relativity shows that Space/Time is
curved. He rejects the idea of boundaries and considers the Universe “finite yet unbounded”. The obvious analogy is a sphere.
This 4-dimensional spherical Space has a finite volume given by:
V = 2 $\pi$^2 R^3
Where R is radius, with dimensions of length. (If anyone can't abide by this, please complain to Einstein.)
Here Einstein found a conflict. The very gravity which causes Space/Time to be curved would cause the sphere to collapse. Here we could add, "Unless it were already expanding." An expanding Universe
it would have been one of history's great predictions. Instead Einstein introduced a fudge factor, a repulsive "cosmological constant" preventing the Universe from collapsing. When Edwin Hubble's
observations showed that the Universe is expanding, Einstein would call the cosmological constant his greatest blunder.
We can express the expanding Universe simply:
R = ct
Again R has dimensions of length and c has dimensions of distance/time. For an expanding Universe, it is axiomatic that R is some multiple of t.
The Universe can't expand at the same rate c forever, for gravity slows it down. We do some math and get:
GM = tc^3
Where GM combines mass of the Universe with its gravitational constant.
Together these simple expressions form a solution to the Einstein-Friedmann equations with stable density:
$\rho$f = (6 $\pi$ G t^2)^{-1}
Here we encounter an interesting difference. If an initial mass M is distributed among this spherical volume V, we get an initial density $\rho$i of:
$\rho$i = M/V where M = (tc^3)/G
$\rho$i = (2 $\pi$G t^2)^{-1}
In addition to expanding and slowing the Universe, GM = tc^3 drives it toward the stable density.
The difference is made up by the matter we are made of. When the Universe is "underweight," quantum mechanics predicts that matter will appear via pair production. The amount of this matter is the
difference between $\rho$i and $\rho$f, or 4.507034%. This unique prediction is precisely matched by the Wilkinson Microwave Anistropy Probe.
Albrecht/Maguiejo paper
can be a help here. Refer to their equation (10). Here R (not a) is scale and e is the deviation from critical density.
e = $\Omega$ - 1
edot = (1 + e)e(Rdot/R)(1 + 3w) + 2(cdot/c)e
Now we have w = 0,
(Rdot/R) = (2/3t) and (cdot/c) = (-1/3t)
edot = e^2 (2/3t)
Is it not reassuring that the other terms cancel? When t is low e is large and a large edot drives density toward a critical value. Today, when t is billions of years and e is very nearly zero,
little mass is being created. Just as scale R began in a Bang and has been slowing since, the amount of mass creation has also been slowing and is now nearly zero.
Can you believe some people act as if this isn't a Theory? It is painful to say that new ideas take time for scientists to figure out. Papers on this subject (including Albrecht and Maguiejo's) face
great difficulties in publishing. Arthur Eddington joked in the 1920's that only 3 people understood Relativity, though he couldn't think of the third one! We are doing much better.
Labels: cosmology
12 Comments:
nige said...
This comment has been removed by the author.
"quantum mechanics predicts that matter will appear via pair production."
Do you mean matter-antimatter?
That's obviously what is meant because that's Dirac's prediction from the spinor of his famous equation. He had to modify the Hamiltonian and one consequence is antimatter.
It was Schwinger, however, who found that pair production occurs spontaneously in the vacuum if the electric field strength exceeds a threshold of 1.3*10^18 volts/metre. See equation 359 in
Dyson's 1951 Lectures on Advanced Quantum Mechanics, Second Edition, http://arxiv.org/abs/quant-ph/0608140, or equation 8.20 of Luis Alvarez-Gaume and Miguel A. Vazquez-Mozo, Introductory
Lectures on Quantum Field Theory, http://arxiv.org/abs/hep-th/0510040
One thing that really annoys me about popular books on the subject is that they claim - falsely - that pairs of fermions are constantly popping into existence and annihilating everywhere in the
vacuum, without limit.
Actually, that only occurs with a distance of 32.953 fm from an electron (see http://nige.wordpress.com/2007/06/13/
feynman-diagrams-in-loop-quantum-gravity-path-integrals-and-the-relationship-of-leptons-to-quarks/ ).
So all those physicists who state that the entire vacuum is a seething foam of Heisenberg-formula controlled pair-production and annihilation (i.e., looped Feynman diagrams), are talking out of
their hats.
It's been known for over fifty years that there is a cut-off on the pair production. It's pair production that allows pairs of short-lived (virtual) fermions to become briefly polarized in a
field, which opposes and partially the primary electric field, thereby explaining physically the reason for electric charge renormalization.
If pair-production occurred throughout the vacuum, there would be no infrared cutoff on the low-energy range for running couplings, and the observable electric charge would get for ever smaller
as you got further from an electron. This doesn't happen, proving that pair production-annihilation certainly doesn't occur everywhere in the vacuum.
Hi Louise,
Sorry for the first comment I made about curved spacetime, which on re-reading was so awfully written.
I made a comment somewhere else at about the same time on Sunday and offended someone there, and I'm sorry for the tacky comment about curvature I also made here.
Nige's comments are thoughtful and always welcome. Matter seems to have been favoured over antimatter, something which I am working on all the time.
This hypothesis has some testable predictions. An easy one is the net mass of the observable universe. plugging in 13.7B years for time and accepted values for G and C, I get M of 1.75*10^53. The
exact value of M isn't determined to any precision, but based on a quick check, http://en.wikipedia.org/wiki/Observable_universe , the calculated value is within reason.
Now I understand. However, the equation ρi = (2 πG t^2)^{-1} needs to have the pi squared. Then the 4.5% follows.
I've been looking for info on Einstein's Sphere and luckily I ran into your blog, it has great info on what I'm looking and is going to be quite useful for the paper I'm working on.
BTW is crazy how many generic viagra blogs I manage to dodge in order to get the right site and the right information.
Thanks for the post and have a nice day
Hello, i need more information about this topic, please send me the info by email.
Hello! Just wanted to say that you have one of the nicest and the most interesting blogs I've ever seen in my life! Good luck!
No, there is a hemisphere cap to the cylinder, since it was removed from the sphere. Easiest way would be to drop it in a bucket of water with known volume and markings, then find the difference
in the water levels.
Discount UGG Boots Yinbai laugh, "Jade knows signature, has been very good."
cheapest uggs ever Look at the situation, the three of them among the Miao Hong best adapt to the new environment. lj43vuh
ugg kenly black Of course, to where I did not forget to leave the audio, so the family at ease, you never know what is urgent.
ugg discounts Ashamed of his mind, how to brazenly stare at his girlfriend's sister, when a people is a mass of ice cream, or how.
www.uggsaustralia.me.uk Hanming Sheng said: "Come on, I send you home."
Links to this post: | {"url":"http://riofriospacetime.blogspot.com/2008/05/einsteins-sphere.html","timestamp":"2014-04-19T04:20:17Z","content_type":null,"content_length":"39305","record_id":"<urn:uuid:8417069e-c498-4386-897f-ca81783ad0fe>","cc-path":"CC-MAIN-2014-15/segments/1398223206770.7/warc/CC-MAIN-20140423032006-00222-ip-10-147-4-33.ec2.internal.warc.gz"} |
What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows
look like in the future? Why do soap bubbles have a shape that gives them the least area?
By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works
at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval
writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more.
Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot.
Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, When Least Is Best is full of fascinating examples and ready-to-try-at-home experiments.
This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics.
"This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . [Nahin shows]
obvious delight and enjoyment--he is having fun and it is contagious."--Bonnie Shulman, MAA Online
"When Least is Best is clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of
problems associated with optimization."--Dennis S. Bernstein, IEEE Control Systems Magazine
"[When Least is Best is] a wonderful sourcebook from projects and is just plain fun to read."--Choice
"This book is highly recommended."--Clark Kimberling, Mathematical Intelligener
"A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia."--D.R. Wilkins, Contemporary Physics
"Nahin delivers maximal mathematical enjoyment with minimal perplexity and boredom. . . . [He lets] general readers in on the thrill of riding high-school geometry and algebra to breakthrough
insights. . . . A refreshingly lucid and humanizing approach to mathematics."--Booklist
"Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book. His enthusiasm is infectious, his writing
style is active and fluid, and his examples always have a point. . . . [H]e loves to tell stories, so even the familiar is enjoyably refreshed."--Donald R. Sherbert, SIAM Review
"This is a delightful account of how the concepts of maxima, minima, and differentiation evolved with time. The level of mathematical sophistication is neither abstract nor superficial and it should
appeal to a wide audience."--Ali H. Sayed, University of California, Los Angeles
More Endorsements
Table of Contents
This book has been translated into:
• Japanese
• Korean
Other Princeton books authored or coauthored by Paul J. Nahin:
Subject Areas: | {"url":"http://press.princeton.edu/titles/7590.html","timestamp":"2014-04-19T11:58:36Z","content_type":null,"content_length":"20670","record_id":"<urn:uuid:70df4757-af85-41a5-834c-9de9ac447f0d>","cc-path":"CC-MAIN-2014-15/segments/1398223206647.11/warc/CC-MAIN-20140423032006-00369-ip-10-147-4-33.ec2.internal.warc.gz"} |
Key Validation Scheme
Patent application title: Key Validation Scheme
Inventors: Donald B. Johnson (Manassas, VA, US) Donald B. Johnson (Manassas, VA, US)
IPC8 Class: AH04L900FI
USPC Class: 380277
Class name: Cryptography key management
Publication date: 2012-01-19
Patent application number: 20120014523
Sign up to receive free email alerts when patent applications with chosen keywords are published SIGN UP
A system and method for validating digital information transmitted by one correspondent to another in a data communication system. The method comprising the steps of generating a public key in
accordance with a predetermined, generating a public key in accordance with a predetermined cryptographic scheme having predetermined arithmetic properties and system parameters. The verifying said
public key conforms to said arithmetic properties of said scheme, transmitting said verified public key to a recipient.
A method performed at an entity for validation of a public key, the public key for use in a communication system, the method comprising: obtaining the public key; and verifying that the public key is
a point on an elliptic curve defined over a finite field.
The method of claim 1, wherein the verifying comprises a substitution of the public key into an equation defining the elliptic curve.
The method of claim 1, wherein the entity is a correspondent device.
The method of claim 1, wherein the elliptic curve is defined by system parameters associated with the communication system.
The method of claim 4, further comprising obtaining a validation of at least one of the system parameters associated with the communication system.
The method of claim 1, wherein the verifying comprises receiving from another entity, an indication of a verification that the public key is a point on the elliptic curve.
The method of claim 1, further comprising providing to another entity, an indication of a verification that the public key is a point on the elliptic curve.
The method of claim 1, further comprising performing a cryptographic operation associated with the public key.
The method of claim 8, wherein the cryptographic operation is a verification of a signature.
The method of claim 8, wherein the cryptographic operation is associated with a key agreement scheme.
The method of claim 1, wherein obtaining the public key comprises receiving the public key.
The method of claim 1, wherein the entity is a certification authority.
The method of claim 6, wherein the other entity is a certification authority.
The method of claim 1, wherein the elliptic curve is of prime order.
The method of claim 8, wherein the cryptographic operation utilizes the public key in combination with a symmetric key.
The method of claim 15, wherein the cryptographic operation comprises enciphering the symmetric key with the public key.
A non-transitory computer-readable medium comprising instructions that are operable when executed by data processing apparatus to perform operations for validation of a public key, the public key for
use in a communication system, the operations comprising: obtaining the public key; and verifying that the public key is a point on an elliptic curve defined over a finite field.
The computer-readable medium of claim 17, wherein the verifying comprises a substitution of the public key into an equation defining the elliptic curve.
The computer-readable medium of claim 17, wherein the elliptic curve is defined by system parameters associated with the communication system.
The computer-readable medium of claim 17, wherein the verifying comprises receiving from another entity, an indication of a verification that the public key is a point on the elliptic curve.
The computer-readable medium of claim 17, the operations further comprising providing to another entity, an indication of a verification that the public key is a point on the elliptic curve.
The computer-readable medium of claim 17, the operations further comprising performing a cryptographic operation associated with the public key.
A computing device comprising data processing apparatus operable to perform operations for validation of a public key, the public key for use in a communication system, the operations comprising:
obtaining the public key; and verifying that the public key is a point on an elliptic curve defined over a finite field.
The computing device of claim 23, wherein the computing device is a correspondent device.
The computing device of claim 23, wherein the computing device is a certification authority device.
The computing device of claim 23, wherein the verifying comprises a substitution of the public key into an equation defining the elliptic curve.
The computing device of claim 23, wherein the elliptic curve is defined by system parameters associated with the communication system.
The computing device of claim 23, wherein the verifying comprises receiving from another entity, an indication of a verification that the public key is a point on the elliptic curve.
The computing device of claim 23, the operations further comprising providing to another entity, an indication of a verification that the public key is a point on the elliptic curve.
The computing device of claim 23, the operations further comprising performing a cryptographic operation associated with the public key.
CROSS REFERENCE TO RELATED APPLICATIONS [0001]
This application is a continuation of U.S. patent application Ser. No. 11/705,020, filed Feb. 12, 2007, which is a continuation of U.S. patent application Ser. No. 10/181,356, filed on Jul. 17, 2002
which is a national entry of PCT Application No. PCT/CA98/00959 filed on Oct. 14, 1998, which claims priority to U.S. application Ser. No. 08/949,781 filed on Oct. 14, 1997, wherein the contents of
each are hereby incorporated by reference.
The present invention relates to secure communication systems and in particular to schemes for validating parameters and keys in such systems.
BACKGROUND OF THE INVENTION [0003]
Secure data communications systems are used to transfer information between a pair of correspondents. At least part of the information that is exchanged is enciphered by a predetermined mathematical
operation by the sender. The recipient may then perform a complimentary mathematical operation to decipher the information. For public key or symmetric key systems, there are certain parameters that
must be known beforehand between the correspondents. For example, various schemes and protocols have been devised to validate the senders public key, the identity of the sender and the like. The
security or validity of these systems is dependent on whether the signature is a valid signature and this is only the case if system parameters if any are valid, the public key is valid and the
signature verifies. Furthermore, an asymmetric system is secure only if system parameters if any are valid, the enciphering public key is valid, the symmetric key is formatted as specified and the
symmetric key recovery checks for format validity.
On the other hand a key agreement protocol is secure only if the system parameters, if any, are valid, the key agreement public keys are valid, and the shared secret and symmetric key is derived as
specified in a standard. In all of these it is assumed that the public key or symmetric key, i.e., the shared secret, is derived and valid as specified in the protocol scheme. Problems, however, will
arise if these parameters are either bogus or defective in some way.
The following scenarios may illustrate the implications of a defect in one or more parameters of a public key cryptographic system. For example digital signatures are used to indicate the
authenticity of a sender. Thus if a Recipient A receives a certified public key from a Sender B, then A verifies the certificate, next B sends A a signed message for which A is able to verify the
signature and thus assume that further communication is acceptable. In this scenario, however, if B has deliberately corrupted the public key then the Recipient A has no way of distinguishing this
invalid public key. Similarly, a Participant C generates a key pair and then subsequently receives a public key certificate, the Participant C then sends the certificate and a subsequent signed
message to B under the assumption that the public key contained in the certificate is valid. The participant B can then determine key information for C. Both the above scenarios describe possible
problems arising from utilizing unauthenticated parameters in signature verification.
In key transport protocols a Correspondent A may inadvertently send its symmetric key to the wrong party. For example, if Correspondent A receives a certified public key from a Sender B, the
certificate is verified by A who then sends a public key enciphered
symmetric key and a symmetric key enciphered message to B, thus A is compromised. Conversely, if one of the correspondents C generates a key pair and gets a public key certificate which is
subsequently sent to A who public key enciphers a symmetric key and message and sends it back to C, thus, in this case, C is compromised.
In key agreement protocols, one of the correspondents, A for example, receives a certified public key from B and sends B A's certified public key. Each of A and B verify the other's certificate and
agree upon a symmetric key. In this scenario A is compromised twice.
It may be seen from the above scenarios that although public key systems are secure the security of the system relies to a large extent on one or both of the correspondents relying on the fact that a
claimed given key is in fact the given key for the particular algorithm being used. Typically the recipients receive a string of bits and then make the assumption that this string of bits really
represents a key as claimed. This is particularly a problem for a symmetric key system where typically any bit string of the right size may be interpreted as a key. If a bit in the key is flipped, it
may still be interpreted as a key, and may still produce a valid crypto operation except that it is the wrong key.
In an asymmetric private key system the owner of the private key knows everything about the private key and hence can validate the private key for correctness. However, should a third party send the
owner system a public key, a question arises as to whether the received key conforms to the arithmetic requirements for a public key or the operations using the claimed public key is a secure crypto
operation. Unless the owner system performs a check it is unlikely to know for certain and then only by the owner.
From the above it may be seen that key establishment may be insecure. In a paper written by Lim and Lee presented at Crypto '97, this problem was demonstrated in context of the Diffie-Heliman scheme
using a bogus public key that did not have the correct order and thus one party was able to find information about the other party's private key. In the RSA or Rabin scheme, which gets its security
from the difficulty of factoring large numbers, the public and private keys are functions of a pair of large prime numbers. The keys are generated from the product of two random large prime numbers.
Suppose, however, that n is a prime instead of the products of two primes then phi(n)=n-1 so anyone can determine d from the bogus "public key" (n, e). These are just examples of the problems a user
of a public key can get into if they cannot validate the arithmetic properties of a claimed public key for conformance with the requirements of the algorithm.
SUMMARY OF THE INVENTION [0012]
This invention seeks to provide an improved validation in a secure communication system. Furthermore the invention seeks to allow such a validation to be performed by anyone at anytime using only
public information.
In accordance with this invention there is provided a method of validating digital signatures in a public key communication system, said method comprising the steps of:
verifying the arithmetic property the public key conforms to the system algorithm; and
verifying said digital signature.
A further step provides for the verification of the system parameters.
A still further step provides for including within a certificate information indicative of the claimed public key having been validated for arithmetic conformance with the algorithm and, where
appropriate, the amount of validation performed.
BRIEF DESCRIPTION OF THE DRAWINGS [0018]
Embodiments of the present invention will now be described by way of example only with reference the accompanying drawings in which:
FIG. 1 is a schematic representation of a communication system.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT [0020]
Referring to FIG. 1 a data communication system 10 includes a pair of correspondents designated as a sender 12 and a recipient 14 who are connected by communication channel 16. Each of the
correspondents 12, 14 includes an encryption unit 18, respectively that may process digital information and prepare it for transmission through the channel 16. In addition the system 10 may include a
certification authority 22.
Embodiments of the invention shall be described with reference to the following aspects of public key algorithms. Key agreement has six routines which are defined as system parameter generation,
system parameter validation, key pair generation, public key validation, shared secret derivation and symmetric key derivation. In the key validation step, anyone at anytime can validate a public key
using only public information. These routines validate the range and order of the public key. If a public key validates, it means that an associated private key can logically exist, although it does
not prove it actually does exist.
For an elliptic curve Digital Signature Algorithm (ECDSA) there are also six routines, defined as system parameter generation, system parameter validation, key pair generation, public key validation,
signature generation and signature verification. On the other hand a first type of DSA has four routines, namely system parameter generation, key pair generation, signature generation and signature
verification. In a more recent DSA has five routines, namely, system parameter generation, (implicit) system parameter validation, key pair generation, signature generation and signature
verification. In order to provide key validation the DSA parameters p, q and g are assumed to have already been validated. The public key=g
mod p, where x is the private key. The range of y is validated to ensure 1<y<p and the order of y is validated to ensure y
mod p=1. These tests ensure that a claimed DSA public key meets the arithmetic requirements of such a key. They can be performed by anyone at anytime using only public information.
In RSA or Rabin signatures there are generally three routines, namely key pair generation, signature generation and signature verification. Validating an RSA public key (n, e) involves three steps.
Firstly validate e, secondly validate n and thirdly validate e and n are consistent with each other. In order to validate the public exponent e, use of made of the fact that the exponent 2<=e<.=
2.sup.(k-160) where k is the length of the modulus n. The requirement that this range be as it is specified is specifically to allow this check. If e>2 then e should be odd. Furthermore, if for a
closed network, it is known that the public exponent e must all meet other criteria, e.g., it must be =3 or 65537 or be a random number larger than 65537, these checks can also be done to further
confirm the validity of the key. These checks may be incorporated as part of the specification of an RSA public key partial validation routine. Even though the above test for e appears trivial, this
test ensures that e was selected before d as intended by the RSA/Rabin algorithm since, it may be shown that de=1 mod (lcm(p-1,q-1) and there are at least 160 high order zeroes in e when compared
with modulus n, and this is infeasible to achieve by selecting d first.
In order to validate the modulus n, the sizes of n may be determined. It is known that n is supposed to contain exactly (1,024 plus 128 s) bits, where s=0, 1, 2, 3 . . . etc. This can be easily
validated and can be part of a partial key validation. Determining whether the modulus n is odd given that n is supposed to be the product of two primes and that all primes after 2 are odd may
perform a further validation of the modulus n. Therefore the product of odd numbers is odd so n should be odd. Furthermore, for Rabin when e=2 we know p should be equal to 3 mod n and q should be 7
mod 8. This means n=pq should be =21 mod 8=5 mod 8. This can be validated by ensuring that if e=2, then n=5 mod 8. Furthermore, we know n should not be a perfect power thus this ensures there be two
distinctive prime factors and this can be validated by a simple check as documented in the Handbook of Applied Cryptography by Menezes, van Oorschot, and Vanstone.
It is also known that n should be a composite number thus if n is prime the transformation is easily invertible and hence is completely insecure. The fact that n should be composite can be validated
by running the Miller-Rabin probable prime test expecting it to actually prove that n is composite. An additional test for validating the modulus n is based on knowing that n is supposed to be the
product of two large primes and is supposed to be hard to factor. Therefore attempt to factor it in some simple way, expecting it to fail. For example calculate GCD (n, i) where i runs through all
the small odd primes up to a certain limit, say the first 50K odd primes.
From the previous two tests above, it may be seen from the former that at least one factor must be of a size of half the bits of the modulus or less. From the latter it may be seen that each factor
must be larger than the largest prime tested. Furthermore there are now only a limited number of potential factors (p, q, r, . . . ) depending on the size of the largest prime test.
The multiple tests above in combination have a synergistic effect. The goal of which is to greatly reduce the freedom of action of an adversary. Even if an attack is not totally impossible, partial
key validation can make an attack much more difficult, hopefully infeasible or at least uneconomical.
Furthermore in validating the modulus n, p and q are not supposed to be too close in value therefore assume they are and try to factor n. Use the square root of n as a starting guess for p and q.
Then let p decrease while q increases and determine if n can be factored up to a predetermined limit. Furthermore we know for a set of RSA moduli, no prime should repeat therefore given a set of RSA
moduli n1, n2 the GCD (ni, nj) can be calculated to ensure the results all equal one.
Offline tests as described above have their limitations. These tests may be extended since the owner of the parameters knows particular information, for example the factorization of n. Thus the owner
may be used as an online oracle. By determining if the answers to these questions asked of the oracle are incorrect anyone may declare public key invalid.
It is shown in the Handbook of Applied Cryptography Vanstone et. al. That the owner can take square roots mod n, but others cannot. The validater can determine if a random number mod n has a Jacobi
symbol 1 or -1, then half are 1 and the other half are -1. If 1, then number is either a square or not a square, again half each. Validater can square a number mod n. A square always has Jacobi
The validater selects either a known square u or a random element r with Jacobi symbol=1. Asks owner "If this is a square?" for these two types of elements. The owner responds either Yes or No. If u
was selected, the owner must say Yes, else key modulus is invalid. If r was selected the owner should say Yes about 1/2 the time and No about 1/2 the time, else key modulus is invalid.
This is repeated a number of times to be confident. If the Validater gave the owner all squares, owner should always respond Yes. If the Validater gave the owner all random elements with Jacobi
Symbol=1, owner should respond 1/2 of the time Yes and 1/2 of the time No. Owner of bogus key only knows that at least half the answers should be Yes. However, owner of the private key knows the
factorization of n, they know the squares and thus just need to lie about the pseudosquares, saying some are squares, in order to fool the validater. What is needed is a way for the validater to ask
the "Is this a square?" question using a known pseudosquare. Normally, determining if a number is a pseudosquare for a given modulus without knowing the factorization of the modulus is an infeasible
problem, however, the owner must respond to the above noted questions with an answer that says that some of the Jacobi=1 numbers are pseudosquares. The validater can form arbitrary known
pseudosquares by multiplying a known pseudosquare by a square modulo the modulus. The result will be a value that the validater knows is a pseudosquare. This third type of value t (known
pseudosquare) can be asked of the owner and now likes by the owner saying that some pseudosquares are squares can be detected by the validater.
In order to validate e and n together GCD (e, p-1)=1 and GCD (e, q-1)=1. If e is odd, we know p should not be of form xe+1 for some integer x and q should not be of form ye+1 for some integer y. If
both p and q are bad then n should not be of form xye
+xe+ye+1 and n≠mod e.
A further method of validating e and n together. It is known that the GCD(e,phi(n)) should be 1. If it is known that phi (n)=(p-1)(q-1), then this is two equations in two unknowns and therefore the
validater can factor n.
Assuming the other requirements on a key pair are met, the reason GCD (e,phi(n))=1 is needed is to ensure the operation using e is a one-to-one (invertible) function. Else, the operation using e is
many-to-one. If the operation using is many-to-one then d (the inverse of e) does not exist, at least as normally conceived. The owner should give evidence that d actually exists, but the question
should not be under the private key owner's control, that is, a self-signed certificate request may not be enough evidence.
The challenge can send the claimed owner some dummy messages to sign. The owner of the private key can verify that they are dummy messages, sign them, and return them to the challenger. This is an
online probabilistic oracle test that d exists.
Thus anyone can do offline validation at any time. Anyone can do online validation if owner is online. Owner can do offline and online validation to assure him/herself public key is valid. CA can do
online validation and tell others exactly what and how much it validated in the public key certificate.
In the ECDSA the system parameters are field size q=p or 2
. An optional seed that generates (a, b) with (a, b) defining an elliptic curve other F
, P a distinguished point on the curve, n, the large prime order of P, h, the cofactor such that the order of curve is hn. The field size, EC defined by (a, b) and point P are primary parameters.
It is important to verify not only the EC system parameters but also the EC public key. For example, given an elliptic curve public key Q, check that Q is on E. In key agreement, and utilizing a
prime order curve, then we do not need to check the order of Q since Q certainly has the correct order if it is on the curve. Checking that Q is on the curve is important since an erroneous key may
give away the private key a in computing a Q, if Q is not on the curve. Verifying the public key is on the curve may be achieved by substitution into the curve or testing.
Thus it may be seen that key validation may reduce exposure to attacks and help detect inadvertent errors and is also is a valuable service for a CA to perform. Those of ordinary skill in the art
will appreciate that the above techniques and methods may be implemented on a suitable processor to carry out the steps of the invention. In addition although the various methods described are
conveniently implemented in a general purpose computer selectively activated or reconfigured by software, one of ordinary skill in the art would also recognize that such methods may be carried out in
hardware, in firmware or in more specialized apparatus constructed to perform the required method steps.
Patent applications by Donald B. Johnson, Manassas, VA US
Patent applications in class KEY MANAGEMENT
Patent applications in all subclasses KEY MANAGEMENT
User Contributions:
Comment about this patent or add new information about this topic: | {"url":"http://www.faqs.org/patents/app/20120014523","timestamp":"2014-04-19T19:07:47Z","content_type":null,"content_length":"49868","record_id":"<urn:uuid:9298e531-1b4b-4d10-a521-952cef982dd3>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00566-ip-10-147-4-33.ec2.internal.warc.gz"} |
East Hills, NY Trigonometry Tutor
Find an East Hills, NY Trigonometry Tutor
...In the past, for example, I've drawn pictures, sung songs, broken down information into bullet points, acted it out, made flash cards, and so many more! Whatever works best for the student
works for me. I travel to student's homes (or any other location you prefer) to make the experience as convenient as possible for you.
37 Subjects: including trigonometry, chemistry, physics, calculus
...I have experience volunteering in an elementary school, and I was there to assist the teachers. I escorted the children to the nurse's, bathroom, etc. I also helped the children with their
projects, for example the counting caterpillar.
13 Subjects: including trigonometry, English, Spanish, algebra 2
...Trigonometry at the elementary level is the study of the properties of ratios of side lengths of a right triangle. Some of these properties carry over into general triangles, such as the Law of
Sines and Law of Cosines. The usual trig course covers definitions of sine, cosine, tangent and the basic identities and addition formulas.
19 Subjects: including trigonometry, reading, writing, calculus
...I have had training in Orton-Gillingham, Wilson Reading Method, including Fundations and Simply Words, and Animated Literacy, for writing I turn to the work of Lucy Calkins. In Math I draw a
great deal from the work of Marilyn Burns and also like to use TouchMath with my students. Because I am ...
39 Subjects: including trigonometry, English, reading, ESL/ESOL
...All must cooperate together in order to win and score goals. I was manager of a church soccer team in 2011 and the team made it to the semi-finals and lost due to penalties. Soccer is the sport
that unites all people into one goal.
27 Subjects: including trigonometry, reading, chemistry, Spanish | {"url":"http://www.purplemath.com/East_Hills_NY_Trigonometry_tutors.php","timestamp":"2014-04-16T19:29:28Z","content_type":null,"content_length":"24444","record_id":"<urn:uuid:23572114-9fb0-4a0b-af9f-2a9fd6695087>","cc-path":"CC-MAIN-2014-15/segments/1397609524644.38/warc/CC-MAIN-20140416005204-00554-ip-10-147-4-33.ec2.internal.warc.gz"} |
The Right Amount of Equity to Give Investors
September 18, 2010
Investors will often seek a share of your company in return for crucial start-up funds. But what is a fair percentage?
This article by Paul Graham was accessed by CISCO institute
An investor wants to give you money for a certain percentage of your startup. Should you take it? You're about to hire your first employee. How much stock should you give him?
These are some of the hardest questions founders face. And yet both have the same answer:
1/(1 - n)
Whenever you're trading stock in your company for anything, whether it's money or an employee or a deal with another company, the test for whether to do it is the same. You should give up n% of your
company if what you trade it for improves your average outcome enough that the (100 - n)% you have left is worth more than the whole company was before.
For example, if an investor wants to buy half your company, how much does that investment have to improve your average outcome for you to break even? Obviously it has to double: if you trade half
your company for something that more than doubles the company's average outcome, you're net ahead. You have half as big a share of something worth more than twice as much.
In the general case, if n is the fraction of the company you're giving up, the deal is a good one if it makes the company worth more than 1/(1 - n).
For example, suppose Y Combinator offers to fund you in return for 6% of your company. In this case, n is .06 and 1/(1 - n) is 1.064. So you should take the deal if you believe we can improve your
average outcome by more than 6.4%. If we improve your outcome by 10%, you're net ahead, because the remaining .94 you hold is worth .94 x 1.1 = 1.034. [1]
One of the things the equity equation shows us is that, financially at least, taking money from a top VC firm can be a really good deal. Greg Mcadoo from Sequoia recently said at a YC dinner that
when Sequoia invests alone they like to take about 30% of a company. 1/.7 = 1.43, meaning that deal is worth taking if they can improve your outcome by more than 43%. For the average startup, that
would be an extraordinary bargain. It would improve the average startup's prospects by more than 43% just to be able to say they were funded by Sequoia, even if they never actually got the money.
The reason Sequoia is such a good deal is that the percentage of the company they take is artificially low. They don't even try to get market price for their investment; they limit their holdings to
leave the founders enough stock to feel the company is still theirs.
The catch is that Sequoia gets about 6000 business plans a year and funds about 20 of them, so the odds of getting this great deal are 1 in 300. The companies that make it through are not average
Of course, there are other factors to consider in a VC deal. It's never just a straight trade of money for stock. But if it were, taking money from a top firm would generally be a bargain.
You can use the same formula when giving stock to employees, but it works in the other direction. If i is the average outcome for the company with the addition of some new person, then they're worth
n such that i = 1/(1 - n). Which means n = (i - 1)/i.
For example, suppose you're just two founders and you want to hire an additional hacker who's so good you feel he'll increase the average outcome of the whole company by 20%. n = (1.2 - 1)/1.2 =
.167. So you'll break even if you trade 16.7% of the company for him.
That doesn't mean 16.7% is the right amount of stock to give him. Stock is not the only cost of hiring someone: there's usually salary and overhead as well. And if the company merely breaks even on
the deal, there's no reason to do it.
I think to translate salary and overhead into stock you should multiply the annual rate by about 1.5. Most startups grow fast or die; if you die you don't have to pay the guy, and if you grow fast
you'll be paying next year's salary out of next year's valuation, which should be 3x this year's. If your valuation grows 3x a year, the total cost in stock of a new hire's salary and overhead is 1.5
years' cost at the present valuation. [2]
How much of an additional margin should the company need as the "activation energy" for the deal? Since this is in effect the company's profit on a hire, the market will determine that: if you're a
hot opportunity, you can charge more.
Let's run through an example. Suppose the company wants to make a "profit" of 50% on the new hire mentioned above. So subtract a third from 16.7% and we have 11.1% as his "retail" price. Suppose
further that he's going to cost $60k a year in salary and overhead, x 1.5 = $90k total. If the company's valuation is $2 million, $90k is 4.5%. 11.1% - 4.5% = an offer of 6.6%.
Incidentally, notice how important it is for early employees to take little salary. It comes right out of stock that could otherwise be given to them.
Obviously there is a great deal of play in these numbers. I'm not claiming that stock grants can now be reduced to a formula. Ultimately you always have to guess. But at least know what you're
guessing. If you choose a number based on your gut feel, or a table of typical grant sizes supplied by a VC firm, understand what those are estimates of.
And more generally, when you make any decision involving equity, run it through 1/(1 - n) to see if it makes sense. You should always feel richer after trading equity. If the trade didn't increase
the value of your remaining shares enough to put you net ahead, you wouldn't have (or shouldn't have) done it.
Do you know an entrepreneurial story that needs to be told?
Blog from your Wamda profile or tell us about it at editor@wamda.com
Wamda is a platform that supports and invests in MENA entrepreneurs. | {"url":"http://www.wamda.com/2010/09/the-right-amount-of-equity-to-give-investors","timestamp":"2014-04-18T23:21:01Z","content_type":null,"content_length":"195561","record_id":"<urn:uuid:79059e43-42c2-4e1b-8c39-71b1da6f79b1>","cc-path":"CC-MAIN-2014-15/segments/1397609535535.6/warc/CC-MAIN-20140416005215-00023-ip-10-147-4-33.ec2.internal.warc.gz"} |
Dunstable Calculus Tutor
Find a Dunstable Calculus Tutor
...I also have more than 6 years of experience tutoring mathematics to students ranging from 7 years old through adult learners. I have taught and/or tutored mathematics from basic addition and
subtraction through calculus. I have also helped students prepare for the GED, SAT and MCAS tests in mathematics.
14 Subjects: including calculus, geometry, trigonometry, SAT math
...I used the skills and knowledge I learned in my subsequent high school and college math and science courses, as well as in my 30 year career as an electrical engineer in industry. During my
first few years teaching math at Lowell High School, MA, I taught Algebra II and used its content and skil...
9 Subjects: including calculus, geometry, algebra 1, algebra 2
...I graduated from MIT and am currently working on a start-up part time and at MIT as an instructor. I miss the one-on-one academic environment and am keen to share some of my knowledge. I would
like to teach math (through BC calculus), science (physics, chemistry, biology, environmental), engine...
63 Subjects: including calculus, chemistry, English, writing
...Able to provide solid foundation in mathematics. Experienced teaching all levels of abilities. Able to clearly and patiently explain concepts and methods.
5 Subjects: including calculus, algebra 1, algebra 2, precalculus
...I am also a musician who plays several instruments including guitar, bass, drums, and a little piano. I have 15 years experience playing guitar, 8 years on drums. And, I am also a video editor
and producer who has designed promotional videos for businesses and non-profit organizations.
10 Subjects: including calculus, geometry, algebra 1, algebra 2 | {"url":"http://www.purplemath.com/Dunstable_Calculus_tutors.php","timestamp":"2014-04-20T03:59:25Z","content_type":null,"content_length":"23830","record_id":"<urn:uuid:790fe2f2-f727-4a1c-aaec-36215fd8f6b1>","cc-path":"CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00349-ip-10-147-4-33.ec2.internal.warc.gz"} |
3D Pie Chart
The initial idea was to create a utility class / class library that could be used for drawing 3-D pie charts. At first, this seemed quite simple, since there is a DrawPie method already available in
the Graphics class. This method accepts start angle and sweep angle as arguments, so it should not be a problem to use it: just sum up all values and then calculate the portion for each one,
converting it to sweep angle for the corresponding pie slice. And this works for a circular chart. However, if you want to add 3-D perspective (i.e., if a chart is drawn with an ellipse shape) this
approach will result in an impression of varying values, as demonstrated in the figure below: pie slices at the left and right side appear larger than those up and down, although all of them have the
same sweep angle.
Instead of a direct insertion of the sweep angle, the parametric equation for ellipse has to be used.
The above problem thus solved, adding a real 3-D look to the chart requires only one additional step: drawing a cylinder brink. However, if you want to draw pie slices displaced from the common
center, then the slice cut sides become visible and have to be drawn too. Since these sides may partially overlap, the order of drawing is of utmost importance to obtain the correct 3-D appearance.
First, note that the coordinate system as shown in the figure below is used:
The parametric equation of ellipse has a form of:
x = a * cos(t)
y = b * sin(t)
where a and b are major and minor semi-axis, respectively, and t is a variable parameter. Note that t does not have direct interpretation in terms of an angle but (as anyone familiar with
trigonometry will conclude from the figure below) can be related to the polar angle from the ellipse center as:
angle = tan^-1(y/x) = tan^-1((b * sin(t)) / (a * cos(t)))
Consequently, when initializing individual shapes for rendering, the corresponding start and sweep angles have to be transformed by the following method:
protected float TransformAngle(float angle) {
double x = m_boundingRectangle.Width * Math.Cos(angle * Math.PI / 180);
double y = m_boundingRectangle.Height * Math.Sin(angle * Math.PI / 180);
float result = (float)(Math.Atan2(y, x) * 180 / Math.PI);
if (result < 0)
return result + 360;
return result;
In the above method, m_boundingRectangle is the boundary rectangle of the ellipse from which the pie shape is cut out. The width and height of this rectangle are equal to the major and minor axes of
the ellipse, respectively.
