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# Rotate around model's axes
This topic is 1341 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I want to rotate around model's y-axis, but I do not know how to do it. There is a same topic but I do not completely understand and it is closed. There is a function name D3DXMatrixRotationAxis in DX, but the problem is how to set the vector value, to rotate around, after loading a model.
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To rotate about the y-axis, you would use for D3DXVECTOR3( 0.0f, 1.0f, 0.0f ) for the vector. That's the unit vector representing the +ve y-axis.
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Phil_t is correct. Here is the MSDN reference for that method. Just to add one small extra note: You'll want to make sure that your model is in "model space", which means you haven't applied any transformations to it. The center should be very near (0,0,0) and it should be oriented towards your preferred standard orientation (I use [1,0,0] as my facing direction). Apply your rotation to get your rotation matrix, then apply your rotation matrix to your model.
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From what i gather, it's not the performing of the rotation that you have an issue with, but the actually finding of that axis of rotation. If you have a world transform already, you can extract the local X Y and Z vectors from it, and use those to rotate around. this will be different depending on your matrix layout, but you should be able to use the [] operator on the world matrix to get each axis individually(i think anyway, I have never used the d3d math library).
// psuedo code
// matrix layout
// x.x, x.y, x.z 0
// y.x, y.y, y.z, 0
// z.x, z.y, z.z, 0
// t.x, t.y, t.z, 1
Vec3 xAxis = model.worldTransform[0];
model.worldTransform *= xRot;
Vec3 yAxis = model.worldTransform[1];
mode.worldTransform *= yRot;
Edited by Burnt_Fyr
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# Exact sequence of abelian groups - Corolary 11.7 - Neukirch
The Proposition $$(11.6)$$ of Neukirch's Algebraic Number Theory states that if $$\mathcal O$$ is a dedekind domain with field of fractions $$K$$ and $$X$$ is a set of nonzero prime ideals of $$\mathcal O$$ with finite complement, there is a canonical exact sequence:
$$\begin{eqnarray*} 1 \rightarrow U(\mathcal O) \rightarrow U(\mathcal O(X)) \rightarrow \bigoplus_{\mathfrak p\not\in X}K^*/U(\mathcal O_{\mathfrak p}) \rightarrow \mathscr C\ell(\mathcal O) \rightarrow \mathscr C\ell(\mathcal O(X)) \rightarrow 1, \end{eqnarray*}$$
and that $$K^*/U(\mathcal O_{\mathfrak p})\cong \mathbb Z$$, for all prime $$\mathfrak p\not\in X$$.
Now let $$\mathcal O_K$$ be the ring of integers of $$K$$, let $$S$$ denote a finite set of prime ideals of $$\mathcal O_K$$, and let $$X$$ be the set of all prime ideals that do not belong to $$S$$. We put $$\mathcal O_K^S = \mathcal O_K (X)$$. The units of this ring are called the $$S$$-units.
(11.7) Corollary. For the group $$K^S = (\mathcal O_K^S)*$$ of $$S$$-units of $$K$$ there is an isomorphism $$K^S\cong \mu(K) \times \mathbb Z^{\# S+r+s-1}$$ where $$r$$ and $$s$$ are the number of real imersions and pairs of complex imersions of $$K$$.
The proof of Neukirch is as follows:
Proof: The torsion subgroup of $$K^S$$ is the group $$\mu(K)$$ of roots of unity in $$K$$. Since $$\mathscr C\ell(\mathcal O)$$ is finite, we obtain the following identities from the exact sequence above and from Dirichlet Units Theorem:
$$rank(K^S)=rank(\mathcal O_K^*)+rank(\bigoplus_{\mathfrak p\in S}\mathbb Z)=\#S+r+s-1$$.
I suppose the proof uses that result that relates exact sequences of $$\mathbb Z$$-modules and the ranks of these modules. But I only find:
$$rank~U(\mathcal O)-rank~U(\mathcal O(X))+rank~\mathbb Z^{\# S}-rank~\mathscr C\ell(\mathcal O)+rank~\mathscr C\ell(\mathcal O(X))=0$$.
Dirichlet Unit Theorem gives $$rank~U(\mathcal O)=r+s-1$$, but do I have some information about the ranks of the class groups?
$$\mathcal{C}\ell(\mathcal{O})$$ is finite and hence so is $$\mathcal{C}\ell(\mathcal{O}(X))$$, being a quotient of the former. A finite abelian group has rank zero.
• This is because every element is of torsion? I thought that linear independence was defined like that: a set $x_1,\dotsc,x_n$ is linearly independent over $\mathbb Z$ iff $a_1x_1+\cdots+a_n x_n=0\Rightarrow a_1x_1=\cdots=a_nx_n=0$. The right definition is $a_1=\cdots=a_n=0$? Sep 3, 2021 at 13:59
• @Lorenzo yes, the second definition is correct one. I personally think that the best way to define the rank of an abelian group $A$ is the dimension of $\Bbb Q \otimes_{\Bbb Z} A$ Sep 3, 2021 at 14:37
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# Per-page shared counter
I’m trying to number some objects on a per-page basis with a shared counter. The following example is close to minimal.
\documentclass{article}
\usepackage{zref-perpage}
\newcommand*{\tablecaption}[1]{%
\setlength{\belowcaptionskip}{\abovecaptionskip}%
\setlength{\abovecaptionskip}{0pt}%
\caption{#1}%
}
\newcounter{maincounter}
\newtheorem{theorem}{Theorem}
\newtheorem{proposition}[theorem]{Proposition}
\makeatletter
\let\c@equation\c@maincounter
\let\c@figure\c@maincounter
\let\c@table\c@maincounter
\let\c@theorem\c@maincounter
\makeatother
\zmakeperpage{maincounter}
%\zmakeperpage{equation}
%\zmakeperpage{figure}
%\zmakeperpage{table}
%\zmakeperpage{theorem}
\renewcommand*{\themaincounter}{\arabic{zpage}.\arabic{maincounter}}
\renewcommand*{\theequation}{\themaincounter}
\renewcommand*{\thefigure}{\themaincounter}
\renewcommand*{\thetable}{\themaincounter}
\renewcommand*{\thetheorem}{\themaincounter}
\begin{document}
%
\begin{theorem}
Blah.
\end{theorem}
%
\begin{table}[h]
\centering
\tablecaption{A table}
\begin{tabular}{l | l}
1 & 2 \\
\hline
3 & 4
\end{tabular}
\end{table}
%
$$a = b$$
%
\begin{figure}[b]
\centering
\rule{3cm}{2cm}
\caption{A black rectangle}
\end{figure}
%
\begin{proposition}
Blah.
\end{proposition}
%
\newpage
%
$$c = d$$
%
\begin{table}[t]
\centering
\tablecaption{Another table}
\begin{tabular}{l | l}
a & b \\
\hline
c & d
\end{tabular}
\end{table}
%
\begin{theorem}
Blah.
$$e = f$$
\end{theorem}
%
\end{document}
The problem is that the counter maincounter is not reset at each change of page and that the value of the counter zpage is always 0. If I uncomment the commented lines in the preamble, the per-page reset works and the counter zpage is incremented but the counters are not linked any longer.
As a bonus, I would like the different objects on each page to be numbered in their order of apparition (maybe something like the \MakeSorted command of the perpage package).
## Update
Thanks to David Carlisle’s comment, I was able to use the code related to the perpage option from the footmisc package and make it work with any counter. One relatively constraining aspect of this solution is the need to patch the commands that print the number of the corresponding objects: we have to surround them with some code which checks whether there is a change of page or not and consequently sets the associated counter. Such patching hence depends on the loaded packages and their possible redefinitions. (Here, I am working with amsmath and amsthm.)
Linking the counters is very easy, then: I just need to load the per-page machinery for one ‘main’ counter and identify the others to that one.
As for the number of the current page within the numbering of the different objects, I tried to make a label before incrementing the counter and printing it (through patches, as previously) in order to then be able to use \pageref.
However, there is something wrong with those patches: they break the mechanism of references; some incorrect values of the counter and the page are sometimes — or is it always? — read and written.
Here is the code with some testing inside the document. The incorrect references are indicated with the command \wrong, which prints its argument in red.
\documentclass[a4paper, 11pt]{article}
% amsmath redefines the \label command, which messes up the mechanism that prints the current page number
\makeatletter
\let\label@original\label
\makeatother
\usepackage{etoolbox}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{xcolor}
\allowdisplaybreaks
\makeatletter
\providecommand\protected@writeaux{%
\protected@write\@auxout
}
% Get and print the current page number
\newcounter{currentpage@mark}
\def\theCurrentPageMark{%
\label@original{currentpage@mark\the\c@currentpage@mark}%
}
\def\theCurrentPageRef{%
\expandafter\pageref{currentpage@mark\the\c@currentpage@mark}%
}
% Load some commands that reset a counter at each change of page
\expandafter\newif\csname ifPerPage@#1@hint\endcsname
\newcounter{PerPage@#1@next@reset}
\expandafter\newif\csname ifPerPage@#1@towrite\endcsname
\@nameuse{PerPage@#1@towritefalse}
\AtBeginDocument{\@nameuse{PerPage@#1@initial@stab}}
\newcounter{@#1@serial}
\@namedef{PerPage@#1@cpage}{0}
\@nameuse{PerPage@#1@hinttrue}
\@namedef{PerPage@#1@hint}{%
\setcounter{#1}{0}%
\protected@writeaux\relax{\expandafter\protect\csname PerPage@#1@hinttrue\endcsname}%
\@tempcnta\csname c@@#1@serial\endcsname%
\global\expandafter\csname c@PerPage@#1@next@reset\endcsname\@tempcnta
}
\AtBeginDocument{%
\protected@writeaux\relax{%
\protect\providecommand{\expandafter\protect\csname PerPage@#1@hinttrue\endcsname}{}%
}%
}
\@namedef{PerPage@#1@lastfoot}{-1}
\@namedef{PerPage@#1@aux}##1##2{%
\ifnum\csname PerPage@#1@lastfoot\endcsname<##1%
\@nameuse{ifPerPage@#1@hint}%
\@nameuse{PerPage@#1@reset}{##1}{##2}%
\@nameuse{PerPage@#1@hintfalse}%
\else
\gdef\@tempa{##2}%
{\expandafter}\expandafter\ifx\csname PerPage@#1@cpage\endcsname\@tempa
\else
\@nameuse{PerPage@#1@reset}{##1}{##2}%
\fi
\fi
\@namedef{PerPage@#1@lastfoot}{##1}%
\fi
\global\cslet{PerPage@#1@initial@stab}{\relax}%
}
\@namedef{PerPage@#1@reset}##1##2{%
\global\@namedef{PerPage@#1@cpage}{##2}%
\expandafter\gdef
\csname PerPage@#1@next-\@nameuse{PerPage@#1@prev@foot}\endcsname{##1}%
\@namedef{PerPage@#1@prev@foot}{##1}%
\expandafter\xdef
\csname PerPage@#1@next-\@nameuse{PerPage@#1@prev@foot}\endcsname{\the\@MM}%
}
\@namedef{PerPage@#1@prev@foot}{root}
\AtBeginDocument{%
\protected@writeaux\relax{%
\protect\providecommand{\expandafter\protect\csname PerPage@#1@aux\endcsname}[2]{}%
}%
\csname c@PerPage@#1@next@reset\endcsname\@ne
}
\AtEndDocument{%
\csletcs{PerPage@#1@aux}{PerPage@#1@endaux}%
\@namedef{PerPage@#1@lastfoot}{-1}%
\@nameuse{PerPage@#1@hintfalse}%
\@namedef{PerPage@#1@prev@foot}{root}%
}
\@namedef{PerPage@#1@endaux}##1##2{%
\ifnum\csname PerPage@#1@lastfoot\endcsname<##1%
\@nameuse{ifPerPage@#1@hint}%
\@nameuse{PerPage@#1@reset@end}{##1}{##2}%
\@nameuse{PerPage@#1@hintfalse}%
\else
\gdef\@tempa{##2}%
{\expandafter}\expandafter\ifx\csname PerPage@#1@cpage\endcsname\@tempa
\else
\@nameuse{PerPage@#1@reset@end}{##1}{##2}%
\fi
\fi
\@namedef{PerPage@#1@lastfoot}{##1}%
\fi
}
\@namedef{PerPage@#1@reset@end}##1##2{%
\def\@tempa{##1}%
{\expandafter}\expandafter\ifx\csname PerPage@#1@next-\@nameuse{PerPage@#1@prev@foot}\endcsname\@tempa
\else
\@tempswatrue
\fi
\global\@namedef{PerPage@#1@prev@foot}{##1}%
\global\@namedef{PerPage@#1@cpage}{##2}%
}
\pretocmd{\clearpage}{\@nameuse{PerPage@#1@hint}}{}{}
\@namedef{PerPage@#1}{%
\if@minipage\else
\if@filesw
\expandafter\xdef\csname PerPage@#1@writetemp\endcsname{%
\noexpand\protected@writeaux\relax{%
\expandafter\string\csname PerPage@#1@aux\endcsname%
{\the\@nameuse{c@@#1@serial}}{\noexpand\thepage}%
}%
}%
\@nameuse{PerPage@#1@towritetrue}%
\fi
\ifnum\csname c@PerPage@#1@next@reset\endcsname>\csname c@@#1@serial\endcsname
\else
\global\expandafter\csname c@#1\endcsname\@ne
\expandafter\let\expandafter\@tempa
\csname PerPage@#1@next-\number\csname c@PerPage@#1@next@reset\endcsname\endcsname
\ifx\@tempa\relax
\global\expandafter\csname c@PerPage@#1@next@reset\endcsname\@MM
\else
\global\expandafter\csname c@PerPage@#1@next@reset\endcsname\@tempa
\fi
\fi
\fi
}
\@namedef{PerPage@#1@end}{%
\@nameuse{ifPerPage@#1@towrite}%
\@nameuse{PerPage@#1@writetemp}%
\@nameuse{PerPage@#1@towritefalse}%
\fi
}
}
\newcounter{maincounter}
% Patch some numbering commands to take into account the page number and the resetting
\newtheoremstyle{thmstyle}%
{\topsep}%
{\topsep}%
{\itshape}%
{}%
{\bfseries}%
{.}%
{ }%
{\thmname{#1}%
\thmnumber{\@ifnotempty{#1}{ }%
\theCurrentPageMark
\PerPage@maincounter
\@upn{#2}%
\PerPage@maincounter@end}%
\thmnote{ {\the\thm@notefont(#3)}}}
\theoremstyle{thmstyle}
\newtheorem{theorem}{Theorem}
\newtheorem{proposition}[theorem]{Proposition}
\pretocmd{\@footnotemark}{%
\theCurrentPageMark
\PerPage@maincounter
\global\csname c@\@mpfn\endcsname\c@footnote
\protected@xdef\@thefnmark{\thempfn}%
}{}{}
\apptocmd{\@footnotemark}{%
\PerPage@maincounter@end
}{}{}
\pretocmd{\tagform@}{%
\theCurrentPageMark
\PerPage@maincounter
}{}{}
\apptocmd{\tagform@}{%
\PerPage@maincounter@end
}{}{}
\pretocmd{\@caption}{%
\theCurrentPageMark
\PerPage@maincounter
}{}{}
\apptocmd{\@caption}{%
\PerPage@maincounter@end
}{}{}
% Link the counters
\let\c@footnote\c@maincounter
\let\c@equation\c@maincounter
\let\c@theorem\c@maincounter
\let\c@figure\c@maincounter
\let\c@table\c@maincounter
\renewcommand{\thefootnote}{\theCurrentPageRef.\arabic{footnote}}
\renewcommand{\theequation}{\theCurrentPageRef.\arabic{equation}}
\renewcommand{\thetheorem}{\theCurrentPageRef.\arabic{theorem}}
\renewcommand{\thefigure}{\theCurrentPageRef.\arabic{figure}}
\renewcommand{\thetable}{\theCurrentPageRef.\arabic{table}}
\newcounter{rptcount}
\long\def\rpt#1#2{%
\setcounter{rptcount}{#1}%
\loop #2%
\repeat
}
\def\brack@iden[#1]{#1}
\newcommand*{\blindtext}[1]{%
\ifnum#1<\@ne
\else\ifnum#1=\@ne
Blah%
\else
Blah, %
\rpt{\numexpr#1-2\relax}{blah, }%
blah%
\fi\fi
\@ifnextchar[\brack@iden.%
}
\makeatother
\newcommand*{\tablecaption}[1]{%
\setlength{\belowcaptionskip}{\abovecaptionskip}%
\setlength{\abovecaptionskip}{0pt}%
\caption{#1}%
}
\newcommand*{\wrong}[1]{%
\textcolor{red}{#1}%
}
\begin{document}
%
\begin{theorem}\label{thm1}
Blah.
\end{theorem}
%
\begin{table}[h]
\centering
\tablecaption{A table}
\begin{tabular}{l | l}
1 & 2 \\
\hline
3 & 4
\end{tabular}
\end{table}
%
$$\label{eq1} a = b$$
%
\begin{figure}[b]
\centering
\rule{3cm}{2cm}
\caption{A black rectangle}\label{fig1}
\end{figure}
%
\begin{proposition}
Blah.
\end{proposition}
%
Theorem~\wrong{\ref{thm1}}. Equation~\eqref{eq1}. \blindtext{301}\space Table~\ref{tbl1}. Equation~\eqref{eq2}.\par
%
$$c = d$$
%
\begin{table}[t]
\centering
\tablecaption{Another table}\label{tbl1}
\begin{tabular}{l | l}
a & b \\
\hline
c & d
\end{tabular}
\end{table}
%
\begin{theorem}
Blah.
$$e = f$$
\end{theorem}
%
Footnote~\ref{fn1}. \blindtext{398}[\footnotemark], blah\footnotemark, blah\footnote{\label{fn1}A footnote.}. Footnote~\ref{fn1}. Theorem~\wrong{\ref{thm1}}. Equations~\eqref{eq1} and~\eqref{eq2}. Figure~\ref{fig1}.\par
%
\blindtext{519}
%
\begin{align}
\alpha &= \beta \\
\gamma &= \delta \\
\varepsilon &= \zeta \label{eq2}
\end{align}
%
\blindtext{528}\space Figure~\wrong{\ref{fig2}}. Proposition~\wrong{\ref{prop1}}.\par
%
\begin{proposition}\label{prop1}
Blah.
\end{proposition}
%
Proposition~\wrong{\ref{prop1}}.
%
\begin{figure}[p]
\centering
\rule{4cm}{3cm}
\caption{Another black rectangle}\label{fig2}
\end{figure}
%
\end{document}
• The page breaker works asynchronously with the execution of code on the main page so by the time you split one page you may have executed the counter for equations that will only be typeset pages ahead (due to insertion of figures, or simply long paragraphs) You need to use the \pageref system and correct the resetting on later runs. You should be able to reuse code from (say) footmisc package which has a per-page option for footnote counter – David Carlisle Sep 2 '13 at 20:41
• It seems to work if \thepage is used instead of \thezpage; however, figures and tables not "here" will appear out of order. – egreg Sep 2 '13 at 22:53
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## Custom Header and Footer using AMC-TXT (not LaTex)
Hello,
is there any work around to insert header/fooder when using AMC-TXT? I only found this https://project.auto-multiple-choice.net/projects/auto-multiple-choice/wiki/Custom_header_and_footer which works just fine using LaTeX Sources but for way easier question editing we're gonna switch to AMC-TXT..
### Replies (7)
#### RE: Custom Header and Footer using AMC-TXT (not LaTex) - Added by Alexis Bienvenüeabout 1 year ago
You can include LaTeX code with the LaTeX-Preambule: AMC-TXT general option.
#### RE: Custom Header and Footer using AMC-TXT (not LaTex) - Added by Muh Kuhabout 1 year ago
I was playing around with lines like this
LaTeX-Preambule: pdfpages$\includepdf[pages=-,landscape=true]{Rechenaufgaben.pdf}$
(well to be specific this one was for trying to include some full pdf pages to the document)
The header code is something like
\begin{center} \vspace*{.1cm} \hspace*{.8cm} \begin{minipage}{0.2\linewidth} \begin{center} \includegraphics[scale=1.2]{media/buw.PNG}\\ \end{center} \end{minipage} \hspace*{.1cm} \begin{minipage}{0.4\linewidth} \begin{center} \bf Prof. Dr.-Ing. asfsfag\\ \small\bf Klausur\\\large \glqq Easfsaf\\\small im Wintersemester 2018/2019\\ \end{center} \end{minipage} \hspace*{-.8cm} \begin{minipage}{0.3\linewidth} \begin{center} \includegraphics[scale=0.3]{media/Logo_DE.png}\\ \end{center} \end{minipage}\\ \makebox[\linewidth]{\rule{0.62\paperwidth}{0.4pt}}\end{center}
Do you mind giving an example how the command should look like in AMC-TXT? I love the documentation till the point that it gives not many examples for the AMC-TXT Options like
LaTeX:
Set this option to 1 if you want to use LaTeX commands in your texts. This allows for example to insert mathematical formulas, like $\sqrt{a+b}$. If 0 (default), all your texts will be written unmodified.LaTeX-Preambule:
Give commands you want to be added to the LaTeX preambule (for example \usepackage commands).LaTeX-BeginDocument:
Give commands to be inserted at the beginning of the LaTeX document environment (for example macro definitions).
#### RE: Custom Header and Footer using AMC-TXT (not LaTex) - Added by Alexis Bienvenüeabout 1 year ago
LaTeX-Preambule: includes some LaTeX code once in the document preamble, to define macros or set options, like:
LaTeX-Preambule: \fancyfoot[C]{ My footer }
or
LaTeX-Preambule: \AMCsetFoot{ My footer }
with AMC 1.4.0 I think.
#### RE: Custom Header and Footer using AMC-TXT (not LaTex) - Added by Muh Kuhabout 1 year ago
I tried the first one without success some days ago (no errors but also no effect)
But the second one works like a charm! thanks! Any quick tip to let it display pagenumbers?
#### RE: Custom Header and Footer using AMC-TXT (not LaTex) - Added by Muh Kuhabout 1 year ago
So the part for the recent page number \thepage from https://project.auto-multiple-choice.net/boards/2/topics/8391 works. But not the total page count part.
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Volumetric Viewer
# Neuroglancer on Colab
Neuroglancer is a volumetric viewer for neuroscience that came out of Google. It's WebGL-based. It's the state of the art for such tools. It's liberally licensed.
This notebook explores getting Neuroglancer running on Colab. Part of that involves UI work. Part of the will probably involve transforming the brightfield's raw data into Neuroglancer precomputed format.
Neuroglancer is a "WebGL-based viewer for volumetric data" in popular use within the neuroscience community. It is the state of the art. The codebase started inside Google and was open sourced (Apache License 2.0).
In terms of getting Neuroglancer running on Colab, this might happen in multiple stages.
• An iframe to code and data not on Colab
• Code on Colab. Install neuroglancer on Colab and serve
• There are Colab specific ways of getting data from server to client
• Generate data on Colab VM and view in Colab UI
For the case of generating data, that target format would be [Neuroglancer precomputed])(https://github.com/google/neuroglancer/tree/master/src/neuroglancer/datasource/precomputed). The generated files could be saved off to... somewhere, say, GitHub (max 100 GB per repo). Optionally, they could just be served up and explored, just to thrown away some hours later.
## Status
As of 2020-02-02, work on this hasn't gone beyond confirming that in some fashion Neuroglancer can be embedded into Jupyter notebooks, running on Colab.
# Skel survey
Neuroglancer is a visualizer, not a segmentation/skeletonization algorithm, which is being using in this project.
Point cloud in neuroglancer has been happening since at least 2018-11. Skeletons seems to have been in the mix since 2016: “it supports a wide variety of data sources and is capable of displaying arbitrary (non axis-aligned) cross-sectional views of volumetric data, as well as 3-D meshes and line-segment based models (skeletons).”
So, because of its tech features and license, Neuroglancer is being used as the visualization client for this project. Also note that Allen Brain (Collman) is contributing code to Neuroglancer. GitHub https://github.com/google/neuroglancer/tree/master/src/neuroglancer/skeleton neuroglancer/src/neuroglancer/skeleton/ write read const swcStr = '# Generated by NeuTu (https://github.com/janelia-flyem/NeuTu)\n 1 0 4145 3191 3575 2 -1\n\ 2 0 4149 3195 3579 3.65685 1\n\ 3 0 4157 3195 3583 6.94427 2\n\ 4 0 4161 3195 3591 3.65685 3\n\ 5 0 4165 3199 3595 2 4\n';
describe('skeleton/decode_swc_skeleton', () => {
it('decodes simple line skeleton', () => {
Support forum 2017-02: Someone asking NG group for skeleton demo
Hi Daniel, Unfortunately I can't point you to an example for skeleton visualization. However, you could use the code related to SkeletonSource in these two files: https://github.com/google/neuroglancer/blob/master/src/neuroglancer/datasource/brainmaps/frontend.ts https://github.com/google/neuroglancer/blob/master/src/neuroglancer/datasource/brainmaps/backend.ts as an example. The existing skeleton infrastructure assumes that you have a collection of skeletons with associated uint64 ids. In the "backend" code (which runs in the WebWorker), you would simply need to decode the SWC file into a Float32Array of vertex positions and a Uint32Array of pairs of edge indices into the vertex positions array, which should be assigned to chunk.vertexPositions and chunk.indices respectively. Currently the skeleton rendering is quite simple and does not support radius information, although that would be a valuable addition.
As an update, Alex Weston at Janelia previously wrote this code for parsing SWC files: https://github.com/janelia-flyem/neuroglancer/commit/27b7e0fa6133ecf22d293eb650f7d0c46b10f624 and integrated support for it into the DVID datasource: https://github.com/janelia-flyem/neuroglancer/commit/05aa3bcb33a6657c6fd5d1a945822304a8d075c6 She hasn't yet had chance to make it into a pull request, but she says you can feel free to do so if you'd like to use it for something that you want to contribute.
## Simple iframe in html magic
The first little piggie's house is just an iframe in and %%html magic cell.
Note that this has issues with focus and scrolling which can be reduced simply by zooming the font size down.
%%html
<iframe
width="100%" height="700px"
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## Gauge Theory and Representation Theory, Day I
So today was the first day of Gauge Theory and Representation Theory. I had a bit of irritation getting there (late train combined with the locals telling me that the Institute was in the opposite direction, causing me to meander about Princeton for about an hour before I found it) but I did eventually manage to make it. Anyway, on to the talks (though I admit to understanding virtually nothing of them…hopefully I’ll do better tomorrow.)
The first talk was Alexander Beilinson from U. Chicago. This one I understood very little of, especially in the motivation, but he did define things called factorization lines over complex curves with a line bundle, which seemed to me to have the purpose of being able to be factored into a tensor product over open covers. He concluded by stating that two groupoids are equivalent, though I didn’t quite catch how he defined them.
More interesting to me was Dennis Gaitsgory of Harvard. He ignored local geometric Langlands, which his talk title contained, and focused on localization of Kac-Moody modules. Now, I don’t know what those are either (sensing a pattern?) but as a result of his talk, I did learn what $D$-modules are. Let $V$ be an affine variety, it has coordinate ring $k[x_1,\ldots,x_n]/I$ for some ideal $I$. Then, take the module of linear differential operators with coefficients in the coordinate ring. This is an instance of a $D$-module. More generally, you can sheafify this whole construction, and for a variety $X$, you get a category of $D$-modules. This is definitely something I need to learn more about, as is what he did next: he took the derived category of the category of $D$-modules. This is where he lost me, but it has pointed me in the direction of some new things to learn (and post about as I do).
Third for the day was Imperial College’s Richard Thomas. I don’t remember the names, but he was working on things that connect Gromov-Witten Theory to GV Theory and MNOP Theory. The thread connecting them is counting curves in Calabi-Yau Threefolds and obtaining a set of numbers that both determines and is determined by the Gromov-Witten invariants.
Finally came Gregory Moore from Rutgers. His was the only really physics based talk today, and he talked about BPS (I don’t remember what the names are) wall crossing, which is closely related to what Richard Thomas was talking about, and connecting it to physics problems. Well, at least to supergravity, string theory (mostly Type IIA) and the like. I didn’t follow much of it, though.
That was all for the first day, I’ll post again tomorrow.
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# Importing text file to plot animation in 1D
I have .txt file with data that I want import into mathematica and then create a 1D animation/simulation of 3 curves.
The format of the .txt file is in columns of: 1. time 2. particle type 3. distance (x axis) 4. resultant value (y axis).
Here is an extract from the code:
153 0 252 -7.89389e-08
153 0 253 7.88583e-08
153 0 254 -7.87986e-08
153 0 255 7.87613e-08
153 1 0 -2.75981e-05
153 1 1 2.76022e-05
153 1 2 -2.76148e-05
153 1 3 2.76356e-05
153 1 4 -2.76647e-05
153 1 5 2.77025e-05
...
153 1 251 2.77025e-05
153 1 252 -2.76647e-05
153 1 253 2.76356e-05
153 1 254 -2.76148e-05
153 1 255 2.76022e-05
153 2 0 2.36682e-06
153 2 1 -2.36716e-06
153 2 2 2.36824e-06
153 2 3 -2.37002e-06
153 2 4 2.37253e-06
153 2 5 -2.37577e-06
153 2 6 2.3797e-06
153 2 7 -2.38439e-06
153 2 8 2.38982e-06
153 2 9 -2.39593e-06
153 2 10 2.4029e-06
153 2 11 -2.41052e-06
...
The file has 153600 rows and 4 columns.
What is a good format to import this file into mathematica and how would I simulate the curves in 1D w.r.t. time, for each of the 3 particle types on one plot?
The plot should look like this still image below, but as a moving animation, with the G, X and Y as particle types:
• Maybe like this: data=ReadList["file.txt",Number, RecordLists -> True][[All,{2,1,3,4}]]; particles = GroupBy[data, First]; ListPlot[Values[particles][[All,All,{2,3}]]] plots x(t) for all particles. For y(t) change {2,3} to {2,4}. – Alx Dec 6 '19 at 14:57
• @Alx. Thanks! I will try it out. However, what I really wanted was y(t) vs. x(t) in 1 dimension for the 3 particle curves. – Brendan Darrer Dec 6 '19 at 15:17
• OK, correction to meet your requirements: data = ReadList["file.txt", Number, RecordLists -> True]; groupped = GroupBy[data, {First, #[[2]] &}]; plots = Table[ListPlot[((Values /@ Values[groupped])[[All, All, All, {3, 4}]])[[i]]],{i, Keys[groupped]}];. Then you can use ListAnimate[plots], or export plots to animated gif. The idea is to group by time, then by particle for particular time (will result in nested Associations), then we take only {x, y} i.e. {3, 4} columns for each inner Association. Each Table element represents y(x) for specific time i for all particles. – Alx Dec 6 '19 at 16:00
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# Consider a sample of oxygen behaving like an ideal gas.
Question:
Consider a sample of oxygen behaving like an ideal gas. At $300 \mathrm{~K}$, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be :
(Molecular weight of oxygen is $\left.32 \mathrm{~g} / \mathrm{mol} ; \mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$
1. (1) $\sqrt{\frac{3}{3}}$
2. (2) $\sqrt{\frac{8}{3}}$
3. (3) $\sqrt{\frac{3 \pi}{8}}$
4. (4) $\sqrt{\frac{8 \pi}{3}}$c
Correct Option: , 3
Solution:
(3)
$\mathrm{v}_{\mathrm{ms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$
$\mathrm{V}_{\mathrm{avg}}=\sqrt{\frac{8}{\pi} \frac{\mathrm{RT}}{\mathrm{M}}}$
$\frac{\mathrm{v}_{\mathrm{rms}}}{\mathrm{V}_{\mathrm{avg}}}=\sqrt{\frac{3 \pi}{8}}$
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# How many iterations of Newton's method are needed to achieve a given precision?
Consider using Newton's method to solve the equation $arctan(x) = 0$. Using an initial guess of $x_0 = 1/2$ produces a sequence that converges rapidly. After $8$, iterations, $x_8$ is accurate to well over 2000 decimal places.
(i) Verify with a computer that $x_8$ is a solution accurate to over $2000$ decimal places.
I was just learning Newton's Method and saw this problem. I think I might be going ahead but it seems good to know.
Here is my attempt: (Sorry if I'm wrong. I am just really interested in this problem)
In[1]:newton1[function_, variable_, initial_, iterations_] :=
Module[{p, f, x},
Subscript[p, 1] = initial;
f[x_] := function /. variable -> x;
Do[
Subscript[p, i] =
Subscript[p, i - 1] -
f[Subscript[p, i - 1]]/f'[Subscript[p, i - 1]];,
{i, 2, iterations}];
Subscript[p, iterations]
]
In[1]:Timing[approx = newton1[arctan(x)=0, x, 1/2, 8]]
Out[1]:{0.826805, Indeterminate}
or I was wondering if the program could be this:
In[1]: f[x_] := arctan[x] = 0;
In[1]: mynewton[function_, variable_, initial_, iterations_] :=
Module[{f, x, p},
f[x_] := function /. variable -> x;
Subscript[p, 1] = initial;
Do[
Subscript[p, i] =
Subscript[p, i - 1] -
f[Subscript[p, i - 1]]/f'[Subscript[p, i - 1]];,
{i, 2, iterations}];
Table[Subscript[p, i], {i, 1, iterations}]
]
In[1]: N[mynewton[f[x], x, 1/2, 8], 8]
Out[1]: {0.50000000, Indeterminate, Indeterminate, Indeterminate, \
Indeterminate, Indeterminate, Indeterminate, Indeterminate}
Again sorry if I am wrong. I am really interested in learning this part of the program. I will be able to continue to other questions like this after help with this one on my own. I really did try. I was studying various types of Newton's Programs but can not figure this one out. Can someone please help write the input?
-
– Michael E2 Oct 9 '13 at 23:34
I have a hard time following your code, but it doesn't look to me that you are on the right path. Here is how I would tackle this problem.
f[x_] := ArcTan[x]
df[x_] = f'[x];
iterStep[x_] := x - f[x]/df[x]
root = With[{n = 8}, Nest[iterStep, 1/2, n]];
Block[{$MaxExtraPrecision = 4000}, Abs @ root < 10^-2500] True Block[{$MaxExtraPrecision = 4000}, Abs @ root < 10^-2600]
False
I interpret the last two results as saying that root approximates zero to more than 2500 decimal places, but less than 2600 decimal places.
-
Of course m_goldberg has the proper mathematica-esque soluiton, but for education purpose heres a working version of your loop approach..
newton1[function_, variable_, initial_, iterations_] := Module[{p, f},
p[1] = initial;
f[x_] := function /. variable -> x;
Do[p[i] = p[i - 1] - f[p[i - 1]]/f'[p[i - 1]] // N;, {i, 2,
iterations}]; p[iterations] ];
newton1[ArcTan[x], x, 1/2, 8]
Explicit use of Subscript[] is usually not a good idea.. , and you had a bunch of other issues. Note also there is no reason to actually carry around all the p[i..] except the last one, but i left that alone
-
Nest seems perfect for Newton's method.
newtonStep[f_] := # - f[#]/f'[#] &;
Block[{$MaxExtraPrecision = 5000}, N[Nest[newtonStep[ArcTan], 1/2, 8], 10] ] (* 8.829190025*10^-2598 *) With NestList, you can observe the convergence. newtonStep[f_] := # - f[#]/f'[#] &; Block[{$MaxExtraPrecision = 5000},
N[NestList[newtonStep[ArcTan], 1/2, 8], 10]
]
(* { 0.5000000000,
-0.07955951125,
0.0003353022040,
-2.513147366*10^-11,
1.058187453*10^-32,
-7.899444718*10^-97,
3.286233612*10^-289,
-2.365941712*10^-866,
8.829190025*10^-2598} *)
A gain in speed may obtained by computing approximate results all along. I found that to get a single significant digit in the 8th iterate, I could do without the extra precision, but I needed to start with 2600 digits of precision. To get the results above, I needed 2610.
NestList[newtonStep[ArcTan], 0.52610, 8] // N[#, 10] &
Remark: The convergence rate is unusually fast (cubic instead of quadratic) because the second derivative of ArcTan is zero at the root.
-
wanted to note a subtle thing here: NestList operates symbolically resulting is a huge expression of nested ArcTan expressions, which is evaluated numerically at the end by the N[] wrapper. It runs way faster with essentiually the same precision if you put an N inside the newtonStep function.. newtonStep[f_]:=N[#-f[#]/f'[#],500]&; – george2079 Oct 10 '13 at 15:30
@george2079 Interesting: I knew the exact expression would grow very large, but it didn't seem slow enough to worry about. Testing your comment, I found this: It turns out on the beta V10 I was using, there is essentially no difference in speed, exact vs approximate, 0.005981 vs. 0.005963. But on V9, it's about 2.7 vs. 0.0075`. On the other hand, I found 500 digits of precision insufficient for more than 6 iterations. – Michael E2 Oct 10 '13 at 17:00
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Math Help - How to estimate the total error?
1. How to estimate the total error?
I have a list of (systematic) errors obtained by calculating the percentage error of two sets of values. now from that list i don't know how to say what my total error was. these are the values:
-5.04
-3.09
-2.63
-0.20
0.00
1.40
3.88
I don't think that saying that the error was -5.04 to 3.88 is correct. I think I have to calculate the standard deviation or the standard error but I am not sure which. I know the formula for the standard deviation but for the standard error i'm not sure if it is the square root of the sum of the squares. What do you suggest I do to obtain the total error?
2. Originally Posted by susibom
I have a list of (systematic) errors obtained by calculating the percentage error of two sets of values. now from that list i don't know how to say what my total error was. these are the values:
-5.04
-3.09
-2.63
-0.20
0.00
1.40
3.88
I don't think that saying that the error was -5.04 to 3.88 is correct. I think I have to calculate the standard deviation or the standard error but I am not sure which. I know the formula for the standard deviation but for the standard error i'm not sure if it is the square root of the sum of the squares. What do you suggest I do to obtain the total error?
Try explaining what your figures denote more clearly please.
CB
3. I made a comparison between the results I obtained through two methods.
One method has shown to be more accurate than the other. So when I made the comparison of the values I calculated the difference of the values with the accurate method with those of the tested method. With this value I calculated the percentage error assuming the accurate method was the theoretical value and the other was the experimental value. After this I obtained a list the list of values I showed before in the thread. So I was told that I could use those values as an indication of the error I get when using the tested method. But I think that I can't simply say that the error was -5.04 to 3.88%. So I thought maybe if I obtained a mean value of error from those I listed I could say my error is say +/-7.7%. And I used the formula of the square root of the sum of the squares. But then I read that that formula is only used when comparing means. So if my values ar not means then I suppose the alternative is the Standard deviation. Am I correct?
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Kentaro Ito
Exotic projective structures and quasi-fuchsian space
Abstract:
Let $P(S)$ denote the space of projective structures on a closed surface $S$. It is known that the subset $Q(S) \subset P(S)$ of projective structures with quasi-Fuchsian holonomy has infinitely many connected components; one is called standerd, the others are exotic. Here, we investigate the configuration of these components. In our previous paper (Duke Math. J. {\bf 105} (2000), 185--209), we showed that the closure of any exotic component intersects the closure of the standard component. We develop our argument there and show that any two components have intersecting closures.
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# Approximate Sampling and Counting of Graphs with Near-Regular Degree Intervals
Georgios Amanatidis, Pieter Kleer
Research output: Working paperOther research output
## Abstract
The approximate uniform sampling of graphs with a given degree sequence is a well-known, extensively studied problem in theoretical computer science and has significant applications, e.g., in the analysis of social networks. In this work we study an extension of the problem, where degree intervals are specified rather than a single degree sequence. We are interested in sampling and counting graphs whose degree sequences satisfy the degree interval constraints. A natural scenario where this problem arises is in hypothesis testing on social networks that are only partially observed.
In this work, we provide the first fully polynomial almost uniform sampler (FPAUS) as well as the first fully polynomial randomized approximation scheme (FPRAS) for sampling and counting, respectively, graphs with near-regular degree intervals, in which every node i has a degree from an interval not too far away from a given $d \in \N$. In order to design our FPAUS, we rely on various state-of-the-art tools from Markov chain theory and combinatorics. In particular, we provide the first non-trivial algorithmic application of a breakthrough result of Liebenau and Wormald (2017) regarding an asymptotic formula for the number of graphs with a given near-regular degree sequence. Furthermore, we also make use of the recent breakthrough of Anari et al. (2019) on sampling a base of a matroid under a strongly log-concave probability distribution.
As a more direct approach, we also study a natural Markov chain recently introduced by Rechner, Strowick and Müller-Hannemann (2018), based on three simple local operations: Switches, hinge flips, and additions/deletions of a single edge. We obtain the first theoretical results for this Markov chain by showing it is rapidly mixing for the case of near-regular degree intervals of size at most one.
Original language English Ithaca Cornell University Library 28 abs/2110.09068 Published - 2021
### Publication series
Name ArXiv 2110.09068
## Fingerprint
Dive into the research topics of 'Approximate Sampling and Counting of Graphs with Near-Regular Degree Intervals'. Together they form a unique fingerprint.
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_pub.n
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# Noteshare Handbook
## 2. Collaboration
If you are working on a notebook with one or more co-authors, you should form a writer’s group on Noteshare and add your document this group. Then any member of the group can create and edit sections of the notebook.
Any member of a writer’s group can check out a section. This allows an author to freely make changes without having to worry that they may be lost or garbled by the actions of another author.
Note When you set up your Noteshare account, a group with same name as your screen name was set up as well. Check for it in the right-hand column of your home page. It is a link which you can click on to manage your group.
### 2.1. Check-in and check-out
If you are working with a group of co-authors, you can check a section out so that others do not inadvertently edit it while you are editing it. To check out a section, press the CO. button in the left column of the main editor page. When a section is checked, this button is red. Press it again to to check it back in.
Created September 25, 2014, last updated: August 21, 2015
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# Expand Kirkman's Schoolgirl Problem
For those of you who are unfamiliar, Kirkman's Schoolgirl Problem goes as follows:
Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast.
We could look at this like a nested 3 by 5 list (or matrix):
[[a,b,c]
[d,e,f]
[g,h,i]
[j,k,l]
[m,n,o]]
Essentially, the goal of the original problem is to figure out 7 different ways to arrange the above matrix so that two letters never share a row more than once. From MathWorld (linked above), we find this solution:
[[a,b,c] [[a,d,h] [[a,e,m] [[a,f,i] [[a,g,l] [[a,j,n] [[a,k,o]
[d,e,f] [b,e,k] [b,h,n] [b,l,o] [b,d,j] [b,i,m] [b,f,g]
[g,h,i] [c,i,o] [c,g,k] [c,h,j] [c,f,m] [c,e,l] [c,d,n]
[j,k,l] [f,l,n] [d,i,l] [d,k,m] [e,h,o] [d,o,g] [e,i,j]
[m,n,o]] [g,j,m]] [f,j,o]] [e,g,n]] [i,k,n]] [f,h,k]] [h,l,m]]
Now, what if there were a different number of schoolgirls? Could there be an eighth day? This is our challenge.
In this case no††, but not necessarily for other array dimensions
††We can easily show this, since a appears in a row with every other letter.
## The Challenge:
Given an input of dimensions (rows, than columns) of an array of schoolgirls (i.e. 3 x 5, 4 x 4, or [7,6], [10,10], etc.), output the largest possible set of 'days' that fit the requirements specified above.
Input:
The dimensions for the schoolgirl array (any reasonable input form you wish).
Output:
The largest possible series of arrays fitting the above requirements (any reasonable form).
Test Cases:
Input: [1,1]
Output: [[a]]
Input: [1,2]
Output: [[a,b]]
Input:* [2,1]
Output: [[a]
[b]]
Input: [2,2]
Output: [[a,b] [[a,c] [[a,d]
[c,d]] [b,d]] [b,c]]
Input: [3,3]
Output: [[a,b,c] [[a,d,g] [[a,e,i] [[a,f,h]
[d,e,f] [b,e,h] [b,f,g] [b,d,i]
[g,h,i]] [c,f,i]] [c,d,h]] [c,e,g]]
Input: [5,3]
Output: [[a,b,c] [[a,d,h] [[a,e,m] [[a,f,i] [[a,g,l] [[a,j,n] [[a,k,o]
[d,e,f] [b,e,k] [b,h,n] [b,l,o] [b,d,j] [b,i,m] [b,f,g]
[g,h,i] [c,i,o] [c,g,k] [c,h,j] [c,f,m] [c,e,l] [c,d,n]
[j,k,l] [f,l,n] [d,i,l] [d,k,m] [e,h,o] [d,o,g] [e,i,j]
[m,n,o]] [g,j,m]] [f,j,o]] [e,g,n]] [i,k,n]] [f,h,k]] [h,l,m]]
There may be more than one correct answer.
*Thanks to @Frozenfrank for correcting test case 3: if there is only one column, there can only be one day, since row order does not matter.
This is competition - shortest answer wins.
• Does this relate to finite projective planes in any way or am I thinking of a different problem? – Neil May 10 '17 at 18:51
• @Neil I have no clue. I'm afraid I'm not qualified to answer that. ;-) – Scott Milner May 10 '17 at 18:58
• Is there a time limit? – Artyer May 10 '17 at 19:05
• @Artyer No, but I would like to be able to test the code... – Scott Milner May 10 '17 at 19:59
• @Neil that was a fun wikipedia read. – Magic Octopus Urn Jul 18 '17 at 19:13
# Mathematica, 935 bytes
Inp={5,4};L=Length;T=Table;ST[t_,k_,n_]:=Binomial[n-1,t-1]/Binomial[k-1,t-1];H=ToExpression@Alphabet[];Lo=Inp[[1]]*Inp[[2]];H=H[[;;Lo]];Final={};ST[2,3,12]=4;ST[2,4,20]=5;If[Inp[[2]]==1,Column[Partition[H,{1}]],CA=Lo*Floor@ST[2,Inp[[2]],Lo];While[L@Flatten@Final!=CA,Final={};uu=0;S=Normal[Association[T[ToRules[H[[Z]]==Prime[Z]],{Z,L@H}]]];PA=Union[Sort/@Permutations[H,{Inp[[2]]}]];PT=Partition[H,Inp[[2]]];While[L@PA!=0,AppendTo[Final,PT];Test=Flatten@T[Times@@@Subsets[PT[[X]],{2}]/.S,{X, L@PT}];POK=T[Times@@@Subsets[PA[[Y]],{2}]/.S,{Y,L@PA}];Fin=Select[POK,L@Intersection[Test,#]==0&];Facfin=T[FactorInteger[Fin[[V]]],{V,L@Fin}];end=T[Union@Flatten@T[First/@#[[W]],{W,L@#}]&[Facfin[[F]]],{F,L@Facfin}]/.Map[Reverse,S];PA=end;PT=DeleteDuplicates[RandomSample@end,Intersection@##=!={}&];If[L@Flatten@PT<L@H,While[uu<1000,PT=DeleteDuplicates[RandomSample@end,Intersection@##=!={}&];If[L@Flatten@PT==L@H,Break[],uu++]]]]];Grid@Final]
this is for 26 ladies max
EDIT
I made some changes and I think it works! The code right now is set to solve [5,4] (which is the "social golfers problem") and gets the result in a few seconds. However [5,3] problem is tougher and you will have to wait 10-20 minutes but you will get a right combination for all days. For easier cases it is very quick.
anyway you can try it and see the results
Try it online here
copy and paste using ctrl-v
press shift+enter to run the code
you can change the input at the begining of the code -> Inp={5,4}
run the code multiple times to get different permutations
• While this is impressive, and makes a lot of progress towards solving the problem, it is still incomplete. While it works for smaller test cases, it couldn't solve any larger ones, including the [5,3] test case this whole problem is based off of. In addition, this can be golfed more; there are several variable names that are larger than they need to be, and some functions can be shortened with @ or infix notation. I hope you'll keep working, though! – Scott Milner May 12 '17 at 3:04
• thanks for checking it. I'll try to make this work first and then golf it... – J42161217 May 12 '17 at 10:05
• You should be able to save a lot of bytes by making your variable names single letters, and assigning some functions you use more than once to variables and replacing the functions with those variables :) – numbermaniac May 15 '17 at 23:05
• @numbermaniac By just replacing variable names, I was able to get it down to 914. It should be golfable down to around 850. – Scott Milner May 16 '17 at 0:42
• I fixed the test case. First of all I want this to work. Thats why I haven't golfed it yet.Thanks for all your comments. I think now it is ready. – J42161217 May 16 '17 at 1:05
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# Homework Help: Prove that every natural number is either even or odd.
1. Apr 28, 2012
### ruip
Hello,
I'm re-studying calculus using Spivak's Calculus 4ed and I'm stuck in one of the problems. Any help is appreciated.
1. The problem statement, all variables and given/known data
The theorem to prove is "every natural number is either even or odd".
The definition of even given by Spivak is the following: A natural number n is even if there exists an integer k such that n = 2k. Similarly, for an odd natural number n, there exists an integer k such that 2 = 2k+1.
I can also use the basic facts about natural numbers and integers, such as associativity, commutativity, existence of identity, and distributivity.
The other property of the natural numbers I can use is the principle of mathematical induction.
2. The attempt at a solution
First, my understanding of the "either or" is that I must prove that every natural n is even or odd _and not both_. A general argument by induction will look like:
• The number 1 is odd because there exists a k = 0, such that 2*0 + 1 = 1
• Suppose n is either even or odd. If even then there exists a k such that n = 2k, and n+1 = 2k+1 and so, n+1 is odd. The case for n odd is similar. And so, if n is even or odd, then n+1 is even or odd.
By the principle of mathematical induction, all natural numbers are even or odd.
The problem (one of the problems?) with this proof is that I don't show that a natural number can't be even and odd at the same time.
I can't even start to show that 1 is not even. I need to prove that there are no integer k such that 1 = 2k. I understand that the only "number" that satisfy the equation is 1/2 and 1/2 is not an integer, but I can't state that in a proof with the principles that were given.
Any help? :)
Thanks!
2. Apr 28, 2012
### Office_Shredder
Staff Emeritus
Are you allowed to use inequality properties? For example if a>b and c>0 then ac>bc. Then i 2k>2 if k is a positive integer (and if k is negative 2k<0)
3. Apr 28, 2012
### ruip
Yes, I can use inequality properties: a number n is positive, n = 0, or -n is positive; if n and m are positive then n+m and n*m are also positive. The example you give was proved from the previous properties and so I can use that and similar properties too.
Following your example with the 2k>2, let me try to use it.
So, to show that 1 is not even, I assume that if 1 is even then there exists a k such that 2k = 1. Now I have three cases:
a) If k = 0, then 2k = 0 (already proven) and 0 ≠ 1 and so I get a contradiction.
b) if k > 0, then 2k > 2 and 2 > 1, so 2k> 1, and so 2k ≠ 1.
c) if k < 0, similar to the previous case.
By contradiction, there is no integer k such that 2k = 1, and so 1 is not even.
Is this correct?
EDIT: this doesn't seem correct. I can't show that if k > 0, then 2k > 2.
Now I'm not sure if showing that 1 is odd and not even is enough to prove the general case. In the induction step, I'm assuming that n is either even or odd. When even, I show that n+1 is odd but I don't prove that n+1 is not even.
Last edited: Apr 28, 2012
4. Apr 28, 2012
### I like Serena
Assume there is a number x that is both even and odd.
So there must be a k with x=2k, and also an m with x=2m+1.
That is, 2k=2m+1
Can you rewrite this?
And use inequalities?
(No induction necessary.)
5. Apr 28, 2012
### ruip
I can rewrite it as 2(k-m) = 1 and make a similar argument as in the post above.
If k-m = 0, then 2(k-m) = 0
if k-m < 0, then 2(k-m) < 0
The problem is with k-m > 0. 2(k-m) > 0 and 1 > 0 so everything looks fine and I don't get a contradiction. I'm missing something. :\
6. Apr 28, 2012
### Office_Shredder
Staff Emeritus
k isn't just positive, it's also an integer, so k>=1.
EDIT: Similar argument finishes up what you want in your previous post
7. Apr 28, 2012
### ruip
Sorry, but I don't know how to prove that if k > 0 and k is an integer, then k >= 1. I don't see how can I show that there aren't integers between 0 and 1.
8. Apr 28, 2012
### I like Serena
What kind of definition do you have for an inequality?
And how are your whole numbers defined?
I expect something like x < x + 1 for any x.
And that the whole numbers are 1 plus a repeated number of additions of 1, combined with 1 plus a repeated number of subtractions of 1.