When drawing a 3-D pie slice (with some finite height), it is necessary to draw the slice cut sides as well as the outer periphery of the cylinder from which the slice is cut out. For this, the
center point and the points on the pie slice periphery (m_center, m_pointStart and m_pointEnd private members of the PieSlice class) and their corresponding siblings on the slice bottom side have to
be calculated first. These points are used to constitute GraphicsPaths: paths for cut sides consist of four lines, while the path for the cylinder periphery consists of two vertical lines and two
It is worthy to note that the slice side corresponding to the start angle is visible only when the start angle is larger than 90 and less than 270 degrees, while the side corresponding to the end
angle is visible only when the angle is between 270 and 90 degrees. Also, the cylinder brink is visible only for angles between 0 and 180 degrees.
As already mentioned, the drawing order is important when the chart contains several slices displaced from the center. The pie shape that is crossing the 270 degrees boundary must be drawn first
because it may be (partially) covered by another pie slice. The slice closest to the 270 degrees axis (regardless if it is from the left or the right side) is drawn next, the procedure being repeated
for the slices to follow.
To achieve this order, the pie slices are stored into an array starting with the shape that crosses the 270 degrees axis. Consequently, neighboring shapes will be placed in the second and in the last
position of the array. Therefore, the search for the next shape to be drawn goes from the start and from the end of the list simultaneously, selecting the shape which is closer to the 270 degrees
axis to be drawn first.
Pie slices crossing the 270 degrees axis have a unique feature: both cut sides (corresponding to the start and the end angle) are visible - c.f. figure below left. Moreover, if both the start and the
end angles are within 0 and 180 degrees range, the slice will have its cylinder brink consisting of two parts (figure below right). To handle this, the slice is split into two sub-slices in the
course of drawing, with the common top side.
This splitting comes into play with drawing charts like the one shown below: if the blue slice was drawn first and completely, the green slice would completely overlap it, resulting in an irregular
illusion. The numbers on each shape indicate the correct order of drawing.
Hit Testing
When the first version of the article was published, several readers suggested to add tool tips and pie slice highlighting when the mouse is over it. This feature has been implemented in version 1.1.
The main problem was to find and implement the algorithm that searches for the pie slice currently under the mouse cursor. The search order for the entire chart is the reverse of the drawing order,
starting from the foremost slice. However, processing of individual slices is cumbersome because of their irregular shapes.
To test if a pie is hit, the pie slice shape has to be decomposed into several surfaces as shown on the figure below, and each of these surfaces is tested if it contains the hit point.
Note that the cylinder outer periphery hitting is not tested directly (in fact, I have no idea how it could be done simply), but is covered by testing the top (1) and the bottom (2) pie surfaces and
the quadrilateral defined by the periphery points (3).
Hit testing for the top and bottom slice surfaces is straightforward - the distance of the point from the center of the ellipse is compared to the ellipse radius for the corresponding angle:
private bool PieSliceContainsPoint(PointF point,
float xBoundingRectangle, float yBoundingRectangle,
float widthBoundingRectangle, float heightBoundingRectangle,
float startAngle, float sweepAngle) {
double a = widthBoundingRectangle / 2;
double b = heightBoundingRectangle / 2;
double x = point.X - xBoundingRectangle - a;
double y = point.Y - yBoundingRectangle - b;
double angle = Math.Atan2(y, x);
if (angle < 0)
angle += 2 * Math.PI;
double angleDegrees = angle * 180 / Math.PI;
// point is inside the pie slice only if between start and end angle
if (angleDegrees >= startAngle &&
angleDegrees <= startAngle + sweepAngle) {
// distance of the point from the ellipse centre
double r = Math.Sqrt(y * y + x * x);
double a2 = a * a;
double b2 = b * b;
double cosFi = Math.Cos(angle);
double sinFi = Math.Sin(angle);
// distance of the ellipse perimeter point
double ellipseRadius =
(b * a) / Math.Sqrt(b2 * cosFi * cosFi + a2 * sinFi * sinFi);
return ellipseRadius > r;
return false;
For quadrilaterals, a well know algorithm for testing if a point is inside a polygon is used: a ray is traced from the point to test and the number of intersections of this ray with the polygon is
counted. If the number is odd, the point is inside the polygon, if it is even, the point is outside (c.f. figure below).
Consequently, all polygon sections are passed, counting intersections with the ray:
public bool Contains(PointF point, PointF[] cornerPoints) {
int intersections = 0;
float x0 = point.X;
float y0 = point.Y;
for (int i = 1; i < cornerPoints.Length; ++i) {
if (DoesIntersect(point, cornerPoints[i], cornerPoints[i - 1]))
if (DoesIntersect(point, cornerPoints[cornerPoints.Length - 1],
return (intersections % 2 != 0);
private bool DoesIntersect(PointF point, PointF point1, PointF point2) {
float x2 = point2.X;
float y2 = point2.Y;
float x1 = point1.X;
float y1 = point1.Y;
if ((x2 < point.X && x1 >= point.X) ||
(x2 >= point.X && x1 < point.X)) {
float y = (y2 - y1) / (x2 - x1) * (point.X - x1) + y1;
return y > point.Y;
return false;
Using the code
The PieChart solution contains three classes: PieSlice, PieChart3D and PieChartControl (derived from the System.Windows.Forms.Panel control). The PieSlice class provides all the functionality
required to draw a 3-D pie slice with given a start and sweep angle, color, height and shadow style.
The PieChart3D represents the entire chart. There are several constructors available, all of them taking a bounding rectangle and an array of values. Some constructors also accept:
• array of colors used to represent values,
• array of slice displacements,
• slice thickness.
Slice displacement is expressed as a ratio of the slice "depth" and ellipse radius; minimum value of 0 means that there is no displacement, while 1 (largest allowed value) means that the shape is
completely taken out of the ellipse.
Slice thickness represents the ratio of pie slice thickness and the ellipse's vertical, minor axis; largest allowed value being 0.5.
It is also possible to set any of the above parameters using public properties. Note that if the number of colors provided is less than the number of values, colors will be re-used. Similarly, if the
number of displacements is exhausted, the last displacement will be used for all the remaining pie slices.
There are also additional public properties that can be set:
• Texts,
• Font,
• ForeColor,
• ShadowStyle,
• EdgeColorType,
• EdgeLineWidth,
• InitialAngle,
• FitToBoundingRectangle.
The meaning of all these properties and their possible values can be seen from the demo sample. The Texts property is an array of strings that are displayed on corresponding slices. Default
implementation places text near the center of the slice's top, but the user may override the PlaceTexts method of the PieChart3D class to implement her/his own placement logic. Font and ForeColor
properties define the font and the color that is used to display these texts.
The PieChart3D class can be used for printing: it is only necessary to initialize the chart object and then call its Draw method, providing the corresponding Graphics object:
public void Draw(Graphics graphics) { ... }
To display the chart on the screen, PieChartControl is more appropriate: it encapsulates the chart into a panel that is responsible for chart (re)painting. The user only has to place it on the form
and set the required values. For example:
private System.Drawing.PieChart.PieChartControl panelDrawing =
new System.Drawing.PieChart.PieChartControl();
panelDrawing.Values = new decimal[] { 10, 15, 5, 35};
int alpha = 80;
panelDrawing.Colors = new Color[] { Color.FromArgb(alpha, Color.Red),
Color.FromArgb(alpha, Color.Green),
Color.FromArgb(alpha, Color.Yellow),
Color.FromArgb(alpha, Color.Blue) };
panelDrawing.SliceRelativeDisplacements = new float[] { 0.1F, 0.2F, 0.2F, 0.2F };
panelDrawing.Texts = new string[] { "red",
"yellow" };
panelDrawing.ToolTips = new string[] { "Peter",
"Brian" };
panelDrawing.Font = new Font("Arial", 10F);
panelDrawing.ForeColor = SystemColors.WindowText
panelDrawing.LeftMargin = 10F;
panelDrawing.RightMargin = 10F;
panelDrawing.TopMargin = 10F;
panelDrawing.BottomMargin = 10F;
panelDrawing.SliceRelativeHeight = 0.25F;
panelDrawing.InitialAngle = -90F;
PieChartControl overrides both OnPaint and OnResize events, taking care of correct chart redrawing.
Note that PieChartControl has an additional ToolTips property accepting an array of strings that are displayed when the corresponding pie slice is hit. If any string in this array is empty, the
corresponding value will be displayed instead.
Points of Interest
To achieve a better 3-D perspective, I have introduced a "gradual" shadow, changing the brightness of the slice cut sides depending on their angles. To achieve this effect on the cylinder brink, a
gradient fill is used for painting the periphery. I used an empirical formula for this. However, the user may change this by deriving a class from PieSlice and overriding the CreateBrushForSide and
the CreateBrushForPeriphery methods in the PieSlice class, implementing her/his own logic.
Similarly, a user can override the CreatePieSliceHighlighted method in the PieChart class; the default implementation draws the highlighted pie slice in a slightly lighter color.
From version 1.4, a simple pie chart printing is included in the demo program; the user just has to click the Print button on the demo form. The printing code is provided in the PrintChart class of
the Test project.
Copyright notice
You are free to use this code and the accompanying DLL. Please include a reference to this web page in the list of credits.
• June 1, 2004 - Initial submission of the article.
• June 22, 2004 - ver. 1.1: Tool tip and pie slice highlighting added. Also (credits for these go to Andreas Krohn), flickering on resize has been removed and assertion failure bug when control is
made very small has been fixed.
• November 11, 2004 - ver. 1.2: bug fixes.
• March 21, 2005 - ver. 1.3: color transparency support added (thanks to Bogdan Pietroiu for this suggestion), and description text for each slice (as suggested by ccarlinx) added.
• November 10, 2005 - ver. 1.4: Pie chart control crashing for angle of 270 degrees bug (found by gabbyr and rafabgood) and "Crash when all slices have 0 value" has been fixed. A simple pie chart
printing sample has been included into the demo project (please note that the quality of the printout depends on the capabilities of the printer and is usually far behind the screen display
• March 12, 2006 - ver. 1.5: Control crashing bug (as noticed by jianingy) has been fixed. | {"url":"http://www.codeproject.com/Articles/7321/D-Pie-Chart","timestamp":"2014-04-18T06:16:08Z","content_type":null,"content_length":"200923","record_id":"<urn:uuid:ccf89aa7-f3ea-4c1e-ad66-9d90ae838c04>","cc-path":"CC-MAIN-2014-15/segments/1397609532573.41/warc/CC-MAIN-20140416005212-00546-ip-10-147-4-33.ec2.internal.warc.gz"} |
Ozone Park Algebra 2 Tutor
Find an Ozone Park Algebra 2 Tutor
...I also assisted fellow classmates when they needed assistance understanding the material. I have tutored this subject online over Skype with a whiteboard and webcam, reviewing problems and
explaining concepts to my student using these tools. Personally, this is probably my favorite subject and a good foundation in Algebra 1 is needed to ensure success.
4 Subjects: including algebra 2, geometry, algebra 1, prealgebra
...Good math work is essential for good physics. I hope this helps you to decide if I am the right kind of tutor for you. Good luck with the studying!I studied Physics with Astronomy at
undergraduate level, gaining a master's degree at upper 2nd class honors level (approx. 3.67 GPA equivalent). I ...
8 Subjects: including algebra 2, physics, geometry, algebra 1
...The Regents exams are meant to stress the students. I will work extremely hard to have your children excel with their exam. I have worked with many students taking many different regents,
ranging from biology, chemistry, algebra I and II, to English, physical science, as well as many others.
17 Subjects: including algebra 2, reading, chemistry, biology
...My hallmark is complete patience, and I will continue to go over the material until the student gains complete comprehension. I hope that this approach will help your child gain mastery and
confidence in math, and I look forward to enabling your child to reach his/her full math potential.I have ...
8 Subjects: including algebra 2, geometry, algebra 1, ACT Math
...Math and science are about thinking logically, which everyone can do. By patiently working one-on-one with students, I can show them how to turn their ability to think logically into success in
math and science. One item of note: I live in Manhattan and do not have ready access to a car.
10 Subjects: including algebra 2, writing, physics, algebra 1 | {"url":"http://www.purplemath.com/ozone_park_ny_algebra_2_tutors.php","timestamp":"2014-04-20T09:15:14Z","content_type":null,"content_length":"24144","record_id":"<urn:uuid:90e15cdf-2c3e-417a-91a1-7b90e694642d>","cc-path":"CC-MAIN-2014-15/segments/1397609538110.1/warc/CC-MAIN-20140416005218-00254-ip-10-147-4-33.ec2.internal.warc.gz"} |
Honing Your Programming Skills with Project Euler
Written by Robert Greiner
March 21, 2010
Project Euler is a programming challenge site that hosts (currently) 272 programming problems of varying difficulty. Users can log in, attempt to solve each problem, and discuss each solution.
Here is an example of one of the Project Euler problems.
Problem #1
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.
The Solution
This problem instantly reminds me of the FizzBuzz problem, so I think I'll start with that for my solution.
One of my goals for this year is to become more proficient in Ruby and C#, so I'll solve each problem using a mixture of both languages.
The C# Solution
int max = 1000;
int sum = 0;
for (int x = 1; x < max; x++) {
if ((x % 3 == 0) || (x % 5 == 0)) {
sum += x;
Pretty straightforward, right? Simply sum up all of the values that are evenly divisible by 3 or 5 and print the final sum. This is probably the solution 99% of programmers would come up with on
their first attempt. But, what about other ways of solving the same problem? For instance, can this problem be solved without looping through each number?
A better way to solve the problem
One of the best parts about Project Euler is the large community of smart developers all working on the same problem sets. Once you submit a correct answer to a problem, you will gain access to a
forum thread for that particular problem and will be allowed to discuss your solution with everyone else who has solved the same problem.
This is one of the more interesting solutions I saw on the problem (converted to Ruby)
This solutions utalizes arithmetic progression to create a more elegant solution to the original problem.
Would you think of solving this problem using arithmetic progression? Probably not (at least for the first attempt anyway), I sure didn't.
Project Euler is a great way to improve your programming and problem solving skills. I hope this brief introduction was interesting enough to motivate you to check Project Euler out for yourself and
try to solve some other problems on your own. Practicing these types of problems will (at the very least) better prepare you for your next job interview, which is never a bad thing.
Image From: Mathematician Pictures | {"url":"http://robertgreiner.com/2010/03/honing-your-programming-skills-with-project-euler/","timestamp":"2014-04-18T05:32:36Z","content_type":null,"content_length":"10602","record_id":"<urn:uuid:b1f10de6-d230-4d3f-82fd-9387ac9dd6b7>","cc-path":"CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00407-ip-10-147-4-33.ec2.internal.warc.gz"} |
Shared Documents - AccuplacerMath
Mathematics Courses at Worcester State University
If you select appropriate mathematics courses, then you are much more likely to do well. It is difficult, if not impossible, to succeed in a mathematics course if you do not have the right
foundation. This information is provided to help you select the most appropriate mathematics course.
Specific Courses:
1. Developmental Math: Arithmetic (MA 098) is a class-based review of Arithmetic.
Math Code 1 or higher is required.
2. Developmental Math: Elementary Algebra (MA 099) is a classroom-based review of Elementary Algebra. Math Code 1 or higher is required.
3. Survey of Mathematics (MA 105) addresses a variety of mathematics topics and is appropriate for students who do not have specific math requirements in their majors. The topics chosen rely less on
a knowledge of Algebra. Math Code 3 or higher is required.
4. College Algebra (MA 110) is required by various majors. It provides you with the background needed for Pre-calculus and Business Calculus. Math Code 5 or higher is required.
5. Mathematical Concepts I; Patterns, Functions and Algebra for Teachers; and Mathematical Concepts II (MA 130, 131 and 132) have been designed for Education majors, but any student may enroll. This
does not mean that grade-school math is taught. Teaching is a challenging profession and these courses seek to provide you with the theoretical background to understand and teach a wide array of
mathematical topics. Math Code 5 or higher is required.
6. Statistics (MA 150) teaches you to make sense of data. This begins with a discussion of how to organize, summarize, analyze, and present data. Most of the course focuses on using data derived from
samples to make inferences about populations. The concepts and procedures studied are applicable in such fields as Biology, Sociology, Psychology, Business and Economics. This course is required for
several majors. Math Code 4 or higher is required.
7. Pre-calculus (MA 190) provides you with the background needed for Calculus I. You must take College Algebra first or have a Math Code 6 or higher.
8. First-Year Seminar (MA 193) if chosen by a first-year student, a Math Code 5 or higher is required.
9. Calculus I (MA 200) is required for Mathematics, Chemistry, Biotechnology, Biology and Computer Science majors. It is a rigorous course that requires a strong mathematics background. Math Code 7
is required.
10. Business Calculus (MA 202) requires a strong background in algebra. Calculus begins by addressing the issue of a rate of change. This can be anything from the rate of inflation to the rate at
which an epidemic spreads. Since this course is required for Business majors, applications focus primarily on business and economics issues. You must take College Algebra first or have a Math Code 6
or higher.
11. Discrete Mathematics (MA 220) is required for Computer Science majors. It is a rigorous course that requires a strong mathematics background. Math Code 7 is required.
Accuplacer and Developmental Mathematics
The Massachusetts Board of Higher Education requires testing of all state college and university students using the Accuplacer exam. You must either pass the Accuplacer Elementary Algebra test, pass
Developmental Mathematics: Elementary Algebra (MA 099), before enrolling in any mathematics course. The Accuplacer exam is taken before building your college schedule.
MA 098 and MA 099 are typically offered each semester (including intersession and summer.)
Many students do not want to take MA 098 or MA 099 because the credits do not count towards graduation. Often they will take a course that they are not prepared for at another institution and fail
once, twice or even three times. With the necessary math background under their belts, they will be better prepared to succeed in their first college level math course.
If you are not confident in your mathematical ability, you will most likely delay taking your math requirements. This also makes things more difficult, since your background becomes weaker if you
have not practiced your math skills in years. Every student must complete a Math course within the first 60 credits. Don't delay!
Math Scores and Codes
On the Arithmetic Test (AR) and Elementary Algebra Test (EA):
Code 1: AR 0-74 & EA 0-81
Code 2: AR 75-120 & EA 0-71
Code 3: AR 75-81 & EA 72-81
Code 4: AR 82-120 & EA 72-81
Code 5: EA 82-120
On the College Level Math Test (CLM):
Code 6: CLM 52-88
Code 7: CLM 89-120
Math Codes and Math Classes
Code Available Courses Credits Comments
1 MA 098: 3 remedial credits MA 098: Does not carry college credit towards graduation
Developmental Math: Arithmetic
MA 098: Does count towards full time student status
MA 098: A classroom-based course covering Arithmetic
2 MA 099: 3 remedial credits MA 099: Does not carry college credit towards graduation
Developmental Math: Elementary Algebra
MA 099: Does count towards full time student status
MA 099: A classroom-based course covering
Elementary Algebra
3 MA 105: 3 college credits If higher level math is required then
Survey of Math
MA 099 must be taken
4 MA 150: 3 college credits If higher level math is required then
Statistics I
3 college credits MA 099 must be taken
MA 105:
Survey of Math
5 MA 110: 3 college credits If higher level math is required then
College Algebra
3 college credits MA 110 is needed first.
3 college credits
MA 130:
Math Concepts I 3 college credits
MA 150:
Statistics I
MA 105:
Survey of Math
6 MA 190: 4 college credits If higher level math is required then
4 college credits MA 190 is needed first.
3 college credits
MA 202:
Business Calculus 3 college credits
or 3 college credits
MA 110: 3 college credits
College Algebra
MA 130:
Math Concepts I
MA 150:
Statistics I
MA 105:
Survey of Math
7 MA 200: 4 college credits If higher level math is required then MA 200 is needed first.
Calculus I
3 college credits
4 college credits
MA 220:
Discrete Math I 4 college credits
or 3 college credits
MA 190: 3 college credits
3 college credits
3 college credits
MA 202:
Business Calculus
MA 110:
College Algebra
MA 130:
Math Concepts I
MA 150:
Statistics I
MA 105:
Survey of Math
*Note: Completing and passing any option above must be done before enrolling into a college-level mathematics course at Worcester State University. | {"url":"http://www.worcester.edu/AcademicSuccess/Shared%20Documents/AccuplacerMath.aspx","timestamp":"2014-04-19T07:01:35Z","content_type":null,"content_length":"61957","record_id":"<urn:uuid:7d6de954-d6af-4b99-8f66-91577134531a>","cc-path":"CC-MAIN-2014-15/segments/1398223203422.8/warc/CC-MAIN-20140423032003-00612-ip-10-147-4-33.ec2.internal.warc.gz"} |
UW-Madison - Physics 311 Spring 2013 Reference Page
Physics 311 Spring 2013 Reference Page
Mechanics: Origin and development of classical mechanics; mathematical techniques, especially vector analysis; conservation laws and their relation to symmetry principles; brief introduction to orbit
theory and rigid-body dynamics; accelerated coordinate systems; introduction to the generalized-coordinate formalisms of Lagrange and Hamilton.
Physics 202 or 208, & Math 320 or 319 or consent of instructor
Times:MWF 11:00-11:50am
Location:2241 Chamberlin Hall
Instructors:Andrey Chubukov
Final Exam
Thursday, May 16, 2013 12:25pm to 2:25pm
Course Home Page
MyUW Course Guide Page
Library Reserves Page | {"url":"http://www.physics.wisc.edu/undergrads/course-reference/spring2013/311/","timestamp":"2014-04-16T11:03:39Z","content_type":null,"content_length":"9631","record_id":"<urn:uuid:2f3f6737-cdc1-4e6e-b1f7-1e63a206ae25>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00580-ip-10-147-4-33.ec2.internal.warc.gz"} |
Series induction (real analysis)
March 7th 2013, 07:29 PM
Series induction (real analysis)
2 questions
#1) prove by induction that 1/k! is less than or equal to 1/(2^k-1))
I showed the base case and assumed it to be true for all k and want to show that it is true for k+1 or that 1/(k+1)! <= 1/2^k
From my assumption I can either multiply both sides by 1/2 and get that 1/2*k! <= 1/(2^k) which gets me the correct rhs or I can multiply both sides by 1/(k+1) to get the correct lhs side but
can't get both at once, any suggestions?
#2) Let s[n] = the sum from k=1 to n of 1/k! and t[n] = the sum from k=1 to n of 1/(2^k-1)
Prove by induction that s[n]<=t[n
]No idea how to do this after showing my base and assuming true for n any help would be great
Thanks a lot!
March 7th 2013, 08:52 PM
Re: Series induction (real analysis) | {"url":"http://mathhelpforum.com/advanced-math-topics/214417-series-induction-real-analysis-print.html","timestamp":"2014-04-16T05:11:56Z","content_type":null,"content_length":"4367","record_id":"<urn:uuid:9af86da1-0005-4d19-b4be-8c9ab801b4c5>","cc-path":"CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00484-ip-10-147-4-33.ec2.internal.warc.gz"} |
Trigonometry Videos -Over 12 Hours-15 Topics
Ask a question about this product.
This video prepares a student to be successful in pre-calculus
and beyond. Topic covered the video include sine, cosine, secant, cosecant,
tangent & cotangent functions, DeMoivre’s theorem and more. Each
example is explained in a step by step fashion that allows the student to
follow the logic. Once again, central to my videos I endeavor to teach the
student how to think mathematically. This video is an excellent
complement to your lectures and can be used with any textbook that
your instructor may be using for this course. I am passionate about
mathematics as well as teaching and I hope that in all of my videos
you can see this. I hope to ignite some passion in the student too
who is taking math at this level.
Topics in Trigonometry Videoss Over 12 Hours-15 Topics
1. The Unit Circle
2. Trig Functions of Real Numbers
3. Sine & Cosine Graphs
4. Cosecant & Secant Graphs
5. Tangent & Cotangent Graphs
6. Angle Measure
7. Trigonometry of Right Triangles
8. Law of Sines
9. Law of Cosines
10. Proving Trig Identities
11. Addition and Subtraction Rules
12. Double Angle, Reduction of Power and Half Angle Formulas
13. Inverse Trig Functions
14. Solving Trig Equations
15. DeMoivre's Theorem | {"url":"http://www.mathondvds.com/online-math-tutor/trigonometry-dvds","timestamp":"2014-04-19T22:06:32Z","content_type":null,"content_length":"29605","record_id":"<urn:uuid:6305e5bd-07f6-44b1-be4a-7d2a60ed986d>","cc-path":"CC-MAIN-2014-15/segments/1397609537754.12/warc/CC-MAIN-20140416005217-00607-ip-10-147-4-33.ec2.internal.warc.gz"} |
Yacht (Dice Game)
A dice game like Yahtzee. How high can you score?
Try to score the highest amount you can.
You can roll the dice up to three times (and can hold dice by clicking on them).
After any Roll (1, 2 or 3) you need to select a category to place the total. Choose Wisely! You must assign a category by the third roll, even if it is a 0 score.
1s 1 point for each 1 thrown
2s 2 points for each 2 thrown
3s 3 points for each 3 thrown
4s 4 points for each 4 thrown
5s 5 points for each 5 thrown
6s 6 points for each 6 thrown
Bonus If 1s to 6s total 63 or above, then 35 points
3 of a Kind 3 of the same number. Scores total value of all dice.
4 of a Kind 4 of the same number. Scores total value of all dice.
Full House A 3-of-a-kind and 2-of-a-kind. Scores 25 points
Small Straight 4 numbers in a row (any order). Scores 30 points
Big Straight 5 numbers in a row (any order). Scores 40 points
The Yacht 5 of a kind. Scores 50 points
Chance No pattern required. Scores total value of all dice.
There are many games like this, such as Yot, Generala, Cheerio, and the commercially available Yahtzee (trademarked by Hasbro).
The game needs Macromedia Flash Player ... it should start soon. | {"url":"http://www.mathsisfun.com/games/yacht-dice-game.html","timestamp":"2014-04-19T02:42:08Z","content_type":null,"content_length":"6957","record_id":"<urn:uuid:573c9da2-837d-4dbc-803e-91cf192a0b70>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00391-ip-10-147-4-33.ec2.internal.warc.gz"} |
Until recently, while I thought currying was kind of cool, I did not really understand what the use of it was. I call a function and I am done with it. It was not until I was cleaning up some code in
my football predictor project that I started to understand how currying could make your life easier.
Let us say that you have a function that takes an input and based on that input does some calculations. Now, this is normal in Perl. For instance,
sub foo {
my ($choice) = @_;
my @float_lst;
my $total;
if($choice eq "win") {
@float_lst = map { run_prediction($_) } (1..10);
$total += $_ for @float_lst;
} elsif($choice eq "lose")
@float_lst = map { run_prediction($_) } (-1..-10);
$total += $_ for @float_lst;
} elsif($choice eq "draw") {
@float_lst = map { run_prediction($_) } (0);
$total += $_ for @float_lst;
return $total;
You probably notice that you repeat a rather long line of statements. In Ocaml, you can use currying to cut down on those (I am sure there are ways of doing this in Perl as well).
type outcome = Win | Lose | Draw
let wins = [1;2;3;4;5;6;7;8;9;10]
let draw = [0]
let lose = [-1;-2;-3;-4;-5;-6;-7;-8;-9;-10]
let calc_outcome outcome =
let calc_outcome_aux = BatList.map run_prediction in
let fold_float = List.fold_left (+.) 0. in
match outcome with
| Win ->
fold_float (calc_outcome_aux wins)
| Lose ->
fold_float (calc_outcome_aux lose)
| Draw ->
fold_float (calc_outcome_aux draw)
Notice how I have called BatList.map and List.fold_left without the required number of arguments. This is not an “off by one error”. What the compiler does is break down the function into a set of
single argument functions that it then stores the next in the chain in the lexical bindings. Once you have fulfilled the required number of arguments, it will return its answer. Of course, you can
imagine using map over a function that has more than one argument that returns a list of functions that have the other required arguments left to fulfill. In addition, you can call functions where
you know one argument will take a long time to compute so you can do the quick arguments first then compute the heavy argument.
In this case, I was able to cut down the length of a line and repeated statements and reuse them based on user input.
4 Comments
You curry by hand in Perl if you’d like, or you can use something like Data::Util::Curry to make it easier.
You don’t need currying to simplify that:
sub foo {
my ($choice) = @_;
my %choices = (
win => [1 .. 10],
lose => [-1 .. -10],
draw => [0],
my $total = 0;
my @float_lst = map { run_prediction($_) } @{$choices{$choice}};
$total += $_ for @float_lst;
return $total;
Of course, you could also get rid of float_list entirely by doing
$total += run_prediction($_) foreach @{$choices{$choice}};
(-1..-10) will not buy you much good.
Here’s one way to add some spice:
sub run_prediction {
rand $_
sub make_prediction_runner {
my (@range) = @_;
return sub {
map { run_prediction($_) } (@range)
my %choice_range_map = (
'win' => [1..10],
'lose' => [reverse -10 .. -1],
'draw' => [0],
no strict 'refs';
while (my ($choice,$range) = each %choice_range_map ){
*{"$choice"} = make_prediction_runner(@$range);
sub foo {
my $choice = shift;
my $total ;
$total += $_ for &{"$choice"}();
print "$_: ${\(foo($_))}\n" foreach (qw (win lose draw));
There are loads of other ways to arrange all this. For the definitive story on Perl’s functional capabilities see “Higher Order Perl” by Mark Jason-Dominus. | {"url":"http://blogs.perl.org/users/cyocum/2010/12/currying-or-how-to-make-life-easier-for-yourself.html","timestamp":"2014-04-20T03:09:50Z","content_type":null,"content_length":"21519","record_id":"<urn:uuid:c1d47527-1209-4dce-bacc-2ad489f6f051>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00529-ip-10-147-4-33.ec2.internal.warc.gz"} |
Palmetto Bay, FL
Miami, FL 33158
A passionate and experienced tutor of math, chemistry, Chinese...
I have a bachelor's degree in mechanical engineering and a master's degree in chemistry. I have a strong background in
and chemistry, and experience in tutoring students of all ages in these two subjects. My special subjects are Algebra 1, Algebra 2, Geometry,...
Offering 9 subjects including algebra 1, algebra 2 and geometry | {"url":"http://www.wyzant.com/geo_Palmetto_Bay_FL_Math_tutors.aspx?d=20&pagesize=5&pagenum=1","timestamp":"2014-04-16T15:30:44Z","content_type":null,"content_length":"60950","record_id":"<urn:uuid:037ae927-2c6c-4c8e-a42f-474b3d09846e>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00317-ip-10-147-4-33.ec2.internal.warc.gz"} |
Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility
Kontek, Krzysztof (2010): Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility.
Download (376Kb) | Preview
This paper discusses two approaches for the analysis of multi-outcome lotteries. The first uses Cumulative Prospect Theory. The second is the Relative Utility Function, which strongly resembles the
utility function hypothesized by Markowitz (1952). It is shown that the relative utility model follows Expected Utility Theory with a transformed outcome domain. An illustrative example demonstrates
that not only it is a simpler model, but it also provides more sound predictions regarding certainty equivalents of multi-outcome lotteries. The paper discusses estimation procedures for both models.
It is noted that Cumulative Prospect Theory has been derived using two-outcome lotteries only, and it is hard to find any evidence in the literature of its parameters ever having been estimated by
using lotteries with more than two outcomes. Least squares (mean) and quantile (including median) regression estimations are presented for the relative utility model. It turns out that the
estimations for two- and three-outcome lotteries are essentially the same. This confirms the correctness of the model and vindicates the homogeneity of responses given by subjects. An additional
advantage of the relative utility model is that it allows multi-outcome lotteries, together with the estimation results, to be presented on a single graph. This is not possible using Cumulative
Prospect Theory.
Item Type: MPRA Paper
Original Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility
Language: English
Keywords: Multi-Prize Lotteries, Lottery / Prospect Valuation, Markowitz Hypothesis, Prospect / Cumulative Prospect Theory, Aspiration / Relative Utility Function.
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation
D - Microeconomics > D0 - General > D03 - Behavioral Economics; Underlying Principles
Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty
C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C21 - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions
C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C91 - Laboratory, Individual Behavior
D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D87 - Neuroeconomics
Item ID: 22947
Depositing Krzysztof Kontek
Date 30. May 2010 06:35
Last 18. Feb 2013 15:56
1. Cameron, A. C., Trivedi, P. K., (2005). Microeconometrics. Methods and Applications, Cambridge University Press.
2. Edwards W., (1961). Behavioral Decision Theory. Ann. Rev. Psych., 12, pp 473-479.
3. Gonzales, R., Wu, G., (1999). On the Shape of the Probability Weighting Function, Cognitive Psychology, 38, pp 129-166.
4. Hey, J. D., Morone, A., Schmidt U., (2009). Noise and bias in eliciting preferences, Journal of Risk and Uncertainty, 39, pp 213-235.
5. Kahneman, D., Tversky, A., (1979). Prospect theory: An analysis of decisions under risk. Econometrica, 47, pp 313-327.
6. Kontek, K., (2009a). On Mental Transformations. MPRA Paper http://mpra.ub.uni-muenchen.de/16516/, Available at SSRN: http://ssrn.com/abstract=1437722 .
7. Kontek, K., (2009b). Lottery Valuation Using the Aspiration / Relative Utility Function, Warsaw School of Economics, Department of Applied Econometrics Working Paper no. 39.
References: Available at SSRN: http://ssrn.com/abstract=1437420 and RePec:wse:wpaper:39.
8. Kontek, K., (2010a). Mean, median or Mode? A Striking Conclusion from Lottery Experiments, MPRA Paper http://mpra.ub.uni-muenchen.de/21758/, Available at SSRN: http://ssrn.com/
9. Kontek, K., (2010b). Density Based Regression for Inhomogeneous Data; Application to Lottery Experiments, MPRA Paper http://mpra.ub.uni-muenchen.de/22268/, Available at SSRN: http://
10. Markowitz H., (1952A). The Utility of Wealth. Journal of Political Economy, Vol. 60, 151-158.
11. Quiggin J., (1982). A theory of anticipated utility. Journal of Economic Behavior and Organization 3(4), 323–43.
12. Traub, S., Schmidt, U., (2009). An Experimental Investigation of the Disparity between WTA and WTP for Lotteries, Theory & Decision, 66, pp 229-262.
13. Tversky A., Kahneman D., (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty, vol. 5(4), October, 297-323.
URI: http://mpra.ub.uni-muenchen.de/id/eprint/22947 | {"url":"http://mpra.ub.uni-muenchen.de/22947/","timestamp":"2014-04-17T04:44:36Z","content_type":null,"content_length":"25167","record_id":"<urn:uuid:67ea3056-7844-41e0-9cbc-7e24b904cb3a>","cc-path":"CC-MAIN-2014-15/segments/1397609526252.40/warc/CC-MAIN-20140416005206-00453-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
How to Get Smart in Math?
• one year ago
• one year ago
Best Response
You've already chosen the best response.
Drink MathShake
Best Response
You've already chosen the best response.
Best Response
You've already chosen the best response.
sleep in math class
Best Response
You've already chosen the best response.
One really important thing I can recommend, never stop learning. Whenever you finish up with your studies in school for the year, keep learning over the summer. Keeping it fresh in your mind will
do wonders for you! :D
Best Response
You've already chosen the best response.
@satellite73, I was expected a more appropriate response.
Best Response
You've already chosen the best response.
@Hero THANKS TATS WT I THOUGHT
Best Response
You've already chosen the best response.
ok how about find some math that you enjoy and study that. it will be a pleasure for example, i enjoy algebra, but and not too fond of analysis,
Best Response
You've already chosen the best response.
But math is math. It should all be equally enjoyable.
Best Response
You've already chosen the best response.
I agree with satelitte73, analysis is not my favorite topic.....it grows on you over time.....
Best Response
You've already chosen the best response.
You know you have done way too much math when your dreams are equations.....
Best Response
You've already chosen the best response.
\(\text{ Don't stop} \) practising what you enjoy :)
Best Response
You've already chosen the best response.
true but just because you are struggling with a topic doesn't mean you can enjoy it. Takes a lot of practice to master any topic, don't be afraid to fail.....
Best Response
You've already chosen the best response.
just do math. first what you like, then step-by-step get into deeper waters.
Best Response
You've already chosen the best response.
math is not supposed to be easy, even if u r a gifted person. always ask for help when u need it.
Best Response
You've already chosen the best response.
Study study study study
Best Response
You've already chosen the best response.
actually pay attention in math class instead of sleep lol
Best Response
You've already chosen the best response.
OMG SHUT UPPPPPPP
Best Response
You've already chosen the best response.
I agree that enjoying it really helps! But you have to make an effort to look at math in that fun light, sometimes. It's also important to understand things in class in your own way of
understanding. This might sound weird, but I think it's okay to understand things in a way that you can't explain verbally. What's most important is understanding things in whatever way you
understand. Also... Some teachers are not great. So learning from other sources might be an excellent idea! Example: OpenStudy.com! :)
Best Response
You've already chosen the best response.
hahahah i know right i have learned that the hard way....not sleeping in class i was totally kiding about that one my teacher sucks
Best Response
You've already chosen the best response.
hate it, curse it, despise it
Best Response
You've already chosen the best response.
the more you hate it, the better you'll get
Best Response
You've already chosen the best response.
A calculator
Best Response
You've already chosen the best response.
Best Response
You've already chosen the best response.
Well,Its An Easy Answer,But Its A Very Difficult Think To Do,Practice Makes You Smart,Practice Makes You Perfect,Practice Is that What Counts. :)
Best Response
You've already chosen the best response.
any ways thanks ya all even tho i dont enough answer
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/507f4959e4b0b56960050ff5","timestamp":"2014-04-17T07:16:14Z","content_type":null,"content_length":"89181","record_id":"<urn:uuid:7090b82b-de5c-4402-bd19-e9236a363581>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00005-ip-10-147-4-33.ec2.internal.warc.gz"} |
Splitting light into colors, mathematical expression (fourier transforms)
Basically, given a function that gives the number of photons hitting a certain area, I want a mathematical way to determine how many of those photons are of a specific frequency (such as red light).
I don't think you can get that distribution simply from the number of photons hitting the area. One thing does not lead to another. You can perfectly have N photons with all kinds of different
frequency distribution.
You mentioned Fourier Transform, yes, it does transform between time domain to frequency domain, but here the "frequency" has a different meaning than what you might have in mind (it means the
spatial periodicity of the underlying time-domain function, not the frequency of the EM wave) | {"url":"http://www.physicsforums.com/showthread.php?p=4185813","timestamp":"2014-04-21T12:14:16Z","content_type":null,"content_length":"32748","record_id":"<urn:uuid:6c60955e-d3bc-4c18-8c47-ef57d6a650e9>","cc-path":"CC-MAIN-2014-15/segments/1397609539776.45/warc/CC-MAIN-20140416005219-00576-ip-10-147-4-33.ec2.internal.warc.gz"} |
Stupid Number Puzzle [Archive] - LucasForums
01-04-2001, 06:27 AM
http://www.escapemi.com/forums/confused.gif Grrrrr I'm gettin really annoyed with the damn stupid number puzzle thing on Phatt Island with the spinny wheel thing and how you have to go to the next
alley and ask the guy behind the door what the next number is gonna be, ok an example is
the guy holds up 3 fingers and says "if this is one than what's this?" then holds up 4 fingers
So I'm going by the assumption that if 3=1 there's a difference of 2 so the answer for the holding up of 4 fingers should = 2, but more often than not it doesn't friggen work and I've been sittin
here for like half an hour trying to get it to work, and each time he changes the formula thing on me so the next time he might hold up fingers and say "if this is 2 then what's this?" and hold up 4
fingers and then I don't know if it's 5 or 3. This is stuffed http://www.escapemi.com/forums/mad.gif http://www.escapemi.com/forums/frown.gif | {"url":"http://www.lucasforums.com/archive/index.php/t-21856.html","timestamp":"2014-04-19T09:45:38Z","content_type":null,"content_length":"5328","record_id":"<urn:uuid:4f58d995-a71f-4726-a408-3a4571fc4ddd>","cc-path":"CC-MAIN-2014-15/segments/1397609537097.26/warc/CC-MAIN-20140416005217-00358-ip-10-147-4-33.ec2.internal.warc.gz"} |
Regression Analysis With Spss Example
Regression Analysis With Spss Example PDF
Sponsored High Speed Downloads
Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is “regression”: “linear.” In the main dialog box, input the dependent variable and several
predictors. In this case, we
a standard regression analysis. 7B.1.2 Statistics Window. Selecting the . ... By default, Estimates. in the . Regression Coefficients. panel is checked. This instructs IBM SPSS to print the value of
the regression coefficient and ... The second important point about regression analysis that this ...
Linear Regression in SPSS This example shows you how to create a basic regression model in SPSS, with one predictor variable and one criterion variable. Both variables have to be measured on an ...
Here’s the SPSS output: Linear Regression with
Example of Interpreting and Applying a Multiple Regression Model ... SPSS Output: By the way, the "adjusted R²" is in Model Summary.758a.575 .562 .39768 ... correlations and results from the
regression analysis multiple regression weights
Let’s look at an example: ... SPSS’ Linear Regression Window Infant Mortality (babymort) is our dependent variable and Female Literacy (lit_fema), our independent variable. Click OK. ... When we use
multiple regression analysis, ...
The SPSS Statistics: Guide to Data Analysis, SPSS Statistics: Statistical Procedures Companion, and SPSS Statistics: ... which can be estimated using traditional methods such as the Linear Regression
procedure. Example. Can population be predicted based on time?
Regression Analysis in SPSS With the exception of the scatterplot, itself, ... or correlation analysis. Example 8.30 – SPSS Correlation Matrix One may wish to begin an investigation into the
relationship between class size, the
that the assumptions for multiple regression analysis are met by the variables in questions. f. ... SPSS know that we want a prediction for this value and not to include the value in any other
computations). (See figure, below.) 3.
To perform a logistic regression analysis, select Analyze-Regression-Binary Logistic from the ... For example, the overall correctly specified group percentage is 74.6%. ... regression window and
change classification cutoff. Logistic Regression on SPSS 3 Classification Tablea Observed Predicted ...
Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year’s sales records in ... Thus, the assumptions for regression analysis appear
to be met. h. At the 10% significance level, ...
The SPSS Guide to Data Analysis for SPSS Statistics 17.0 is also in development. Announcements ... You can specify options for your logistic regression analysis: Statistics and ... estimated using
traditional methods such as the Linear Regression procedure. Example. Can population be predicted ...
Suppose, for example, ... Click Start > Programs > SPSS for Windows > SPSS 10.1 for Windows. At this point a window will ... A standard multiple regression analysis was conducted to evaluate how well
high school grade point
SPSS Guide: Correlation & Regression Once the data are entered, go to Analyze, Correlation, Bivariate to get this dialogue box. Move the variables (quantitative only) that you wish to correlate into
the variables box and hit OK. Correlations
Table 1 example, then the odds ratio is equal to e, ... Table 3.—Logistic Regression Analysis of 189 Children’s Referrals for Remedial Reading Programs by SAS PROC LOGISTIC (Version 8) ... If either
C8057 (Research Methods II): Factor Analysis on SPSS Dr. Andy Field Page 1 10/12/2005 Factor Analysis Using SPSS The theory of factor analysis was described in your lecture, or read Field (2005)
Chapter 15. Example Factor analysis is ... (as was the case for multiple regression ...
To illustrate the procedures involved in conducting a multiple regression analysis, we will use data from a campus survey of randomly selected students ... analysis is provided by the defaul settings
for the SPSS Regression routine. To
Binary Logistic Regression with SPSS ... Let me close with an example of how to present the results of a logistic regression. In the example below you will see that I have included both the
multivariate analysis (logistic regression) 16
Doing Multiple Regression with SPSS ... Next we want to specify a multiple regression analysis for these data. The menu bar for SPSS offers several options: In this case, ... For example, Copy on
this selected output produced the
Linear Regression Analysis Example: analyze the model 1) Click Analyze →Regression →Linear from the main menu. 2) Put ... Example: use data from the SPSS data file “Employee data.sav”, to assess
whether the variable Current salary is
Methodology and Statistics | University of Maastricht © Bjorn Winkens 2007 Statistics: part 2 Regression Analysis and SPSS Logistic Regression I
• Simple regression in SPSS • Correlation analysis in SPSS ... October 8, 2009 Regression in SPSS 57 An example From Kleinbaum et al. (2008) October 8, 2009 Regression in SPSS 58 One way to do
multiple regression in SPSS. 30
Survival Analysis Using SPSS By Hui Bian Office for Faculty Excellence . ... for example: Cox regression −Parametric: specify the shape of baseline hazard function and ... Example (from IBM SPSS
20.0): data file: recidivism
Logistic Regression Analysis M uch like ordinary least squares (OLS) linear regression analysis ... For our example logistic regression, ... SPSS/PASW Statistics to produce the final equation depends
on numerous
an analysis of the residuals ... is the slope. So, in this example the equation for the regression line is: Y’ = 58.831 + .972(X) • The numbers in the Standardized Coefficients section were computed
using scores ... SPSS -- regression.doc Author:
Regression Analysis and SPSS Linear Regression II (syllabus chapter 3) Bjorn Winkens Methodology and Statistics University of Maastricht ... Example: SBP and AGE 1) SPSS: input (syllabus: table 1.1)
or open file (Colton6r) 2) Check assumptions of linear regression
Regression Analysis: In order to run a regression analysis in SPSS, you first have to come up with a regression model. A thorough regression analysis follows the following steps: Identify dependent
variable. ... An Example of Factor Analysis
Regression Analysis Tutorial INTRODUCTION ... For example, the standard deviation for a data set can easily be determined, and any data points existing outside of the 3σ range can be reviewed to
determine if they are valid points.
procedures available in SPSS PC Version 10. Regression analysis allows us to examine the substantive impact of one or more variables on another by using ... • For example, if I wanted to look at how
the educational attainment of the women in our NSFG data is
Part 3: Regression Analysis . Summer 2010, Version 1.0 . ... For example, it is possible to predict a salesperson’s total annual sales ... IBM SPSS Statistics 18 Part 3: Regression Analysis Author:
Information Technology Services Created Date:
It is easy to do forward and backwards stepwise regression in SPSS. For example REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE ... the same throughout an analysis, e.g. 10,000
cases might be analyzed in one regression, 9,700 might be analyzed in another, etc.
SPSS Guide: Regression Analysis ... Peform a regression analysis (both bivariate and multivariate) Interpret the output o Which variables are significant? o How is an unstandardized coefficient used?
Standardized? ... For this example, ...
Binary Logistic Regression Example ... distance is an option in SPSS logistic regression. 2. Introduction We have examined response variables that are ... For multiple regression analysis, we could
use a statistics like Mallow’s Cp to compare model
BUSI 6220 (Taken from SPSS Help) Logistic Regression in SPSS PASW Statistics ... analysis. Example. ... Obtaining a Logistic Regression Analysis From the menus choose: ...
HOW DOES MULTIPLE REGRESSION RELATE TO CORRELATION AND ANALYSIS OF VARIANCE? In a previous section (Chapter 4, ... Performing a multiple regression on SPSS EXAMPLE STUDY ... Tip The SPSS multiple
regression option was set to Exclude cases listwise.
Multiple Regression analysis on SPSS 3 Model selection (Variable selection) For variable selection procedure we can choose stepwise, remove, backward, and forward.
Regression Analysis To perform the regression, click on Analyze\Regression\Linear. Place nhandgun in the ... Logistic Regression in SPSS Data: logdisea.sav Goals: • Examine relation between disease
(binary response) and other explanatory variables
regression analysis and the trustworthiness of summary statistics such as the coefficient of ... This is a warning example against the use of R2 as the ... To perform a regression analysis of data
set A in SPSS, go to Analyze →→→→ Regression →→→ Linear, select y as dependent ...
Regression allows you to predict variables based on another variable. In this ... Let’s begin with the example used in the text in ... different data analysis program. Exit SPSS.
In this example, we are interested in ... ANNOTATED OUTPUT--SPSS Center for Family and Demographic Research Page 3 ... a third variable), first run a regression analysis, including both independent
variables (IV and moderator) and their interaction (product) term.
not it is reasonable to consider that the assumptions for multiple regression analysis are met ... SPSS know that we want a prediction for this value and not to include the value in any other
computations). (See figure, below.) 3.
Linear Regression Analysis. ... SPSS Analysis. Analyze⇒Regression⇒Linear ... Linear Regression vs. ANOVA. Example : ScientificQuestion : Isthere anydifferenceinthelonelinessbetweenfemale and male? H.
Multiple Regression Analysis Continuous Any type To describe the direction, strength of the relationship between variables ... Ordinal logistic regression: Example The low birth weight data: Suppose
we have categorized the birth weight BWT as: BWTCAT =
Use SPSS regression diagnostic to identify outliers among independent variables and in the dependent variable. ... Chatterjee, S., Hadi, A., & Price, B. (2000) Regression analysis by example. New
York: Wiley.
Guide to SPSS Statistical Analysis III: Linear Regression BIOL 300, ... Linear Regression analysis. Choose from the menu Analyze, Regression, Linear. ... In this example, P=0.001, which is much less
than 0.05, ...
IBM Software IBM SPSS Regression ... For example, you can model which factors predict if the customer buys product A, product B or product C. Easily classify your data into two groups ... analysis of
variance, and t tests of individual coefficient for
regression analysis with examples in IBM SPSS. Steve Simon P.MeanConsulting ... I will be using a data example that shows information about mortality for the 1,313 ... Here is the output from a
logistic regression model in SPSS. 38. Conclusion
Stat Computing > SPSS > Output Annotated SPSS Output Ordered Logistic Regression This page shows an example of an ordered logistic regression analysis with footnotes explaining the output.
To carry out a linear regression analysis in SPSS, click on the “Analyze” drop-down menu, ... regression analysis) ... example. Standardized regression weights (β’s) ...
Regression Analysis: Basic Concepts Allin Cottrell ... In this example, based on a sample of 14 houses, yi is sale price in thousands of dollars and xi is square footage of living area. Table 1:
Example of finding residuals Given O 0 D52:3509 ; O
Commonality Analysis: Demonstration of an SPSS Solution for Regression Analysis Kim Nimon, Ph. D. University of North Texas College of Information 3940 N. Elm, Suite G150 ... regression [8]. Based on
the example, Tables 1 and 2 respectively contain the contents of YaoCommonalityMatrix.sav and | {"url":"http://ebookilys.org/pdf/regression-analysis-with-spss-example","timestamp":"2014-04-20T14:31:05Z","content_type":null,"content_length":"45050","record_id":"<urn:uuid:cb4285f9-4aa4-4da1-ae00-4954eb3b9227>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00560-ip-10-147-4-33.ec2.internal.warc.gz"} |
We present new format for storing sparse matrices on GPU. We compare it with several other formats including CUSPARSE which is today probably the best choice for processing of sparse matrices on
GPU in CUDA. Contrary to CUSPARSE which works with common CSR format, our new format requires conversion. However, multiplication of sparse-matrix and vector is significantly faster for many
matrices. We demonstrate it on set of 1 600 matrices and we show for what types of matrices our format is profitable.
(Heller M., Oberhuber T.: “Improved Row-grouped CSR Format for Storing of Sparse Matrices on GPU”, Proceedings of Algoritmy 2012, 2012, Handlovičová A., Minarechová Z. and Ševčovič D. (ed.), pages
282-290, ISBN 978-80-227-3742-5) [ARXIV preprint] | {"url":"http://gpgpu.org/tag/data-structures","timestamp":"2014-04-16T21:52:18Z","content_type":null,"content_length":"36550","record_id":"<urn:uuid:ff873fc8-73ae-4e1a-8a4e-52a75e86f07c>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00191-ip-10-147-4-33.ec2.internal.warc.gz"} |
Diminishing Returns - Math! [Archive] - TankSpot
10-05-2007, 09:31 PM
Here we deal with mitigation due to armour using some Calculus to show its properties.
We begin with the basic formula for physical damage mitigation from armour for opponents level 60 and higher:
M = -------------------------------
Armour + (467.5*level - 22167.5)
For the purposes here (467.5*level - 22167.5) is a constant (C). The variable x will be used to represent armour (simply because I'm too lazy to re-do all the graphic calculus bits with an a.) Using
these definitions, the basic formula for mitigation simply looks like:
M = -----
x + C
It's important to realize that there are two significant effects of damage mitigation:
1) The effect on the rate of health loss
2) The effect on the amount of time it takes to go from full health to dead.
Both are significant to the healer in different ways. The former affects how much health/sec must be restored to keep you alive, and the latter affects the amount of mana that can be regenerated
between burst healing.
Effect of Armour on Rate of Health Loss
If h is the health at any instant in time, H is the maximum health, D is the pre-mitigation damage per second incoming, t is time, and P(t) represents healing as a function of time, then the formula
for health at a given time looks like:
Then, this term represents post-mitigation damage:
The rate of change of health would be the derivative of health with respect to t:
This makes sense: dh/dt increases as x increases, and goes to (0 + dP/dt) as x goes to infinity. Now we can examine the effect change in armour has on the rate of health loss. The change in the rate
of health loss with the change of armour (that is x) can be found by taking the derivative of the above equation with respect to x. Note that as healing is not a function of armour, the healing term
P(t) drops out as zero.
(Remember back to the quotient rule if you don't see how to get here (d/dx)(u/v)=[v(du/dx)-u(dv/dx)]/v^2). This equation represents the change in health/second of damage taken with change in armour.
We see the slope of the armour v. mitigation curve is on the order of 1/(x+C)^2. The extent of diminishing returns (i.e. the change in the slope of the relationship between armour and damage
mitigation) can be found by taking the second derivative with respect to x:
(If you've forgotten, the rule to get here is (d/dx)(u^n)=nu^(n-1)(du/dx)). The negative second derivative signifies a flattening of the slope as armour increases, meaning a lessening of returns for
each quantity of armour added. We see that there are diminishing returns on armour with respect to health/sec mitigated. It diminishes as -2DC/((x+C)^3).
We can also take the second derivative with respect to armour of the mitigation function above and see that it is also negative, and thus there are diminishing returns on mitigation in the absence of
time. As expected, mitigation alone diminishes as -2C/((x+C)^3) - the same as the health/sec mitigation, less the damage per second component.
Effect of armour on lifespan
It may seem contradictory to say the effect of armour on the time it takes to go from full health to dead is different than the effect on health/sec mitigated, but it is. For the purposes of this
section, we refer to the amount of time it takes to go from full health to dead as "lifespan" which we'll call T going forward here. The difference between the analysis of lifespan and the analysis
of damage mitigated stems from the nature of mitigation. As mitigation approaches 100%, each 1% increase has a greater effect on lifespan than the last. (e.g. going from 50% mitigation to 51%
mitigation will extend your lifespan approximately 2%; whereas going from 98% mitigation to 99% mitigation will extend your lifespan by 100%). Using the basic formula for health (h) from the previous
section, we see that t=T when h=0. Therefore, solving for T with h=0 yields:
Now with this equation, we can examine the effect of armour on lifespan by taking the derivative of T with respect to x (uses the same division rule noted above).
This is a very interesting equation, and can be rearranged as:
After a bunch of factoring:
The term x^2+Cx factors into x(x+C), which cancels the denominator and results in simply x, giving:
Which leads simply to:
It is interesting (and significant) that dT/dx is not a function of x. This means that the slope of armour vs. lifespan is a constant (i.e. d^2T/dx^2=0) so there are no diminishing returns on
lifespan as armour increases. As the saying goes, mitigation is subject to diminishing returns, but armour is not. More properly, mitigation is subject to diminishing returns, but lifespan is not.
1) As armour increases, the damage mitigated per second is subject to diminishing returns. The effects diminish as:
Where D is the unmitigated damage per second, x is armour, and C = 467.5*level - 22167.5.
2) As armour increases, the effect of increasing the amount of time required to go from full health to dead is not subject to diminishing returns. Each increase of some quantity of armour will
increase a tank's lifespan equally (that is, if going from 4000 to 6000 armour increases your lifespan by 1 minute, then going from 12000 to 14000 armour will also increase your lifespan by 1 | {"url":"http://www.tankspot.com/archive/index.php/t-33109.html","timestamp":"2014-04-17T19:38:16Z","content_type":null,"content_length":"9855","record_id":"<urn:uuid:f8a48e32-aff1-4777-bd8f-3051332616e0>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00024-ip-10-147-4-33.ec2.internal.warc.gz"} |
Summary: Daniel Allcock
12 March 2010
Research Interests
Group theory, Lie theory, algebraic geometry.
1996 University of California, Berkeley: Ph.D., Mathematics
Dissertation: The Leech Lattice and Hyperbolic Geometry
Thesis advisor: Richard Borcherds
1991 University of Texas, Austin: B.S.(special honors), Mathematics
1991 University of Texas, Austin: B.S.(honors), Physics
2010 Professor, U.T. Austin math department
20022010 Associate Professor (tenured), U.T. Austin math department
19992002 Assistant Professor (not tenure-track), Harvard University
19981999 Postdoctoral Fellow, Harvard University
19961998 Instructor, University of Utah
19951996 Research Assistant, U.C. Berkeley math department
1995 Teaching Assistant, U.C. Berkeley math department
1995 Teaching Assistant, U.C. Berkeley physics department
1991 Geophysicist, Shell Offshore Inc., New Orleans | {"url":"http://www.osti.gov/eprints/topicpages/documents/record/472/2084296.html","timestamp":"2014-04-17T19:01:58Z","content_type":null,"content_length":"7943","record_id":"<urn:uuid:325f0905-ed38-4573-98e9-c141ba56067b>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00331-ip-10-147-4-33.ec2.internal.warc.gz"} |
How to solve Slitherlink puzzles
How to play Slitherlink
Slitherlink is a wonderfully pure logic puzzle which doesn't require you to learn any complex rules. To solve a puzzle:
• Draw a single loop on the puzzle grid, such that the loop doesn't touch or cross itself at any point.
• Wherever a number appears in the grid, the loop must pass by that many sides of the square with the number in.
If, for example, a square in the grid has a '3' in it then that square must have 3 shaded sides, and all those shaded sides must form part of the single loop. If a square has a '0' in it then there
must be no parts of the loop neighbouring the square. Not all squares have numbers in - how many times the loop neighbours these squares is left for you to deduce as you solve the puzzle.
Here's an example puzzle:
There are various places you can start solving this puzzle. Although the ultimate aim is to mark in the shaded segments that make up the loop, it's very useful to make a note of which segments can't
contain any part of the loop. The '0' squares indicate some of these clear segments straight away, so we can begin by marking these in.
On puzzlemix you simply right-click or ALT-click to mark segments as clear, remembering that you can also drag the mouse if you want to select multiple segments or are having problems clicking
accurately enough. I have marked them pink here so that they show up clearly in these pictures:
If you look at the '3' nearest to the top-left, you can see that there are only 3 remaining sides that can be shaded, since the neighbouring '0' precludes the bottom side from being shaded. So we can
shade these 3 sides in right away, since we are certain they must form part of the loop we are searching for.
Because we know there is only one loop, we know that the two ends of the three-segment path we have drawn must be connected to something else, so we can extend the loop either side of the '3'. We
also know the loop can't cross or overlap itself, so the top side of the second '3' must be empty. We can then extend the loop further still using this and similar logic:
At the top-left the loop cannot go left or up from here. The up option is eliminated because we already have '2' sides shaded, but the option to the left can be excluded because the loop would have
nowhere to go if it went left here. So it must go down.
Looking also at the '0' in the left-most column, we can see that there is only one possible solution to the '2' directly below it. If we shade that only solution in and extend it in the only way it
can be extended, we end up with this result:
At this point there are then a series of further extensions of the loop that can be made by going back and forth between the two loop segments we are building. You can start by observing that the '2'
in the third row of the second column can only be solved using its top and right-hand sides, and then continuing from there. The result of stepping further using relatively simple logic is as
At this point although it is possible to progress these line segments using more complex reasoning, by far the easiest way to continue the puzzle is to look at another area. Let's consider the two
'3's at the top-right.
A '3' in the corner of a puzzle must have its two corner-most segments shaded, otherwise the loop would not be able to extend through it. If we mark these in at the top-right and then consider how it
must interact with the '3' immediately below it, we can shade in segments as shown here in dark purple:
Corners and other restricted areas of the puzzle are often useful places to look when you're stuck. A '3' with two neighbouring 'exits' blocked can always have those two sides shaded in the same way
as applies when it is in the corner of the grid.
The two '3's diagonally next to one another in the penultimate and last columns are also interesting. Experimentation on a piece of paper will show that all solutions to '3's arranged like this
involve shading in the two outer-most line segments on both squares, rather like shading the top and bottom of a figure '8' if you were to look at the puzzle from a diagonal angle. By shading these
in and extending both these segments and those on the '3's at the top-right, we end up with this result:
At this point there are various places you can progress, using slightly more complex logic. The '2' square at the bottom-right cannot be shaded to the top and left because the '1' square next to it
would then have no remaining sides to be shaded, and the loop would not be able to 'escape' from the bottom-right corner. So the solution must go via the right and bottom-hand sides.
At the bottom-left, experimentation with the '2' and '3' will reveal there is only one possible solution. Continuing in a similar vein will soon result in the final solution:
The final solved puzzle, redrawn without the colours, looks like this:
Good luck! Slitherlink can sometimes be a very challenging puzzle, but it can also be a wonderfully rewarding puzzle. As you play it more and more you will begin to spot more and more patterns - but
you'll probably never find it universally 'easy'!
On the right of the puzzlemix player you might notice the ability to change colours.. Although this is purely decorative and so you are welcome to ignore it, it can be very useful when solving the
puzzle in order to make notes or try out test solutions. There is no difference between the colours so far as the correct/incorrect status of the puzzle is concerned, but using different colours has
the additional advantage that if you decide against a test solution you can simply 'del'ete all segments of a colour in a single click. You can also 'fix' a colour to convert it into black and white
if you decide it is correct (although you don't need to do this to be judged to have solved the puzzle correctly). You can of course also always use the 'undo' button or press 'Z' to undo moves at
any point - this will even undo deleting and fixing colours. You can also 'redo' any or all changes you decide against 'undo'ing!
Back to puzzle rules choice page | {"url":"http://www.puzzlemix.com/rules-slitherlink.php","timestamp":"2014-04-21T09:36:07Z","content_type":null,"content_length":"20101","record_id":"<urn:uuid:9fd2b1ed-bf7d-46c5-8697-b9e38eb9386b>","cc-path":"CC-MAIN-2014-15/segments/1398223203422.8/warc/CC-MAIN-20140423032003-00105-ip-10-147-4-33.ec2.internal.warc.gz"} |
1. Build And Test The Operational Amplifier Summing ... | Chegg.com
1. Build and test the operational amplifier summing circuit you designed for the Prelab using 741-type op-amps. Use VA = 2 V and VB = 3 V with power supply rails of ±18 V. Ask your lab instructor to
give the correct pin-out of the 741 if necessary. To obtain the approximate input voltages, use the voltage divider circuit shown below; if you don’t have 30-? resistors available, use two 15-?
resistors in series for each. Some component “tweaking” may be necessary if your particular circuit is an appreciable load on the voltage divider. When connecting the bipolar power supply, make sure
the center terminal is connected to the same common ground as the rest of the circuit; otherwise, it will not work properly. What is the output voltage? Does your circuit achieve the mathematical
expression Vout = 2VA + 3VB? Use the space provided for mathematical computations if necessary. Vout = __________
Electrical Engineering | {"url":"http://www.chegg.com/homework-help/questions-and-answers/1-build-test-operational-amplifier-summing-circuit-designed-prelab-using-741-type-op-amps--q2756918","timestamp":"2014-04-21T15:53:41Z","content_type":null,"content_length":"22690","record_id":"<urn:uuid:a44bfba0-aac0-4fc8-a15c-e0e8bc362a99>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00489-ip-10-147-4-33.ec2.internal.warc.gz"} |
[SciPy-user] Triangular Matrix, Matrix Manipulations
Ed Schofield schofield at ftw.at
Fri Jun 9 01:31:20 CDT 2006
On 08/06/2006, at 11:57 PM, Chris Lasher wrote:
> Hi all,
> ...
> I am interested in learning if a triangular matrix (lower or upper,
> does not matter to me) structure exists in SciPy or NumPy. I'd like to
> work with DNA or protein distance matrices, which are symmetric about
> the central axis ([0][0] to [n][n]) and such a structure might help
> greatly.
> The main two things I am looking to do are:
> * Tally the number of entries in a matrix that are equal to or
> greater/less than a specified value.
> * Randomly shuffle the values in a matrix.
> I'm interested in using an approach with these libraries to keep
> memory usage and execution times lower, as some of these distance
> matrices can be thousands x thousands of sequences. A triangular
> matrix structure might be nice to halve the amount of iteration and
> also make it easier to randomly shuffle the values (since a square
> matrix requires the values to be shuffled symmetrically, or to be
> built from scratch one value at a time).
Are the upper triangles of your matrices sparse? If not, I suggest
you use dense arrays, since the memory overhead will only be a factor
of two and implementing it will be easier.
SciPy doesn't currently have a symmetric sparse matrix format, but
this probably wouldn't help with your problem anyway; the CSR or CSC
type should serve you just as well. The first point you mentioned is
easy to support with these types, but the second could be problematic
unless the shuffle keeps the zeros in the same places ...
-- Ed
More information about the SciPy-user mailing list | {"url":"http://mail.scipy.org/pipermail/scipy-user/2006-June/008243.html","timestamp":"2014-04-16T07:42:51Z","content_type":null,"content_length":"4364","record_id":"<urn:uuid:715fc98e-b9e8-4e02-a082-928c0319822c>","cc-path":"CC-MAIN-2014-15/segments/1397609521558.37/warc/CC-MAIN-20140416005201-00604-ip-10-147-4-33.ec2.internal.warc.gz"} |
Discharging a capacitor through a resistor
In the circuit below, the time required (s) for the charge on the capacitor to drop to 47% of its value after the switch is closed is 2.83 s. If R = 1340 ohms, what is C in μF (microfarad)?
(dq/dt) + q/(RC) = 0
(.47q)/(t) = q/(RC)
t/(.47R)= C
Convert C from F to uF by multiplying by 10^6
I am getting 4993 uF, but that is the wrong answer and I'm not sure where I'm going wrong. Thanks for any help.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution | {"url":"http://www.physicsforums.com/showthread.php?t=297926","timestamp":"2014-04-16T04:25:29Z","content_type":null,"content_length":"26677","record_id":"<urn:uuid:3be985f6-6e51-4d70-8595-9838d5591349>","cc-path":"CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00129-ip-10-147-4-33.ec2.internal.warc.gz"} |
Physics Department, Princeton University
Math Phys Seminar: Sourav Chatterjee (Courant Inst. NYU) 'Invariant measures and the soliton resolution conjecture'
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually
resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multi-soliton solution. Considered to be one of the fundamental
problems in the area of nonlinear dispersive equations, this conjecture has eluded a proof or even a precise formulation till date. I will present a theorem that proves a "statistical version" of
this conjecture at mass-subcritical nonlinearity. The proof involves a combination of techniques from large deviations, PDE, harmonic analysis and bare hands probability theory.
Location: Jadwin A06
Date/Time: 03/27/12 at 3:30 pm - 03/27/12 at 5:00 pm
Category: Mathematical Physics Seminar
Department: Physics | {"url":"http://www.princeton.edu/physics/events_archive/viewevent.xml?id=378","timestamp":"2014-04-18T23:08:42Z","content_type":null,"content_length":"10436","record_id":"<urn:uuid:cf52ac1d-ca5a-4f63-976d-c04c4a65ac58>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00177-ip-10-147-4-33.ec2.internal.warc.gz"} |
RSI(2) vs. DV(2)
In this post I want to flesh out the differences between tried and true RSI(2) and a new indicator I introduced yesterday DV(2) from friend of the blog, David Varadi.
The graph above shows the results of two trading strategies applied to the S&P 500 ETF SPY, versus buy & hold in grey, from 2000 to present.
The first (blue) is an extreme RSI(2) strategy that goes long at today’s close if RSI(2) closes below 10, and goes short if closes above 90. The second (red) is an extreme DV(2) strategy that goes
long if DV(2) closes below 10, and short above 90.
Geek note: this is a proof of concept so these results are frictionless (i.e. do not account for transaction costs, slippage, or return on cash). Also, I am not purporting that these threshold (10/
90) are the best (in fact, they’re very binary which I am an opponent of), but I’m trying to keep things simple and compare apples to apples.
And for the number lovers… note that I’ve also included trading a 50/50% blend of the two as well:
At first glance of the performance graph, it would appear that these strategies are more similar than they actually are. Only about a fourth of the time that at least one triggered did the other
trigger. The other three fourths of the time, only one or the other signaled a trade.
This opens up an opportunity I think to analyze divergences between the two, or at least gain some level of diversification of short-term strategies (note reduced average drawdown and improved
risk-adjusted returns in table for 50/50% strategy).
Other Thoughts…
First, RSI(2) tends to only work well at extreme readings such as the 10/90 tested here. DV(2) does the same, but also works pretty well at less extreme readings (above or below the midpoint) which
we saw in my previous post.
Second, even though both indicators are using similar lookback periods (2 days), they are using very different data sources. RSI(2) relies purely on close-to-close price changes, while DV(2) is
looking at the close relative to the day’s trading range. Again, an opportunity to analyze divergences or at least trade in parallel (which, as I talked about in Same Strategy, Different Data, can
lead to improved risk-adjusted performance).
Third, I’m not cheerleading for DV(2). It’s an interesting addition to the toolbox, but as I preach incessantly (and recently gave a bit of a negative book review because of), at the end of the day,
trading success or failure is driven by much bigger concepts (ex. confidence-based strategies, trading in multiple timeframes, etc.)
[Edit: click for a summary of all posts in this series on the DV(2) indicator]
Happy Trading,
P.S. A big thank you to David for sharing his work with us and allowing us to pick it apart in a public forum.
To stay up to date with what’s happening at the MarketSci Blog, we recommend subscribing to our RSS Feed or Email Feed.
Filed under: Trading Strategies
11 Comments
1. How about using a dynamic oversold/overbought measure on these strategies? For example by using bollinger bands?
□ Sure…I think there’s all sorts of neat things that could be done with this indicator (but that’s outside the scope of what I usually post about…I just give a vanilla test of the indicator and
then let readers torture it to their hearts content =)
2. Great post!! How many buy and sell signals did both strategies generate? Also, how many days on average were you in the market after the signal was generated?
□ RE to Raj: thanks for the kind words. 314 with an avg. hold of 1.9 days for RSI(2) and 309/1.7 for DV(2). michael
3. On a lark I tried Ver 1 (unbounded) of DV(2) for SPY, IWM, and DIA for their full histories. My results were positive, but not exceptional. Two notes/questions:
1. For DV(2) I am averaging today’s DV and yesterday’s DV(2). This may be different than your calculation (which is slightly ambiguous). Do you have this 2-day running average, or is your
calculation DV(2) = 0.5*DV(today) + 0.5*DV(yesterday). I suspect that may lead to some of my underperformance.
2. In my version (running avg. DV(2)) shorts almost always did poorly – either flat or slightly losing, except in the last year and a bit of extreme market collapse. Have you looked at a
long-only version of this?
I’ve been impressed by what I’ve seen on you site so far.
□ RE to Zack: I’ve had quite a few people a bit confused over my less-than-robust calculation description. See this xls file: http://www.marketsci.com/supporting.docs/dv2_calculation.xls
Strategy #1 and #2 in the file are the unbounded DV(2) above/below 0, and the bounded DV(2) below 10/above 90 strategies.
4. Michael, yet another great post. Thanks for the ideas to shake and bake.
5. hi Michael,
in my past efforts at testing these, i had noticed that some of these applied to broad ETFs like SPY seemed to work far better in high volatility environments. Your graphs seems to bear that out.
they work better in the bear markets (characterized by higher volatility) vs. the bull period between 2003-2007.
comments ?
as always, congrats on the high quality work !
□ Two immediate thoughts…(1) even if win % was constant, it will always appear that a strategy is more effective in a high vol. environment (more money to be made on daily swings), and (2) I
didn’t test the following statement on this particular strategy, but generally speaking, I’ve found short-term mean-reversion indicators to work at least reasonably well long in all
environments (bull, bear, and sideways) but short only in sideways and bear markets – I think this has something to do with the market’s tendency to slowly grind upwards, but fall very
quickly. michael
☆ thanks for your comments and insight..
i’ve had to use more medium term momentum strategies (RSI being too short term) for the bull markets, intermixed with short term based on RSI and such for the bear market areas to get a
better bang for the buck in the past.
• about the marketsci blog
Michael Stokes
Developer of the
family of trading strategies. This blog is a repository for my (geeky) research on wrangling these unruly markets.
• blogroll
My blogroll is simple.
All the quant nerds you'll find at:
Plus Abnormal Returns and Kirk Report for curated goodness.
And Volatility Made Simple, VIX & More, Six Figure, Only VIX, and Condor Options for my VIX related geekery.
• Recent Posts | {"url":"http://marketsci.wordpress.com/2009/07/16/rsi2-vs-dv2/","timestamp":"2014-04-18T10:35:49Z","content_type":null,"content_length":"51035","record_id":"<urn:uuid:d3877dae-a7ea-4d0b-bd03-51b9f681768c>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00137-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Help
November 23rd 2009, 05:24 AM #1
Sep 2009
1- Express 12cosx+ 9sinx in the form Rcos(x-A) where R is greater than 0 and A is between 0 and 90.
I did this one and got 15cos(x-0,644) (in radians)
I cant do the second part.
b) Use the method of part a to find the smallest positve root of A of the equation 12cosx+9sinx = 14
Hello Oasis1993
1- Express 12cosx+ 9sinx in the form Rcos(x-A) where R is greater than 0 and A is between 0 and 90.
I did this one and got 15cos(x-0,644) (in radians)
I cant do the second part.
b) Use the method of part a to find the smallest positve root of A of the equation 12cosx+9sinx = 14
You're right so far!
For part (b), just say:
$15\cos(x-A) = 14$
$\Rightarrow \cos(x-A)=\frac{14}{15}= 0.9333$
$\Rightarrow x-A = \pm 0.3672 +2n\pi, n \in \mathbb{Z}$ (Do you understand this bit?)
$\Rightarrow x = A \pm 0.3672 + 2n\pi$
And for the smallest positive value of $x$, which sign do we take, and which value of $n$? (I get the answer $x=0.277$. Do you?)
Thank you!
Yes your answer is correct.
But i didnt understand that part where you asked...?
Hello Oasis1993
The principal value of $(x - A)$ is $0.3672$ radians. Other angles that will have the same cosine as this will be $0.3672$ radians on either side of a multiple of $2\pi$. Any multiple of $2\pi$
is $2n\pi$, and 'on either side' of this means adding or subtracting $0.3672$ from $2n\pi$. Hence $\pm0.3672 + 2n\pi$.