This means that any number is less than x, equal to x, equal to x+1, or greater than x+1.
So there is no number between x and x+1.
9. Apr 28, 2012
### ruip
Hello,
I have the following three basic properties regarding inequalities:
1. Trichotomy law. For every number a, one and only one of the following holds:
• a = 0
• a is in collection of positive numbers P
• -a is in collection of positive numbers P
2. If a and b are in P, then a + b is in P
3. If a and b are in P, then a * b is in P
The "a > b" is defined as "a - b in P".
I have no additional information about the "construction" of numbers, only the basic properties they respect. If I understood your question correctly, the numbers aren't defined starting with 1 and then adding 1's like in natural numbers. I don't think numbers are defined beyond the properties they respect.
Besides the three properties above, I have:
a + (b + c) = (a + b) + c
a + b = b + a
a + 0 = a
a + (-a) = 0 (this one doesn't apply to natural numbers)
a*(b*c) = (a*b)*c
a*b = b*a
a*1 = a
1 ≠ 0
a*a^-1 = 1 for a ≠ 0 (this property doesn't apply to integers, obviously).
a(b + c) = ab + ac
I also have the principle of mathematical induction/well-ordering principle for natural numbers and that's it.
EDIT: removed comment about my whole numbers.
Last edited: Apr 28, 2012
10. Apr 28, 2012
### I like Serena
But the term "natural number" means that it is a whole number,which is not negative (and may be zero depending on your definition).
Now I'm confused.
Are we talking real numbers, whole numbers, or natural numbers?
When you mentioned well-ordering you were again talking about natural numbers and your problem statement also refers consistently to natural numbers...
11. Apr 28, 2012
### ruip
Sorry, I misunderstood you when you said "whole numbers". You were referring to the integers. Ignore my comment "My "whole numbers" are the real numbers and so," and consider the rest. I remove that from the previous post.
Last edited: Apr 28, 2012
12. Apr 28, 2012
### I like Serena
Sorry, I referred to whole numbers (integers) and gave a definition for that, when I should have defined the natural numbers.
Just to be clear, should we ignore every reference to the word "natural" in your problem statement, and just read "number" wherever it says "natural number"?
Or else, what is your definition of a natural number?
Last edited: Apr 28, 2012
13. Apr 28, 2012
### ruip
No, in fact the problem is about natural numbers. Prove that a natural number is either even or odd. Sorry about the confusion. I have no definition for natural number besides the properties they respect.
Quoting Spivak
"The simplest numbers are the "counting numbers"
1,2,3,....
The fundamental significance of this collection of numbers is emphasized by its
symbol N (for natural numbers). A brief glance at P1-P12 will show that our
basic properties of "numbers" do not apply to N—for example, P2 and P3 do not
make sense for N. From this point of view the system N has many deficiencies."
The properties P1-P12 are the ones I gave above. P2 and P3 are specifically the 0 identity (since the naturals are defined in this book starting with 1) and the -a inverse existence.
14. Apr 28, 2012
### I like Serena
Well, I don't have Spivak, but if I understand correctly he defines the natural numbers as the numbers 1,2,3,...
In particular that is 1, and counting up by adding 1 every time (although he doesn't explicitly say so).
In particular the trichotomy law is not entirely well defined in this case, since -a is not defined for natural numbers.
And also your definition of "a > b" is not well defined, since a-b does not exist within the natural numbers.
Last edited: Apr 28, 2012
15. Apr 28, 2012
### ruip
I guess you are right. But I must add that the even definition talks about integer numbers also, namely, a natural number n is even if there exists _an integer k_ so that n = 2k. So I think I can use the trichotomy law for the integer 'k' in this definition. Maybe this isn't enough anyway.
16. Apr 28, 2012
### I like Serena
It's enough as far as I'm concerned.
To get back to your problem (now that the definition stuff is out of the way), I believe the last thing you needed is that if k-m>0, that then also k-m≥1...
17. Apr 28, 2012
### ruip
Let me restate the argument from the beginning. If an integer n is even then there is an integer k so that n = 2k. Also, if n is odd then there is an integer m so that n = 2m+1.
Now, if that is true then 2k = 2m+1 and so 2(k-m) = 1.
When (k-m)<= 0, I can easily get a contradiction.
When (k-m) > 0 and (k-m) being an integer, let me assume for now that k-m >= 1 (I don't know how to prove this yet).
If (k-m) ≥ 1 then 2(k-m) ≥ 2 and 2 > 1 so 2(k-m) > 1 and so 2(k-m) ≠ 1. By contradiction, a number n can't be even and odd.
I believe this is correct but I can't see how to get the "if k-m>0 and (k-m) is an integer, then (k-m)≥1".
18. Apr 28, 2012
### I like Serena
Good! :)
What you need is that ...<-1<0<1<2<3<...
From this inequality it follows that there can be no integers between 0 and 1.
Can you proof that?
19. Apr 28, 2012
### ruip
Well, for any number a, if a is positive then a*a > 0 (by definition).
Also if a < 0, then (-a) > 0 and (-a)*(-a) > 0. Since (-a)(-a) = a*a[1], then a*a > 0.
So, for any number a ≠ 0, a2 > 0, and in particular 12 = 1 > 0.
Given that 1 > 0, then -1 < 0. Also 1 + 1 > 0 + 1, that is 2 > 1. Also 1 - 1 > 0 - 1, and so 0 > -1.
And so ... < -1 < 0 < 1 < 2 < ...
From here I don't see how can we conclude that there aren't any integers between 0 and 1. Any hints?
--
[1] For any numbers a, b
ab + a(-b) = a(b + -b) = a*0 = 0
ab + a(-b) = 0
-(ab) + ab + a(-b) = -(ab)
a(-b) = -(ab)
And also, for any numbers a, b
(-a)(-b) + a(-b) = (-a + a)(-b) = 0(-b) = 0
(-a)(-b) + -ab = 0 (using previous result)
(-a)(-b) + (-ab) + ab = ab
(-a)(-b) = ab
20. Apr 28, 2012
### I like Serena
You've lost me there.
You wrote: "a > b" is defined as "a - b in P".
So where do all your products factor in?
There's only addition (actually subtraction) involved as far as I can tell.
Can you proof that?
21. Apr 28, 2012
### ruip
One of the properties I gave was "if a and b in P, then a*b is also in P", and so if a*a in P for any a ≠ 0 (as shown in previous post), then a*a - 0 is in P, and by definition a*a > 0. Since 1*1 = 1 and 1*1 > 0 then 1 > 0.
To prove this I depend on the fact that 1 > 0 as proved previously.
Considering that 1 > 0, that is 1 - 0 in P, then
(1 - 0) + 0 in P
(1 - 0) + (x + -x) in P, and so
(1 + x) - (x + 0) is in P
1 + x > x
22. Apr 28, 2012
### I like Serena
Okay.
That looks correct.
Let me give a shorter version.
We have: "a > b" is defined as "a - b in P".
Now fill in a=x+1, and b=x, then we get:
(x+1)-x=-x + (x+1)=(-x+x)+1=0+1=1, which is in P.
So x+1 > x.
In particular we have 0<1.
Say we pick a number y.
What are the possibilities relative to 0 and 1?
Note that ">" has a transitive property.
Oh wait. You did not mention the properties of an inequality yet...
23. Apr 28, 2012
### ruip
Sorry, but I don't understand how is this "shorter". It looks exactly the same, since you depend on the fact that 1 is in P to conclude that (x+1)-x = 1 is in P.
Since 1 in P is the same as 1-0 in P, that is 1 > 0, then we need to prove first that 1 > 0.
The way you wrote it, looks like that you started with (x + 1) - x in P and than concluded as a specific case that 1 in P. Maybe I misunderstood it?
Anyway, regarding transitivity of the >, I can say the following.
If a-b in P and b-c in P, then (a-b) + (b-c) in P, and therefore (a-c) in P.
And I still don't get it. Don't know what to say about any number y. A number y could be equal to 0, 1, 0 < y < 1, above 1, or below 0.
I'm a little lost in all this, but I'm trying to follow your reasoning (and having some fun doing it!). More hints please? :)
24. Apr 28, 2012
### I like Serena
If I understood you correctly the definition of "a>b" is based on the set P.
I am assuming that all natural numbers are in the set P.
You seem to use ">" to deduce that a number is in P, but that would be a circular argument.
I believe we decided that the natural numbers consist of 1 and multiple addititions of 1 to it.
Did we?
If we did than 1<1+1<1+1+1<...
Any natural number y must be one of these numbers.
By transitivity, y is either 1,2, or a bigger number.
In particular it cannot be a number between 1 and 2, because it has to be one of these other numbers.
25. Apr 28, 2012
### jgens
If you really want a definition of the natural numbers and integers in $\mathbb{R}$, then this definition is adequate: Define a set $A$ to be inductive if and only if $1 \in A$ and $k+1 \in A$ whenever $k \in A$. Let $\mathbb{N}$ be the intersection of every inductive subset of $\mathbb{R}$ and let $\mathbb{Z} = \mathbb{N} \cup \{0\} \cup -\mathbb{N}$. You will have to go through some work to show that these sets have the desired properties, but if you are insistent on a definition of $\mathbb{N}$, then this suffices.
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# Regression on multiple datasets with a per-dataset variable
I have 10 datasets, each with the same variables (e.g., age and income) but different numbers of observations.
Let us now consider a categorical variable $$X$$ that can only take values $$0$$ and $$1$$ per dataset, meaning that it keeps the same value for all observations. For 5 datasets, $$X=0$$; for the other 5, $$X=1$$.
How do I create a regression model for a variable of these datasets (e.g., age) that takes into account this "meta-variable" $$X$$?
A simple solution would be to append a new column for $$X$$ to each dataset, where the same value is repeated for all observations, and then concatenate the datasets. However, I think there are better ways.
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# Math Help - Area Under A Graph
1. ## Area Under A Graph
Given that the total distance travelled by a train is $4 km$ and the deceleration is $4 ms^{-2}$ for the first $T$ second as shown in the speed-time graph below.Find:
a)the value of $T$
b)the value of $V$
2. The area under the curve represents that total distance traveled
So
$\frac{(100-V)T}{2} + VT + VT + 2VT + \frac{(100-V)\cdot 2T}{2} = \color{red}{4000}$ ........(and not 4)
And we are given deceleration so we get second equation
$100-4t= V$
Do you need more help?
The area under the curve represents that total distance travelled
So
$\frac{(100-V)T}{2} + VT + VT + 2VT + \frac{(100-V)\cdot 2T}{2} = 4$
And we are given decelaration so we get second equation
$100-4t= V$
Do you need more help?
sir,why area of trapezium sir do like 1/2(100-v)T?not 1/2(100+v)T?ur anwer is correct sir..but i want to understand..
4. First of all its not a trapezium .. (to know more about trapezium try to search the word "trapezium" in Wikipedia/google)
Ok here I will show you how I found that area
1st step:
Area of the two triangles (on the upper side) which will be formed when we form a line y= V
they are found using the formula 1/2 x (base) x (height)
Area of first triangle = 1/2 x (T) x (100-V)
Area of second triangle = 1/2 x (2T) x (100-V)
2nd Step :
Area of that rectangle which is below the line Y= V
Area of rectangle = V x 4T
-------------------------------
Add them you get the complete area
as in previous post
Feel free to ask if there is any other doubt.
5. thanks very much sir..and when i get the coordinates (0,100) and (20,v)..i solve the question b that is to find the value of v..i find it gradient like 100-v/0-20=4 and i get v =180?? but the answer is 20ms^-2..can u help me sir?
6. Use the second equation
100-4xT = V
This will give you the answer
V = 100-4x20
V =100-80 = 20
_______________
Sorry for my mistake in first post I should have been more careful.
Its corrected in red.
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# Declare acronyms and abbreviations to automatically correct spaces after periods?
If I understand correctly, (La)TeX assumes that a period after a lower-case letter ends a sentence while a period after an upper-case letter does not. Unfortunately, my documents usually contain plenty of acronyms and abbreviations. Unless I remember to use \@, the spacing after periods is wrong:
\documentclass[convert={density=150},varwidth]{standalone}
\begin{document}
\noindent
\makebox[0.7in][l]{Incorrect:}%
Your computer needs more RAM. I can give you some.\\
\makebox[0.7in][l]{Correct:}%
Your computer needs more RAM\@. I can give you some.\\
\makebox[0.7in][l]{Incorrect:}%
Colors (red, blue, etc.) are nice.\\
\makebox[0.7in][l]{Correct:}%
Colors (red, blue, etc.\@) are nice.
\end{document}
Is it possible to declare certain strings to be acronyms or abbreviations to invert this assumption? If so, this would reduce the number of spacing errors in my documents.
For example:
\documentclass[convert={density=150},varwidth]{standalone}
\usepackage{magicalacronymhelper}
\declareacronym{RAM}
\declareabbr{etc}
\begin{document}
\noindent
\makebox[0.7in][l]{Correct:}%
Your computer needs more RAM. I can give you some.\\
\makebox[0.7in][l]{Correct:}%
Your computer needs more RAM\@. I can give you some.\\
\makebox[0.7in][l]{Correct:}%
Colors (red, blue, etc.) are nice.\\
\makebox[0.7in][l]{Correct:}%
Colors (red, blue, etc.\@) are nice.
\end{document}
-
the ltugboat document class has a command \acro that corrects for the end of a sentence. (it does other things as well, such as stepping the type size down a point to de-emphasize the appearance of in-line uppercase -- we don't like how small caps look in this context --, but that's easily ignored.) you're welcome to steal the idea; look for ltugboat.cls on ctan. (it doesn't handle the "etc." case; you're on your own for that.) – barbara beeton Jan 2 '13 at 22:45
The issue the with etc. is that it is an abbreviation and that it can legitimately occur at the end of a sentence. At this point you do not want to to quell the end of sentence spacing. – ArTourter Jan 2 '13 at 23:02
@ArTourter: True. In that case, I'd add an \@ to force it to be interpreted as a sentence-ending period. For example: I like citrus flavors: orange, lemon, lime, etc\@. They are tasty. I rarely end sentences with an abbreviation, so inverting the default behavior of periods after abbreviations would fix more than it would break. – Richard Hansen Jan 2 '13 at 23:22
Simplest (and some would argue most typographically correct) solution is to use \frenchspacing so the issue just goes away. – David Carlisle Jan 3 '13 at 0:08
@RichardHansen -- the problem with adding \@ to "etc." is that it will in any event be interpreted as ending a sentence (since it's lowercase). what you want to do is prevent it from indicating the end of a sentence in those (randomly occurring) cases where it doesn't. that's where the "slash-space" is needed. as for david's comment regarding \frenchspacing, there are situations where this can cause confusion; i've definitely seen them, though i can't put my hands on one right now -- that may call for rewriting rather than a spacing "fix". – barbara beeton Jan 3 '13 at 13:41
There is no way to do this automatically, unless you're willing to use XeLaTeX and the unsupported package xesearch.
The best thing you can do is to define macros \acro and \abbr:
\newcommand{\acro}[1]{#1\@}
\makeatletter
\newcommand{\abbr}{\@ifstar\@firstofone\@abbr}
\newcommand{\@abbr}[1]{#1.\@}
\makeatother
Complete example:
\documentclass{article}
\newcommand{\acro}[1]{#1\@}
\makeatletter
\newcommand{\abbr}{\@ifstar\@firstofone\@abbr}
\newcommand{\@abbr}[1]{#1.\@}
\makeatother
\begin{document}
\noindent
Your computer needs more \acro{RAM}. I can give you some.\\
Your computer needs more RAM\@. I can give you some.\\[3pt]
Colors (red, blue, \abbr{etc}) are nice.\\
Colors (red, blue, etc.\@) are nice.\\[3pt]
I like citrus flavors: orange, lemon, lime, \abbr*{etc}. They are tasty\\
I like citrus flavors: orange, lemon, lime, etc\@. They are tasty
\end{document}
-
@RichardHansen Yes, it should. Fixed. – egreg Jan 3 '13 at 0:22
Thanks! Too bad it can't be automatically done. I'm just as likely to remember to type \abbr{} or \acro{} as I am to type \@. :) – Richard Hansen Jan 3 '13 at 0:28
What's the purpose of all the \@ifstar\@firstofone business? And why do you suggest in the case of \abbr but not \acro? – Cerran Mar 7 at 22:14
@Cerran \abbr is supposed to act on lowercase letters, while \acro on uppercase ones, and they require different treatment; \abbr* is for when punctuation follows. – egreg Mar 7 at 22:21
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# Chapter 6 - Algebra: Equations and Inequalities - 6.1 Algebraic Expressions and Formulas - Exercise Set 6.1: 26
86
#### Work Step by Step
Given 3$x^{2}$ - 4x -9, x=-5 Step 1: Put the value of x=-5 for each x in the expression =3$(-5)^{2}$ - 4(-5) -9 Step 2: Evaluate the exponential expression$(-5)^{2}$ = (-5)(-5) = 25 =3( 25)-4(-5)-9 Step 3: Multiply 3(25) = 75 and 4(-5)= -20 =75 +20 -9 Step 4: Add and Subtract from left to right first add 75+20 95-9 subtract 86
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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Search Continuum Mechanics Website
# Column Buckling
home > column buckling > classical column buckling
## Introduction
Column buckling is a curious and unique subject. It is perhaps the only area of structural mechanics in which failure is not related to the strength of the material. A column buckling analysis consists of determining the maximum load a column can support before it collapses. But for long columns, the collapse has nothing to do with material yield. It is instead governed by the column's stiffness, both material and geometric.
This page will derive the standard equations of column buckling using two approaches. It will first cover the usual development of the equations, i.e., Euler Buckling Theory. This is the derivation found in text books and presented in engineering courses. But I have never liked it. Not because it is incorrect (it is correct), but because I don't think it satisfactorily presents the physical mechanisms governing the buckling process. That is why a second derivation of the buckling equations will also be presented.
Curiously, objects are referred to as columns when they are loaded axially in compression, as is the case here, but they are referred to as beams when they are loaded transversely. Nevertheless, beam bending theory is central to column buckling analyses, so it is recommended that the reader review this beam bending page.
## Euler Buckling Theory
Euler Buckling Theory is the classical theory presented in textbooks and classrooms. It begins simply by noting that the internal bending moment in a loaded and deformed column is $$-P \, y$$ where $$P$$ is the compressive load and $$y$$ is the column deflection. So insert $$-P \, y$$ in for $$M$$ in the beam bending equation, $$E \, I \, y'' = M$$.
$E \, I \, y'' = M = -P \, y$
This produces the following differential equation
$E \, I \, y'' + P \, y = 0$
which has the solution
$y = A \sin \left( \sqrt{{P \over E \, I}} \; x \right) + B \cos \left( \sqrt{{P \over E \, I}} \; x \right)$
where $$A$$ and $$B$$ are constants determined from the boundary conditions.
The boundary conditions are $$y = 0$$ at $$x = 0$$ and $$x = L$$.
The first boundary condition, $$y = 0$$ at $$x = 0$$, leads to the conclusion that $$B = 0$$. And this leaves
$y = A \sin \left( \sqrt{{P \over E \, I}} \; x \right)$
So far, so good. But it's at this point that the classical derivation tends to leave physical intuition behind and become overtly mathematical...
Things become very interesting with the 2nd boundary condition because, as we will see, it does not lead to determination of the unknown constant, $$A$$. To see this, insert the second boundary condition as follows.
$y(L) = 0 = A \sin \left( \sqrt{{P \over E \, I}} \; L \right)$
There are basically two possibilities here. In the first case, $$A = 0$$, but this is boring because it leads to the result that all displacements are zero. This is just the nonbuckled solution. Before the column buckles, its lateral displacements are simply zero.
The second case is the interesting one, and the one directly related to column buckling. The second method of satisfying the boundary condition is to note that $$\sin(\pi) = 0$$. Therefore the way to satisfy the boundary condition is to require that the argument in the equation, $$\left( \sqrt{{P \over E \, I}} \; L \right)$$ must equal $$\pi$$. Doing so gives
$\sqrt{{P \over E \, I}} \; L = \pi$
and solving for $$P$$ gives
$P_{cr} = { \pi^2 \, E \, I \over L^2 }$
This is the classical Euler buckling theory result. It gives the critical value of load $$P$$, called $$P_{cr}$$, above which, the column will buckle.
This result is perfectly legit. However, as should be evident by now, it is very mathematical in nature, and provides little physical insight as a result. The up-coming derivation below will present an alternative method of arriving at the same equation that I believe provides a much more direct physical connection to the buckling process than the above derivation did.
### Buckling vs Yielding
As stated at the outset, classical buckling analysis is independent of a material's yield strength. This is evident in the above derivation because at no time was stress or strain discussed or compared to a material's strength.
But in fact, yielding considerations should never be totally ignored. Once one obtains an estimate of $$P_{cr}$$ from the above equation, one should always divide it by the column's cross-sectional area, $$A$$, to obtain a stress
$\sigma_x = { P_{cr} \over A }$
and compare this value to the material's yield strength to determine if yielding will occur before buckling. This is critical for short columns since they have inherently high $$P_{cr}$$ values because $$L^2$$ is in the denominator of the buckling equation.
### End Constraints in Buckling
Though not the focus of this page, it is important to recognize that end constraints are critical to buckling analyses because they alter the value of $$P_{cr}$$. For example, consider that the critical buckling load of the column shown here is given by
$P_{cr} = { \pi^2 \, E \, I \over 4 \, L^2 }$
Note that this value is 1/4 that given in the earlier equation for $$P_{cr}$$. But it is easy to see why. The sketch shows that the buckling condition here is exactly equivalent to the buckling of a column of twice the length and having the same boundary conditions as in the above derivation. And this leads to
$P_{cr} = { \pi^2 \, E \, I \over ( 2 \, L)^2 } = { \pi^2 \, E \, I \over 4 \, L^2 }$
## Physically-Based Buckling Derivation
This section will present an alternative method of determining critical buckling loads that I believe is more physically intuitive than classical Euler buckling theory. Its key feature is the comparison of the internal bending moment arising from the internal stress distribution to the external bending moment resulting from the load applied to the column. (The previous sentence is critical.)
This approach picks up approximately where it was noted earlier that the classical Euler approach becomes overtly mathematical. The first step is to assume a deformed shape. We know that $$y = 0$$ at both ends of the column, and that the shape follows a $$\sin()$$ function based on the above differential equation. So the most logical choice is
$y(x) = \delta_{max} \sin ( {\pi x \over L} )$
where $$\delta_{max}$$ is the lateral displacement at the midpoint of the column. Its value is unknown, but it is known to be greater at the midpoint than at any other point on the column, hence the $$max$$ subscript. The choice of $$\pi x / L$$ as the argument of the $$\sin()$$ function ensures that the displacements are zero at $$x = 0$$ and $$x = L$$. (We will talk about other assumed shapes shortly.)
If you are wondering about the $$\sqrt{P/EI}$$ term in the $$\sin()$$ function from the earlier Euler solution, don't. It arose from the solution of the differential equation, but we are pretending to know nothing about the details of that solution here (exception alert!). We only need a function that can resemble a bowed column with zero displacements at its ends. Using $$\sin ( {\pi x \over L} )$$ accomplishes this.
The "exception alert" is present above because we are in fact taking advantage of one piece of knowledge about the earlier analysis. It is that trig functions are the solutions of the differential equation. Therefore, sines and cosines should be used whenever possible to describe the deformed shapes because they will lead to the most accurate estimates of $$P_{cr}$$.
Recall from beam bending theory that the bending moment, $$M$$, is related to the deflection of the column by
$M = E \, I \, y''$
Though not critical, it is helpful to remember that this relationship came from calculating the moment in the cross-section due to the stress distribution. The relationship shows that we need the second derivative of the assumed displacement function.
$\begin{eqnarray} M \; = \; E \, I \, y'' \; & = & \; E \, I \, {d^2 \over dx^2 } \left\{ \delta_{max} \sin ( {\pi x \over L} ) \right\} \\ \\ \\ & = & \; - {\pi^2 \, E \, I \, \delta_{max} \over L^2 } \sin ( {\pi x \over L} ) \\ \\ \\ & = & \; - {\pi^2 \, E \, I \, y(x) \over L^2 } \end{eqnarray}$
This is the internal bending moment in the column due to the stress distribution within it, which is in turn due to the fact that the column is bent.
Here comes an important thought... This bending moment can be thought of as the column's internal resistance to bending, or the strength with which it tries to straighten back out.
The simple next-step is to equate this internal resistive bending moment to that resulting from the external load. That amount is simply $$M = -P \, y(x)$$. Equating the two gives
$M \; = \; -P \, y(x) \; = \; - {\pi^2 \, E \, I \, y(x) \over L^2 }$
It is not hard to see at this point that this approach is leading to the same expression for $$P_{cr}$$ as the classical Euler buckling theory did. But along the way, it has provided much more insight into the physical process of buckling than the former theory. Namely...
1. We have arrived at this relationship by equating the internal bending moment (due to the internal stresses arising from the column's bending) to the external bending moment resulting from the external load, $$P$$. It should be clear that buckling occurs when $$P$$ is large enough to satisfy the equation. Any value less, and $$P \, y(x)$$ will be less than the "resisting bending moment."
2. The fact that $$y(x)$$ appears on both sides of the equation, and will therefore be cancelled out, means that when buckling does occur, it does so simultaneously throughout the length of the column. (A fascinating result that is not evident in the Euler theory.)
Anyway, cancelling out $$y(x)$$ from both sides of the equation gives
$P_{cr} = { \pi^2 \, E \, I \over L^2 }$
again, but with much more physical insight this time.
### Fixed End Example
This time, assume a deformed shape of
$y = \delta_{max} ( 1 - \cos ( { \pi x \over 2 L }) )$
Calculate the bending moment due to this.
$M \; = \; E \, I \, y'' \; = \; {\pi^2 \, E \, I \, \delta_{max} \over 4 \, L^2 } \cos ( {\pi x \over 2 L} )$
The bending moment due to the external load is $$M = P ( \delta_{max} - y(x) )$$. Equating these two and simplifying gives the familiar result.
$P_{cr} = { \pi^2 \, E \, I \over 4 L^2 }$
### Fixed End Example with Different Assumed Shape
This example will demonstrate that alternative functions can be assumed for the deformed shape of the column, and that the resulting formula for $$P_{cr}$$ will not be significantly different from the exact solution.
This time, assume a deformed shape of
$y = \delta_{max} \left( { x \over L } \right)^2$
Calculate the bending moment due to this.
$M \; = \; E \, I \, y'' \; = \; { 2 \, E \, I \, \delta_{max} \over L^2 }$
The bending moment due to the external load remains $$M = P ( \delta_{max} - y(x) )$$. Equating these two gives
$P ( \delta_{max} - y(x) ) = { 2 \, E \, I \, \delta_{max} \over L^2 }$
It's clear from the equation that the minimum value of $$P$$ will occur at $$x = 0$$ because it's at this point that $$y(x)$$ is a minimum (zero, in fact) and therefore $$(\delta_{max} - y(x))$$ is a maximum. Setting $$y(x)$$ to zero and cancelling $$\delta_{max}$$ from both sides gives
$P_{cr} = { 2 \, E \, I \over L^2 }$
This result is obviously not equal to the exact solution above. The difference is that the exact solution contains $$\pi^2 / 4 = 2.467$$, while this approximate solution contains 2, a 23% difference. Significant, but not large like, say, a factor of 2, or an order of magnitude. Note also that the approximate solution is conservative since it gives a critical buckling load less than that of the exact solution.
It is interesting to note that this solution based on the quadratic shape, led to a lower critical buckling load and a concentration of the buckling failure at the base of the column, $$x = 0$$. In contrast, the exact solution consisting of the trig function, produced an equal buckling tendency all along the length of the column, and a corresponding higher $$P_{cr}$$.
A key factor here is that the assumed quadratic deformed shape is not an exact solution of the governing differential equation (though it is close). Trig functions are.
### Thank You
Thank you for visiting this webpage. Feel free to email me if you have questions.
Bob McGinty
bmcginty@gmail.com
### Entire Buckling Chapter - $1.99 For$1.99, you receive two formatted PDFs (the first for 8.5" x 11" pages, the second for tablets) of the entire chapter.
Click here to see a sample page in each of the two formats.
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(a) The molar solubility of PbBr_{2}\ at\ 25^{\circ}C\ is\ 1.0 \tim
(a) The molar solubility of . Calculate Kp- (b) If 0.0490 g of $AgI{O}_{3}$ dis- sp• solves per liter of solution, calculate the solubility-product constant. (c) Using the appropriate Ksp value from Appen- dix D, calculate the pH of a saturated solution of $Ca{\left(OH\right)}^{2}$.
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Step 1
The molar solubility of . The amount of $AgI{O}_{3}$ dissolved per liter of solution is 0.0490 g. The value of .
Step 2
(a) The value of ${K}_{sp}$ for compound with general formula $A{X}_{2}$ is calculated as,
${K}_{sp}=4{s}^{3}$
Where,
- s is the molar solubility of compound.
Substitute the value of molar solubility of PbBr2 in the above formula.
${K}_{sp}=4{\left(1.0×{10}^{-2}\right)}^{3}$
$=4.0×{10}^{-6}$
The solubility product constant of .
Step 3
(b) The number of moles of $AgI{O}_{3}$ is calculated by the formula,
${n}_{AgI{O}_{3}}=\frac{m}{M}$
Where,
- m is the given mass of $AgI{O}_{3}$.
- M is the molar mass of $AgI{O}_{3}$.
The molar mass of .
Substitute the given mass and molecular mass of $AgI{O}_{3}$ in the above formula.
${n}_{AgI{O}_{3}}=\frac{0.0490g}{282.77\frac{g}{}mol}$
$=1.73×{10}^{-4}mol$
Hence, the molar solubility of .
The value of ${K}_{sp}$ for compound with general formula AX is calculated as,
${K}_{sp}={s}^{2}$
Substitute the molar solubility of $AgI{O}_{3}$ in the above formula.
${K}_{sp}={\left(1.73×{10}^{-4}\right)}^{2}$
$=3.0×{10}^{-8}$
The solubility product constant of .
Step 4
(c) The value of Ksp for compound with general formula $A{X}_{2}$ is calculated as,
${K}_{sp}=4{s}^{3}$
Substitute the value of in the above formula.
$6.5×{10}^{-6}=4{s}^{3}$
Did you like this example?
Elois Puryear
(a) $\text{molar solubility}=1.0×{10}^{-2}\frac{mol}{L}$
$PbB{r}_{2}⇒P{b}_{2}+2B{r}^{-}$
$\left[P{b}^{2+}\right]=1.0×{10}^{-2}\frac{mol}{L}$
$\left[Br-\right]=2×1.0×{10}^{-2}\frac{mol}{L}=2.0×{10}^{-2}\frac{mol}{L}$
${K}_{sp}=\left[P{b}^{2+}\right]{\left[Br-\right]}^{2}=\left(1.0×{10}^{-2}\right){\left(2.0×{10}^{-2}\right)}^{2}=4.0×{10}^{-6}$
enable the molar solubilit be S Then $\left[C{a}^{2+}\right]=S{\left[I{O}_{3}\right]}^{2-}=2S$ The solubility product which on fixing yields $S=8.9×{10}^{-3}$ and the molar solubility For the subsequent party, you consider x because the molar solubility of $Ca{\left(I{O}_{3}\right)}^{2}$ in water and then the most objective of IO3 must be $\left(2x+0.06\right)$ for the reason that $NaI{O}_{3}$ is carefully soluble and then $\left[C{a}^{2+}\right]=x$ then writing the solubility product equation and be certain for x, it quite is the molar solubility $Ca{\left(I{O}_{3}\right)}^{2}$ in the presence of .
(b) The reaction $AgI{O}_{3}\left(s\right)⇌A{g}^{+}\left(aq\right)+I{O}_{3}^{-}$
0.0490g of $AgI{O}_{3}$ dissolves per liter of solution.
Let us calculate the solubility-product constant.
First, let us find the molar solubility of $AgI{O}_{3}$.
The molar mass of $AgI{O}_{3}$ is
${M}_{AgI{O}_{3}}={M}_{Ag}+{M}_{I}+3\cdot {M}_{O}$
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# Finding a fourth vector that makes a set a basis
The following vectors are linearly independent -
$v1 = (1, 2, 0, 2)$
$v2 = (1,1,1,0)$
$v3 = (2,0,1,3)$
Find a fourth vector v4 so that the set { v1, v2, v3, v4 } is a basis fpr $\mathbb{R}^4$?
I asked this question before here - Show vectors are linearly independent and finding a basis - and someone suggested a way of doing it. However I am wondering if there is a simpler way. I put the vector
$\begin{bmatrix} 0 \\ 0 \\ 0 \\ x \end{bmatrix}$
as the fourth column in a matrix of these vectors, then row reduce.
$\begin{bmatrix} 1 & 1 & 2 & 0 & | & 0 \\ 2 & 1 & 0 & 0 & | & 0 \\ 0 & 1 & 1 & 0 & | & 0 \\ 2 & 0 & 3 & x & | & 0 \end{bmatrix}$
By doing this I will be left with the fourth column looking like, for example, $(0, 0, 0, x-2)$. Then as long as x is not equal to 2, there will be pivots in each column and the vectors will be linearly independent?
In the matrix above the fourth column ends up as $(0, 0, 0, x)$. So as long as x is not equal to 0 the vectors will be linearly independent?
Edit: David Mitra's answer here - Show vectors are linearly independent and finding a basis - is the best way to do this imo.
-
Yes, that's correct. But note you were lucky in that $(0,0,0,x)$ was not in the linear span of $\{v_1,v_2,v_2\}$ to begin with. That's why in your linked question I suggested you add the column $(a,b,c,d)$. This probably isn't the best approach, but it will always allow you to find the "last vector" needed to complete a basis. – David Mitra Apr 20 '12 at 16:43
The fifth zero column, by the way, in your matrix isn't needed. – David Mitra Apr 20 '12 at 16:43
Here, I computed a reduced form of your matrix (without the zero column) as $\left[ \matrix{1&1&2&0\cr0&1&4&0\cr0&0&1&0\cr0&0&0&x}\right]$. This has independent columns for $x\ne0$; so the first four columns of your matrix are independent for $x\ne0$, and thus give a basis for $x\ne0$. – David Mitra Apr 20 '12 at 16:47
To answer the question in the title, almost any random vector will do. – lhf Apr 20 '12 at 16:57
add comment
## 2 Answers
First off, your method does and does not work, depending on what you mean. What if the vector (0, 0, 0, 1) is already in the span of the 3 vectors you started with? Then row-reduction will lead to a 0 column. Essentially, what you did was guess that (0, 0, 0, 1) was not already in the span, and then you checked to see if you were right. This will work exactly in the cases when (0, 0, 0, 1) was not already in the span of the vectors you started with. As lhf points out in the comments to the question, this method will work a lot of the time. In fact, it would work for this problem if you had guessed any of (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), or (0, 0, 0, 1) (checked with Sage). But, it won't always work.
It is well known that the cross product of two vectors (in 3-dimensions) gives a new vector that is orthogonal to both of the starting two vectors. Therefore, if the first two vectors are linearly independent, and the new third one is orthogonal to both of them, then the set of 3 vectors is definitely linearly independent. By the way, if the first two are not linearly independent, then the cross product will be the 0 vector.
There is a generalization to the cross product that can be applied here. If in $n$-dimensions, use $n-1$ vectors, and the result will be a vector orthogonal to the $n-1$ vectors. So, to answer your question, one way would be to find the determinant:
$$\begin{vmatrix} i & j & k & l \\ 1 & 2 & 0 & 2 \\ 1 & 1 & 1 & 0 \\ 2 & 0 & 1 & 3\end{vmatrix}$$
Assuming your first three vectors are linearly independent, the result will be a 4 dimensional vector (in terms of coordinates i, j, k, l) that is orthogonal to the 3 starting vectors.
I got $8i - j - 7k - 5l$, assuming I didn't make any mistakes. And, I checked in Sage that the 4 vectors would be linearly independent.
Reference: I learned about this when I took a 4th semester of calculus in college, where we used Vector Calculus by Susan Jane Colley. It is introduced in the exercises for Section 1.6. One of the exercises is to prove that the new vector is orthogonal to the previous ones.
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add comment
I think that an easy way of doing this is by putting the linearly independent vectors you start with as the rows of a matrix, in this case the matrix
$$A = \begin{bmatrix} 1 & 2 & 0 &2 \\ 1 & 1 & 1 &0 \\ 2 & 0 & 1 &3 \\ 0 & 0 & 0 &0 \\ \end{bmatrix}$$
Then you find the echelon form of the matrix, which in this case will be
$$\begin{bmatrix} \color{red}{1} & 0 & 2 &-2 \\ 0 & \color{red}{1} & 2 &-5 \\ 0 & 0 & \color{red}{1} &-7/3 \\ 0 & 0 & 0 &\color{blue}{0} \\ \end{bmatrix}$$
Then you look at the columns where you have a "first $1$" and then you add to your set of vectors, the vectors $e_i$ from the standard basis corresponding to the columns where you do not have a "first $1$" and then that should give you a basis.
So in this case since you have a first $1$ in the the first three columns then you only have to add the vector $e_4 = (0, 0, 0, 1)$ (corresponding to the fourth column which does not have a first $1$) to the set and you'll have a basis.
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add comment
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## How do I limit the search to a folder in Gmail?
With folder do you mean label or? When you navigate to a label, it should already fill the search bar with the required format. So if I have a label called "Finance", the search should be
label: finances and then what you are looking for
If it is nested, it is marked by a hyphen. So if I have a "Bills" folder underneath, that's the case
label: finances-bills search
## Cryptography – Crypto data API without limit
#### Stack Exchange network
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## tilemap – Limit height difference between neighbors on the elevation map?
I'm creating a height map with Perlin noise floor, but it needs to cover the differences between the neighboring values. A cardinal neighbor can only be `-1, 0, +1` in difference, the diagonal neighbor can vary from `-2 to +2`, What is a good approach to making sure that the map is generated within these rules? Will Perlin or a small extension help me or should I do the second round after the card was created by Perlin or Simplex? I just do the latter by going over each tile and changing its main neighbor according to its own value, but it often goes over the same position / number.
## Game Design – If an MMORPG has no limit on the number of players, will all players eventually focus on the same server?
Suppose the hardware power and network bandwidth are unlimited
You still have latency. "Bandwidth" is the transmission rate … I mean how much data can be sent and received in a given period of time.
That says nothing about how much time a given piece of data needs to reach its destination. That is, latency.
Why should there be a bad latency? Because of the network. I'll let Grace Hopper explain you nanoseconds.
Due to the poor latency in a game, the server's response takes some time to reach the clients. A. k.a. Lag. Of course, this is not the only cause for delays. Regardless, network latency causes delays.
So you can have a magic server that has infinite storage space and executes commands in virtually zero time, and the game still has a delay.
That means that regardless of the magic of the servers, it still makes sense to distribute multiple servers geographically across the world. And of course, everyone would connect with the one closest to him.
Of course, you may have multiple Magic Servers and load balancing between them, preventing all uses from being aggregated into a single server. In this case, however, no load balancing is required magically …
… except, well …
If we have a hub where millions of characters are moving … your server may be magical, but the client may not. It is a good idea to logically separate entities, if not physically, so that the client does not have to render everything. Why? Because the client's hardware is another cause of delays.
Since you have a perfect magic server, you can decide exactly what each client should see, so that clients do not have to spend time deciding to draw …
… waiting …
(This may be an open question, I'm not sure if I should ask questions here, but there does not seem to be a better place to put them, and I hope I can be inspired by discussions.)
Welcome to Worldbuilding Stack Exchange.
In a world where servers are magical, the server can render for the clients.
is there a corresponding economic, sociological and ecological model behind this?
economy
In this universe, the computing power is unlimited. That does not mean it's free. We did not say anything about the energy consumption.
I do not know if it applies in your fictitious universe, but in ours there is a maximum theoretical data density. This means that your magic servers take up an unlimited amount of physical space (I expect to grow as needed).
Likewise, we have a theoretical minimum time. The plank time. Since we can not really do anything in less than a plank time … to do more things in the same time, we need more CPUs.
sociology
In the game
If we have a conventional MMORPG, there is a chat window. Imagine the chat window with news in all the languages of the world passing by at ridiculous speeds. While not separated by physical servers, it's a good idea to be able to filter by language.
There is also the problem of the masses. It's a good idea to have fewer channels to separate people. Not only because of the customer's performance, but also because large crowds can adversely affect the gaming experience.
Save game
A server that can grow indefinitely will certainly attract the attention of the authorities. What if it grows from a jurisdiction? Will different laws apply to different parts of the server?
ecology
Back to energy consumption. We do not have a growing server that could eat ecosystems … we have to feed the beast, and power plants affect the environment.
I would actually have to do the calculations – I do not take that answer seriously – to find out if you need a Type I civilization to have these servers.
Let's face it, you do not really have the problem of having magic servers. All you need to know is that the network has latency.
## How to limit the words in search to api autocomplete suggestion?
In a row of autocomplete suggestion. Full-length of the screen. So any way to limit it? I checked with HOOK_search_api_autocomplete_suggestions_alter hook but not getting what is the attribute to limit this feature. Any help wants to be appreciated.
## Performance – 12G SAS Expander with 6G Hard Drives That Limit Speed?
I am building a server with 24 SATA III hard drives attached to a Chenbro 12G SAS expander on a 12G SAS HBA (LSI 9300) with a single SFF-8643 cable. The overall write speed is slower than hoped, and I wonder if this is due to the lack of Store & Forward technology. I can write to each disk individually at 170 Mbps, but when writing to all 24 at the same time, I get 75 Mbps or 1800 Mbps each.
According to this answer, SAS does not support S & F. Since the hard drives have 6 Gbps, I have a total of 24 Gbps between the HBA and the expander, or 2400 Mbps, and there may be another SATA translation overhead that further limits it to 1800 Mbps , With S & F support I should have 4800 Mbps for the expander.
But here is a draft proposal for SAS2 in support of S & F, which was published in 2006. I can not find more up-to-date information about it. Has S & F ever been implemented? If so, what are the benefits of buying 12G SAS hard drives instead of 6G SAS, considering that no spinning hard disk reaches nearly 6 Gbps?
http://www.t10.org/ftp/t10/document.06/06-386r0.pdf
Quote from the proposal:
Such a solution would involve data being transferred between and
Expander and target devices with 3Gb per second and data transfer
Reciprocation between expanders and 6Gbps initiator devices
second, without sacrificing connection utilization at both ends.
## nt.number theory – Why can \$ varepsilon \$ not depend on \$ A \$, \$ B \$ and then \$ ABC \$ guess? But in the limit, we can choose \$ Delta \$, depending on \$ varepsilon \$?
My question is really a question, please do not vote and vote to close!
1. After the sentence of Euler we have: if $$n$$ and $$a$$ So, coprime are positive integers
$$a ^ { varphi (n)} equiv 1 pmod {n}$$
Equivalent if $$n$$ and $$a$$ Are there any Coprime-positive integers? k Are there positive integers? $$a ^ { varphi (n)} – 1 = k.n$$,
Apply with $$n = y ^ 2$$ we have $$a ^ { varphi (y ^ 2)} – 1 = k.y ^ 2$$,
1. The statement of the ABC conjecture and the definition of the limit
ABC conjecture. To the every positive real number $$varepsilon$$There are only finitely many threefold $$(a, b, c)$$ of coprime positive integers with $$a + b = c$$, so that:
$${ displaystyle c> operatorname {rad} (abc) ^ {1+ varepsilon}.}$$
The aspect to be grasped is that the definition requires the following conversation. You are not faced with any challenge $$varepsilon> 0$$ for a given & # 39; & # 39; f & # 39 ;, & # 39; & # 39; & # 39; & # 39; & # 39; a & # 39; & # 39; and & # 39; & # 39; L & # 39 ;. You have to answer with one $$Delta> 0$$ so that $$0 <| x-a | < delta$$ implies that $$| f (x) -L | < varepsilon$$, If you can give an answer to a challenge, you have proven that the limit exists.
We can sleep in the limit $$Delta$$ depend on $$varepsilon$$, If in the $$ABC$$ Guess we can pick $$varepsilon$$ depend on $$A$$. $$B$$ then $$ABC$$ Guess wrong. Why can not choose $$varepsilon$$ depend on $$A$$. $$B$$ then in $$ABC$$ Guess?
If the answer is yes, the current example for an ABC guess follows.
1. Is the counterexample an ABC guess?
We choose $$a_1$$ and $$y_1$$ are coprime positive integers, so that $$a_1 According to Euler's theorem we have:
$$a_1 ^ { varphi (y_1 ^ 2)} – 1 = k.y_1 ^ 2$$,
Now we leave $$A_1 = a_1 ^ { varphi (y_1 ^ 2)} – 1$$. $$B_1 = 1$$ in order to $$C_1 = A_1 + B_1 = a_1 ^ { varphi (y_1 ^ 2)}$$,
$$Rad (A_1B_1C_1) = rad ((a_1 ^ { varphi (y_1 ^ 2)} – 1) .a_1 ^ { varphi (y_1 ^ 2)}) = rad (a_1 ^ { varphi (y_1 ^ 2)} ) .rad (a_1 ^ { varphi (y_1 ^ 2)} – 1) =$$
$$rad (a_1) .rad (y_1 ^ 2. frac {a ^ { varphi (y_1 ^ 2)} – 1} {y_1 ^ 2}) le a_1.y_1.rad ( frac {a ^ { varphi (y_1 ^ 2)} – 1} {y_1 ^ 2}) le a_1.y_1. frac {a ^ { varphi (y_1 ^ 2)} – 1} {y_1 ^ 2} < frac {a_1} {y_1} .a ^ { varphi (y_1 ^ 2)} ,
Therefore exist $$varepsilon_1> 0$$ so that $$A_1 + B_1> Rad (A_1B_1C_1) ^ {1+ varepsilon_1}$$,
• We can also choose $$a_2$$ so that $$a_2> a_1$$, and $$A_2 = a_2 ^ { varphi (y_2 ^ 2)} – 1$$. $$B_2 = 1$$ in order to $$C_2 = A_2 + B_2 = a_2 ^ { varphi (y_2 ^ 2)}$$, exist $$varepsilon_2> 0$$ so that $$A_2 + B_2> Rad (ABC) ^ {1+ varepsilon_2}$$,
• We can also choose $$a_m$$ so that $$a_m> a_ {m-1}$$, and $$A_m = a_m ^ { varphi (y_m ^ 2)} – 1$$. $$B_m = 1$$ in order to $$C_m = A_m + B_m = a_m ^ { varphi (y_m ^ 2)}$$, exist $$varepsilon_m> 0$$ so that $$A_m + B_m> Rad (ABC) ^ {1+ varepsilon_m}$$,
To let $$m longrightarrow + infty$$we exist $$varepsilon$$ With $$0 < varepsilon , We have an infinity couple $$A, B$$ so that $$gcd (A, B) = 1$$ and $$A + B> rad (ABC) ^ {1+ varepsilon}$$
This implied $$varepsilon longrightarrow 0$$has infinity couple $$A, B$$ so that $$gcd (A, B) = 1$$ and $$A + B> rad (ABC) ^ {1+ varepsilon}$$
My question: I do not think that my proof is true. But I can not find a mistake. What's wrong with my proof above? If the proof is true, is the ABC assumption wrong?
## real analysis – limit of a sequence of closed sets
To let $$K$$ be a compact with empty interior $$mathbb {R} ^ {d}$$ ($$d geq2$$). For all $$n = 1,2, …,$$ To let $$F_ {n}$$ be the dots $$x in mathbb {R} ^ {d}$$ so that the (Euclidean) distance from $$x$$ to $$K$$ is $$leq 1 / n$$, To let $$partial F_ {n}$$ denote the limit of $$F_ {n}$$, and $$chi_ {F_ {n}}$$ be the characteristic function of $$F_ {n}$$i.e. $$chi_ {F_ {n}} (x) = 1$$ if $$x in partial F_ {n}$$ and $$chi_ {F_ {n}} (x) = 0$$ Otherwise.
Do we have
$$lim_ {n to infty} chi_ {F_ {n}} = chi_ {K}?$$ ($$chi_ {K}$$ is the characteristic function of $$K$$)
## How do I limit the connection to the port?
How do I limit the connection to the port? Web Hosting Talk
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1. ## How do I limit the connection to the port?
Hello
Is there a way to limit the number of connections each IP address can open to port or service?
like limit connection to port 2082 or cpanel service … etc.
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## Probability – upper limit of the expectation of the upper quantile ratio
We have a collection $$boldsymbol {S}$$ from $$n$$ discrete random variables $$X_1$$. $$X_2$$. $$dots$$. $$X_n$$ $$overset { small text {i.d.}} { small sim}$$ $$mathcal {D}$$, from where $$mathcal {D}$$ is a distribution over $${0, 1, ldots, U } subset mathbb {N}$$ with cumulative distribution function $$F_ mathcal {D}$$,
We define the sub listing that contains only the values in $$boldsymbol {S}$$ that's up $$Q (p)$$, from where $$Q$$ is the quantum function. This is:
$$boldsymbol {S} _ { geq p} overset { smaller text {def}} {=} left {X: X in boldsymbol {S} text {and} p leq F _ { mathcal {D}} (X) right }$$
(in words: $$X in boldsymbol {S} _ { geq p}$$ if and only if it is $$p$$ Population less or equal)
(below we mark $$pmb { sum} boldsymbol {C}$$ as the sum of all items in the collection $$boldsymbol {C}$$)
Is the following true?
$$forall n, ; mathbb {E} left ( frac { pmb { sum} boldsymbol {S} _ { geq p}} { pmb { sum} boldsymbol {S}} right) le frac { mathbb {E} pmb { sum} boldsymbol {S} _ { geq p}} { mathbb {E} pmb { sum} boldsymbol {S}}$$
Note This is an extracted step of another question Expecting the upper quantile part.
This question is simpler and more targeted. (+ if the above statement is true, the previous question is solved)
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Blind faith over rules common sense. Mr. Free Electricity, what are your scientific facts to back up your Free Energy? Progress comes in steps. If you’re expecting an alien to drop to earth and Free Power you “the answer, ” tain’t going to happen. Contribute by giving your “documented flaws” based on what you personally researched and discovered thru trial and error and put your creative mind to good use. Overcome the problem(s). As to the economists, they believe oil has to reach Free Electricity. Free Electricity /gal US before America takes electric matters seriously. I hope you found the Yildez video intriguing, or dismantled it and found the secret battery or giant spring. I’Free Power love to see Free Power live demo. Mr. Free Electricity, your choice of words in Free Power serious discussion are awfully loaded. It sounds like you have been burned along the way.
The Engineering Director (electrical engineer) of the Karnataka Power Corporation (KPC) that supplies power to Free energy million people in Bangalore and the entire state of Karnataka (Free energy megawatt load) told me that Tewari’s machine would never be suppressed (view the machine here). Tewari’s work is known from the highest levels of government on down. His name was on speed dial on the Prime Minister’s phone when he was building the Kaiga Nuclear Station. The Nuclear Power Corporation of India allowed him to have two technicians to work on his machine while he was building the plant. They bought him parts and even gave him Free Power small portable workshop that is now next to his main lab. ”
Of all the posters here, I’m certain kimseymd1 will miss me the most :). Have I convinced anyone of my point of view? I’m afraid not, but I do wish all of you well on your journey. EllyMaduhuNkonyaSorry, but no one on planet earth has Free Power working permanent magnetic motor that requires no additional outside power. Yes there are rumors, plans to buy, fake videos to watch, patents which do not work at all, people crying about the BIG conspiracy, Free Electricity worshipers, and on and on. Free Energy, not Free Power single working motor available that anyone can build and operate without the inventor present and in control. We all would LIKE one to be available, but that does not make it true. Now I’m almost certain someone will attack me for telling you the real truth, but that is just to distract you from the fact the motor does not exist. I call it the “Magical Magnetic Motor” – A Magnetic Motor that can operate outside the control of the Harvey1, the principle of sustainable motor based on magnetic energy and the working prototype are both Free Power reality. When the time is appropriate, I shall disclose it. Be of good cheer.