November 23rd 2009, 07:44 AM #2
November 23rd 2009, 11:07 AM #3
Sep 2009
November 23rd 2009, 11:24 AM #4 | {"url":"http://mathhelpforum.com/trigonometry/116281-trig.html","timestamp":"2014-04-21T13:04:06Z","content_type":null,"content_length":"43155","record_id":"<urn:uuid:4f8b3e9c-9de5-496c-a31e-6ef5a9352c63>","cc-path":"CC-MAIN-2014-15/segments/1398223206118.10/warc/CC-MAIN-20140423032006-00088-ip-10-147-4-33.ec2.internal.warc.gz"} |
Third Grade Math Worksheets
You may freely use any of the third grade worksheets below in your classroom or at home. Just click on the math worksheet title and click on the download link under the worksheet image. Feel free to
duplicate as necessary.
Your student can color this car correctly by solving the multiplication problems in this color by number page.
This multiplication color by number page of a kitten is the “cat’s meow.”
It’s “Batter up!” for this multiplication color by number page for baseball fans.
This multiplication color by number page features a darling dinosaur.
Make math fun with this duck color by number page using multiplication!
You’ll go ape over this multiplication color by number page featuring a monkey!
This color by number page is a “grrr-eat” way to practice multiplication!
In this worksheet, your young one will take the numbers from the dice and write a number sentence.
For study purposes, here’s a complete set of multiplication flash cards for factors 0-9.
Here’s a multiplication match game with numbers 1 through 6.
This multiplication match game features numbers 5-9.
This multiplication maze is a fun way to practice math!
Your student can have fun while practicing his multiplication with this maze worksheet.
Your student will write a number sentence based on the numbers on the dice.
This worksheet is a timed multiplication drill where the second factor is 0 through 6.
Here’s a multiplication worksheet where the bottom factor is 0 through 10.
This multiplication practice worksheet has your student solving problems where the second factor is 0-11.
Your student will be proficient in multiplication after practicing with this worksheet where the factors are between 0 and 12.
Start your student off right with this multiplication practice where the second factor is 0-2.
You can time your little mathematician in this multiplication timed exercise where the bottom factor is 0-3. | {"url":"http://www.k12mathworksheets.com/grade-level/third-grade-worksheets/","timestamp":"2014-04-17T06:58:36Z","content_type":null,"content_length":"38153","record_id":"<urn:uuid:3490ef23-bed9-453c-8d5d-af8a06a6b916>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00418-ip-10-147-4-33.ec2.internal.warc.gz"} |
Lake Worth Algebra Tutor
Find a Lake Worth Algebra Tutor
...I am passionate about learning and expanding access to higher education, and I believe that everyone can enjoy learning and writing when equipped with the right tools. I have experience
tutoring high school and college students, primarily in English, literary studies, and writing. In high school I scored 800 on the SAT Verbal section, and I scored in the 600s in SAT Math.
40 Subjects: including algebra 2, GED, calculus, GRE
...Qualifications: bachelor degree from university of science in Palermo, Italy, 1983. Note: I am a very patient and understandable man when it comes to teach students, they deserve all the
attention they require, they depend on us.I was born in Italy, and before I came to the USA, I had to finish middle school. Then I completed high school in in New York.
17 Subjects: including algebra 1, algebra 2, geometry, ASVAB
You came looking for a tutor because there is a subject that is just not clicking for you or your child. Have you ever thought that maybe there was another way of looking at it or maybe a little
more one-on-one would help you to grasp the concepts? My approach is that we first start by speaking with the one another and get an idea of what you already understand.
17 Subjects: including algebra 2, grammar, algebra 1, literature
This summer, I will be starting the Masters program in Education at the University of Florida while teaching as a student teacher in a Palm Beach County School. I have tutored in the past and feel
comfortable with a variety of subjects and ages. I have my degree in Elementary Education and am reading and ESOL endorsed.
13 Subjects: including algebra 2, algebra 1, reading, ESL/ESOL
- Economics major in undergrad at JMU who completed CPA requirements at FAU while working.- Worked for a Big 4 public accounting firm for 4 1/2 years as an auditor, included teaching staff and
clients proper accounting processes and GAAP. I have direct experience with Sarbanes-Oxley 404 (SOX), acco...
6 Subjects: including algebra 1, accounting, SAT math, prealgebra | {"url":"http://www.purplemath.com/lake_worth_algebra_tutors.php","timestamp":"2014-04-18T00:35:05Z","content_type":null,"content_length":"24318","record_id":"<urn:uuid:598c130d-7447-4f71-be28-e32ddb093630>","cc-path":"CC-MAIN-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00375-ip-10-147-4-33.ec2.internal.warc.gz"} |
Geometry question
September 20th 2010, 03:16 PM #1
Sep 2010
Geometry question
Okay I am having a problem with this story problem it says Kim wants to put a small fence in the shape of a circle around a tree in her backyard. She wants the radius of the circle to be 3 feet,
leaving room to plant flowers around the tree. How many feet of fencing does she need to buy if it is sold by the foot? (use 3.14 to approximate pie.) I am not sure where to begin.
You were not taught how to find the circumference of a circle?
yes I was my brain was not thinking thanks so much for reminding me.
September 20th 2010, 05:43 PM #2
MHF Contributor
Dec 2007
Ottawa, Canada
September 20th 2010, 05:47 PM #3
Sep 2010 | {"url":"http://mathhelpforum.com/geometry/156839-geometry-question.html","timestamp":"2014-04-17T08:23:17Z","content_type":null,"content_length":"33277","record_id":"<urn:uuid:01bc4ae1-512d-4bfc-bf39-fde0eb846e47>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00617-ip-10-147-4-33.ec2.internal.warc.gz"} |
Thorsten Kellermann
Thorsten Kellermann
Room: 0.62
Phone: +49 (0) 331 567 7186
Fax: +49 (0) 331 567 7298
email: (@aei.mpg.de) thorsten.kellermann
As a member of the numerical relativity group my research covers two main parts. On the one hand I am developing new numerical methods to solve the equations which come up in the field of
relativistic astrophysics. On the other hand I am looking for scenario which can be described with equations in ideal relativistic hydrodynamics in an axisymmetric approach.
Improving numerical methods
In the first part of my PhD work, I developed an axisymmetric version of theĀ Whisky Code . During working out the formulations of relativistic hydrodynamics in cylindrical coordinates I realised,
that there are two ways two ways to write down the equations. From a mathematical point of few the equations are equal, but from the numerical point of few the equations show different behaviour in
the precision of the results an the convergence behaviour. A detailed analysis can be find the related publication (see below).
Critical behaviour in relativistic hydrodynamics
Two colliding neutron stars can end up in a new neutron star or in a black hole. With the Whisky2D code I consider the head on collision of two equal neutron stars initial data. The initial data are
part of a n-dimensional parameter space which includes e.g. speed, central density, parameter of the equation of state and so on. An investigation of the head on collision shows that the parameter
space is divided in a part which results in a new neutron star and a part which results in a black hole. Furthermore there is an n-1 dimensional hyper surface between the two parts of parameter
space. Taking initial data which are very close to the hyper surface produce after the merging of the two stars a metastable equilibrium. It means before the system come up with a stable neutron star
or a black hole, there is a intermediate star. The life time of this metastable equilibrium is related to the aberration of the taken initial parameter to parameter which are on the hyper surface. A
mathematical investigation of the problem shows, that initial data taken from the hyper surface produce an intermediate star with infinite life time.
In this project I am looking for parameter sets which are as close a possible to the metastable equilibrium. The goal is two figure out the physical properties of the system in the close the critical
limit. Results could be use to figure out new upper limits of the occurrence of black holes.
Here is a link to my publications since 2000 (from Spires) | {"url":"http://numrel.aei.mpg.de/people/kellermann","timestamp":"2014-04-20T23:26:37Z","content_type":null,"content_length":"13326","record_id":"<urn:uuid:cbaf4ba3-e52f-4d89-8c23-262747173d32>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00226-ip-10-147-4-33.ec2.internal.warc.gz"} |
A Design Principle for Hash Functions
, 1996
"... The use of cryptographic hash functions like MD5 or SHA for message authentication has become a standard approach inmanyInternet applications and protocols. Though very easy to implement, these
mechanisms are usually based on ad hoc techniques that lack a sound security analysis. We present new cons ..."
Cited by 476 (38 self)
Add to MetaCart
The use of cryptographic hash functions like MD5 or SHA for message authentication has become a standard approach inmanyInternet applications and protocols. Though very easy to implement, these
mechanisms are usually based on ad hoc techniques that lack a sound security analysis. We present new constructions of message authentication schemes based on a cryptographic hash function. Our
schemes, NMAC and HMAC, are proven to be secure as long as the underlying hash function has some reasonable cryptographic strengths. Moreover we show, in a quantitativeway, that the schemes retain
almost all the security of the underlying hash function. In addition our schemes are e cient and practical. Their performance is essentially that of the underlying hash function. Moreover they use
the hash function (or its compression function) as a black box, so that widely available library code or hardware can be used to implement them in a simple way, and replaceability of the underlying
hash function is easily supported.
- Proceedings of the 37th Symposium on Foundations of Computer Science, IEEE , 1996
"... Abstract Pseudorandom function families are a powerful cryptographic primitive, yielding, in partic-ular, simple solutions for the main problems in private key cryptography. Their existence
based on general assumptions (namely, the existence of one-way functions) has been established.In this work we ..."
Cited by 92 (20 self)
Add to MetaCart
Abstract Pseudorandom function families are a powerful cryptographic primitive, yielding, in partic-ular, simple solutions for the main problems in private key cryptography. Their existence based on
general assumptions (namely, the existence of one-way functions) has been established.In this work we investigate new ways of designing pseudorandom function families. The goal is to find
constructions that are both efficient and secure, and thus eventually to bring thebenefits of pseudorandom functions to practice.
- CryptoBytes , 1996
"... Introduction Two parties communicating across an insecure channel need a method by which any attempt to modify the information sent by one to the other, or fake its origin, is detected. Most
commonly such a mechanism is based on a shared key between the parties, and in this setting is usually calle ..."
Cited by 46 (1 self)
Add to MetaCart
Introduction Two parties communicating across an insecure channel need a method by which any attempt to modify the information sent by one to the other, or fake its origin, is detected. Most commonly
such a mechanism is based on a shared key between the parties, and in this setting is usually called a MAC, or Message Authentication Code. (Other terms include Integrity Check Value or Cryptographic
Checksum). The sender appends to the data D an authentication tag computed as a function of the data and the shared key. At reception, the receiver recomputes the authentication tag on the received
message using the shared key, and accepts the data as valid only if this value matches the tag attached to the received message. The most common approach is to construct MACs from block ciphers like
DES. Of such constructions Department of Computer Science & Engineering, Mail Code 0114, University of California at San Diego, 9500 Gilman Driv
, 2001
"... In this paper, we study several issues related to the notion of "secure" hash functions. Several necessary conditions are considered, as well as a popular sufficient condition (the so-called
random oracle model). We study the security of various problems that are motivated by the notion of a secure ..."
Cited by 28 (2 self)
Add to MetaCart
In this paper, we study several issues related to the notion of "secure" hash functions. Several necessary conditions are considered, as well as a popular sufficient condition (the so-called random
oracle model). We study the security of various problems that are motivated by the notion of a secure hash function. These problems are analyzed in the random oracle model, and we prove that the
obvious trivial algorithms are optimal. As well, we look closely at reductions between various problems. In particular, we consider the important question "does preimage resistance imply collision
resistance?". Finally, we study the relationship of the security of hash functions built using the Merkle-Damgard construction to the security of the underlying compression function.
- Advances in Cryptology – EUROCRYPT ’04, Lecture Notes in Computer Science , 2004
"... Abstract. Textbooks tell us that a birthday attack on a hash function h with range size r requires r 1/2 trials (hash computations) to find a collision. But this is quite misleading, being true
only if h is regular, meaning all points in the range have the same number of pre-images under h; if h is ..."
Cited by 27 (2 self)
Add to MetaCart
Abstract. Textbooks tell us that a birthday attack on a hash function h with range size r requires r 1/2 trials (hash computations) to find a collision. But this is quite misleading, being true only
if h is regular, meaning all points in the range have the same number of pre-images under h; if h is not regular, fewer trials may be required. But how much fewer? This paper addresses this question
by introducing a measure of the “amount of regularity ” of a hash function that we call its balance, and then providing estimates of the success-rate of the birthday attack, and the expected number
of trials to find a collision, as a function of the balance of the hash function being attacked. In particular, we will see that the number of trials can be significantly less than r 1/2 for hash
functions of low balance. This leads us to examine popular design principles, such as the MD (Merkle-Damg˚ard) transform, from the point of view of balance preservation, and to mount experiments to
determine the balance of popular hash functions. 1
- In ICALP 2008, Part II , 2008
"... Abstract. We consider how to build an efficient compression function from a small number of random, noncompressing primitives. Our main goal is to achieve a level of collision resistance as
close as possible to the optimal birthday bound. We present a 2n-to-n bit compression function based on three ..."
Cited by 15 (3 self)
Add to MetaCart
Abstract. We consider how to build an efficient compression function from a small number of random, noncompressing primitives. Our main goal is to achieve a level of collision resistance as close as
possible to the optimal birthday bound. We present a 2n-to-n bit compression function based on three independent n-to-n bit random functions, each called only once. We show that if the three random
functions are treated as black boxes then finding collisions requires Θ(2 n/2 /n c) queries for c ≈ 1. This result remains valid if two of the three random functions are replaced by a fixed-key ideal
cipher in Davies-Meyer mode (i.e., EK(x) ⊕ x for permutation EK). We also give a heuristic, backed by experimental results, suggesting that the security loss is at most four bits for block sizes up
to 256 bits. We believe this is the best result to date on the matter of building a collision-resistant compression function from non-compressing functions. It also relates to an open question from
Black et al. (Eurocrypt’05), who showed that compression functions that invoke a single non-compressing random function cannot suffice. We also explore the relationship of our problem with that of
doubling the output of a hash function and we show how our compression function can be used to double the output length of ideal hashes.
, 1994
"... We outline constructions for both pseudo-random generators and one-way hash functions. These constructions are based on the exact TSP (XTSP), a special variant of the well known traveling
salesperson problem. We prove that these constructions are secure if the XTSP is infeasible. Our constructions a ..."
Cited by 2 (1 self)
Add to MetaCart
We outline constructions for both pseudo-random generators and one-way hash functions. These constructions are based on the exact TSP (XTSP), a special variant of the well known traveling salesperson
problem. We prove that these constructions are secure if the XTSP is infeasible. Our constructions are easy to implement, appear to be fast, but require a large amount of memory. | {"url":"http://citeseerx.ist.psu.edu/showciting?cid=1367474","timestamp":"2014-04-19T02:59:01Z","content_type":null,"content_length":"30120","record_id":"<urn:uuid:30276740-3f3a-4d03-a902-1a3969252e93>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00311-ip-10-147-4-33.ec2.internal.warc.gz"} |
Probability counting excercise
March 8th 2011, 02:27 PM
Probability counting excercise
Ten cards are drawn randomly from a deck of 52 cards (13 cards of each of the 4 different suits).
Each selected card is put into a pile that depends on what suit the card is. (4 total piles)
a) What is the probability that the largest pile contains 4 cards, the next largest pile has 3 cards, the next largest has two cards and the smallest has 1 card?
I am not sure how to begin part a. You want to select 4 of one suit, 3 of a different suit, then 2 of a yet again different suit and then a single card of the last suit. If the numbers were tied
to specific suits I could see how to do part a, but this more general case is confusing me.
b) What is the probability that two of the piles have 3 cards, one has 4 cards, and one has no cards?
So when you draw ten cards you don't get 1 of the 4 suits. However, like part a, since the numbers aren't tied to specific suits, I am confused on how to proceed.
Any help would be greatly appreciated. Thank you kindly.
March 8th 2011, 04:01 PM
a) Do you suppose you can solve the problem if given the suits? Say 4 hearts, 3 clubs, 2 diamonds, and 1 spade?
If so, then just multiply your answer by 4! to allow for the possible arrrangements of the suits.
March 8th 2011, 05:47 PM
so the answer to part a is
$\frac{4!*\begin{pmatrix}\;\;13<br /> &\\\;\;4<br /> \end{pmatrix}*\begin{pmatrix}\;\;13<br /> &\\\;\;3<br /> \end{pmatrix}\begin{pmatrix}\;\;13<br /> &\\\;\;2<br /> \end{pmatrix}\begin{pmatrix}
\;\;13<br /> &\\\;\;1<br /> \end{pmatrix}}{\begin{pmatrix}\;\;52<br /> &\\\;\;10<br /> \end{pmatrix}}$
two questions
why isn't the denominator $52*51*50*49*48*47*46*45*44*43$
also in part b do we multiply by $3!$ or still by $4!$ since we still have to consider the pile of zero cards?
March 8th 2011, 06:23 PM
Hello, Sheld!
Here's another approach . . . I'll do part (a).
Ten cards are drawn randomly from a deck of 52 cards.
Each selected card is put into a pile that depends on what suit the card is.
(a) What is the probability that the largest pile contains 4 cards, the next largest
has 3 cards, the next largest has 2 cards and the smallest has 1 card?
There are: . $\displaystyle{52\choose10}$ possible 10-card hands.
. . This is the denominator of the probability.
It is not $_{52}P_{10}$ because the order of the cards is not considered.
For the first pile, there are 4 choices for the suit.
. . Then there are ${13\choose4}$ ways to get 4 cards of that suit.
For the second pile, there are 3 choices for the suit.
. . Then there are ${13\choose3}$ ways to get 3 cards of that suit.
For the third pile, there are 2 choices for the suit.
. . Then there are ${13\choose2}$ ways to get 2 cards of that suit.
For the fourth pile, there is 1 choice for the suit.
. . Then there are ${13\choose1}$ ways to get 1 card of that suit.
Hence, the numerator is: . $\displaystyle 4\!\cdot\!{13\choose4}\!\cdot\! 3\cdot\!{13\choose3}\!\cdot\!2\cdot\!{13\choose2}\ !\cdot\!1\!\cdot\!{13\choose1}$
March 8th 2011, 07:49 PM
Ah I understand now. The 10 cards are the 10 cards, it doesnt matter what order they are in.
I also believe I got the answer to part b)
$\frac{4!*\begin{pmatrix}\;\;13<br /> &\\\;\;4<br /> \end{pmatrix}*\begin{pmatrix}\;\;13<br /> &\\\;\;3<br /> \end{pmatrix}\begin{pmatrix}\;\;13<br /> &\\\;\;3<br /> \end{pmatrix}\begin{pmatrix}
\;\;13<br /> &\\\;\;0<br /> \end{pmatrix}}{\begin{pmatrix}\;\;52<br /> &\\\;\;10<br /> \end{pmatrix}}$
$\begin{pmatrix}\;\;13<br /> &\\\;\;0<br /> \end{pmatrix} = 1$
Thanks a lot! | {"url":"http://mathhelpforum.com/statistics/173893-probability-counting-excercise-print.html","timestamp":"2014-04-18T06:11:14Z","content_type":null,"content_length":"11204","record_id":"<urn:uuid:b0afe3e8-24d8-48dc-86f2-ade6299e7647>","cc-path":"CC-MAIN-2014-15/segments/1397609532573.41/warc/CC-MAIN-20140416005212-00341-ip-10-147-4-33.ec2.internal.warc.gz"} |
Simplify, `(3x^-4 d^5)^2 times 12cd^-4`
give answer with non-negative exponents
(3x to the -4 power d to the 5th... - Homework Help - eNotes.com
Simplify, `(3x^-4 d^5)^2 times 12cd^-4`
give answer with non-negative exponents
(3x to the -4 power d to the 5th power) squared times 12cd to the negative 4th power
To simplify:
`(3x^-4 d^5)^2 times 12cd^-4`
First remove the breackets and use the rules of exponents by multiplying exponents due to the bracket:
`therefore = 3^2x^(-4 times2)d^(5 times2) times 12 c d^-4`
Now arrange in terms of the rules of exponents. Negartive exponents indicate division:
`therefore = (9 d^10)/x^8 times (12c)/d^4`
Now create one expression by combining like terms where appropriate:
`therefore = (108 c d ^(10-4))/x^8`
Note that the base "d" has been combined using the rules.
Ans: `therefore = (108cd^6)/x^8`
Join to answer this question
Join a community of thousands of dedicated teachers and students.
Join eNotes | {"url":"http://www.enotes.com/homework-help/simplify-give-answer-with-non-negative-exponents-441221","timestamp":"2014-04-19T07:13:07Z","content_type":null,"content_length":"25840","record_id":"<urn:uuid:5896a207-2e8d-4ae5-9f36-edfcedd9e038>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00336-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Forum - Problems Library - Math Fundamentals, Geometry: 3-D Figures
This page:
2-D figures
About Levels
of Difficulty
Math Fundamentals
operations with numbers
number sense
number theory
parts of wholes
ratio & proportion
algebraic reasoning
discrete math
logical reasoning
statistics & data analysis
Browse all
Math Fundamentals
Math Fundamentals
About the
PoW Library
3-D Figures
These problems focus on three-dimensional objects.
Related Resources
Interactive resources from our Math Tools project:
Math 4: Geometry in Space
The closest match in our Ask Dr. Math archives:
Elementary Geometry
NCTM Standards:
Geometry Standard for Grades 3-5
Access to these problems requires a Membership. | {"url":"http://mathforum.org/library/problems/sets/fun_geometry_3d.html","timestamp":"2014-04-16T13:40:59Z","content_type":null,"content_length":"11949","record_id":"<urn:uuid:554bb767-492d-4983-9633-3430074e9d45>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00571-ip-10-147-4-33.ec2.internal.warc.gz"} |
NAEP Assessment Item, Grade 4: List fractions equivalent to given fractions
Professional Commentary
Students are asked to identify equivalent fractions. This constructed-response question is an "easy" test item used in grade 4 of the 2007 National Assessment of Educational Progress (see About NAEP
). The URL link (above) takes the user to the NAEP test item, with access to performance data by various subgroups of students, a scoring guide, sample student responses, and a discussion of the
content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP
Reference Number: 2007-4M9, No. 11. (sw)
Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Benchmarks (3–4)
Recognize and generate equivalent representations for whole numbers, fractions and decimals.
Grade Level Indicators (Grade 4)
Identify and generate equivalent forms of fractions and decimals. For example: a. Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., 1/2, 5/10,
"five tenths," 0.5, shaded rectangles with half, and five tenths. b. Understand and explain that ten tenths is the same as one whole in both fraction and decimal form.
Principles and Standards for School Mathematics
Number and Operations Standard
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Expectations (3–5)
recognize and generate equivalent forms of commonly used fractions, decimals, and percents; | {"url":"http://www.ohiorc.org/record/11008.aspx","timestamp":"2014-04-19T14:39:54Z","content_type":null,"content_length":"22067","record_id":"<urn:uuid:b3406bdc-2852-4d08-bb8d-9519715e2288>","cc-path":"CC-MAIN-2014-15/segments/1398223203422.8/warc/CC-MAIN-20140423032003-00469-ip-10-147-4-33.ec2.internal.warc.gz"} |
Bialgebraic Methods and Modal Logic in Structural Operational Semantics
"... A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is re-examined and improved in some aspects. Firstly, a more
abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal l ..."
Cited by 3 (1 self)
Add to MetaCart
A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is re-examined and improved in some aspects. Firstly, a more abstract,
conceptual proof of the main compositionality theorem is given, based on an understanding of modal logic as a study of coalgebras in slice categories of adjunctions. Secondly, a more concrete
understanding of the assumptions of the theorem is provided, where proving compositionality amounts to finding a syntactic distributive law between two collections of predicate liftings. Keywords:
structural operational semantics, modal logic, coalgebra 1
"... Distributive laws of syntax over behaviour (cf. [1, 3]) are, among other things, a well-structured way of defining algebraic operations on final coalgebras. For a simple example, consider the
set B ω of infinite streams of elements of B; this carries a final coalgebra w = 〈hd,tl〉: B ω → B × B ω for ..."
Cited by 2 (2 self)
Add to MetaCart
Distributive laws of syntax over behaviour (cf. [1, 3]) are, among other things, a well-structured way of defining algebraic operations on final coalgebras. For a simple example, consider the set B ω
of infinite streams of elements of B; this carries a final coalgebra w = 〈hd,tl〉: B ω → B × B ω for the endofunctor F = B × − on Set. If B comes with a binary operation +, one can define an
addition operation ⊕ on streams coinductively: hd(σ ⊕ τ) = hd(σ) + hd(τ) tl(σ ⊕ τ) = tl(σ) ⊕ tl(τ). It is easy to see that these equations define a distributive law, i.e., a natural transformation λ:
ΣF ⇒ FΣ, where ΣX = X 2 is the signature endofunctor corresponding to a single binary operation. The operation ⊕: B ω × B ω → B ω is now defined as the unique morphism to the final coalgebra as in:
ΣB ω B ω
- MATH. STRUCT. IN COMP. SCIENCE , 2010
"... This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, state-based modelling of components. The feedback operator on components is shown to
satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of sta ..."
Add to MetaCart
This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, state-based modelling of components. The feedback operator on components is shown to satisfy
the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of standard string diagrams for monoidal categories, for representing and manipulating component
diagrams. The microcosm principle then yields a canonical “inner” traced monoidal structure on the category of resumptions (elements of final coalgebras / components). This generalises an observation
by Abramsky, Haghverdi and Scott.
"... In this paper, we study extensions of mathematical operational semantics with algebraic effects. Our starting point is an effect-free coalgebraic operational semantics, given by a natural
transformation of syntax over behaviour. The operational semantics of the extended language arises by distributi ..."
Add to MetaCart
In this paper, we study extensions of mathematical operational semantics with algebraic effects. Our starting point is an effect-free coalgebraic operational semantics, given by a natural
transformation of syntax over behaviour. The operational semantics of the extended language arises by distributing program syntax over effects, again inducing a coalgebraic operational semantics, but
this time in the Kleisli category for the monad derived from the algebraic effects. The final coalgebra in this Kleisli category then serves as the denotational model. For it to exist, we ensure that
the the Kleisli category is enriched over CPOs by considering the monad of possibly infinite terms, extended with a bottom element. Unlike the effectless setting, not all operational specifications
give rise to adequate and compositional semantics. We give a proof of adequacy and compositionality provided the specifications can be described by evaluation-in-context. We illustrate our techniques
with a simple extension of (stateless) while programs with global store, i.e. variable lookup.
"... Abstract. Process algebra, e.g. CSP, offers different semantical observations (e.g. traces, failures, divergences) on a single syntactical system description. These observations are either
computed algebraically from the process syntax, or “extracted ” from a single operational model. Bialgebras cap ..."
Add to MetaCart
Abstract. Process algebra, e.g. CSP, offers different semantical observations (e.g. traces, failures, divergences) on a single syntactical system description. These observations are either computed
algebraically from the process syntax, or “extracted ” from a single operational model. Bialgebras capture both approaches in one framework and characterize their equivalence; however, due to use of
finality, lack the capability to simultaneously cater for various semantics. We suggest to relax finality to quasi-finality. This allows for several semantics, which also can be coarser than
bisimulation. As a case study, we show that our approach works out in the case of the CSP failures model. 1
, 2010
"... Abstract. Jonsson and Larsen’s notion of probabilistic simulation is studied from a coalgebraic perspective. The notion is compared with two generic coalgebraic definitions of simulation: Hughes
and Jacobs ’ one, and the one introduced previously by the author. We show that the first almost coincide ..."
Add to MetaCart
Abstract. Jonsson and Larsen’s notion of probabilistic simulation is studied from a coalgebraic perspective. The notion is compared with two generic coalgebraic definitions of simulation: Hughes and
Jacobs ’ one, and the one introduced previously by the author. We show that the first almost coincides with the second, and that the second is a special case of the last. We investigate implications
of this characterization; notably the Jonsson-Larsen simulation is shown to be sound, i.e. its existence implies trace inclusion. 1 | {"url":"http://citeseerx.ist.psu.edu/showciting?doi=10.1.1.106.5730","timestamp":"2014-04-21T02:31:58Z","content_type":null,"content_length":"26688","record_id":"<urn:uuid:1e44b91a-6a7b-42ad-bfca-d756e89890fa>","cc-path":"CC-MAIN-2014-15/segments/1397609539447.23/warc/CC-MAIN-20140416005219-00472-ip-10-147-4-33.ec2.internal.warc.gz"} |
Suggestions for textbook?
Suggestions for textbook?
This fall I will be teaching a 1-credit seminar for freshmen in our
honors program.
They will be taking this at the same time as they get the introductory
CS course (out of How to Design Programs, by Felleisen et al), and a
discrete math course (taught out of Rosen, Discrete Mathematics and
its Applications 5ed).
My goal is to give them something that will challenge but not
overwhelm them and that will somehow complement what they are getting
in these courses.
My plan is to give them a look at computability theory, using
lambda-calculus as a vehicle. This will allow them to think about
doing mathematics about programs and writing programs about
mathematical objects.
If I can get them through the undecidability of the halting problem in the
term, I will count myself successful.
Does anyone have suggestions for a text or other materials that might
be suitable for this?
Chris Hankin's book on Lambda Calculi is about right, but is out of
print. Barendregt's article on Functional Programming and Lambda
Calculus in the Handbook of Theoretical Computer Science B covers the
right material, but is probably scary for freshmen.
Additional parameters: I will have these folks for 1 hour per week
for 15 weeks. The average SAT will be 1250-1300 or so. I could cover
the material using some other machine model, but they will get this
material again in Theory of Computation, using the standard models,
and I'd like to avoid making life difficult for the instructor in that
Any thoughts? | {"url":"http://www.seas.upenn.edu/~sweirich/types/archive/1999-2003/msg01383.html","timestamp":"2014-04-21T10:30:23Z","content_type":null,"content_length":"3443","record_id":"<urn:uuid:a7811f3c-58da-48b8-acd0-802aa298dfca>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00301-ip-10-147-4-33.ec2.internal.warc.gz"} |
Paterson, NJ Algebra 2 Tutor
Find a Paterson, NJ Algebra 2 Tutor
...I took Biostatistics in the graduate level during my Master's program and received an A. It dealt with applying statistical methods in biology and medicine. Topics covered were Statistical
analysis for cross-sectional studies and case-control studies.
18 Subjects: including algebra 2, calculus, statistics, algebra 1
...I have a great deal of experience with college admissions, especially ivy league admissions. I was admitted to three of the eight ivy league schools before selecting UPenn. I am familiar with
all of the aspects of the admissions process, including alumni interviews, essay writing, test preparation, etc.
43 Subjects: including algebra 2, English, calculus, reading
...Upon graduation, I was granted "distinction in the major" for outstanding scholarship, and awarded a coveted prize for my undergraduate research pursuits. I have extensive experience in
tutoring/teaching biochemistry through my work as a peer tutor during college. I recently graduated with an I...
24 Subjects: including algebra 2, reading, English, Spanish
...At present I teach test preparation and tutor while I work on a book. In the past, I have taught middle school science, high school English, and elementary math and test-based preparation for
the SAT, SSAT, ISEE in English and math. My main background is in English, but I started college in engineering school.
30 Subjects: including algebra 2, reading, English, geometry
...I worked for 5 years in Marketing Analytics which utilized my Econometrics and Statistical background. In high school I graduated in the Top 10, and had the highest SAT score in my graduating
class, with a perfect score in Math. I have some experience tutoring during high school, but I also hav...
13 Subjects: including algebra 2, calculus, statistics, economics
Related Paterson, NJ Tutors
Paterson, NJ Accounting Tutors
Paterson, NJ ACT Tutors
Paterson, NJ Algebra Tutors
Paterson, NJ Algebra 2 Tutors
Paterson, NJ Calculus Tutors
Paterson, NJ Geometry Tutors
Paterson, NJ Math Tutors
Paterson, NJ Prealgebra Tutors
Paterson, NJ Precalculus Tutors
Paterson, NJ SAT Tutors
Paterson, NJ SAT Math Tutors
Paterson, NJ Science Tutors
Paterson, NJ Statistics Tutors
Paterson, NJ Trigonometry Tutors
Nearby Cities With algebra 2 Tutor
Clifton, NJ algebra 2 Tutors
Elmwood Park, NJ algebra 2 Tutors
Fair Lawn algebra 2 Tutors
Fairlawn, NJ algebra 2 Tutors
Garfield, NJ algebra 2 Tutors
Haledon algebra 2 Tutors
Hawthorne, NJ algebra 2 Tutors
Little Falls, NJ algebra 2 Tutors
North Haledon, NJ algebra 2 Tutors
Passaic algebra 2 Tutors
Passaic Park, NJ algebra 2 Tutors
Prospect Park, NJ algebra 2 Tutors
Totowa algebra 2 Tutors
Wayne, NJ algebra 2 Tutors
Woodland Park, NJ algebra 2 Tutors | {"url":"http://www.purplemath.com/Paterson_NJ_algebra_2_tutors.php","timestamp":"2014-04-21T12:54:57Z","content_type":null,"content_length":"24147","record_id":"<urn:uuid:768d609e-2329-4608-88c7-0e8bc8c77dc2>","cc-path":"CC-MAIN-2014-15/segments/1397609539776.45/warc/CC-MAIN-20140416005219-00081-ip-10-147-4-33.ec2.internal.warc.gz"} |
CIRCUITS Assignment Help Please :)
1. The problem statement, all variables and given/known data
Alright I was given an assignment and I have done all the questions, but I'm not sure if they are right and would like some help if they aren't.
1. A wire has resistivity 5.6 x 10^-8 Ωm at 20 °C and a temperature coefficient of resistance 4.5 x 10^-3 °C-1^-1. What length of the wire (radius 12.5mm) would you need to make a heating element
that would dissipate 1000 watts? The heating element operates at 220 volts and has a temperature of 700°C.
_40v----80Ω---- l l ------- (ignore the ______ that's the only way it would let me place the 40ohm and 10ohm there.
___l _____________10Ω___l
So there is a voltage source of 40v connected in series with an 80 ohm resistor connected in series with two resistors (40 ohm and 10 ohm) that are connected in parallel with eachother.
It asks to find the current, the power dissipated by each of the 3 resistors, and the power supplied by the 40v source.
3. We have a sawtooth wave, current with respect to time. The current increases linearly from 0 seconds to 1 second with respect to time with a slope 1 so the current starts at 0 and ends at 1A, at 1
second it drops to a current of -1 and increases for one more second with a slope 1 until the current is at 0. We also have a power source with a 5000Ω resistor.
Calculate the total energy supplied by the source to the resistance over the 2 second period.
4. The last question gives us a graph of current vs. voltage (current on the y-axis, voltage on the x-axis), the initial current is 3A and initial voltage is 0V, it decreases linearly from 0-1V with
a slope of -3. So initial current and voltage is 3A and 0V, and final current and voltage is 0A and 1V.
Find the open current voltage of the cell, the short circuit current, and the maximum power that the cell can deliver to an external resistance.
3. The attempt at a solution
1. I=P/E=1000W/220V=50A/11
R=V/I = 220V/(5A/11)=484Ω
ρ=ρ0(1+αΔT) = (5.6 x 10^-8Ωm)(1+4.5 x 10^-3 °C-1^-1(700°C-20°C)) = 2.27x10^-7 Ωm.
L=RA/ρ = [484x((2.5x10^-4)/2)^2]/2.27x10^-7 Ωm = 1.0 x 10^2m
Can someone tell me whether what I did is correct or not?
2. a) To find the current I found the equivalent resistance of the resistors in parallel, = (1/10+1/40^)^-1=8Ω, then I find the total resistance which is 80Ω+8Ω=88Ω.
I then did I=V/R = 40v/88Ω= 5A/11.
b)For the power dissipated I used the equation P=I^2R.
For R1, P=(5A/11)^2(80Ω)=2000W/121
For R2 (10Ω) I found the current to be 4A/11, and P=(4A/11)^2(10Ω)=160W/121
For R3 (40Ω), P=(1A/11)^2(40Ω)=40W/
c) For the power supplied by the 40v source, I did P=IE=(5A/11)(40v)=200W/11
3. What I did was integrated the current with respect to time to get the total current supplied, so the equation of the line from 0-1 second is y'=xdx, and the integral is (x^2)/2. However at 1
second the current drops from 1 to -1 and increases for one second until zero, so the area under the graph from 0 to 1 second is the same as the area under the graph from 1-2 seconds, so I added the
areas together: (x^2)/2+(x^2)/2=x^2.
I integrated it from 0-1 second to get 1A.
E=PT=5000W(2seconds)=10 000J
Edit: Ok I think for this one I wasn't allowed to just add the areas together, I had to integrate each function separately, correct? (can someone briefly explain why I can't just add the areas of the
triangles together though?)
4. a) For the open circuit voltage of the cell I simply looked at when the current was 0 on the graph, so the answer is 1V.
b) For the short-circuit current I looked when the voltage was 0, so the answer is 3A.
c) For the maximum power that the cell can deliver to an external resistance I did I=-3V+3 (from the graph) and multiplied that by V because P=IV =(-3V+3)V=-3V^2+3V.
I then derived this equation to find when the power is at a maximum, so dP=-6V+3 which equals 0 at V=1/2.
So the maximum power that the cell can deliver to an external resistance is P=-3(1/4)+3(1/2) = 3/4W
So I did my best to do these problems, I don't have anyone I'm close with in the class to ask questions too especially since the class just started so help is much appreciated! Thanks. | {"url":"http://www.physicsforums.com/showthread.php?t=368078","timestamp":"2014-04-19T15:17:09Z","content_type":null,"content_length":"44339","record_id":"<urn:uuid:697fcee6-d1fa-4189-9df3-478d73b500dc>","cc-path":"CC-MAIN-2014-15/segments/1397609537271.8/warc/CC-MAIN-20140416005217-00616-ip-10-147-4-33.ec2.internal.warc.gz"} |
Solubility of the quintic?
up vote 23 down vote favorite
Over the p-adics, every Galois group is solvable. Does this imply that the quintic (and higher-order polynomials for that matter) can be solved by radicals over $\mathbb{Q}_p$?
EDIT: The original place I learned that the p-adic galois groups were solvable was in Milne's Algebraic Number Theory text (Chapter 7, Cor 7.59).
As was pointed out the comments, I should clarify that I meant to ask 2 questions. Namely, whether the general quintic can be solved by radicals in this context (still no) and whether any given one
can be (which I now believe is yes).
@Jon: You may want to add the reference to the fact that the Galois groups of finite extensions of $\mathbb{Q}_p$ are solvable. It follows from the fact that the absolute Galois group of $\mathbb
{Q}_p$ is pro-$p$ which, I think, was proved by Koch or Yakovlev in the 60s, and from the recent result of Segal and Nikolov about finite index subgroups of pro-$p$-groups. Is there a simpler
proof? – Mark Sapir Apr 9 '12 at 13:18
1 Yes: the Hilbert ramification groups provide a family of normal subgroups of the decomposition group of a global extension. – Franz Lemmermeyer Apr 9 '12 at 13:33
@Franz: Thanks! – Mark Sapir Apr 9 '12 at 14:01
6 «The quintic can be solved by radicals» can mean either «the general quntic has a solution by radicals» or «the roots of every specific quintic can be constructed using radicals from the field of
coefficients». It would probably be best if the question were explicit about which of the two meanins it is about. (The wording suggests to me the second meaning is intended...) – Mariano
Suárez-Alvarez♦ Apr 9 '12 at 16:41
5 OK, I am beginning to understand. Analogously: over the reals every Galois group is solvable, since any polynomial can be factored into factors of degrees 1 and 2. That doesn't mean there is a
formula for the zeros in terms of the coefficients of the original polynomial. – Gerald Edgar Apr 9 '12 at 17:56
show 3 more comments
5 Answers
active oldest votes
Even though every extension of $\mathbb{Q}_p$ is solvable, I don't think one can write down a formula for the solution to a general quintic in terms of radicals; if one could, then the
up vote 17 $S_5$-extension $\mathbb{Q}_p(r_1,...,r_5)/\mathbb{Q}_p(e_1,...,e_5)$ would be solvable, where the $e_i$ are the elementary symmetric polynomials in the $r_i$.
down vote
6 What I meant was that there doesn't exist a formula for the roots of a quintic in terms of the coefficients. Here, the $e_i$ are of course the coefficients. It is weird, though -- the
roots can all be expressed using radical operations, and they only depend on the coefficients, but there isn't a general formula in terms of radicals of the coefficients to spit them
out! – Raju Apr 9 '12 at 14:56
7 @RK: Yes, it is a nice illustration of the fact that Abel's and Galois' formulations are different. – Mark Sapir Apr 9 '12 at 15:10
This answer and the comments are enlightening, thanks! – Martin Brandenburg Apr 9 '12 at 20:27
Nevertheless, Lazard and Dummit give a formula analogous to Cardano's for solving any solvable quintic; see my second answer below. – Chandan Singh Dalawat May 26 '12 at 7:50
add comment
If you want to solve the quintic over the $p$-adics, two cases naturally arise : $p\neq5$ and $p=5$.
Suppose first that $p\neq5$ and let $f\in\mathbf{Q}_p[T]$ be an irreducible polynomial of degree $5$. Then the extension $K$ obtained by adjoining a root $\alpha$ of $f$ to $\mathbf{Q}
_p$ is always contained in $F(\root5\of{F^\times})$, where $F=\mathbf{Q}_p(\root5\of1)$. So you see immediately that $\alpha$ can be expressed by radicals.
In fact, $f$ can always be taken to be of the form $f=T^5-x$ in the generic case when $K$ is (totally) ramified over $\mathbf{Q}_p$, so if you wish I can claim to have solved the quintic
by radicals by just saying that $\alpha=\root5\of x$.
up vote 15 Now let $f\in\mathbf{Q}_5[T]$ be an irreducible polynomial of degree $5$. Then the extension $K$ obtained by adjoining a root $\alpha$ of $f$ to $\mathbf{Q}_5$ is always contained in $F
down vote (\root5\of{F^\times})$, where $F=\mathbf{Q}_5(\root4\of{\mathbf{Q}_5^\times})$. Here again you see that $\alpha$ can be expressed by radicals.
There is nothing special about the prime $5$ or the base field $\mathbf{Q}_p$. You can replace $5$ by any prime $l$, and $\mathbf{Q}_p$ by any finite extension thereof, and you will get
similar results depending on whether $l\neq p$ or $l=p$.
You can even replace $\mathbf{Q}_p$ by a finite extension of $\mathbf{F}_p((\pi))$, provided you replace the "radical" $\root p\of{x}$ (which denotes a root of the binomial $T^p-x$) by
its characteristic-$p$ cousin $\wp^{-1}(x)$ (which denotes a root of the trinomial $T^p-T-x$).
add comment
The fact is true for every field $K$ of characteristic 0: every finite algebraic extension of $K$ with solvable Galois group is inside an extension obtained by adding radicals (i.e.
solutions of equations $x^n=a$). The field is separable since its characteristic is 0. Hilbert's Theorem 90 (see Google) holds over every field of characteristic 0. Therefore if a finite
up vote extension $K'$ of $K$ contains primitive roots of 1 of degree $n$, then any extension $E$ of $K'$ with cyclic Galois group of order $n$ is obtained by adding a root of the equation $x^n=a$
7 down for some $a\in K'$. Now you can apply the fundamental theorem of Galois theory.
1 So what is the solution of the general quinting over $Q_p?$ – Igor Rivin Apr 9 '12 at 14:03
@Kevin: Thanks! Is it only pro-solvable then? I thought Franz agreed above that it is pro-$p$. – Mark Sapir Apr 9 '12 at 15:23
I deleted my comments: these were wrong (because of Kevin's remark). – Mark Sapir Apr 9 '12 at 15:25
The simplest way to see that the absolute Galois group $G$ of $k=\mathbf{Q}_p$ is not a pro-$p$-group is to remark that $k$ has quadratic extensions (for example $k(\sqrt{p})$) for $p$
odd, and cubic extensions (for example $k(\root3\of2)$) for $p=2$. – Chandan Singh Dalawat Apr 9 '12 at 18:38
At the same time, it is true that the most interesting part of $G$ is a pro-$p$-group : there is a canonical filtration $V\subset T\subset G$ by closed subgroups in which the quotients $G
/T$ and $T/V$ are fully understood, and the wild inertia subgroup $V$ is a pro-$p$-group. – Chandan Singh Dalawat Apr 9 '12 at 18:43
show 5 more comments
Dave Dummit's paper "Solving Solvable Quintics" http://www.ams.org/journals/mcom/1991-57-195/S0025-5718-1991-1079014-X/S0025-5718-1991-1079014-X.pdf constructs a sextic out of the
coefficients of the quintic which has a rational root if and only if the quintic has a solvable Galois Group. Although this is stated over $\mathbb{Q}$ I believe that it applies over any
up vote 5 field of characteristic 0 or > 5.
down vote
add comment
Try Lazard (Daniel), Solving quintics by radicals, in The legacy of Niels Henrik Abel, 207–225, Springer, Berlin, 2004.
MR2077574 (2005g:12002) says : Let $F$ be a field of characteristic different from 2 and 5. Let $f$ be a univariate irreducible polynomial of degree 5 over $F$. The polynomial $f$ is said to
be solvable by radicals if the Galois group over $F$ of the field generated by all the roots of $f$ is solvable. In the paper the author gives a formula for solving by radicals any
up vote polynomial $f$ of degree 5 which is solvable by radicals. The field extension which is generated by the radicals which appear in the result is always minimal, when only one root is produced,
3 down as well as when all roots are given. This formula has been implemented in Maple.
Reviewed by Jerzy Urbanowicz.
1 This paper as well as its Maple implementation can be found on Lazard's home page: www-polsys.lip6.fr/~dl – Martin Brandenburg May 26 '12 at 10:31
Great ! I didn't succeed in locating his homepage, so many thanks for having done so. – Chandan Singh Dalawat May 26 '12 at 10:52
add comment
Not the answer you're looking for? Browse other questions tagged galois-theory or ask your own question. | {"url":"http://mathoverflow.net/questions/93553/solubility-of-the-quintic/93582","timestamp":"2014-04-18T18:38:17Z","content_type":null,"content_length":"86722","record_id":"<urn:uuid:22350763-e8cc-4d7d-a610-e653291248eb>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00187-ip-10-147-4-33.ec2.internal.warc.gz"} |
Calculus: Analysis of Functions and Curve Sketching
April 21st 2010, 04:49 PM
Calculus: Analysis of Functions and Curve Sketching
Can anyone please help me complete the following given tasks for the functions :
a. f (x) = 2x^3 - 3x^2 + 12x +9
b. f (x) = x^2-1/x^2-16
c. f(x) = x(x-1)^3
d. f(x) = x-1/x^2-4
1. Find the zeros of the function. Find the values at which the function is undefined.
2. Find the domain of the function.
3. Find the horizontal and vertical asymptotes.
4. Find the x- and y-intercepts.
5. Find the limits at infinity and negative infinity to determine the function’s end behavior.
6. Find the first derivative and the second derivative.
7. Find the critical numbers and the possible points of inflection.
8. Use the x-intercepts and vertical asymptotes to divide the x-axis into open intervals. Complete the following table:
Test Value
Sign of f(x)
+ or -
Above or below x-axis
9. Use the critical numbers to divide the x-axis to into open intervals. Complete the following table:
Test Value
Sign of f(x)
+ or -
Increasing or Decreasing
10. Use the possible points of inflection to divide the x-axis to into open intervals. Complete the following table:
Test Value
Sign of f(x)
+ or -
Concave Up or Concave Down
11. Determine the relative extrema and points of inflection based on analysis of your charts.
12. Generate a graph of the function using your graphing utility.
P.S. CAN U SHOW STEPS PLEASE. THANKS IN ADVANCE.
April 21st 2010, 05:01 PM
Can anyone please help me complete the following given tasks for the functions :
a. f (x) = 2x^3 - 3x^2 + 12x +9
b. f (x) = x^2-1/x^2-16
c. f(x) = x(x-1)^3
d. f(x) = x-1/x^2-4
1. Find the zeros of the function. Find the values at which the function is undefined.
2. Find the domain of the function.
3. Find the horizontal and vertical asymptotes.
4. Find the x- and y-intercepts.
5. Find the limits at infinity and negative infinity to determine the function’s end behavior.
6. Find the first derivative and the second derivative.
7. Find the critical numbers and the possible points of inflection.
8. Use the x-intercepts and vertical asymptotes to divide the x-axis into open intervals. Complete the following table:
Test Value
Sign of f(x)
+ or -
Above or below x-axis
9. Use the critical numbers to divide the x-axis to into open intervals. Complete the following table:
Test Value
Sign of f(x)
+ or -
Increasing or Decreasing
10. Use the possible points of inflection to divide the x-axis to into open intervals. Complete the following table:
Test Value
Sign of f(x)
+ or -
Concave Up or Concave Down
11. Determine the relative extrema and points of inflection based on analysis of your charts.
12. Generate a graph of the function using your graphing utility.
P.S. CAN U SHOW STEPS PLEASE. THANKS IN ADVANCE.
Wow that is a lot of problems, and you didn't show any work/attempt. Would you like us to write your term paper for you too?
Please show at least a little work...
April 21st 2010, 05:18 PM
(Doh)Sorry, I am struggling to start off (a): f(x) 2x^3 - 3x^2 + 12x + 9.
I set 2x^3 - 3x^2 + 12x + 9 = 0 ( from there I am lose)
for (b) f(x) = x^2 -1/x^2-16
x^2 -1/X^2-16 = 0
zero: x^2-1= 0
x = +/- 1
domain: x^2 - 16 = 0
x = +/- 4
(- infinity, 4) u (-4, 4) u (4, infinity)
but c and d is confusing
I just need help starting them off
Thank you....
April 21st 2010, 09:08 PM
(Doh)Sorry, I am struggling to start off (a): f(x) 2x^3 - 3x^2 + 12x + 9.
I set 2x^3 - 3x^2 + 12x + 9 = 0 ( from there I am lose)
for (b) f(x) = x^2 -1/x^2-16
x^2 -1/X^2-16 = 0
zero: x^2-1= 0
x = +/- 1
domain: x^2 - 16 = 0
x = +/- 4
(- infinity, 4) u (-4, 4) u (4, infinity)
but c and d is confusing
I just need help starting them off
Thank you....
It's understandable that you'd have trouble finding the roots of f(x) defined in part (a). This is a cubic polynomial, and although the general cubic has a solution, it's not something taught in
most school curricula. Using the rational root theorem reveals that there are no rational roots. Just use a graphing calculator. The root is approximately equal to -0.616119.
The domain is all values for which f(x) is defined. If f(x) is defined for all real numbers, then the domain is the set of real numbers.
The horizontal/vertical asymptotes question deals with limits as x approaches a certain value, or as x approaches positive or negative infinity.
The f(x) defined in (b), is it supposed to be f (x) = x^2-1/(x^2-16)? The parentheses are very important. If so then your domain is fine except that you missed a negative sign.
Of course you'll have to know how to do derivatives.
Is that enough help to get you started? | {"url":"http://mathhelpforum.com/calculus/140590-calculus-analysis-functions-curve-sketching-print.html","timestamp":"2014-04-20T10:39:59Z","content_type":null,"content_length":"16951","record_id":"<urn:uuid:4c6b6cba-a17d-468a-9a06-230d34d58fcd>","cc-path":"CC-MAIN-2014-15/segments/1397609538110.1/warc/CC-MAIN-20140416005218-00487-ip-10-147-4-33.ec2.internal.warc.gz"} |
reading data from excel and summing it up
SAS to excel
Hello, I used ODS to output data as an excel file. In the file there is a field with numbers like '95-1234', '03-2345', etc. However, when I opened the file in excel, it displays a date for these
numbers. What do I need to do to keep numbers the way they should be? TIA Here is the code to output the data: ods html file='/projects/example.xls' style=minimal; proc print data=test; run ; ods
html close ; With this kind of transfer sometimes it is necessary to send Excel instructions on formatting a particular item.... Try something like this in your proc print.....
User Entered Data(Read Only Data) to Excel
Hi All, I am new to Ruby, new task has been given to me by the company and they asked me to use ruby for it 1. Capture the User Entered data's in a webpage which is Readonly ( Data's can be in Text,
List, Radio button, Check box) i need to capture the datas present in above fields and export to Excel with column heading. People please help me to solve this problem i dont know how and where to
start Regards Md Rafiq -- Posted via http://www.ruby-forum.com/. ...
the data that is in the table is from excel, so the data to be read can changed?
for example the data before is EXEC 1,how if i'll changed the value to 1 how can i read those data if he changed the EXEC 1 to 1. that's why i said the data is changeable. can you give me a simple
example about this? Thank You thank you for your help, but how if EXEC 1 can be EXECUTE 1 of EXE 1. I use the scan from string and it only reads EXEC, EXECUTE and EXE not 1 and space. Either EXECUTE
1, EXEC 1, EXE 1 and 1 can be the value that can get from excel. The string parse example is working at LV 7.0, I'm using LV 6.1. ...
read data from 2 excel sheets and write both into 1 excel sheet
Greetings. Let me explain this a bit. I am wondering what would be the best way to go about this. I have 2 small Excel spreadsheets. I want to be able to read the first 5 cells&
nbsp;in the first row from each spreadsheet. I then want to write the data from those 2 sheets into a third different spreadsheet starting in different columns. I do not have the Excel Report
set. I was hoping to do this with active X, but I'm not sure if this can be done. Thank you, bob Hi RLemo, yes it is possible. See this thread for more informatio...
Problem in reading excel sheet data from sheet .How to usw this data for further for identification of model
Hello, 1)I have CSTR data for Two In put Two Out put System(Temp, Flow). Data is in Excel sheet format(stored in PC desk top). I have use xlsread function (by giving correct path ) to read data .It
gives me error. what should I do now to read my excel sheet data. 2) After getting the data from excel sheet .I want to find the model of this process. So is " iduidemo " will be helpful for me. In
iduidemo file type is .sid how to create .sid file from excel sheet. data. 3) Is there any other way to find first order plus delay time model using process react...
How to Read data from excel file without converting a excel file into .csv or any other format
Hello, Can somebody suggest me how to read from an excel file (consisting of 10 work sheets) to an array? Thanks, She Hello, it's right that you can use activeX. (For example with rhe report
generation toolbox from ni) But there are some problems: 1. You have to have excel installed on the targed PC. (to get the ActiveX interface) 2. There exists different "Microsoft
Excel x.x Object Library Version x.x" which have different methods and properties. If a costumer has an other version, it could be that it doesn't work. 3....
how to read data from EXCEL
I need to read data from EXCEL worksheets in this way: The script perl asks me to write a number . I type a Number f.e. 1000 , the script should look for the number 1000 inside a excel worksheet file
and if it find it, should capture all the other numbers reported in the raw where there is the number 1000. the mother number (1000) is always in the first colomn of excel sheet. col1 col2 col3 col4
col5 raw1 900 002 004 006 raw2 1000 345 445 888 777 once the script had found the wanted number (1000) in the raw2 col1 , it giv...
Reading excel data
I have generated a "dat" file from a mathematica simulation. I then brought the data back into Mathematica to graph using the code below. All of this worked fine. Then, when I did a few manipulations
in excel on the "dat" file (adding a column of data) and resaved the file as a tab delimited file as it was before my manipulations, the code below does not work. I get the following error messages.
Transpose::nmtx: The first two levels of the one-dimensional list cannot be transposed Part::partw: Part All of the Transpose... does not exist. I did not manipulate at...
Dear all, I made a SAS code to read some data in an excel file. It works fine. However, I have data in the excel spreadsheet up to line 61. However, SAS reads data until line 147 (it reads until line
147 but considers for analysis only the first 60 data, which is correct). Dou you know how I can teel SAS to read only the first 60 data? Please, see my code below. Thanks in advance for any help
(sorry if it is a simple question, but I am new to SAS). Regards, R=F4mulo PROC IMPORT DBMS=3DEXCEL OUT=3DWORK.FABIO REPLACE DATAFILE=3D"C:\FABIOTE.XLS"; SHEET=3D"NNP"; GETNAMES=3D... | {"url":"http://compgroups.net/comp.soft-sys.matlab/reading-data-from-excel-and-summing-it-u/399038","timestamp":"2014-04-20T23:28:02Z","content_type":null,"content_length":"35949","record_id":"<urn:uuid:939a8c8e-25dc-4bd3-8fa7-5fa601582873>","cc-path":"CC-MAIN-2014-15/segments/1397609539337.22/warc/CC-MAIN-20140416005219-00163-ip-10-147-4-33.ec2.internal.warc.gz"} |
Proved that a physical system described by a Lagrangian invariant with respect to the symmetry transformations of a Lie group has, in the case of a group with a finite (or countably infinite) number
of independent, infinitesimal generators, a conservation law for each such generator, and certain `dependencies' in the case of a larger infinite number of generators. The latter case applies, for
example, to the general theory of relativity and gives the Bianchi identities. These `dependencies' lead to understanding of energy-momentum conservation in the general theory. Her paper proves both
the theorems described above and their converses.These are collectively referred to by physicists as Noether's Theorem.
The key to the relation of symmetry laws to conservation laws is Emmy Noether's celebrated Theorem. ... Before Noether's Theorem the principle of conservation of energy was shrouded in mystery,
leading to the obscure physical systems of Mach and Ostwald. Noether's simple and profound mathematical formulation did much to demystify physics. --- Feza Gursey [encp1983nj]
An historical account of how she came to make this discovery is given in E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws.
The main body of her work was in the creation of modern abstract algebra. As the topologist P. S. Alexandrov wrote
It was she who taught us to think in terms of simple and general algebraic concepts - homomorphic mappings, groups and rings with operators, ideals ...theorems such as the `homomorphism and
isomorphism theorems', concepts such as the ascending and descending chain conditions for subgroups and ideals, or the notion of groups with operators were first introduced by Emmy Noether and
have entered into the daily practice of a wide range of mathematical disciplines. ... glance at Pontryagin's work on ..continuous groups, Kolmogorov on ... combinatorial topology ..., ... Hopf on
continuous mappings, ... van der Waerden on algebraic geometry, ... to sense the influence of Emmy Noether's ideas. This influence is also keenly felt in H. Weyl' book Gruppentheories und
Quantenmechanik. ---[en1981ad]
Specifically, Nathan Jacobson writes
Abstract algebra can be dated from the publication of two papers by Noether, the first a joint paper with Schmeidler and .. a truly monumental work Idealtheorie in Ringbereichen [which] belongs
to one of the mainstreams of abstract algebra, commutative ring theory, and may be regarded as the first paper in this vast subject ... [encp1983nj]
And Hermann Weyl writes of her important later work
The theory of non-commutative algebras and their representations wa built up by Emmy Noether in a new unified, purely conceptual manner by making use of all the results that has been accumulated
by the ingenious labors of decades by Frobenius, Dickson, Wedderburn and others. ---[sm1935hw]
Some Important Publications
"Invariante Variationsprobleme," Nachr. v. d. Ges. d. Wiss. zu Göttingen 1918, pp 235-257 [[[ ]]] English translation by M. A. Tavel.
"Moduln in nichtkommutativen bereichen, insobesondere aus Differential- und Differen-zenaus-drucken," Math. Zs. 8:1 (1920) with W. Schmeidler.
"Idealtheories in Ringbereichen," Math. Ann. 83:24 (1921).
"Hyperkomplexe Grossen und Darstellungstheorie," Math. Zs. 30:641 (1929).
"Beweis eines Hauptsatzes in der Theorie de Algebren," Journal f. d. reine u. amgew. Math. 167:399 (1932) with R. Brauer and H. Hasse.
"Nichtkommutative Algebren," Math. Zs. 37:514 (1933).
1907 Doctorate summa cum laude University of Erlangen
1908 member of the Circolo mathematico di Palermo [en1981ad]
1909 member Deutsche Mathematiker Vereinigung (DMV) [en1981ad]
1932 Co-winner, Alfred Ackermann-Teubner Memorial Prize for the Advancement of Mathematical Knowledge
1958 A conference at the University of Erlangen was held to commemorate the 50th anniversary of Noether's doctorate.
1982 Emmy Noether Gymnasium, a co-educational school emphasizing mathematics, natural sciences and language, opened in Erlangen, Germany on the 100th anniversary of Noether's birth.
1992 Emmy Noether Institute for Mathematical Research established in Bar Ilan University, Tel Aviv, Israel.
1908-1915 unpaid lecturer and supervisor of doctoral student in University of Erlangen.
1916-1922 unpaid lecturer and member of Hilbert's research team in the University of Göttingen.
1922-1933 nicht-beamteter ausserordentlicher Professor (adjunct, not-ordinary Professor - untenured), University of Göttingen.
1922-1933 Lehrauftrag for algebra - which brought her a small stipend; "the first and only salary she was ever paid in Göttingen." [h1970cr]
1933-1935 Visiting Professor, Bryn Mawr College.
1903 Reifeprüfung, Königliches Realgymnasium, Nuremburg
1907 Doctorate in Mathematics, University of Erlangen
1919 habilitation, University of Göttingen
[[[ ]]]Additional Information/Comments
Emmy Noether's name is used to designate many concepts specific to abstract algebra ; for example,
• a ring is called Noetherian if each ideal has a finite basis;
• a group is called Noetherian if each subgroup can be generated by a finite basis;
• and mathematicians speak of Noetherian equations, Noetherian modules, Noetherian factor systems, etc..
She was never elected to the Königl. Gesellschaft der Wissenschaften zu Göttingen . [h1970cr]
Her great 1918 paper on symmetries and conservation laws was communicated to the Gesellschaft by Felix Klein.
Auguste Dick raises interesting questions regarding the fact that Noether wa never appointed to a paid position in the faculty of the University of Göttingen:
How was it then that in her academic career she did not go beyond the [unpaid] level of nicht-beamteter ausserordentlicher Professor? ... Was it because she was Jewish? There were several Jewish
Ordinarii in Göttingen. Was it because she was a member of the social- democratic party? ... Or was it her firm stance as a pacifist that was frowned upon? ..." -- [en1981ad]
As a Jewish woman, in 1933 Emmy Noether was fired from her position as a privat docent in Göttingen. By decree no Jew was allowed to teach after Hitler came to power. (In 1934 women were dismissed
from University posts.)
Hermann Weyl wrote about her in this period
" A stormy time of struggle like this one we spent in Göttingen in the summer of 1933 draws people closely together; thus I have a vivid recollection of these months. Emmy Noether - her courage,
her frankness, her unconcern about her own fate, her conciliatory spirit - was in the midst of all the hatred and meaness, despair and sorrow surrounding us, a moral solace." [sm1935hw]
Part of a Letter to the Editor of the New York Times that Albert Einstein wrote on the occasion of her untimely death:
``The efforts of most human beings are consumed in the struggle for their daily bread, but most of those who are, either through fortune or some special gift, relieved of this struggle are
largely absorbed in further improving their worldly lot. ... There is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying
experiences open to humankind are not derived from the outside, but are bound up with the development of the individual's own feeling, thinking and acting. The genuine artists, investigators and
thinker have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable
contributions which one generation can make to its successors.''[NYT1935ae]
Recommended further reading on Emmy Noether's contributions to mathematics: There are two papers by Nina Byers on her contributions to physics:
Field Editor: Nina Byers | {"url":"http://cwp.library.ucla.edu/Phase2/Noether,_Amalie_Emmy@861234567.html","timestamp":"2014-04-19T19:42:42Z","content_type":null,"content_length":"15918","record_id":"<urn:uuid:1784b809-74f2-4cc3-9470-6ad040326bed>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00649-ip-10-147-4-33.ec2.internal.warc.gz"} |
More Beautiful Math: The Dragon Curve
Mar 18 2013
More Beautiful Math: The Dragon Curve
The Dragon Curve Explained
Try It Yourself
Are you bored, or dying to do something tedious? Do you need a geometry project that will keep your students busy all afternoon? Try drawing a giant dragon curve. No computer necessary!
Supplies required:
• sharp colored pencils,
• sturdy eraser,
• ruler (optional if you use graph paper),
• several pieces of plain or graph paper,
• clear tape, for sticking pages together to make an even bigger dragon,
• a light table (or tape your paper to the window for tracing),
• and a large dose of OCD-quality patience.
Get all our new math tips and games: Subscribe in a reader, or get updates by Email.
7 comments on “More Beautiful Math: The Dragon Curve”
1. I often find it fun to make a dragon curve, by taking a long strip of paper (like rolls for a cash register) and folding it in half repeatedly, then unfolding it and setting it so that each fold
is a right angle.
There’s a lot of interesting math here, like why it can touch itself but never cross itself, so that it is actually possible to make it out of a sheet of paper like that! The right angles never
steer you in an impossible direction “through” a previously placed bit of the strip of paper.
2. I like the paper-folding approach, too, except I find it easy to forget which way I’m going and flip my paper over, so the folds go different ways. I did draw the curve ages ago by repeated use
of copy, paste, and group in Microsoft Word — which is about the limit of my techiness.
Is there a proof that the curve never crosses itself that can be understood by someone who doesn’t remember much beyond high school math?
3. I have kids tape one end of the paper to the table, and always fold toward the tape, before finally removing the tape and unfolding it.
The proof is understandable indeed, but hard to discover. Maybe the most straightforward path starts out by putting the curve on the coordinate plane, with turns each one unit, so that you can
categorize points into even and odd based on whether the sum of the coordinates (or the total distance traveled to get to that point) is odd or even. Then take a look at whether you’re moving up
or down, or right or left, when you arrive at that point, and look at whether you have a valley or mountain fold and how that affects which way you turn.
I did this by getting a sheet of paper with a big grid on it, at least 1cm per square, so I could easily label each vertex with all the relevant information and see what patterns started
emerging. Once I made the diagram and saw the patterns, it wasn’t too huge of a leap to figure out why the folding pattern made the patterns turn out that way, and why the patterns guaranteed no
4. Thanks for the kind mention though I don’t know about “dying to do something tedious” ;) As you can see I did a number of posts on the “Fractals You Can Draw” topic and they should all be getting
an update sometime soon (They’re some of the most popular posts on my blog!). In addition, I’m compiling those posts as a booklet as a companion piece to my forthcoming fractal book (Fractals – A
Programmer’s Approach) soon to be available on Amazon and Bundle Dragon (okay shameless plug over). Thanks again for linking to the posts.
5. The “tedious” comment was yet another example of why I should stick to being the straight man. Trying to be wry just doesn’t work online. To tell the truth, even in real life it can be awfully
Readers: Check out Ben’s fractal posts here.
6. Don’t worry about it, wry is how I took it ;)
7. Very cool. Thanks for posting this on Math Monday Blog Hop!! | {"url":"http://letsplaymath.net/2013/03/18/more-beautiful-math-the-dragon-curve/","timestamp":"2014-04-17T15:26:01Z","content_type":null,"content_length":"74886","record_id":"<urn:uuid:8d7b716d-9227-48cd-8d25-0d7432c2e7b6>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00085-ip-10-147-4-33.ec2.internal.warc.gz"} |
I have finally started uploading apps to the Android app store. The three apps I previously wrote about (Scientific Name Search, Plasmatic and Dutch Public Holidays) are uploaded to the app store, as
well as a few apps I created based on a version of my astronomical library ported to Java.
The crowning glory of these astronomical apps I have uploaded to the app store is Night Sky Tools (https://play.google.com/store/apps/details?id=com.smeunier.nightskytools).
The features included in the app are:
• Angular separation
• Astronomical Time
• Atmospheric refraction
• Coordinate convertor
• Eclipses
• Magnitude
• Precession
• Conjunctions and Oppositions
• Ephemerides of the planets, sun and moon
• Equinoxes
• Positions of Jupiter’s moons
• Planetary orbits
• Constellations
• Stellar Classification
• Telescope Airy Disc
• Telescope F-Ratio
• Telescope Magnification
Go ahead and check out the app. | {"url":"http://www.smokycogs.com/blog/","timestamp":"2014-04-21T04:31:25Z","content_type":null,"content_length":"89863","record_id":"<urn:uuid:696579b5-dd5d-4505-a1d1-4b66223e36e2>","cc-path":"CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00180-ip-10-147-4-33.ec2.internal.warc.gz"} |
Exception "raise LinAlgError, 'Singular matrix'" when attribute has value of o in all examples in Linear Regression
Ticket #1211 (closed bug: worksforme)
Exception "raise LinAlgError, 'Singular matrix'" when attribute has value of o in all examples in Linear Regression
Reported by: skokko Owned by: lanz
Milestone: Component: library
Severity: minor Keywords: Singular matrix
Cc: Blocking:
Blocked By:
I have an Example Table, and one of the variables always has the value 0.0 in every example. When running Linear Regression, I was expecting that the beta for this variable would be 0 and the
algorithm would ignore this variable and solve for the rest. Instead it raises an exception 'Singular matrix' in line 328 of file linalg.py: " if resultsinfo? > 0: raise LinAlgError, 'Singular
Change History
• Status changed from new to assigned
• Owner set to lanz
Could you be a little more specific about which version of orange and numpy you are using (try the latest if you are not using it already) and how to reproduce this error.
I tried adding a constant variable (all 0.0) to the housing.tab data set and when I ran Orange.regression.linear.LinearRegressionLearner it worked without problems. The coefficient for the constant
variable was 0.0, as you suggest it should be.
I have the same behavior without the constant variable. I opened a new ticket for this, since it is not exactly the same problem (ticket $1217)
Thank you
• Status changed from assigned to closed
• Resolution set to worksforme
OK, I am closing this ticket. | {"url":"http://orange.biolab.si/trac/ticket/1211","timestamp":"2014-04-16T10:37:51Z","content_type":null,"content_length":"14167","record_id":"<urn:uuid:82c08782-fa7a-4a9b-872c-57d44c059e95>","cc-path":"CC-MAIN-2014-15/segments/1397609523265.25/warc/CC-MAIN-20140416005203-00364-ip-10-147-4-33.ec2.internal.warc.gz"} |
The n-Category Café
Philosophising in Brussels
Posted by David Corfield
I’m off to Brussels tomorrow. Fortunately someone pointed out to me that the clocks go forward tonight or I might have missed my train. I’m speaking at a conference called
Perspectives on Mathematical Practices 2007
are some notes for my talk.
Posted at March 24, 2007 9:52 PM UTC
Re: Philosophising in Brussels
Wow. Big thanks for clock info!!! :-) I could miss my plane as well (accidentally I also go to Belgium, but to Louvain-la-Neuve, for Ulrike Tillmann lectures).
Thanks once more and have a good philosophising :-).
Posted by: sirix on March 25, 2007 1:55 AM | Permalink | Reply to this
Re: Philosophising in Brussels
These notes are very interesting.
Posted by: bhb on March 25, 2007 12:43 PM | Permalink | Reply to this
Re: Philosophising in Brussels
I enjoyed seeing that part of the discussion of two things and 2-things has made it into your talk (slide 6).
Another good class of examples for complicated-looking conglomerates of data that can be realized as mere components of a single $n$-categorical gadget are a plethora of various “cocycle relations”
that people usually write out as long lists of symbols with, usually, confusingly many signs scattered all over the place.
Often these can be seen to be nothing but coherence conditions for structure morphisms in higher categories.
Well, I guess the encapsulation of structure is actually a recursive phenomenon:
highly complicated-looking structures may be realized as algebras for operads.
Defining an operad itself in the standard way also takes a couple of lines.
But then we follow Tom Leinster and realize that all this data going into the definition of an operad in turn may be re-assembled into the mere statement of a monad in generalized spans.
And a monad, in turn, is just a component way of saying “lax functor on the trivial 2-category”.
Posted by: urs on March 26, 2007 7:53 PM | Permalink | Reply to this
Re: Philosophising in Brussels
As the laws of physics only ever get modified so as to speed up time when one is giving a talk, that material on 2-class functions, inserted in case of an impossible, yet ever hoped for, slowing of
time, had to be ignored.
But it would be good to collect some prize examples of this phenomenon.
Posted by: David Corfield on March 29, 2007 10:16 AM | Permalink | Reply to this
Re: Philosophising in Brussels
David talked about
Mathematics organised by stories or dramatic narratives
By the way, probably you have mentioned this elsewhere, but I’d think that one reason why physics, and in particular what might be called “modern formal high energy physics” has been such a rich
source of mathematical insight, at least at the level of conjectures (Witten, Kontsevich,…) is that whatever its relation to the physical world really is (which is an issue of heated – and overheated
– debate, as we know #) it does a great job of identifying lots of mathematical entities as secretly being actors in one grand story: it allows to “visualize” all kinds of sophisticated math in terms
of something like physical processes.
Posted by: urs on March 28, 2007 11:37 AM | Permalink | Reply to this
Re: Philosophising in Brussels
Yes, I’d thoroughly agree with that.
It’s interesting, however, how easy it is to slip from there to the position that ‘purely’ mathematical intuition is quite weak so physical intuition is doing a huge amount of the work. Philosophers
of physics often fail to observe that mathematics can pay back to physics by lending its intuitive stories. I was discussing this with Jacques Distler once at his blog.
Of course, we take for granted this intuitive story-like aspect of mathematics, due in large part to the expository efforts of a certain person from Riverside.
Posted by: David Corfield on March 29, 2007 9:29 AM | Permalink | Reply to this | {"url":"http://golem.ph.utexas.edu/category/2007/03/philosophising_in_brussels.html","timestamp":"2014-04-21T07:05:04Z","content_type":null,"content_length":"18927","record_id":"<urn:uuid:36ba888b-7ffc-4031-afa5-ef7a2331f404>","cc-path":"CC-MAIN-2014-15/segments/1398223206147.1/warc/CC-MAIN-20140423032006-00588-ip-10-147-4-33.ec2.internal.warc.gz"} |
BLS Handbook of Methods
Chapter 7.
National Longitudinal Surveys
The NLS surveys are based upon stratified multistage random samples, with oversamples of blacks in all cohorts, oversamples of Hispanics in the NLSY79 and NLSY97, and additional oversamples of
disadvantaged nonblack non-Hispanics and youths in the military in the NLSY79. Data from each interview year include a weight specific to that year. When this weight is applied, the number of sample
cases is translated into the number of persons in the population that those observations represent.
The assignment of individual respondent weights involves at least three stages. The first stage involves the reciprocal of the probability of selection at the baseline interview. Specifically, this
probability of selection is a function of the probability of selection associated with the household in which the respondent was located, as well as the subsampling (if any) applied to individuals
identified in screening. The second stage of weighting adjusts for differential response (cooperation) rates in the screening phase. Differential cooperation rates are computed (and adjusted) on the
basis of geographic location and group membership, as well as by group subclassification. The third stage of weighting attempts to adjust for certain types of random variation associated with
sampling, as well as sample "undercoverage." The estimated ratios are used to conform the sample to independently derived population totals.
Subsequent to the initial interview of each cohort, reductions in sample size have occurred due to noninterviews (the failure, for one reason or another, of the person to be interviewed). In order to
compensate for these losses, the sampling weights of the individuals who were interviewed had to be revised. A revised weight for each respondent was calculated for each interview year, using the
method just described.
In the event that one wishes to tabulate characteristics of the sample for a single interview year in order to describe the population being represented, it is necessary to weight the observations by
using the weights provided. For example, to compute the average hours worked in 1987 by individuals in the NLSY79 (persons born in 1957 1964 and living in the United States in 1978), one simply
weights the average hours worked by the 1987 sample weight. The weights are correct when used in this way.
Often, users confine their analyses to subsamples for which respondents provide valid answers to certain questions. Weighted means here will represent, not the entire population, but rather those
persons in the population who would have given a valid response to the specified questions. Nonresponse to any item because of refusals or invalid skips is generally quite small, so the degree to
which the weights are incorrect also is probably quite small. In these instances, although the population estimates may be moderately in error, the population distributions (including means, medians,
and proportions) are reasonably accurate. Exceptions to this assumption might occur for data items that have relatively high nonresponse rates, such as family income.