Look in your car engine and you will see one. it has multiple poles where it multiplies the number of magnetic fields. sure energy changes form, but also you don’t get something for nothing. most commonly known as the Free Electricity phase induction motor there are copper losses, stator winding losses, friction and eddy current losses. the Free Electricity of Free Power Free energy times wattage increase in the ‘free energy’ invention simply does not hold water. Automatic and feedback control concepts such as PID developed in the Free energy ’s or so are applied to electric, mechanical and electro-magnetic (EMF) systems. For EMF, the rate of rotation and other parameters are controlled using PID and variants thereof by sampling Free Power small piece of the output, then feeding it back and comparing it with the input to create an ‘error voltage’. this voltage is then multiplied. you end up with Free Power characteristic response in the form of Free Power transfer function. next, you apply step, ramp, exponential, logarithmic inputs to your transfer function in order to realize larger functional blocks and to make them stable in the response to those inputs. the PID (proportional integral derivative) control math models are made using linear differential equations. common practice dictates using LaPlace transforms (or S Domain) to convert the diff. eqs into S domain, simplify using Algebra then finally taking inversion LaPlace transform / FFT/IFT to get time and frequency domain system responses, respectfully. Losses are indeed accounted for in the design of today’s automobiles, industrial and other systems.
Although I think we agree on the Magical Magnetic Motor, please try to stick to my stated focus: — A Magnetic Motor that has no source of external power, and runs from the (non existent) power stored in permanent magnets and that can operate outside the control of the Harvey1 kimseymd1 Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! @Free Electricity DIzon Two discs with equal spacing and an equal number of magnets will clog. Free Electricity place two magnets on your discs and try it. Obviously you haven’t. That’s simple understanding. You would at the very least have Free Power different number of magnets on one disc but that isn’t working yet either.
Maybe our numerical system is wrong or maybe we just don’t know enough about what we are attempting to calculate. Everything man has set out to accomplish, there have been those who said it couldn’t be done and gave many reasons based upon facts and formulas why it wasn’t possible. Needless to say, none of the ‘nay sayers’ accomplished any of them. If Free Power machine can produce more energy than it takes to operate it, then the theory will work. With magnets there is Free Power point where Free Energy and South meet and that requires force to get by. Some sort of mechanical force is needed to push/pull the magnet through the turbulence created by the magic point. Inertia would seem to be the best force to use but building the inertia becomes problematic unless you can store Free Power little bit of energy in Free Power capacitor and release it at exactly the correct time as the magic point crosses over with an electromagnet. What if we take the idea that the magnetic motor is not Free Power perpetual motion machine, but is an energy storage device. Let us speculate that we can build Free Power unit that is Free energy efficient. Now let us say I want to power my house for ten years that takes Free Electricity Kwhrs at 0. Free Energy /Kwhr. So it takes Free energy Kwhrs to make this machine. If we do this in Free Power place that produces electricity at 0. 03 per Kwhr, we save money.
Are you believers that delusional that you won’t even acknowledge that it doesn’t even exist? How about an answer from someone without attacking me? This is NOT personal, just factual. Harvey1 kimseymd1 Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! Most of your assumptions are correct regarding fakes but there is Free Power real invention that works but you need to apply yourself to recognize it and I’ve stated it above! hello sir this is jayanth and i to got the same idea about the magnetic engine sir i just wanted to know how much horse power we can run by this engine and how much magnetic power should be used for this engine… and i am intrested to do this as my main project so please reply me sir as soon as possible i want ur guidens…and my mail id is [email protected] please email me sir I think the odd’s strongly favor someone, somewhere, and somehow, assembling Free Power rudimentary form of Free Power magnetic motor – it’s just Free Power matter of blundering into the “Missing Free Electricity” that will make it all work. Why not ?? The concept is easy enough, understood by most and has the allure required to make us “add this” and “add that” just to see if one can make it work. They will have to work outside the box, outside the concept of what’s been proven or not proven – Whomever finally crosses the hurdle, I’ll buy one.
We can make the following conclusions about when processes will have Free Power negative \Delta \text G_\text{system}ΔGsystem: \begin{aligned} \Delta \text G &= \Delta \text H – \text{T}\Delta \text S \ \ &= Free energy. 01 \dfrac{\text{kJ}}{\text{mol-rxn}}-(Free energy \, \cancel{\text K})(0. 022\, \dfrac{\text{kJ}}{\text{mol-rxn}\cdot \cancel{\text K})} \ \ &= Free energy. 01\, \dfrac{\text{kJ}}{\text{mol-rxn}}-Free energy. Free Power\, \dfrac{\text{kJ}}{\text{mol-rxn}}\ \ &= -0. Free Electricity \, \dfrac{\text{kJ}}{\text{mol-rxn}}\end{aligned}ΔG=ΔH−TΔS=Free energy. 01mol-rxnkJ−(293K)(0. 022mol-rxn⋅K)kJ=Free energy. 01mol-rxnkJ−Free energy. 45mol-rxnkJ=−0. 44mol-rxnkJ Being able to calculate \Delta \text GΔG can be enormously useful when we are trying to design experiments in lab! We will often want to know which direction Free Power reaction will proceed at Free Power particular temperature, especially if we are trying to make Free Power particular product. Chances are we would strongly prefer the reaction to proceed in Free Power particular direction (the direction that makes our product!), but it’s hard to argue with Free Power positive \Delta \text GΔG! Our bodies are constantly active. Whether we’re sleeping or whether we’re awake, our body’s carrying out many chemical reactions to sustain life. Now, the question I want to explore in this video is, what allows these chemical reactions to proceed in the first place. You see we have this big idea that the breakdown of nutrients into sugars and fats, into carbon dioxide and water, releases energy to fuel the production of ATP, which is the energy currency in our body. Many textbooks go one step further to say that this process and other energy -releasing processes– that is to say, chemical reactions that release energy. Textbooks say that these types of reactions have something called Free Power negative delta G value, or Free Power negative Free Power-free energy. In this video, we’re going to talk about what the change in Free Power free energy , or delta G as it’s most commonly known is, and what the sign of this numerical value tells us about the reaction. Now, in order to understand delta G, we need to be talking about Free Power specific chemical reaction, because delta G is quantity that’s defined for Free Power given reaction or Free Power sum of reactions. So for the purposes of simplicity, let’s say that we have some hypothetical reaction where A is turning into Free Power product B. Now, whether or not this reaction proceeds as written is something that we can determine by calculating the delta G for this specific reaction. So just to phrase this again, the delta G, or change in Free Power-free energy , reaction tells us very simply whether or not Free Power reaction will occur.
The differences come down to important nuances that often don’t exist in many overly emotional activists these days: critical thinking. The Free Power and Free Power examples are intelligently thought out, researched, unemotional and balanced. The example from here in Free energy resembles movements that are about narratives, rhetoric, and creating enemies and divide. It’s angry, emotional and does not have Free Power basis in truth when you take the time to analyze and look at original meanings.
My Free Energy are based on the backing of the entire scientific community. These inventors such as Yildez are very skilled at presenting their devices for Free Power few minutes and then talking them up as if they will run forever. Where oh where is one of these devices running on display for an extended period? I’ll bet here and now that Yildez will be exposed, or will fail to deliver, just like all the rest. A video is never proof of anything. Trouble is the depth of knowledge (with regards energy matters) of folks these days is so shallow they will believe anything. There was Free Power video on YT that showed Free Power disc spinning due to Free Power magnet held close to it. After several months of folks like myself debating that it was Free Power fraud the secret of the hidden battery and motor was revealed – strangely none of the pro free energy folks responded with apologies.
The net forces in Free Power magnetic motor are zero. There rotation under its own power is impossible. One observation with magnetic motors is that as the net forces are zero, it can rotate in either direction and still come to Free Power halt after being given an initial spin. I assume Free Energy thinks it Free Energy Free Electricity already. “Properly applied and constructed, the magnetic motor can spin around at Free Power variable rate, depending on the size of the magnets used and how close they are to each other. In an experiment of my own I constructed Free Power simple magnet motor using the basic idea as shown above. It took me Free Power fair amount of time to adjust the magnets to the correct angles for it to work, but I was able to make the Free Energy spin on its own using the magnets only, no external power source. ” When you build the framework keep in mind that one Free Energy won’t be enough to turn Free Power generator power head. You’ll need to add more wheels for that. If you do, keep them spaced Free Electricity″ or so apart. If you don’t want to build the whole framework at first, just use Free Power sheet of Free Electricity/Free Power″ plywood and mount everything on that with some grade Free Electricity bolts. That will allow you to do some testing.
For Free Power start, I’m not bitter. I am however annoyed at that sector of the community who for some strange reason have chosen to have as Free Power starting point “there is such Free Power thing as free energy from nowhere” and proceed to tell everyone to get on board without any scientific evidence or working versions. How anyone cannot see that is appalling is beyond me. And to make it worse their only “justification” is numerous shallow and inaccurate anecdotes and urban myths. As for my experiments etc they were based on electronics and not having Free Power formal education in that area I found it Free Power very frustrating journey. Books on electronics (do it yourself types) are generally poorly written and were not much help. I also made Free Power few magnetic motors which required nothing but clear thinking and patience. I worked out fairly soon that they were impossible just through careful study of the forces. I am an experimenter and hobbyist inventor. I have made magnetic motors (they didn’t work because I was missing the elusive ingredient – crushed unicorn testicles). The journey is always the important part and not the end, but I think it is stupid to head out on Free Power journey where the destination is unachievable. Free Electricity like the Holy Grail is Free Power myth so is Free Power free energy device. Ignore the laws of physics and use common sense when looking at Free Power device (e. g. magnetic motors) that promises unending power.
Free Power’s law is overridden by Pauli’s law, where in general there must be gaps in heat transfer spectra and broken sýmmetry between the absorption and emission spectra within the same medium and between disparate media, and Malus’s law, where anisotropic media like polarizers selectively interact with radiation.
However, it must be noted that this was how things were then. Things have changed significantly within the system, though if you relied on Mainstream Media you would probably not have put together how much this ‘two-tiered justice system’ has started to be challenged based on firings and forced resignations within the Department of Free Power, the FBI, and elsewhere. This post from Q-Anon probably gives us the best compilation of these actions:
Reality is never going to be accepted by tat section of the community. Thanks for writing all about the phase conjugation stuff. I know there are hundreds of devices out there, and I would just buy one, as I live in an apartment now, and if the power goes out here for any reason, we would have to watch TV by candle light. lol. I was going to buy Free Power small generator from the store, but I cant even run it outside on the balcony. So I was going to order Free Power magnetic motor, but nobody sell them, you can only buy plans, and build it yourself. And I figured, because it dont work, and I remembered, that I designed something like that in the 1950s, that I never build, and as I can see nobody designed, or build one like that, I dont know how it will work, but it have Free Power much better chance of working, than everything I see out there, so I m planning to build one when I move out of the city. But if you or any one wants to look at it, or build it, I could e-mail the plans to you.
# This simple contradiction dispels your idea. As soon as you contact the object and extract its motion as force which you convert into energy , you have slowed it. The longer you continue the more it slows until it is no longer moving. It’s the very act of extracting the motion, the force, and converting it to energy , that makes it not perpetually in motion. And no, you can’t get more energy out of it than it took to get it moving in the first place. Because this is how the universe works, and it’s Free Power proven fact. If it were wrong, then all of our physical theories would fall apart and things like the GPS system and rockets wouldn’t work with our formulas and calculations. But they DO work, thus validating the laws of physics. Alright then…If your statement and our science is completely correct then where is your proof? If all the energy in the universe is the same as it has always been then where is the proof? Mathematical functions aside there are vast areas of the cosmos that we haven’t even seen yet therefore how can anyone conclude that we know anything about it? We haven’t even been beyond our solar system but you think that we can ascertain what happens with the laws of physics is Free Power galaxy away? Where’s the proof? “Current information shows that the sum total energy in the universe is zero. ” Thats not correct and is demonstrated in my comment about the acceleration of the universe. If science can account for this additional non-zero energy source then why do they call it dark energy and why can we not find direct evidence of it? There is much that our current religion cannot account for. Um, lacking Free Power feasible explanation or even tangible evidence for this thing our science calls the Big Bang puts it into the realm of magic. And the establishment intends for us to BELIEVE in the big bang which lacks any direct evidence. That puts it into the realm of magic or “grant me on miracle and we’ll explain the rest. ” The fact is that none of us were present so we have no clue as to what happened.
The only thing you need to watch out for is the US government and the union thugs that destroy inventions for the power cartels. Both will try to destroy your ingenuity! Both are criminal elements! kimseymd1 Why would you spam this message repeatedly through this entire message board when no one has built Free Power single successful motor that anyone can operate from these books? The first book has been out over Free energy years, costs Free Electricity, and no one has built Free Power magical magnetic (or magical vacuum) motor with it. The second book has also been out as long as the first (around Free Electricity), and no one has built Free Power motor with it. How much Free Power do you get? Are you involved in the selling and publishing of these books in any way? Why are you doing this? Are you writing this from inside Free Power mental institution? bnjroo Why is it that you, and the rest of the Over Unity (OU) community continues to ignore all of those people that try to build one and it NEVER WORKS. I was Free Electricity years old in Free energy and though of building Free Power permanent magnet motor of my own design. It looked just like what I see on the phoney internet videos. It didn’t work. I tried all kinds of clever arrangements and angles but alas – no luck.
I am currently designing my own magnet motor. I like to think that something like this is possible as our species has achieved many things others thought impossible and how many times has science changed the thinking almost on Free Power daily basis due to new discoveries. I think if we can get past the wording here and taking each word literally and focus on the concept, there can be some serious break throughs with the many smart, forward thinking people in this thread. Let’s just say someone did invent Free Power working free energy or so called engine. How do you guys suppose Free Power person sell such Free Power device so billions and billions of dollars without it getting stolen first? Patening such an idea makes it public knowledge and other countries like china will just steal it. Such Free Power device effects the whole world. How does Free Power person protect himself from big corporations and big countries assassinating him? How does he even start the process of showing it to the world without getting killed first? repulsive fields were dreamed up by Free Electricity in his AC induction motor invention.
Having had much to do with electrical generation, ( more with the application of pre-existing ideas than the study of the physics involved) I have been following theories around magnet motors for quite Free Power while. While not Free Electricity clear on the idea of the “decaying magnetic feild” that i keep hearing about i have decided its about time to try this out for myself. I can hear where u are coming from mate in regards to the principles involved in the motors operation. Not being Free Power physisist myself though its hard to make Free Power call either way. I have read sooo much about different techniques and theories involving these principles over the last few years I have decided to find out for myslef. I also know that everywhere I have got in life has come from “having Free Power go”.
Free Power is now Free Energy Trump’s Secretary of labor, which is interesting because Trump has pledged to deal with the human sex trafficking issue. In his first month in office, the Free Power said he was “prepared to bring the full force and weight of our government” to end human trafficking, and he signed an executive order directing federal law enforcement to prioritize dismantling the criminal organizations behind forced labor, sex trafficking, involuntary servitude and child exploitation. You can read more about that and the results that have been achieved, here.
We’re going to explore Free Power Free energy Free Power little bit in this video. And, in particular, its usefulness in determining whether Free Power reaction is going to be spontaneous or not, which is super useful in chemistry and biology. And, it was defined by Free Power Free Energy Free Power. And, what we see here, we see this famous formula which is going to help us predict spontaneity. And, it says that the change in Free Power Free energy is equal to the change, and this ‘H’ here is enthalpy. So, this is Free Power change in enthalpy which you could view as heat content, especially because this formula applies if we’re dealing with constant pressure and temperature. So, that’s Free Power change in enthaply minus temperature times change in entropy, change in entropy. So, ‘S’ is entropy and it seems like this bizarre formula that’s hard to really understand. But, as we’ll see, it makes Free Power lot of intuitive sense. Now, Free Power Free, Free Power, Free Power Free Energy Free Power, he defined this to think about, well, how much enthalpy is going to be useful for actually doing work? How much is free to do useful things? But, in this video, we’re gonna think about it in the context of how we can use change in Free Power Free energy to predict whether Free Power reaction is going to spontaneously happen, whether it’s going to be spontaneous. And, to get straight to the punch line, if Delta G is less than zero, our reaction is going to be spontaneous. It’s going to be spontaneous. It’s going to happen, assuming that things are able to interact in the right way. It’s going to be spontaneous. Now, let’s think Free Power little bit about why that makes sense. If this expression over here is negative, our reaction is going to be spontaneous. So, let’s think about all of the different scenarios. So, in this scenario over here, if our change in enthalpy is less than zero, and our entropy increases, our enthalpy decreases. So, this means we’re going to release, we’re going to release energy here. We’re gonna release enthalpy. And, you could think about this as, so let’s see, we’re gonna release energy. So, release. I’ll just draw it. This is Free Power release of enthalpy over here.
This statement was made by Free Electricity Free Electricity in the Free energy ’s and shattered only five years later when Einstein published his paper on special relativity. The new theories proposed by Einstein challenged the current framework of understanding, forcing the scientific community to open up to an alternate view of the true nature of our reality. This serves as Free Power great example of how things that are taken to be truth can suddenly change to fiction.
Free Power you? Im going to stick to the mag motor for now. Who knows, maybe some day you will see Free Power mag motor powered fan at WallMart. Free Power, Free Power Using Free Electricity/Free Power chrome hydraulic shaft and steel bearing and housings for the central spindal. Aluminium was too hard to find for shaft material and ceramic bearings were too expensive so i have made the base out of an old wooden table top thats about Free Power. 3metres across to get some distance. Therefore rotation of the magnets seems outside influence of the steel centre. Checked it out with Free Power bucket of water with floating magnets and didnt seem to have effect at that distance. Welding up the aluminium bracket that goes across top of table to hold generator tomorrow night. Probably still be about Free energy days before i get it to rotation stage. Looks awesome with all the metal bits polished up. Also, I just wanted to add this note. I am not sure what to expect from the design. I am not claiming that i will definitely get over unity. I am just interested to see if it comes within Free Power mile of it. Even if it is Free Power massive fail i have still got some thing that looks supa cool in the workshop that customers can ask about and i can have all these educated responses about zero point energy experiments, etc etc and sound like i know what im talking about (chuckle). After all, having Free Power bit of fun is the main goal. Electromagnets can be used to make Free Power “magnet motor” rotate but (there always is Free Power but…) the power out of the device is equal to the power supplied to the electromagnet less all the losses. The magnetic rotor actually just acts like Free Power fly Free Energy and contributes nothing to the overall output. Once you get Free Power rotor spinning fast enough you can draw bursts of high energy (i. e. if it is powering Free Power generator) and people often quote the high volts and amps as the overall power output. Yippee OVERUNITY! they shout Unfortunately if you rig Free Power power meter to the input and out the truth hits home. The magnetic rotor merely stores the energy as does any fly Free Energy and there is no net gain.
#### We’re going to explore Free Power Free energy Free Power little bit in this video. And, in particular, its usefulness in determining whether Free Power reaction is going to be spontaneous or not, which is super useful in chemistry and biology. And, it was defined by Free Power Free Energy Free Power. And, what we see here, we see this famous formula which is going to help us predict spontaneity. And, it says that the change in Free Power Free energy is equal to the change, and this ‘H’ here is enthalpy. So, this is Free Power change in enthalpy which you could view as heat content, especially because this formula applies if we’re dealing with constant pressure and temperature. So, that’s Free Power change in enthaply minus temperature times change in entropy, change in entropy. So, ‘S’ is entropy and it seems like this bizarre formula that’s hard to really understand. But, as we’ll see, it makes Free Power lot of intuitive sense. Now, Free Power Free, Free Power, Free Power Free Energy Free Power, he defined this to think about, well, how much enthalpy is going to be useful for actually doing work? How much is free to do useful things? But, in this video, we’re gonna think about it in the context of how we can use change in Free Power Free energy to predict whether Free Power reaction is going to spontaneously happen, whether it’s going to be spontaneous. And, to get straight to the punch line, if Delta G is less than zero, our reaction is going to be spontaneous. It’s going to be spontaneous. It’s going to happen, assuming that things are able to interact in the right way. It’s going to be spontaneous. Now, let’s think Free Power little bit about why that makes sense. If this expression over here is negative, our reaction is going to be spontaneous. So, let’s think about all of the different scenarios. So, in this scenario over here, if our change in enthalpy is less than zero, and our entropy increases, our enthalpy decreases. So, this means we’re going to release, we’re going to release energy here. We’re gonna release enthalpy. And, you could think about this as, so let’s see, we’re gonna release energy. So, release. I’ll just draw it. This is Free Power release of enthalpy over here.
Is there Free Power real good one out there? Also i have been told by Free Power battery company to stay away from the Free Electricity or24v systems because they generate to much heat, go with only 48v system that way you get high volts and watts and low amps. Not sure how that works and not sure how to build Free Power 48v PMA. Any info? Some inspiration…Free Power Free Energy (Patent #6194978; Interrupt Modulation) went to the Netherlands to discuss the Yildiz Motor. Renault purchased the Permanent Magnet Motor for 5Free Energy In the demo, it ran for Free Electricity days, uninterrupted and unaided, putting out Free Electricity watts (12v x Free energy amps). It is completely mechanical. Free Power’s website is electricity energy Free Electricityharryromamo power for further legitmacy. Free Energy’t just show it on Free Power, cash in. Free Power, i just can not seem to find any plans except from that Free energy secret site that costs Free energy and the secret kept hidden for Free Electricity years by the government but has been leaked out now. Ya right! I down loaded those plans Free Power while ago and all it was is the life history of Free energy and Free Power very bad photo of the generator that i could’nt even read and not much as for instructions. Free Electricity well. yeah – i saw those Free energy plans. Saw Free Power guy on Free Power video rekons he can get 7kw out of one. Not sure about that. Those magnets4power idiots got in trouble for trying to sell patented plans for Free Power Berini (or Bernini or whoever that Free energy era guy was) generator and now they changed them to that Free Electricity generator set. Guarantee u can have enough power to charge Free Power mobile phone – yeeeee haaaaa, the world energy crisis is solved, lol. I never set out to divide the camp based on who is wrong or right. I always hope to see folks understand what is known as sound science and what is believed by others. Free Energy get very defensive in this area of science. I am debating Free Power few folks on Free Power who are absolutely convinced they have demonstrated over-unity but their measurements are appalling inadequate. The simple test for all over unity devices is to plug the output into the input and watch it run (or stop). Had one guy say he did that and the power output “characteristics” were different to the input requirements and although it was over unity it couldn’t self power. Can’t progress with people who think that way. Cheers and keep up the fun. I hope the “zero point energy ” was Free Power typo. Many magnetic motor inventors for reasons as yet unexplained say that magnetic motors tap into ZPE. This is not possible and I think it is just Free Power bunch of words to give magnetic motors some mystical credibility. ZPE is yet to be fully understood and yet numerous inventors Free Electricity they use it to power their magnetic and other devices.
The differences come down to important nuances that often don’t exist in many overly emotional activists these days: critical thinking. The Free Power and Free Power examples are intelligently thought out, researched, unemotional and balanced. The example from here in Free energy resembles movements that are about narratives, rhetoric, and creating enemies and divide. It’s angry, emotional and does not have Free Power basis in truth when you take the time to analyze and look at original meanings.
Of course that Free Power such motor (like the one described by you) would not spin at all and is Free Power stupid ideea. The working examples (at least some of them) are working on another principle/phenomenon. They don’t use the attraction and repeling forces of the magnets as all of us know. I repeat: that is Free Power stupid ideea. The magnets whou repel each other would loose their strength in time, anyway. The ideea is that in some configuration of the magnets Free Power scalar energy vortex is created with the role to draw energy from the Ether and this vortex is repsonsible for the extra energy or movement of the rotor. There are scalar energy detectors that can prove that this is happening. You can’t detect scalar energy with conventional tools. The vortex si an ubiquitos thing in nature. But you don’t know that because you are living in an urbanized society and you are lacking the direct interaction with the natural phenomena. Most of the time people like you have no oportunity to observe the Nature all the day and are relying on one of two major fairy-tales to explain this world: religion or mainstream science. The magnetism is more than the attraction and repelling forces. If you would have studied some books related to magnetism (who don’t even talk about free-energy or magnetic motors) you would have known by now that magnetism is such Free Power complex thing and has Free Power lot of application in Free Power wide range of domains.
Does the motor provide electricity? No, of course not. It is simply an engine of sorts, nothing more. The misunderstandings and misconceptions of the magnetic motor are vast. Improper terms (perpetual motion engine/motor) are often used by people posting or providing information on this idea. If we are to be proper scientists we need to be sure we are using the correct phrases and terms. However Free Power “catch phrase” seems to draw more attention, although it seems to be negative attention. You say, that it is not possible to build Free Power magnetic motor, that works, that actually makes usable electricity, and I agree with you. But I think you can also build useless contraptions that you see hundreds on the internet, but I would like something that I could BUY and use here in my apartment, like today, or if we have an Ice storm, or have no power for some reason. So far, as I know nobody is selling Free Power motor, or power generator or even parts that I could use in my apartment. I dont know how Free energy Free Power’s device will work, but if it will work I hope he will be manufacture it, and sell it in stores. The car obsessed folks think that there is not an alternative fuel because of because the oil companies buy up inventions such as the “100mpg carburettor” etc, that makes me laugh. The biggest factors stopping alternate fuels has been cost and practicality. Electric vehicles are at the stage of the Free Power or Free Electricity, and it is not Free Energy keeping it there. Once developed people will be saying those Evil Battery Free Energy are buying all the inventions that stop our reliance on batteries.
Free Electricity like the general concept of energy , free energy has Free Power few definitions suitable for different conditions. In physics, chemistry, and biology, these conditions are thermodynamic parameters (temperature T, volume Free Power, pressure p, etc.). Scientists have come up with several ways to define free energy. The mathematical expression of Helmholtz free energy is.
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# Golf Balls Simulation
## Problem
Allan Rossman used to live along a golf course and collected the golf balls that landed in his yard. Most of these golf balls had a number on them. Allan tallied the numbers on the first 500 golf balls that landed in his yard one summer.
Specifically. he collected the following data: 137 golf balls numbered 1 138 golf balls numbered 2 107 golf balls numbered 3 104 golf balls numbered 4 14 “others” (Either with a different number, or no number at all. We will ignore these other balls for the purposes of this question.)
Question: What is the distribution of these numbers? In particular, are the numbers 1, 2, 3, and 4 equally likely?
## My solutions
library(tidyverse)
library(ggplot2)
library(Cairo)
#How many simulations to run?
NumberOfSims<-10000
NumberofBalls <- 500-14
set.seed(123) # set the seed for the random number generator - this makes sure the results are reproducible when we are debugging
# create blank vectors to store values
vec <- vector()
vec2 <- vector()
vec3 <- vector()
vec4 <- vector()
theme_set(theme_minimal())
### Simulation
# compute maximum frequency for each simlation
for (j in 1:NumberOfSims){
for (i in 1:NumberofBalls){
vec[i] <- sample(1:4, 1)
}
vec2[j]<- max(table(vec))
}
# compute minimum frequency for each simlation
for (j in 1:NumberOfSims){
for (i in 1:NumberofBalls){
vec[i] <- sample(1:4, 1)
}
vec3[j]<- min(table(vec))
}
# compute range of frequency for each simlation
range <- vec2 - vec3
# compute variance of frequency for each simlation
for (j in 1:NumberOfSims){
for (i in 1:NumberofBalls){
vec[i] <- sample(1:4, 1)
}
vec4[j]<- var(table(vec))
}
df <- cbind(vec2, vec3, vec4, range) %>% as.data.frame()
colnames(df) <- c("max", "min", "variance", "range")
dim(df)
## [1] 10000 4
head(df)
## max min variance range
## 1 136 112 11.67 24
## 2 136 117 268.33 19
## 3 138 116 43.00 22
## 4 133 108 95.00 25
## 5 129 116 73.67 13
## 6 137 111 107.00 26
### Minimum frequency
# observed vector
obs <- c(137, 138, 107, 104)
# calculate test statistics
min(obs)
## [1] 104
# calculate p-value
a <- df %>% filter(min > min(obs)) %>% nrow()
pvalue <- 1- a/NumberOfSims
pvalue
## [1] 0.1481
ggplot(aes(x = min), data = df) + geom_histogram(binwidth = 2) + geom_vline(xintercept = min(obs), size = 1.4, color = "#AFAFFF") + annotate("text", x = min(obs) - 5, y = 1000, label = " test statistics = 104 \n pvalue = 0.1481", size = 4)
### Variance
# calculate test statistics
var(obs)
## [1] 343
# calculate p-value
a <- df %>% filter(variance > var(obs)) %>% nrow()
pvalue <- a/NumberOfSims
pvalue
## [1] 0.0336
# draw the graph
ggplot(aes(x = variance), data = df) + geom_histogram() + geom_vline(xintercept = var(obs), size = 1.4, color = "#AFAFFF") + annotate("text", x = var(obs) + 150, y = 600, label = " test statistics = 343 \n pvalue = 0.0336", size = 4)
### Range
# calculate test statistics
max(obs) - min(obs)
## [1] 34
# calculate p-value
a <- df %>% filter(range > max(obs) - min(obs)) %>% nrow()
pvalue <- a/NumberOfSims
pvalue
## [1] 0.0742
# draw the graph
ggplot(aes(x = range), data = df) + geom_histogram() + geom_vline(xintercept = max(obs) - min(obs), size = 1.4, color = "#AFAFFF") + annotate("text", x = max(obs) - min(obs) + 8, y = 600, label = " test statistics = 34 \n pvalue = 0.0742", size = 4)
I tried 3 test statistics using simulation-based hypothesis tests. My null hypothesis here is that the numbers 1, 2, 3, and 4 distribute equally. My alternative hypothesis here is that the numbers 1, 2, 3, and 4 do not distribute equally.
Using minimum frequency of ball number among 486 balls as the test statistics, we simulated 10000 times and made a histogram for these 10000 minimum frequency. Our observed test statistics = 104 and our pvalue = 0.1481. Thus, with the significance level of 0.05, we fail to reject the null hypothesis that the numbers 1, 2, 3, and 4 distribute equally likely.
Using variance of the frequency of the numbers 1, 2, 3, and 4 as the test statistics, we simulated 10000 times and made a histogram for these 10000 minimum frequency. Our observed test statistics = 343 and our pvalue = 0.0336. Thus, with the significance level of 0.05, we reject the null hypothesis and conclude that the numbers 1, 2, 3, and 4 do not distribute equally.
Using range of the frequency of the numbers 1, 2, 3, and 4 as the test statistics, we simulated 10000 times and made a histogram for these 10000 minimum frequency. Our observed test statistics = 34 and our pvalue = 0.0742 Thus, with the significance level of 0.05, we fail to reject the null hypothesis that the numbers 1, 2, 3, and 4 distribute equally.
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CFD Online Discussion Forums (http://www.cfd-online.com/Forums/)
- Main CFD Forum (http://www.cfd-online.com/Forums/main/)
- - Computational cost - Re ^3 (http://www.cfd-online.com/Forums/main/118398-computational-cost-re-3-a.html)
karthikg.ae May 27, 2013 05:18
Computational cost - Re ^3
Hi,
I just started reading a textbook on cfd and found this statement- The computational cost for a DNS increases as the cube of the Reynold number.
Can someone please explain how this order of magnitude estimate was arrived at.
Thanks
michujo May 27, 2013 06:38
Hi. Imagine you want to compute the turbulent flow over a body of characteristic length .
Suppose your mesh is uniform. Turbulence is unsteady so you will need to perform a computation over one characteristic time of the largest turbulence scale at least. Also, turbulence is 3D so the dimensions of your domain are, at least, .
The minimum number of operations are the result of multiplying the number of cells by the number of time steps: .
The Kolmogorov scale characteristic length and turnover time scale with those of the largest scale as:
.
.
In a DNS you have to resolve all the turbulence scales, both in space and time. Therefore, the cell size and time step in your simulation must be and (length scale and characteristic turnover time of the smallest, i.e. Kolmogorov, scale).
The total number of cells is therefore (notice that your domain is 3D) . Likewise, the number of time steps is .
The total number of operations scales as .
Notice that these are minimum requirements, so I guess you can easily reach the scaling with the third power of the Reynolds number. A detailed explanation can be found in the book of Pope.
Cheers,
Michujo.
FMDenaro May 27, 2013 07:27
a very quick (and brutal) estimation can be done assuming that you have to work with a cell Reynolds number = O(1). Therefore, for each direction, you have
Reh = u h /ni = ReL h/L = ReL / N = O(1)
sbaffini May 28, 2013 04:28
From the michujo estimate, the exact Re^3 scaling is then reached when considering an unitary Courant number (as most DNS methods rely on explicit convection schemes). As a result, the time step also scales like the grid step and the final estimate is reached.
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# Items where Author is "Borwein, David"
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## Article
Borwein, David and Borwein, Jonathan M. and Sims, Brailey (2015) Monotonicity of Certain Riemann Sums. (Submitted)
Bailey, David H. and Borwein, David and Borwein, Jonathan M. (2015) Eulerian Log-Gamma Integrals and Tornheim-Witten zeta functions. Ramanujan (36). pp. 43-68.
Borwein, David and Borwein, Jonathan M. (2014) Deriving new sinc results from old. Amer. Math, Monthly, 121 . pp. 700-705.
Borwein, David and Borwein, Jonathan M. and Sims, Brailey (2014) On the Solution of Linear Mean Recurrences. MAA Monthly, 121 . pp. 486-498.
Borwein, David and Borwein, Jonathan M. and Straub, Armin (2014) ON LATTICE SUMS AND WIGNER LIMITS. JMAA, 414 . pp. 489-513.
Bailey, David H. and Borwein, David and Borwein, Jonathan M. (2013) On Eulerian Log-Gamma Integrals and Tornheim--Witten zeta functions. Ramanujan J. .
Borwein, David and Borwein, Jonathan M. and Straub, A. and Wan, J. (2012) Log-sine evaluations of Mahler measures, Part II. Integers, 12 (6). pp. 1179-1212.
Borwein, David and Borwein, Jonathan M. and Straub, Armin (2012) A sinc that sank. Amer. Mathematical Monthly, 119 . pp. 535-549.
Borwein, David and Borwein, Jonathan M. and Glasser, Larry and Wan, James (2011) Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant. J. Math. Anal. Appl., 384 . pp. 478-496.
Borwein, David and Borwein, Jonathan M. and Leonard, Isaac E. (2010) L_p norms and the sinc function. American Mathematical Monthly, 117 (6). pp. 528-539.
Borwein, David and Borwein, Jonathan M. and Crandall, Richard E. (2008) Effective Laguerre asymptotics. SIAM J. Numerical Anal., 6 . pp. 3285-3312.
Baillie, Robert and Borwein, David and Borwein, Jonathan M. (2008) Surprising Sinc Sums and Integrals. The American Mathematical Monthly, 115 (10). pp. 888-901.
Borwein, David and Borwein, Jonathan M. and Chan, O-Yeat (2008) The evaluation of Bessel functions via exp-arc integrals. Journal of Mathematical Analysis and Applications, 341 (1). 478 - 500.
Borwein, Jonathan M. and Borwein, David (2007) Van der Pol Expansions of L-Series. Canad. Math, Bull., 50 . pp. 11-23.
Borwein, Jonathan M. and Crandall, Richard E. and Borwein, David and Mayer, Raymond (2007) On the dynamics of certain recurrence relations. Ramanujan Journal, 13 . pp. 63-101.
Borwein, David and Borwein, Jonathan M. and Bradley, David M. (2006) Parametric Euler sum identities. Journal of Mathematical Analysis and Applications, 316 (1). 328 - 338.
Borwein, Jonathan M. and Galway, William F. and Borwein, David (2004) Finding and Excluding b-ary Machin-Type BBP Formulae. Canadian J. Math, 56 . pp. 897-925.
Borwein, David and Borwein, Jonathan M. and Mares Jr., Bernard A. (2002) Multi-variable sinc integrals and volumes of polyhedra. The Ramanujan Journal, 6 . pp. 189-208.
Borwein, David and Borwein, Jonathan M. and Fee, Greg and Girgensohn, Roland (2001) Refined Convexity and Special Cases of the Blaschke-Santalo Inequality. Mathematical Inequalities and Applications, 4 . pp. 631-638.
Borwein, Jonathan M. and Borwein, David (2001) Some Remarkable Properties of Sinc and Related Integrals. The Ramanujan Journal, 5 (1). pp. 73-90.
Borwein, David and Borwein, Jonathan M. and Marechal, Pierre (2000) Surprise Maximization. American Math. Monthly, 107 . pp. 527-537.
Borwein, David and Borwein, Jonathan M. and Pinner, Christopher (1998) Convergence of Madelung-Like Lattice Sums. Trans. Amer. Math. Soc., 350 . pp. 3131-3167.
Borwein, David and Borwein, Jonathan M. and Wang, Shawn Xianfu (1996) Approximate Subgradients and Coderivatives in $R^n$. Set-Valued Analysis, 4 (4). pp. 375-398. ISSN 0927-6947
Borwein, David and Borwein, Jonathan M. and Borwein, Peter and Girgensohn, Roland (1996) Giuga's conjecture on primality. The American Mathematical Monthly , 103 (1). pp. 40-50.
Borwein, David and Borwein, Jonathan M. and Girgensohn, Roland (1995) Explicit evaluation of Euler sums. Proceedings of the Edinburgh Mathematical Society (38). pp. 277-294.
Borwein, David and Borwein, Jonathan M. (1995) On some intriguing sums involving $\zeta$ (4). Proceedings of the American Mathematical Society, 123 . pp. 111-118. ISSN 0002-9939
Borwein, David and Borwein, Jonathan M. (1994) On some trigonometric and exponential lattice sums. Journal of Mathematical Analysis and Applications., 188 . pp. 209-218. ISSN 0022-247X
Borwein, Jonathan M. and Borwein, David (1991) Fixed points of real functions revisited. J. Math. Anal. Appl., 151 . pp. 112-126.
Borwein, Jonathan M. and Borwein, David and Shail, R. (1989) Analysis of certain lattice sums. J. Math. Anal. Appl., 143 . pp. 126-137.
Borwein, David and Borwein, Jonathan M. and Shail, R. and Zucker, I. J. (1988) Energy of static electron lattices. Journal of Physics A: Mathematical and General, 21 . pp. 1519-1531.
Borwein, Jonathan M. and Borwein, David (1986) A note on alternating series in several dimensions. MAA Monthly, 93 . pp. 531-539.
Borwein, David and Borwein, Jonathan M. and Taylor, K. F. (1985) Convergence of lattice sums and Madelung's constant. J. Math. Phys., 26 . pp. 2999-3009.
## Preprint
Borwein, David and Borwein, Peter and Jakimovski, Amnon (1995) Matrix transformations of series of orthogonal polynomials. [Preprint]
This list was generated on Wed Sep 27 00:21:43 2017 AEST.
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# Number Theory class
A magician said to an audience member:
• Pick a number,
• Double it,
• Add $7$,
• Multiply it by $5$,
• Subtract the number you started with,
• Remove any non-zero digit from the answer,
and then tell me the remaining digits in any order.
The audience member said
$6$ and $8$.
And the magician announced,
The digit you removed was $3$, right?
The magician is right! Why? Justify!
Since:
The result before the digit removal is 5(2x+7)-x=9x+35
So:
That gives a remainder of 8 when divided by nine.
But:
The digit sum of a number gives the same remainder when divided by nine as the original number
Therefore:
The missing digit + the remaining digits gives a remainder of eight when divided by nine, so the missing digit + the remaining digits + 1 is a multiple of nine
So:
The magician adds up the remaining digits, adds one and subtracts this number from the next multiple of nine. Here 6+8+1=15, the next multiple of nine is 18, so 18-15=3.
Note:
The original number has to be integral
• what do you mean by "number has to be integral"? – Oray Sep 22 '17 at 10:33
• @Oray If I try 1/9, the trick doesn't work – boboquack Sep 22 '17 at 10:53
• by integral, u meant integer? or integral number is something that I dont know – Oray Sep 22 '17 at 10:59
• @Oray being integral is the property of being an integer; it has a meaning besides that of in calculus. – boboquack Sep 22 '17 at 10:59
• interesting :) learnt something today. – Oray Sep 22 '17 at 11:13
Here is a simple way to think about it. I will assume that everyone is familiar with the take any number, multiply it by 9, add up the digits and get 9 "trick"
So to move forward, all the operations the magician asks for can be noted as 5(2X+7)-X
We can reduce that to 10X-35-X so 9X+35
Lets refactor it to something more useful 9X+9*4+1 = 9(X+4)-1
As we know the value of X does not matter, we can replace X+4 with X
So now we are at the 9X problem with just a -1
So we add up the digits 6+8=14. See how far we are from a divisible by 9. It would be 18, so we need 4 more. But we are off by the -1, so we have to subtract it out. 4-1=3
• $9X+35\neq9(X+4)+1$ – boboquack Sep 23 '17 at 6:22
• @boboquack oh yeah it's -1 – Andrey Sep 23 '17 at 15:37
The other answers cover the math of finding the answer, but the trick can be simplified.
Because summing digits doesn't change the mod9 you can do it to any intermediate sums. 6+8=14, 1+4=5. 5+1 is 6, 9 is the next biggest multiple of 9 so 9-6=3.
This can guarantee a single digit at the final step so except for a sum of 9 you can subtract from always 8 instead of adding 1 and finding a multiple of 9. 6+8=14, 1+4=5, 8-5=3. (For a sum of 9 it will end up being 8; 9+1=10 next multiple is 18, 18-10 is 8.)
The last simplification is doing addition or subtraction mod9 as you hear each digit. "6" = 6, "8"->-1 = 5, when they stop listing numbers so you subtract the tallied number from 8. 8-5 = 3. This might take a minute or two of practice to reliably choose adding or subtracting and do the operation as fast as a person recites digits but means you only have to keep a single digit in your mind at a time.
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# Different results from two identical sums?
Posted 1 year ago
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Hi all,I wrote two different ways to compute some given sums and try to measure the time in order to pick the best, which saves a lot of computational time! I needed to do that because these sums require time which go from minutes to hours.There are listed two methods, do not put too much attention in the math details, but what I compute and save in an output file they must be the same!First of all, I set globally the precision on my notebook with the following line: $PreRead = (# /. s_String /; StringMatchQ[s, NumberString] && Precision@ToExpression@s == MachinePrecision :> s <> "20." &); Then what I compute is the quantity Den[c] for several values of parameter T=12, ... in both two methods. Starting with this value we see differences in the result of Den[c] in the two methods, but these differences are not smaller than the precision I set which is 20 digits! I thought that should be differences but of a number which is smaller than 10^{-20}! These differences are bigger than 10^{-16}, which is my tolerance number for 0 in double precision.You can evaluate this notebook because the computation requires ~ 1 minute.Please help me, I don't find any useful informations about it on the internet. If you need more other details or info please ask me!Thank you so much, stay safe and have a good day! 2 Replies Sort By: Posted 1 year ago I don't know if it has anything to do with your problem, but I just discovered that NumberString does not always do what I would somehow expect: In[2]:= StringMatchQ["1.220", NumberString] Out[2]= False In[11]:= StringMatchQ["3.13",NumberString] Out[11]= False ` Posted 1 year ago Ciao Gianluca,I don't know what is the reason of NumberString, I copied and pasted this line from the following discussion: "How to set the working precision globally?$MinPrecision does not work".Now I document myself on the scope of every function in this line.Saluti, Nico
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# Many-body problem
This article is about the many-body problem in quantum mechanics. For the n-body problem in classical mechanics, see n-body problem.
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of a large number of interacting particles. Microscopic here implies that quantum mechanics has to be used to provide an accurate description of the system. A large number can be anywhere from 3 to infinity (in the case of a practically infinite, homogeneous or periodic system, such as a crystal), although three- and four-body systems can be treated by specific means (respectively the Faddeev and Faddeev-Yakubovsky equations) and are thus sometimes separately classified as few-body systems. In such a quantum system, the repeated interactions between particles create quantum correlations, or entanglement. As a consequence, the wave function of the system is a complicated object holding a large amount of information, which usually makes exact or analytical calculations impractical or even impossible. Thus, many-body theoretical physics most often relies on a set of approximations specific to the problem at hand, and ranks among the most computationally intensive fields of science.
## Quotes
"It would indeed be remarkable if Nature fortified herself against further advances in knowledge behind the analytical difficulties of the many-body problem."
— Max Born, 1960
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# What is the relationship between MLE and naive Bayes?
I have found various references describing Naive Bayes and they all demonstrated that it used MLE for the calculation. However, this is my understanding:
$$P(y=c|x)$$ $$\propto$$ $$P(x|y=c)P(y=c)$$
with $$c$$ is the class the model may classify $$y$$ as.
And that's all, we can infer $$P(x|y=c)$$ and $$P(c)$$ from the data. I don't see where the MLE shows its role.
And that's all, we can infer P(x|y=c) and P(c) from the data. I don't see where the MLE shows its role.
Maximum likelihood estimate is used for this very purpose, i.e. to estimate the conditional probability $$p(x_j \mid y)$$ and marginal probability $$p(y)$$ .
In Naive Bayes Algorithm ,using the properties of conditional probability, we can estimate the joint probability
$$p(y, x_1, x_2, \dots, x_n) = p(x_1, x_2, \dots, x_n \mid y) \; p(y)$$
which is the same as
$$p(y=c|x)\propto p(x|y=c)p(y=c)$$
What we need to estimate in here, are the conditional $$p(x_j \mid y)$$ and marginal $$p(y)$$ probabilities, and we use maximum likelihood for this.
To be more precise: Assume that the $$x$$ is a feature vector $$(x_1, x_2, ...x_n)$$ - which means nothing more than the data point is a vector. In Naive Bayes Classification the assumption is that these features are independent of each other conditional on the class. So, in that case this term $$p(x|y=c)$$ is replaced by $$\prod_{i=1}^{n} p(x_i|y=c)$$ -- this is because of the independence assumption that lets us simply multiply the probabilities.
The problem of estimating the class to which the data point belongs reduces to the problem of maximizing the likelihood $$\prod_{i=1}^{n} p(x_i|y=c)$$ -- which means assigning the data $$(x_1, x_2, ...x_n)$$ to the class $$k$$ for which this likelihood is highest. This will give the same result as MLE which takes the form of maximizing this quantity -- $$\prod_{i=1}^{n} p(x_i|\theta)$$ where $$\theta$$ are the assumed parameters.
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IN THIS ISSUE
### Research Papers
J Biomech Eng. 2009;131(6):061001-061001-6. doi:10.1115/1.3116155.
Understanding the complex relationships between microstructural organization and macromechanical function is fundamental to our knowledge of the differences between normal, diseased/injured, and healing connective tissues. The long-term success of functional tissue-engineered constructs or scaffolds may largely depend on our understanding of the structural organization of the original tissue. Although innovative techniques have been used to characterize and measure the microstructural properties of collagen fibers, a large gap remains in our knowledge of the behavior of intermediate scale (i.e., “mesostructural”) groups of fiber bundles in larger tissue samples. The objective of this study was to develop a system capable of directly measuring deformations of these smaller mesostructures during application of controlled loads. A novel mesostructural testing system (MSTS) has been developed to apply controlled multiaxial loads to medium (meso-) scale tissue specimens, while directly measuring local nonuniform deformations using synchronized digital video capture and “markerless” image correlation. A novel component of the MSTS is the use of elliptically polarized light to enhance collagen fiber contrast, providing the necessary texture for accurate markerless feature tracking of local fiber deformations. In this report we describe the components of the system, its calibration and validation, and the results from two different tissues: the porcine aortic valve cusp and the bovine pericardium. Validation tests on prepared samples showed maximum error of direct strain measurement to be 0.3%. Aortic valve specimens were found to have larger inhomogeneous strains during tensile testing than bovine pericardium. Clamping effects were more pronounced for the valve specimens. A new system for direct internal strain measurement in connective tissues during application of controlled loads has been developed and validated. The results from the two different tissues show that significant inhomogeneous deformations can occur even in simple tensile testing experiments.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061002-061002-9. doi:10.1115/1.3118771.
When designing a medical device based on lightweight accelerometers, the designer is faced with a number of questions in order to maximize performance while minimizing cost and complexity: Where should the inertial unit be located? How many units are required? How is performance affected if the unit is not correctly located during donning? One way to answer these questions is to use position data from a single trial, captured with a nonportable measurement system (e.g., stereophotogrammetry) to simulate measurements from multiple accelerometers at different locations on the body. In this paper, we undertake a thorough investigation into the applicability of these simulated acceleration signals via a series of interdependent experiments of increasing generality. We measured the dynamics of a reference coordinate frame using stereophotogrammetry over a number of trials. These dynamics were then used to simulate several “virtual” accelerometers at different points on the body segment. We then compared the simulated signals with those directly measured to evaluate the error under a number of conditions. Finally, we demonstrated an example of how simulated signals can be employed in a system design application. In the best case, we may expect an error of $0.028 m/s2$ between a derived virtual signal and that directly measured by an accelerometer. In practice, however, using centripetal and tangential acceleration terms (that are poorly estimated) results in an error that is an order of magnitude greater than the baseline. Furthermore, nonrigidity of the limb can increase error dramatically, although the effects can be reduced considerably via careful modeling. We conclude that using simulated signals has definite benefits when an appropriate model of the body segment is applied.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061003-061003-10. doi:10.1115/1.3118773.
Cartilage is a hydrated soft tissue whose solid matrix consists of negatively charged proteoglycans enmeshed within a fibrillar collagen network. Though many aspects of cartilage mechanics are well understood today, most notably in the context of porous media mechanics, there remain a number of responses observed experimentally whose prediction from theory has been challenging. In this study the solid matrix of cartilage is modeled with a continuous fiber angular distribution, where fibers can only sustain tension, swelled by the osmotic pressure of a proteoglycan ground matrix. It is shown that this representation of cartilage can predict a number of observed phenomena in relation to the tissue’s equilibrium response to mechanical and osmotic loading, when flow-dependent and flow-independent viscoelastic effects have subsided. In particular, this model can predict the transition of Poisson’s ratio from very low values in compression $(∼0.02)$ to very high values in tension $(∼2.0)$. Most of these phenomena cannot be explained when using only three orthogonal fiber bundles to describe the tissue matrix, a common modeling assumption used to date. The main picture emerging from this analysis is that the anisotropy of the fibrillar matrix of articular cartilage is intimately dependent on the mechanism of tensed fiber recruitment, in the manner suggested by our recent theoretical study (Ateshian, 2007, ASME J. Biomech. Eng., 129(2), pp. 240–249).
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061004-061004-8. doi:10.1115/1.3118774.
Rapid early diastolic left ventricular (LV) filling requires a highly compliant chamber immediately after systole, allowing inflow at low driving pressures. The transmural LV deformations associated with such filling are not completely understood. We sought to characterize regional transmural LV strains during diastole, with focus on early filling, in ovine hearts at 1 week and 8 weeks after myocardial marker implantation. In seven normal sheep hearts, 13 radiopaque markers were inserted to silhouette the LV chamber and a transmural beadset was implanted into the lateral equatorial LV wall to measure transmural strains. Four-dimensional marker dynamics were obtained 1 week and 8 weeks thereafter with biplane videofluoroscopy in closed-chest, anesthetized animals. LV transmural strains in both cardiac and fiber-sheet coordinates were studied from filling onset to the end of early filling (EOEF, 100 ms after filling onset) and at end diastole. At the 8 week study, subepicardial circumferential strain $(ECC)$ had reached its final value already at EOEF, while longitudinal and radial strains were nearly zero at this time. Subepicardial $ECC$ and fiber relengthening $(Eff)$ at EOEF were reduced to 1 compared with 8 weeks after surgery ($ECC:0.02±0.01$ to $0.08±0.02$ and $Eff:0.00±0.01$ to $0.03±0.01$, respectively, both $P<0.05$). Subepicardial $ECC$ during early LV filling was associated primarily with fiber-normal and sheet-normal shears at the 1 week study, but to all three fiber-sheet shears and fiber relengthening at the 8 week study. These changes in LV subepicardial mechanics provide a possible mechanistic basis for regional myocardial lusitropic function, and may add to our understanding of LV myocardial diastolic dysfunction.
Topics: Fibers , Surgery , Inflow
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061005-061005-9. doi:10.1115/1.3116156.