Next: Uses | {"url":"http://www.bls.gov/opub/hom/homch7_e.htm","timestamp":"2014-04-17T07:23:51Z","content_type":null,"content_length":"34305","record_id":"<urn:uuid:390be6c9-2f4c-47b5-b532-f751a54f030c>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00553-ip-10-147-4-33.ec2.internal.warc.gz"} |
Finding a Vertical Asymptote
Date: 05/11/2000 at 13:32:54
From: Audrey Connor
Subject: Calculus - finding vertical asymptote
In a calculus problem, one task was to find the vertical asymptote of
the equation:
xy^2 - x^3y = 6
I tried, and thought maybe it was x = sqrt(2y), but that doesn't seem
to make sense, and I can't seem to get a sense of what the graph looks
Date: 05/11/2000 at 16:12:46
From: Doctor Rob
Subject: Re: Calculus - finding vertical asymptote
Thanks for writing to Ask Dr. Math, Audrey.
Write the equation in the form
y*(y-x^2) = 6/x.
Near a vertical asymptote x is bounded and y grows without bound, so
the left side grows without bound. That implies that 6/x grows without
bound. That happens if and only if x approaches zero. That means that
there is a vertical asymptote at x = 0, and it is the only vertical
A general way to find asymptotes is as follows. Start with the
equation and discard all terms whose degree is not the same as the
highest degree term, bring all terms to one side, and factor what you
have. Set any first-degree factors equal to zero, and you'll have
equations that give you the slopes of the asymptotes. If one of these
looks like:
A*x + B*y = 0
then there is an asymptote with slope m = -A/B. The equation of the
asymptote will have the form:
A*x + B*y = C
Use this to eliminate one of the variables from the original equation
by substitution. Take the term with the highest power of the remaining
variable, and set its coefficient equal to zero. Solve the resulting
equation for C, and you have the equation of the asymptote.
In your case, you started with:
x*y^2 - x^3*y - 6 = 0
The highest degree term is -x^3*y, which has linear factors x and y.
Then the equations of the asymptotes will have the form:
0*x + 1*y = C
1*x + 0*y = C
that is, y = C or x = C. Thus in this case, the asymptotes are either
horizontal or vertical. For y = C, substituting, you get:
-C*x^3 + C^2*x - 6 = 0
The highest power of x is x^3, so we set its coefficient -C = 0, and
solve, getting C = 0. Thus the horizontal asymptote is y = 0.
For x = C, substituting, you get:
C*y^2 - C^3*y - 6 = 0
The highest power of y is y^2, so we set its coefficient C = 0, and
solve, getting C = 0. Thus the vertical asymptote is x = 0.
- Doctor Rob, The Math Forum | {"url":"http://mathforum.org/library/drmath/view/52106.html","timestamp":"2014-04-21T00:42:38Z","content_type":null,"content_length":"7318","record_id":"<urn:uuid:89fadc6e-9ab0-487a-a1e2-9b20cd3075f2>","cc-path":"CC-MAIN-2014-15/segments/1397609539337.22/warc/CC-MAIN-20140416005219-00133-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math differentiation
Posted by Marissa on Tuesday, August 26, 2008 at 11:44pm.
Can somebody please check these over for me? I really want to know what I did wrong if I made mistakes!
Differentiate the following:
1. y = ln [(4-x)/(4+x)]
Since it's the ln of the entire thing, then I can apply ln a - ln b
so, dy/dx = y' = 1/(4-x) *(-1) - 1/(4+x) *(1)
dy/dx = y' = -1/(4-x) - 1/(4+x)
2. y = ln √((3u+2)/(3u-2))
so that's the same as
y = ln ((3u+2)/(3u-2))^(1/2)
= 1/2 ln ((3u+2/3u-2))
using the ln a - ln b property again:
1/2[ln(3u+2) - ln(3u-2)]
dy/dx = 1/2 [1/(3u+2)*3 - 1/(3u-2)*3]
dy/dx = 1/2[3/(3u+2) - 3/(3u-2)
3. y = f(x) = tan(ln(4x+1))
so first I found the derivative of ln 4x+1
= 1/(4x+1)*4 = 4/(4x+1)
I plugged that number back into the original, making it
y = f(x) = tan(4/(4x+1))
Since the d/dx of tan x = sec^2x,
does it just end up being
dy/dx = sec^2(4/(4x+1)) ?
I am confused on how to do a problem like this:
4. f(t) = ln (2t+1)^3/(3t-1)^4
I can't apply the ln a - ln b property since it's not the ln of the entire thing, so how should I do it?
Related Questions
Maths differentiation - Differentiate (ln(ax+b))^n
integration by parts - s- integral s ln (2x+1)dx ? = ln(2x+1)x - s x d( ln (2x+1...
Math differentiation - 1. y = x^x 2. y = (sin^2xtan^4x)/(x^2+1)^2 3. y = x^(1/x...
Differentiate - Can someone please differentiate y = sin x / x for me? What I ...
calculus - hi, just wondering on how i should approach differentiating: loge1/(3...
calculus - Implicit Differentiation question x^y = y^x I was wondering if I was ...
Integrals- Log/Ln - Can you check this please i'm not sure why it's wrong .__. 1...
English - Can you please check the following sentences? I had left them out. ...
integral calculus - intergrate the following: a) (y+1)^-1 dy b) (1+1/x) dx I ...
Math(please check) - 1) Differentiate the following: a) y=(x^3+5x)^6 (x^2+1)^7 (... | {"url":"http://www.jiskha.com/display.cgi?id=1219808657","timestamp":"2014-04-18T17:12:53Z","content_type":null,"content_length":"9702","record_id":"<urn:uuid:ede241e0-e161-4829-8338-6e8f78cc5b03>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00049-ip-10-147-4-33.ec2.internal.warc.gz"} |
Quantum Computing Since Democritus Lecture 12: Proof
After a ten-month hiatus, the Quantum Computing Since Democritus series sheepishly returns with Lecture 12, which explores how, over the past couple of decades, theoretical computer scientists have
bent, twisted, and kneaded the concept of mathematical proof into strange and barely-recognizable forms. Read about proofs that don’t impart any knowledge beyond their own validity, proofs you can
check by examining a few random symbols, and (for those who already know that stuff) proofs that certain interpretations of quantum mechanics would predict you can see over the course of your life,
yet can’t hold in your mind at any individual time.
I apologize if this lecture isn’t as polished as some earlier ones — but while I’m working on this, I’m now also teaching a new course at MIT, 6.080/6.089 Great Ideas in Theoretical Computer Science.
Barring unforeseen delays, the lecture notes for that course should be available by 2043.
djm Says:
Comment #1 February 12th, 2008 at 2:42 am
Excellent! I look forward to seeing it narrated by attractive women in the form of a printer advert on Australian TV.
Coin Says:
Comment #2 February 12th, 2008 at 3:25 am
Hoping you someday get at least to Lecture 13 before giving up, I’m curious about that one…
By the way, one very small thing I’m not sure you noticed: On your blog front page, the Quantum Computing Since Democritus sidebar has the lectures in strict lexical order… such that “Lecture 11:” is
sorted before “Lecture 1:”…
John Sidles Says:
Comment #3 February 12th, 2008 at 7:27 am
A fun “confection” for the Great Ideas course is the SIAM News 22(4) Editors Name Top Ten Algorithms. I especially enjoyed the SIAM editors comment “Most algorithms take shape over time, with many
contributors.” Who should know better than an editor?
Scott Says:
Comment #4 February 12th, 2008 at 9:18 am
Coin: Unfortunately, one “feature” of the latest version of WordPress is that apparently they took away the ability to sort the links as one wishes. Does anyone know how to get that ability back?
(Update: Alright, I figured out how to edit the PHP script so that the lectures are correctly sorted. Enjoy!)
steve Says:
Comment #5 February 12th, 2008 at 9:28 am
Okay, so if I understand correctly, ever NP problem admits a PCP. The naive intuition is demonstrated by using the exponential encoding that you mentioned, but you claim there is always a poly-sized
encoding. So given a valid proof, what is the computational complexity of finding a valid poly-sized encoding?
Scott Says:
Comment #6 February 12th, 2008 at 9:29 am
Steve: Polynomial.
Jack in danville Says:
Comment #7 February 12th, 2008 at 12:28 pm
Thank you!
Michael Bacon Says:
Comment #8 February 12th, 2008 at 1:19 pm
Here is one of my favorite quotes regarding physics, quantum computation and mathematical proofs:
“Among the many ramifications of quantum computation for apparently distant fields of study are its implications for the notion of mathematical proof. Performing any computation that provides a
definite output is tantamount to proving that the observed output is one of the possible results of the given computation. Since we can describe the computer’s operations mathematically, we can
always translate such a computation into the proof of some mathematical theorem. This was the case classically too, but in the absence of interference effects it is always possible to keep a record
of the steps of the computation, and thereby produce (and check the correctness of) a proof that satisfies the classical definition – as “a sequence of propositions each of which is either an axiom
or follows from earlier propositions in the sequence by the given rules of inference”. Now we are forced to leave that definition behind. Henceforward, a proof must be regarded as a process — the
computation itself — for we must accept that in future, quantum computers will prove theorems by methods that neither a human brain nor any other arbiter will ever be able to check step-by-step,
since if the
‘sequence of propositions’ corresponding to such a proof were printed out, the paper would fill the observable universe many times over.”
Machines, Logic and Quantum Physics
David Deutsch and Artur Ekert
November 19, 1999
Jon Says:
Comment #9 February 12th, 2008 at 1:27 pm
…proofs that certain interpretations of quantum mechanics predict you can have seen over the course of your life but can’t hold in your mind at any individual time
This doesn’t parse. =) Can you give a translation?
Scott Says:
Comment #10 February 12th, 2008 at 2:20 pm
Jon: Read the lecture!
lylebot Says:
Comment #11 February 12th, 2008 at 2:39 pm
I had trouble parsing that too. I had to read it three or four times to understand that “that certain interpretations…” is not what’s being proved, but an adjectival clause describing the proofs.
Since I’m currently in editing mode, let me suggest “proofs that certain interpretations of quantum mechanics would predict that you can see over the course of your life but that you can’t hold in
your mind at any individual time.”
Michael Bacon Says:
Comment #12 February 12th, 2008 at 2:48 pm
Sorry, I should have noted that the paper I reference above was co-authored as well by Rossella Lupacchini.
Scott Says:
Comment #13 February 12th, 2008 at 3:27 pm
Michael: While that quote from Deutsch et al. is music to my ears, the one thing I’d add is that even before quantum computing became a field, computer scientists had already generalized the notion
of proof in the way they describe (from a static sequence of symbols to a computational process) for completely unrelated reasons.
Geordie Says:
Comment #14 February 12th, 2008 at 8:45 pm
Michael: One criticism of Deutsch’s quote above is that it is probably not possible even in principle to know what the Hamiltonian of your actual quantum computer is over time. This seems to me to be
a big issue.
“Performing any computation that provides a definite output is tantamount to proving that the observed output is one of the possible results of the given computation. Since we can describe the
computer’s operations mathematically, we can always translate such a computation into the proof of some mathematical theorem.”
All the statements here are true BUT knowing exactly what “the given computation” actually was seems problematic. Another way of saying this is that which “mathematical theorem” is being proved
depends on the details of your physical system, which you probably can’t know. You can write down an effective Hamiltonian which you think describes your system, and assume that this is the
mathematical machinery of interest, but in actuality the true physics of the system is probably not fully described by the best effective Hamiltonian you can generate.
Imagine you set up your quantum computation to test whether or not the answer “zero” is possible. You run the computation and lo and behold you get “zero”. Is this an ironclad “proof” that zero is
possible for this computation? No, because your model of the QC may not in actuality be what the QC is doing (the Hamiltonian problem above), and it may be this (potentially very small difference)
that’s allowing the answer to be zero, and not some fundamental truth about nature.
Scott Says:
Comment #15 February 12th, 2008 at 9:16 pm
Geordie: Yes, I agree that a computational proof is only as good as the assumptions about the underlying physics (even if the assumption is just that the prover can’t predict the verifier’s random
coin tosses, as for PCP’s). Maybe I didn’t stress that enough in the lecture.
Job Says:
Comment #16 February 12th, 2008 at 11:12 pm
In the zero-knowledge proof section you have:
That person then asks: “which graph did I start with?” If the graphs are not isomorphic, then you should be able to answer this question with certainty.
Should that not be there? If so then i don’t understand that section.
harrison Says:
Comment #17 February 12th, 2008 at 11:38 pm
I’m not sure I understand the proof sketch for 3-colorability in CZK. When you encrypt the colors, are you throwing in some additional data along with it (so, instead of hashing “red” over and over
again, you’re hashing “red12349″ versus “red29304″ etc.?) Otherwise I don’t see how the prover isn’t just giving the verifier a 3-coloring.
Scott Says:
Comment #18 February 12th, 2008 at 11:56 pm
Job: Yes, the “not” should be there. If two graphs are isomorphic, then obviously you can’t know which one you’re looking at a permutation of.
Job Says:
Comment #19 February 12th, 2008 at 11:57 pm
Harrison, i think that’s the case. And i have another question: why would the verifier become convinced if it can’t verify that the prover is properly decoding the colors? Is the verifier taking for
granted that the prover is honest? Otherwise the prover can always “decode” the colors such that they’re different (the verifier doesn’t have the decoder algorithm, so he’s none the wiser).
Scott Says:
Comment #20 February 12th, 2008 at 11:58 pm
Harrison: Yes, you throw in additional random data along with the colors. (Modern encryption schemes always throw in additional data, for exactly the reason you say.)
Job Says:
Comment #21 February 13th, 2008 at 12:01 am
Thanks – duh! on my original coment.
Scott Says:
Comment #22 February 13th, 2008 at 12:03 am
Job: After the prover decrypts the colors, the verifier just checks for himself whether the decryptions are correct. (For this to work, obviously you need a cryptosystem with unique decryption, but
that’s known to exist assuming one-way functions.)
I apologize for skipping these details; will fill them in when I get a chance.
Hatem Says:
Comment #23 February 13th, 2008 at 6:25 am
Just one question from someone who is not familiar with interactive protocols:
In the protocol of 3-colorability, how could the verifier know if the decryption is valid? You, the prover, are the one who encrypted the colors of the two vertices and you are the one who decrypted
them, so you can decrypt them as red and blue all the time (cheating) and the verifier won’t know whether this is a valid decryption or not.
Have I missed something?
Hatem Says:
Comment #24 February 13th, 2008 at 6:31 am
Sorry, I didn’t notice that my question was already posed by someone else.
Scott Says:
Comment #25 February 13th, 2008 at 9:37 am
Again, you encrypt in such a way that there’s only one valid way to decrypt. For example, let’s say you want to encrypt a single bit. If the bit is 0, then multiply together two huge prime numbers
neither of which ends with a ’7′. If the bit is 1, multiply together two huge prime numbers at least one of which ends with a ’7′. Use the product as the ciphertext.
Because every number has a unique prime factorization, and because it’s possible to determine efficiently whether a number is prime, you just have to send the verifier the prime factors and then the
verifier can check for himself that the decryption is correct.
Michael Bacon Says:
Comment #26 February 13th, 2008 at 10:02 am
” . . . computer scientists had already generalized the notion of proof in the way they describe (from a static sequence of symbols to a computational process) for completely unrelated reasons.”
Is this the same as the authors’ contention that quantum computation shows ” . . . that neither a human brain nor any other arbiter will ever be able to check step-by-step, since if the ‘sequence of
propositions’ corresponding to such a proof were printed out, the paper would fill the observable universe many times over.”
My sense was that the implications of quantum computation — even if only based on our assumptions about the underlying physics (what isn’t?) — can be thought of as proving the classical intuition.
Perhaps though this isn’t the right way to look at it.
Scott Says:
Comment #27 February 13th, 2008 at 10:10 am
Michael, if the set of all possible challenges and responses that could be exchanged in a classical interactive protocol were printed out, it would also fill the observable universe.
As for what doesn’t depend on any assumptions about physics: arguably, conventional mathematical proofs (like the proof that √2 is irrational). But I don’t want to start another flamewar about this.
Michael Bacon Says:
Comment #28 February 13th, 2008 at 10:15 am
Thanks Scott.
Jonathan Vos Post Says:
Comment #29 February 13th, 2008 at 4:25 pm
See also:
“… The [Princeton] Companion [of Philosophy] also has a section on history of mathematics; for instance, here is Leo Corry’s PCM article “The development of the idea of proof”, covering the period
from Euclid to Frege. We take for granted nowadays that we have precise, rigorous, and standard frameworks for proving things in set theory, number theory, geometry, analysis, probability, etc., but
it is worth remembering that for the majority of the history of mathematics, this was not completely the case; even Euclid’s axiomatic approach to geometry contained some implicit assumptions about
topology, order, and sets which were not fully formalised until the work of Hilbert in the modern era. (Even nowadays, there are still a few parts of
mathematics, such as mathematical quantum field theory, which still do not have a completely satisfactory formalisation, though hopefully the situation will improve in the future.)…”
I’d previously cross-posted:
5 January, 2008 at 2:21 pm
Jonathan Vos Post
I’ve cited this thread, and excerpted the wonderful Leo Corry’s article “The development of the idea of proof”, over at January 2, 2008 Two Cultures in the Philosophy of Mathematics? Posted by David
Corfield, on the n-Category Cafe.
Or am I thinking of the book “The Princeton Companion to Mathematics” by Gowers, T., ?
I cannot resist adding:
36 Methods of Mathematical Proof
Proof by obviousness
“The proof is so clear that it need not be mentioned.”
Proof by intuition
“I just have this gut feeling. . .”
[JVP: and the last is not as silly as it sounds, because the human gastrointestinal tract has approximately 10^9 neurons embedded in its layers of the 20+ feet of nonaxisymmetric concentric
cylinders, histologically speaking, with is fully 1% as many neurons as in the brain in your skull, and more than are in the spinal cord. I am simulating this system in SBML (Systems Biology Markup
Language) for a paper by myself and Dr. Thomas L. Vander Laan, M.D., F.A.C.S, FCCWS, to be submitted to "Nature" on what I unofficially call a General Unified Theory of the Gut, or G.U.T. of GUT, and
is to be clinically tested at USC Medical School. This is, in a sense, an application of the absolutely gorgeous (and includes proofs) paper "Nonlinear Dynamics of Networks: The Groupoid Formalism"
by Ian Stewart and
Martin Golubitsky, Bull. Amer. Math. Soc., July 2006, pp.305-364)] | {"url":"http://www.scottaaronson.com/blog/?p=238","timestamp":"2014-04-16T19:04:54Z","content_type":null,"content_length":"28558","record_id":"<urn:uuid:33425efd-592a-45c2-b095-cc26f84e3d5a>","cc-path":"CC-MAIN-2014-15/segments/1397609524644.38/warc/CC-MAIN-20140416005204-00012-ip-10-147-4-33.ec2.internal.warc.gz"} |
Haskell and principal types
Karl-Filip Faxen kff@it.kth.se
Fri, 05 Oct 2001 21:25:57 +0200
Hi all!
I've been spending some time the last year writing up a formalization
of the Haskell type system (actually, most of the static semantics).
In doing so, I've come across an oddity. It seems that Haskell does not
have the principal type property, ie there are Haskell expressions
which, in a given typing environment, can be assigned at least two types
that are not generic instances of each other but can not be assigned
any type more generic that the two. The culprit is the monomorphism
restriction. I was kind of surprised, thinking that principal types
were likely to hold for Haskell, but it seems not.
The monomorphism restriction goes like this in my inference rules:
If a declaration group contains a pattern binding with a nonvariable pattern
or one where there is no type signature for the variable, then the context
parts of the type schemes derived for the bound variables must be empty.
The difference to for instance "Typing Haskell in Haskell" is that my
formalization is a set of inference rules (starting from the draft static
semantics by Peyton Jones and Wadler), so many different types can be
derived for the same typing environment and expression, wheras THIH is
a program which computes a single type.
So here is the offending program:
class IsNil a where
isNil :: a -> Bool
instance IsNil [b] where
isNil [] = True
isNil _ = False
f x y = let g = isNil
in (g x, g y)
The monomorphism restriction applies to the binding of "g" since
there is no type signature. Thus it is not legal to derive
"forall a . IsNil a => a -> Bool", but two legal possibilities are
- forall b . [b] -> Bool, and
- a -> Bool (without quantification and with "IsNil a" among the predicates).
These two choices lead to different types for "f":
- forall a b . [a] -> [b] -> (Bool,Bool), and
- forall a . IsNil a => a -> a -> (Bool,Bool)
These two are incomparable (neither is a generic instance of the other).
I can not see that it is legal to derive a type for "g" which will allow
some type for "f" that is more general than both of these.
As far as I can see, the inference algorithm from "Typing Haskell in Haskell"
would give the second type, which is also what GHC derives.
The trick here is the instance declaration for "IsNil [a]" which has an
empty instance context, ie it is not important what the element type is.
So, is this already well known in the Haskell community, or is it a new
result? Of course, it is not a result until one has *proved* that *no*
type more general than the two above is derivable, but it is a
strong conjecture. In the "Type Classes in Haskell" paper from TOPLAS,
the smaller system without the monomorphism restriction was conjectured
to have principal types. Also, the Haskell Report (section 4.1.4) states:
"Haskell 's extended Hindley-Milner type system can infer the principal
type of all expressions, including the proper use of overloaded class
methods (although certain ambiguous overloadings could arise, as described in
Section 4.3.4)."
But there is no ambiguity involved here.
Jones: Typing Haskell in Haskell, in Proceedings of the Third Haskell Workshop
Hall et al: Type Classes in Haskell, TOPLAS vol 18 no 2
Peyton Jones and Wadler: A Static Semantics for Haskell, draft paper, Glasgow | {"url":"http://www.haskell.org/pipermail/haskell/2001-October/008062.html","timestamp":"2014-04-16T15:00:51Z","content_type":null,"content_length":"5409","record_id":"<urn:uuid:e6792ef5-2262-4815-a5ca-4ce01673f498>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00444-ip-10-147-4-33.ec2.internal.warc.gz"} |
Looping over a function in Haskell
up vote 1 down vote favorite
I'm just puzzled with this one, it's a Haskell loop-sort-of-thing which I can't figure out how to write. Basically, I've defined three functions split, riffle and shuffle.
split :: [a] -> ([a],[a])
split xs = splitAt (length xs `div` 2) xs
riffle :: [a] -> [a] -> [a]
riffle xs [] = xs
riffle [] ys = ys
riffle (x:xs) (y:ys) = x:y:riffle xs ys
shuffle :: Int -> [a] -> [a]
shuffle 0 xs = xs
shuffle n xs = shuffle (n-1) (riffle a b)
where (a, b) = split xs
Basically split just splits a list in half, riffle is supposed to 'interlace' two lists, so for example:
riffle [1,2,3] [4,5,6] = [1,4,2,5,3,6]
And shuffle is to iterate the amount of splitting and riffling of the list items. Now I need to define a function repeats which outputs how many iterations of shuffle would it take to get the
original list again. The function is defined as such:
repeats :: [Int] -> Int
I'm just stuck as to how you can perform a loop over the shuffle... I think it has something to do with list comprehension but I couldn't get anything. I have yet to try a lambda expression but I
don't think it's necessary. By the way, the shuffle should be done on lists with even number of items. Any ideas?
haskell loops repeat shuffle
add comment
3 Answers
active oldest votes
One way of solving this is to take advantage of laziness and use iterate to generate the infinite list of iterated shuffles of the input.
> iterate (uncurry riffle . split) "ABCDEF"
["ABCDEF","ADBECF","AEDCBF","ACEBDF","ABCDEF","ADBECF","AEDCBF","ACEBDF", ...]
The first element of the list is the original one, so we drop that with tail, then use takeWhile to get the ones that were different from the original.
up vote 12 down vote accepted
> takeWhile (/= "ABCDEF") . tail $ iterate (uncurry riffle . split) "ABCDEF"
Now, you just need to take the length of that list and add one to get the required number of shuffles.
1 You can also generate the list with tail $ iterate as @hammar describes, and use elemIndex to find the index of recurrence. – dflemstr May 1 '12 at 19:32
add comment
In Haskell, iteration is most commonly expressed using recursion rather than through looping.
This is often done by using an inner function that tells you how to do the iteration, and then simply calling the inner function with the appropriate arguments.
Perhaps you can fill in the gaps in the following code?
repeats xs = iter 1 (...) where
iter n ys = if ys == xs
then n
up vote 3 down else iter (...) (...)
An alternative approach is to exploit Haskell's laziness and do it with an infinite list, using the higher-order function iterate, which repeatedly applies a function to an initial
repeats xs = (...) $ takeWhile (...) $ iterate (shuffle 1) (...)
Although iterate returns an infinite list, we will only ever use a finite portion of it, and so we don't get into an infinite loop.
add comment
In many cases you can use an infinite list rather than a "loop". This is one of them.
The prelude function "iterate" repeatedly applies a function to a value, so (from memory)
up vote 5 down iterate f x = [x, f x, f (f x), f (f (f x)) ....]
So if you apply "iterate shuffle" to a starting list then you get the progressive shuffle. Then use takeWhile to find the first entry in the list that is equal to your starting
point,and then "length" to find out how long that is.
add comment
Not the answer you're looking for? Browse other questions tagged haskell loops repeat shuffle or ask your own question. | {"url":"http://stackoverflow.com/questions/10400891/looping-over-a-function-in-haskell?answertab=active","timestamp":"2014-04-20T14:56:55Z","content_type":null,"content_length":"71111","record_id":"<urn:uuid:fd7aa05f-fc82-4d47-bf0f-b93bc4578bf6>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00553-ip-10-147-4-33.ec2.internal.warc.gz"} |
Metrics for Reactive Wetting in Complex Systems
We have implemented a numerical solution scheme to solve these equations and are examining the predictions. Four coupled partial differential equations comprise the model: a mass balance equation, a
modified Navier-Stokes equation for the velocity of the matter in the various phases, a modified diffusion equation for the concentration field, and an equation to treat the dynamics of the
solid-fluid interface (phase field). Solving this system of coupled equations accurately with appropriate parameters requires sophisticated numerical solution techniques and long simulation times.
Our approach thus far has yielded a complete solution of the equations in two dimensions with a slightly nonrealistic parameter set to enable the solution of the equations in a practical time frame.
To date we have been able to develop:
1. Methods that suppress unphysical surface flows
2. Relationships between thermodynamic parameters and equilibrium surface energies/contact angles
3. A numerical algorithm that enables large physical parameter differences between phases
4. Methods that stabilize simulations of compressible flow.
The first test of the model will be a comparison to simple experiment in a metallurgical context. One such experiment is the spreading of a liquid metal droplet of tin on a bismuth substrate. Here
wetting is accompanied by dissolution of the substrate so that the triple junction motion is governed by solute diffusion as well as capillary processes.
A reactive wetting experiment of liquid Bi-20 wt%Sn spreading on solid Bi.
To date, we cannot match the physical parameters of this experiment in a reasonable computation time, and considerable effort is being devoted to improving our solution methods. However below are
shown two time slices from a calculation of the change in shape, composition and accompanying fluid flow pattern when the temperature of a droplet is reduced. The first slice shows the droplet at
equilibrium for the high temperature (shown by the black lines). The droplet contracts and dissolves the substrate at a later time and lower temperature. These results show promise for the approach.
Numerical results obtained for Numerical results obtained for
spreading of a liquid droplet. spreading of a liquid droplet.
Initial state. Final state. | {"url":"http://nist.gov/mml/msed/thermodynamics_kinetics/metrics_for_reactive_wetting.cfm","timestamp":"2014-04-17T06:46:10Z","content_type":null,"content_length":"25610","record_id":"<urn:uuid:166b27e1-358a-4d79-8cd7-d5205e5a4be8>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00166-ip-10-147-4-33.ec2.internal.warc.gz"} |
Using a Closed Formula to find Coefficients
March 3rd 2010, 05:51 PM #1
Junior Member
May 2009
Using a Closed Formula to find Coefficients
The formula is:
(1 + x + x^2) / [(1 - x^3)^2]
The question itself asks for coefficient of x^100, which I have calculated by finding the corresponding pairs by splitting up the function, using the knowledge that
1/(1-x^3) = 1 + x^3 + x^6 + x^9 ..... and I got the answer to be 34.
However, I was wondering what if I was just looking for the coefficient of some x^n. How would I go about finding the closed formula for this? Because from my understanding if you have a closed
formula you can find this...
Follow Math Help Forum on Facebook and Google+ | {"url":"http://mathhelpforum.com/discrete-math/131940-using-closed-formula-find-coefficients.html","timestamp":"2014-04-18T03:58:26Z","content_type":null,"content_length":"29159","record_id":"<urn:uuid:90c88416-ed1c-4fdc-aca4-440fcb0e1a3e>","cc-path":"CC-MAIN-2014-15/segments/1397609539447.23/warc/CC-MAIN-20140416005219-00271-ip-10-147-4-33.ec2.internal.warc.gz"} |
Number of results: 7,912
x^2+2x-15=0 solve by completing the square
Thursday, June 9, 2011 at 9:13pm by Angel
x^2+2x+1=16+1 (x+1)^2=16 take the sqrt each side x+1=+-4 x=-5, 3
Thursday, June 9, 2011 at 9:13pm by bobpursley
Pre Alegbra
I love Pre Alegbra but i don't get it
Wednesday, October 24, 2007 at 5:36pm by Rachel
Trig 30
x/2 = 2pi/3 yields a unique solution of x = 4pi/3 Does this answer come from some trig equation? Your subject title suggests that. In that case find the period of the trig function, then add k
(period) to 4pi/3, k an integer.
Friday, March 19, 2010 at 7:59pm by Reiny
Subtract 2 pi from 7pi/3. The trig functions of 7 pi/3 will be the same values as the trig functions of pi/3, which is 60 degrees. The cosine of pi/3 is 1/2. That makes the secant 3. The tangent is
sqrt3 You should be able to look up or figure out the other funtions of that ...
Tuesday, January 12, 2010 at 9:50pm by drwls
could someone please refresh my memory of the basic trig functions? ex) cos^2 + sin^2 = 1? That is a trig identity. http://www.sosmath.com/trig/Trig5/trig5/trig5.html
Thursday, April 12, 2007 at 10:18pm by raychael
Math - Solving Trig Equations
Start by recalling the most important identity. My math teacher calls this "the #1 Identity." sin^2(x) + cos^2(x) = 1 We want to simplify our trig equation by writing everything in terms of sine.
Let's solve the #1 Identity for cos^2(x) because we have that in our trig ...
Wednesday, November 21, 2007 at 6:29pm by Michael
Z = 2
Tuesday, October 16, 2007 at 3:32pm by Ms. Sue
2 maybe?
Wednesday, November 4, 2009 at 5:56pm by Rain
Thank you
Sunday, May 30, 2010 at 3:17pm by Ami
then h=3/2 v h=-1
Friday, September 17, 2010 at 4:45pm by PLINIO
Monday, February 14, 2011 at 8:12pm by Donna
Thank you
Thursday, February 17, 2011 at 10:16pm by Donna
Thank you
Friday, February 18, 2011 at 6:39am by Donna
5/8 - (-5) = 5/8 + 5 = ?
Tuesday, April 19, 2011 at 2:33pm by PsyDAG
Sunday, May 30, 2010 at 3:38pm by dani
m=-4/5, T(1/3)=7/4
Thursday, March 19, 2009 at 4:57pm by pam
Thursday, June 14, 2012 at 4:11pm by kevin
Alegbra 2
Thank you
Monday, August 27, 2012 at 8:26pm by Marie
Alegbra 2
You're welcome.
Monday, August 27, 2012 at 8:26pm by Ms. Sue
Thanks! So, 0.5?
Wednesday, March 26, 2014 at 4:25pm by Hailey
Wednesday, March 26, 2014 at 4:25pm by Damon
You are welcome.
Wednesday, March 26, 2014 at 6:22pm by Damon
You are welcome :)
Wednesday, March 26, 2014 at 6:22pm by Damon
What kind of reflection does the trig function y = cos(4x/3 minus 1) have?
Monday, April 21, 2008 at 8:53pm by Priya
What kind of reflection does the trig function y = cos(4x/3 minus 1) have?
Tuesday, April 22, 2008 at 12:03am by Chaitanya
how do i do this? give the signs of the six trig functions for each angle: 74 degrees?
Wednesday, December 3, 2008 at 6:59pm by Tay
express the trig. ratios sinA,secA n tanA in terms of cotA.
Saturday, May 7, 2011 at 5:49am by Anonymous
How do you solve cos(2arcsin 1/4) using inverse trig. functions??!! PLEASE HELP ME!
Monday, May 9, 2011 at 11:20am by Tor
Find (if possible) the trig function of the quadrant angle. sec 3pi/2
Monday, June 6, 2011 at 4:00pm by Master chief
find the 5 trig ratios when sin theta = -5/13 and lies in quadrant 3
Wednesday, September 14, 2011 at 10:38pm by karen
graphing trig functions
I see the equation of a straight line, not a trig function
Sunday, May 20, 2012 at 10:15pm by Reiny
surely you have learned the basic definitions of the trig functions, tanŲ = y/x = 4/3
Sunday, January 20, 2013 at 5:17pm by Reiny
its in the first chapter of my trig course. i know its review frm geometry and alg
Friday, November 14, 2008 at 11:25am by y912f
simplify to a constant or basic trig function.. 1+tan(x)/1+cot(x)
Sunday, March 14, 2010 at 1:14pm by hilde
This subject is not trig. You will have to use your own graphic calculator.
Sunday, May 15, 2011 at 12:10am by drwls
first of all, this is not trig, secondly your expression makes no sense.
Monday, January 7, 2013 at 10:03pm by Reiny
What kind of reflections are the following trig functions? y = 3cos(x-1) y = sin(-3x+3) y = -2sin(x)-4
Sunday, April 20, 2008 at 10:27pm by Joshua
What kind of reflections are the following trig functions? y = 3cos(x-1) y = sin(-3x+3) y = -2sin(x)-4
Monday, April 21, 2008 at 12:33am by Joshua
What is the shift along x of the following trig functions? y = (3sinx/2) + 4 y = -2sin(x)-4 y = sin(-3x + 3)
Monday, April 21, 2008 at 12:34am by Amandeep
How would you solve this trig function: cos2x=sin^2-2 how do you know what trig identities to use?
Saturday, August 6, 2011 at 5:39pm by Jess
find the exact values of the six trig functions of angle... sin(-315degrees) how do i do this?
Thursday, September 1, 2011 at 9:16pm by ALISON
I don't know to find the derivative of the following trig functions. Please help. f(x)= cotx h(x)= secx i(x)= cscx
Thursday, January 19, 2012 at 8:45am by Claire
TRIG Identities, Gr. 12: Prove: cot4x=1-tan^2x/2tan2x
Thursday, May 23, 2013 at 2:56pm by Josh
i=p(1+r) solve for r
Monday, February 18, 2008 at 5:57pm by kirsten
h(0)= 0 + 5= ___?
Friday, March 21, 2008 at 6:57pm by ~christina~
Correct! :)
Tuesday, March 3, 2009 at 4:50pm by Cassie
what are we doing? is there an equation , and is it (a+4)/2 = (a+4)/a ?
Sunday, May 16, 2010 at 6:20pm by Reiny
Sunday, May 30, 2010 at 3:10pm by Damon
Thank you Damon
Sunday, May 30, 2010 at 3:10pm by Ami
Sunday, May 30, 2010 at 7:06pm by bobpursley
thanks qudditch
Saturday, June 26, 2010 at 7:58pm by sean
College Alegbra
(b-1/a)/(b^2+2/a^2 )
Friday, August 13, 2010 at 1:50pm by Jessica
alegbra 1
what is means?
Monday, October 11, 2010 at 12:54pm by china
Why do i never get any help
Thursday, February 17, 2011 at 10:16pm by Donna
Why do i never get any help
Thursday, February 17, 2011 at 10:16pm by Donna
College Alegbra
Thanks for the help.
Thursday, March 3, 2011 at 7:39pm by Chris
alegbra 1
What are your choices?
Friday, June 3, 2011 at 2:37pm by Ms. Sue
Wednesday, August 10, 2011 at 7:38pm by Audrey
Alegbra help
Friday, September 9, 2011 at 8:33pm by PsyDAG
how do i simpllify 5/x + 4/x^2 - 3/x^3
Thursday, March 1, 2012 at 1:00pm by allen
Alegbra 1a
8 + b
Sunday, April 8, 2012 at 1:27am by Steve
Alegbra 2
Monday, August 27, 2012 at 8:26pm by Ms. Sue
tn = (-1)n(n) A. -1, -2, -3, -4 B. -1, 2, -3, 4 C. 1, ½, 2/3, ¾ D. 1, 2, 3, 4
Tuesday, June 25, 2013 at 1:14pm by Dale
If you mean (-1)^n * n then (B)
Tuesday, June 25, 2013 at 1:14pm by Steve
2x=1 x=0.5 y=-o.5
Sunday, March 2, 2014 at 8:49pm by Java
x+y=6 x-y=4 - 2y=2 y=1 x=5
Sunday, March 2, 2014 at 8:46pm by Java
I gave you x and y y is 1/2
Wednesday, March 26, 2014 at 4:25pm by Damon
Thank you Damon :)
Wednesday, March 26, 2014 at 6:22pm by Hailey
So I am rightt
Wednesday, March 26, 2014 at 6:22pm by Hailey
Yes, right :)
Wednesday, March 26, 2014 at 6:22pm by Damon
alegbra 1
And your question is???
Thursday, March 27, 2014 at 12:22pm by Ms. Sue
alegbra 1 (?)
What is your question?
Saturday, March 29, 2014 at 6:30am by PsyDAG
Does anybody know a good website that will hlp me with finding the six trig functions of a point NOT on the unit cricle?
Wednesday, September 16, 2009 at 7:59pm by Anonymous
use the unit circle to find the exact value for all the trig functions of č=2š/3.
Monday, February 1, 2010 at 9:54pm by Anonymous
find the 5 other trig functions if cos(theta) = square root of 2/2 and cotangent is less than 0
Wednesday, June 9, 2010 at 7:04pm by kelly
I don't know to find the derivative of the following trig functions. Please help. f(x)= cotx h(x0= secx i(x)= cscx
Thursday, January 19, 2012 at 8:45am by Claire
trig! please help!
to bobpursely: i need to simplify the expression using trig identities. and no i meant for there to only be x
Sunday, May 13, 2012 at 8:59pm by Brianna
Physics (trig)
If the angle is x, tan x = 12.3333/19.2 Better review your trig ratios...
Wednesday, June 19, 2013 at 9:10pm by Steve
what is the exact value of 7pi for all trig func.?
Monday, February 1, 2010 at 10:23pm by claire
Find (if possible) the trig function of the quadrant angle.
Monday, June 6, 2011 at 3:59pm by Master chief
write a product of two trig functions that equals 1.
Sunday, November 6, 2011 at 9:38pm by Dani
any calculus text will list the trig functions and their derivatives.
Thursday, January 19, 2012 at 8:45am by Steve
Solve the following trig equation 2cos(x-π/6)=1
Tuesday, January 31, 2012 at 2:51am by Matt
csc thea= -2, quadrant 4. what are the six trig functions?
Monday, May 6, 2013 at 4:17pm by Shay
Do you mean find the six trig functions (sin, cos, tan, csc, sec, and cot)?
Wednesday, December 3, 2008 at 6:59pm by Anonymous1
Let Q be an acute angle such that sinQ=.6. Find the values of the following using Trig Identities: cosQ and tanQ
Tuesday, July 27, 2010 at 10:06pm by student
Use Trig identities to verify that sec^4(x)-tan^4(x)=1+2tan^2(x), Only work with one side of the equation
Tuesday, March 1, 2011 at 5:23pm by Anonymus
Just noticed this was for trig, not calculus. Algebraically, note that a(y) is a parabola, whose vertex occurs where y=60/4 = 15.
Thursday, August 29, 2013 at 9:44pm by Steve
What is the range of the trig function sin(-3x+3)?
Monday, April 21, 2008 at 12:35am by Chaitanya
please show me again in trig way
Saturday, May 17, 2008 at 12:40pm by Doni --i didnt get this one can please show me the trig way a little bit more clrealy
how to i find the six trig values for (7pi/3)
Tuesday, January 12, 2010 at 9:50pm by Rak
Trig Identity. 1-sin^2x/1-cosx
Sunday, May 15, 2011 at 5:56pm by Jill
what's the single trig. function of cos6xcosx-sin6xsinx
Thursday, May 17, 2012 at 4:44pm by MIK
write 2+2 squareroot of 3i in trig form.
Thursday, May 17, 2012 at 5:01pm by ky
no idea what "p" and "o" represent, or which trig function is required.
Monday, July 22, 2013 at 8:09pm by Reiny
-48 divided by ( ) = 6 -8
Tuesday, March 20, 2007 at 1:11pm by Anonymous
Answer: Z2 Thank you
Tuesday, October 16, 2007 at 3:32pm by Rusty
do you know what the variable equals?
Wednesday, October 17, 2007 at 5:53pm by Bailey
I totally understand. Thanks
Monday, February 18, 2008 at 5:47pm by greatdanelola
Pages: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Next>> | {"url":"http://www.jiskha.com/search/index.cgi?query=alegbra%2Ftrig","timestamp":"2014-04-20T04:11:30Z","content_type":null,"content_length":"24161","record_id":"<urn:uuid:c132cef0-9ef8-42e5-a389-6ad589b3acfb>","cc-path":"CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00159-ip-10-147-4-33.ec2.internal.warc.gz"} |
subset of a vector space
October 10th 2009, 04:54 PM #1
Super Member
Aug 2009
subset of a vector space
how do you prove this theorem?
let S be a subset of a vector space V
(a) Then span S is a subspace of V which contains S
(b) if W is a subspace of V containing S, then span s ⊆ W
i would think that,
assume v, w ∈ span S, where
v= a1va + a2v2+...+ amvm and w=b1w1+b2w2+...bmwm
thus span S is a linear combination of the vectors in S.
does that show that it is a subspace of V? it seems to me that i have just proven that span S is a vector space....
then how do i do the second part?
how do you prove this theorem?
let S be a subset of a vector space V
(a) Then span S is a subspace of V which contains S
(b) if W is a subspace of V containing S, then span s ⊆ W
i would think that,
assume v, w ∈ span S, where
v= a1va + a2v2+...+ amvm and w=b1w1+b2w2+...bmwm
thus span S is a linear combination of the vectors in S.
does that show that it is a subspace of V? it seems to me that i have just proven that span S is a vector space....
then how do i do the second part?
For part 1. Please show that if $x\in$span(S) => $x\in V$
You will be done (This will prove span is a subset)
You have already done it in part one. Just replace V with W - the question is similar to part 1 above. Here you jut have to prove span S is a subset of W. A stronger inference is that it is a
sub-space of W as well
could you explain further becos i cant understand what you mean..
how do you prove this theorem?
let S be a subset of a vector space V
(a) Then span S is a subspace of V which contains S
(b) if W is a subspace of V containing S, then span s ⊆ W
i would think that,
assume v, w ∈ span S, where
v= a1va + a2v2+...+ amvm and w=b1w1+b2w2+...bmwm
thus span S is a linear combination of the vectors in S.
Be more careful here: the span of S is not a linear combination of the vectors of S. Instead it is the set of all linear combinations of vectors from S.
does that show that it is a subspace of V? it seems to me that i have just proven that span S is a vector space....
First, before attempting to prove any proposition you have to be very clear about how the terms in that proposition have been defined.
Because the span of a set S with respect to a vector space V can be defined in different ways, you may or may not have been successful in your attempt. (I can think of at least three ways to
define the span of S: first, as the set of all linear combinations of S; second, as the smallest subspace of V containing S; and, third, as the intersection of all subspaces of V containing S.)
Basically, you need to show, basing yourself on the definition of span S that you have been given (somwhere), that that set of vectors satisfies all the axioms of a vector space.
then how do i do the second part?
Surely, if S is a subset of W and you are forming a linear combination of elements of S (and thus of W), you get another element of W, because W is a vector (sub-)space: vector (sub-)spaces are,
by definition, closed under the operation of forming linear combinations of some of their elements.
October 10th 2009, 07:28 PM #2
Super Member
Apr 2009
October 11th 2009, 01:56 AM #3
Super Member
Aug 2009
October 11th 2009, 03:00 AM #4 | {"url":"http://mathhelpforum.com/advanced-algebra/107243-subset-vector-space.html","timestamp":"2014-04-21T10:56:48Z","content_type":null,"content_length":"40788","record_id":"<urn:uuid:852dd796-89b5-4ad4-9f2f-4c36cd866f28>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00409-ip-10-147-4-33.ec2.internal.warc.gz"} |
BDBComp - Biblioteca Digital Brasileira de Computação
Regular Expression Transformations to Extend Regular Languages
Robson da Luz, Martin Musicante.
We consider the problem of extending a regular language using one positive and one negative example. This problem can be stated as follows: given (i) a regular expression E and (ii) a pair of words
w, w´, such that w ? L(E) and w´? L(E) (L(E) is the language associated to E), supposing that w´ is obtained from w by adding or removing one or more symbols, then we are interested in building new
regular expressions E´ such that they are similar to E and such that L(E) ? {w´} ? L(E´). A previous paper proposes a solution to this problem by defining a graph-transformation algorithm called
GREC. GREC performs changes on the graph of a finite-state automaton accepting L(E), in order to derive the new regular expressions E´. In this paper, a new, graphless, version of GREC is defined.
Our algorithm (called dGREC) obtains the same solutions as the original GREC, but working on the regular expression. The main advantage of dGREC over GREC is its simplicity, since it manipulates
regular expressions and not automata graphs. The algorithm proposed here is being used as a part of a tool for the conservative extension of schemata for XML.
Caso o link acima esteja inválido, faça uma busca pelo texto completo na Web: Buscar na Web | {"url":"http://www.lbd.dcc.ufmg.br/bdbcomp/servlet/Trabalho?id=11945","timestamp":"2014-04-18T21:12:27Z","content_type":null,"content_length":"7184","record_id":"<urn:uuid:3e386fe8-3476-43ae-aada-56fb626810c4>","cc-path":"CC-MAIN-2014-15/segments/1398223206770.7/warc/CC-MAIN-20140423032006-00358-ip-10-147-4-33.ec2.internal.warc.gz"} |
South Boston, MA Algebra 1 Tutor
Find a South Boston, MA Algebra 1 Tutor
...Advanced algebra was one of my favorite subjects in graduate school, where I earned an "A" in at least three or four such courses. The same concepts are in elementary algebra, and I have a
good amount of experience tutoring at this level. As a doctoral student I assistant-taught several semesters of Calculus, and taught summer courses myself on a few occasions.
29 Subjects: including algebra 1, reading, English, geometry
...I continue to use undergraduate level linear algebra in my physics research. I use MATLAB routinely in my research. It was my primary simulation and computational physics tool throughout
graduate school, and I continue to use it on a daily basis.
16 Subjects: including algebra 1, calculus, physics, geometry
...My references will gladly provide details about their own experiences. I have a master's degree in computer engineering and run my own data analysis company. Before starting that company, I
developed software for large and small companies and was most recently the IT director at a large accounting firm.
11 Subjects: including algebra 1, geometry, algebra 2, precalculus
I have instructed undergraduate students in Macroeconomics, Microeconomics and International Management, advancing their understanding and application of sometimes confusing concepts. I
facilitate learning by promoting open and comfortable academic discourse. I have been thanked for making economi...
6 Subjects: including algebra 1, accounting, algebra 2, economics
...The test may seem intimidating, but with the right study habits it can be a great experience. I am also a long-time percussionist who currently plays for the Harvard Wind Ensemble, and I love
to share my passion for percussion with those willing to listen. I have always believed that the best w...
20 Subjects: including algebra 1, reading, elementary math, ACT Science
Related South Boston, MA Tutors
South Boston, MA Accounting Tutors
South Boston, MA ACT Tutors
South Boston, MA Algebra Tutors
South Boston, MA Algebra 2 Tutors
South Boston, MA Calculus Tutors
South Boston, MA Geometry Tutors
South Boston, MA Math Tutors
South Boston, MA Prealgebra Tutors
South Boston, MA Precalculus Tutors
South Boston, MA SAT Tutors
South Boston, MA SAT Math Tutors
South Boston, MA Science Tutors
South Boston, MA Statistics Tutors
South Boston, MA Trigonometry Tutors | {"url":"http://www.purplemath.com/South_Boston_MA_algebra_1_tutors.php","timestamp":"2014-04-18T16:16:54Z","content_type":null,"content_length":"24378","record_id":"<urn:uuid:78941294-b351-4825-bcba-ef6ed8227ccd>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00183-ip-10-147-4-33.ec2.internal.warc.gz"} |
I was wondering if someone could just explain me how to write a program. I am having a hard time trying to start writing my code. I can show you what I wrote so far.
This is the problem:
Part A: Write a program for a theater that will keep track of how many people in each of 5 age categories attended a particular movie. Use the 5 age categories listed below in the sample screen
output. The user will enter a number of ages, entering a negative number when there are no more ages to enter. Your program will then report on how many people in each age group attended. Sample
screen output:
Enter age of attendee (negative number to quit): 34
Enter age of attendee (negative number to quit): 16
Enter age of attendee (negative number to quit): 68
Enter age of attendee (negative number to quit): 53
Enter age of attendee (negative number to quit): 39
Enter age of attendee (negative number to quit): 23
Enter age of attendee (negative number to quit): 21
Enter age of attendee (negative number to quit): -1
age 0 to 18: 1
age 19 to 30: 2
age 31 to 40: 2
age 41 to 60: 1
over 60: 1
Part B: Modify your program so that, in addition to the report that the program currently produces, it also gives the average age of the people in attendance, the age of the oldest person in
attendance, and the age of the youngest person in attendance. Sample screen output:
Enter age of attendee (negative number to quit): 34
Enter age of attendee (negative number to quit): 16
Enter age of attendee (negative number to quit): 68
Enter age of attendee (negative number to quit): 53
Enter age of attendee (negative number to quit): 39
Enter age of attendee (negative number to quit): 23
Enter age of attendee (negative number to quit): 21
Enter age of attendee (negative number to quit): -1
age 0 to 18: 1
age 19 to 30: 2
age 31 to 40: 2
age 41 to 60: 1
over 60: 1
The average age was 36.
The youngest person in attendance was 16.
The oldest person in attendance was 68.
Part C: Modify your program so that it also asks for the gender of each attendee. Your program should then break the attendance down by gender as well as by age. Sample screen output:
Enter age of attendee (negative number to quit): 34
Enter gender (M or F): M
Enter age of attendee (negative number to quit): 16
Enter gender (M or F): M
Enter age of attendee (negative number to quit): 68
Enter gender (M or F): F
Enter age of attendee (negative number to quit): 53
Enter gender (M or F): F
Enter age of attendee (negative number to quit): 39
Enter gender (M or F): F
Enter age of attendee (negative number to quit): 23
Enter gender (M or F): F
Enter age of attendee (negative number to quit): 21
Enter gender (M or F): F
Enter age of attendee (negative number to quit): -1
age 0 to 18: 1
age 19 to 30: 2
age 31 to 40: 2
age 41 to 60: 1
over 60: 1
males: 2
females: 5
The average age was 36.
The youngest person in attendance was 16.
The oldest person in attendance was 68.
Your program should do something reasonable if no ages are entered (the user enters a negative number the first time).
Don't forget the code tags - The <> button on the right
And post your compiler output, if it doesn't compile.
These things will help us a lot, and will attract more replies.
Hope al goes well.
Topic archived. No new replies allowed. | {"url":"http://www.cplusplus.com/forum/beginner/82704/","timestamp":"2014-04-20T21:01:32Z","content_type":null,"content_length":"10754","record_id":"<urn:uuid:86fc813f-ae28-44bd-b68a-2b72d5f25cc6>","cc-path":"CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00416-ip-10-147-4-33.ec2.internal.warc.gz"} |
Number of days between February 26th, 1906 and April 5th, 1908
›› Date difference from Feb 26, 1906 to Apr 5, 1908
The total number of days between Monday, February 26th, 1906 and Sunday, April 5th, 1908 is 769 days.
This is equal to exactly 2 years, 1 month, and 10 days.
This does not include the end date, so it's accurate if you're measuring your age in days, or the total days between the start and end date. But if you want the duration of an event that includes
both the starting date and the ending date, then it would actually be 770 days.
769 days is equal to 109 weeks and 6 days.
The total time span from 1906-02-26 to 1908-04-05 is 18,456 hours.
This is equivalent to 1,107,360 minutes.
You can also convert 769 days to 66,441,600 seconds.
›› February, 1906 calendar
Su M Tu W Th F Sa
February 26th, 1906 is a Monday. It is the 57th day of the year, and in the 9th week of the year (assuming each week starts on a Sunday), or the 1st quarter of the year. There are 28 days in this
month. 1906 is not a leap year, so there are 365 days in this year. The short form for this date used in the United States is 2/26/1906.
›› April, 1908 calendar
Su M Tu W Th F Sa
April 5th, 1908 is a Sunday. It is the 96th day of the year, and in the 15th week of the year (assuming each week starts on a Sunday), or the 2nd quarter of the year. There are 30 days in this month.
1908 is a leap year, so there are 366 days in this year. The short form for this date used in the United States is 4/5/1908.
›› Date calculator
This site provides an online date calculator to help you find the difference in the number of days between any two calendar dates. Simply enter the start and end date to calculate the duration of any
event. You can also use this tool to determine how many days have passed since your birthday, or measure the amount of time until your baby's due date. The calculations use the Gregorian calendar,
which was created in 1582 and later adopted in 1752 by Britain and the eastern part of what is now the United States. For best results, use dates after 1752 or verify any data if you are doing
genealogy research. Historical calendars have many variations, including the ancient Roman calendar and the Julian calendar. Leap years are used to match the calendar year with the astronomical year.
If you're trying to figure out the date that occurs in X days from today, switch to the Days From Now calculator instead.
This page was loaded in 0.0054 seconds. | {"url":"http://www.convertunits.com/dates/from/Feb+26,+1906/to/Apr+5,+1908","timestamp":"2014-04-18T05:31:58Z","content_type":null,"content_length":"23107","record_id":"<urn:uuid:19e96044-d8f1-49e4-9c21-8f044755037a>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00003-ip-10-147-4-33.ec2.internal.warc.gz"} |
- -
Please install Math Player to see the Math Symbols properly
Click on a 'View Solution' below for other questions:
cc Find the interval in which f (x) = xe^9x is concave upward. View Solution
cc Find the interval in which f(x) = 8x(ln 9x) is concave upward. View Solution
cc What is the interval in which f(x) = (ln(4x))(x) is concave upward ? View Solution
cc What is the interval in which f (x) = 2x^3 + 18x^2 + 6x + 30 is concave downward? View Solution
cc Find the interval in which f (x) = 2x - 12x is concave downward. cc View Solution
cc Find the interval in which f (x) = e^- 7x is concave downward. cc View Solution
cc In (0, π2), f (x) = 8x cos x + 48 is cc View Solution
cc Find the largest interval in which f (x) = 30x^4 + 6x^2 + 41 is concave upward. cc View Solution
cc For the function f (x) = 3ax^2 + 2bx + 33 where a ≠ 0, which of the following is true? cc View Solution
cc What is the interval in which f(x) = x - 3x - 2 is concave downward ? View Solution
cc What is the interval in which f (x) = sin^2 6x is concave upward? View Solution
cc What is the interval in which f (x) = tan 4x is concave upward? View Solution
cc What is the interval in which f (x) = e^7x - e^- 7 x is concave downward? cc View Solution
cc What is the interval in which f (x) = e^4x sin 4x is concave downward? cc View Solution
cc Find the interval in which f(x) = x22 + ln 5x is concave downward. cc View Solution
cc Find the interval in which f(x) = 7x ^2 ln 6x is concave downward. View Solution
cc Find the interval in which f(x) = sin 18x is concave upward. cc View Solution
cc Find the interval in which f (x) = (ln 7x) ^2 is concave downward. View Solution
cc What is the interval in which f(x) = x(ln 9x)^2 is concave downward? cc View Solution
cc Find the point of inflection of f(x) = x^3 - 12x^2 + 195. cc View Solution
cc Determine the point of inflection of the graph of f(x) = 11x e^17x. View Solution
cc f(x) = 4x in (0, ∞) has cc View Solution
cc Find the minimum possible perimeter of a rectangle of area 900 m^2. View Solution
cc The sum of two positive numbers is 80. Find the smallest possible value of the sum of their squares. View Solution
cc The sum of two positive numbers is 4. Find the minimum possible value of the sum of the cubes of these numbers. View Solution
cc What is the maximum possible area of a rectangle of perimeter 12 m? cc View Solution
cc x, y are two positive numbers whose sum is 7. What is the possible greatest value of x^2 y? View Solution
cc Find the minimum possible perimeter of a rectangle of area 1600 m^2. View Solution
cc Find the interval in which f(x) = 5x(ln 6x) is concave upward. View Solution
cc What is the interval in which f(x) = (ln(7x))(x) is concave upward ? View Solution
cc What is the interval in which f (x) = 3x^3 + 45x^2 + 12x + 38 is concave downward? View Solution
cc Find the interval in which f (x) = 8x - 22x is concave downward. cc View Solution
cc Find the interval in which f (x) = e^- 3x is concave downward. cc View Solution
cc In (0, π2), f (x) = 4x cos x + 46 is cc View Solution
DDD Find the largest interval in which f (x) = 4x^4 + 2x^2 + 28 is concave upward. DDD View Solution
DDD What is the interval in which f(x) = x - 8x - 7 is concave downward ? View Solution
DDD Find the interval in which f (x) = xe^5x is concave upward. View Solution
DDD What is the interval in which f (x) = sin^2 4x is concave upward? View Solution
DDD For the function f (x) = 8ax^2 + 5bx + 31 where a ≠ 0, which of the following is true? DDD View Solution
DDD What is the interval in which f (x) = tan 5x is concave upward? View Solution
DDD What is the interval in which f (x) = e^6x - e^- 6 x is concave downward? DDD View Solution
DDD What is the interval in which f (x) = e^7x sin 7x is concave downward? DDD View Solution
DDD Find the interval in which f(x) = x22 + ln 8x is concave downward. DDD View Solution
DDD Find the interval in which f(x) = 5x ^2 ln 4x is concave downward. View Solution
DDD Find the interval in which f(x) = sin 4x is concave upward. DDD View Solution
DDD Find the interval in which f (x) = (ln 3x) ^2 is concave downward. View Solution
DDD What is the interval in which f(x) = x(ln 5x)^2 is concave downward? DDD View Solution
DDD What is the maximum possible area of a rectangle of perimeter 16 m? DDD View Solution
DDD The sum of two positive numbers is 40. Find the smallest possible value of the sum of their squares. View Solution
DDD The sum of two positive numbers is 14. Find the minimum possible value of the sum of the cubes of these numbers. View Solution
DDD x, y are two positive numbers whose sum is 10. What is the possible greatest value of x^2 y? View Solution
DDD Find the point of inflection of f(x) = x^3 - 6x^2 + 28. DDD View Solution
DDD Determine the point of inflection of the graph of f(x) = 7x e^13x. View Solution
DDD If f(x) = ax^2 + bx + c, a ≠ 0, then which of the following is correct? View Solution
DDD f(x) = 9x in (0, ∞) has DDD View Solution
DDD For a real function y = f(x), which of the following holds true? DDD View Solution | {"url":"http://www.icoachmath.com/solvedexample/sampleworksheet.aspx?process=/__cstlqvxbefxexbgbmbxkhhgk&.html","timestamp":"2014-04-18T10:34:59Z","content_type":null,"content_length":"114005","record_id":"<urn:uuid:23153f56-0821-4f19-ab4a-7c02b5a4209d>","cc-path":"CC-MAIN-2014-15/segments/1398223210034.18/warc/CC-MAIN-20140423032010-00364-ip-10-147-4-33.ec2.internal.warc.gz"} |
Revamping the numeric classes
Bjorn Lisper lisper@it.kth.se
Thu, 8 Feb 2001 10:02:23 +0100 (MET)
>> It is quite similar in spirit to the concept of principal type in
>> Hindley-Milner type systems. An expression can have many types but
>> only one "best" (most general) type in that system.
>Now, I'm not any kind of expert on this, but isn't the most general
>HM type one that encompasses the others, and *not* one out of a set of
>ambigous (and mutually exclusive) types?
In a sense. You define a partial order on types by a < a' (a more general
than a') if there is a substitution s of type variables such that
a' = sa. The interesting property of HM type systems is that for each term t
and all type judgements t:a that can be derived, there is a type judgement
t:a' such that a' < a. a' is called the most general type of t.
What I suggested was to define a different relation between types, measuring
"relative liftedness". We can call it "<<". Now, if it is the case that for
all judgements t -> t':a in the type system I sketch, there is a judgement
t -> t'':a' where a' << a, the we can select the transformation to be
t -> t''. t'' will then have a "most general type" among the possible
transformed terms, but wrt << rather than <.
Ambiguity between types depends on the ordering between types that you
Björn Lisper | {"url":"http://www.haskell.org/pipermail/haskell/2001-February/006644.html","timestamp":"2014-04-17T12:35:47Z","content_type":null,"content_length":"3390","record_id":"<urn:uuid:f35f56d1-3a4c-40cb-8aae-faea1e43374a>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00462-ip-10-147-4-33.ec2.internal.warc.gz"} |
Simulation of pp-collision and Z boson production
For your procedure of producing the Z on shell. It is correct to only sample the u-PDF in my opinion. You automatically sample all possibilities at the same time here.
My guess is that when you find a suitable solution of x1 and x2. i.e. one where you get the z mass you can store these x1' values, then calculate the sum of,
u ubar @ x1'
d dbar @ x1'
s sbar @ x1'
c cbar @ x1'
b bbar @ x1'
If you want to make things more detailed etc. that is always possible. In event generators, I think the hard process is sampled first, then evolution back to the parton distribution function is done.
This way you don't have to veto lots and lots of processes which don't give you the right energy exchange to produce the Z {though you are sort of doing this by forcing Z on shell}.
But at this point I think you may need to consult publications and text books - my normal approach is to look here first,
or search online to try and find something useful. | {"url":"http://www.physicsforums.com/showthread.php?s=bfc00a1115007fb7d60cf2e17fde83e1&p=4602776","timestamp":"2014-04-18T10:41:02Z","content_type":null,"content_length":"61114","record_id":"<urn:uuid:c0202914-90be-496a-88d0-3929fdaf8907>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00570-ip-10-147-4-33.ec2.internal.warc.gz"} |
The Everett Interpretation
When one introduces hidden-variables or state reduction, certain kinds of physical quantities (the “preferred” ones) get to be value-definite - among them the observed quantities (quantities like
position, which are well-localized in space). Eschewing hidden-variables or state-reduction, still we have to pick out preferred quantities. How? And precisely which ones? This is the preferred basis
problem. The tightrope that must be walked (if we are to make sense of quantum mechanics without hidden-variables or state reduction) is to show first, how certain sorts of quantities get to be
preferred (the preferred basis problem), and second, how particular values get to be assigned to such quantities (the problem that going over to many worlds or - as has been suggested by Albert and
Loewer, in an approach which has received a lot of subsequent attention - going over to a many minds approach is supposed to solve).
The first is the problem that has been attacked by the physicists. They have made systematic progress with it: it is exactly the business of decoherence theory to extract “effective” equations of
motion, concerning those dynamical variables for which value-assignments can be made in a way which is stable over time, and without “interference effects” linking their different values. And indeed
it turns out that the variables arrived at in this way are well-localised in space. But decoherence theory does not solve the preferred-basis problem on its own. One question that remains is why,
even given that such-and-such a basis decoheres, should that be the basis that we see? My suggestion is that complex functional systems, capable of encoding records and processing information, can
only be constituted out of stable sequences of states - and stability, and indeed the possibility of reliably encoding records, is only possible with decohering sequences of states. And of course
anything like an observing system - computer, amoeba, or human - is going to have to be a complex functional system.
For an explanation of why complex adaptive systems should be composed of decohering variables (in the sense of the consistent histories approach) see my:
"Decoherence and Evolutionary Adaptation", Physics Letters A 184 (1994), p.1-5.
"Decoherence, Relative States, and Evolutionary Adaptation", Foundations of Physics, 23 (1993), 1553-1585.
For more formal properties of decohering variables, and specifically a proof that decoherence (in the sense of consistency) implies that value-definiteness as a relational construct is transitive (in
general it isn 't), see my:
"Relativism", in Perspectives on Quantum Reality, R. Clifton, ed., Kluwer, Dordrecht (1995), p.125-42.
Physicists today are largely agreed that an approximate, FAPP basis can be defined for its intrinsic utility in quantum mechanics: among the various patterns one can make out in the universal state,
the ones governed by effective equations, as defined in the decoherence basis, are the most important. But it may still be thought there is a problem of intelligibility: what does it mean to say
worlds divide, or are subject to branching? What does it mean to say there are other worlds at all, when ours alone appears real?, In what sense is our world even apparently privileged? But here
there are analogous and well-known - indeed ancient - problems in the philosophy of time. What does it mean to speak of time's passage? What does it mean to say "the now" is what is real? These and
other parallels are developed at length in my
"Time, Quantum Mechanics, and Decoherence", Synthese, 102, 235-66 (1995), which you can download here as a pdf file.
The other great bugbear of the Everett interpretation is the interpretation of probability. The fundamental difficulty, if one really tries to make do with pure quantum mechanics, is that there is no
univocal criterion of identity over time, not of persons and not of objects; or none that is locally coded into the formalism. Most philosophers of physics writing on this subject are sure this is
needed (physicists tend not to think about it): for how else are we to make sense of talk of what we will see? (We, the very same?) Or of what the apparatus, the very same, will record? But I think
the notion of personal identity already collapses in classical physics. Identity over time does not have to have the formal properties of identity.
For a systematic account of probability in the Everett interpretation see my:
"Time, Quantum Mechanics, and Probability", Synthese, 114 (1998), 405-44 (also available at http://xxxx.arXiv.org/abs/quant-ph/0111047). You can download it here as a pdf file.
The essential ideas of this paper are that the right attitude to have to the immenent prospect of branching is uncertainty; that physical characteristics of branches should dictate one's
expectations; and that an account of objective chance in terms of relative norms of branches is no worse off than any of its competitors. Relative frequencies of outcomes, on repeated trials, remain
as ever our guide to quantifying objective chance; but for well-known reasons (independent of the Everett interpretation) cannot be identified with them.
I still believe that argument is substantially correct - but I did not expect to find positive arguments as to why the relative norms of branches are what matters. Here Deutsch's argument of 1999
from decision theory came as a welcome surprise; Wallace's more detailed treatment is a revelation. It is something of a footnote to note (if the Everett approach is correct) that the key ideas are
enough to force the Born rule on purely operational assumptions. (The argument has the merit of applying to every school of foundations that shares these operational assumptions.) For the details,
see my
"Derivation of the Born Rule from Operational Assumptions", Proceedings of the Royal Society of London , A, 460, 1-18 (2004) (available at http://xxxx.arXiv.org/abs/quant-ph/0211138, but with a
trivial but mildly embarrassing error in one of the proofs). You can download it here as a pdf file.
What becomes clear is that probability in the Everett interpretation is not a fundamental concept - equivalently, that it only has meaning in the context of decoherence. Probabilistic events at the
sub-decoherence level are entirely a matter of (and only have meaning insofar as) they are correlated with decohering states. That in turn raises a question mark over derivations of the Born rule
(including mine, the Deutsch-Wallace theory, and Gleason's) which assume probability should make sense (and be well-defined) for arbitrary choices of basis. But in fact it need not, as my derivation
of the Born rule for a basis fixed once and for all shows. It is contained in my coming article
"What is Probability?", in Quo Vadis Quantum Mechanics, Elitzur, S. Dolev, and N. Kolenda, eds., Springer (2005), which you can by download here as a pdf file.
In this article the lattice theoretic, formal properties of the basis required can be motivated directly by the approximate nature of decoherence. There too I show how one can derive Lewis's
"principal principle", along lines first sketched out by Wallace. Wallace's work has informed most of my recent thinking about many-worlds: you can find his papers on the Los Alamos archives, in
print in Studies in the History and Philosophy of Modern Physics, and on his website
For difficulties with "one-world" interpretations of the histories formalism see also my:
"Space-Time and Probability", in Chance in Physics: Foundations and Perspectives, J. Bricmont, D. Dürr, M.C. Galavotti, G. Ghirardi, F. Petruccione, N. Zanghi (eds.), Springer-Verlag, (2001),which
you can download here as a pdf file.
The interpretation of probability in the Everett interpretation has long been thought it's weakest link. On the contrary, it is one of the strongest points in its favour.
Copyright Simon Saunders 2001. Last updated: 8 October 2004. | {"url":"http://users.ox.ac.uk/~lina0174/Everett.html","timestamp":"2014-04-18T13:18:07Z","content_type":null,"content_length":"8946","record_id":"<urn:uuid:a8345c43-ba76-4346-a899-c04f037af6a5>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00256-ip-10-147-4-33.ec2.internal.warc.gz"} |
Posts by
Total # Posts: 171
Thank you so much
The sales goal for your store this week is $22,682. The sales goal for your store this week last year was $20,128. Your store has averaged 1775 transactions per week for the last four weeks. Assuming
the number of transactions is consistent, what is the average basket size (tr...
A baby whale gets lost from his mother while swimming through a large underwater canyon. Frantically the baby whale yells for his mommy. 1.5 seconds later, the whale hears his yell's ECHO from the
canyon wall. How far is it to the canyon wall? The speed of sound in water i...
I need help (Physics)
A 28 kg ball initially at rest rolls down a 159 m hill. When the ball reaches the bottom it is traveling at 31.3 m/s. How much energy is dissipated by friction on the ball?
For what value of a, would the system have an infinite number of solutions? 2x-y=5 8x-47=2a A) 2 B) 4 C)5 D)10 E)20
THANK STEVE i HAVE THE ASNWER
If A point K is the reflection of L (2,5) IN THE Y AXIS WHAT IS THE LENGTH OF KL
Oakwood Plowing company purchased two new plows. In 170 days they must make a payment of $24,330.00 to pay for them. As of today they have $23,600 what rate of interest will be needed.
Three moles of an ideal monatomic gas are at a temperature of 396 K. Then 2438 J of heat is added to the gas, and 897 J of work is done on it. What is the final temperature of the gas?
A container holds 1.3 mol of gas. The total average kinetic energy of the gas molecules in the container is equal to the kinetic energy of a 6.6x10-3 kg bullet with a speed of 670 m/s. What is the
Kelvin temperature of the gas?
Imagine that you collected your data above, threw away the gel, and re-ran PCR again on the same samples, but using a different set of primers. How will the 2nd gel differ from the first since you're
using a different set of primers?
(a) Transform the expression (x − a)^2 + y^2 = a^2 into polar coordinates. (b) Sketch the region R bounded by the curve given in part (a). (c) Use a double integral in polar coordinates to find the
area of the region R.
The drawing shows a 25.1-kg crate that is initially at rest. Note that the view is one looking down on the top of the crate. Two forces, 1 and 2, are applied to the crate, and it begins to move. The
coefficient of kinetic friction between the crate and the floor is μk = 0...
15. To travel a fixed distance, the number of gallons needed is inversely proportional to the miles per gallon rating P of the car that gets 42 miles per gallon (mpg) needs 33 gallons to travel the
distance. a. Find an equation of variation N= b. A car that gets 77 mpg needs _...
Two cars, A and B, are traveling in the same direction, although car A is 204 m behind car B. The speed of A is 22.9 m/s, and the speed of B is 18.6 m/s. How much time does it take for A to catch B?
A rifle that has been "sighted in" for a 94.6-meter target. If the muzzle speed of the bullet is v0 = 429 m/s, what are the two possible angles è1 and è2 between the rifle barrel and the horizontal
such that the bullet will hit the target? One of these ...
thank you
A truck rolls down a hill subject to acceleration due to gravity and resistance (including air resistance, rolling friction, etc) and the distance si (metres) travelled after ti seconds is observed.
Classical mechanics predicts that the distance travelled by the truck should b...
For every prime p consider all polynomials f(x) with integer coefficients from 1 to p and degree at most p−1, such that for all integers x the number f(2x)−f(x) is divisible by p. Find the sum of all
primes p<1000 such that the number of such polynomials is stri...
MATH hard problem...HELLPPPPPP
Let S={1,2,3, 11} and T1,T2 ,TN be distinct subsets of S such that |Ti∩Tj|≤2 for all values i≠j. What is the maximum possible value of N? clue: The empty set is a subset of every set. Thanks
MATH Help please.....
Let S={1,2,3, 11} and T1,T2 ,TN be distinct subsets of S such that |Ti∩Tj|≤2 for all values i≠j. What is the maximum possible value of N? (The empty set is a subset of every set.)
i input your formula and false
Physics..Elena or anybody please help
Physics..Elena or anybody please help
I(mass=80 kg) sit down in the center of a trampoline and the surface sinks down by a distance of 10 cm when I reach equilibrium. How far above the ground in m must the trampoline be placed so that if
I jump onto the trampoline from a height of 3 m above the surface of the tram...
Thank you Steve.
Having a problem writing an expanded number in notation in descending order. Ex. 92,563,174. I know the placements and the number but have a problem when it comes to write it. Can you please help. I
would appreciate an example so much.
Elements of Calculus
I cant seem to figure this one out, please help. A company is manufacturing kayaks and can sell all that it manufactures. The revenue (in dollars) is given by R=750-(X^2/30) where the production
output in 1 day is x kayaks. If production is increasing at 3 kayaks per day when ...
In a solar water heater, energy from the Sun is gathered by water that circulates through tubes in a rooftop collector. The solar radiation enters the collector through a transparent cover and warms
the water in the tubes; this water is pumped into a holding tank. Assume that ...
Given a study of 9804 overweight or obese subjects with preexisting cardiovascular disease and/or type 2 diabetes. Subjects randomly assigned to subitramine (4906 subjects) or a placebo (4898
subjects) in a double-blind fashion. Primary outcome was observed in 561 subjects in ...
75% of teenagers own cell phones and ofthose who own cell phones, 87% use text messaging. 1. What % of teens own cell phones AND text? 2. Among those who own cell phones and text, 15% send more than
200 texts a day, or more than 6,000 texts a month. What % of all teens own a c...
A ray of light is incident at an angle of 20degrees to the normal on one face of an equilateral prism made in glass of refractive index 1.523. Find the total deviation produced.
Why did you need to know the density of the bleach solution? Why didn't you measure the density of h2o2 solution as well? Stoichiometry lab problem
To move a large crate across a rough floor, you push on it with a force F at an angle of 21° below the horizontal, as shown in the figure. Find the force necessary to start the crate moving, given
that the mass of the crate is m = 29 kg and the coefficient of static fricti...
Thank you very much Elena for that and also for promptly answering my question on a timely manner!!!
You are pulling your little sister on her sled across an icy (frictionless) surface. When you exert a constant horizontal force of 114 N, the sled has an acceleration of 2.3 m/s2 If the sled has a
mass of 7.6 kg, what is the mass of your little sister? I don't need the ans...
Thank you!
A light of ray is incident at an angle of 58degrees on the plane surface of a block of glass of refractive index 1.60. Some light is reflected on the other side of the normal at the same angle as the
angle of incidence. Find: a.the angle between the light reflected from the su...
physics/light reflection
A light of ray is incident at an angle of 58degrees on the plane surface of a block of glass of refractive index 1.60. Some light is reflected on the other side of the normal at the same angle as the
angle of incidence. Find: a.the angle between the light reflected from the su...
=12+24*6*2-17 =283
thank you!
The following four lenses are placed together in close contact. Find the focal length of the combination. Lens 1- F'= +200mm Lens 2- F'= -125mm Lens 3- F'= -400mm Lens 4- F'= +142.9mm
You are riding on a jet ski directed at an angle upstream on a river flowing with a speed of 2.8 m/s. If your velocity relative to the ground is 8.9 m/s at an angle of 26.0° upstream, what is the
speed of the jet ski relative to the water? (Note: Angles are measured relati...