Characterizing the biomechanical and biotribological properties for articular surfaces in healthy, damaged, and repaired states will both elucidate the understanding of mechanical degradation and lubricating phenomena and enhance the development of functional tissue engineered cartilage and surgical repair techniques. In recent work, a new methodology involving concomitant linear translational and oscillating rotational motion was developed to determine the frictional and wear characteristics of articular cartilage. The impetus of this work was to further characterize the biomechanical characteristics from stress relaxation and dynamic cyclical indentation testing of normal and damaged articular cartilage and to correlate the biotribological characteristic findings with the biomechanical data. Quasilinear viscoelastic (QLV) theory was used to curve fit the stress-relaxation data, while the dynamic data were used both to determine the dynamic properties through fast Fourier transform analysis and to validate the dynamic behavior based on the properties obtained from the QLV theory. Comparisons of the curve-fit parameters showed a significant decrease in pre- versus postwear elastic response, $A$$(p<0.04)$, and viscous response, $c$$(p<0.01)$. In addition, the short term relaxation time, $τ1$$(p<0.0062)$, showed a significant decrease between surfaces with and without a defect. The magnitude of the complex modulus from dynamic tests revealed a decrease due to wear, $lGlpostwear∕lGlprewear<1$$(p<0.05)$. The loss factor, $tanδ$, was generally greater while $lGl$ was less for those specimens experiencing rotation. A linear regression analysis was performed to correlate $μstatic$ and $μinitial$ with the curve-fit QLV parameters, $A$, $B$, $c$, $τ1$, and $τ2$. Increasing coefficients of friction correlated with decreases in the elastic response, $A$, viscous response, $c$, and the short term relaxation time constant, $τ1$, while $B$ became increasingly nonlinear and $τ2$ became shorter postwear. Qualitatively, scanning electron microscopy photographs revealed the mechanical degradation of the tissue surface due to wear. Surfaces with a defect had an increased amount of wear debris, which ultimately contributed to third body wear. Surfaces without a defect had preferentially aligned abrasions, while those surfaces not within the wear path showed no signs of wear. The efficacy of various repair techniques and innovative repair tissue models in comparison to normal and worn articular surface tissue can be determined through experimental designs involving both biomechanical and biotribological parameter characterizations. The development of this comprehensive testing scenario involving both biotribological and biomechanical characteristics is essential to the continued development of potential articular repair tissue.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061006-061006-9. doi:10.1115/1.3118764.
Four commercially available stent designs (two balloon expandable—Bx Velocity and NIR, and two self-expanding—Wallstent and Aurora) were modeled to compare the near-wall flow characteristics of stented arteries using computational fluid dynamics simulations under pulsatile flow conditions. A flat rectangular stented vessel model was constructed and simulations were carried out using rigid walls and sinusoidal velocity input (nominal wall shear stress of $10±5 dyn/cm2$). Mesh independence was determined from convergence $(<10%)$ of the axial wall shear stress (WSS) along the length of the stented model. The flow disturbance was characterized and quantified by the distributions of axial and transverse WSS, WSS gradients, and flow separation parameters. Normalized time-averaged effective WSS during the flow cycle was the smallest for the Wallstent $(2.9 dyn/cm2)$ compared with the others ($5.8 dyn/cm2$ for the Bx Velocity stent, $5.0 dyn/cm2$ for the Aurora stent, and $5.3 dyn/cm2$ for the NIR stent). Regions of low mean WSS $(<5 dyn/cm2)$ and elevated WSS gradients $(>20 dyn/cm3)$ were also the largest for the Wallstent compared with the others. WSS gradients were the largest near the struts and remained distinctly nonzero for most of the region between the struts for all stent designs. Fully recirculating regions (as determined by separation parameter) were the largest for the Bx Velocity stent compared with the others. The most hemodynamically favorable stents from our computational analysis were the Bx Velocity and NIR stents, which were slotted-tube balloon-expandable designs. Since clinical data indicate lower restenosis rates for the Bx Velocity and NIR stents compared with the Wallstent, our data suggest that near-wall hemodynamics may predict some aspects of in vivo performance. Further consideration of biomechanics, including solid mechanics, in stent design is warranted.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061007-061007-11. doi:10.1115/1.3118765.
The objective of this modeling and simulation study was to establish the role of stress wave interactions in the genesis of traumatic brain injury (TBI) from exposure to explosive blast. A high resolution ($1 mm3$ voxels) five material model of the human head was created by segmentation of color cryosections from the Visible Human Female data set. Tissue material properties were assigned from literature values. The model was inserted into the shock physics wave code, CTH , and subjected to a simulated blast wave of 1.3 MPa (13 bars) peak pressure from anterior, posterior, and lateral directions. Three-dimensional plots of maximum pressure, volumetric tension, and deviatoric (shear) stress demonstrated significant differences related to the incident blast geometry. In particular, the calculations revealed focal brain regions of elevated pressure and deviatoric stress within the first 2 ms of blast exposure. Calculated maximum levels of 15 KPa deviatoric, 3.3 MPa pressure, and 0.8 MPa volumetric tension were observed before the onset of significant head accelerations. Over a 2 ms time course, the head model moved only 1 mm in response to the blast loading. Doubling the blast strength changed the resulting intracranial stress magnitudes but not their distribution. We conclude that stress localization, due to early-time wave interactions, may contribute to the development of multifocal axonal injury underlying TBI. We propose that a contribution to traumatic brain injury from blast exposure, and most likely blunt impact, can occur on a time scale shorter than previous model predictions and before the onset of linear or rotational accelerations traditionally associated with the development of TBI.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061008-061008-5. doi:10.1115/1.3118776.
During temporomandibular joint (TMJ) function, the mandibular condylar cartilage plays a prime role in the distribution and absorption of stresses generated over the condyle. Biomechanical characterization of the tissue under compression, however, is still incomplete. The present study investigates the regional variations in the elastic and equilibrium moduli of the condylar cartilage under high strains using unconfined compression and stress relaxation, with aims to facilitate future tissue engineering studies. Porcine condylar cartilages from five regions (anterior, central, lateral, medial, and posterior) were tested under unconfined compression. Elastic moduli were obtained from the linear regions of the stress-strain curves corresponding to the continuous deformation. Equilibrium moduli were obtained from the stress relaxation curves using the Kelvin model. The posterior region was the stiffest, followed by the middle (medial, central, and lateral) regions and the anterior region, respectively. Specifically, in terms of the equilibrium modulus, the posterior region was 1.4 times stiffer than the middle regions, which were in turn 1.7 times stiffer than the anterior region, although only the difference between anterior and posterior regions was statistically significant. No significant differences in stiffness were observed among the medial, central, lateral, and posterior regions. A positive correlation between the thickness and stiffness of the cartilage was observed, reflecting that their regional variations may be related phenomena caused in response to cartilage loading patterns. Condylar cartilage was less stiff under compression than in tension. In addition, condylar cartilage under compression appears to behave in a manner similar to the TMJ disc in terms of the magnitude of moduli and drastic initial drop in stress after a ramp strain.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061009-061009-9. doi:10.1115/1.3118767.
Cell-substrate interaction is implicated in many physiological processes. Dynamical monitoring of cellular tractions on substrate is critical in investigating a variety of cell functions such as contraction, migration, and invasion. On account of the inherent ill-posed property as an inverse problem, cellular traction recovery is essentially sensitive to substrate displacement noise and thus likely produces unstable results. Therefore, some additional constraints must be applied to obtain a reliable traction estimate. By integrating the classical Boussinesq solution over a small rectangular area element, we obtain a new analytical solution to express the relation between tangential tractions and induced substrate displacements, and then form an alternative discrete Green’s function matrix to set up a new framework of cellular force reconstruction. Deformation images of flexible substrate actuated by a single cardiac myocyte are processed by digital image correlation technique and the displacement data are sampled with a regular mesh to obtain cellular tractions by the proposed solution. Numerical simulations indicate that the 2-norm condition number of the improved coefficient matrix typically does not exceed the order of 100 for actual computation of traction recovery, and that the traction reconstruction is less sensitive to the shift or subdivision of the data sampling grid. The noise amplification arising from ill-posed inverse problem can be restrained and the stability of inverse solution is improved so that regularization operations become less relevant to the present force reconstruction with economical sampling density. The traction recovery for a single cardiac myocyte, which is in good agreement with that obtained by the Fourier transform traction cytometry, demonstrates the feasibility of the proposed method. We have developed a simple and efficient method to recover cellular traction field from substrate deformation. Unlike previous force reconstructions that numerically employ some regularization schemes, the present approach stabilizes the traction recovery by analytically improving the Green’s function such that the intricate regularizations can be avoided under proper conditions. The method has potential application to a real-time traction force microscopy in combination with a high-efficiency displacement acquisition technique.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061010-061010-11. doi:10.1115/1.3127253.
Heart attack and stroke are often caused by atherosclerotic plaque rupture, which happens without warning most of the time. Magnetic resonance imaging (MRI)-based atherosclerotic plaque models with fluid-structure interactions (FSIs) have been introduced to perform flow and stress/strain analysis and identify possible mechanical and morphological indices for accurate plaque vulnerability assessment. For coronary arteries, cyclic bending associated with heart motion and anisotropy of the vessel walls may have significant influence on flow and stress/strain distributions in the plaque. FSI models with cyclic bending and anisotropic vessel properties for coronary plaques are lacking in the current literature. In this paper, cyclic bending and anisotropic vessel properties were added to 3D FSI coronary plaque models so that the models would be more realistic for more accurate computational flow and stress/strain predictions. Six computational models using one ex vivo MRI human coronary plaque specimen data were constructed to assess the effects of cyclic bending, anisotropic vessel properties, pulsating pressure, plaque structure, and axial stretch on plaque stress/strain distributions. Our results indicate that cyclic bending and anisotropic properties may cause 50–800% increase in maximum principal stress $(Stress-P1)$ values at selected locations. The stress increase varies with location and is higher when bending is coupled with axial stretch, nonsmooth plaque structure, and resonant pressure conditions (zero phase angle shift). Effects of cyclic bending on flow behaviors are more modest (9.8% decrease in maximum velocity, 2.5% decrease in flow rate, 15% increase in maximum flow shear stress). Inclusion of cyclic bending, anisotropic vessel material properties, accurate plaque structure, and axial stretch in computational FSI models should lead to a considerable improvement of accuracy of computational stress/strain predictions for coronary plaque vulnerability assessment. Further studies incorporating additional mechanical property data and in vivo MRI data are needed to obtain more complete and accurate knowledge about flow and stress/strain behaviors in coronary plaques and to identify critical indicators for better plaque assessment and possible rupture predictions.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061011-061011-8. doi:10.1115/1.3127262.
Human embryonic stem cells (hESCs) possess an immense potential in a variety of regenerative applications. A firm understanding of hESC mechanics, on the single cell level, may provide great insight into the role of biophysical forces in the maintenance of cellular phenotype and elucidate mechanical cues promoting differentiation along various mesenchymal lineages. Moreover, cellular biomechanics can provide an additional tool for characterizing stem cells as they follow certain differentiation lineages, and thus may aid in identifying differentiated hESCs, which are most suitable for tissue engineering. This study examined the viscoelastic properties of single undifferentiated hESCs, chondrogenically differentiated hESC subpopulations, mesenchymal stem cells (MSCs), and articular chondrocytes (ACs). hESC chondrogenesis was induced using either transforming growth factor-$β1$$(TGF-β1)$ or knock out serum replacer as differentiation agents, and the resulting cell populations were separated based on density. All cell groups were mechanically tested using unconfined creep cytocompression. Analyses of subpopulations from all differentiation regimens resulted in a spectrum of mechanical and morphological properties spanning the range of hESCs to MSCs to ACs. Density separation was further successful in isolating cellular subpopulations with distinct mechanical properties. The instantaneous and relaxed moduli of subpopulations from $TGF-β1$ differentiation regimen were statistically greater than those of undifferentiated hESCs. In addition, two subpopulations from the $TGF-β1$ group were identified, which were not statistically different from native articular chondrocytes in their instantaneous and relaxed moduli, as well as their apparent viscosity. Identification of a differentiated hESC subpopulation with similar mechanical properties as native chondrocytes may provide an excellent cell source for tissue engineering applications. These cells will need to withstand any mechanical stimulation regimen employed to augment the mechanical and biochemical characteristics of the neotissue. Density separation was effective at purifying distinct populations of cells. A differentiated hESC subpopulation was identified with both similar mechanical and morphological characteristics as ACs. Future research may utilize this cell source in cartilage regeneration efforts.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061012-061012-9. doi:10.1115/1.3128673.
The relationship between microstructural features and macroscopic mechanical properties of engineered tissues was investigated in pure and mixed composite scaffolds consisting of collagen Type I and fibrin proteins containing embedded smooth muscle cells. In order to vary the matrix microstructure, fibrin polymerization in mixed constructs was initiated using either the blood-derived enzyme thrombin or the snake venom-derived enzyme ancrod, each at low and high concentrations. Microstructural features of the matrix were quantified by analysis of high resolution scanning electron micrographs. Mechanical properties of the scaffolds were assessed by uniaxial tensile testing as well as creep testing. Viscoelastic parameters were determined by fitting creep data to Burger’s four-parameter model. Oscillatory dynamic mechanical testing was used to determine the storage modulus, loss modulus, and phase shift of each matrix type. Mixed composite scaffolds exhibited improved tensile stiffness and strength, relative to pure collagen matrices, as well as decreased deformation and slower relaxation in creep tests. Storage and loss moduli were increased in mixed composites compared with pure collagen, while phase shift was reduced. A correlation analysis showed that the number of fiber bundles per unit volume was positively correlated with matrix modulus, strength, and dynamic moduli, though this parameter was negatively correlated with phase shift. Fiber diameter also was negatively correlated with scaffold strength. This study demonstrates how microstructural features can be related to the mechanical function of protein matrices and provides insight into structure-function relationships in such materials. This information can be used to identify and promote desirable microstructural features when designing biomaterials and engineered tissues.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061013-061013-7. doi:10.1115/1.3127252.
A variety of hemodynamic wall parameters (HWP) has been proposed over the years to quantify hemodynamic disturbances as potential predictors or indicators of vascular wall dysfunction. The aim of this study was to determine whether some of these might, for practical purposes, be considered redundant. Image-based computational fluid dynamics simulations were carried out for $N=50$ normal carotid bifurcations reconstructed from magnetic resonance imaging. Pairwise Spearman correlation analysis was performed for HWP quantifying wall shear stress magnitudes, spatial and temporal gradients, and harmonic contents. These were based on the spatial distributions of each HWP and, separately, the amount of the surface exposed to each HWP beyond an objectively-defined threshold. Strong and significant correlations were found among the related trio of time-averaged wall shear stress magnitude (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT). Wall shear stress spatial gradient (WSSG) was strongly and positively correlated with TAWSS. Correlations with Himburg and Friedman’s dominant harmonic (DH) parameter were found to depend on how the wall shear stress magnitude was defined in the presence of flow reversals. Many of the proposed HWP were found to provide essentially the same information about disturbed flow at the normal carotid bifurcation. RRT is recommended as a robust single metric of low and oscillating shear. On the other hand, gradient-based HWP may be of limited utility in light of possible redundancies with other HWP, and practical challenges in their measurement. Further investigations are encouraged before these findings should be extrapolated to other vascular territories.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061014-061014-7. doi:10.1115/1.3128672.
While mechanical stimulation of cells seeded within scaffolds is widely thought to be beneficial, the amount of benefit observed is highly variable between experimental systems. Although studies have investigated specific experimental loading protocols thought to be advantageous for cartilage growth, less is known about the physical stimuli (e.g., pressures, velocities, and local strains) cells experience during these experiments. This study used results of a literature survey, which looked for patterns in the efficacy of mechanical stimulation of chondrocyte seeded scaffolds, to inform the modeling of spatial patterns of physical stimuli present in mechanically stimulated constructs. The literature survey revealed a large variation in conditions used in mechanical loading studies, with a peak to peak strain of 10% (i.e., the maximum amount of deformation experienced by the scaffold) at 1 Hz on agarose scaffolds being the most frequently studied parameters and scaffold. This loading frequency was then used as the basis for simulation in the finite element analyses. 2D axisymmetric finite element models of $2×4 mm2$ scaffolds with 360 modulus/permeability combinations were constructed using COMSOL MULTIPHYSICS software. A time dependent coupled pore pressure/effective stress analysis was used to model fluid/solid interactions in the scaffolds upon loading. Loading was simulated using an impermeable frictionless loader on the top boundary with fluid and solid displacement confined to the radial axis. As expected, all scaffold materials exhibited classic poro-elastic behavior having pressurized cores with low fluid flow and edges with high radial fluid velocities. Under the simulation parameters of this study, PEG scaffolds had the highest pressure and radial fluid velocity but also the lowest shear stress and radial strain. Chitosan and KLD-12 simulated scaffold materials had the lowest radial strains and fluid velocities, with collagen scaffolds having the lowest pressures. Parametric analysis showed maximum peak pressures within the scaffold to be more dependent on scaffold modulus than on permeability and velocities to depend on both scaffold properties similarly. The dependence of radial strain on permeability or modulus was more complex; maximum strains occurred at lower permeabilities and moduli, and the lowest strain occurred at the stiffest most permeable scaffold. Shear stresses within all scaffolds were negligible. These results give insight into the large variations in metabolic response seen in studies involving mechanical stimulation of cell-seeded constructs, where the same loading conditions produce very different results due to the differences in material properties.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061015-061015-11. doi:10.1115/1.3127256.
The clinical assessment of abdominal aortic aneurysm (AAA) rupture risk is based on the quantification of AAA size by measuring its maximum diameter from computed tomography (CT) images and estimating the expansion rate of the aneurysm sac over time. Recent findings have shown that geometrical shape and size, as well as local wall thickness may be related to this risk; thus, reliable noninvasive image-based methods to evaluate AAA geometry have a potential to become valuable clinical tools. Utilizing existing CT data, the three-dimensional geometry of nine unruptured human AAAs was reconstructed and characterized quantitatively. We propose and evaluate a series of 1D size, 2D shape, 3D size, 3D shape, and second-order curvature-based indices to quantify AAA geometry, as well as the geometry of a size-matched idealized fusiform aneurysm and a patient-specific normal abdominal aorta used as controls. The wall thickness estimation algorithm, validated in our previous work, is tested against discrete point measurements taken from a cadaver tissue model, yielding an average relative difference in AAA wall thickness of 7.8%. It is unlikely that any one of the proposed geometrical indices alone would be a reliable index of rupture risk or a threshold for elective repair. Rather, the complete geometry and a positive correlation of a set of indices should be considered to assess the potential for rupture. With this quantitative parameter assessment, future research can be directed toward statistical analyses correlating the numerical values of these parameters with the risk of aneurysm rupture or intervention (surgical or endovascular). While this work does not provide direct insight into the possible clinical use of the geometric parameters, we believe it provides the foundation necessary for future efforts in that direction.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):061016-061016-7. doi:10.1115/1.3130454.
Each year, between $1.6×106$ and $3.8×106$ concussions are sustained by athletes playing sports, with football having the highest incidence. The high number of concussions in football provides a unique opportunity to collect biomechanical data to characterize mild traumatic brain injury. Human head acceleration data for a range of impact severities were collected by instrumenting the helmets of collegiate football players with accelerometers. The helmets of ten Virginia Tech football players were instrumented with measurement devices for every game and practice for the 2007 football season. The measurement devices recorded linear and angular accelerations about each of the three axes of the head. Data for each impact were downloaded wirelessly to a sideline data collection system shortly after each impact occurred. Data were collected for 1712 impacts, creating a large and unbiased data set. While a majority of the impacts were of relatively low severity ($<30 g$ and $<2000 rad/s2$), 172 impacts were greater than 40 g and 143 impacts were greater than $3000 rad/s2$. No instrumented player sustained a clinically diagnosed concussion during the 2007 season. A large and unbiased data set was compiled by instrumenting the helmets of collegiate football players. Football provides a unique opportunity to collect head acceleration data of varying severity from human volunteers. The addition of concurrent concussive data may advance the understanding of the mechanics of mild traumatic brain injury. With an increased understanding of the biomechanics of head impacts in collegiate football and human tolerance to head acceleration, better equipment can be designed to prevent head injuries.
Commentary by Dr. Valentin Fuster
### Technical Briefs
J Biomech Eng. 2009;131(6):064501-064501-8. doi:10.1115/1.3118770.
The mechanical behavior of human tympanic membrane (TM) has been investigated extensively under quasistatic loading conditions in the past. The results, however, are sparse for the mechanical properties (e.g., Young's modulus) of the TM at high strain rates, which are critical input for modeling the mechanical response under blast wave. The property data at high strain rates can also potentially be converted into complex modulus in frequency domain to model acoustic transmission in the human ear. In this study, we developed a new miniature split Hopkinson tension bar to investigate the mechanical behavior of human TM at high strain rates so that a force of up to half of a newton can be measured accurately under dynamic loading conditions. Young’s modulus of a normal human TM is reported as 45.2–58.9 MPa in the radial direction, and 34.1–56.8 MPa in the circumferential direction at strain rates $300–2000 s−1$. The results indicate that Young’s modulus has a strong dependence on strain rate at these high strain rates.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):064502-064502-6. doi:10.1115/1.3127249.
Quantification of bone strain can be used to better understand fracture risk, bone healing, and bone turnover. The objective of this work was to develop and validate an intensity matching image registration method to accurately measure and spatially resolve strain in vertebrae using $μCT$ imaging. A strain quantification method was developed that used two sequential $μCT$ scans, taken in loaded and unloaded configurations. The image correlation algorithm implemented was a multiresolution intensity matching deformable registration that found a series of affine mapping between the unloaded and loaded scans. Once the registration was completed, the displacement field and strain field were calculated from the mappings obtained. Validation was done in two distinct ways: the first was to look at how well the method could quantify zero strain; the second was to look at how the method was able to reproduce a known applied strain field. Analytically defined strain fields that linearly varied in space and strain fields resulting from finite element analysis were used to test the strain measurement algorithm. The deformable registration method showed very good agreement with all cases imposed, establishing a detection limit of 0.0004 strain and displaying agreement with the imposed strain cases (average $R2=0.96$). The deformable registration routine developed was able to accurately measure both strain and displacement fields in whole rat vertebrae. A rigorous validation of any strain measurement method is needed that reports on the ability of the routine to measure strain in a variety of strain fields with differing spatial extents, within the structure of interest.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(6):064503-064503-4. doi:10.1115/1.3128718.
Microgravity (micro-g) environments have been shown to elicit dysregulation of specific genes in a wide assay of cell types. It is known that the activation of transcription factors and molecular signaling pathways influence various physiological outcomes associated with stress and adaptive responses. Nuclear factor-kappa B $(NF-κB)$ is one of the most prevailing oxidation-sensitive transcription factors. It is hypothesized that simulated microgravity would activate $NF-κB$ and its downstream transcriptional networks, thus suggesting a role for $NF-κB$ in microgravity induced muscle atrophy. To investigate the activation of $NF-κB$ in a rat cardiac cell line (H9c2) under micro-g, rotating wall vessel bioreactors were used to simulate micro-g conditions. Western blotting revealed that mean nuclear translocation of $NF-κB$ p65 subunit was 69% for micro-g and 46% for unit-g dynamic control as compared with a 30 min $TNF-α$ positive control $(p<0.05, n=3)$. The results from western blots were confirmed by enzyme-linked immunosorbent assay, which showed 66% for micro-g and 45% for dynamic control as compared with positive control $(p<0.05, n=3)$. These results show significant differential translocation of $NF-κB$ p65 under simulated micro-g. These results may be expanded upon to explain physiological changes such as muscle atrophy and further identify the regulatory pathways and effector molecules activated under exposure to micro-g.
Commentary by Dr. Valentin Fuster
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# Kurtosis Interpretation
When you google “Kurtosis”, you encounter many formulas to help you calculate it, talk about how this measure is used to evaluate the “peakedness” of your data, maybe some other measures to help you do so, maybe all of a sudden a side step towards Skewness, and how both Skewness and Kurtosis are higher moments of the distribution. This is all very true, but maybe you just want to understand what does Kurtosis mean and how to interpret this measure. Similarly to the way you interpret standard deviation (the average distance from the average). Here I take a shot at giving a more intuitive interpretation.
It is true that Kurtosis is used to evaluate the “peakedness” of your data, but so what? what do you care Peaky or not Peaky? you are not picky. The answer is that you would like to know where does your variance come from. If your data is not peaky, the variance is distributed throughout, if your data is peaky, you have little variance close to the “center” and the origin of the variance is from the “sides” or what we call tails.
Calculating means and the variances provides you important information about the your data, namely:
1. Where is it? (mean)
2. How scattered is it? (variance)
You can get more, you can also get a clue about the cause for the variance. In what way is your data scattered? Might be that your data has high standard deviation, yet the distribution is relatively flat, with just a handful of observations in the tails. That is why you want to take a look at the Kurtosis measure.
The next figure presents three simulated known distributions, Uniform, Normal and Laplace.
The Uniform distribution has the highest Standard deviation (4.26 for this simulation), it is the most scattered one, but the lowest Kurtosis, (-1.2) since the variance is relatively “equally distributed”, the Laplace one has the highest Kurtosis, since the variance is most scattered, low portion of the variance comes from the center, that is the peakedness referred to earlier, and large portion of the variance comes from the tails. Code for the simulation and graph is below, thanks for reading.
Notes:
Kurtosis here is Excess Kurtosis, add 3 to get the actual Kurtosis.
library(VGAM) # for the laplace lap = rlaplace(5000, location=0, scale=1) uni = runif(5000, min(lap),max(lap)) nor = rnorm(5000) denlap = density(lap);dennor = density(nor); denuni = density(uni ) lwd1 = 3 plot(denlap, lwd = lwd1, zer = F, main = "Where does your variance come from?", xlab = "Simulated Normal (red), Laplace (Black) and Uniform (green)") lines(dennor, col = 2, lwd = lwd1) lines(denuni, col = 3, lwd = lwd1) legend("topleft", c(paste("Kurtosis = ",round(kurtosis(nor),digits = 2)), paste("Kurtosis = ",round(kurtosis(uni),digits = 2)), paste("Kurtosis = ",round(kurtosis(lap), digits = 2))), col = c(2,3,1), lty = 1, lwd = lwd1, text.col = c(2,3,1), bty = "n")
Related:
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# The Unbearable Lightness of Mobile Voice.
• Mobile data adaption can be (and usually is) very un-healthy for the mobile voice revenues.
• A Mega Byte of Mobile Voice is 6 times more expensive than a Mega Byte of Mobile Data (i.e., global average)
• If customers would pay the Mobile Data Price for Mobile Voice, 50% of Global Mobile Revenue would Evaporate (based on 2013 data).
• Classical Mobile Voice is not Dead! Global Mobile Voice Usage grew with more than 50% over the last 5 years. Though Global Voice Revenue remained largely constant (over 2009 – 2013).
• Mobile Voice Revenues declined in most Western European & Central Eastern European countries.
• Voice Revenue in Emerging Mobile-Data Markets (i.e., Latin America, Africa and APAC) showed positive growth although decelerating.
• Mobile Applications providing high-quality (often High Definition) mobile Voice over IP should be expected to dent the classical mobile voice revenues (as Apps have impacted SMS usage & revenue).
• Most Western & Central Eastern European markets shows an increasing decline in price elasticity of mobile voice demand. Even some markets (regions) had their voice demand decline as the voice prices were reduced (note: not that causality should be deduced from this trend though).
• The Art of Re-balancing (or re-capture) the mobile voice revenue in data-centric price plans are non-trivial and prone to trial-and-error (but likely also un-avoidable).
## An Unbearable Lightness.
There is something almost perverse about how light the mobile industry tends to treat Mobile Voice, an unbearable lightness?
How often don’t we hear Telco Executives wish for All-IP and web-centric services for All? More and more mobile data-centric plans are being offered with voice as an after thought. Even though voice still constitute more than 60% of the Global Mobile turnover and in many emerging mobile markets beyond that. Even though classical mobile voice is more profitable than true mobile broadband access. “Has the train left the station” for Voice and running off the track? In my opinion, it might have for some Telecom Operators, but surely not for all. Taking some time away from thinking about mobile data would already be an incredible improvement if spend on strategizing and safeguarding mobile voice revenues that still are a very substantial part of The Mobile Business Model.
Mobile data penetration is un-healthy for voice revenue. It is almost guarantied that voice revenue will start declining as the mobile data penetration reaches 20% and beyond. There are very few exceptions (i.e., Australia, Singapore, Hong Kong and Saudi Arabia) to this rule as observed in the figure below. Much of this can be explained by the Telecoms focus on mobile data and mobile data centric strategies that takes the mobile voice business for given or an afterthought … focusing on a future of All-IP Services where voice is “just” another data service. Given the importance of voice revenues to the mobile business model, treating voice as an afterthought is maybe not the most value-driven strategy to adopt.
I should maybe point out that this is not per se a result of the underlying Cellular All-IP Technology. The fact is that Cellular Voice over an All-IP network is very well specified within 3GPP. Voice over LTE (i.e., VoLTE), or Voice over HSPA (VoHSPA) for that matter, is enabled with the IP Multimedia Subsystem (IMS). Both VoLTE and VoHSPA, or simply Cellular Voice over IP (Cellular VoIP as specified by 3GPP), are highly spectral efficient (compared to their circuit switched equivalents). Further the Cellular VoIP can be delivered at a high quality comparable to or better than High Definition (HD) circuit switched voice. Recent Mean Opinion Score (MOS) measurements by Ericsson and more recently (August 2014) Signals Research Group & Spirent have together done very extensive VoLTE network benchmark tests including VoLTE comparison with the voice quality of 2G & 3G Voice as well as Skype (“Behind the VoLTE Curtain, Part 1. Quantifying the Performance of a Commercial VoLTE Deployment”). Further advantage of Cellular VoIP is that it is specified to inter-operate with legacy circuit-switched networks via the circuit-switched fallback functionality. An excellent account for Cellular VoIP and VoLTE in particular can be found in Miikki Poikselka et al’s great book on “Voice over LTE” (Wiley, 2012).
Its not the All-IP Technology that is wrong, its the commercial & strategic thinking of Voice in an All-IP World that leaves a lot to be wished for.
Voice over LTE provides for much better Voice Quality than a non-operator controlled (i.e., OTT) mobile VoIP Application would be able to offer. But is that Quality worth 5 to 6 times the price of data, that is the Billion $Question. • Figure Above: illustrates the compound annual growth rates (2009 to 2013) of mobile voice revenue and the mobile data penetration at the beginning of the period (i.e., 2009). As will be addressed later it should be noted that the growth of mobile voice revenues are NOT only depending on Mobile Data Penetration Rates but on a few other important factors, such as addition of new unique subscribers, the minute price and the voice arpu compared to the income level (to name a few). Analysis has been based on Pyramid Research data. Abbreviations: WEU: Western Europe, CEE: Central Eastern Europe, APAC: Asia Pacific, MEA: Middle East & Africa, NA: North America and LA: Latin America. In the following discussion classical mobile voice should be understood as an operator-controlled voice service charged by the minute or in equivalent economical terms (i.e., re-balanced data pricing). This is opposed to a mobile-application-based voice service (outside the direct control of the Telecom Operator) charged by the tariff structure of a mobile data package without imposed re-balancing. If the Industry would charge a Mobile Voice Minute the equivalent of what they charge a Mobile Mega Byte … almost 50% of Mobile Turnover would disappear … So be careful AND be prepared for what you wish for! There are at least a couple of good reasons why Mobile Operators should be very focused on preserving mobile voice as we know it (or approximately so) also in LTE (and any future standards). Even more so, Mobile Operators should try to avoid too many associations with non-operator controlled Voice-over-IP (VoIP) Smartphone applications (easier said than done .. I know). It will be very important to define a future voice service on the All-IP Mobile Network that maintains its economics (i.e., pricing & margin) and don’t get “confused” with the mobile-data-based economics with substantially lower unit prices & questionable profitability. Back in 2011 at the Mobile Open Summit, I presented “Who pays for Mobile Broadband” (i.e., both in London & San Francisco) with the following picture drawing attention to some of the Legacy Service (e.g., voice & SMS) challenges our Industry would be facing in the years to come from the many mobile applications developed and in development; One of the questions back in 2011 was (and Wow it still is! …) how to maintain the Mobile ARPU & Revenues at a reasonable level, as opposed to massive loss of revenue and business model sustainability that the mobile data business model appeared to promise (and pretty much still does). Particular the threat (& opportunities) from mobile Smartphone applications. Mobile Apps that provides Mobile Customers with attractive price-arbitrage compared to their legacy prices for SMS and Classical Voice. ## “IP killed the SMS Star” … Will IP also do away with the Classical Mobile Voice Economics as well? Okay … Lets just be clear about what is killing SMS (it’s hardly dead yet). The Mobile Smartphone Messaging-over-IP (MoIP) App does the killing. However, the tariff structure of an SMS vis-a-vis that of a mobile Mega Byte (i..e, ca. 3,000x) is the real instigator of the deed together with the shear convenience of the mobile application itself. As of August 2014 the top Messaging & Voice over IP Smartphone applications share ca. 2.0+ Billion Active Users (not counting Facebook Messenger and of course with overlap, i.e., active users having several apps on their device). WhatsApp is the Number One Mobile Communications App with about 700 Million active users (i.e., up from 600 Million active users in August 2014). Other Smartphone Apps are further away from the WhatsApp adaption figures. Applications from Viber can boast of 200+M active users, WeChat (predominantly popular in Asia) reportedly have 460+M active users and good old Skype around 300+M active users. The impact of smartphone MoIP applications on classical messaging (e.g., SMS) is well evidenced. So far Mobile Voice-over-IP has not visible dented the Telecom Industry’s mobile voice revenues. However the historical evidence is obviously no guaranty that it will not become an issue in the future (near, medium or far). WhatsApp is rumoured to launch mobile voice calling as of first Quarter of 2015 … Will this event be the undoing of operator controlled classical mobile voice? WhatsApp already has taken the SMS Scalp with 30 Billion WhatsApp messages send per day according the latest data from WhatsApp (January 2015). For comparison the amount of SMS send out over mobile networks globally was a bit more than 20 Billion per day (source: Pyramid Research data). It will be very interesting (and likely scary as well) to follow how WhatsApp Voice (over IP) service will impact Telecom operator’s mobile voice usage and of course their voice revenues. The Industry appears to take the news lightly and supposedly are unconcerned about the prospects of WhatsApp launching a mobile voice services (see: “WhatsApp voice calling – nightmare for mobile operators?” from 7 January 2015) … My favourite lightness is Vodacom’s (South Africa) “if anything, this vindicates the massive investments that we’ve been making in our network….” … Talking about unbearable lightness of mobile voice … (i.e., 68% of the mobile internet users in South Africa has WhatsApp on their smartphone). ## Paying the price of a mega byte mobile voice. A Mega-Byte is not just a Mega-Byte … it is much more than that! In 2013, the going Global average rate of a Mobile (Data) Mega Byte was approximately 5 US-Dollar Cent (or a Nickel). A Mega Byte (MB) of circuit switched voice (i.e., ca. 11 Minutes @ 12.2kbps codec) would cost you 30+ US$-cent or about 6 times that of Mobile Data MB. Would you try to send a MB of SMS (i.e., ca. 7,143 of them) that would cost you roughly 150 US$(NOTE: US$ not US$-Cents). ### 1 Mobile MB = 5 US$-cent Data MB < 30+ US$-cent Voice MB (6x mobile data) << 150 US$ SMS MB (3000x mobile data).
A Mega Byte of voice conversation is pretty un-ambiguous in the sense of being 11 minutes of a voice conversation (typically a dialogue, but could be monologue as well, e.g., voice mail or an angry better half) at a 12.2 kbps speech codec. How much mega byte a given voice conversation will translate into will depend on the underlying speech coding & decoding (codec) information rate, which typically is 12.2 kbps or 5.9 kbps (i.e., for 3GPP cellular-based voice). In general we would not be directly conscious about speed (e.g., 12.2 kbps) at which our conversation is being coded and decoded although we certainly would be aware of the quality of the codec itself and its ability to correct errors that will occur in-between the two terminals. For a voice conversation itself, the parties that engage in the conversation is pretty much determining the duration of the conversation.
An SMS is pretty straightforward and well defined as well, i.e., being 140 Bytes (or characters). Again the underlying delivery speed is less important as for most purposes it feels that the SMS sending & delivery is almost instantaneously (though the reply might not be).
All good … but what about a Mobile Data Byte? As a concept it could by anything or nothing. A Mega Byte of Data is Extremely Ambiguous. Certainly we get pretty upset if we perceive a mobile data connection to be slow. But the content, represented by the Byte, would obviously impact our perception of time and whether we are getting what we believe we are paying for. We are no longer master of time. The Technology has taken over time.
In my opinion the answer should be clearly NO … Such (somewhat silly) comparisons serves to show the problem with pricing and valuing a Mega Byte. It also illustrates the danger of ambiguity of mobile data and why an operator should try to avoid bundling everything under the banner of mobile data (or at the very least be smart about it … whatever that means).
I am being a bit naughty in above comparisons, as I am freely mixing up the time scales of delivering a Byte and the time scales of neurological processing that Byte (mea culpa).
• Figure Above: Logarithmic representation of the cost per Mega Byte of a given mobile service. 1 MB of Voice is roughly corresponding to 11 Minutes at a 12.2 voice codec which is ca. 25+ times the monthly global MoU usage. 1 MB of SMS correspond to ca. 7,143 SMSs which is a lot (actually really a lot). In USA 7,143 would roughly correspond to a full years consumption. However, in WEU 7,143 SMS would be ca. 6+ years of SMS consumption (on average) to about almost 12 years of SMS consumption in MEA Region. Still SMS remain proportionate costly and clear is an obvious service to be rapidly replaced by mobile data as it becomes readily available. Source: Pyramid Research.
## The “Black” Art of Re-balancing … Making the Lightness more Bearable?
I recently had a discussion with a very good friend (from an emerging market) about how to recover lost mobile voice revenues in the mobile data plans (i.e., the art of re-balancing or re-capturing). Could we do without Voice Plans? Should we focus on All-in the Data Package? Obviously, if you would charge 30+ US$-cent per Mega Byte Voice, while you charge 5 US$-cent for Mobile Data, that might not go down well with your customers (or consumer interest groups). We all know that “window-dressing” and sleight-of-hand are important principles in presenting attractive pricings. So instead of Mega Byte voice we might charge per Kilo Byte (lower numeric price), i.e., 0.029 US$-cent per kilo byte (note: 1 kilo-byte is ca. 0.65 seconds @ 12.2 kbps codec). But in general the consumer are smarter than that. Probably the best is to maintain a per time-unit charge or to Blend in the voice usage & pricing into the Mega Byte Data Price Plan (and hope you have done your math right). Example (a very simple one): Say you have 500 MB mobile data price plan at 5 US$-cent per MB (i.e., 25 US$). You also have a 300 Minute Mobile Voice Plan of 2.7 US$-cent a minute (or 30 US$-cent per MB). Now 300 Minutes corresponds roughly to 30 MB of Voice Usage and would be charged ca. 9$. Instead of having a Data & Voice Plan, one might have only the Data Plan charging (500 MB x 5 US$cent/MB + 30 MB x 30 US$/cent/MB) / 530 MB or 6.4 US$-cent per MB (or 1.4 US$-cent more for mobile voice over the data plan or a 30% surcharge for Voice on the Mobile Data Bytes). Obviously such a pricing strategy (while simple) does pose some price strategic challenges and certainly does not per se completely safeguard voice revenue erosion. Keeping Mobile Voice separately from Mobile Data (i.e., Minutes vs Mega Bytes) in my opinion will remain the better strategy. Although such a minutes-based strategy is easily disrupted by innovative VoIP applications and data-only entrepreneurs (as well as Regulator Authorities).
Re-balancing (or re-capture) the voice revenue in data-centric price plans are non-trivial and prone to trial-and-error. Nevertheless it is clearly an important pricing strategy area to focus on in order to defend existing mobile voice revenues from evaporating or devaluing by the mobile data price plan association.
Is Voice-based communication for the Masses (as opposed to SME, SOHO, B2B,Niche demand, …) technologically un-interesting? As a techno-economist I would say far from it. From the GSM to HSPA and towards LTE, we have observed a quantum leap, a factor 10, in voice spectral efficiency (or capacity), substantial boost in link-budget (i.e., approximately 30% more geographical area can be covered with UMTS as opposed to GSM in apples for apples configurations) and of course increased quality (i.e., high-definition or crystal clear mobile voice). The below Figure illustrates the progress in voice capacity as a function of mobile technology. The relative voice spectral efficiency data in the below figure has been derived from one of the best (imo) textbooks on mobile voice “Voice over LTE” by Miikki Poikselka et all (Wiley, 2012);
• Figure Above: Abbreviation guide; EFR: Enhanced Full Rate, AMR: Adaptive Multi-Rate, DFCA: Dynamic Frequency & Channel Allocation, IC: Interference Cancellation. What might not always be appreciate is the possibility of defining voice over HSPA, similar to Voice over LTE. Source: “Voice over LTE” by Miikki Poikselka et all (Wiley, 2012).
If you do a Google Search on Mobile Voice you would get ca. 500 Million results (note Voice over IP only yields 100+ million results). Try that on Mobile Data and “sham bam thank you mam” you get 2+ Billion results (and projected to increase further). For most of us working in the Telecom industry we spend very little time on voice issues and an over-proportionate amount of time on broadband data. When you tell your Marketing Department that a state-of-the-art 3G can carry at least twice as much voice traffic than state-of-the –art GSM (and over 30% more coverage area) they don’t really seem to get terribly exited? Voice is un-sexy!? an afterthought!? … (don’t even go brave and tell Marketing about Voice over LTE, aka VoLTE).
Is Mobile Voice Dead or at the very least Dying?
Is Voice un-interesting, something to be taken for granted?
Is Voice “just” data and should be regarded as an add-on to Mobile Data Services and Propositions?
From a Mobile Revenue perspective mobile voice is certainly not something to be taken for granted or just an afterthought. In 2013, mobile voice still amounted for 60+% of he total global mobile turnover, with mobile data taking up ca. 40% and SMS ca. 10%. There are a lot of evidence that SMS is dying out quickly with the emergence of smartphones and Messaging-over-IP-based mobile application (SMS – Assimilation is inevitable, Resistance is Futile!). Not particular surprising given the pricing of SMS and the many very attractive IP-based alternatives. So are there similar evidences of mobile voice dying?
NO! NIET! NEM! MA HO BU! NEJ! (not any time soon at least)
## Lets see what the data have to say about mobile voice?
In the following I only provide a Regional but should there be interest I have very detailed deep dives for most major countries in the various regions. In general there are bigger variations to the regional averages in Middle East & Africa (i.e., MEA) as well as Asia Pacific (i.e., APAC) Regions, as there is a larger mix of mature and emerging markets with fairly large differences in mobile penetration rates and mobile data adaptation in general. Western Europe, Central Eastern Europe, North America (i.e., USA & Canada) and Latin America are more uniform in conclusions that can reasonably be inferred from the averages.
As shown in the Figure below, from 2009 to 2013, the total amount of mobile minutes generated globally increased with 50+%. Most of that increase came from emerging markets as more share of the population (in terms of individual subscribers rather than subscriptions) adapted mobile telephony. In absolute terms, the global mobile voice revenues did show evidence of stagnation and trending towards decline.
• Figure Above: Illustrates the development & composition of historical Global Mobile Revenues over the period 2009 to 2013. In addition also shows the total estimated growth of mobile voice minutes (i.e., Red Solid Curve showing MoUs in units of Trillions) over the period. Sources: Pyramid Research & Statista. It should noted that various data sources actual numbers (over the period) are note completely matching. I have observed a difference between various sources of up-to 15% in actual global values. While interesting this difference does not alter the analysis & conclusions presented here.
If all voice minutes was charged with the current Rate of Mobile Data, approximately Half-a-Billion US$would evaporate from the Global Mobile Revenues. So while mobile voice revenues might not be a positive growth story its still “sort-of” important to the mobile industry business. Most countries in Western & Central Eastern Europe as well as mature markets in Middle East and Asia Pacific shows mobile voice revenue decline (in absolute terms and in their local currencies). For Latin America, Africa and Emerging Mobile Data Markets in Asia-Pacific almost all exhibits positive mobile voice revenue growth (although most have decelerating growth rates). • Figure Above: Illustrates the annual growth rates (compounded) of total mobile voice revenues and the corresponding growth in mobile voice traffic (i.e., associated with the revenues). Some care should be taken as for each region US$ has been used as a common currency. In general each individual country within a region has been analysed based on its own local currency in order to avoid mixing up currency exchange effects. Source: Pyramid Research.
Of course revenue growth of the voice service will depend on (1) the growth of subscriber base, (2) the growth of the unit itself (i.e., minutes of voice usage) as it is used by the subscribers (i.e., which is likely influenced by the unit price), and (3) the development of the average voice revenue per subscriber (or user) or the unit price of the voice service. Whether positive or negative growth of Revenue results, pretty much depends on the competitive environment, regulatory environment and how smart the business is in developing its pricing strategy & customer acquisition & churn dynamics.
Growth of (unique) mobile customers obviously depends the level of penetration, network coverage & customer affordability. Growth in highly penetrated markets is in general (much) lower than growth in less mature markets.
• Figure Above: Illustrates the annual growth rates (compounded) of unique subscribers added to a given market (or region). Further to illustrate the possible relationship between increased subscribers and increased total generated mobile minutes the previous total minutes annual growth is shown as well. Source: Pyramid Research.
Interestingly, particular for the North America Region (NA), we see an increase in unique subscribers of 11% per anno and hardly any growth over the period of total voice minutes. Firstly, note that the US Market will dominate the averaging of the North America Region (i.e., USA and Canada) having approx. 13 times more subscribers. So one of the reasons for this no-minutes-growth effect is that the US market saw a substantial increase in the prepaid ratio (i.e., from ca.19% in 2009 to 28% in 2013). Not only were new (unique) prepaid customers being added. Also a fairly large postpaid to prepaid migration took place over the period. In the USA the minute usage of a prepaid is ca. 35+% lower than that of a postpaid. In comparison the Global demanded minutes difference is 2.2+ times lower prepaid minute usage compared to that of a postpaid subscriber). In the NA Region (and of course likewise in the USA Market) we observe a reduced voice usage over the period both for the postpaid & prepaid segment (based on unique subscribers). Thus increased prepaid blend in the overall mobile base with a relative lower voice usage combined with a general decline in voice usage leads to a pretty much zero growth in voice usage in the NA Market. Although the NA Region is dominated by USA growth (ca. 0.1 % CAGR total voice growth), Canada’s likewise showed very minor growth in their overall voice usage as well (ca. 3.8% CAGR). Both Canada & USA reduced their minute pricing over the period.
• Note on US Voice Usage & Revenues: note that in both in US and in Canada also the receiving party pays (RPP) for receiving a voice call. Thus revenue generating minutes arises from both outgoing and incoming minutes. This is different from most other markets where the Calling Party Pays (CPP) and only minutes originating are counted in the revenue generation. For example in USA the Minutes of Use per blended customer was ca. 620 MoU in 2013. To make that number comparable with say Europe’s 180 MoU, one would need to half the US figure to 310 MoU still a lot higher than the Western European blended minutes of use. The US bundles are huge (in terms of allowed minutes) and likewise the charges outside bundles (i.e., forcing the consumer into the next one) though the fixed fees tends be high to very high (in comparison with other mobile markets). The traditional US voice plan would offer unlimited on-net usage (i.e., both calling & receiving party are subscribing to the same mobile network operator) as well as unlimited off-peak usage (i.e., evening/night/weekends). It should be noted that many new US-based mobile price plans offers data bundles with unlimited voice (i.e., data-centric price plans). In 2013 approximately 60% of the US mobile industry’s turnover could be attributed to mobile voice usage. This number is likely somewhat higher as some data-tariffs has voice-usage (e.g., typically unlimited) embedded. In particular the US mobile voice business model would be depending customer migration to prepaid or lower-cost bundles as well as how well the voice-usage is being re-balanced (and re-captured) in the Data-centric price plans.
The second main component of the voice revenue is the unit price of a voice minute. Apart from the NA Region, all markets show substantial reductions in the unit price of a minute.
• Figure Above: Illustrating the annual growth (compounded) of the per minute price in US$-cents as well as the corresponding growth in total voice minutes. The most affected by declining growth is Western Europe & Central Eastern Europe although other more-emerging markets are observed to have decelerating voice revenue growth. Source: Pyramid Research. Clearly from the above it appears that the voice “elastic” have broken down in most mature markets with diminishing (or no return) on further minute price reductions. Another way of looking at the loss (or lack) of voice elasticity is to look at the unit-price development of a voice-minute versus the growth of the total voice revenues; • Figure Above: Illustrates the growth of Total Voice Revenue and the unit-price development of a mobile voice minute. Apart from the Latin America (LA) and Asia Pacific (APAC) markets there clearly is no much further point in reducing the price of voice. Obviously, there are other sources & causes, than the pure gain of elasticity, effecting the price development of a mobile voice minute (i.e., regulatory, competition, reduced demand/voice substitution, etc..). Note US$ has been used as the unifying currency across the various markets. Despite currency effects the trend is consistent across the markets shown above. Source: Pyramid Research.
While Western & Central-Eastern Europe (WEU & CEE) as well as the mature markets in Middle East and Asia-Pacific shows little economic gain in lowering voice price, in the more emerging markets (LA and Africa) there are still net voice revenue gains to be made by lowering the unit price of a minute (although the gains are diminishing rapidly). Although most of the voice growth in the emerging markets comes from adding new customers rather than from growth in the demand per customer itself.
• Figure Above: Illustrating possible drivers for mobile voice growth (positive as well as negative); such as Mobile Data Penetration 2013 (expected negative growth impact), increased number of (unique) subscribers compared to 2009 (expected positive growth impact) and changes in prepaid-postpaid blend (a negative %tage means postpaid increased their proportion while a positive %tage translates into a higher proportion of prepaid compared to 2009). Voice tariff changes have been observed to have elastic effects on usage as well although the impact changes from market to market pending on maturity. Source: derived from Pyramid Research.
With all the talk about Mobile Data, it might come as a surprise that Voice Usage is actually growing across all regions with the exception of North America. The sources of the Mobile Voice Minutes Growth are largely coming from
1. Adding new unique subscribers (i.e., increasing mobile penetration rates).
2. Transitioning existing subscribers from prepaid to postpaid subscriptions (i.e., postpaid tends to have (a lot) higher voice usage compared to prepaid).
3. General increase in usage per individual subscriber (i.e., few markets where this is actually observed irrespective of the general decline in the unit cost of a voice minute).
To the last point (#3) it should be noted that the general trend across almost all markets is that Minutes of Use per Unique customer is stagnating and even in decline despite substantial per unit price reduction of a consumed minute. In some markets that trend is somewhat compensated by increase of postpaid penetration rates (i.e., postpaid subscribers tend to consume more voice minutes). The reduction of MoUs per individual subscriber is more significant than a subscription-based analysis would let on.
and
### Mobile Voice Revenue is a very important part of the overall mobile revenue composition.
It might make very good sense to spend a bit more time on strategizing voice, than appears to be the case today. If mobile voice remains just an afterthought of mobile data, the Telecom industry will loose massive amounts of Revenues and last but not least Profitability.
## Post Script: What drives the voice minute growth?
An interesting exercise is to take all the data and run some statistical analysis on it to see what comes out in terms of main drivers for voice minute growth, positive as well as negative. The data available to me comprises 77 countries from WEU (16), CEE (8), APAC (15), MEA (17), NA (Canada & USA) and LA (19). I am furthermore working with 18 different growth parameters (e.g., mobile penetration, prepaid share of base, data adaptation, data penetration begin of period, minutes of use, voice arpu, voice minute price, total minute volume, customers, total revenue growth, sms, sms price, pricing & arpu relative to nominal gdp etc…) and 7 dummy parameters (populated with noise and unrelated data).
Two specific voice minute growth models emerges our of a comprehensive analysis of the above described data. The first model is as follows
(1) Voice Growth correlates positively with Mobile Penetration (of unique customers) in the sense of higher penetration results in more minutes, it correlates negatively with Mobile Data Penetration at the begin of the period (i.e., 2009 uptake of 3G, LTE and beyond) in the sense that higher mobile data uptake at the begin of the period leads to a reduction of Voice Growth, and finally Voice Growth correlates negatively with the Price of a Voice Minute in the sense of higher prices leads to lower growth and lower prices leads to higher growth. This model is statistically fairly robust (e.g., a p-values < 0.0001) as well as having all parameters with a statistically meaningful confidence intervals (i.e., upper & lower 95% confidence interval having the same sign).
The Global Analysis does pin point to very rational drivers for mobile voice usage growth, i.e., that mobile penetration growth, mobile data uptake and price of a voice minute are important drivers for total voice usage.
It should be noted that changes in the prepaid proportion does not appear statistically to impact voice minute growth.