I ran this an an independent samples t-test. It is a t rest according to the professor, just want to make sure I have the right one. A researcher wanted to answer the following question: What is the
difference in students' computer anxiety based on whether or not they own ...
1. A bullet of 0.0500 kg is fired into a block of wood. Knowing that the bullet left the gun with a muzzle velocity of 350. m/s, and the bullet penetrates .15 m into the block of wood, determine: a)
The average force required to stop the bullet. b) The impulse exerted by the w...
A researcher wanted to answer the following question: What is the difference in students' computer anxiety based on whether or not they own computers? The researcher surveyed 92 undergraduate
education students via an online survey. In the survey, the researcher asked a ye...
I bemieve the t test is paired , want to make usre beofre I run the stats. A researcher wanted to answer the following question: What is the difference in students' computer anxiety based on whether
or not they own computers? The researcher surveyed 92 undergraduate educat...
The sales goal for your store this week is $22,682. The sales goal for your store this week last year was $20,128. Your store has averaged 1775 transactions per week for the last four weeks. Assuming
the number of transactions is consistent, what is the average basket size (tr...
A proton that has a mass m and is moving at 250 m/s in the + direction undergoes a head-on elastic collision with a stationary oxygen nucleus of mass 16m. Find the velocities of the proton and the
oxygen nucleus after the collision
A proton that has a mass m and is moving at 250 m/s in the + direction undergoes a head-on elastic collision with a stationary oxygen nucleus of mass 16m. Find the velocities of the proton and the
carbon nucleus after the collision
A 2.0-kg ball moving at 10 m/s makes an off-center collision with a 3.0-kg ball that is initially at rest. After the collision, the 2.0-kg ball is deflected at an angle of 30° from its original
direction of motion and the 3.0-kg ball is moving at 4.0 m/s. Find the speed of...
A 2.0-kg ball moving at 10 m/s makes an off-center collision with a 3.0-kg ball that is initially at rest. After the collision, the 2.0-kg ball is deflected at an angle of 30° from its original
direction of motion and the 3.0-kg ball is moving at 4.0 m/s. Find the speed of...
Allegra's favorite ride at the Barrel-O-Fun Amusement Park is the Flying Umbrella, which is lifted by a hydraulic jack. The operator activates the ride by applying a forcce of 72 N to a 3.0-cm-wide
cylindrical piston, which holds the 20000. N ride off the ground. What is t...
A 5450-m^3 blimp circles Fenway Park duing the World Series, suspended in the earth's 1.21-kg/m^3 atmosphere. The density of the helium in the blimp is 0.178 kg/m^3. A) What is the buoyant force that
suspends the blimp in the air? B) How does this buotant force compare to ...
how many grams of CO are needed to react with an excess of Fe2O3 to produce 209.7gFe? Fe2O3(s) + 3CO(g) => 3CO2(g) + 2Fe(s)
sorry. time is in minutes not seconds
Suppose that you place exactly 100 bacteria into a flask containing nutrients for the bacteria and that you find the following data at 37 °C: TIme (s) number of bacteria 0 100 19 200 38 400 57 800 76
1600 what is the rate order? What is rate constant? how many bacteria wil...
A certain reaction has an activation energy of 74.38 kJ/mol. At what Kelvin temperature will the reaction proceed 7.00 times faster than it did at 313 K?
A certain reaction has an activation energy of 74.38 kJ/mol. At what Kelvin temperature will the reaction proceed 7.00 times faster than it did at 313 K?
Someone please answer my question below in AP CHEMISTRY.
A)In a chemical reaction two gases combine to form a solid. What do you expect for the sign of ΔS? B) For which of the following processes does the entropy of the system increase? (Select all that
apply.) -> alignment of iron filings in a magnetic field -> the melti...
Calculate the solubility of LaF3 in grams per liter in the following solutions. (Ksp = 2. 10-19.) a) pure water Ans: .00182g/L b) 0.037 M KF solution c) 0.055 M LaCl3 solution NEED b&c PLEASE HELP
SOMEONE PLEASE EXPLAIN AND ANSWER THIS QUESTION : Will Co(OH)2 precipitate from solution if the pH of a 0.034 M solution of Co(NO3)2 is adjusted to 9.45? (Ksp of Co(OH)2 is 1.3 10-15) Support your
answer by calculating the ion product (Q) of the Co(OH)2 solution.
Calculate the solubility of Mn(OH)2 in grams per liter when buffered at each of the following. a) pH 7.4 b) pH 9.2 c) pH 11.5 ALL IN GRAMS PER LITER. PLEASE HELP ME AND EXPLAIN
AP Chemistry
A buffer, consisting of H2PO4− and HPO42−, helps control the pH of physiological fluids. Many carbonated soft drinks also use this buffer system. What is the pH of a soft drink in which the major
buffer ingredients are 7.20 g of NaH2PO4 and 4.90 g of Na2HPO4 per 35...
find max, min and saddle points of the give function f(x,y)=sin(x)+sin(y)+sin(x+y) 0<=x<=pi/4 0<=y<=pi/4 i have that dz/dx=cos(x)+cos(x+y) dz/dy=cos(y)+cos(x+y) and i set them equal to zero but im
kinda confused on how to really solve that. i mean i got an answer b...
i asked another question in my post below pleaseeeeeeeee answer it.. THANX!!!!!!!
Write the formula for the following compound, being sure to use brackets to indicate the coordination sphere. A) potassium tetrabromo(ortho-phenanthroline)- cobaltate(III)
thank u and next time i will show some work
THANX. but did u guess 8.7 or did u calculate it? if so could u show howw???
it says the titration of 0.145g of a weak acid with 0.100M NaOH as the titrant
The following acid-base indicators are available to follow the titration. Which of them would be most appropriate for signaling the endpoint of the titration? EXPLAIN ------- COLOR CHANGE ------
INDICATOR <-> Acid form <-> Base Form <-> pH Transition Interva...
The following acid-base indicators are available to follow the titration. Which of them would be most appropriate for signaling the endpoint of the titration? EXPLAIN ------- COLOR CHANGE ------
INDICATOR <-> Acid form <-> Base Form <-> pH Transition Interva...
AP Chemistry
SOMEONE PLEASEEEEEEEEE ANSWER MY PROBLEM IN THE POST BELOW!!!!!!!!!!!!!!!!!!!!!!!!!!!
IS IT 0.1167 M ?????
1) Calculate the molarity of a solution of sodium hydroxide, NaOH,if 23.64 mL of this solution is needed to neutralize 0.5632g of potassium hydrogen phthalate. 2) It is found that 24.68 mL of 0.1165M
NaOH is needed to titrate 0.2931 g of an unknown acid to the phenolphthalein ...
would the units be grams????
Calculate the equivalent mass of each of the following acids. a) HC2H3O2 b) KHCO3 c) H2SO3
AP CHEM5
answer my question beloww!!
potassium tetrabromo(ortho-phenanthroline)- cobaltate(III)
COuld u please answer this Ineed the formula for bis(bipyridyl)cadmium(II) chloride
formula for bipyridyl
Math Help Please
Would someone please be kind enough to explain steps for this one. Thank you. If m and n are positive integers and m is 250% of n, what percent of m is 2n?
A) At 800 K the equilibrium constant for I2(g) <=> 2 I(g) is Kc = 3.1 10-5. If an equilibrium mixture in a 10.0-L vessel contains 3.44*10-2 g of I(g), how many grams of I2 are in the mixture? answer
is .060g B)For 2 SO2(g) + O2(g)<=> 2 SO3(g), Kp = 3.0*104 at 700 K...
You select 8 cards randomly from a deck of 52 cards. What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)
find the integral of e^x/[(e^x-3)(e^x+4)] dx
You have 300 g of coffee at 55 degrees celcius. Coffee has the same specific heat as water. How much 10 degrees celcius water do you need to add in order to reduce the coffee's temperature to a more
bearable 49 degrees celcius?
You have 300 g of coffee at 55 degrees celcius. Coffee has the same specific heat as water. How much 10 degrees celcius water do you need to add in order to reduce the coffee's temperature to a more
bearable 49 degrees celcius?
You have arrived at a new planet and put your starship into a circular orbit at a height above the surface that is equal to two times the radius of the planet. Your speed is 4300 m/s and it takes 7
hours and 18 minutes to complete an orbit. a. What is the radius of the planet?...
A perfect minor wholetone is a frequency rtio of 10:9. A perfect major wholetone is a frequency ratio of 9:8. Are these noticeably different from an equal temper wholetone? (200 cents)
sig figs
70.74074074 ^ 1/4 = a 2.900129566 = a Now I have to round to 3 significant digits. Is it 2.90 or 2.9001?
Whitney invested $19,000, part at 5% and part at 7%. If the total interest at the end of the year is $1,110.,how much did she invest at 5%. I know the answer is $11,000. I would like to know how to
actually solve the equation.
I love chocolate and coffee. I begin by making one cup of hot chocolate. I drink half of my cup and then I fill the cup with coffee. I stir the new mixture and drink half of the cup and then fill the
cup again with coffee. I continue this pattern until I have consumed two full...
Pages: 1 | 2 | Next>> | {"url":"http://www.jiskha.com/members/profile/posts.cgi?name=help+please","timestamp":"2014-04-18T07:51:07Z","content_type":null,"content_length":"29891","record_id":"<urn:uuid:90f2cada-20f0-4d02-b884-46665bb7ec20>","cc-path":"CC-MAIN-2014-15/segments/1397609532573.41/warc/CC-MAIN-20140416005212-00351-ip-10-147-4-33.ec2.internal.warc.gz"} |
Moment of inertia equation
Also, when I tried to accomplish this on my own, I attempted to think of it not as a union of concentric rings, but as a union of pie-piece-shaped wedges. This didn't work, but it did get me the
moment of inertia equation for a ring.
Sorry about the double integral. Fortunately it can be done without it.
For a ring (circle) the moment of inertia is really simple. Since all the mass is at a distance R from the center, r in the integral is constant. So you can bring it outside of the integral and the
integral over dm simply gives the mass.
[tex]I_{ring}=\int_{C} r^2 dm = R^2 \int_{C}dm=MR^2[/tex]
where C is the circle you are integrating over.
If you consider the uniform disc as a collection of polar 'rectangles', you'll end up with a double integral.
I think the only way to get a single integral is to consider the disc as a collection of concentric rings with width dr. Then express dm in terms of r:
[tex]dm = (\frac{M}{\pi R^2})(2\pi rdr)=\frac{2M}{R^2}rdr[/itex]
Now that you know dm in terms of dr, can you set up the integral and get the moment of inertia?
BTW: This is identical to the method in dexter's second post and to a double integral after having integrated wrt theta. | {"url":"http://www.physicsforums.com/showthread.php?t=59068","timestamp":"2014-04-16T10:38:32Z","content_type":null,"content_length":"55265","record_id":"<urn:uuid:79d71213-dfba-4c77-aa46-52c07d1d26a2>","cc-path":"CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00354-ip-10-147-4-33.ec2.internal.warc.gz"} |
x.Hm="left">Consider a discrete-time causal LTI system defined by the following difference equation:
y[n] + a1y[n - 1] + a2y[n - 2] = b1x[n - 1] + b2x[n - 2]:
In particular, consider two systems parameterized as follows:
System A: a1 = -1.6; a2 = 0.6; b1 = 1; b2 = -0.8
System B: a1 = 1.6; a2 = -0.6; b1 = 1; b2 = -0.8
1. Signal processing in the time domain.
Consider the following input signals:
x1[n] = cos(n) u[n]; x2[n] = r[n]u[n];
where u[n] is the unit step function and r[n] is a sequence of independent random numbers
uniformly distributed in the interval [0; 1] (hint: Use the rand function to generate r[n]).
(a) Write a program to compute the impulse response numerically for each of the two systems
and in each case plot h[n] (0 <= n <= 50).
(b) Write a program that uses the conv function to compute and plot the output signals
y1[n] and y2[n] (0 <=n <= 50) for each of the two systems.
(c) Repeat 1(b) using the filter function instead of the conv function. Compare the results
with those of 1(b).
2. Signal processing in the frequency domain.
(a) Write a program that uses the freqz function to compute the frequency response for each
of the two systems. For each system, plot the magnitude and phase of the frequency
(b) For each system, determine whether the system is lowpass, highpass, bandpass, or band-
stop. For each system, determine a frequency Wp in the passband such that the gain of
the system is approximately 90% of the maximum gain and a frequency Ws in the stop-
band such that the gain of the system is approximately 10% more than the minimum
(c) For system A, de ne the following two signals:
xp[n] = sin Wpn; xs[n] = sin Wsn:
Calculate and plot the corresponding output signals yp[n] and ys[n] using the filter func-
tion. Then calculate and plot the output y[n] when the input x[n] = xp[n] + xs[n] is
applied to the system. Discuss your results.
(d) Repeat 2(c) for system B.
x.Hm0Ôx.Hmú x.Hm | {"url":"http://www.chegg.com/homework-help/questions-and-answers/xhm-left-consider-discrete-time-causal-lti-system-defined-following-difference-equation-y--q840895","timestamp":"2014-04-17T16:39:35Z","content_type":null,"content_length":"23862","record_id":"<urn:uuid:d1819969-12e9-4bb0-841c-d8e5a1744505>","cc-path":"CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00100-ip-10-147-4-33.ec2.internal.warc.gz"} |
st: RE: Re: Bar labels in stacked bar chart
[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]
st: RE: Re: Bar labels in stacked bar chart
From "Nick Cox" <n.j.cox@durham.ac.uk>
To <statalist@hsphsun2.harvard.edu>
Subject st: RE: Re: Bar labels in stacked bar chart
Date Mon, 12 Apr 2004 18:17:20 +0100
Yes, you can do this, but not on the fly, so
far as I am aware.
The re-ordering you achieve with -graph bar- can be achieved
(only?) by generating indicator variables and then supplying
them in the desired order.
The analogous procedure needed for -catplot- is to provide
a variable giving the desired sort order, say by
. recode rep78 3=1 4=2 5=3 1=4 2=5, gen(Rep78)
(69 differences between rep78 and Rep78)
Then you need something like
. catplot bar rep78 foreign, percent(foreign) asyvars stack
oversubopts(sort(Rep78)) legend(order(3 4 5 1 2))
-oversubopts()- is an undocumented option. Also, make
sure that you have the latest public domain -catplot-, 1.1.2.
To put this in context, let me refer you to the original
Statalist posting (recombine this URL)
on 18 February 2003. Here it is, in part:
Thanks to Kit Baum, a new package -catplot-
has been posted on SSC. This is for plots
of categorical data in Stata 8, specifically
for bar or dot charts of the same showing
frequencies, or fractions, or percents.
(For Stata 7 or earlier there are other
user-written programs available in the same
territory, such as -fbar-, -tabhbar-, -vbar-.)
Those who have looked at Stata 8's new
graphics may well ask: Surely all that is very
well done in Stata 8, with -graph bar-, -graph
hbar- and -graph dot- offering a great range of
The answer is "Yes indeed", and that is
what I am building on, the aim being to add
a convenience command in one particular
I work a lot with students and others who want bar
charts of categorical data, for example, of counts
of categories from one-way, two-way or even three-way
tables from questionnaires and other survey data.
In addition, many of these users want to tell me
for some reason that it's very easy in Excel, so
I really want to be able to say to them that it's
also very easy in Stata.
How does Stata size up on this task?
1. -histogram- is optimised for histograms,
naturally. It can be used for this purpose by
invoking options like
, discrete xla(, valuelabel ang(45)) gap(50)
for a one-way table or
, discrete xla(, valuelabel ang(45)) gap(50)
by(myvar, rows(1))
for a two-way table. Typing this -- or issuing
the equivalent through a dialog -- is a
little more complicated than some Stata beginners
might expect for this task. In any case,
some problems then frequently arise:
a. it doesn't take much for value labels to become
unreadable or to require what I call giraffe graphics,
in which the graphic necessitates a great deal of neck
movement. (That's why I have "ang(45)" in the examples
b. The number of cells you can show easily and effectively
appears to be ~20, given that you will want value
labels shown to indicate the categories. Any long
value labels make this problem worse.
c. Representing a 3-way table seems impossible, except by
producing and then combining separate histograms.
2. -graph hbar- etc. is good _if_ the
frequencies come predefined as a variable, because
then you can just sum the frequencies. But
if you want Stata to do the counting for you,
this seems to require you to set up something
to count. In particular,
. graph hbar (count) rep78
doesn't give you the frequencies of the
categories of -rep78-. Roughly, we want -graph-
here to -contract-, not -collapse-.
The way to do it is to calculate something in
advance, as in
. gen freq = 1
. graph hbar (count) freq, over(rep78)
but arguably we shouldn't have to do that.
And as for percents, catching missings,
and working with -if- and -in-: it
really needs a program.
That is, -catplot- started out as the
simplest program I could devise for bar
charts of frequencies of categorical data --
given also that people do want two or more variables,
percent calculations, etc., etc.
Since birth, -catplot- has accumulated
extra features both because users reasonably
suggested them and because I found myself wanting
them. This creates a small worry for the author,
as the original intent was to keep it very simple.
So -oversubopts()- was kept undocumented partly
as an experiment to see how often it is needed,
although some smart users looked at the code and
discovered that it was there.
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Friedrich
> Huebler
> Sent: 12 April 2004 05:31
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Re: Bar labels in stacked bar chart
> Nick,
> Thank you, -catplot- is easier to use than -graph bar- because
> several steps can be skipped. Another advantage is that -catplot-
> works with numeric values and strings.
> However, with -graph bar yvars, over(varname) stack- it is possible
> to stack the bars in a specific order by varying the order in which
> the yvars are listed.
> . sysuse auto
> . tab rep78, gen(rep)
> . graph bar rep3 rep4 rep5 rep1 rep2, over(foreign) stack percent
> Can the same be accomplished with -catplot-?
> Thank you.
> Friedrich Huebler
> --- Nick Cox <n.j.cox@durham.ac.uk> wrote:
> > Another way to do it is (in total)
> >
> > . catplot bar rep78 for , percent(for) asyvars stack
> > blabel(bar, pos(center) format(%3.2f))
> >
> > where I've added a format control. Here -catplot- can be
> > installed from SSC.
> __________________________________
> Do you Yahoo!?
> Yahoo! Tax Center - File online by April 15th
> http://taxes.yahoo.com/filing.html
> *
> * For searches and help try:
> * http://www.stata.com/support/faqs/res/findit.html
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/ | {"url":"http://www.stata.com/statalist/archive/2004-04/msg00266.html","timestamp":"2014-04-18T10:50:13Z","content_type":null,"content_length":"11304","record_id":"<urn:uuid:096e088b-9531-4a17-8639-c9272e10d2f1>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00360-ip-10-147-4-33.ec2.internal.warc.gz"} |
Bayesian theories of conditioning in a changing world
Results 1 - 10 of 22
- Current Directions in Psychological Science , 2003
"... explaining many phenomena in learning. The mechanism of selective attention in learning is also well motivated by its ability to minimize proactive interference and enhance generalization,
thereby accelerating learning. Therefore, not only does the mechanism help explain behavioral phenomena, it mak ..."
Cited by 37 (9 self)
Add to MetaCart
explaining many phenomena in learning. The mechanism of selective attention in learning is also well motivated by its ability to minimize proactive interference and enhance generalization, thereby
accelerating learning. Therefore, not only does the mechanism help explain behavioral phenomena, it makes sense that it should have evolved (Kruschke & Hullinger, 2010). The phrase “learned selective
attention ” denotes three qualities. First, “attention ” means the amplification or attenuation of the processing of stimuli. Second, “selective” refers to differentially amplifying and/or
attenuating a subset of the components of the stimulus. This selectivity within a stimulus is different from attenuating or amplifying all aspects of a stimulus simultaneously (cf. Larrauri &
Schmajuk, 2008). Third, “learned ” denotes the idea that the allocation of selective processing is retained for future use. The allocation may be context sensitive, so that attention is allocated
differently in different contexts. There are many phenomena in human and animal learning that suggest the involvement of learned selective attention. The first part of this chapter briefly reviews
some of those phenomena. The emphasis of the chapter is not the empirical phenomena, however. Instead, the focus is on a collection of models that formally express theories of learned attention.
These models will be surveyed subsequently. Phenomena suggestive of selective attention in learning There are many phenomena in human and animal learning that suggest that learning involves
allocating attention to informative cues, while ignoring uninformative cues. The following subsections indicate the benefits of selective allocation of attention, and illustrate the benefits with
particular findings.
"... For over 200 years, philosophers and mathematicians have been using probability theory to describe human cognition. While the theory of probabilities was first developed as a means of analyzing
games of chance, it quickly took on a larger and deeper significance as a formal account of how rational a ..."
Cited by 23 (1 self)
Add to MetaCart
For over 200 years, philosophers and mathematicians have been using probability theory to describe human cognition. While the theory of probabilities was first developed as a means of analyzing games
of chance, it quickly took on a larger and deeper significance as a formal account of how rational agents should reason in situations of uncertainty
- Learning & Behavior , 2008
"... Traditional associationist models represent an organism’s knowledge state by a single strength of association on each associative link. Bayesian models instead represent knowledge by a
distribution of graded degrees of belief over a range of candidate hypotheses. Many traditional associationist mode ..."
Cited by 18 (7 self)
Add to MetaCart
Traditional associationist models represent an organism’s knowledge state by a single strength of association on each associative link. Bayesian models instead represent knowledge by a distribution
of graded degrees of belief over a range of candidate hypotheses. Many traditional associationist models assume that the learner is passive, adjusting strengths of association only in reaction to
stimuli delivered by the environment. Bayesian models, on the other hand, can describe how the learner should actively probe the environment to learn optimally. The first part of this article reviews
two Bayesian accounts of backward blocking, a phenomenon that is challenging for many traditional theories. The broad Bayesian framework, in which these models reside, is also selectively reviewed.
The second part focuses on two formalizations of optimal active learning: maximizing either the expected information gain or the probability gain. New analyses of optimal active learning by a Kalman
filter and by a noisy-logic gate show that these two Bayesian models make different predictions for some environments. The Kalman filter predictions are disconfirmed in at least one case. Bayesian
formalizations of learning are a revolutionary advance over traditional approaches. Bayesian models assume that the learner maintains multiple candidate hypotheses with differing degrees of belief,
unlike traditional
, 2007
"... Bayesian treatments of animal conditioning start from a generative model that specifies precisely a set of assumptions about the structure of the learning task. Optimal rules for learning are
direct mathematical consequences of these assumptions. In terms of Marr’s (1982) levels of analyses, the mai ..."
Cited by 4 (2 self)
Add to MetaCart
Bayesian treatments of animal conditioning start from a generative model that specifies precisely a set of assumptions about the structure of the learning task. Optimal rules for learning are direct
mathematical consequences of these assumptions. In terms of Marr’s (1982) levels of analyses, the main task at the computational level
- ADAPTIVE BEHAVIOR 2007; 15; 73 , 2007
"... ..."
- Cognitive Science Society , 2009
"... Inductive inferences about objects, properties, categories, relations, and labels have been studied for many years but there are few attempts to chart the range of inductive problems that humans
are able to solve. We present a taxonomy that includes more than thirty inductive problems. The taxonomy ..."
Cited by 3 (1 self)
Add to MetaCart
Inductive inferences about objects, properties, categories, relations, and labels have been studied for many years but there are few attempts to chart the range of inductive problems that humans are
able to solve. We present a taxonomy that includes more than thirty inductive problems. The taxonomy helps to clarify the relationships between familiar problems such as identification, stimulus
generalization, and categorization, and introduces several novel problems including property identification and object discovery.
"... Contrast discrimination functions for simple gratings famously look like a dipper. Discrimination thresholds are lower than detection thresholds for moderate pedestal contrasts, and the rate of
growth of thresholds as the pedestal contrast gets larger typically lies between the values implied by two ..."
Cited by 1 (0 self)
Add to MetaCart
Contrast discrimination functions for simple gratings famously look like a dipper. Discrimination thresholds are lower than detection thresholds for moderate pedestal contrasts, and the rate of
growth of thresholds as the pedestal contrast gets larger typically lies between the values implied by two popular treatments of noise. Here, we suggest a new normative treatment of the dipper,
showing how it emerges from Bayesian inference based on the responses of a population of orientation-tuned units. Our central assumption concerns the noise corrupting the outputs of these units as a
function of the contrast: We suggest that it has the shape of a hinge. We show the match to the psychophysical data and discuss the neurobiological and statistical rationales for this form of noise.
Finally, we relate our model to other major accounts of contrast discrimination.
"... This paper describes a unifying framework for five highly influential but disparate theories of natural learning and behavioral action selection. These theories are normally considered
independently, with their own experimental procedures and results. The framework presented builds on a structure of ..."
Add to MetaCart
This paper describes a unifying framework for five highly influential but disparate theories of natural learning and behavioral action selection. These theories are normally considered independently,
with their own experimental procedures and results. The framework presented builds on a structure of connection types, propagation rules and learning rules, which are used in combination to integrate
results from each theory into a whole. These connection types and rules form the Action Selection Calculus. The Calculus will be used to discuss the areas of genuine difference between the factor
theories and to identify areas where there is overlap and where apparently disparate findings have a common source. The discussion is illustrated with exemplar experimental procedures. The paper
focuses on predictive or anticipatory properties inherent in these action selection and learning theories, and uses the Dynamic Expectancy Model and its computer implementation SRS/E as a mechanism
to conduct this discussion.
"... What is the value of an action that has never been tried before? One way to frame this question is as an inductive problem: how can I generalize my previous experience with one set of actions to
a novel action? We show how hierarchical Bayesian inference can be used to solve this problem, and descri ..."
Add to MetaCart
What is the value of an action that has never been tried before? One way to frame this question is as an inductive problem: how can I generalize my previous experience with one set of actions to a
novel action? We show how hierarchical Bayesian inference can be used to solve this problem, and describe an equivalence between the Bayesian model and temporal difference learning algorithms that
have been proposed as models of human reinforcement learning. In two experiments we test several predictions of this model, providing behavioral evidence that humans learn and exploit structured
inductive knowledge to make predictions about novel actions. We suggest a new interpretation of dopaminergic responses to novelty in light of this model. Keywords: reinforcement learning, Bayesian
inference, exploration, exploitation
"... To explore human deviations from Bayes ’ rule in numerically explicit problems, prior and likelihood probabilities or frequencies are manipulated and their effects on posterior probabilities or
surprisals are measured. Results show that people use both priors and likelihoods in Bayesian directions, ..."
Add to MetaCart
To explore human deviations from Bayes ’ rule in numerically explicit problems, prior and likelihood probabilities or frequencies are manipulated and their effects on posterior probabilities or
surprisals are measured. Results show that people use both priors and likelihoods in Bayesian directions, but the effect of likelihood information is stronger than that of prior information. Use of
frequency information and surprisal measures increase deviations from Bayesian predictions. There is evidence that people do compute something like the standardizing marginal data term when asked for
probability estimates, but not when asked for surprisal ratings. | {"url":"http://citeseerx.ist.psu.edu/showciting?cid=4280519","timestamp":"2014-04-18T13:47:55Z","content_type":null,"content_length":"36102","record_id":"<urn:uuid:94e2e4b5-59b1-47ae-9642-70b93404d398>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00496-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
Hey this is where I am... problem set 2 (1) My thought was to call a function that determined the length of the tuple -- used that information to create an empty list that would than dump the data
from the tuple into the list. Call each element in the list and apply their corresponding powers. I'm thinking I need some sort of while or for statement that takes the tuple length and creates the
powers. Am I on the right track? I know I could make this super simple but I assumed the point was create a polynomial function that could have a varied length... Sorry about my math vernacular.
• one year ago
• one year ago
Best Response
You've already chosen the best response.
You're on the right track but you're also making it a bit more complicated than it should be. "For" is a good direction and use the indexes to access tuple elements. Applying powers and
accumulating the results shouldnt be hard then.
Best Response
You've already chosen the best response.
for i in range(len(tuple)): list[i] = tuple[i] will give you a list, but I think the only advantage here is that you can change the list values directly. there is also a one line version list =
[element for i in range(len(tuple))]
Best Response
You've already chosen the best response.
On the third problem do you want to embed the function you created in the first problem?
Best Response
You've already chosen the best response.
Ok i'm still struggling with this code -- I think it's basically because I'm not writing the functions correctly. But I can't seem to add or change the list via call the locationn in the list.
while guessedValue == k: print 'got here' print rangeBegin print unguessList unguessList = unguessList.insert(rangeBegin,guessedValue) print unguessList del unguessList[rangeBegin:rangeBegin] if
guessedValue == k: guessCorrect = 1 else: guessCorrect = 0 All I want is for list to be checked and if it matches remove the '*" and add the called letter. There seems to be no embedded function
that does this...
Best Response
You've already chosen the best response.
You don't need to do this: for i in range(len(tuple)): list[i] = tuple[i] use list = tuple [:] (clonning) You're using tuples, use them to simplify your task, take one for the letters of the
word, another one with the wrong guess, and another with the good guess, using that tuples you can make a cleaner comparison; and I think that another definition about list_maker can be avoided,
but it's ok anyway.
Best Response
You've already chosen the best response.
if i do that won't that just insert the entire tuple into the spot [o] on the list?
Best Response
You've already chosen the best response.
no, doing this "list = tuple [:]" will be exactly the same, and if you do list == tuple, will say True. if you do, for list[i] = tuple[i]; will look the same, but list == tuple, will say False
Best Response
You've already chosen the best response.
so i want to use (ex. list_sample = tuple_sample[:]) this will create list that is identical (for all intents and purposes to a tuple)
Best Response
You've already chosen the best response.
that's what I'm saying, clonning, why don't you try it on your Python shell so can be more familiar.
Best Response
You've already chosen the best response.
will do this should make things a bit easier :) thanks!
Best Response
You've already chosen the best response.
you're welcome!
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/50ec4508e4b0d4a537ccb701","timestamp":"2014-04-20T16:09:24Z","content_type":null,"content_length":"56993","record_id":"<urn:uuid:31903b2e-4c35-4117-a1e1-7137200b4500>","cc-path":"CC-MAIN-2014-15/segments/1397609538824.34/warc/CC-MAIN-20140416005218-00192-ip-10-147-4-33.ec2.internal.warc.gz"} |
Quick Sort (3 Way Partition)
# choose pivot
swap a[n,rand(1,n)]
# 3-way partition
i = 1, k = 1, p = n
while i < p,
if a[i] < a[n], swap a[i++,k++]
else if a[i] == a[n], swap a[i,--p]
else i++
→ invariant: a[p..n] all equal
→ invariant: a[1..k-1] < a[p..n] < a[k..p-1]
# move pivots to center
m = min(p-k,n-p+1)
swap a[k..k+m-1,n-m+1..n]
# recursive sorts
sort a[1..k-1]
sort a[n-p+k+1,n]
• Not stable
• O(lg(n)) extra space
• O(n^2) time, but typically O(n·lg(n)) time
• Adaptive: O(n) time when O(1) unique keys
The 3-way partition variation of quick sort has slightly higher overhead compared to the standard 2-way partition version. Both have the same best, typical, and worst case time bounds, but this
version is highly adaptive in the very common case of sorting with few unique keys.
The 3-way partitioning code shown above is written for clarity rather than optimal performance; it exhibits poor locality, and performs more swaps than necessary. A more efficient but more elaborate
3-way partitioning method is given in Quicksort is Optimal by Robert Sedgewick and Jon Bentley.
When stability is not required, quick sort is the general purpose sorting algorithm of choice. Recently, a novel dual-pivot variant of 3-way partitioning has been discovered that beats the
single-pivot 3-way partitioning method both in theory and in practice.
• Click on
• Click directly on an animation image to start or restart it.
• Click on a problem size number to reset all animations.
• Black values are sorted.
• Gray values are unsorted.
• Dark gray values denote the current interval.
• A pair of red triangles mark k and p (see the code).
Algorithms in Java, Parts 1-4, 3rd edition by Robert Sedgewick. Addison Wesley, 2003.
Programming Pearls by Jon Bentley. Addison Wesley, 1986.
Quicksort is Optimal by Robert Sedgewick and Jon Bentley, Knuthfest, Stanford University, January, 2002.
Dual Pivot Quicksort: Code and Discussion.
Bubble-sort with Hungarian ("Csángó") folk dance YouTube video, created at Sapientia University, Tirgu Mures (Marosvásárhely), Romania.
Select-sort with Gypsy folk dance YouTube video, created at Sapientia University, Tirgu Mures (Marosvásárhely), Romania.
Sorting Out Sorting, Ronald M. Baecker with the assistance of David Sherman, 30 minute color sound film, Dynamic Graphics Project, University of Toronto, 1981. Excerpted and reprinted in SIGGRAPH
Video Review 7, 1983. Distributed by Morgan Kaufmann, Publishers. Excerpt. | {"url":"http://www.sorting-algorithms.com/quick-sort-3-way","timestamp":"2014-04-21T12:25:54Z","content_type":null,"content_length":"13868","record_id":"<urn:uuid:1326f2bf-302b-454f-963a-c87dde952e4a>","cc-path":"CC-MAIN-2014-15/segments/1397609539776.45/warc/CC-MAIN-20140416005219-00541-ip-10-147-4-33.ec2.internal.warc.gz"} |
MathGroup Archive: July 1998 [00298]
[Date Index] [Thread Index] [Author Index]
Re: 2-D Chebyshev Polynomial Regression
• To: mathgroup at smc.vnet.net
• Subject: [mg13321] Re: 2-D Chebyshev Polynomial Regression
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Mon, 20 Jul 1998 02:49:42 -0400
• Organization: University of Western Australia
• References: <6nske5$fc8@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com
Chris Farr wrote:
> Has anyone created a function in Mathematica to approximate a function
> of two variables using 2-D Chebyshev Polynomial Regression?
> That is, has someone created a Mathematica algorithm which takes as its
> input a real valued function f(x,y) defined on [a,b] X [c,d] and
> returns a Chebyshev polynomial approximation p(x,y)?
The following code may do what you want. It takes a real valued function
f[x,y] defined on [-1,1] X [-1,1] and returns a Chebyshev polynomial
approximation p[f][x,y].
Extending the one-dimensional Chebyshev formula to two dimensions in an
obvious fashion,
In[1]:= c[i_, j_, m_, n_][f_] := c[i, j, m, n][f] =
Chop[N[4/(n m) Sum[f[Cos[Pi (k-1/2)/m], Cos[Pi (l-1/2)/n]]*
Cos[Pi i (k-1/2)/m] Cos[Pi j (l-1/2)/n],{k,1,m},{l,1,n}]]]
and defining a short-hand notation for the Chebyshev T polynomials (with
the correction for the zeroth coefficient incorporated into the
polynomial itself to simplify the notation),
In[2]:= t[n_][x_]=ChebyshevT[n,x];
In[3]:= t[0][x_] = 1/2;
then the (m,n)-th order polynomial approximation for f reads
In[4]:= p[m_,n_][f_]:= p[m,n][f] =
Function[{x,y},Sum[c[k,l,m,n][f] t[k][x]
For example, with the (pure) function
In[5]:= f = Function[{x,y},(x y^2)/(x + y + 1)];
the (3,3)-approximation reads
In[6]:= p[3,3][f][x,y]
2 2 0.375 y x + 0.125
(2 y - 1) x + 0.125 x + 0.125 (2 x - 1) -
0.375 (2 x - 1) y - 0.375 y + 0.125 (2 x - 1) (2 y - 1) +
0.125 (2 y - 1) + 0.125
This code uses dynamic programming (i.e., g[x_]:= g[x] = ...) to store
intermediate computations and pure functions (so that computation for
new functions f is immediate).
The transformation from [a,b] X [c,d] to [-1,1] X [-1,1] is
x -> (2x-a-b)/(b-a)
y -> (2y-c-d)/(d-c)
with inverse
x -> ((b-a)x+a+b)/2
y -> ((d-c)y+c+d)/2
so only a simple modification of the above code is required to
generalize it to [a,b] X [c,d].
Note also that Mathematica includes a number of packages for related
computations including NumericalMath`Approximations` and
Hope that this helps.
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
God IS a weakly left-handed dice player | {"url":"http://forums.wolfram.com/mathgroup/archive/1998/Jul/msg00298.html","timestamp":"2014-04-17T06:51:04Z","content_type":null,"content_length":"37282","record_id":"<urn:uuid:e425a754-954f-40c9-87bd-3ab9b3cac85d>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00595-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
solve with full induction: sum_{k=1}^{n} k^2 = 1/6n(n + 1)(2n+1)
• one year ago
• one year ago
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/50cee6f7e4b0031882dca6c7","timestamp":"2014-04-21T07:40:02Z","content_type":null,"content_length":"46997","record_id":"<urn:uuid:3a45999a-cae6-42ea-99d4-337105de2426>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00331-ip-10-147-4-33.ec2.internal.warc.gz"} |
Sent To Explore A Large Spherical Planetoid With ... | Chegg.com
Sent to explore a large spherical planetoid with diameter of 3000 km. Assume no atmosphere and assume constant gravitational force is produced.
When landing craft's engines produce 4700 N of vertical thrust (lift force) you accelerate toward the surface with a magnitude of 1
A) What is the mass of the landing craft?
B) What is the average gravitational acceleration provided by planetoid?
C) What is approximate density of planetoid?
After exploring you blast off with a thrust of 10,000 N.
D) What is the minimum time required to travel a vertical distance of 2000 km? | {"url":"http://www.chegg.com/homework-help/questions-and-answers/sent-explore-large-spherical-planetoid-diameter-3000-km-assume-atmosphere-assume-constant--q950437","timestamp":"2014-04-18T00:36:31Z","content_type":null,"content_length":"22579","record_id":"<urn:uuid:75ebea83-ec21-4001-a103-a0e04e75fe99>","cc-path":"CC-MAIN-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00214-ip-10-147-4-33.ec2.internal.warc.gz"} |