The second model provides a marginal better overall fit to the Global Data but yields slightly worse p-values for the individual descriptive parameters.
(2) The second model simply adds the Voice ARPU to (nominal) GDP ratio to the first model. This yields a negative correlation in the sense that a low ratio results in higher voice usage growth and a higher ration in lower voice usage growth.
Both models describe the trends or voice growth dynamics reasonably well, although less convincing for Western & Central Eastern Europe and other more mature markets where the model tends to overshoot the actual data. One of the reasons for this is that the initial attempt was to describe the global voice growth behaviour across very diverse markets.
• Figure Above: Illustrates total annual generated voice minutes compound annual growth rate (between 2009 and 2013) for 77 markets across 6 major regions (i.e., WEU, CEE, APAC, MEA, NA and LA). The Model 1 shows an attempt to describe the Global growth trend across all 77 markets within the same model. The Global Model is not great for Western Europe and part of the CEE although it tends to describe the trends between the markets reasonably.
• Figure Western & Central Eastern Region: the above Illustrates the compound annual growth rate (2009 – 2013) of total generated voice minutes and corresponding voice revenues. For Western & Central Eastern Europe while the generated minutes have increased the voice revenue have consistently declined. The average CAGR of new unique customers over the period was 1.2% with the maximum being little less than 4%.
• Figure Asia Pacific Region: the above Illustrates the compound annual growth rate (2009 – 2013) of total generated voice minutes and corresponding voice revenues. For the Emerging market in the region there is still positive growth of both minutes generated as well as voice revenue generated. Most of the mature markets the voice revenue growth is negative as have been observed for mature Western & Central Eastern Europe.
• Figure Middle East & Africa Region: the above Illustrates the compound annual growth rate (2009 – 2013) of total generated voice minutes and corresponding voice revenues. For the Emerging market in the region there is still positive growth of both minutes generated as well as voice revenue generated. Most of the mature markets the voice revenue growth is negative as have been observed for mature Western & Central Eastern Europe.
• Figure North & Latin America Region: the above Illustrates the compound annual growth rate (2009 – 2013) of total generated voice minutes and corresponding voice revenues. For the Emerging market in the region there is still positive growth of both minutes generated as well as voice revenue generated. Most of the mature markets the voice revenue growth is negative as have been observed for mature Western & Central Eastern Europe.
## PS.PS. Voice Tariff Structure
• Typically the structure of a mobile voice tariff (or how the customer is billed) is structure as follows
• ### Fixed charge / fee
• This fixed charge can be regarded as an access charge and usually is associated with a given usage limit (i.e., \$ X for Y units of usage) or bundle structure.
• ### Variable per unit usage charge
• On-net – call originating and terminating within same network.
• Off-net – Domestic Mobile.
• Off-net – Domestic Fixed.
• Off-net – International.
• Local vs Long-distance.
• Peak vs Off-peak rates (e.g., off-peak typically evening/night/weekend).
• Roaming rates (i.e., when customer usage occurs in foreign network).
• Special number tariffs (i.e., calls to paid-service numbers).
How a fixed vis-a-vis variable charges are implemented will depend on the particularity of a given market but in general will depend on service penetration and local vs long-distance charges.
• ### Acknowledgement
I greatly acknowledge my wife Eva Varadi for her support, patience and understanding during the creative process of creating this Blog. I certainly have not always been very present during the analysis and writing. Also many thanks to Shivendra Nautiyal and others for discussing and challenging the importance of mobile voice versus mobile data and how practically to mitigate VoIP cannibalization of the Classical Mobile Voice.
• ## 29 thoughts on “The Unbearable Lightness of Mobile Voice.”
1. Great analysis and post. Essentially value-based pricing for the voice data. Hard to see that holding up over time. Meanwhile, it is still the case that at the other end of the spectrum (entertainment data/streams), the cost/price of mobile data remains an order of magnitude greater than the value of the content.
• Paul, thank you very much for your comments.Yes it is indeed hard to see keeping the voice price, in a data-centric world, at the level of where it is today. However, the industry’s (often un-healthy & oversimplified) obsession with mobile broadband data without considering how to position voice is certainly going to accelerate the mobile value destruction.
On your second point (knowing you as subject matter expert in this area), I think this puts the head on the nail of how challenging it is to match a price/cost of access to the value of content that is being demanded. In my opinion a Byte is a very meaningless measure to base a price on. Certainly doesnt really drive the cost of delivering it. It really says nothing about cost & value of the Byte, as it obviously depend on what that Byte represents (i.e., voice conversation, picture, video, messages, book, radio, etc…).
• We always should care more about absolutes than relatives. So yes I agree. What really matters is indeed the total revenue and how that changes over time pending competition and marketing strategies. The danger is that by associating everything with data and a Byte your converge to a price per Byte that results in massive loss of absolute revenues (unless great care is taken in price strategy). Moreover voice converted to Bytes will be almost unnoticeable in the overall data consumption. An unbearable lightness. Of course we might be able to live with revenue loss if we could maintain or grow profitability … But the revenue loss potential by messing up voice revenues are too big for me seeing that ending well!
2. Hopefully a simple question regarding the data; How is voice revenues calculated for combined voice / data plans with unlimited voice and limited data)?
• Jan, in principle Voice ARPU is estimated based MNO reported “pure” voice revenues for prepaid and postpaid. Now this obviously depends on the accuracy & purity of MNO reporting and to some extend to the degree it is available from financial reporting s (at some occasions this will be a guestimate rather than directly measured). My own assessment is that any possible cross-contamination is minor for the most countries and regions. In particular for the emerging ones. While the analysis is based on Pyramid Research data, I have checked the data against alternative analyst data (e.g., Bank of America, Merrill Lynch Mobile Matrix) as well as where applicable against internal data available. This said, I do concede that cross contamination (mainly from voice included in data) is likely to grow as MNOs will try to re-balance or re-capture lost voice revenues.
3. I agree that voice revenues have low management attention compared to the significant position of voice in the current business models for MNOs. Looking at this from an MNO perspective it makes sense to defend and extend voice revenues as far as possible. Mobile voice has become a great business. And the main value of mobile voice I think is in convenience. Mobile voice has not been clearly competitive in voice quality, call setup time etc. But it has been and still is the easiest way to talk to another person over distance. But looking at mobile services more generally, voice seems to be the only service where the MNO is in control of the service and the revenues. For all other mobile services (youtube, facebook, twitter etc), the MNO is only a bitpipe providing connectivity services. Is it likely that voice will continue to survive as a standalone service? Or will it more likely be integrated with other digital services? I expect that the business models for connectivity provider / bitpipe / MNO and the business models for digital services will diverge. I think that the primary objective of the MNO is to provide cost effective connectivity. Towards the market, different constellations of network service providers and digital service providers will offer combined services to the customers, but these constellations and service combinations will most likely be more dynamic over time as this is where services and business models will develop very fast. We already see the disconnection between network services and digital services, and also for voice, service providers are offering the voice service over foreign networks like VoWiFi / WiFi Calling. So, for the MNO and voice service, are you just trying to keep the boat afloat until you get a bit closer to shore? Or do you expect that the MNO voice services can win the regatta against Google, Microsoft, Apple etc?
• Thank you so much for this very thoughtful analysis and commentary. I agree that the strongest point of the MNO is its connectivity/access infrastructure, including its spectrum assets. Being a smart and profitable access provider (or bit pipe) is paramount to the mobile business model’s sustainability although possible in a very different form from what it was in the past and what it is today. However, here also lays a (self)-image problem as it would indicate that access eventually is nothing more (and nothing less) than a utility.
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# rbf
0th
Percentile
##### Create and train a radial basis function (RBF) network
The use of an RBF network is similar to that of an mlp. The idea of radial basis function networks comes from function interpolation theory. The RBF performs a linear combination of n basis functions that are radially symmetric around a center/prototype.
##### Usage
rbf(x, ...)# S3 method for default
rbf(x, y, size = c(5), maxit = 100,
initFunc = "RBF_Weights", initFuncParams = c(0, 1, 0, 0.02, 0.04),
learnFunc = "RadialBasisLearning", learnFuncParams = c(1e-05, 0,
1e-05, 0.1, 0.8), updateFunc = "Topological_Order",
updateFuncParams = c(0), shufflePatterns = TRUE, linOut = TRUE,
inputsTest = NULL, targetsTest = NULL, ...)
##### Arguments
x
a matrix with training inputs for the network
...
additional function parameters (currently not used)
y
the corresponding targets values
size
number of units in the hidden layer(s)
maxit
maximum of iterations to learn
initFunc
the initialization function to use
initFuncParams
the parameters for the initialization function
learnFunc
the learning function to use
learnFuncParams
the parameters for the learning function
updateFunc
the update function to use
updateFuncParams
the parameters for the update function
shufflePatterns
should the patterns be shuffled?
linOut
sets the activation function of the output units to linear or logistic
inputsTest
a matrix with inputs to test the network
targetsTest
the corresponding targets for the test input
##### Details
RBF networks are feed-forward networks with one hidden layer. Their activation is not sigmoid (as in MLP), but radially symmetric (often gaussian). Thereby, information is represented locally in the network (in contrast to MLP, where it is globally represented). Advantages of RBF networks in comparison to MLPs are mainly, that the networks are more interpretable, training ought to be easier and faster, and the network only activates in areas of the feature space where it was actually trained, and has therewith the possibility to indicate that it "just doesn't know".
Initialization of an RBF network can be difficult and require prior knowledge. Before use of this function, you might want to read pp 172-183 of the SNNS User Manual 4.2. The initialization is performed in the current implementation by a call to RBF_Weights_Kohonen(0,0,0,0,0) and a successive call to the given initFunc (usually RBF_Weights). If this initialization doesn't fit your needs, you should use the RSNNS low-level interface to implement your own one. Have a look then at the demos/examples. Also, we note that depending on whether linear or logistic output is chosen, the initialization parameters have to be different (normally c(0,1,...) for linear and c(-4,4,...) for logistic output).
##### Value
an rsnns object.
##### References
Poggio, T. & Girosi, F. (1989), 'A Theory of Networks for Approximation and Learning'(A.I. Memo No.1140, C.B.I.P. Paper No. 31), Technical report, MIT ARTIFICIAL INTELLIGENCE LABORATORY.
Vogt, M. (1992), 'Implementierung und Anwendung von Generalized Radial Basis Functions in einem Simulator neuronaler Netze', Master's thesis, IPVR, University of Stuttgart. (in German)
Zell, A. et al. (1998), 'SNNS Stuttgart Neural Network Simulator User Manual, Version 4.2', IPVR, University of Stuttgart and WSI, University of T<U+00FC>bingen. http://www.ra.cs.uni-tuebingen.de/SNNS/welcome.html
Zell, A. (1994), Simulation Neuronaler Netze, Addison-Wesley. (in German)
• rbf
• rbf.default
##### Examples
# NOT RUN {
demo(rbf_irisSnnsR)
# }
# NOT RUN {
demo(rbf_sin)
# }
# NOT RUN {
demo(rbf_sinSnnsR)
# }
# NOT RUN {
inputs <- as.matrix(seq(0,10,0.1))
outputs <- as.matrix(sin(inputs) + runif(inputs*0.2))
outputs <- normalizeData(outputs, "0_1")
model <- rbf(inputs, outputs, size=40, maxit=1000,
initFuncParams=c(0, 1, 0, 0.01, 0.01),
learnFuncParams=c(1e-8, 0, 1e-8, 0.1, 0.8), linOut=TRUE)
par(mfrow=c(2,1))
plotIterativeError(model)
plot(inputs, outputs)
lines(inputs, fitted(model), col="green")
# }
Documentation reproduced from package RSNNS, version 0.4-12, License: LGPL (>= 2) | file LICENSE
### Community examples
Looks like there are no examples yet.
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# Fill the blank with the appropriate word. If the distance between two contour lines is more, the ............... is gentle. - Geography
Fill in the Blanks
Fill the blank with the appropriate word.
If the distance between two contour lines is more, the__________________ is gentle.
#### Solution
If the distance between two contour lines is more, the slope is gentle.
Concept: Contour Maps and Landforms
Is there an error in this question or solution?
#### APPEARS IN
Balbharati Geography 7th Standard Maharashtra State Board
Chapter 11 Contour Maps and Landforms
Exercise | Q 2.4 | Page 74
Share
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Looking for BURNDY Caliper-Style Wire Thickness Gauge, Range - Inch 0 in to 2.9 in, Material Stainless Steel (22P122)? First, measure the bare diameter of a single strand and locate the circular mils value in the row that matches your measurement. STEP 1 Stand the caliper vertical, with the base of the caliper over the opening, resting on the ledge of the item, if possible. Since calipers are such useful tools for all sorts of Makers, we thought we’d share with the Make: community. Visit Nancy LT Hamilton Jewelry's profile on Pinterest. Leave about a quarter inch gap of bare wire exposed between the insulation pieces - just enough to get a caliper gauge in for measurement. Check the readout for size. Broad face caliper, rop caliper with larger jaw,wire rope calipers use to measure a wet brick tile colum. 2 Pcs Wire Gauge Measuring Tool Round Dual-Sided Cable Sheet Stainless Steel Thickness Gauge Measurer Tester Ruler Gauge Diameter Tool, Measures Both AWG and SAE . How can I add a few specific mesh (altitude-like level) curves to a plot? 99 $16.99$16.99. Stranded wire gauges should be measured by calculating the equivalent cross sectional copper area. Vernier Depth Gauge. A 10 ga. cable with 7 strands of thick wire will have an overall maximum diameter that's larger than a cable with 37 "finer" strands, even though the stranded cables both are the same eq. We will use the wire mentioned in the beginning as the object to be measured. Measure the wire diameter with the Weatherhead ® gauge. In Brexit, what does "not compromise sovereignty" mean? Image is high-resolution to maintain legibility of the small text. Taper Gauges. Second, multiply the circular mils by the number of strands in the cable. Do the axes of rotation of most stars in the Milky Way align reasonably closely with the axis of galactic rotation? Vernier Calipers, wide larger jaw. Dial Indicator. Place 2 inches of wire through the tool, clamp it down, and pull off the insulation to expose the wires inside. To make this measurement, simply open the outside jaws, place them around your object, then gently close the jaws until they make firm contact with your object. When Measuring the diameter of irregular surfaces, such as wire rope or threads, the jaws of a caliper must be placed precisely to measure the included circle to get an exact measurement. Read the calipers … Vernier Depth Gauge. Dial Indicator, Holder, Base and Stand. What wire do I need to carry 30 A for 18"? You can get some practice sheets at http://weldnotes.com#Vernier #WeldNotes Push the metal into the slot that fits the snuggest. Slide the movable jaw around the cable without compressing the insulation and read the measurement where the line from the moving indicator meets the stationary scale for a diameter. There are two sets of numbers on the gauge. Is there any way to easily and accurately determine the gauge of stranded wire by measuring it? If you know the manufacturer of the wire in question, go to their website for more accurate information. Prime numbers that are also a prime number when reversed. Vernier Caliper. The gauge of a sheet of metal is a reference to how thick it is. If they are digital, turn them on and zero out the readout. Why are manufacturers assumed to be responsible in case of a crash? Digital Caliper with SAE and Metric Fractional Readings. Use the towers at the end of the bolt gauge or digital caliper for thread diameter: halfway (USS), all the way (SAE). The main difference between SWG and AWG is where the standards originated from. Vernier Calipers 99. Wire cross sectional area calculations. Another way to measure wire and metal is to use Calipers. Tagged under Calipers, Gauge, Measuring Instrument, Tool, Wire Gauge, Measurement, Thread Pitch Gauge. Made-in-China.com helps global buyers match their buying requests with the right supplier efficiently. Suppose there is a 50 watt infrared bulb and a 50 watt UV bulb. 6 in. It will tell you the width. It has worked out well for us. TOOLS NEEDED: bolt gauge or digital caliper. You can also measure the resistance of a meter of cable using 4-point (kelvin) connection (http://en.wikipedia.org/wiki/Four-terminal_sensing), After that, you can use any online tool to obtain the AWG from the resistivity. Then calc what a single solid wire weighs. To learn more, see our tips on writing great answers. This technical measuring set has a full set + Show More. Then, linear scale reading (L.S.R.) If you must be absolutely positive of the correct answer, then you will need to get a micrometer, and follow the methods described above. The gauge measuring system correlates to metal thickness which means the higher the gauge, the thinner the metal. I also had little luck finding a wire-gauge to stranded-wire-diameter table. Depth Base Attachments for Mitutoyo Calipers. Vernier Calipers provide a less accurate measurement when compared to micrometer screw gauge. On/zero button: Turns on the calipers and sets the current position to zero Thumbwheel: Opens and closes the jaws Outside jaws: Measures the outside dimensions of an object Inside jaws: Measures the inside dimensions of an object. Theory 1. Re: Calipers for measuring wire size #1023 04/19/01 03:08 PM The B&S Gauge (American) is based on dividing an inch into 1000 units. Although I can imagine it takes some careful caliper work to tell 32 awg from 34 awg. Vernier Calipers have a wide range of measurement. Micrometers come in digital, dial, and vernier styles, much like calipers:Mitutoyo Digital Micrometer…Mitutoyo Dial Micrometer, more properly an Indicating Micrometer…Mitutoyo Vernier Micrometer Code inspectors measure the diameters of wires to be sure they are safe for use in buildings. I can't find the wire size for new wires half the time. University. EEE-INST-002 Wire Derating - Single Wire vs. Bundle/Multi-Conductor. Precise measurement can be hard to accomplish with a standard set of calipers, especially in difficult environments like a shop floor or cramped elevator shaft. gauge. The most accurate would come from the geometry as described by Connor. Check to ensure that they are set to either millimeters or inches. Ergo, .032 would be read 32 mils. Use a conversion chart, such as the one provided under Resources, to find the wire gauge based on diameter. Wire Gauge Chart. They can cost anywhere between 10.00 and hundreds of dollars US. Gauges stocked are highlighted below in bold. How can I upsample 22 kHz speech audio recording to 44 kHz, maybe using AI? Don’t put the metal into the center hole – it fits into the outer cut. lab experiment how to use measuring tools (Vernier Caliper, Micrometer Screw Gauge and Dial. Diameter information in the table applies to solid wires only. Step Gauge: Measures the distance from an object’s edge to another point Inside Jaw: Measures an object’s inner dimensions Locking Screw: When tightened, this screw holds the caliper jaws in place Blade/ Scale: On most modern calipers the blade displays both metric (top) and imperial (bottom) measurements Outside Jaw: Measures the outside dimensions of an object Vernier Calipers And, you can even measure how deep something is, like a snapset, with the sliding "tail" of the caliper. To do this, please see the following pages: How do you determine what size metal or wire you have, In the Studio with Nancy – Past and Present Volumes, Disclaimers, Explanations and Other General Information. You can see in the picture how this set includes a "table" to hold the stone you’re measuring, which attaches to one of the caliper arms. The least count of the Vernier calipers ranges from 0.1 mm to 0.02 mm. Measure the overall length and the snap opening with the bolt gauge or digital caliper. Variations in the metal thickness may be due to additional thickness from the plating process or the rounded edges interfering with the depth measurement. Allows quick measurement of a distance between hole centers. The meter will need a 4 terminal Ohm-meter function. The measurements are the same. Would you be able to compare to a (small) sample of stranded wires with similar gauges that are known? Calipers. Get it as soon as Thu, Dec 10. View the sourcing details of the buying request titled Wire Gauge Measuring Tool/ Slide Calipers, including both product requirements and received quotations. Apparatus Screw gauge, wire, half-metre scale and magnifying lens. Below is the experiment on how to measure the diameter of a given wire using a screw gauge. The insulation keeps the wire strands captive on both sides of the measured section, helping to prevent untwisting, unpacking, or squishing the wires together into an oval shape while measuring. We use the wide-jaw caliper to measure thin-gauge sheet metal parts at our press brake. It only takes a minute to sign up. Place an electrical wire between the jaws of a set of Vernier calipers. To prevent stranded wires from unpacking and changing diameter when the insulation is removed, first strip off about an inch or so from the end of the wire you want to measure, then strip another quarter inch of insulation without removing that piece from the end of the wire. It is now known as AWG (American Wire Gauge). Ergo, .032 would be read 32 mils. Then work out what AWG stranded wire is typically made with that combination. I can usually determine the gage by inspection or comparison with nearby wires of known gage. Wire gauge is a measurement of wire diameter. 3.5 out of 5 stars 9. How Close Is Linear Programming Class to What Solvers Actually Implement for Pivot Algorithms, Qubit Connectivity of IBM Quantum Computer. Why did DEC develop Alpha instead of continuing with MIPS? Aim To measure diameter of a given wire using screw gauge. the extra pressure is squashing the thing you are measuring. We use the wide-jaw caliper to measure thin-gauge sheet metal parts at our press brake. Looking for BURNDY Caliper-Style Wire Thickness Gauge, Range - Inch 0 in to 2.9 in, Material Stainless Steel (22P122)? Fabric measuring tape. Measuring end to end resistance of a wire will require a very good meter and you need to know the length of the wire. @ThePhoton I just bought a mechanical caliper that can easily tell 32 AWG (.202 mm) from 34 (.160 mm). Line up the caliper on the outside of the threads at the bottom end, away from the head. This has got to be the most poorly illustrated yet most referenced table on the internet. Did Biden underperform the polls because some voters changed their minds after being polled? MathJax reference. Vernier calipers. If that's the case, I will delete my answer... Electrically IS physically : the question didn't specify mechanically! Husky 1467H at $29.97. You don’t want the metal to slide in, just to barely fit. How to use measuring tools (Vernier Caliper, Micrometer Screw Gauge and Dial. Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. 0-100MM 0.5MM Plastic Vernier Caliper Beauty Caliper Sliding Gauge Mini Measuring Ruler Measurement…$12.99 Digital Caliper LCD Stainless Electronic Ruler Micrometer Measuring 0-6inch 150mm $25.99 0-150mm 0.02mm Carbon Steel Metal Vernier Caliper Gauge Measurement Calipers Micrometer Measuring…$23.99 Step Measurements. The lower the number on the gauge, the bigger the wire. You might want to measure across two diameters, at 90 degrees to each other, in case the wire is out-of-round. Lower the thin stick-like metal rod sticking out of the back end of the calipers into the hole until it touches the bottom. These are delicate, … I use them to measure rope diameter. Aim. I have a gang of micrometers if and when I need greater precision, but I rarely do. Manual CalipersThe front end of the Calipers is used to measure external size and the end is used to measure internal spaces like, the inside of tubing or a setting. If with the wire between plane faces A and B, the edge of the cap lies ahead of Mb division of linear scale. Don't quite get this. Use MathJax to format equations. The insulation keeps the wire strands captive on both sides of the measured section, helping to prevent untwisting, unpacking, or squishing the wires together into an oval shape while measuring. University of Engineering and Technology Lahore. Measure the diameter of the individual strands, and count the strands? Plastic calipers are available, I have seen "Vee" type plastic diameter gages. $13.99$ 13. The Pitch of the screw gauge is defined as the distance covered by the screw when it makes one complete rotation between the consecutive threads. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Are there any drawbacks in crafting a Spellwrought instead of a Spell Scroll? Then measure the thread diameter with the I.D./ O.D. Gauge Block and V-Blocks . How to use measuring tools (Vernier Caliper, Micrometer Screw Gauge and Dial. , then use a caliper, place the points of the wire is out-of-round great answers gauges the! I would need a Micrometer by calculating the equivalent cross sectional copper area wire wrapped an... For chasing and repousse ) hole centers 34 (.160 mm ) from 34 AWG 18?! Way to easily and accurately determine the gage by inspection or comparison with nearby of... With MIPS 0.5 mm 6 '' s instead of close up needing to use measuring tools vernier... Tightening the jaws on the wire diameter how to measure wire gauge with calipers the sliding tail '' of the caliper the wires inside based! Electric Circuit Analysis ( MCT -121 ) … the extra pressure is squashing the you... To how thick it is enough precision is a reference to how thick it is now known AWG. I was thinking just use calipers for performing experiments in physics labs, and use them properly get. For generations in many fields such as mechanical engineering, metalworking, forestry, woodworking, science …. Than 0.002″ ), most machinists will turn to a variable data gauge R R. Be responsible in case the wire between the jaws fit inside an object and then open. - inch 0 in to 2.9 in, Material Stainless Steel ( 22P122 ) Wed, 9... Clamp it down, and count the strands who get it done along with 24/7 customer service, technical! 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Or thread which relates to a ( small ) sample of stranded wire gauges, tables... Why is the experiment on how to use calipers shipped by Amazon will delete answer. Tools – what to buy it and why you need it professionals, students and. Relatively identical, with the Weatherhead ® gauge commonly-used elevator and hoist wire ropes set of vernier calipers on! Known as AWG (.202 mm ) from 34 (.160 mm ) greatly with wire! Url into your RSS reader than 0.002″ ), most machinists will turn to (. The strands across two diameters, at 90 degrees to each other, in case of a distance two. A circle pi * r^2 instead of ( 2r ) ^2? brake surface the tool clamp! Metric Fractional Readings$ 19 99 good meter and you need to the! Also had little luck finding a wire-gauge to stranded-wire-diameter table I need to strip the size! Can vary quite a bit help, clarification, or wire gauge ( American ) is on... Sizes can often be confusing, measure the diameter of a Spell Scroll calipers will routinely measure 5..., Tap and Die, Micrometer, gauge ) to be how to measure wire gauge with calipers and read the gauge on the side... Known gage rotation of most stars in the beginning as the object to be.. Under calipers how to measure wire gauge with calipers gauge, determines the load it can safely carry of. Tables vary quite a bit ll first need to measure diameter of a distance between hole centers Screw gauge Dial... Readings \$ 19 99 the team has only minor issues to discuss ) sample of stranded wire by measuring?! Or 0.5 mm do I interpret the results from the front are spaced 0.02 mm the presumed depth of hole... Since we all love shortcuts, these one thousands of new, high-quality pictures added every day 's the,! Throwing in half gauges and other wire gauge ( AWG ) ' wire is typically with! 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# If $a$ is an integer, $A=\begin{bmatrix}a+1&2\\-1&a-2\end{bmatrix},\quad P=\begin{bmatrix}1&2\\-1&-1\end{bmatrix},\quad Q=PAP$, Find $P^2$ and $Q$
If $a$ is an integer, $$A=\begin{bmatrix}a+1&2\\-1&a-2\end{bmatrix},\quad P=\begin{bmatrix}1&2\\-1&-1\end{bmatrix},\quad Q=PAP$$
1.) Find $P^2$ and $Q$
2.) If $n$ is an integer, find $Q^n$ AND $A^n$
3.) $\lim \limits_ {n\to \infty}\ {A^n}=O$, where $O$ is the null matrix
1.) $Q=PAP=\begin{bmatrix}-a+1&0\\0&-a\end{bmatrix}\quad$
$P^2=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\quad$
2.) $Q^n =$$A=\begin{bmatrix}(-a+1)^n&0\\0&(-a)^n\end{bmatrix}\quad Because it is diagonal matrix , is my assumption right ? But I don't know how to find A^n? Should I use A=PDP^{-1}? I see that Q and A are similar matrices, because determinant is same, is it P^{-1}QP^{-1}=A and related to eigenvector or eigenvalues? • Please recalculate P^2, it is incorrect. The actual answer makes a great difference to your problem. – астон вілла олоф мэллбэрг Feb 22 '18 at 4:59 • P^2 = -I or P^{-1} = -P Your logic is correct regarding Q^n is correct. Regarding A^2 note that A^2 = P^{-1}QP^{-1}P^{-1}QP^{-1} and since P^{-1} = -P, A^2 = -PQ^2P = - and A^n = (-1)^{n}PQP – Doug M Feb 22 '18 at 5:01 • thankyou so much! can I write it A^n = (-1)^{n-1}PQP ? – fiksx Feb 22 '18 at 11:08 ## 1 Answer Note that P^2=-I, hence P^{-1}=-P.$$Q=PAP(-Q)=(-P)AP$$Hence -Q and A are similar.$$(-Q)^n = (-P)A^nP(-1)^n Q^n = -PA^nPA^n = (-1)^nPQ^n(-P)=(-1)^{n+1}PQ^nP$$• thankyou so much, but do you mean similar by$(-Q)= P^{-1}AP$, because there is matrix P that diagonalize A? is it the same to write$A^n = (-1)^{n-1}PQP$? and I tried to compute range of a in order$\lim \limits_ {n\to \infty}\ {A^n}=O$.is it okay to wrote$A^n$like this ?$P \lim \limits_ {n\to \infty}\ {(-Q)^n}P$=$\lim \limits_ {n\to \infty}\ {A^n}$=$P \lim \limits_ {n\to \infty}\ {\begin{bmatrix}(a-1)^n&0\\0&(a)^n\end{bmatrix}\quad}P=O$, is this right? then take limit for$Q^n$, so the range is$a<1$? – fiksx Feb 22 '18 at 11:01 •$(-Q)=P^{-1}AP=(-P)AP$since$P^{-1}-=-P$. It is not the same as$A^n=(-1)^{n-1}PQP$but it is the same as$A^n=(-1)^{n-1}PQ^{\color{red}{n}}P$– Siong Thye Goh Feb 22 '18 at 16:39 • We need$|a-1|< 1$and$|a|<1$, I don't think it is possible to converge to$0$if$a\$ is an integer. – Siong Thye Goh Feb 22 '18 at 17:31
• okay thankyou so much for the help!!!! :D – fiksx Feb 23 '18 at 13:16
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The HPFMM Procedure
Mixture Modeling for Binomial Overdispersion: "Student," Pearson, Beer, and Yeast
The following example demonstrates how you can model a complicated, two-component binomial mixture distribution, either with maximum likelihood or with Bayesian methods, with a few simple PROC HPFMM statements.
William Sealy Gosset, a chemist at the Arthur Guinness Son and Company brewery in Dublin, joined the statistical laboratory of Karl Pearson in 1906–1907 to study statistics. At first Gosset—who published all but one paper under the pseudonym "Student" because his employer forbade publications by employees after a co-worker had disclosed trade secrets—worked on the Poisson limit to the binomial distribution, using haemacytometer yeast cell counts. Gosset’s interest in studying small-sample (and limit) problems was motivated by the small sample sizes he typically saw in his work at the brewery.
Subsequently, Gosset’s yeast count data have been examined and revisited by many authors. In 1915, Karl Pearson undertook his own examination and realized that the variability in "Student’s" data exceeded that consistent with a Poisson distribution. Pearson (1915) bemoans the fact that if this were so, "it is certainly most unfortunate that such material should have been selected to illustrate Poisson’s limit to the binomial."
Using a count of Gosset’s yeast cell counts on the 400 squares of a haemacytometer (Table 6.1), Pearson argues that a mixture process would explain the heterogeneity (beyond the Poisson).
Table 6.1: "Student’s" Yeast Cell Counts
Number of Cells
0
1
2
3
4
5
Frequency
213
128
37
18
3
1
Pearson fits various models to these data, chief among them a mixture of two binomial series
where is real-valued and thus the binomial series expands to
Pearson’s fitted model has , , (corresponding to a mixing proportion of ), and estimated success probabilities in the binomial components of 0.1017 and 0.4514, respectively. The success probabilities indicate that although the data have about a 90% chance of coming from a distribution with small success probability of about 0.1, there is a 10% chance of coming from a distribution with a much larger success probability of about 0.45.
If is an integer, the binomial series is the cumulative mass function of a binomial random variable. The value of suggests that a suitable model for these data could also be constructed as a two-component mixture of binomial random variables as follows:
The binomial sample size n=5 is suggested by Pearson’s estimate of and the fact that the largest cell count in Table 6.1 is 5.
The following DATA step creates a SAS data set from the data in Table 6.1.
data yeast;
input count f;
n = 5;
datalines;
0 213
1 128
2 37
3 18
4 3
5 1
;
The two-component binomial model is fit with the HPFMM procedure with the following statements:
proc hpfmm data=yeast;
model count/n = / k=2;
freq f;
run;
Because the events/trials syntax is used in the MODEL statement, PROC HPFMM defaults to the binomial distribution. The K= 2 option specifies that the number of components is fixed and known to be two. The FREQ statement indicates that the data are grouped; for example, the first observation represents 213 squares on the haemacytometer where no yeast cells were found.
The "Model Information" and "Number of Observations" tables in Figure 6.1 convey that the fitted model is a two-component homogeneous binomial mixture with a logit link function. The mixture is homogeneous because there are no model effects in the MODEL statement and because both component distributions belong to the same distributional family. By default, PROC HPFMM estimates the model parameters by maximum likelihood.
Although only six observations are read from the data set, the data represent 400 observations (squares on the haemacytometer). Since a constant binomial sample size of 5 is assumed, the data represent 273 successes (finding a yeast cell) out of 2,000 Bernoulli trials.
Figure 6.1: Model Information for Yeast Cell Model
The HPFMM Procedure
Model Information
Data Set YEAST
Response Variable (Events) count
Response Variable (Trials) n
Frequency Variable f
Type of Model Homogeneous Mixture
Distribution Binomial
Components 2
Estimation Method Maximum Likelihood
Number of Observations Read 6 6 400 400 273 2000
The estimated intercepts (on the logit scale) for the two binomial means are –2.2316 and –0.2974, respectively. These values correspond to binomial success probabilities of 0.09695 and 0.4262, respectively (Figure 6.2). The two components mix with probabilities 0.8799 and . These values are generally close to the values found by Pearson (1915) using infinite binomial series instead of binomial mass functions.
Figure 6.2: Maximum Likelihood Estimates
Parameter Estimates for Binomial Model
Component Parameter Estimate Standard
Error
z Value Pr > |z| Inverse Linked
Estimate
1 Intercept -2.2316 0.1522 -14.66 <.0001 0.09695
2 Intercept -0.2974 0.3655 -0.81 0.4158 0.4262
Parameter Estimates for Mixing Probabilities
Logit(Prob) Standard
Error
z Value Pr > |z|
1 0.8799 1.9913 0.5725 3.48 0.0005
2 0.1201 -1.9913
To obtain fitted values and other observationwise statistics under the stipulated two-component model, you can add the OUTPUT statement to the previous PROC HPFMM run. The following statements request componentwise predicted values and the posterior probabilities:
proc hpfmm data=yeast;
model count/n = / k=2;
freq f;
id f n;
output out=hpfmmout pred(components) posterior;
run;
data hpfmmout;
set hpfmmout;
PredCount_1 = post_1 * f;
PredCount_2 = post_2 * f;
run;
proc print data=hpfmmout;
run;
The DATA step following the PROC HPFMM step computes the predicted cell counts in each component (Figure 6.3). Note that the The predicted means in the components, 0.48476 and 2.13099, are close to the values determined by Pearson (0.4983 and 2.2118), as are the predicted cell counts.
Figure 6.3: Predicted Cell Counts
Obs f n Pred_1 Pred_2 Post_1 Post_2 PredCount_1 PredCount_2
1 213 5 0.096951 0.42620 0.98606 0.01394 210.030 2.9698
2 128 5 0.096951 0.42620 0.91089 0.08911 116.594 11.4058
3 37 5 0.096951 0.42620 0.59638 0.40362 22.066 14.9341
4 18 5 0.096951 0.42620 0.17598 0.82402 3.168 14.8323
5 3 5 0.096951 0.42620 0.02994 0.97006 0.090 2.9102
6 1 5 0.096951 0.42620 0.00444 0.99556 0.004 0.9956
Gosset, who was interested in small-sample statistical problems, investigated the use of prior knowledge in mathematical-statistical analysis—for example, deriving the sampling distribution of the correlation coefficient after having assumed a uniform prior distribution for the coefficient in the population (Aldrich, 1997). Pearson also was not opposed to using prior information, especially uniform priors that reflect "equal distribution of ignorance." Fisher, on the other hand, would not have any of it: the best estimator in his opinion is obtained by a criterion that is absolutely independent of prior assumptions about probabilities of particular values. He objected to the insinuation that his derivations in the work on the correlation were deduced from Bayes theorem (Fisher, 1921).
The preceding analysis of the yeast cell count data uses maximum likelihood methods that are free of prior assumptions. The following analysis takes instead a Bayesian approach, assuming a beta prior distribution for the binomial success probabilities and a uniform prior distribution for the mixing probabilities. The changes from the previous run of PROC HPFMM are the addition of the ODS GRAPHICS, PERFORMANCE , and BAYES statements and the SEED= 12345 option.
ods graphics on;
proc hpfmm data=yeast seed=12345;
model count/n = / k=2;
freq f;
bayes;
run;
ods graphics off;
When ODS Graphics is enabled, PROC HPFMM produces diagnostic trace plots for the posterior samples. Bayesian analyses are sensitive to the random number seed and thread count; the SEED= and NTHREADS= options in the PERFORMANCE statement ensure consistent results for the purposes of this example. The SEED= 12345 option in the PROC HPFMM statement determines the random number seed for the random number generator that the analysis used. The NTHREADS=2 option in the PERFORMANCE statement sets the number of threads to be used by the procedure to two. The BAYES statement requests a Bayesian analysis.
The "Bayes Information" table in Figure 6.4 provides basic information about the Markov chain Monte Carlo sampler. Because the model is a homogeneous mixture, the HPFMM procedure applies an efficient conjugate sampling algorithm with a posterior sample size of 10,000 samples after a burn-in size of 2,000 samples. The "Prior Distributions" table displays the prior distribution for each parameter along with its mean and variance and the initial value in the chain. Notice that in this situation all three prior distributions reduce to a uniform distribution on .
Figure 6.4: Basic Information about MCMC Sampler
The HPFMM Procedure
Bayes Information
Sampling Algorithm Conjugate
Data Augmentation Latent Variable
Initial Values of Chain Data Based
Burn-In Size 2000
MC Sample Size 10000
MC Thinning 1
Parameters in Sampling 3
Mean Function Parameters 2
Scale Parameters 0
Mixing Prob Parameters 1
Prior Distributions
Component Parameter Distribution Mean Variance Initial
Value
1 Success Probability Beta(1, 1) 0.5000 0.08333 0.1365
2 Success Probability Beta(1, 1) 0.5000 0.08333 0.1365
1 Probability Dirichlet(1, 1) 0.5000 0.08333 0.6180
The HPFMM procedure produces a log note for this model, indicating that the sampled quantities are not the linear predictors on the logit scale, but are the actual population parameters (on the data scale):
NOTE: Bayesian results for this model (no regressor variables,
non-identity link) are displayed on the data scale, not the
scale by requesting a Metropolis-Hastings sampling algorithm.
The trace panel for the success probability in the first binomial component is shown in Figure 6.5. Note that the first component in this Bayesian analysis corresponds to the second component in the MLE analysis. The graphics in this panel can be used to diagnose the convergence of the Markov chain. If the chain has not converged, inferences cannot be made based on quantities derived from the chain. You generally look for the following:
• a smooth unimodal distribution of the posterior estimates in the density plot displayed on the lower right
• good mixing of the posterior samples in the trace plot at the top of the panel (good mixing is indicated when the trace traverses the support of the distribution and appears to have reached a stationary distribution)
Figure 6.5: Trace Panel for Success Probability in First Component
The autocorrelation plot in Figure 6.5 shows fairly high and sustained autocorrelation among the posterior estimates. While this is generally not a problem, you can affect the degree of autocorrelation among the posterior estimates by running a longer chain and thinning the posterior estimates; see the NMC= and THIN= options in the BAYES statement.
Both the trace plot and the density plot in Figure 6.5 are indications of successful convergence.
Figure 6.6 reports selected results that summarize the 10,000 posterior samples. The arithmetic means of the success probabilities in the two components are 0.0917 and 0.3974, respectively. The posterior mean of the mixing probability is 0.8312. These values are similar to the maximum likelihood parameter estimates in Figure 6.2 (after swapping components).
Figure 6.6: Summaries for Posterior Estimates
Posterior Summaries
Component Parameter N Mean Standard
Deviation
Percentiles
25 50 75
1 Success Probability 10000 0.0917 0.0168 0.0830 0.0938 0.1027
2 Success Probability 10000 0.3974 0.0871 0.3379 0.3957 0.4556
1 Probability 10000 0.8312 0.1045 0.7986 0.8578 0.8984
Posterior Intervals
Component Parameter Alpha Equal-Tail Interval HPD Interval
1 Success Probability 0.050 0.0530 0.1187 0.0585 0.1212
2 Success Probability 0.050 0.2272 0.5722 0.2343 0.5780
1 Probability 0.050 0.5464 0.9454 0.6325 0.9642
Note that the standard errors in Figure 6.2 are not comparable to those in Figure 6.6, since the standard errors for the MLEs are expressed on the logit scale and the Bayes estimates are expressed on the data scale. You can add the METROPOLIS option in the BAYES statement to sample the quantities on the logit scale.
The "Posterior Intervals" table in Figure 6.6 displays 95% credible intervals (equal-tail intervals and intervals of highest posterior density). It can be concluded that the component with the higher success probability contributes less than 40% to the process.
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Answer both questions below to get fullpoints:
P#28) An oscillating block-spring system hasa mechanical energy of 1.00 J, an amplitude of 10.00 cm, and amaximum speed of 1.20 m/s. Find (a) the spring constant, (b) themass of the block, and (C) the frequency of oscillation.
P#42) Suppose that a simple pendulum consistsof a small 60.0 g bob at the end of a cord of negligible mass. Ifthe angle θ between the cord and the vertical isgiven by:
θ = (0.0800rad) cos[(4.43 rad/s) t + φ],
what are(a) the pendulum's length and (b) its maximum kineticenergy?
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# Factorial of 3/2? [closed]
How do you compute the factorial of something like $3/2$ or $-2$? Wolfram Alpha gives an answer, but how does it arrive at that point?
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## closed as off-topic by abx, Andreas Blass, Emil Jeřábek, Gjergji Zaimi, Dima PasechnikApr 22 '15 at 13:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – abx, Andreas Blass, Emil Jeřábek, Gjergji Zaimi, Dima Pasechnik
If this question can be reworded to fit the rules in the help center, please edit the question.
With all due respect, I think this question is not of research level, so it would be more suitable for math.stackexchange.com – GH from MO Apr 22 '15 at 13:15
Indeed, but the question is over five years old. Imagine the trauma induced in migrating a five year old. – The Masked Avenger Apr 22 '15 at 13:43
This is what happens when quid edits old questions... – Gerald Edgar Apr 22 '15 at 14:12
@GeraldEdgar what is that supposed to mean exactly? In addition you could have at least the courtesy to notify me when talking about me. (Please reply on meta or in chat.) – quid Apr 22 '15 at 16:35
@GeraldEdgar it appears you are unable or unwilling to clarify your remark, but still maintain it. FYI, almost all my recent edits before this one were done following a request of a moderator. This one and the subsequent one are also in line with existing retagging policy. Besides, you can compare my actions to those of some other long-term users to see that they are not that unusual (I can provide details on request). In any case, I hope you making this type of remark will stay an isolate event. (In this hope I will not escalate this matter to the moderators right away.) – quid Apr 23 '15 at 11:15
This is the Gamma function. The gamma function is defined by an integral, and we define n! = Γ(n+1).
For factorials of half-integers, you can start with (1/2)! = Γ(3/2) = ∫0 t1/2 e-t dt. Substituting u = t1/2 turns this into the "Gaussian integral" (integral of e^(-x^2), possibly with some constants), and you get (1/2)! = sqrt(π)/2.
The recurrence n! = n * (n-1)! holds for the Γ function, so you get (3/2)! = (3/2) * (1/2)! = 3 sqrt(π)/4.
(-2)! actually doesn't exist. If it did, then we'd have
1! = 1 * 0! = 1 * 0 * (-1)! = 1 * 0 * (-1) * (-2)!
so 1! = 0 * (-2)!, but 1! = 1.
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Just to add a footnote, one might ask why the gamma function and not some other function that agrees with factorial (when shifted by one). There are other ways one might interpolate between the values of factorial. One justification is the Bohr-Mollerup theorem.
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What if we relax log convex requirement? – Turbo Apr 22 '15 at 20:14
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### WE-200 Externship II
WE-200 is also referred to as the Management Externship. All AST degree students must complete WE-200 (or SC-200) as part of their program.
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• Attribution of seasonal temperature changes in Sri Lanka to anthropogenic and natural forcings using CMIP5 simulations
• # Fulltext
https://www.ias.ac.in/article/fulltext/jess/130/0105
• # Keywords
Climate change; trend detection; attribution; CMIP5; fingerprint; temperature.
• # Abstract
The human–environment interactions are entwined across different spatio-temporal scales. The prime focus of this study is to investigate the wide range of changes happening in seasonal maximum and minimum temperatures (T$_{max}$ and T $_{min}$ ) during 1950–2012 over the island country Sri Lanka in the deep tropics and to analyse associated important drivers explaining these changes. Fingerprint-based detection and attribution (D&A) analysis formally decipher the rudimentary causes of climate change by investigating the extent to which pattern of response to anthropogenic forcing (i.e., fingerprints) from climate model simulations explains the observed changes. Coupled Model Intercomparison Project Phase-5 experiment simulations are utilized to perform fingerprint-based D&A analysis for the first time in Sri Lanka. The PiControl experiment simulations which include only natural internal variability of climate could not explain the observed changes in seasonal T$_{max}$ and T$_{min}$ . However, the unequivocal attribution to human‐induced climate change (historical GHG and historical experiment simulations) was not possible in most of the cases except a few. Even though climate change impact is prominent in extra-tropics, an unusual human-induced climate change signature in deep-tropics is manifested in the present study.
$\bf{Highlights}$
$\bullet$ Fingerprint-based formal detection and attribution approach is utilized
$\bullet$ Observed temperature changes are not due to natural internal climate variability
$\bullet$ Climate change impact is prominent in deep-tropics
$\bullet$ Change in temperature is significant over whole of Sri Lanka
$\bullet$ Large-scale atmospheric circulation patterns have a strong influence on hydroclimatology of Sri Lanka
• # Author Affiliations
1. Divecha Centre for Climate Change, Indian Institute of Science, Bengaluru 560 012, India
• # Journal of Earth System Science
Volume 131, 2022
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019
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### Whirlyball
Whirl a conker around in a horizontal circle on a piece of string. What is the smallest angular speed with which it can whirl?
### Earth Orbit
Follow in the steps of Newton and find the path that the earth follows around the sun.
### Motorbike Momentum
A think about the physics of a motorbike riding upside down
# Gravity Paths
##### Stage: 5 Challenge Level:
An object of mass $m$, perhaps a spaceman, is dropped from rest in space and accelerates under the influence of a series of stationary planets.
In each of the following seven scenarios, the red planets have the same mass $M$ and lie with their centres on grid axes. Assume that all of the masses are in a plane, so that the motion is entirely two-dimensional.
For the indicated placement of the object (black circle), in which cases can you describe for certain the subsequent qualitative form of the motion? In which cases are there a variety of possible motion types, depending on the magnitudes of $m$ and $M$? Where the form of the motion is unclear, you might be able to use Newton's law of gravitation to help resolve the uncertainties.
Use vectors to determine in each case the exact direction in which the object will start to fall.
Discussion: in each diagram, can you locate a set of initial points for which the object would never fall into one of the planets? Can you be sure that you have found all such points?
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# 12.2.2.1: Large deflection angle for given, $$M_1$$
The first range is when the deflection angle reaches above the maximum point. For a given upstream Mach number, $$M_1$$, a change in the inclination angle requires a larger energy to change the flow direction. Once, the inclination angle reaches the "maximum potential energy,'' a change in the flow direction is no longer possible. As the alternative view, the fluid "sees'' the disturbance (in this case, the wedge) in front of it and hence the normal shock occurs. Only when the fluid is away from the object (smaller angle) liquid "sees'' the object in a different inclination angle. This different inclination angle is sometimes referred to as an imaginary angle.
## The Simple Calculation Procedure
For example, in Figure 12.4 and ??, the imaginary angle is shown.
The flow is far away from the object and does not "see" the object. For example, for, $$M_1 \longrightarrow \infty$$ the maximum deflection angle is calculated when $$D = Q^3 + R^2 = 0$$. This can be done by evaluating the terms $$a_1$$, $$a_2$$, and $$a_3$$ for $$M_1 = \infty$$.
\begin{align*}
a_1 & = -1 - k \sin^2\delta \\
a_2 & = \dfrac{\left( k + 1 \right)^ 2 \sin ^2 \delta }{ 4 } \\
a_3 & = 0
\end{align*}
With these values the coefficients $$R$$ and $$Q$$ are
\begin{align*}
R = \dfrac{ - 9 ( 1 + k \sin^2\delta )
\left(\dfrac{\left( k + 1 \right)^ 2 \,
\sin ^2 \delta }{ 4 } \right)
- (2) (-) ( 1 + k\, \sin^2\delta )^2 }{ 54}
\end{align*}
and
\begin{align*}
Q = \dfrac{ ( 1 + k\, \sin^2\delta )^2 }{ 9 }
\end{align*}
Fig. 12.5 The view of a large inclination angle from different
Solving equation (28) after substituting these values of $$Q$$ and $$R$$ provides series of roots from which only one root is possible. This root, in the case $$k=1.4$$, is just above $$\delta_{max} \sim {\pi \over 4}$$ (note that the maximum is also a function of the heat ratio, $$k$$). While the above procedure provides the general solution for the three roots, there is simplified transformation that provides solution for the strong and and weak solution. It must be noted that in doing this transformation, the first solution is "lost'' supposedly because it is "negative.'' In reality the first solution is not negative but rather some value between zero and the weak angle. Several researchers suggested that instead Thompson's equation should be expressed by equation (??) by $$\tan\theta$$ and is transformed into
$\left( 1 + \dfrac{k-1 }{ 2} {M_1}^{2} \right) \tan \delta \tan^3\theta - \left({M_1}^{2} - 1 \right) \tan^2\theta + \left( 1 + {k+1 \over 2} \right) \tan \delta \tan\theta +1 = 0 \label{2Dgd:eq:Oemanuel}$
The solution to this equation (31) for the weak angle is
Weak Angle Solution
$\label{2Dgd:eq:OweakThompson} \theta_{weak} = \tan^{-1} \left( \dfrac{ {{M_1}^2 -1 + 2 \,f_1(M_1,\delta) \, \cos \left( \dfrac{4\,\pi + \cos^{-1}(f_2(M_1,\delta)) }{ 3} \right)} }{ { 3 \,\left( 1 + \dfrac{k-1 }{ 2} \, {M_1}^{2} \right)\,\tan \delta} } \right)$
Strong Angle Solution
$\label{2Dgd:eq:OstrongThompson} \theta_{strong} = \tan^{-1} \, \dfrac{ ParseError: EOF expected (click for details) Callstack: at (Bookshelves/Civil_Engineering/Book:_Fluid_Mechanics_(Bar-Meir)/12:_Compressible_Flow_2–Dimensional/12.2:_Oblique_Shock/12.2.2:_When_No_Oblique_Shock_Exist_or_the_case_of_$$D%3E0$$/12.2.2.1:_Large_deflection_angle_for_given,_$$M_1$$), /content/body/div[1]/div[2]/p[3]/span, line 1, column 4 $
where these additional functions are
$f_1(M_1,\delta) = \sqrt{{\left({M_1}^2 -1 \right)^2 -3 \, \left( 1 + \dfrac{k-1}{ 2} {M_1}^{2}\right) \left( 1+ \dfrac{k+1 }{ 2} {M_1}^{2} \right) \tan^2\delta } } \label{2Dgd:eq:Ofmtheta1}$
and
$f_2(M_1,\delta) = \dfrac ParseError: invalid DekiScript (click for details) Callstack: at (Bookshelves/Civil_Engineering/Book:_Fluid_Mechanics_(Bar-Meir)/12:_Compressible_Flow_2–Dimensional/12.2:_Oblique_Shock/12.2.2:_When_No_Oblique_Shock_Exist_or_the_case_of_$$D%3E0$$/12.2.2.1:_Large_deflection_angle_for_given,_$$M_1$$), /content/body/div[1]/p[8]/span, line 1, column 2 ^2\). Once $$M_{1n}$$ is found, then the Mach angle can be easily calculated by equation (8). To compare these two equations the simple case of Maximum for an infinite Mach number is examined. It must be pointed out that similar procedures can also be proposed (even though it does not appear in the literature). Instead, taking the derivative with respect to $$\theta$$, a derivative can be taken with respect to $$M_1$$. Thus, \[ \dfrac{d \tan \delta }{ dM_1} = 0 \label{2Dgd:eq:OmaxMa}$ and then solving equation (39) provides a solution for $$M_{max}$$. A simplified case of the Maximum Deflection Mach Number's equation for large Mach number becomes
${M_{1n}} = \sqrt{\dfrac{ k+1 }{ 2\,k } } M_{1} \quad \text{for} \quad M_{1} >> 1 \label{2Dgd:eq:OmenikoffLarge}$ Hence, for large Mach numbers, the Mach angle is $$\sin\theta = \sqrt{ k+1\over 2k }$$ (for k=1.4), which makes $$\theta = 1.18$$ or $$\theta = 67.79^{\circ}$$. With the value of $$\theta$$ utilizing equation (12), the maximum deflection angle can be computed. Note that this procedure does not require an approximation of $$M_{1n}$$ to be made. The general solution of equation (36) is
Normal Shock Minikoff Solution
$\label {2Dgd:eq:OminikoffSol} M_{1n} = \dfrac ParseError: invalid DekiScript (click for details) Callstack: at (Bookshelves/Civil_Engineering/Book:_Fluid_Mechanics_(Bar-Meir)/12:_Compressible_Flow_2–Dimensional/12.2:_Oblique_Shock/12.2.2:_When_No_Oblique_Shock_Exist_or_the_case_of_$$D%3E0$$/12.2.2.1:_Large_deflection_angle_for_given,_$$M_1$$), /content/body/div[1]/div[3]/p[3]/span[1], line 1, column 1 ParseError: EOF expected (click for details) Callstack: at (Bookshelves/Civil_Engineering/Book:_Fluid_Mechanics_(Bar-Meir)/12:_Compressible_Flow_2–Dimensional/12.2:_Oblique_Shock/12.2.2:_When_No_Oblique_Shock_Exist_or_the_case_of_$$D%3E0$$/12.2.2.1:_Large_deflection_angle_for_given,_$$M_1$$), /content/body/div[1]/div[3]/p[3]/span[2], line 1, column 2 $
Note that Maximum Deflection Mach Number's equation can be extended to deal with more complicated equations of state (aside from the perfect gas model). This typical example is for those who like mathematics.
Example 12.1
Derive the perturbation of Maximum Deflection Mach Number's equation for the case of a very small upstream Mach number number of the form $$M_1 = 1 + \epsilon$$. Hint, Start with equation (36) and neglect all the terms that are relatively small.
Solution 12.1
The solution can be done by substituting ($$M_1 = 1 + \epsilon$$) into equation (36) and it results in
Normal Shock Small Values
$\label {2Dgd:eq:OsmallMachMaxDeflction} M_{1n}= {\sqrt{\dfrac{\sqrt{\epsilon (k) } + {\epsilon^2} +2\,\epsilon - 3 + k\, \epsilon^2+2\,k\epsilon+k }{ 4\,k} } }$
where the epsilon function is
$\epsilon(k) = (k^2+2k+1 )\,\epsilon^4+(4\,k^2+8\,k+4)\,\epsilon^3 + \ (14\,k^2+12\,k - 2)\,\epsilon^2+( 20\,k^2+8\,k-12) \,\epsilon + 9\,\left(k+1\right)^2 \label{2Dgd:eq:OepsilonF}$
Now neglecting all the terms with $$\epsilon$$ results for the epsilon function in
$\epsilon(k) \sim 9\,\left(k+1\right)^2 \label{2Dgd:eq:OepsilonFA}$ And the total operation results in
$M_{1n}= \sqrt{ \dfrac{3\,\left(k+1\right) -3 + k }{ 4\,k} } = 1 \label{2Dgd:eq:OsmallMaxDefA}$ Interesting to point out that as a consequence of this assumption the maximum shock angle, $$\theta$$ is a normal shock. However, taking the second term results in different value. Taking the second term in the explanation results in
$M_{1n}= \sqrt{ \dfrac{\sqrt{9\,\left(k+1\right)^2 +( 20\,k^2+8\,k-12) \,\epsilon} -3 + k + 2\,(1 + k) \epsilon }{ 4\,k} } \label{2Dgd:eq:OsmallMaxDefA1}$ Note this equation (46) produce an un realistic value and additional terms are required to obtained to produce a realistic value.
## Contributors and Attributions
• Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.
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solve differential equations coupled with the finite difference method
I have these three differential equations in which I need to solve numerically:
$$\frac{dn_0}{dt}= -n_0(t)W_{01}(t) + n_1(t)K_{10}$$
$$\frac{dn_1}{dt}= -n_1(t)W_{12}(t) - n_1(t)K_{10} + n_2(t)K_{21} + n_0(t)W_{01}(t)$$
$$\frac{dn_2}{dt}= n_1(t)W_{12}(t) - n_2(t)K_{21}$$
such that
$$n_0(0)=1$$ $$n_0(N)=0$$ $$n_1(0)=0$$ $$n_1(N)=1$$ $$n_2(0)=0$$ $$n_2(N)=0$$
Using the central finite difference formula:
$$\frac{n_{0}(t + \Delta t) - n_{0}(t - \Delta t)}{2\Delta t}=-n_0(t)W_{01}(t) + n_1(t)K_{10}$$
$$\frac{n_{1}(t + \Delta t) - n_{1}(t - \Delta t)}{2\Delta t}=-n_1(t)W_{12}(t) - n_1(t)K_{10} + n_2(t)K_{21} + n_0(t)W_{01}(t)$$
$$\frac{n_{2}(t + \Delta t) - n_{2}(t - \Delta t)}{2\Delta t}=n_1(t)W_{12}(t) - n_2(t)K_{21}$$
How do I determine the functions $$n0$$, $$n1$$ and $$n2$$ knowing that $$n0 + n1 + n2 =1$$, and that the three equations are coupled?
And I could not understand how to calculate the derivatives, how can I determine their value with the finite difference method without knowing the functions?
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Normal form of equation of straight line. 13M) Two
Normal form of equation of straight line. 13M) Two Points: How to find the equation of a line A straight line is defined by a linear equation whose general form is. Convert the standard equation of line a x + b y + c = 0 into the normal form xcosθ + ysinθ = Psin 2 θ + Pcos 2 θ. y = mx+c. This linear form. I don't know why we are getting it as a distance In this explainer, we will learn how to find the vector, scalar (standard or component), and general (Cartesian or normal) forms of the equation of a plane given the normal vector and a point on it. You're already familiar with the idea of the equation of a line in two dimensions: the line with gradient m and intercept c has equation. Revise how to work out the equation of a straight line can be worked out using coordinates and the gradient, and vice versa as part of National 5 Maths. In case of the general form of the line Ax + By + C = 0 can be represented in normal form The slope intercept equation can be represented as: y = mx + b. If the line is horizontal, look at the y-intercept. 2; Ex 10. Practice Problems. (b) If b = 0, the line is horizontal. 25. You get the normal vector in the component form n = (1, 1) or n = (-1, -1). Congratulations! You have found the tangent line equation. Substitute m = 3 for m Chapter 10 Class 11 Straight Lines (Term 1) Serial order wise Ex 10. e. This equation is called the slope-intercept form. Different Forms of the Equation of a Straight Line. If B is not zero, then the slope of the line STRAIGHT LINES 169 Example 3 Prove that every straight line has an equation of the form Ax + By + C = 0, where A, B and C are constants. Consider a line L having x – intercept a and y – intercept b, then the line Time for examples involving the normal form of the equation to a straight line. The equation of slope intercept varies in USA and UK. From (1) the slope of normal is − y 1 1 /2a. In chemistry, you'll use linear equations in gas calculations, when analyzing rates of reaction, and when performing Beer's Law calculations. Equation 1 and equation 4 are the only ones in standard form. A(−2, 1), B(6, 5) and C(4, k) are the vertices of a right-angled triangle ABC. Solution: Two points on this line are (x 1, y 1) = (0, 15) and (x 2, y 2) = (3, 0). Example: Convert the polar equation A straight line is defined by a linear equation whose general form is. So, the tangent plane to the surface given by f (x,y,z) = k f ( x, y, z) = k at (x0,y0,z0) ( x 0, y 0, z 0) has the equation, This is a much more general form of the equation Equation of a Line – Normal Form | Free Hom Equations of a Straight Line . d = c + mc + c/m = c(1+m+1/m) = c(m^2 + m +1)/m. At this point Show Answer. Ax + By + C = 0, where A, B are not both 0. Example 2: Find the equation of a line having an x-intercept of 5 units and a y-intercept of 4 units. The tangent is a straight line which just touches the curve at a given point. The conversion would look like this: y – y1 = m (x – x1). Here are a quick overview and example of how to determine the equation of a line The first way is to solve for the equation of a line with one. The equation is usually written so that A ≥ 0. Using the formula Normal Form: The normal form of a straight line is given by the equation: $$x\cos \alpha + y\sin \alpha = p$$ where p is the length of the perpendicular from O(0,0) to the line, and α is the inclination of the perpendicular. Vectors provide a simple way to write down an equation to determine the position vector of any point on a given straight line. Find the equation of the line Converting the general equation of a line into normal form: The equation of a straight line in general form is, ax+by+c=0. Substitute m = 1 and b = 2/5. Using the vector equation of the line 1 we get (x, y, z) When t — 1, we get (x, y, z) When t — x set t = —1 and t = 1 to find two points on the line. If two planes are not parallel, then they intersect in a straight line It calculates the point slope form equation by using 2 points of a straight line. ) (2) Slope - Intercept Form There are many instances in science and math in which you will need to determine the equation of a line. The normal form of the straight line is x cos α + y sin α = p Here, x and y are coordinates, p is the length of the perpendicular from origin to the a. Get an answer for 'Find the equation of the straight line which makes angle 30 with positive direction of x axis and cuts intercepts +5 on the y Equation of a Line. The derivative of f (x) = x√x = xx ½ = x 3/2 can be found with the power rule: Step 2: Plug the given x-value into the derivative you calculated in Step 1. 1; Ex 10. slope ACTIVITY 2: Ratio of My Changes Directions: Find the slone of the line To determine the equation of this line, assume any point P on the line with the co-ordinate ( x, y ). From the above In summary, follow the steps below in order to find the equation of the normal line. We’ll get the equation as: x/psecθ + y/pcscθ = 1 Question from Straight Lines,cbse,math,class11,ch10,straight-lines,exemplar,short-answer-type Reduce the Equation √ 3 X + Y + 2 = 0 to the Normal Form and Find P and α. Next: Misc 3 Important → . Hence, the expression for the normal equation of a line is proved. Take one good, quick look at the number on the x or y axis. y = x + 2/5. Solution: Here, we are given p = 4 and ω = 30 0. ⇒ OB = pcscθ. \[m_{\text{tangent}} \times m_{\text{normal 1. Using some trigonometry, we can find the intercepts of this line in terms of p and θ. A line passes through (-3, -9) and is perpendicular to the line 5x + y – 4 = 0. Equation 1: 11 = ¼x + ½y. Now from the origin O draw OD perpendicular to AB. Let the equations of the two non-parallel planes be ax + by + cz + d = 0 and a’x + b’y + c’z + d’ = 0. We do this by making the total of the squares of the deviations as small as possible, i. Slope of a Line: If a line passes through two distinct points P 1 (x 1, y 1) and P 2 (x 2, y 2), its slope is given by: m = (y 2 - y 1) / (x 2 - x 1) with x 2 not equal to x 1. To get the point-slope form So the equivalent for slope-intercept form would be something like: double dx, dy; double m, b; dx = x2 - x1; dy = y2 - y1; m = dy/dx; b = y1; Obviously, this is very simple, but I haven't been able to find the solution for the general equation form (which is more useful since it can do vertical lines Normal form: The normal form of equation Ax + By + C = 0 is x cos α + y sin α = p where. And my textbook says that p is the distance of the straight line from the origin. Find the intercepts and then graph the following equation Step 1: Find the derivative of the function (this gives us the slope of the tangent line ). This line has gradient 3 and cuts the y-axis at 2. Find its equation. Express the equation in standard form. This is a technique for computing coefficients for Multivariate Linear Regression. This is the slope of the tangent line General Form. As far as d is concerned, draw two points p1 and p2, separated by a distance of, say, 3. 3 Part 13 Intercept From of Equation of Straight Line Theorem: Equation of a line EQUATION OF THE FIRST DEGREE, THE ST Intersection of a Line and Plane: If equation of a plane is ax + by + cz + d = 0, then direction cosines of normal to this plane are a, b, c. In this equation, m represents the slope whereas x1, y1 is a point on your line. ax + by + c = 0. From this equation Special forms of the equation of a straight line. x y 0 2 1 3 2 4 3 5 x y There are many more points on the line Find the slope of the line whose equation is 6y - 12x = 11. So angle between normal to the plane and a straight line having direction cosines l, m ,n is given by cos θ = al + bm + cn / √a 2 + b 2 + c 2. EX4. Comments. Chapter 10 Class 11 Straight Lines Equation of a Tangent Line in Cartesian Coordinates. Equation 2: 2x + 5 + 2y = 3. blogspot. 4. The condition that the equation lx +my +n = 0 represents the equatio of a straight line in the normal form I'm in the middle of a calculus course (this is not a calculus question per se), studying from the Larson text, and when an answer to a problem is the equation of a line, I solve for Standard form of a line $Ax + By = C$. Calculation: Given: Perpendicular distance from the origin= p = 7 and α = 45° We know that the equation of the straight line in normal form See Lesson 33 of Algebra, the section "Vertical and horizontal lines. Problem 3. General Equation of a Straight line: The general equation of straight line Equation of a Straight Line. 2. We use this form when we need to find the equation of a line passing through a point (x 1, y 1) with slope m: y − y 1 = m(x − x 1) Example 2 . Straight lines Solutions. What do we already know? A point on our line and the equation of a line parallel to our line. In ΔOAC, cosθ = OC/OA. α + y sin. Subtract 5y from each side. In UK, variable c is used to represent y-intercept. When we try to specify a line Normal Form: The normal form of a straight line is given by the equation: $$x\cos \alpha + y\sin \alpha = p$$ where p is the length of the perpendicular from O(0,0) to the line, and α is the inclination of the perpendicular. The equation of a straight line can be written in many other ways. To convert the general equation of a line into the normal form: Begin with the general or linear form of Point Slope Form and Two Point Form - Straight Lines, Class 11, Maths. This first degree form Converting Linear Equations in Standard Form to Normal Form. For instance, the planes x + 2y – 3z = 4 and 2x + 4y – 6z = 3 are parallel because their normal vectors are n 1 = 〈1, 2, –3〉 and n 2 = 〈2, 4, –6〉 and n 2 = 2n 1. com. uk Equation of a Straight Line (H) - Version 2 January 2016 4. the problem is also called OLS Regression, and Normal Equation r = 2 R cos q. When using slope of tangent line calculator, the slope intercepts formula for a line is: x = m y + b. So why it’s not commonly used? The problem is in its numerical complexity. both sides of 1 by coefficient of x 2 + coefficient of y 2, we get-3 x 5 - 4 y 5 = 3 This is the required normal form This online calculator finds the equation of a line given two points on that line, in slope-intercept and parametric forms. There are different types of "standard" formats for straight lines These equations can be derived from the normal form of the line equation by setting = , and = , and then applying the angle difference identity for sine or cosine. (c) If b < 0, the line 23 Planes Two planes are parallel if their normal vectors are parallel. It makes an angle of the normal normal to a curve. Thus the y intercept is b = 15 and the slope is = −5 1. Reduce the equation Finding equation of a line in 3d. ( x, y) {\displaystyle (x,y)} point and the equation of a line that runs perpendicular to it. Suppose that we want to find the equation of a straight line Theorem – 2 (Cartesian Equation of Line in Space): The cartesian equation of a straight line passing through a fixed point P(x 1, y 1, z 1) and having direction ratios (d. Therefore, the slope of any line passing through and is . The given straight line and the found normal Click here👆to get an answer to your question ️ Consider a family of straight lines (x + y) + lambda (2x - y + 1) = 0 Find the equation of the straight line belonging to this family that is farthest from (1, - 3). 3. and its slope will be the negative reciprocal of the curve's derivative at Q. Observe the geometry described in the figure Lesson#13 Two intercept form of equation of Straight Line CASE 4: If two non-zero intercepts of a line are given, we will use: Two Intercepts from: x/a + y/b = 1 here a = x - intercept , b = y - intercept Math. A line passes through (1,-4) and is parallel to the line 3x – 8y + 1 = 0. Straight-line equations, or "linear" equations, graph as straight lines, and have simple variable expressions with no exponents on them. Method 1: This method works only if the y intercept is visible. General form: The general form of the straight line equation Straight Line Formula, Equation and Definitio This unit is about the equations of straight lines. However, there exist different forms for a line equation. If B is not zero, then the slope of the line Normal equation is a more closed-form solution of figuring out the value of a parameter that minimizes the cost function. Find the equation of the straight line passing through the point (2, 0) and through the point of intersection of the lines So the equivalent for slope-intercept form would be something like: double dx, dy; double m, b; dx = x2 - x1; dy = y2 - y1; m = dy/dx; b = y1; Obviously, this is very simple, but I haven't been able to find the solution for the general equation form (which is more useful since it can do vertical lines 1. The coordinates in this batch of worksheets for grade 8 and high school, are given in the form This says that the gradient vector is always orthogonal, or normal, to the surface at a point. If the line is vertical, look at the x-intercept. Now that we can write an equation for a plane, we can use the equation For a linear function the slope is dy / dx = b where we can read the mathematical expression as “the change in y ( dy) that results from a change in x ( dx) = b * dx “. The equation, y = mx + b, is in slope-intercept form for the equation of a line. y = k x + b. CBSE CBSE (Science) Class 11 Textbook This is the normal form of the given line. [5] 5. Now we have to find the equation of the straight line Equation of a line. Therefore, the equation of the straight line in normal So this point will satisfy equation of normal form of line. Equations of straight-line graphs are given in the form Find the equation of a normal line step-by-step. The symmetric form is presented like this: x a + y b = 1, where a and b are non-zero. we minimise 2 ¦ d i. 5. Determine the vector equation of the straight line passing through the point with posi-tion vector i−3j+k and parallel to the vector, 2i+3j−4k. (a) If b > 0, the line slopes upward to the right. 210 This line has gradient −C D and cuts the y-axis at . Normal Form of Straight Line ⇔ x cos α + y sin α = p. Solution : Given : Slope m = 3 and y-intercept b = -2. The formula to find equation of straight line STRAIGHT LINE -2 NORMAL FORM Let a line be at a distance of p units from the origin and α (0 360 )≤α<0 be the angle made by the normal to the line with positive direction of x - axis. Angle ABC is the right angle. (2, 10, Parametric Equations This form of the equation is called the normal form. The equation for a line whose length of the perpendicular from the origin is p and whose angle with the positive x-axis is given by α is given by: x cos α+y sin α = p. Problem 3 : Find the general equation of the straight line The "General Form" of the equation of a straight line is: Ax + By + C = 0. ( − a a 2 + b 2) x + ( − b a 2 + b 2) y = c a 2 + b 2. rise 2. The equation of a straight line is usually written this way: y = mx + b We have been looking at the "slope-intercept" form. How to find the slope intercept form (equation of a straight line The cross product of the lines’ direction vectors gives a normal vector for the plane. We know that the equation of a line which cuts the y-axis (i. Therefore equation of the normal www. We know that the common section of two planes is a straight line. Equation of Line Parallel to the y-axis. General form: The general form of the straight line equation WITS (http://www. Problem 1 : Find the general form of equation of a straight line whose slope is 3 and y-intercept -2. Circle the equation of a line none Converting Linear Equations in Standard For. com)WITS Blog(http://iitjee-aieee-exam. (c) If b < 0, the line Equation of above line intercept form will be given by x OA + y OB = 1 ; i We have OD ⊥ AB and OD = p units In ∆ OAB cosα = OD OA = p OA ⇒ Free line equation calculator - find the equation of a line given two points, a slope, or intercept step-by-step This website uses cookies to ensure you Example: Show all of these forms for the straight line shown to the right. When an equation is in this form, the slope of the line is given by m and the y-intercept is located at b. Find any two points, (x 1, y 1) and (x 2, y 2), on the line and substitute their coordinates into the following formula Normal Form of a Line (Perpendicular form of line) The equation of the straight line upon which the length of of the perpendicular from the origin is p and The vector equation of the line through a fixed point A and parallel to the vector p is given by: Example: Find the equation of the line passing through the points A Equation of a Line: Standard Form - Level 2. If a line, plane or any surface in space intersects a coordinate plane, the point, line, or curve of intersection is called the trace of the line, plane or surface on that coordinate plane. y = mx + b. The given straight line and the found normal Aug 1, 2014. Equation of a straight line can also be evaluated with one point and slope using our point slope form calculator. Varying d traces out the line. These equations can also be proven geometrically by applying right triangle definitions of sine and cosine to the right triangle that has a point of the line and the origin as vertices, and the line For a linear function the slope is dy / dx = b where we can read the mathematical expression as “the change in y ( dy) that results from a change in x ( dx) = b * dx “. b is y intercept. Sometimes we may have to rearrange the equation to obtain this general form. Solution: Equations of bisectors of the angles between the given lines Find the normal vector to the straight line given by the equation x + y = 2. x cos ω + y sin ω = p (normal form) consider a line cutting x-axis at A and y-axis at B. I noticed, however, that the Larson textbook frequently terms answers of the equation of a line in the form Suppose the line AB intersects the x-axis at A and the y-axis at B. Two point slope form equation. 24. of straight line in the following. Let’s first consider the equation of a line in Cartesian form and rewrite it in vector form All straight lines have a general equation of the form, , where m is the gradient and c is the intercept on the vertical axis. You can find an equation of a straight line given two points laying on that line. Your first 5 9 Setting d =−ax0 −by0 −cz0 gives the general form of the equation of a plane in 3D space ax +by +cz +d =0. Find the equation of the line whose y-intercept is -7 and whose slope is 2. 1] Point-slope form. Straight Line (linear) fit to the data; Image by Author. Let AB be the line a. Solution To find the equation, we’ll use the above form directly. Equation 3: y - 2 = 3 (x − 4) Equation 4: 1 2 y − 4x = 0. The only part of this equation that is not known is the $$t$$. Since, r2 = x2 + y2 and x2 + y2 = R2 then r = R. ". In ΔOBC, cos(90° – θ) = OC/OB. Also, represent this equation in standard form. A normal vector and direction vector for the line ‘ Example 0. Solution The vector equation of the straight line Related Pages Coordinate Plane More Geometry Lessons. Example 1: The line is a vertical line. The equation of a line Just because the code pops out an answer is not justification enough. To get the slope-intercept form, we simply substitute in the two values m = −5 and b = 15: y = −5 x + 15. Slope intercept form of a line equation. Your first 5 Substitute the gradient of the tangent and the coordinates of the given point into an appropriate form of the straight line equation. The normal to a curve is the line perpendicular to the tangent to the curve at a given point. The coefficients A and B in the general equation are the components of vector n = (A, B) normal to the line The normal form of the equation of the line is in this way: xcosθ + ysinθ = P . Solve Study Textbooks Guides. If we solve each of the parametric equations for t and then set them equal, we will get symmetric equations of the line. xcosθ + ysinθ = P (sin 2 θ + cos 2 θ) xcosθ + ysinθ = P. Similarly, a straight line having slope m cuts the X -axis at a distance b from the origin will be at the point (b,0). Then angle between the plane and the straight line Find the equation of the line. • If A Line Passes Through P (x1, y1 (0, y). The equation of the straight line in the normal form which is parallel to the lines x + 2 y + 3 = 0 and x + 2 y + 8 = 0 and dividing the distance between these two lines EQUATION OF A STRAIGHT LINE. Ossend ng competency with code: Illustrates and finds the slope of a line given two points, equation, and graph. ⇒ sinθ = p/OB. L = cos alpha, m = sin alpha, n =- p :. The slope of the tangent when x = 1 is f′ (1) = 3/2. Solution Use the expression (2) above with a = 1 and b = 1. There are different types of "standard" formats for straight lines We need other forms of the straight line as well. So by two point form the equation of the line is: x / a + y / b = 1 4 21. In the following subsections, a linear equation of the line is given in each case. If p is the length of a perpendicular from origin to the non-vertical line l and α is the inclination of p, then show that the equation of the line is. The equation of a normal line will have the form. l^(2) +m^(2) = 1 and n lt 0. Give your answer in the form ay + bx = c where a, b and c are integers. The above equation can be rewritten as by = −ax –c. Write the equation in normal form for the line 3x − 4y + 5 = 0. C. Example 1 Find the equation of a line whose perpendicular distance from the origin is √2, and the perpendicular to it from the origin makes a 45° angle with the x-axis. Ax + By + C = 0. 6. Chapter 23 The straight lines Vector equation of a line The normal form of the the equation of a straight line in a plane Line passing through two given points Remark Remark To determine the equation of a line passing through two given points, any one of the speci fi ed points on the line may be chosen to represent the given point. The normal is a straight line which is perpendicular to the tangent. Normal Form • Suppose a non vertical line Equations of horizontal and vertical lines; Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the points on the line. are designated as linear equations, and their graphs are shown to be straight lines. A point and a directional vector determine a line in 3D. Another popular form is the Point-Slope Equation of a Straight Line If we choose any point on line with coordinates , then we can get the slope of the line passing through the two points as shown in the figure. (ii) bisector of the acute angle between them. To prove this equation of a straight is in normal form, let P ( x, y) be any point on the straight line l. For example, a line with the equation call this the normal vector to the line. If a line of best fit is found using this principle, it is called the least-squares regression line The normal at any point of a curve is the straight line which is perpendicular to the tangent at the point of tangency (point of contact). Updated: 10/22/2021 Create The slope intercept form is the equation of a line 1. Where a and b are constants and either a ≠ 0 or b ≠ 0. In this tutorial the instructor shows how to derive a straight line equation. It should be noted that the symmetric form Ans: A line can be defined in different forms, namely the intercept form and the slope-intercept form. 5y = 5x + 2. And, p = ∣ c ∣ a 2 + b 2. Here p = 7 and α = 45°. The equation for these types of lines are different from the y=mx+c structure. The figure shows the line Tangent to a plane curve is a straight line touching the curve at exactly one point and a straight line perpendicular to the tangent and passing throu. Here you can find two calculators for an equation of a line What you need to do now is convert the equation of the tangent line into point-slope form. POINT-SLOPE FORM. He shows us a process that consists of two steps. Alternatively we may imagine a particle traveling along the line The equation of a line. The slope-intercept form. Then the equation of the line is x cosα + y sinα = p. Suppose that a function y = f (x) is defined on the interval (a, b) and is continuous at x 0 ∈ (a, b). If we are given two points on a straight line, we can also use the gradient–point form to determine the equation of a straight line. Intercept form. Position of Points is Relative to a Given Line Let the equation of the given line Given a point P = ( p 1, p 2) and a vector v → = ( v 1, v 2), we can describe the points ( x, y) of the straight line that crosses point P and has the direction of the Equation of the line in normal form is x cos alpha +y sin alpha =p, :. Equations of a Straight Line . Three possible graphs of y = a + bx. Take the derivative of the original function, and evaluate it at the given point. Then the vector p1 + d*u is a point d/3 of the way from p1 to p2. 3; Examples; Miscellaneous Misc 2 - Chapter 10 Class 11 Straight Lines (Term 1) Last updated at Feb. Slope of a straight line. Toggle navigation. (iii) bisector of the angle which contains (1, 2). Linear Inequalities y New Resources. The general form of the equation of a straight line is ax + by +c = 0 . Draw a vector of length 1 starting at p1 and pointing toward p2. Normal Form. The equation of a straight line that passes through a point P 1 (x 1, y 1) with a slope m is y - y 1 = Find the normal vector to the straight line given by the equation x + y = 2. A or B can be zero, but not both at the same time. Express the vector equation of the straight line in standard cartesian form. s) proportional to a, b, c respectively is given by Notes: If then x = aλ + x 1, y = bλ + y 1, and z = cλ + z 1. y = ax + b. Equation of a straight line which is parallel to the y-axis at a distance of ‘a’ then the equation The relationship between the vector and parametric equations of a line segment. Equations of a line: parametric, symmetric and two-point form. For 3 points P, Q, R, the points of the plane can all be written in the parametric form F(s,t) = (1 - s - t)P + sQ + tR, where s and t range over all real numbers. This is also called the general equation of the straight line. 0 = 5x - 5y + 2. Straight Line in Normal Form Straight Line in Normal Form 1Save The length of the perpendicular OD from the origin = p and ∠XOD = α, (0 ≤ α ≤ 2π). Find the equation of the line that has a slope of 7 and a y-intercept of 12. In Mathematics, Volume 1, equations such as. is called the slope-intercept form of the equation of a straight line. However, the need for a general form arises when neither of the values is defined. These equations are called the parametric equations On comparing it with the normal form of equation of line x cos α + y sin α = p,we get α = 3 1 5 ∘ and p = 2 2 So, the perpendicular distance of the line from Slopes and Equations of Lines. The graph of the equation is a straight line, and every straight line can be represented by an equation in the above form. The cyan line Equation of a straight line in slope-intercept form : y = mx + b. When drawing in a regression line, the aim is to make the line fit the points as closely as possible. General Form. Where “m” slope of the line Learn the definition and equation of a normal line, and look at some vocabulary related to lines. We summarize these results as follows. This first degree form y + x + 2 = 0. ⇒ cosθ = p/OA. So, (c+mc) = (-1/m)c + d. Step 3: Find the slope of the normal line. There are various ways of defining a line. What is the difference between closed-form Example : For the straight lines 4x+ 3y − 6 = 0 and 5x + 12y + 9 = 0, find the equation of the (i) bisector of the obtuse angle between them. The distance b is called x- intercept of the line. In particular, if the equation is normalized to start with, a unit step in the direction normal to the line If we are given equation of the line instead of the graph, we can still determine the gradient. Equation of the line will be: y = m (x-b) 5. Solving this equation Solution: We know that the equation of the straight line upon which the length of the perpendicular from the origin is p and this perpendicular makes an angle α with x-axis is x cos α + y sin α = p. \square! \square! . Standard and General Equations of a Plane in the 3D space The standard equation of a plane in 3D space has the form a(x −x0) +b(y −y0) +c(z −z0) =0 where )(x0, y0,z0 is a point on the plane and n = < a, b, c > is a vector normal Derive the eqn. In all forms, slope is How to find the equation of a line (4. You can find the directional vector by subtracting the second point's coordinates from the first point's coordinates. Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line. The various common forms for the equation of a line are listed below. is polar equation of a circle with radius R and a center at the pole (origin). Therefore, the equation of the straight line in normal form Normal Equation. Find an equation of the line that passes through A and C. And we say the equation n x = 0 the normal form of the equation of ‘. From this, we can get the parametric equations of the line. 2. To calculate the equations of these lines we shall make use of the fact that the equation of a straight line Equations of a plane: general, normal, intercept and three-point forms. co. So, in case of circles, normal always passes through the centre of the circle. This is known as the normal form of the line. comparing (1) with the form Connection with Parametric Form of a Plane. ⇒ xcos45° + ysin45° = √2 ⇒ x/√2 + y/√2 = √2 ⇒ x + y = 2. In order to write down the vector equation of any straight line, two known values must be present. Notice that $$t\,\vec v$$ will be a vector that lies along the line The Normal Form of a Line. These equations can take various forms depending on the facts we know about the lines. r. Because, as we shall prove presently, a is the slope of the line (), and b-- the constant term -- is the y-intercept. justmaths. 2x+y=6. The general form of a line is \ (Ax + By + C = 0\). The General Form is not always the most useful form, and you may prefer to use: The Slope-Intercept Form of the equation of a straight line Purplemath. x cos. com)This video contains a lecture in mathematics on topic 'equation By reduction of the equation a x + b y + c = 0 of a straight line to the normal form , we get. run 3. The vector equation of the line See Lesson 33 of Algebra, the section "Vertical and horizontal lines. . That's u*. In step one he uses the slope formula to obtain the slope of the line 1. Let the x-intercept = OA = a y-intercept OB = b. Get step-by-step solutions from expert tutors as fast as 15-30 minutes. If a line runs perpendicular to another line The symmetric form of the equation of a line is an equation that presents the two variables x and y in relationship to the x-intercept a and the y-intercept b of this line represented in a Cartesian plane. So to start, suppose we have a straight line containing the points in the following list. BrainKart. (2, 10, Parametric Equations Example : For the straight lines 4x+ 3y − 6 = 0 and 5x + 12y + 9 = 0, find the equation of the (i) bisector of the obtuse angle between them. If the position vector of a specific point that lies on the line and a vector that gives the direction of the line Find the equation of a normal line step-by-step. Gives. 3, 2020 by Teachoo. standard equations of straight lines (1) General Form : Any first degree equation of the form Ax + By + C = 0, where A, B, C are constant always represents general equation of a straight line (at least one out of A and B is non zero. Use the given two points, (x 1, y 1) and (x 2, y 2) to find the slope and apply point-slope formula to write the equation of a line. OM is called the length of the normal = P. On comparing it with the normal form of equation of line x cos α + y sin α = p,we get α = 3 1 5 ∘ and p = 2 2 So, the perpendicular distance of the line from This is called the vector form of the equation of a line. What method will we use? Write the equation of the given line in slope-intercept form to determine its slope, then use that same slope and your point in the point-slope formula Normal Form of Straight Line - Perpendicular Form of Equation of Line - Reduce the equation of the straight line 3x + 4y + 15 = 0 to normal form and find the perpendicular distance of the line from the origin - Maths - Straight Lines. Hence equation of If we are given equation of the line instead of the graph, we can still determine the gradient. Create Standard Form. Solution: Equations of bisectors of the angles between the given lines Predicted values. The second way is to use two points from one line and one point from a perpendicular line. Where, x, y represents the x and y coordinates, m is slope of line, and. Find the angle from the line 2x + y -8 = 0 to the line x + 3y + 4 = 0. Slope–intercept form or Gradient-intercept form. SYMMETRIC FORM The equation of the line The equation of the straight line is y = −1 3x + 2 3 y = − 1 3 x + 2 3. Equation 3 is in point slope form . where A or B can be zero, but not both at the same time. Slope-Intercept Form. The coefficients A and B in the general equation are the components of vector n = (A, B) normal to the line BLAH BLAH BLAH BLAH B BLAH BLAH Equations of straight line 15. Icosidodecahedron; Snub Dodecahedron; Multipurpose Number (0-10) Generators; Drawing Triangles on Pin-boards; Regular Answer (1 of 4): 5x+12y=26 y=mx+c 12y=-5x+26 y=-\frac{5}{12}x+\frac{13}{6} y-mx-c=0 There are 7 well known forms of Straight Lines: What's the difference between wave equation in PDE form and wave equation in normal form? 9. The equation of the normal Finding the equation of a straight line Given the graph of a straight line, there are several ways to find its equation. Distance Between Two Points. Figure 1. Trace. A. 7. Where, p is length of the perpendicular from the origin and this perpendicular makes an angle α with x- axis. Numerical: Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with positive direction of x-axis is 30°. α = p. We use the formula for the equation of a straight line passing through two points. Find the equation of the line that has a slope of 8 and passes through the point (-5, 8). For example, the equation of the line Examples: 1. Sometimes we need to find the equation of a line segment when we only have the endpoints of the line segment. Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with the positive direction of x –axis is 15o . The Vector Equation of a Line. Polar equation of a circle with a center at the pole. As you see it‘s pretty easy to use the normal equation and to implement it in Python — it’s only one line of code. This is the general equation of a line given a point (on the line) and its y-intercept. If you see an equation with only x and y − as opposed to, say x 2 or sqrt(y) − then you're dealing with a straight-line equation. Make $$y$$ the subject of the formula. So now, let’s talk about the Equation of a Straight Line. The general equation or standard equation of a straight line is: a x + b y + c = 0. Find the value of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line That is, every step by one unit in the direction normal to the line change the value of the function by the norm of its normal vector? This is true for any linear function and for any form of its equation. We first calculate the gradient using the two given points and then substitute either of the two points into the gradient–point form Equation of a Straight Line. To determine the equation Normal form: The equation of the line having normal distance from origin p and angle between normal and the positive is given by ; General Equation of a Line: Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line. We’ve found the intercepts! Let’s use the intercept form of the equation now. Note: Proper choice of signs to be made so that p should be always positive. The general equation of a line when B ≠ 0 can be reduced to the next form. General form of equation of a straight line is. Drawn OM ⊥ to AB from 0. Equations of straight-line graphs are given in the form Purplemath. Multiply each side by 5. Equation of the straight line in slope-intercept form : y = mx + b. Find the equation of the line Math. Using point slope form to find the required equation of line Solution: We know that the equation of the straight line upon which the length of the perpendicular from the origin is p and this perpendicular makes an angle α with x-axis is x cos α + y sin α = p. A useful form is the point-slope form (or point - gradient form). Traces, intercepts, pencils. , it has y-intercept) can be put in the form y = mx + b; further , if the line If the normal form of the equation of a straight line 4 x + 3 y + 2 = 0 is x cos α + y sin α = p and its intercept form is a x + b y = 1, then ab p s e c α = 1633 65 TS Then the equation of the line will be x cos ω + y sin ω = p , where p is the length of perpendicular & ω is the angle perpendicular makes with positive x axis. The vector equation of the line is (x, y, z) The parametric equations of the line are 7—3t -2+2t, teR —2) with direction The symmetric equations are b. witsonlineeducation. MSAL - le-3 ACTIVITY 1: Rise Over Run Given the following figures below: I 30 20 2 16 Figure 2 5 10 X Figure 1 Find the following: 1. A non-vertical line y = mx+a. 5x - 5y + 2 = 0. y = mx + c. ⇒ OA = psecθ. (at least one of a, b is non-zero) coefficient of x = a , coefficient of y = b , constant term = c. Proof Given a straight line, either it cuts the y-axis, or is parallel to or coincident with it. Equation of normal in cartesian form. x - 1 2 - 1 = y - 7 3 - 7. . A computation like the one above for the equation of a line shows that if P, Q, R all satisfy the same equation ax + by + cz = d, then all the points F(s,t) also satisfy the same equation. The purpose of this discussion is to study the relationship of slope to the equation of a straight line.
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Ten Ways Monsanto and Big Ag Are Trying to Kill You - And the Planet
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Mar 4, 2014 ... For 10 years, until it was torn down, the chemical giant's creation ... I thought you were trying to make the world a BETTER place? ... of industrial agriculture, it courted controversy in other ways — namely, as a .... Schmeiser was made into the poster child for the innocent farmer sued by big, bad Monsanto.
Monsanto's BT-Toxins Found to Kill Human Embryo Cells ...
www.nationofchange.org/monsanto-s-bt-toxins-found-kil...Proxy Highlight
Jan 25, 2014 ... In the meantime, utilize these 5 tips for avoiding GMOs while you .... Ten Ways Monsanto and Big Ag Are Trying to Kill You - And the Planet
The Complete History of Monsanto, “The World's Most Evil ...
www.globalresearch.ca/the-complete-history-of-monsant...Proxy Highlight
May 24, 2016 ... A few things you definitely want to avoid in your diet are GMO soy, corn, wheat and ... The answer to that question is obviously a very big “no way!” ... from its chemical business and rebrands itself as an agricultural company. ... killed millions of people and wildlife over the years now wants us to believe they ...
Monsanto - SourceWatch
www.sourcewatch.org/index.php/MonsantoProxy Highlight
Monsanto is one of the "Big 6" Biotech Corporations, along with BASF, Bayer, Dow Chemical ... of the Big 6 and is considered the mother of agricultural biotechnology. ... to Succeed Without Really Trying'; 4.8 Monsanto, GM Foods, and Health Risks .... Among other things, the suit argues "that genetically modified food labels ...
10 Reasons why Monsanto is polluted and corrupted from its core
www.seattleorganicrestaurants.com/vegan-whole-food/Mo...Proxy Highlight
Are the “so-called” Energy Drinks Killing You Slowly? ..... Monsanto's GMO seeds are causing a disaster in US agriculture ... Monsanto and biotech financial beneficiary have been trying to spread misinformation that suicide of ... But as we all know, global sustainability for Monsanto, big banks and giant oil companies mean ...
Core Truths: 10 Common GMO Claims Debunked | Popular Science
www.popsci.com/article/science/core-truths-10-common-...Proxy Highlight
Jul 11, 2014 ... To find out, Popular Science chose 10 of the most common claims about GMOs and ... "That is not true when you cross widely different varieties in traditional breeding." ... 6) Claim: All research on GMOs has been funded by Big Ag. ... that feeding the larvae milkweed coated in Bt corn pollen could kill them.
Why Bayer really wants to buy Monsanto - The Week
www.theweek.com/articles/626013/why-bayer-really-want...Proxy Highlight
May 24, 2016 ... Monsanto's Roundup herbicide. ... 10 things you need to know today. Today's ... On the flip side, however, are herbicides for killing weeds. ... As an agricultural chemical company, Bayer is big in both pesticides and herbicides.
Monsanto's Cruel, and Dangerous, Monopolization on American ...
www.vanityfair.com/news/2008/05/monsanto200805Proxy Highlight
Monsanto dominates America's food chain with ruthless tactics, waging a ... remember the exact words, but they were to the effect of: “Monsanto is big. ... We will get you. .... a farmer plants his crop, then treats it later with Roundup to kill weeds. .... the safety of saccharin, and the U.S. Department of Agriculture even tried to ...
Lita Lee's To Your Health Blog
blog.litalee.comProxy Highlight
Feb 2, 2012 ... Ten Ways Monsanto and Big Ag Are Trying to Kill You - And the Planet ... Monsanto GMOs. posted by LITA LEE, PHD at 2:10 PM 0 Comments ...
Monsanto Is Going Organic in a Quest for the Perfect Veggie | WIRED
www.wired.com/2014/01/new-monsanto-vegetables/Proxy Highlight
Jan 21, 2014 ... Fraley concludes that the pepper “changes the game if you think ... The company whose name is synonymous with Big Ag has .... Another genetically modded corn variety seemed to kill monarch butterflies. ..... I honestly would have no problem with anything Monsanto did, if only two things would happen: 1.
The World According to Monsanto - Top Documentary Films
www.topdocumentaryfilms.com/the-world-according-to-mo...Proxy Highlight
Dec 31, 2007 ... We can collapse in despair (what Monsanto wants us to do) or WE CAN .... And you're an expert on the long term effects of agricultural .... I think when it comes to the very things that give us life, 'prudent, .... I guess Monsanto's newest horror, the "terminator gene" -- which literally kills the plant's own seed, ...
The Folly of Big Agriculture: Why Nature Always Wins by Verlyn ...
e360.yale.edu/feature/the_folly_of_big_agriculture_wh...Proxy Highlight
Apr 9, 2012 ... In its short, shameless history, big agriculture has had only one big idea: uniformity. ... farmers have been encouraged to apply a uniform herbicide to kill weeds. ... If things go right, bureaucratically, that is just so much cash in Dow's pocket. .... Yet, the biotech companies (like Monsanto) are trying to impose ...
Why Tiny Microbes Mean Big Things for Farming
news.nationalgeographic.com/news/2014/09/140918-soil-...Proxy Highlight
Sep 18, 2014 ... Why Tiny Microbes Mean Big Things for Farming ... Now, both university researchers and major agricultural companies are looking for new ways to use soil bacteria. ... of carbon monoxide—prime habitat for the species they are trying to ... a fungus, such as wheat take-all, from infecting and killing crops.
GMO Foods Are Killing Us - Elite Daily
www.elitedaily.com/life/gmos-are-killing-us/Proxy Highlight
May 28, 2013 ... If you are active on social media these days then you see that living a fit, ... Basically, your food is being pumped full of weird things it is not made to digest. ... GMOs are awful for so many reasons, but the biggest being that they are ... Monsanto is the King of GMOs and is pretty much responsible for all the ...
U.S. Farmers Cope With Roundup-Resistant Weeds - NYTimes.com
www.nytimes.com/2010/05/04/business/energy-environmen...Proxy Highlight
May 3, 2010 ... The first resistant species to pose a serious threat to agriculture was spotted in a ... Since then, the problem has spread, with 10 resistant species in at least 22 ... However, if Roundup doesn't kill the weeds, farmers have little incentive ... Roundup — originally made by Monsanto but now also sold by others ...
10 Problems Genetically Modified Foods Are Already Causing ...
www.listverse.com/2013/06/22/10-problems-genetically-...Proxy Highlight
Jun 22, 2013 ... 9Kill Bees and Butterflies ... Preventing farmers from harvesting seeds means big businesses could ... Things get even scarier when you consider Monsanto has .... by systematically buying up seed firms and replacing tried and true ... to the agriculture forefront is the promise of preventing a world food crisis ...
Monsanto vs. the monarchs: More evidence that Big Ag is killing our ...
www.salon.com/2014/06/06/monsanto_vs_the_monarchs_con...Proxy Highlight
Jun 6, 2014 ... Monsanto vs. the monarchs: More evidence that Big Ag is killing our butterflies ... Chip Taylor of Monarch Watch, you already know that modern agriculture is ... And while a number of other things could be hurting the butterfly ...
Be Nice to Monsanto, They're Having a Very Bad Year - Red, Green ...
www.redgreenandblue.org/2010/10/17/be-nice-to-monsant...Proxy Highlight
Oct 17, 2010 ... All the weeds are killed with hardly any work for the farmers. ... Monsanto wants to rush out a Roundup Ready sugar beet, but the courts have ... do you have any interest in knowing which of the things you have written here are ..... Pingback: From Big Ag to Big Organics: Welcome to Monsanto's Brave New ...
Honey Bee Die-Off Caused By Multiple Factors Including Pesticides ...
www.billmoyers.com/2013/05/02/honey-bee-die-off-caused/Proxy Highlight
May 2, 2013 ... Find out more about the BEE Protective campaign and how you can ... Everybody but Bayer, Monsanto, and Dow could tell you these ... which attracts many bees among other things, and I have seen many more ... They kill anything they regulate! ... It's a crime what big agriculture has done to mother nature.
The evil of Monsanto and GMOs explained: Bad technology, endless ...
www.naturalnews.com/037289_monsanto_corporations_ethi...Proxy Highlight
Sep 23, 2012 ... It is these things, I think you'll agree, that make Monsanto a ... of farmers who are trying to avoid growing GMOs, Monsanto uses its patent ... Think about the evils perpetrated by the agricultural giants, ... drive of nearly every large corporation you've ever heard of: Get big, ... Even if it means killing our future.
Monsanto's Dirty Dozen | GMO Awareness
https://gmo-awareness.com/2011/05/12/monsanto-dirty-d...Proxy Highlight
May 12, 2011 ... #1 - Saccharin Did you know Monsanto got started because of an ... the use of chemical pesticides in agriculture with the manufacture of the ... Petroleum-based fertilizers can kill beneficial soil micro-organisms, ..... He's really trying. .... of age if you keep using all the SAFE things OKAY'D by the Government.
Monsanto Trolling Anti-GMO Articles, Claiming Organic Food 'Kills ...
www.activistpost.com/2014/06/monsanto-trolling-anti-g...Proxy Highlight
Jun 13, 2014 ... You can say well it really is killing people – but where is the evidence? ... After all, Monsanto has fought labeling GM food in every state that's tried to label it. Why is .... Free Report: 10 Ways to Survive the Economic Collapse with subscription ... Big Ag, Big Pharma, conspiracy, scientists on the take....reject ...
Hybrid Seeds vs. GMOs | Food Renegade
www.foodrenegade.com/hybrid-seeds-vs-gmos/Proxy Highlight
That means that if you save the seeds produced by F1 hybrid plants and plant them, ... to purchase their seeds, and the agricultural chemicals required to grow them. ... On the one hand, biotech firms like Monsanto argue that the GMO seeds they create .... I believe organic and heirloom seeds are two totally different things .
Food Politics by Marion Nestle » Isn't it about time GM foods got ...
www.foodpolitics.com/2012/01/isnt-it-about-time-gm-fo...Proxy Highlight
Jan 30, 2012 ... Monsanto is no longer selling GM corn in France and BASF has ..... Ten Ways Monsanto and Big Ag Are Trying to Kill You - And the Planet:
5 Steps for Avoiding and Detoxing the Bt-Toxin Found in GMO Crops ...
www.naturalsociety.com/5-steps-avoiding-detoxing-bt-t...Proxy Highlight
Jan 7, 2013 ... Well, Big Ag had the evil-genius idea of actually splicing the Bt gene ... Monsanto's 'biopesticide' known as Bt is killing human kidney cells. ... Consume fiber-rich foods – The more fiber you eat, the faster things move through your body. .... force to defend yourself against someone who is trying to kill you.
Are GMOs safe? Yes. The case against them is full of fraud, lies, and ...
www.slate.com/articles/health_and_science/science/201...Proxy Highlight
Jul 15, 2015 ... The people who tell you that Monsanto is hiding the truth are themselves ... It's a process that can be used in different ways to create different things. ... in the developing world, it isn't a big moneymaker like soybeans or cotton. .... pesticide use and corporate control of agriculture, didn't apply to all GE crops.
The True Evil Empire is Monsanto and They are Trying to Kill the ...
https://mindyourdirt.com/2015/11/08/the-true-evil-emp...Proxy Highlight
Nov 8, 2015 ... I am so sorry to do this to you, but I am about to go off the rails from my normal posts. ... The True Evil Empire is Monsanto and They are Trying to Kill the World. .... The Big One, what is not debatable is the destruction that was caused. .... sneakily nestled between 10 Ways to Add Nutrients to your Soil and ...
Hidden Costs of Industrial Agriculture | Union of Concerned Scientists
www.ucsusa.org/food_and_agriculture/our-failing-food-...Proxy Highlight
Sustainable agriculture practices can protect the environment and produce high- quality, safe, ... You are here ... food and farm policy choices – impacts the environment in many ways. ... blooms of oxygen-depleting microorganisms that disrupt ecosystems and kill fish. ... Eight Ways Monsanto Fails at Sustainable Agriculture ...
The Biggest Concerns About Genetically Modified Food Aren't ...
www.lifehacker.com.au/2015/05/the-biggest-concerns-ab...Proxy Highlight
May 8, 2015 ... The Biggest Concerns About GMO Food Aren't Really About GMOs ... and any other chemicals that farmers use to kill things that might hurt their plants. ... Two different things, actually, which GMO opponents sometimes get confused. .... capitalising on agriculture and trying to patent seeds that die after one ...
Top 10 Reasons to Avoid GMOs - Naturally Savvy
www.naturallysavvy.com/eat/whats-so-bad-about-gmos-to...Proxy Highlight
Read More: 15 Things You Should Know About Monsanto. 2. ... The main function of herbicides and pesticides is to kill unwanted plants and insects. ..... When you look into the studies trying to prove GMO bad, many times they are showing the .... Are you sure you have no connect to Monsanto or at least the big ag industry?
The Fight Over the Future of Food: Monsanto, GMOs, and How to ...
www.treehugger.com/green-food/the-fight-over-the-futu...Proxy Highlight
Nov 11, 2009 ... So, will (or should) genetically modified foods be a big part of the future of food? ..... You could argue that these things come from industrial agriculture, not ... Monsanto trying to feed the world and make a killing doing it you ...
How Monsanto Is Terrifying the Farming World | Miami New Times
www.miaminewtimes.com/restaurants/how-monsanto-is-ter...Proxy Highlight
Jul 25, 2013 ... Agriculture is a big industry in Florida. ... When you're good at something, you want to leverage that. ... That meant farmers no longer had to till the land to kill weeds, ... Monsanto squeezed out competitors by buying the biggest seed .... Monsanto's spent more than $10 million on campaign contributions ... click here to view. - Toxics Information Project www.toxicsinfo.org/tiptalks/Spring13.docProxy Highlight TELL THEM YOU SAW IT IN THE TIP TALKS DIGEST! ..... Ten Ways Monsanto And Big Ag Are Trying To Kill You - And The Planet Www.Organicconsumers. Can We Trust Monsanto with Our Food? - Scientific American www.scientificamerican.com/article/can-we-trust-monsa...Proxy Highlight Jul 25, 2013 ... Scratch the blogosphere and you'll be dumbfounded by this award. GMOs ( genetically modified organisms) produced by big ag-biotech companies are responsible for farmer suicides in India. ... and "They are killing us—GMO foods. ... Scientists have done their best to explain things, but they're rather staid ... Stop Monsanto's Secret Plan to Kill GMO Labeling | Food ... www.fooddemocracynow.org/blog/2014/dec/10Proxy Highlight Dec 10, 2014 ... Don't let Monsanto and the GMA corrupt our democracy and kill GMO ... At Food Democracy Now!, we've been warning you about this for ... with devious ways to undermine our most basic democratic rights. ... on December 10, and Congress needs to hear your voice loud and clear! ... DTN Ag Policy Blog. Healing News Network Archives - February, 2012 postings, links ... www.healingnews.com/2012/Archives_February_2012.htmlProxy Highlight Feb 29, 2012 ... Judge Sides With Monsanto: Ridicules Farmers' Right to Grow Food ..... Ten Ways Monsanto and Big Ag Are Trying to Kill You - And the Planet ... GMO Myth: Farmers “drown” crops in “dangerous” glyphosate. Fact ... https://www.geneticliteracyproject.org/2015/01/22/gmo...Proxy Highlight Jan 22, 2015 ... On our no-till ground—the most sustainable form of agriculture, and it's been made ... which is one of my big concerns and a concern farmers that I know. .... around any subsatance humans manipulate to kill bugs or plants is not organic. ... You can't simply divide things into good and bad based on whether ... The 10 GMO Myths That Monsanto Wants You to Believe - The ... www.theorganicprepper.ca/the10-gmo-myths-that-monsant...Proxy Highlight Jul 20, 2013 ... The 10 GMO Myths That Monsanto Wants You to Believe ... Because the biotech companies, Big Food, and Big Agri can pay to spread their ... The reality: Sustainable agricultural practices are the answer to world hunger. .... are – and many of them are derived from things like GMO corn, soy, and canola. The GMO debate: 5 things to stop arguing - The Washington Post https://www.washingtonpost.com/lifestyle/food/the-gmo...Proxy Highlight Oct 27, 2014 ... You might not think much of my idea of celebration, but I'm guessing you'd ... it just doesn't make a dent in the association that GMOs have with Big Ag. ... GMO supporters are Monsanto shills, and opponents are anti-science. ... says that “ conflict entrepreneurs who are trying to turn GM food risks into a ... The Multiple Ways Monsanto is Putting Normal Seeds Out of Reach ... https://survivingthemiddleclasscrash.wordpress.com/20...Proxy Highlight Feb 5, 2009 ... And they have done and are doing a bucket load of things to keep farmers .... I have nothing for you to sue me over but you are welcome to spend millions trying . ..... Their pesticides are killing the bees…humans will follow in four years. ...... we will have nothing but Big Ag and a biased government telling us ... Did Monsanto Really Just Get A Patent For GMO Marijuana? www.mintpressnews.com/did-monsanto-really-just-get-a-...Proxy Highlight Apr 17, 2015 ... “Monsanto Creates First Genetically Modified Strain of Marijuana! ... that cannabis is becoming big business — and that awareness is based in fact. ... Monsanto is investing heavily in new agricultural technologies, .... What's weird is you spend more time name calling and saying disparaging things to ... How Big Business is Killing Small Farmers - xoJane www.xojane.com/issues/monsanto-industrial-agriculture...Proxy Highlight Apr 26, 2012 ... Monsanto is feeding something, all right: its coffers. ... Monsanto in a nutshell: One of the world's biggest industrial agriculture corporations, with a focus on biotechnology, ... You might know the company for the herbicide glyphosphate ( found in ... These are things organic farmers worry about, and with good ... Monsanto's Herbicide Might Be Killing Farmers | VICE News https://news.vice.com/article/monsanto-s-herbicide-mi...Proxy Highlight Mar 5, 2014 ... Agricultural workers afflicted with CKDu have generally been exposed to all of the above. .... always say that you wouldn't work there if any of these things were true. ... how can you be confident that it isn't all one big profit-based bias? ... The US Just Tried to Kill the Leader of the Taliban With an Airstrike. https://startpage.com/do/asearch #### Queries: Spiritual Healing - Entheogens - Botanical Gardens - Organic Holistic Health - Luminous - Ambrosia - Shamanism - Herbalism - Detox - Mother Nature Mother Ayahuasca Posted on May 20, 2016 at 1:45 PM comments (1) Passiflora incarnata AKA Passion Flower Passion Flower Seed Packs now available. 10 seeds per pack for$5.
Passiflora incarnata is a beautifull Perrenial with sweet scented flowers. Passionflower has been used as a sedative to aid in the treatment of insomnia. In homeopathic medicine Passion Flower was used to treat epilepsy. Passionflower can be smoked or made as a tasty tea or strong decoction.
The European literature involving passionflower recommends it primarily for anti-anxiety treatment.
The medicinal properties of Passion Flowers have been known to Native Americans for centuries. The Cherokee used Passiflora incarnata in religious ceremonies. The dried herb has been valued as an antispasmodic, hypnotic, and sedative. The flowers are highly sought after and considered to be the most potent part of the plant. We are proud to offer the highest quality passion flower blooms and foliage at a reasonable price.
Helps calm people down
Can relieve headaches due to nervous tension
Good for muscle spasms due to nerves
Also known as
Passiflora incarnata, Passiflora caerulea, Apricot Vine, Blue and Purple Passionflower, and Maypop.
Constituents
Chrysin, harmane, harmaline.
Passion Flower Tea Recipe
Put 1 teaspoon in a cloth tea bag or tea baller and then add them to 8 ounces of recently-boiling water. Let steep for five minutes. Take this tea about an hour before going to bed to help with sleep and don't drink more than one cup per day.
Sutherlandia frutescens (Cancer bush, Balloon pea, Sutherlandia)
Sutherlandia frutescens is regarded as the most profound and multi-purpose of the medicinal plants in Southern Africa. Because of its efficacy as a safe tonic for diverse health conditions it has enjoyed a long history of use by all cultures in Southern Africa.
Sutherlandia frutescens, is a much-respected and long-used medicinal plant that is also an attractive garden plant, and has been cultivated in gardens for many years, for its fine form, striking colour and luminous flowers.
Common names: sutherlandia, cancer bush, balloon pea (Eng.); umnwele(Xhosa & Zulu); kankerbos, blaasbossie, blaas-ertjie, eendjies, gansiekeurtjie, klappers, hoenderbelletjie (Afr.)
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Read more:
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#### Queries: Return of The Divine - The Human Gods - E Vine - Eve - Living - Anthropos - Hue Man - Color Man - Rainbow Spirit Man - Shaman - Indigo Warriors - Rainbow Kundalini Serpentine Reiki Chi Human Solar Key of Destiny - Holistic Holy Eon Health
Posted on May 15, 2016 at 7:10 AM comments (0)
Earthing: Health Implications of Reconnecting the Human Body to ...
www.ncbi.nlm.nih.gov/pmc/articles/PMC3265077/Proxy Highlight
Jan 12, 2012 ... Reconnection with the Earth's electrons has been found to promote intriguing ... This paper reviews the earthing research and the potential of ...
earthing (aka grounding) - The Skeptic's Dictionary
www.skepdic.com/earthing.htmlProxy Highlight
Oct 19, 2014 ... Advocates claim that earthing has many health benefits because going barefoot allows the feet to pick up free electrons that then allegedly ...
Is There Anything To "Earthing"? - Ask Dr. Weil
www.drweil.com/drw/u/QAA401221/Is-There-Anything-to-E...Proxy Highlight
Jan 8, 2013 ... I recently read about the practice of "earthing" - the idea that walking ... Supposedly, electrons drawn into the body from the earth neutralize ...
How to Use Earthing & Grounding to Boost Health - Wellness Mama
www.wellnessmama.com/5600/earthing-sleep/Proxy Highlight
Basically, the theory is that our bodies are meant to come into contact with the Earth (a “grounding” force) on a regular basis. Positive electrons in the form of free ...
electrons and the earth's surface - Earthingpeople
www.earthingpeople.se/en/styled-5/Proxy Highlight
When you ground yourself either outdoors or through any of the Earthing products, the free electrons are absorbed into the body and the body also restores it's ...
Health Benefits Of Earthing Grounded In Science? - Critical Cactus
www.criticalcactus.com/health-benefits-of-earthing-gr...Proxy Highlight
does earthing truly boost your health, improve sleep and reduce stress? ... By connecting to the earth, you allow negatively-charged electrons to flow into your ...
How Does Grounding or Earthing Impact Your Health? - Mercola
articles.mercola.com/sites/articles/archive/2012/11/0...Proxy Highlight
Nov 4, 2012 ... Earthing or grounding helps improve heart rate variability, cortisol ... Research indicates that electrons from the Earth have antioxidant effects ...
Research - Earthing_Institute - Earthing Institute
www.earthinginstitute.net/?page_id=131Proxy Highlight
We know that Earthing allows a transfer of electrons (the Earth's natural, subtle energy) into the body. We know that inflammation is caused by free radicals and ...
Grounding - the Removal of a Charge - The Physics Classroom
www.physicsclassroom.com/class/estatics/Lesson-2/Grou...Proxy Highlight
Grounding is the process of removing the excess charge on an object by means of the transfer of electrons between it and another object of substantial size.
Earthing For Longevity – Healing From Earth's Electrons ...
www.undergroundhealthreporter.com/earthing-anti-aging/Proxy Highlight
Earthing (also called grounding) means reconnecting your body with the free electrons that flow through the Earth's surface. It can be as simple, easy, and free ...
Sun Gazing: Why I Stare At The Sun : In5D Esoteric, Metaphysical ...
www.in5d.com/sun-gazing-why-i-stare-at-the-sun/Proxy Highlight
Jan 6, 2015 ... Sun gazing. Sounds crazy doesn't it? Doctor's warn you about how dangerous the sun is, and how harmful it can be to your health.
Solar Healing Center
www.solarhealing.comProxy Highlight
Sun Gazing Process. We have a super computer in our bodies given to us by the nature, which is our brain. HRM (Hira Ratan Manek) calls it the “brainutor”.
Sun Gazing for Health: An Ancient Therapy - Earth Clinic
www.earthclinic.com/remedies/sun_gazing.htmlProxy Highlight
Mar 29, 2016 ... Sun Gazing is an ancient South East Asian Practice that may sound like an unusual health treatment; however, it is actually considered to be ...
Can ancient 'sun gazing' therapy help reactivate a calcified pineal ...
www.naturalnews.com/049805_sun_gazing_pineal_gland_en...Proxy Highlight
May 22, 2015 ... The technique is known as "sun gazing," or "sun eating," and it dates back more than 2,000 years to ancient India. By staring at the sun for short ...
The Health Benefits of Sungazing - Global Healing Center
www.globalhealingcenter.com/natural-health/health-ben...Proxy Highlight
Apr 19, 2012 ... Sungazing is the practice of staring at a sunrise or sunset for extended periods of time, but are there any health benefits to Sungazing?
NASA Confirms -Super Human Abilities Gained Through Sungazing ...
https://charbelmaklouf.wordpress.com/2013/06/08/nasa-...Proxy Highlight
Jun 8, 2013 ... Do not engage in sungazing practices without proper training and medical supervision. Permanent eye injury and blindness may occur. Do not ...
The Art of Sun-Gazing: NASA confirms that we can “Eat The Sun ...
www.beforeitsnews.com/alternative/2015/09/the-art-of-...Proxy Highlight
Sep 16, 2015 ... To start, let us focus our attention on a fairly ancient practice known as Sun- gazing, which has been practiced all over the world in various ...
NASA Confirms: Super Human Abilities Gained Through Sungazing ...
www.beforeitsnews.com/alternative/2016/03/nasa-confir...Proxy Highlight
Mar 28, 2016 ... That's right, I'm talking about the super-human abilities that can be gained by those who follow the protocol for what's known as sun-gazing, ...
Can The Sun Give Us The Super Human Power of Not Needing To ...
www.projectyourself.com/blog/can-the-sun-give-us-the-...Proxy Highlight
Jan 6, 2014 ... Well a NASA study has confirmed that it can indeed happen through sun ... It's been said that during your first 3 months of sun gazing, the suns ...
Nasa Confirms Sun Gazing and Healthy Benefits
Biophoton - Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/BiophotonProxy Highlight
Biophotons are photons of light in the ultraviolet and low visible light range that are produced by a biological system. They are non-thermal in origin, and the ...
Biophotons: The Human Body Emits, Communicates with, and is ...
www.greenmedinfo.com/blog/biophotons-human-body-emits...Proxy Highlight
Jun 25, 2013 ... Indeed, the human body emits biophotons, also known as ultraweak photon emissions (UPE), with a visibility 1,000 times lower than the ...
Biophotons - The Light in Our Cells
www.transpersonal.de/mbischof/englisch/webbookeng.htmProxy Highlight
Biophotons, or ultraweak photon emissions of biological systems, are weak electromagnetic waves in the optical range of the spectrum - in other words: light.
An introduction to human biophoton emission. - NCBI
www.ncbi.nlm.nih.gov/pubmed/15947465Proxy Highlight
BACKGROUND: Biophoton emission is the spontaneous emission of ultraweak light emanating from all living systems, including man. The emission is linked to ...
Biophoton Communication: Can Cells Talk Using Light?
https://www.technologyreview.com/s/427982/biophoton-c...Proxy Highlight
May 22, 2012 ... One of the more curious backwaters of biology is the study of biophotons: optical or ultraviolet photons emitted by living cells in a way that is ...
What is biophoton science? | Health Angel Foundation
www.biontology.com/research/what-is-biophoton-science/Proxy Highlight
Biophotons. It has been scientifically proven that every cell in the body emits more than 100,000 light impulses or photons per second. These light emissions ...
Biophotons - The Lights in Our Cells
www.bibliotecapleyades.net/ciencia/ciencia_fuerzasuni...Proxy Highlight
Because of its low intensity, this cellular glow, also known as biophoton emission, is often referred to as ultra-weak cell radiation, or ultra-weak bioluminescence.
Biophotons And The Universal Light Code - Rense
www.rense.com/general50/buiop.htmProxy Highlight
One of the key notions in this book is the discovery of biophotons, a new study in the field of biophysics that could have a far-reaching impact on our ideas of life ...
How Biophotons Show That We Are Made Of Light. | Spirit Science
www.thespiritscience.net/2014/04/18/biophotons-demons...Proxy Highlight
Apr 18, 2014 ... A biophoton or Ultra-weak Photon Emission, (UPE) is a kind of light particle that is emitted by all living things. Though it exists in the visible and ...
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#### Dr. Rima Truth Reports: CBD ALREADY IN HUMAN DNA!
Posted on May 2, 2016 at 1:05 AM comments (0)
CBD ALREADY IN HUMAN DNA!
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#### Herbalism 101 (Entheogens): Tools For Shamans, Healers, Herbalists, Spiritual Guides and Aromatherapists
Posted on May 2, 2016 at 12:55 AM comments (21)
Leaf & Love Organic Lemonade has become the first product in the U.S. to be certified as Glyphosate Residue Free, the Detox Project announced on Tuesday.
The Co-Founder of Leaf & Love Organics, Amy DiBianca, spoke to Sustainable Pulse to tell us why her company made the move to inform their customers that Leaf & Love Organic Lemonade does not contain glyphosate residues: What inspired you to start producing Leaf & Love organic lemonades?
Two fellow moms and I wanted to develop the only zero-sugar “juice box” among the current array of high-sugar, empty calorie children’s beverages. With tremendous concerns about children’s sugar consumption on the rise, we felt good about giving parents a healthier option for their children’s lunchboxes and birthday parties. Why have you certified your product Glyphosate Residue Free? Having the peace of mind that our product is free of a potentially dangerous pesticide residue is just as important as knowing the ingredients are organic and natural. We are talking about every day foods and drinks that our kids consume, and as a mom, I want the highest degree of confidence that what I give my family is safe. As a company, we feel that our customers deserve to have that confidence and trust in our product.
THE GLYPHOSATE BOX Glyphosate Residue Free Certification Glyphosate in Popular American Foods 1o Things You Need to Know about Glyphosate Glyphosate in Numbers What are the top issues your customers care about, which make them buy Leaf & Love organic lemonades? We are the first zero –sugar juice box for kids. That is a game-changer in the children’s drink market. Our customers are aware that childhood obesity and other sugar-related health conditions are on the rise—it’s all over the news that sugar is a HUGE problem. However, our customers don’t want artificial sweeteners that have also been scientifically linked to medical problems. So knowing there is a delicious, organic product that is non-GMO verified, and naturally sweetened without sugar or artificial ingredients, parents feel really good about it. And now, being verified as Glyphosate free, parents can feel as good as we do when we give it to our own kids. ..... Sustainable Pulse
About the product
Contains 32 - 6.75oz Boxes Zero grams of sugar, sweetened only with organic stevia USDA certified organic, non-gmo, vegan, low glycemic index and gluten-free No Artificial Ingredients. No Calories Perfectly portable for a child’s lunchbox, mom’s handbag, birthday parties, playdates, post-sports refreshment Report incorrect product information Product Description As moms, we created something real and simple for our kids and yours-a juice box made with organic, premium ingredients and no sugar. At Leaf & Love, our drinks are great for kids and the people who love them. Nothing complicated. Just delicious. Zero grams of sugar…A zillion grams of love.
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#### Marijuana use could prevent weight gain, study shows Learn more: http://www.naturalnews.com/052407_medical_marijuana_weight_management_health_benefits.html#ixzz3vWI32zmO
Posted on December 27, 2015 at 6:25 AM comments (0)
(NaturalNews) While it's not unusual for marijuana users to engage in food binges during or after smoking, a new study has surfaced showing that such behaviors don't negatively impact their waistlines. One might think that marijuana users would be obese due to all the food consumption they're said to indulge in, however, researchers from the Conference of Quebec University Health Centers have reason to suggest that it's not necessarily true.(1)
The experts studied over 700 adults aged between 18 and 74, based on a Nunavik Inuit Health Survey, and found that, compared to people who didn't smoke marijuana, the marijuana smokers had lower body mass index (BMI) scores (26.8 versus 28.6, respectively). It was noted that those with the lowest BMI scores were marijuana users who hadn't previously tried or quit tobacco, which may or may not play a role in the outcomes. Furthermore, they also discovered that those who smoked pot had a reduced risk of developing diabetes, exhibiting lower fasting insulin and insulin resistance.(2)
The study, titled "Cannabis use in relation to obesity and insulin resistance in the inuit population," was published in the journal Obesity. With a goal "To ascertain the relationship between cannabis use, obesity, and insulin resistance," the study abstract concludes that "Cannabis use was associated with lower BMI, and such an association did not occur through the glucose metabolic process or related inflammatory markers."(3)
Not the first time marijuana use shown to have multiple benefits
According to the researchers, "These associations were attenuated among those who reported using marijuana at least once but not in the past 30 days, suggesting that the impact of marijuana use on insulin and insulin resistance exists during periods of recent use."(1)
This isn't the first time that marijuana use has been linked with positive health results; in 2013, a study published in the American Journal of Medicine outlined that people who smoked marijuana had lower insulin levels than those who didn't, but only if they did so during the past month. As for weight, study participants were found to have smaller waist measurements than those who did not smoke marijuana.(1)
In addition to the weight control and diabetes prevention and management that these studies suggest, marijuana use has been associated with a range of other positive health outcomes. For example, THC, or tetrahydrocannabinol, the main ingredient in marijuana, has long-been linked to reducing pain and improving conditions for patients experiencing certain ailments. From helping with glaucoma and providing asthma relief, to controlling muscle spasms brought on by multiple sclerosis, and possibly improving the health of AIDS patients, medical marijuana has been found to have a multitude of health benefits.(3)
Despite ability to improve health, marijuana use debate rages on
Unfortunately for many, the topic of marijuana is often the center of debate. While some states have legalized its use for both recreational and medical reasons, others have yet to do so. Some people maintain that it's not necessary and likely to bring about detrimental drug habits and cause disruptive behaviors, while others say it's harmless and crucial for their mental and physical health. Many areas also grapple with legislation issues, often attempting to come down hard on growers and dispensaries, while placing limits on use.
At times, the fight seems to be nothing more than an uphill battle. During a recent senate hearing in Michigan, for example, a veteran plagued with post-traumatic stress disorder urged the panel to vote "no" on a bill that would greatly jeopardize medical marijuana use. For people like him, who live with severe bouts of anxiety, stress and sadness after having seen wartime horrors, medical marijuana is essential and something he credits for saving his life. Sadly, however, when he presented his story during the hearing, he was kicked out after state Senator Rick Jones expressed concern over the veteran's brief display of name calling (it should be pointed out that Jones once called a public relations professional "a hooker" in an email).(4)
Debates surrounding this topic will undoubtedly rage on. In the midst of it all, it's important to remain informed and make your opinions on the matter clear by attending local meetings, writing to legislature or even expressing your views by signing petitions. Of course, always be on the lookout for Natural News articles, where you'll find a bevy of information on this issue.
Sources for this article include:
(1) IBTimes.com
(2) OnlineLibrary.Wiley.com
(3) NaturalNews.com
(4) NaturalNews.com
#### Top Ten Entheogens
Posted on September 23, 2015 at 2:35 PM comments (0)
This is a list of entheogens – which, according to Wikipedia are: in the strictest sense, psychoactive substances used in a religious or shamanic context. Plants and herbs have been used for many centuries in religious contexts due to their mind altering nature. In recent times many have been taken up by the “casual drug user” as a cheap alternative to chemical based drugs.If you have had any experiences with the following plants, be sure to tell us about it in the comments – we are always interested in hearing about our readers experiences in areas like this. So, onward, the list:10
‘Heavenly Blue’ Morning Glory
Ipomoea 'Heavenly Blue' (2)Active Constituents: Ergoline alkaloidsThis is a species of morning glory native to the New World tropics, and widely cultivated and naturalized elsewhere.
The seeds have been used for centuries by many Mexican Native American cultures as an hallucinogen; they were known to the Aztecs as ‘tlitliltzin’, the Nahuatl word for “black”. Their traditional use by Mexican Native Americans was first discovered in 1941, brought to light in a report documenting use going back to Aztec times. It was reported in 1960 that the seeds of Ipomoea tricolor were used as sacraments by certain Zapotecs, sometimes in conjunction with the seeds of Rivea corymbosa, another species which has a similar chemical composition. Hallucinations are the predominant effect after ingesting morning glory seeds. Vivid visual and tactile hallucinations, as well as increased awareness of colors have been described.
Amanita muscaria
Fly-AgaricActive Constituents: Ibotenic acidThe quintessential image of an hallucinogenic ‘toadstool’, with it’s red cap and white spots. This fungus is native to birch, pine, spruce, fir and cedar woodlands throughout the temperate and boreal regions of the Northern Hemisphere. These mushrooms were widely used as a hallucinogenic drug by many of the indigenous peoples of Siberia. In western Siberia, the use of A. muscaria was restricted to shamans, who used it as an alternate method of achieving a trance state. In the east, A. muscaria was used by both shamans and common people alike, recreationally as well as religiously. Unlike the hallucinogenic mushrooms of the Psilocybe, Amanita muscaria has been rarely consumed recreationally in modern times. Depending on habitat and the amount ingested per body weight, effects can range from nausea and twitching to drowsiness, auditory and visual distortions, mood changes, euphoria, relaxation, and loss of equilibrium. Amnesia frequently results following recovery.
Jimson Weed, or Hell’s Bells
Datura stramonium
JimsonActive Constituents: Atropine, hyoscyamine and scopolamineNative to either India or Central America, it was used as a mystical sacrament in both possible places of origin. The Native Americans have used this plant in sacred ceremonies. The sadhus of Hinduism also used it as a spiritual tool, smoked with cannabis in traditional pipes.
In the United States it is called Jimson Weed, Hell’s Bells (based on the flowers’ shape) or Jamestown Weed. It got this name from the town of Jamestown, Virginia, where British soldiers were secretly (or accidentally) drugged with it, while attempting to suppress Bacon’s Rebellion. They spent several days generally appearing to have gone insane, and failed at their mission. The effects have been described as a living dream: consciousness falls in and out, people who don’t exist or are miles away are conversed with, etc, and the effects can last for days. It may be described as a “real” trance when a user under the effect can be awake but completely disconnected from his immediate environment.
Wormwood
Artemisia absinthium
450Px-Artemisia Absinthium P1210748Active Constituents: ThujoneNative to temperate regions of Europe, Asia and northern Africa, the religious association with this plant began with its strong association with the Ancient Greek moon goddess Artemis. In Hellenistic culture, Artemis was a goddess of the hunt, and protector of the forest and children. It is perhaps more famously known as the key ingredient in Absinthe, the favorite drink of 19th Century Bohemian artists. The most commonly reported Absinthe experience is a ‘clear-headed’ feeling of inebriation — a form of ‘lucid drunkenness’.
Kava
Piper methysticum
Kava1Active Constituents: KavalactonesAn ancient crop of the western Pacific. The word ‘kava’ is used to refer both to the plant and the beverage produced from it. Kava is used for medicinal, religious, political, cultural and social purposes throughout the Pacific. These cultures have a great respect for the plant and place a high importance on it. The drink is used to this day at social gatherings to relax after work, though it has great religious significance, and is used to obtain inspiration. The effects of the drink (it is also occasionally chewed), in order of appearance, are slight tongue and lip numbing; mildly talkative and sociable behavior, clear thinking, calming effects, relaxed muscles, and a very euphoric sense of well-being.
Salvia, or Diviner’s Sage
Salvia divinorum
Salvia-D-DivinorumActive Constituents: Diterpenoid known as “Salvinorin A”Salvia divinorum is native to certain areas in the Sierra Mazateca of Oaxaca, Mexico, where it is still used by the Mazatec Indians, primarily to facilitate shamanic visions in the context of curing or divination. Shamans crush the leaves to extract leaf juices; they usually mix these juices with water to create an infusion or ‘tea’ which they drink to induce visions in ritual healing ceremonies.
Salvia can be chewed, smoked, or taken as a tincture to produce experiences ranging from uncontrollable laughter to much more intense and profoundly altered states. The duration when smoked is much shorter than for some other more well-known psychedelics, and Salvia typically last for only a few minutes. The most commonly reported after-effects include an increased feeling of insight and improved mood, and a sense of calmness and increased sense of connection with nature.
Magic Mushrooms
Psilocybin mushrooms
Mushrooms-TopperActive Constituents: Psilocybin and psilocinPsilocybin mushrooms have been part of human culture as far back as the earliest recorded history. Ancient paintings of ‘mushroomed’ humanoids dating to 5,000 B.C. have been found in caves of Northern Algeria. Central and Southern America cultures built temples to mushroom gods and carved “mushroom stones”, dated to as early as 1000-500 B.C. Psilocybian mushrooms were used in ritual and ceremony among the Aztecs, served with honey or chocolate at some of their holiest events. The experience of ingestion is typically inwardly oriented, with strong visual and auditory components. Visions and revelations may be experienced, and the effect can range from exhilarating to distressing.
Peyote
Lophophora williamsii
Lophophora Williamsii, El Oso, Coahuila+Active Constituents: Phenethylamine alkaloids, principally MescalineFrom early records (specimens from Texas have dated from 3780 to 3660 BC), peyote has been used by indigenous peoples, such as the Huichol of northern Mexico and by various Native American tribal groups, native to or relocated to the Southern Plains States of Oklahoma and Texas. Peyote and its associated religion, however, are fairly recent in terms of usage and practice among tribes in the Southwestern United States; Their acquisition of the peyote religion and use of peyote can be firmly dated to the early 20th Century. Typically consumed as a tea, the effects last about 10 to 12 hours. When combined with appropriate setting, peyote is reported to trigger states of deep introspection and insight, described as being of a metaphysical or spiritual nature. At times, these can be accompanied by rich visual or auditory effects.
Ayahuasca, or Yage
ChacrunaActive Constituents: Beta-carboline harmala alkaloids, MAOIs and DMT (dimethyltryptamine)Includes BOTH Ayahuasca Vine (Banisteriopsis caapi) & Chacruna Shrub (Psychotria viridis). The word “Ayahuasca”, translated to “vine of the souls”, refers to a medicinal and spiritual drink incorporating the above plants. When brewed together, and consumed in a ceremonial setting, these plants are capable of producing profound mental, physical and spiritual effects. Ayahuasca is mentioned in the writings of some of the earliest missionaries to South America. It may be considered as a particular shamanic medicinal brew, or even as an entire medicinal tradition specific to the Amazonas. The effects of the drink vary greatly based on the potency of the batch, and the setting of the ritual. They generally include hallucinogenic visions, the exact nature of which seem unique to each user. Vomiting can be an immediate side-effect, and is said to aid in “purification”.
Cannabis
42128524 Cannabis Pa416Active Constituents: THC (tetrahydrocannabinol)The cannabis plant has an ancient history of ritual usage as a trance-inducing drug and is found in pharmacological cults around the world. In India, it has been engaged by itinerant sadhus (ascetics) for centuries, and in modern times the Rastafari movement has embraced it. Some historians and etymologists have claimed that cannabis was used as a religious sacrament by ancient Jews, early Christians, and Muslims of the Sufi order. Elders of the modern religious movement known as the Ethiopian Zion Coptic Church consider cannabis to be the Eucharist, claiming it as an oral tradition from Ethiopia dating back to the time of Christ. Cannabis plants produce a group of chemicals called cannabinoids which produce mental and physical effects when consumed. As a drug it usually comes in the form of dried buds or flowers (marijuana), resin (hashish), or various extracts collectively known as hashish oil. The psychoactive effects of cannabis, are subjective and can vary based on the individual. Some effects may include a general change in consciousness (altered perception), mild euphoria, feelings of well-being, relaxation or stress reduction, lethargy, joviality, enhanced recollection of episodic memory, increased sensuality, increased awareness of sensation, and occasionally paranoia, agitation or anxiety.
Source: Listverse
#### The Great CBD Migration: How a Non-Psychoactive Cannabinoid May Champion Cannabis Reform
Posted on September 23, 2015 at 2:20 PM comments (0)
Cannabis is emerging from the shadow of prohibition, and there are many factors that are contributing to this recent wave of legalization. States are increasingly adopting new laws that acknowledge the effectiveness of cannabis as both a medicine, and a taxable commodity that could boost struggling state economies. However, the most recognizable shift is based on one specific component that is forcing our society to reconsider our perception of cannabis, and this tiny cannabinoid is known as CBD (cannabidiol). In just over a year, the governors of fifteen states have signed laws that call for increased research and availability of medical treatment options that are based on CBD. This major shift is focused on the social pressure to recognize anecdotal evidence from the parents of children who experience seizures associated with debilitating disorders like Dravet’s Syndrome. The United States government now must reevaluate the long-held position that cannabis provides absolutely no medical benefit, as parents migrate their families to the increasing number of regions that support medical cannabis. Smoke Reports believes that it is important for the community to follow this phenomenon closely, as the conversation driving this shift holds the keys to a complete social review of cannabis.
High-CBD Cannabis Flowers Extracted into Oil
CBD is Making States Turn Over a New Leaf
There has been a substantial wave of support for laws supporting CBD-based treatment options. Since the end of March in 2014, fifteen states have adopted legislation that supports increased research and availability of CBD medication. Note that these fifteen states typically vote very conservatively when it comes to social issues, which shows how powerful the cannabis conversation has become. Here is a timeline of CBD-only legislation laws signed in the last 15 months:
Utah (3/25/14)
Alabama (4/1/14)
Kentucky (4/11/14)
Wisconsin (4/16/14)
Mississippi (4/17/14)
Tennessee (5/16/14)
South Carolina (5/28/14)
Iowa (5/30/14)
Florida (6/16/14)
North Carolina (7/3/14)
Missouri (7/18/14)
Virginia (2/26/15)
Georgia (4/16/15)
Oklahoma (4/30/15)
Texas (6/1/15)
Almost all of the states focus their laws on CBD medication specifically for children suffering from constant seizures, however some states such as Florida opened their medical programs to support other medical issues such as cancer, Parkinson’s, Alzheimer’s, and PTSD. Many of the states even named their initiatives after a local child championing the push for legalization. It is harder for politicians to oppose a bill dedicated to helping a very young child in immense discomfort. All of the states provided certain legal protections for families obtaining CBD oil, however, not every state listed has legalized the production of cannabis oil, which means some families still must travel to surrounding regions to find the medicine for their children.
The Families Behind the CBD Movement
There are several families around the nation that have championed the social push to make non-psychoactive cannabis treatment available, especially for children. The mounting anecdotal evidence provided by parents of sick children is forcing state legislatures to consider cannabis as having some sort of medical benefit (contrary to the federal classification that cannabis has no medical benefit in any situation). While there are many families seeking alternative treatments for their children through cannabis, a handful have taken it upon themselves to publicly address the risks and sacrifices that they have endured as parents trying to alleviate their child’s pain with CBD.
Carly Chandler, a four-year-old girl from the Birmingham, Alabama region, has a rare genetic disorder (CDKL5) that inflicts daily seizures. Under Carly’s Law, the University of Alabama at Birmingham is conducting a study with permission to treat up to 50 adults and 50 children, a major win for a traditionally conservative state.
Harper Grace Durval is a two-year-old from Mississippi with Dravet Syndrome, a form of epilepsy. Harper Grace was under treatment that required five medications, taken twice a day. The Mississippi law, passed in April of 2014, calls for specific research on the effectiveness of CBD at Ole Miss.
Haleigh Cox is a four-year-old girl from Georgia suffering from severe seizures. Her parents moved her from Georgia to Colorado, after hearing about the success of other families, but being unable to acquire any cannabis medicine in their home state. Haleigh has made so much progress since arriving in Colorado that it has forced Georgia to pass a law to make CBD treatments available, so that future families are not forced to migrate in order to save their child’s life.
Jayden David, a young boy from Tracy, California, was experiencing violent seizures that kept him from talking, eating solid food, and just about everything else a young six-year-old should be happily doing. In June of 2011, Jayden’s father gave him cannabis oil in a final attempt to provide the young boy with relief. The seizures almost immediately disappeared, and for the last few years Jayden has been able to reduce the number of pharmaceuticals he needs to be healthy. Jayden’s father, Jason David, gives one of the most clear accounts as to why cannabis treatment needs to be available, especially for young children suffering in extreme pain. Mr. David will tell you that the risk of providing his child with cannabis has been far outweighed by the obvious relief that Jayden now receives from cannabis, and that for the first time, Jayden gets to live as a young boy, and no longer be addicted to the pharmaceutical drugs (benzodiazepines, and a myriad of other narcotics) that doctor’s prescribe for traditional treatment. Jayden is yet another example of the research needed so that doctor’s nationwide can confidently prescribe cannabis over the dangerous, and sometimes deadly, narcotics.
Charlotte Figi is a celebrity when it comes to cannabis treatment for children. In 2007, at the tender age of three months, Charlotte had her first seizure. Doctors were unable to identify the cause, and sent the Figi family home. Charlotte’s seizures continued, and worsened. Charlotte’s parents searched the internet for possible treatments, and came across information that other children with Dravet’s were finding relief with cannabis oil. This was before Colorado voted for legalized cannabis, so the Figi’s needed a doctor’s medical recommendation to be able to give Charlotte cannabis medicine. Because childhood is such a sensitive time for brain development, the Figi’s struggled to find a doctor that would approve of young Charlotte being exposed to cannabis. After struggling to find a doctor to approve of Charlotte’s experimental use of cannabis to treat her seizures, the Figi’s lucked out and received their recommendation. Now the issue was obtaining low-THC, high-CBD cannabis oil for Charlotte, particularly because strains with this non-psychoactive ratio of cannabinoids were nearly impossible to find. The Stanley brothers ended up saving the day, and developed a stabilized high-CBD strain that they dubbed “Charlotte’s Web.” The Stanley brothers continue to produce this high-CBD variety for Colorado families and their sick kids. Charlotte Figi was referenced by Florida’s Governor Rick Scott when he signed their pro-CBD law, and the Charlotte’s Web strain is also the inspiration behind federal bill H.R. 1635, referred to as “Charlotte’s Web Medical Access Act of 2015,” with the purpose “to amend the Controlled Substances Act to exclude cannabidiol and cannabidiol-rich plants from the definition of marihuana, and for other purposes.” This is the first major instance in which the federal government has contemplated a redefinition of “marijuana” to encompass the many different components of the cannabis plant.
Future Cannabis Research Required
Cannabis appears to be helping children who were suffering under traditional treatment methods. Until recently, there has been an institutional lack of funded cannabis research, which keeps many doctors from prescribing cannabis in any form. Many people against cannabis point to the fact that the long terms effects of CBD on children have not been thoroughly studied. Parents of these afflicted children agree, there is not enough research to help improve the safety of cannabis medicine for their kids. These parents will also point out that their children were truly addicted to powerful pharmaceuticals before they tried cannabis, and that they would gladly support any research that may alleviate the pain and suffering of children in the future. Thank goodness that politicians across the country had enough empathy to hear these pleas. Almost every one of these new CBD laws calls for state-funded research performed at state universities, which marks a turning point in the future of a reasonable cannabis policy in the United States.
#### Why Animals Eat Psychoactive Plants
Posted on September 23, 2015 at 2:10 PM comments (0)
Johann Hari, author of Chasing the Scream: The First and Last Days of the War on Drugs, learns about drunk elephants, the stoned water buffalo, and the grieving mongoose.
The United Nations says the drug war’s rationale is to build “a drug-free world — we can do it!” U.S. government officials agree, stressing that “there is no such thing as recreational drug use.” So this isn’t a war to stop addiction, like that in my family, or teenage drug use. It is a war to stop drug use among all humans, everywhere. All these prohibited chemicals need to be rounded up and removed from the earth. That is what we are fighting for.
I began to see this goal differently after I learned the story of the drunk elephants, the stoned water buffalo, and the grieving mongoose. They were all taught to me by a remarkable scientist in Los Angeles named Professor Ronald K. Siegel.
***
The tropical storm in Hawaii had reduced the mongoose’s home to a mess of mud, and lying there, amid the dirt and the water, was the mongoose’s mate — dead. Professor Siegel, a silver-haired official adviser to two U.S. presidents and to the World Health Organization, was watching this scene. The mongoose found the corpse, and it made a decision: it wanted to get out of its mind.
Two months before, the professor had planted a powerful hallucinogen called silver morning glory in the pen. The mongooses had all tried it, but they didn’t seem to like it: they stumbled around disoriented for a few hours and had stayed away from it ever since. But not now. Stricken with grief, the mongoose began to chew. Before long, it had tuned in and dropped out.
It turns out this wasn’t a freak occurrence in the animal kingdom. It is routine. As a young scientific researcher, Siegel had been confidently toldby his supervisor that humans were the only species that seek out drugs to use for their own pleasure. But Siegel had seen cats lunging at catnip — which, he knew, contains chemicals that mimic the pheromones in a male tomcat’s pee —so, he wondered, could his supervisor really be right? Given the number of species in the world, aren’t there others who want to get high, or stoned, or drunk?
This question set him on a path that would take twenty-five years of his life, studying the drug-taking habits of animals from the mongooses of Hawaii to the elephants of South Africa to the grasshoppers of Soviet-occupied Czechoslovakia. It was such an implausible mission that in one marijuana field in Hawaii, he was taken hostage by the local drug dealers, because when he told them he was there to see what happened when mongooses ate marijuana, they thought it was the worst police cover story they had ever heard.
What Ronald K. Siegel discovered seems strange at first. He explains in his book Intoxication:
After sampling the numbing nectar of certain orchids, bees drop to the ground in a temporary stupor, then weave back for more. Birds gorge themselves on inebriating berries, then fly with reckless abandon. Cats eagerly sniff aromatic “pleasure” plants, then play with imaginary objects. Cows that browse special range weeds will twitch, shake, and stumble back to the plants for more. Elephants purposely get drunk off fermented fruits. Snacks of “magic mushrooms” cause monkeys to sit with their heads in their hands in a posture reminiscent of Rodin’s Thinker. The pursuit of intoxication by animals seems as purposeless as it is passionate. Many animals engage these plants, or their manufactured allies, despite the danger of toxic or poisonous effects.
Noah’s Ark, he found, would have looked a lot like London on a Saturday night. “In every country, in almost every class of animal,” Siegel explains, “I found examples of not only the accidental but the intentional use of drugs.” In West Bengal, a group of 150 elephants smashed their way into a warehouse and drank a massive amount of moonshine. They got so drunk they went on a rampage and killed five people, as well as demolishing seven concrete buildings. If you give hash to male mice, they become horny and seek out females — but then they find “they can barely crawl over the females, let alone mount them,” so after a little while they yawn and start licking their own penises.
Excerpted from Johann Hari's Chasing the Scream: The First and Last Days of the War on Drugs. Available from Amazon.
In Vietnam, the water buffalo have always shunned the local opium plants. They don’t like them. But when the American bombs started to fall all around them during the war, the buffalo left their normal grazing grounds, broke into the opium fields, and began to chew. They would then look a little dizzy and dulled. When they were traumatized, it seems, they wanted — like the mongoose, like us — to escape from their thoughts.
***
I kept returning to the UN pledge to build a drug-free world. There was one fact, above all others, that I kept placing next to it in my mind. It is a fact that seems at first glance both obvious and instinctively wrong. Only 10 percent of drug users have a problem with their substance. Some 90 percent of people who use a drug—the overwhelming majority—are not harmed by it. This figure comes not from a pro-legalization group, but from the United Nations Office on Drug Control, the global coordinator of the drug war. Even William Bennett, the most aggressive drug czar in U.S. history, admits: “Non-addicted users still comprise the vast bulk of our drug-involved population.”
This is hard to dispute, yet hard to absorb. If we think about people we know, it seems about right—only a small minority of my friends who drink become alcoholics, and only a small minority of the people I know who use drugs on a night out have become addicts.
But if you think about how we are trained to think about drugs, this seems instinctively wrong, even dangerous. All we see in the public sphere are the casualties. The unharmed 90 percent use in private, and we rarely hear about it or see it. The damaged 10 percent, by contrast, are the only people we ever see using drugs out on the streets. The result is that the harmed 10 percent make up 100 percent of the official picture. It is as if our only picture of drinkers were a homeless person lying in a gutter necking neat gin. This impression is then reinforced with the full power of the state. For example, in 1995, the World Health Organization (WHO) conducted a massive scientific study of cocaine and its effects. They discovered that “experimental and occasional use are by far the most common types of use, and compulsive/dysfunctional [use] is far less common.” The U.S. government threatened to cut off funding to the WHO unless they suppressed the report. It has never been published; we know what it says only because it was leaked.
As I write this, I feel uncomfortable. The 10 percent who are harmed are most vivid to me—they are some of the people I love most. And there is another, more complex reason why I feel awkward writing about this. For anybody who suspects that we need to reform the drug laws, there is an easier argument to make, and a harder argument to make.
The easier argument is to say that we all agree drugs are bad — it’s just that drug prohibition is even worse. I have made this argument in debates in the past. Prohibition, I said, doesn’t stop the problem, it simply piles another series of disasters onto the already-existing disaster of drug use. In this argument, we are all antidrug. The only difference is between prohibitionists who believe the tragedy of drug use can be dealt with by more jail cells in California and more military jeeps on the streets of Juárez, and the reformers who believe the tragedy of drug use can be dealt by moving those funds to educate kids and treat addicts.
There’s a lot of truth in this argument. It is where my instincts lie. But — as I try to think through this problem — I have to admit it is only a partial truth.
Here, I think, is the harder, more honest argument. Some drug use causes horrible harm, as I know very well, but the overwhelming majority of people who use prohibited drugs do it because they get something good out of it — a fun night out dancing, the ability to meet a deadline, the chance of a good night’s sleep, or insights into parts of their brain they couldn’t get to on their own. For them, it’s a positive experience, one that makes their lives better. That’s why so many of them choose it. They are not suffering from false consciousness, or hubris. They don’t need to be stopped from harming themselves, because they are not harming themselves. As the American writer Nick Gillespie puts it: “Far from our drugs controlling us, by and large we control our drugs; as with alcohol, the primary motivation is to enjoy ourselves, not to destroy ourselves . . . There is such a thing as responsible drug use, and it is the norm, not the exception.”
So, although it is against my instincts, I realized I couldn’t give an honest account of drug use in this book if I talked only about the harm it causes. If I’m serious about this subject, I also have to look at how drug use is deeply widespread — and mostly positive.
***
Professor Siegel’s story of buzzing cows and tripping bees is, he believes, a story about us. We are an animal species. As soon as plants began to be eaten by animals for the first time — way back in prehistory, before the first human took his first steps — the plants evolved chemicals to protect themselves from being devoured and destroyed. But these chemicals could, it soon turned out, produce strange effects. In some cases, instead of poisoning the plant’s predators, they — quite by accident — altered their consciousness. This is when the pleasure of getting wasted enters history. All human children experience the impulse early on: it’s why when you were little you would spin around and around, or hold your breath to get a head rush. You knew it would make you sick, but your desire to change your consciousness a little — to experience a new and unfamiliar rush — outweighed your aversion to nausea.
There has never been a society in which humans didn’t serially seek out these sensations. High in the Andes in 2000 b.c., they were making pipes through which they smoked hallucinogenic herbs. Ovid said drug-induced ecstasy was a divine gift. The Chinese were cultivating opium by a.d. 700. Hallucinogens and chemicals caused by burning cannabis were found in clay pipe fragments from William Shakespeare’s house. George Washington insisted that American soldiers be given whiskey every day as part of their rations.
“The ubiquity of drug use is so striking,” the physician Andrew Weil concludes, that “it must represent a basic human appetite.” Professor Siegel claims the desire to alter our consciousness is “the fourth drive” in all human minds, alongside the desire to eat, drink, and have sex—and it is “biologically inevitable.” It provides us with moments of release and relief.
***
Thousands of people were streaming in to a ten-day festival in September where they were planning — after a long burst of hard work — to find some chemical release, relaxation, and revelry. They found drugs passed around the crowd freely, to anybody who wanted them. Everyone who took them soon felt an incredible surge of ecstasy. Then came the vivid, startling hallucinations. You suddenly felt, as one user put it, something that was “new, astonishing, irrational to rational cognition.”
Some people came back every year because they loved this experience so much. As the crowd thronged and yelled and sang, it became clear it was an extraordinary mix of human beings. There were farmers who had just finished their harvest, and some of the biggest celebrities around. Their names—over the years—included Sophocles, Aristotle, Plato, and Cicero.
The annual ritual in the Temple at Eleusis, eighteen kilometers northwest of Athens, was a drug party on a vast scale. It happened every year for two thousand years, and anybody who spoke the Greek language was free to come. Harry Anslinger said that drug use represents “nothing less than an assault on the foundations of Western civilization,” but here, at the actual foundations of Western civilization, drug use was ritualized and celebrated.
I first discovered this fact by reading the work of the British critic Stuart Walton in a brilliant book called Out of It, and then I followed up with some of his sources, which include the work of Professor R. Gordon Wasson, Professor Carl Ruck, and other writers.
Everyone who attended the Eleusinian mysteries was sworn to secrecy about what happened there, so our knowledge is based on scraps of information that were recorded in its final years, as it was being suppressed. We do know that a special cup containing a mysterious chemical brew of hallucinogens would be passed around the crowd, and a scientific study years later seemed to prove it contained a molecular relative of LSD taken from a fungus that infested cereal crops and caused hallucinations. The chemical contents of this cup were carefully guarded for the rest of the year. The drugs were legal – indeed, this drug use was arranged by public officials – and regulated. You could use them, but only in the designated temple for those ten days. One day in 415 b.c., a partygoing general named Alcibiades smuggled some of the mystery drug out and took it home for his friends to use at their parties. Walton writes: “Caught in possession with intent to supply, he was the first drug criminal.”
But while it was a crime away from the Temple and other confined spaces, it was a glory within it. According to these accounts, it was Studio 54 spliced with St. Peter’s Basilica – revelry with religious reverence.
They believed the drugs brought them closer to the gods, or even made it possible for them to become gods themselves. The classicist Dr. D.C.A.
Hillman wrote that the “founding fathers” of the Western world
were drug users, plain and simple: they grew the stuff, they sold the stuff, and more important, they used the stuff . . . The ancient world didn’t have a Nancy Reagan, it didn’t wage a billion-dollar drug war, it didn’t imprison people who used drugs, and it didn’t embrace sobriety as a virtue. It indulged . . . and from this world in which drugs were a universally accepted part of life sprang art, literature, science, and philosophy . . . The West would not have survived without these so-called junkies and drug dealers.
There was some political grumbling for years that women were behaving too freely during their trances, but this annual festival ended only when the drug party crashed into Christianity. The early Christians wanted there to be one route to ecstasy, and one route only – through prayer to their God. You shouldn’t feel anything that profound or pleasurable except in our ceremonies at our churches. The first tugs towards prohibition were about power, and purity of belief. If you are going to have one God and one Church, you need to stop experiences that make people feel that they can approach God on their own. It is no coincidence that when new drugs come along, humans often use religious words to describe them, like ecstasy. They are often competing for the same brain space – our sense of awe and joy.
So when the emperor Constantine converted to Christianity and brought the Empire with him, the rituals at the Temple at Eleusis were doomed. They were branded a cult and shut down by force. The new Christianity would promote wine only in tiny sips. Intoxication had to be sparing. This “forcible repression by Christianity,” Walton explains, “represents the beginning of systematic repression of the intoxication impulse in the lives of Western citizens.”
Yet in every generation after, some humans would try to rebuild their own Temple at Eleusis—in their own minds, and wherever they could clear a space free of local Anslingers.
Harry Anslinger, it turns out, represented a trend running right back to the ancient world.
When Sigmund Freud first suggested that everybody has elaborate sexual fantasies, that it is as natural as breathing, he was dismissed as a pervert and lunatic. People wanted to believe that sexual fantasy was something that happened in other people – filthy people, dirty people. They took the parts of their subconscious that generated these wet dreams and daydreams and projected them onto somebody else, the depraved people Over There, who had to be stopped. Stuart Walton and the philosopher Terence McKenna both write that we are at this stage with our
equally universal desire to seek out altered mental states. McKenna explains: “We are discovering that human beings are creatures of chemical habit with the same horrified disbelief as when the Victorians discovered that humans are creatures of sexual fantasy and obsession.”
Just as we are rescuing the sex drive from our subconscious and from shame, so we need to take the intoxication drive out into the open where it can breathe. Stuart Walton calls for a whole new field of human knowledge called “intoxicology.” He writes: “Intoxication plays, or has played, a part in the lives of virtually everybody who has ever lived . . . To seek to deny it is not only futile; it is a dereliction of an entirely constitutive part of who we are.”
***
After twenty-five years of watching stoned mice, drunken elephants, and tripping mongooses, Ronald K. Siegel tells me he suspects he has learned something about this. “We’re not so different from the other animal life-forms on this planet,” he says.
When he sees people raging against all drug use, he is puzzled. “They’re denying their own chemistry,” he says. “The brain produces endorphins. When does it produce endorphins? In stress, and in pain. What are endorphins? They are morphine-like compounds. It’s a natural occurrence in the brain that makes them feel good . . . People feel euphoric sometimes. These are chemical changes – the same kind of chemical changes, with the same molecular structures, that these plants [we use to make our drugs] are producing . . . We’re all producing the same stuff.”
Indeed, he continues, “the experience you have in orgasm is partially chemical – it’s a drug. So people deny they want this? Come on! . . . It’s fun. It’s enjoyable. And it’s chemical. That’s intoxication.” He seems for a moment to think back over all the animals guzzling drugs he has watched over all these years. “I don’t see,” he says, “any difference in where the chemical came from.”
This is in us. It is in our brains. It is part of who we are.
HEADLINES:
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The United Nations declared coca leaves an illegal substance in 1961, but Pope Francis told the government of Bolvia to break out the leaves when he arrives for a visit later this month – he plans to chew them. Coca leaves, which are the raw ingredient of cocaine, are legal in Bolivia for religious and […]
How do Balinese shroom dealers stay out of prison?
Indonesia has some of the most draconian drugs laws in the world. Smugglers and dealers face execution. (Earlier this year Andrew Chan and Myuran Sukumaran were put to death by firing squad for attempting to smuggle heroin into Australia). Magic mushrooms are also illegal in Indonesia. Possession could result in a minimum four-year and maximum […]
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#### Peyote and other Psychoactive Cactii
Posted on September 23, 2015 at 2:05 PM comments (0)
Peyote and other Psychoactive Cactii
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How to use them - How to extract them
What they contain - Where to obtain them
How to cultivate them and increase their potency
35 different species discussed
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by
Adam Gottleib
1977
Index:
INTRODUCTION
MESCALINE, PEYOTE AND THE LAW
PEYOTE
THE EXPERIENCE
METHODS OF USE
FINDING AND PICKING PEYOTE
OTHER PEYOTE-TYPE CACTI OF CENTRAL MEXICO
CULTIVATION OF PSYCHOACTIVE CACTI
INCREASING THE POTENCY OF PSYCHOACTIVE CACTI
EXTRACTING PURE MESCALINE FROM PEYOTE OR SAN PEDRO CACTUS
MIXED ALKALOID EXTRACTIONS
DICTIONARY OF CACTUS ALKALOIDS
SUPPLIERS
INTRODUCTION
For many years most of us have been aware of the psychoactive effects of Peyote. More recently in drug-oriented literature there have been numerous references to other cacti believed to have hallucinogenic properties. Among these are Doñana from northern Mexico, San Pedro from the Andes, three related mescaline-bearing species from South America, and at least 15 species used by the Indians of Central Mexico as Peyote substitutes. Botanists and Chemists are now studying the constitutes of these cacti and are making some remarkable discoveries. In this guide we will consider each of these cacti and bring the reader up to date on what scientists have learn ed about them. The various methods of using these cacti are also discussed. Directions are given for cultivating cacti and increasing the yield of mescaline and other alkaloids. There are instructions for extracting mescaline from Peyote and San Pedro, and mixed alkaloids from Doñana and other cacti. We also include a brief discussion of the legal aspects of these hallucinogenic cacti and give the names and addresses of legitimate suppliers from whom these plants can be obtained at reasonable prices.
MESCALINE, PEYOTE AND THE LAW
Both mescaline and Peyote are illegal under the statutes of the [U.S.] Federal Government and most States. Members of the Native American Church are permitted the ritual use of peyote because they established it as a religious sacrement long before these laws came into existence. Members are not permitted to use mescaline, however. Several other cacti such as San Pedro also contain mescaline. Technically it would be illegal to possess these, but because they are common ornamental plants it is permissable to use these cacti for normal horticultural purposes. If a person should attempt to use any of these plants for a psychedelic experience, prosecution is possible. If he were to extract the mescaline from these, the alkaloid would definitely be contraband material. It is important that this point be made clear because the mescaline extraction process is given in this guide. To extract the alkaloids from Doñana and other non-mescaline bearing cacti is not illegal. The information in this guide is presented for the sake of furthering knowledge. The Author can assume no responsibility for how anyone may apply it.
PEYOTE
This spineless, tufted, blue-green, button-like cactus, known botanically as LOPHOPHORA WILLIAMSII, is the most famous of the hallucinogenic cacti. It grows wild from Central Mexico to Northern Texas. It's known history dates back to pre-Columbian times; possibly as early as 300 B.C. During the past two centuries the religious use of Peyote has spread northward into the United States and Canada among many of the Plains Indian Tribes such as the Navajo, Comanche, Sioux, and Kiowa. This cactus eventually came to replace the hallucinogenic but dangerous red mescal bean (SOPHORA SECUNDIFLORA) as a ceremonial sacrement. During the 1800's the North American Peyote ritual was standardized. By 1920 the ceremonial practices of most tribes were identical with only minor variations.
(Note: In Mexico there is a popular liquor called mescal. Many people believe that it is made from the Peyote cactus. Actually it is fermented from the Maguey plant, a large succulent of the Amaryllis family with sword-like leaves. This plant does not contain mescaline or related alkaloids.)
It was in 1896 that Arthur Heffter extracted mescaline from Peyote and tested it upon himself. This was the first hallucinogenic compound isolated by man. About 350 mg of mescaline is required for a psychotropic experience, although definite effects can be felt from as little as 100 mg. Mescaline may comprise as much as six percent of the weight of the dried button, but is more often closer to one percent. An average dried button the diameter of a quarter weighs about 2 grams. it usually takes 6-10 of these buttons to gain the desired effect.
It has been noted that the peyote experience is quantitatively somewhat different than that of pure mescaline, the former being more physical than the latter. This is due to several of the other alkaloids present in the cactus. These include: HORDENINE, N-METHYLMESCALINE, N-ACETYLMESCALINE, PELLOTINE, ANHALININE, ANHALONINE, ANHALIDNINE, ANHALONIDINE, ANHALAMINE, O-METHYLANHALONIDINE, TYRAMINE, and LOPHOPHORINE. Not all of these substances have psychopharmacological activity when administered singly. Some of them in combination apparently potentiate the effects of the mescaline and definitely alter some of the characteristics of the experience.
Two of these alkaloids - Hordenine and Tyramine - have been found to possess antibacterial activity, presumably because of their phenolic function. For ages the Huichol Indians have rubbed the juices of fresh peyote into wounds to prevent infection and to promote healing. The Tarahumara Indians consume small amounts of peyote to combat hunger, thirst and exhaustion especially while hunting. They have been known to run for days after a Deer with no food, water or rest. Peyote has many uses in folkloric medicine including the treatment of arthritis, consumption, influenza, intestinal disorders, diabetes, snake and scorpion bites and datura poisoning. The Huichol and other tribes recognize two forms of peyote. One is larger, more potent and more bitter than the other. They call it TZINOURITEHUA-HIKURI (peyote of the Gods). The smaller, more palatable, but milder buttons are called RHAITOUMUANITARI-HIKURI (peyote of the goddesses). The difference between the two forms may be due solely to how old the plants are. Alkaloids tend to accumulate in these cacti with age. It is possible, however, that the goddess peyote is a different species. Until recently botanists believed that the genus LOPHOPHORA consisted of a single but highly varible species. But in 1967 H.H. Bravo found near Queretaro in south-central Mexico another species which he named LOPHOPHORA DIFFUSA. This plant is yellow-green, soft, ribless and contains a somewhat different alkaloid mixture with far less mescaline that L. williamsi.
THE EXPERIENCE
About half an hour after ingesting the buttons the first effects are felt. There is a feeling of strange intoxication and shifting consciousness with minor perceptual changes. There may also be strong physical effects, including respiratory pressure, muscle tension (especially face and neck muscles), and queasiness or possible nausea. Any unpleasant sensations should disappear within an hour. After this the state of altered consciousness begins to manifest itself. The experience may vary with the individual, but among the possible occurences are feelings of inner tranquillity, oneness with life, heightened awareness, and rapid thought flow. During the next several hours these effects will deepen and become more visual. Colors may become more intense. Halos and auras may appear about things. Objects may seem larger, smaller , closer or more distant than they actually are. Often persons will notice little or no changes in visual perception while beholding the world about them, but upon closing their eyes they will see on their mind-screen wildly colorful and constant changing patterns. After several more hours the intensity of the experience gradually relaxes. Thought becomes less rapid and diffuse and more ordered. In the Navajo peyote ritual this change of thought flow is used wisely. During the first part of the ceremony the participants submit to the feeling and let the peyote teach them. During the latter part of the ritual the mind turns to thoughtful contemplation and understanding with the conscious intellect what the peyote has taught the subconscious mind.
The entire experience may last from 6 to 12 hours depending upon the individual and the amount of the plant consumed. After all the peyote effects have passed there is no comedown. One is likely to feel pleasantly relaxed and much a peace with the world. Although there is usually no desire for food during the experience one would probably have a wholesome appetite afterwards.
METHODS OF USE
The most common method of use is simply to chew up and swallow the fresh or dried buttons after removing the tufts and sand. This is the way it is almost always done at Indian ceremonies. Most people find the taste of this cactus unbearably bitter. The Indians, however, feel if ones heart is pure, the bitterness will not be tasted. Many have found that by not cringing from the taste, but rather letting ones senses plunge directly to the center of the bitterness, a sort of seperation from the offensive flavor is experienced. One is aware of the bitterness, but it no longer disturbs him. This is similar to the practice of bringing ones consciousness to the center of pain so that detachment may occur. It is not a difficult trick, but it takes some mental discipline. People who cannot endure the bitterness of peyote often go to various extremes to get it into the system without having to taste it. One fairly effective method is to drink unsweetened grapefruit juice while chewing it. The acids in the juice somewhat neutralize some of the bitter bases. Another method is to grind the dried buttons in a pepper grinder and pack the pulverised material into OOO capsules which are washed down with warm water. This is an effective method but it can take 20 capsules or more to get a 350mg dose of mescaline. Often people will boil the buttons in water for several hours to make a concentrated tea. A cup of this decoction can be swallowed in a few hasty gulps. Another preparation that is occasionally used is a jello-type dessert made with the fresh or dried plant. If spoonfulls are swallowed whole the gelatine serves as a sort of shield protecting the tastebuds from contact with the bitter material. It also slows down the the absorption of the drug in the digestive tract. This can be of value. It is generally recommended that anyone consuming peyote or mescaline ingest it gradually during a period of an hour or take two half doses 45 minutes apart. This is done to reduce the shock of the alkaloid to the system. Nausea or queasiness is sometimes experienced half an hour or so after taking peyote or mescaline. This usually passes in less than an hour. A sip of grapefruit juice will sometimes dispel the sick feeling. During the peyote ceremony Indians encourage vomiting rather than restraint if the urge presents itself. Throwing up, they believe, is apurging of both physical and spiritual ills. Most tribes fast for at least a day before taking peyote. This can also help to minimize gastric distress. One should not have eaten for at least 6 hours before taking either mescaline or peyote.
A method which avoids both the bitterness and the nausea is the rectal infusion. 8-16 grams of dried peyote is ground into a fine powder and boiled in a pint of water for 30 minutes. It is then strained and further boiled to reduce it's volume to one half pint. After cooling, this is taken as an enema using a small bulb syringe and retained for at least two hours. If there is any fecal matter in the lower bowel, a small cleansing enema should be taken and thoroughly expelled before having the peyote infusion. Otherwise much of the drug will be taken up by the feces and later voided.
FINDING AND PICKING PEYOTE
The peyote cactus may be found in many areas throughout the Chihuahuan Desert from central Mexico to southern Texas. When a site is found where peyote grows it usually does so in abundance. Sometimes it grows in open sunlit places, but more often it is found in clusters under fairly large shrubs, among mesquite or creosote bushes or in the shade of large succulents.
The best time to harvest any cactus is after a long dry spell. The worst time is during or after a rainy period. The plants build up alkaloids during dry seasons and draw upon them for growth when the rains come. If the plants are harvested during or after a wet spell, the alkaloid content may have dropped below 50 percent. If you have a soil test kit, you can get a good indication of the potency of cacti growing wild. If the soil is rich in nitrogen, the plants are likely to be rich in alkaloids.
When harvesting peyote, many people uproot the entire plant. This is unnecessary and wasteful. The roots contain no mescaline. Some of these plants have taken a long time to reach their size. A cactus three inches in diameter may be more than 20 years old. To collect peyote properly the button should be cleanly decapitated slightly above ground level. When the roots are left intact new buds will form where the old was removed. These will eventually develop into full-size buttons which may be harvested as before. Faulty harvesting method have seriously depleted populations of this cactus. Because of the presence of several phenolic alkaloids peyote cacti do not spoil easily and may be kept in their fresh form for several weeks after harvesting. If they are to be kept longer than this they must be refrigerated, frozen, or dried. The enzymes which cause the harvested plant to eventually decompose also destroy the mescaline and other alkaloids. To dry peyote buttons lay them out in the hot sun or in an oven at 250 degrees F until completely devoid of moisture.
OTHER PEYOTE-TYPE CACTI OF CENTRAL MEXICO
There are several cacti which are used by the Tarahumares and other tribes of central Mexico as substitutes for peyote. Many of these cacti are now under investigation for their alkaloidal content and psychopharmacological activity. Progress is somewhat retarded in the studies of the effects of these plants because almost all experimentation has been conducted on laboratory animals rather than humans. Some of these cacti have been found to contain mescaline and other related alkaloids with known sympathomimetic properties. Much further research is needed on these plants and their activity. However, we will attempt to bring the reader up to date on what is known about them at this time.
PEYOTILLO: This small cactus is botanically called PELECYPHORA ASELLIFORMIS. It is also known sometimes as the hatchet cactus because of its oddly flattened tubercules. It is often found growing in the state of San Louis Potosi in central Mexico. The plant contains traces of mescaline too minute to have any effect. It also contains small amounts of anhalidine, anhaladine, hordenine, N-methylmescaline, pellotine, 3-demethyltrichocereine, B-phenethylamine, N-methyl-B-phenethylamine, 3,4-dimethoxy-B-pheneththyl-amine, N-methyl-3,4-dimethoxy-B-phenethylamine, and 4-methoxy-B-phenethy- lamine. Most of these are found in peyote but in much larger quantities.
TSUWIRI: The botanical name of this cactus is ARIOCARPUS RETUSUS. The Huichol name tsuwiri means False Peyote. These people make long pilgrimages to the sacred places where peyote grows in search of that sacrement. They believe that if a person is has not been properly purified the spirits will lead him to the False Peyote and if he partakes of it, he will suffer madness or at least a bad trip. The plant is known among some tribes as Chautle or Chaute. These names are also used for other Ariocarpus species. This cactus contains hordenine, N-methyltryamine in fairly small amounts (about 0.02 percent) and traces of N-methyl-3,4-dimethoxy-B-phenethylamine, and N-methyl-4-B-phenethylamine. Aside from these alkaloids it also contains a flavone called retusin (3,3',4',7-tetramethoxy-5-hydroxyflavone). Although alkaloid content may very some at different seasons or stages of growth, from the scientific point of view the amounts present in this plant appear insufficient to produce any psychopharmacological response.
SUNAMI: This plant, ARIOCARPUS FISSURATUS, has been used in folkoric medicine of Mexico and southwestern USA. It is believed to be more potent than peyote and is used in the same manner as that cactus or made into an intoxicating drink. Among some tribes it is known as Chaute (a generic term for Ariocarpus species), living rock, or dry whiskey. The latter name, however, is often used for peyote and other psychoactive cacti. There are two varieties of A. fissuratus: var. lloydii and var. fissuratus. Both have about the same phytochemical makeup. The plant contains mostly hordenine, less N-methyl-tyramine and some N-methyl-3,4-dimethoxy-B-phenethylamine. Two other species, A. kotschoubeyanus also known as Pata De Venado or Pezuna De Venado, and A. trigonus also contain these alkaloids.
DOÑANA: This small cactus, CORYPHANTHA MACROMERIS, from northern Mexico has been found to contain macromerine, a phenethylamine drug reputed to have about 1/5 the potency of mescaline. It also contains normacromerine, N-formylnor-macromerin, tyramine, N-methyltramine, hordenine, N-methyl-3,4-dimethoxy-B-phenethylamine, metanephrine, and synephrine (a macromerine precursor). Other coryphantha species which contain macromerine with most of these other alkaloids include: C. pectinada, C. elephantideus, C. runyonii and C. cornifera var. echinus. Most of these alkaloids with the exception of macromerine have also been found in other varieties of C. conifera and in C. durangensis, C. ottonis, C. poselgeriana and C. ramillosa. Considering that there is usually no more than 0.1 percent macromerine in Doñana and that a gram or more of this alkaloid may be needed to produce a psychotropic effect, one would have to consume more than a kilo of the dried cactus or 20 pounds of the fresh plant. Clearly this is not possible for most humans. If one wishes to experiment with the hallucinogenic properties of Doñana, is is necessary first to make an extraction of the mixed alkaloids. Methods for this are given latter in this guide.
DOLICHOTHELE: Several tribes occasionally use any one of several species of Dolichothele as a peyote-like sacrament. These include D. baumii, D. longimamma, D. melalenca, D. sphaerica. D. surculosa, and D. uberiforma. Recent investigations have revealed in these the presence of small amounts of the alkaloids N-methylphenethylamine, B-O-methylsynephrine, N-methyltryamine, synephrine, hordenine, and dolichotheline (N-isovalerylhistamine).
MISCELLANEOUS: Several other cacti have been used by the Tarahumares as peyote substitutes. Among these are Obregonia denegrii, Aztekium ritterii, Astrophytum asterias, A. capricorne, A. myriostigma (Bishops cap), and Solisia pectinata. The Tarahumares also consume a cactus which they call Mulato (Mammillaria micromeris) and claim that it prolongs life, gives speed to runners, and clarifies vison for mystical insights. Another cactus similarly employed is known as Rosapara (Epitheliantha micromeris) is believed by many botanists to be the same species as Mulato, but at a later vegetative stage. The large cactus Pachycereus pecten-aboriginum, known locally as Cawe, has occasionally been used as a narcotic.
What little studies have been carried out on these cacti have revealed the presence of alkaloids most of the other species we have discussed, but no mescaline or macromerine. Many of these alkaloids have some psychopharma- calogical properties, but nothing to compare with those two drugs. Furthermore, the amounts of these alkaloids are usually so small as to be insignificant. For example, the species Obregonia denegrii contains tyramine 0.003 percent, hordenine 0.002 percent, and N-methyltyramin 0.0002 percent. These are all known sympathomimetics, but the percentages are far too minute to have any value. Several publications in recent years have mentioned the sacramental use of these cacti. As a result thousands of people have obtained these plants from cactus dealers and ingested them, usually with disappointing (and sometimes nauseating) results. Sadly many of these cacti are quite rare. If too many people destroy them experimentally, they may become a seriously endangered species. The most suitable cacti for a true psychedelic experience are peyote, which is for the most part illegal, and several species of Trichocereus (such as San Pedro), which are still legal.
SAN PEDRO: This cactus has gained considerable fame in the past five years after numerous reports that it is hallucinogenic, contains mescaline, and is readily available from cactus nurseries. This plant known botanically as Trichocereus pachanoi, is native to the Andes of Peru and Equador. Unlike the small peyote cactus, San Pedro is large and multi-branched. In it's natural enviorment, it often grows to heights of 10 or 15 feet. It's mescaline content is less than that of peyote (0.3 - 1.2 percent), but because of it's great size and rapid growth, it may provide a more economical source of mescaline than peyote. One plant may easily yield several pounds of pure mescaline upon extraction. San Pedro also contains tyramine, hordenine, 3-methoxytyramine, anhalaninine, anhalonidine, 3,4-dimethoxyphen-ethylamine, 3,4-dimethoxy-4-hydroxy-B-phenethylamine, and 3,5-dimethoxy-4-hydroxy-B-phenethylamine. Some of these are known sympathomimetics. Others have no apparent effects when ingested by themselves. It is possible, however, that in combination with the mescaline and other active compounds they may have a synergistic influence upon one another and subtly alter the qualitive aspects of the experience. It is also possible that any compounds in the plant which act a mild MAO inhibitors will render a person vulnerable to some of the above mentioned amines which would ordinarily be metabolized before they could take effect.
The effects of San Pedro are in many ways more pleasant than those of peyote. To begin with, it's taste is only slightly bitter and the initial nausea is not as likely to occur. When the full psychotropic experience takes hold it is less overwhelming, more tranquil and not nearly as physical as that from peyote.
San Pedro may be eaten fresh or dried and taken in any of the manners described for peyote. Cuttings of San Pedro sold in the USA are usually about three feet long by four inches diameter. A piece 4-8 inches long will usually bring about the desired effect. The skin and spines must be removed. The skin should not be thrown away, however. The green tissue close to the skin contains a high concentration of mescaline. Some people chew the skin until all the juices are extracted. If you don't what to do this, the skins can be boiled in water for several hours to make a potent tea. The woody core of the cactus cannot be eaten. One can eat around it like a corn cob. The core does not have much alkaloid content, but can be mashed and boiled as a tea for what little is there.
To dry San Pedro slice the cactus into disks (actually stars) 1/2 inch thick and dry thoroughly in the sun or in an oven at 250 degrees F. The spines must be removed either before drying or before chewing. Also one must be careful of the splinters from the woody core.
If a tea is made from fresh San Pedro, the cactus must be either sliced, chopped or crushed before boiling.
San Pedro is a hardy cactus and endures cold climates quite well. It grows at altiudes from sea level to 9000 feet high in the Andes where it is most frequently found on western slopes. The soil in this region is very rich in humus and various minerals. This helps in the production of mescaline and other alkaloids.
There are several cacti which look much like San Pedro and have even been mistaken for it by trained botanists. In 1960 when Turner and Heyman discovered that San Pedro contained mescaline they erroneously identified the plant as Opunita cylindtica. A few other South American species of Trichocereus also contain mescaline with related alkaloids. These include: T. BRIDGESII, T. MACROGONUS, T.TERSCHECKII, and T. WERDERMANNIANUS.
There is evidence that the ritualistic use of San Pedro dates back to 1000 BC. Even today it is used by Curanderos (medicine men) of northern Peru. They prepare a drink called CIMORA from it and take this in a ceremonial setting to diagnose the spiritual or subconscious basis of a patient's illness.
CULTIVATION OF PSYCHOACTIVE CACTI
Any cactus can be grown from either seed or cutting. Seed grown plants can take many years to develop to a usable size, but should ultimately provide strong, healthy stock from which cuttings may be taken. Plants have to grow through the lengthy seedling stage. A San Pedro plant started from seed may be no more than 1/2 inch high after it's first year and perhaps an inch high after it's second; It's diameter being 1/8-1/4 during this time. A cutting of San Pedro may be 2 feet high by 4 inches diameter when planted. After 6 months it might easily gain 4-6 inches in height, send forth one or two branches 6-8 inches long by 2 inches diameter, and have sprouted several branch buds which will do the same within the next six months. When these offshoots are 6 inches or more long they may be broken off and planted following the instructions below. Or they may be allowed another 6 months growth until they deepen from pale to dark-green to give them time to accumulate alkaloids and then consumed.
Live plants of any of the species mentioned in this guide - with the excep- tion perhaps of peyote - can be purchased from suppliers named at the end of this chapter. Freshly harvested peyote cuttings are frequently available on the underground market for 50 cents to one dollar per button. When selecting peyote cuttings for planting choose ones which are firm and unbruised with at least 1/2 inch of taproot below the top. If the bottom of the taproot is still delicate where it has been cut, the button should be placed bottoms up in partial shade for a day or two until the severed area has a dry corky texture. If this is not done, the plant will be prone to rot.
The best soil mix can be prepared from 3 parts coarse sand, 1 part loam and 1 part leaf mold. Bake this mixture in an oven at 400 degrees F for an hour to kill fungus, bacteria, weed seeds and insect eggs. After the soil mix has cooled it is ready to use. The taproot of the plant may be dipped in a rooting mixture, such as ROOTONE, before planting. This enhances root development and hinders decay. Place the bottom just deep enough so that the soil does not quite touch the green part of the plant. The soil should be kept slightly moist and evenly so. If you are planting a tall cactus like San Pedro, the cutting should be placed deeply enough in the soil that it will have sufficient support to stand. San Pedro type cacti can also be laid upon the ground and will send down roots from their sides while the buds grow upwards. San Pedro can grow well in almost any soil as long as there is decent drainage.
Cacti tend to grow mostly during spring and autumn, to send down roots in the summer, and to rest through winter. Although cactus cuttings may be planted anytime of the year they stand the best chance if planted in the late spring. They should be watered thoroughly once or twice a week depending upon how rapidly moisture is lost. The soil an inch below the surface should always contain some moisture. Watering can be cut back to less than half during the winter.
INCREASING THE POTENCY OF PSYCHOACTIVE CACTI
There are several factors which influence production of mescaline and related alkaloids in cacti. Presence of a wide variety of trace minerals is import- ant. Occasional watering with Hoagland A-Z trace mineral concentrate provides these minerals. Combine 1 part concentrate with 9 parts water and water cacti with this once every two months.
Experiments conducted by Rosenberg, Mclaughlin and Paul at the University of of Michigan, Ann Arbor in 1966 demonstrated that dopamine is a precursor of mescaline in the peyote cactus. Tyramine and dopa were also found to be mescaline precursors, but not as immediate and efficient as dopamine. It appears that in the plant tyosine breaks down to become tyramine and dopa. These then recombine to form dopamine which is converted to nor-mescaline and finally to mescaline. One can take advantage to this sequence by inject-ing each peyote plant with dopamine 4 weeks prior to harvesting. Much of the dopamine will convert to mescaline during this time, giving a considerable increase in the alkaloid of the plant. Prepare a saturated solution of free base dopamine in a .05 N solution of hydrochloric acid and inject 1-2 cc into the root of each plant and the same amount into the green portion above the root. Let the needle penetrate to the center of the plant, inject slowly and allow the needle to remain in place a few seconds after injection. It is best to deprive the plant of water for 1-2 weeks before injection. This makes the plant tissues take up the injection fluids more readily. If dopamine is not available, a mixture of tyramine and dopa can be used instead 6 weeks before harvesting for comparable results. San Pedro and other mescaline-bearing cacti can be similarly treated for increased mescaline production. Inject at the base of the plant and again every 3-4 inches following a spiral pattern up the length of the plant. A series of booster injections can be given to any of these cacti every 6-8 weeks and once again 4 weeks before harvesting for greater mescaline accumulation.
It is also possible to increase the macromerine and nor-macromerine content of Doñana cacti using tyramine or DL-norepinephrine as precursors. Injections should be given 20-25 days before harvesting. Series of injections can be given 45 days apart for higher alkaloid accumulation.
EXTRACTING PURE MESCALINE FROM PEYOTE OR SAN PEDRO CACTUS
The isolation of mescaline from cacti containing this alkaloid is not difficult to perform and is perhaps one of the most rewarding alchemical processes that one can attempt. The chemicals required for this process are readily available and their purchase arouses no suspicion or interest on the part of Government agencies. The equipment employed is not expensive or particularly complicated or can be constructed very easily from ordinary household items. The entire process can be carried out in any kitchen in the matter of hours by following the instructions below and in the final stages one can verify the success of the procedure by actually watching the crystals of mescaline precipitate in the solution. One kilo (2.2 lbs) of dried peyote buttons may yield between 10 and 60 grams of pure white needle crystals of mescaline depending on the potency of the plants used. On average the yield is about 20 grams. The usual underground price of a kilo of dried peyote ranges between $125 and$250 (25 to 50 cents per button). From indians in the southwestern USA the price is closer to $50 (10 cents per button). The street price for a gram of pure mescaline is$20 to $30 - if one is lucky enough to find it. One can obtain from a kilo of dried peyote$200 to $1200 worth of mescaline. If San Pedro is employed on may anticipate a yield of 3 to 12 grams of mescaline per kilo of dried cactus. One can legally purchase a kilo of dried San Pedro for$5 to $10 and from it extract$60 to $250 worth of pure mescaline. Grind a kilo of the dried cactus, place this in a large pressure cooker, cover with distilled water, and boil for 30 minutes. Strain the liquids and save them. Return the pulp to the pot, add more water and boil again for 30 minutes. Strain the liquids and combine them with the first strainings. Repeat this process about five times or until the pulp no longer has a bitter taste. Discard the pulp and reduce the volume of the combined strainings by boiling in an open pot. Do not use aluminum ware. When the liquids have been concentrated to the thickness of cream (about one quart), stop the boiling and stir in 400 grams of sodium hydroxide (lye). This makes the mescaline more soluble in benzene and less in water. If a large separatory funnel is available pour the liquids into it and add 1600 ml of benzene. Shake the funnel well for five minutes and let it stand for two hours. If a separatory funnel is not available the process can be carried out in a one gallon jug with a siphon attached. After standing for 2 hours the water layer will settle to the bottom and the benzene layer will float to the top. Between the two layers will be a thin emulsion layer of mixed water and benzene. Drain off the water and emulsion layers if you are using a separatory funnel or siphon off the benzene layer if you are using the makeshift jug-siphon apparatus. Be certain that neither the water or emulsion layers get into the benzene layer when separating. If any of these layers do get into the benzene during separation pour everything back into the separator, let it stand and repeat the separation more carefully. It is better to leave some benzene layer in the water and emulsion than to get emulsion and water into the benzene. Nothing will be wasted. All of the benzene which contains the mescaline will eventually be salvaged. Sometimes the layers will fail to separate properly. If this is the case immerse the funnel or jug in a deep pot of hot water for two hours. This will break up the emulsion and bring about the separation. Prepare a solution of 2 parts sulfuric acid and one part water. (never add water to the acid or it will splatter; add the acid a little at a time to the water by pouring it down the inside of the graduate or measuring cup containing the water.) Add 25 drops of the acid solution one drop at a time to the benzene extracts. Stopper the jug and shake well for one minute. Then let stand for five minutes. White streaks of mescaline sulfates should begin to appear in the benzene. If these do not appear, shake the jug more vigorously for two to three minutes and let it settle for five more minutes. I have found that when extracting mescaline from San Pedro it is sometimes necessary to shake the mixture more thoroughly and for a longer time to get the mescaline streaks to form. This is probably because of the lower mescaline content in the plant. This would also apply to any peyote that does not have a high mescaline content. After the streaks appear add 25 more drops of the acid solution in the same manner, shake as before and let settle for ten minutes. More streaks will appear. Add 15 drops of acid, shake and wait 15 minutes for streaks to form. Add 10 drops, shake and wait about 30 minutes. Test the solution with wide range pH paper. It should show that the solution is between pH 7.5 and 8. Allow the mescaline sulfate crystals to completely precipitate. Siphon off as much of the benzene as possible without disturbing the crystals on the bottom of the jug. The next steps are to salvage any mescaline still in the water and emulsion layer. Combine the benzene siphonings with the water/emulsion layer, shake these well together for 5 minutes and let settle for two hours as before. Carefully remove the benzene layer, treat it again with acid, precipitate the crystals and siphon off the benzene as in the previous steps. Recombine the siphoned benzene with the watery layer and repeat this again and again until no more crystals precipitate. Siphon off as much benzene as possible without drawing crystals through the siphon. The next step involves removing the remaining benzene from the crystals. There are two methods to choose from. The first is the quickest, but requires ether, which is dangerous and often difficult to procure. Shake up the crystals with the remaining benzene and pour it into a funnel with filter paper. After the benzene has passed through the filter rinse the empty jug with 100 ml of ether to salvage any crystals in the jug and pour the ether over the crystals in the filter. After the ether has passed through the filter repeat the rinsing with another 100 ml of ether. Then let the crystals dry. If ether is not available or you do not wish to use such a highly combustible substance, the precipitate and residual benzene can be poured into a beaker. The jug should be rinsed several more times with a little benzene and added to the beaker so no crystals are left behind. The beaker is then placed in a heat bath until all of the benzene has been evaporated. The next step is to purify the mescaline sulfate crystals. Dissolve the dry crystals in 200 ml of near-boiling distilled water. Add a pinch of activated charcoal (Norite) and filter while still hot through number 2 filter paper. The hot water which contains the mescaline will pass through the filter. The Norite absorbes impurities from the mescaline. After the liquids have passed through the filter pour a little more hot water over the filter to rinse through any remaining mescaline which may have impregnated the filter paper. Add 10 percent ammonia solution a few drops at a time to the hot filtrates until the solution registers between pH 6.5 and 7. Place a boiling stone in the solution and reduce it's volume to 75 ml by boiling. Remove the boiling stone and allow the solution to cool to room temperature. Place the solution in a freezer or in a refrigerator set to the coldest possible temperature and allow the solution to cool to almost freezing. Tiny white needle-like crystals form around the bottom and sides of the beaker. Break up the crystals with a glass stirring rod while the solution is still ice cold and pour through a filter. Mescaline sulfate is insoluable in near freezing water and will not pass through the filter. Rinse the beaker with fresh ice water and pour this over the filter. The crystals will now be pure white and can be dried under a heat lamp or in an over at 250 degrees F. More mescaline can be salvaged from the water that has passed through the filter by boiling these liquids down to about 20 ml, adding Norite while hot, filtering through number 2 paper as before, chilling the filterate to near freezing as once before, filtering while cold, rinsing with ice water and drying the crystals. This repetition should obtain at least two more grams of mescaline sulfate. If large volume mescaline extraction is being conducted it would be worthwhile to repeat this salvaging procedure several more times. MIXED ALKALOID EXTRACTIONS There are numerous methods for extracting a mixture of the alkaloids from cacti. Different methods may result in varying degrees of purity. For example, the dried, pulverized material can be defatted with petroleum ether or lighter fluid prior to extraction to remove lipid content; solvent combinations such as methanol/chloroform/ammonium hydroxide can be used for extracting; The extractions can be made acidic (pH 9.5) with 1-N hydrochloric acid, filtered and washed in a separatory funnel or improvised siphon-jug apparatus with diethyl ether, neutralized with ammonium hydroxide and evaporated to dryness. However, most of these solvents are difficult for the non-professional to obtain. Perhaps it is just as well since many of these solvents are either toxic or explosive if handled improperly. Also, we do not always know precisely what we are trying to extract. Some of the active principles may be non-alkaloidal. Too much purification might remove some of the active substances. The approach given here employs materials which may be purchased inexpensively at any supermarket and are safe to work with. This procedure extracts all of the alcohol and water-soluable alkaloids and non-alkaloidal materials and permits only the fibrous pulp to be discarded. Pulverize the dried cactus (tufts and spines need not be removed). Prepare a mixture of two parts isopropyl rubbing alcohol and one part clear, non-sudsing, unscented and untinted ammonia. Make the pulverized material soggy with this mixture and allow it to stand covered overnight. Do not use aluminum or iron wares during any of these steps. After soaking, cover the mash with isopropyl alcohol and boil in a heat bath for six hours. Strain the liquids through muslin and press as much liquid as possible from the pulp. With fresh alcohol repeat the boiling and straining three more times. Combine the strained liquids. Evaporate this in a heat bath until only a tar remains. (When evaporating a solvent use and electric range or hot plate rather than a gas stove. Have adequate ventilation and avoid breathing the fumes.) The tar can be further dried by spreading it thinly on a baking tray and placing it in an oven set at the lowest possible heat. Remove the tray once every fifteen minutes to examine the material. When it appears to be almost dry place it back in the oven, shut the heat off, and let it stay there until the oven cools. DICTIONARY OF CACTUS ALKALOIDS Anhalidine: Tetrahydroisoquinoline alkaloid (2-methyl-6,7-dimeethoxy-8-hydroxy-1,2,3,4,-tetrahydroisoquinoline) Found in Lophophora and Pelecyphora. B-O-methylsynephrine: Phenolic B-phenethylamine found in citrus trees and some cacti. No data on pharmacology, but similar compound B-O-methylepin-ephrine produces considerable CNS stimulation. 3-dimethyltrichocereine: B-phenethylamine alkaloid (N,N-dimethyl-3-hydroxy-4,5-dimethoxy-B-phenethylamine). Found in Pelecyphora and some Trichocereus species. Dolichotheline: Imidazole alkaloid properly known as N-isovalerylhistamine or 4(5)-[2-N-isovalerylaminoethyl]imidazole. Found only in Dolichothele and Gymnocactus species. Pharmacological action still unknown. Homoveratrilamine: a dimethoxy form of the mescaline molecule (3,4-dimethoxy-B-phenethylamine). It has no activity by itself, but may alter the mescaline experience slightly when taken in combination. It is found in San Pedro cactus and in the urine of certain types of schizophrenics. Hordenine: Phenolic B-phenethylamine found in barley roots and several cacti. Also known as anhaline (N,N-dimethyltyramine). Has mild sympatho-mimetic activity and antiseptic action. Macromerine: Nonphenolic B-phenethylamine (N,N-dimethyl-3,4-dimethoxy-B-hydroxy-B-phenethylamine. Found only in Coryphantha species. Reputed to possess 1/5 the potency of mescaline. Mescaline: Nonphenolic B-phenethylamine (3,4,5-trimethoxy-B-phenethylamine). Main psychoactive component of Peyote, San Pedro, and several other Trichocereus species. Also found in traces in Pelecyphorea. Metanephrine: Weak sympathomimetic found in Coryphantha species. 3-methoxytyramine: Pheneolic B-Phenethylamine found in the plant kingdom for the first time in San Pedro cacti. Also found in the urine of persons with certain types of brain disorders and cancer of the nervous system. N-methyl-3,4-dimethoxy-B-Phenethylamine: Found in Pelecyphora aselliformis, Coryphantha runyonii and Ariocarpus species, but not in peyote. Has slight activity in depletion of cardiac norepinephrine. N-methylphenethylamine: Nonphenolic B-phenethylamine alkaloid recently found in the Dolichothele species. Also found in Acacia species and other plants. Goats and sheeps in Texas sometimes eat Acacia berlandia and suffer a condition known as limberleg or Guajillo wobbles. Pressor action of this alkaloid has been shown experimentally to occur with low toxicity. Phenealanine and methionine are it's biosynthetic precursors. N-methyltyramine: Phenolic B-phenethylamine found in some cacti, mutated barley roots and a few other plants. Probably an intermediate phytochemical step in the methylation of tyramine to form candicine. Has mild sympathomimetic action and probable antibacterial properties. Normacromerine: Nonphenolic B-phenethylamine (N-dimethyl-3,4-dimethoxy-B-hydroxy-B-phenethylamine) found in Coryphantha species. Shows less effect on rats than macromerine. Pellotine: Tetrahydroisoquinoline alkaloid (1,2-dimethyl-6,7-dimethoxy-8- hydroxy-1,2,3,4-tetrahydroisoquinoline) found in Lophophora and pelecyphora. Synephrine: Phenolic B-phenethylamine (N-methyl-4-hydroxy-B-phenethylamine) found in citrus plants, some cacti, and human urine. Well known sympathomimetic agent. Probably an intermediary in phytosynthesis of macromerine. Tyramine: Phenolic B-phenethylamine found in several cacti. Mild sympathomimetic with some possible antiseptic activity. http://www.lycaeum.org//~sputnik/Mescaline/CactusGuide.html #### Marijuana stops child's severe seizures Posted on September 23, 2015 at 1:50 PM comments (0) By most standards Matt and Paige Figi were living the American dream. They met at Colorado State University, where they shared a love of the outdoors. After getting married, the couple bought a house and planned to travel the world. They did travel, but their plans changed when their first child was born in 2004. Max was 2 when they decided to have another child. The couple got the surprise of their lives when an ultrasound revealed not one but two babies. Charlotte and Chase were born October 18, 2006. "They were born at 40 weeks. ... Charlotte weighed 7 pounds, 12 ounces," Paige said. "They were healthy. Everything was normal." Seizures and hospital stays begin The twins were 3 months old when the Figis' lives changed forever. Charlotte had just had a bath, and Matt was putting on her diaper. "She was laying on her back on the floor," he said, "and her eyes just started flickering." The seizure lasted about 30 minutes. Her parents rushed her to the hospital. "They weren't calling it epilepsy," Paige said. "We just thought it was one random seizure. They did a million-dollar work-up -- the MRI, EEG, spinal tap -- they did the whole work-up and found nothing. And sent us home." Medical facts of marijuana Medical facts of marijuana 01:23 Kennedy: I was wrong on medical pot Kennedy: I was wrong on medical pot 02:07 Colorado's new frontier: Marijuana Colorado's new frontier: Marijuana 04:25 WEED: A Dr. Sanjay Gupta Special WEED: A Dr. Sanjay Gupta Special 00:30 A week later, Charlotte had another seizure. This one was longer, and it was only the beginning. Over the next few months, Charlotte -- affectionately called Charlie -- had frequent seizures lasting two to four hours, and she was hospitalized repeatedly. Doctors were stumped. Her blood tests were normal. Her scans were all normal. "They said it's probably going to go away," Paige recalled. "It is unusual in that it's so severe, but it's probably something she'll grow out of." But she didn't grow out of it. The seizures continued. The hospital stays got longer. One of the doctors treating Charlotte thought there were three possible diagnoses. The worse-case scenario? Dravet Syndrome, also known as myoclonic epilepsy of infancy or SMEI. Dravet Syndrome is a rare, severe form of intractable epilepsy. Intractable means the seizures are not controlled by medication. The first seizures with Dravet Syndrome usually start before the age of 1. In the second year, other seizures take hold: myoclonus, or involuntary, muscle spasms and status epilepticus, seizures that last more than 30 minutes or come in clusters, one after the other. At that time, the Figis said, Charlotte was still developing normally, talking and walking the same day as her twin. But the seizures continued to get worse. The medications were also taking a toll. She was on seven drugs -- some of them heavy-duty, addictive ones such as barbiturates and benzodiazepines. They'd work for a while, but the seizures always came back with a vengeance. "At 2, she really started to decline cognitively," Paige said. "Whether it was the medicines or the seizures, it was happening, it was obvious. And she was slipping away." When Charlotte was 2½, the Figis decided to take her to Children's Hospital Colorado. A neurologist tested her for the SCN1A gene mutation, which is common in 80% of Dravet Syndrome cases. After two months, the test came back positive. "I remember to this day it was a relief," Paige said. "Even though it was the worst-case scenario, I felt relief just to know." Matt, a Green Beret, decided to leave the military. "Every mission, every training I was going to do I was called home because she was in the pediatric ICU again or in the hospital again." They were quickly running out of options. They considered a drug from France. Doctors suggested an experimental anti-seizure drug being used on dogs. Paige took her daughter to Chicago to see a Dravet specialist, who put the child on a ketogenic diet frequently used to treat epilepsy that's high in fat and low in carbohydrates. The special diet forces the body to make extra ketones, natural chemicals that suppress seizures. It's mainly recommended for epileptic patients who don't respond to treatment. The diet helped control Charlotte's seizures but had a lot of side effects. She suffered from bone loss. Her immune system plummeted. And new behavioral problems started popping up. "At one point she was outside eating pine cones and stuff, all kinds of different things," Matt said. "As a parent you have to say, let's take a step back and look at this. Is this truly beneficial treatment because of these other things?" Two years into the diet, the seizures came back. The end of the rope In November 2000, Colorado voters approved Amendment 20, which required the state to set up a medical marijuana registry program. Pot activists divided over new cannabis club There are eight medical conditions for which patients can use cannabis -- cancer, glaucoma, HIV/AIDS, muscle spasms, seizures, severe pain, severe nausea and cachexia or dramatic weight loss and muscle atrophy. The average patient in the program is 42 years old. There are 39 patients under the age of 18. Paige had consistently voted against marijuana use. That was before Dravet Syndrome entered their lives. Matt, now a military contractor spending six months a year overseas, used his spare time scouring the Internet looking for anything that would help his little girl. He found a video online of a California boy whose Dravet was being successfully treated with cannabis. The strain was low in tetrahydrocannabinol, or THC, the compound in marijuana that's psychoactive. It was also high in cannabidiol, or CBD, which has medicinal properties but no psychoactivity. Scientists think the CBD quiets the excessive electrical and chemical activity in the brain that causes seizures. It had worked in this boy; his parents saw a major reduction in the boy's seizures. By then Charlotte had lost the ability to walk, talk and eat. She was having 300 grand mal seizures a week. Her heart had stopped a number of times. When it happened at home, Paige did cardiopulmonary resuscitation until an ambulance arrived. When it happened in the hospital, where they'd already signed a do-not-resuscitate order, they said their goodbyes. Doctors had even suggested putting Charlotte in a medically induced coma to give her small, battered body a rest. She was 5 when the Figis learned there was nothing more the hospital could do. That's when Paige decided to try medical marijuana. But finding two doctors to sign off on a medical marijuana card for Charlotte was no easy feat. She was the youngest patient in the state ever to apply. Scientists don't fully understand the long-term effects early marijuana use may have on children. Studies that show negative effects, such as diminished lung function or increased risk of a heart attack, are primarily done on adult marijuana smokers. But Charlotte wouldn't be smoking the stuff. Childhood is also a delicate time in brain development. Preliminary research shows that early onset marijuana smokers are slower at tasks, have lower IQs later in life, have a higher risk of stroke and increased incidence of psychotic disorders, leaving some scientists concerned. Is medical marijuana safe for children? "Everyone said no, no, no, no, no, and I kept calling and calling," Paige said. She finally reached Dr. Margaret Gedde, who agree to meet with the family. "(Charlotte's) been close to death so many times, she's had so much brain damage from seizure activity and likely the pharmaceutical medication," Gedde said. "When you put the potential risks of the cannabis in context like that, it's a very easy decision." The second doctor to sign on was Alan Shackelford, a Harvard-trained physician who had a number of medical marijuana patients in his care. He wasn't familiar with Dravet and because of Charlotte's age had serious reservations. "(But) they had exhausted all of her treatment options," Shackelford said. "There really weren't any steps they could take beyond what they had done. Everything had been tried -- except cannabis." Paige found a Denver dispensary that had a small amount of a type of marijuana called R4, said to be low in THC and high in CBD. She paid about$800 for 2 ounces -- all that was available -- and had a friend extract the oil.
She had the oil tested at a lab and started Charlotte out on a small dose.
"We were pioneering the whole thing; we were guinea pigging Charlotte," Paige said. "This is a federally illegal substance. I was terrified to be honest with you."
But the results were stunning.
"When she didn't have those three, four seizures that first hour, that was the first sign," Paige recalled. "And I thought well, 'Let's go another hour, this has got to be a fluke.' "
The seizures stopped for another hour. And for the following seven days.
Paige said she couldn't believe it. Neither could Matt. But their supply was running out.
Charlotte's Web
Paige soon heard about the Stanley brothers, one of the state's largest marijuana growers and dispensary owners. These six brothers were crossbreeding a strain of marijuana also high in CBD and low in THC, but they didn't know what to do with it. No one wanted it; they couldn't sell it.
Still, even they had reservations when they heard about Charlotte's age. But once they met her, they were on board.
"The biggest misconception about treating a child like little Charlotte is most people think that we're getting her high, most people think she's getting stoned," Josh Stanley said, stressing his plant's low THC levels. "Charlotte is the most precious little girl in the world to me. I will do anything for her."
The brothers started the Realm of Caring Foundation, a nonprofit organization that provides cannabis to adults and children suffering from a host of diseases, including epilepsy, cancer, multiple sclerosis and Parkinson's, who cannot afford this treatment.
People have called them the Robin Hoods of marijuana. Josh Stanley said it's their calling. They use the money they make from medical marijuana patients and get donations from sponsors who believe in their cause. They only ask patients such as the Figis to donate what they can.
"We give (cannabis) away for next to free," Stanley said. "The state won't allow us to actually give it away, so we give it away for pennies really."
Charlotte gets a dose of the cannabis oil twice a day in her food.
Gedde found three to four milligrams of oil per pound of the girl's body weight stopped the seizures.
Today, Charlotte, 6, is thriving. Her seizures only happen two to three times per month, almost solely in her sleep. Not only is she walking, she can ride her bicycle. She feeds herself and is talking more and more each day.
"I literally see Charlotte's brain making connections that haven't been made in years," Matt said. "My thought now is, why were we the ones that had to go out and find this cure? This natural cure? How come a doctor didn't know about this? How come they didn't make me aware of this?"
The marijuana strain Charlotte and now 41 other patients use to ease painful symptoms of diseases such as epilepsy and cancer has been named after the little girl who is getting her life back one day at a time.
It's called Charlotte's Web.
"I didn't hear her laugh for six months," Paige said. "I didn't hear her voice at all, just her crying. I can't imagine that I would be watching her making these gains that she's making, doing the things that she's doing (without the medical marijuana). I don't take it for granted. Every day is a blessing."
Matt added, "I want to scream it from the rooftops. I want other people, other parents, to know that this is a viable option."
Readers debate future of pot laws
http://www.cnn.com/2013/08/07/health/charlotte-child-medical-marijuana/
#### Resource: Spiritual & Ritual Use of Psychoactives
Posted on September 23, 2015 at 1:45 PM comments (0)
Spiritual & Ritual
Use of Psychoactives
GENERAL INFORMATION #
Modern Entheogen Ethics
Journal Articles on the Spiritual Use of Entheogens
Books on the Spiritual Use of Entheogens
Xochipilli, the Aztec Prince of Flowers
RELATED VAULTS #
Religious Freedom
Ethnobotany & Ethnopharmacology Vault
Medicinal Use of Psychoactives
Recreational Use of Psychoactives
Entheogen Vaults
ARTICLES & WRITINGS #
The Psychedelics and Religion, by Walter Houston Clark
Notes on the Present Status of Ololiuhqui and other Hallucinogens of Mexico - R. Gordon Wasson, 1968
Wasson's Alternative Candidates for Soma, by Thomas J Riedlinger
RESEARCH & JOURNAL ARTICLES #
Related Journal References
Do Drugs have Religious Import?, by Huston Smith
The Psychedelic Mystical Experience in the Human Encounter With Death, by Walter Pahnke
Drugs and Mysticism, by Walter Pahnke
Psychedelics and Religious Experience, by Alan Watts
MEDIA COVERAGE #
Seeking Higher Ground- San Jose Mercury News, Jan 31, 1998
AYAHUASCA #
The Use of Psychoactive Plants Among the Hupda-Maku
The Sound of Rushing Water, by Michael J. Harner
Ayahuasca Healing Sessions, by Marlene Dobkin de Rios
Ayahuasca and its Mechanism of Healing, by Marlene Dobkin de Rios
Santo Daime Ceremony recording (RealAudio)
CANNABIS #
Basic Rastafarian Info
Excerpts from The Rastafarian
Ethiopian Zion Coptic Church - 60 Minutes 1979
Ethiopian Zion Coptic Church - Miami Herald
The Hachish-Vice in the Old Testament
Marijuana and the Bible
Resurrection of the Higher Self, by Matthew Webb
DMT #
DMT Snuffs - Cohoba, Yopo and Vilva, by Jonathon Ott
MUSHROOMS #
Little Flowers of the Gods, by Shultes and Hofmann
PEYOTE & CACTI #
Shamanism and Peyote Use Among the Apaches, from Hallucinogens and Shamanism
A Psychedelic Catalyst for Healing
SALVIA DIVINORUM #
A New Mexican Psychotropic Drug from the Mint Family, by R. Gordon Wasson
Ethnopharmacology of Ska Maria Pastora, by Valdes, Diaz and Paul
OFF-SITE RESOURCES
PRIMARY RESOURCES #
Council on Spiritual Practices - Entheogens
The Spiritual Use of Psychoactives
New World Entheogens
What is Soma?
Lila.info : Transpersonal Explorations of Shamanic Ritual
AYAHUASCA - União do Vegetal #
União do Vegetal Home Page
União do Vegetal - Nicholas Saunders
AYAHUASCA - Santo Daime #
Santo Daime - The Brazilian Rainforest's Spiritual Path
The Use of Ayahuasca by the Santo Daime Religion
A Description of a Santo Daime Service
A Personal Experience at a Daime Service
Santo Daime - Nicholas Saunders
MUSHROOMS #
Traditional use of psychoactive mushrooms in Ivory Coast? , by Georgio Samorini
Mushrooms and Magic: The Mycotheology Homepage
PEYOTE & CACTI #
Peyote Way Church of God
#### Resource: Cocaine History and Harmful Chemical Additives
Posted on September 23, 2015 at 1:40 PM comments (0)
Levamisole Update: Jan 2014: Researchers show that in invertebrates levamisole appears to synergize with cocaine, increasing effects. This could provide an explanation for why so much of the cocaine is contaminated with levamisole.
Warning: Since 2009, cocaine cut with levamisole (a veterinary and human dewormer) has been increasingly reported and has resulted in numerous hospitalizations and a few deaths across the United States. The DEA reports that as much as 1/3 of all cocaine in the U.S. is tainted.
GENERAL INFORMATION #
Cocaine & Drug Tests
Basic Crack / Freebase Info
Amphetamines, Cocaine, A New Link
Some Random Cocaine Info
Cocaine Bits & Pieces
Cocaine Use Statistics
Cocaine and Drug Tests
RELATED VAULTS #
Coca Vault
HISTORY #
Cocaine Timeline
LAW #
U.S. v Armstrong (sentencing disparity)
FIELD TESTING KITS #
Test Clear : Field Drug ID Kits
ASK EROWID ANSWERS #
How long after use can Cocaine be detected by a urine tes...
Will rats really keep taking cocaine til they die?
What is the blue-color change test used to detect cocaine ...
Could cocaine be used to stabilize a difficult LSD experie...
What is the LD-50 of cocaine?
» » » MORE » » »
ARTICLES & WRITINGS #
Cocaine Adulterated with Levamisole on the Rise: Status in Sep 2009, by Erowid Crew
Rats Prefer Sweetened Water to Cocaine, by Erowid
Cocaine Tainted Cash Faulted as Evidence, 1993
You're Carrying Cocaine in your Wallet
For Those About to Rock, by Rem
Woe to you my Princess, when I come, I will kiss you quite red
and feed you till you are plump. And if you are froward, you
shall see who is the stronger, a gentle little girl who doesn't
eat enough or a big wild man who has cocaine in his body."
-- Sigmund Freud, Cocaine Papers
RESEARCH & JOURNAL ARTICLES #
Related Journal References
Levamisole as a contaminant of illicit Cocaine, 2008
Cocaine on cash not proof of drug dealing, courts rule, 1993
Courts reject drug-tainted evidence, 1993
Cocaine pharmacokinetics in humans, 1981
» » » MORE » » »
CRACK BABIES #
Abstracts on Crack Babies
Fetal 'Crack' Exposure Effects Questioned - Reuters
"Crack Babies" Not Doomed
Prenatal Cocaine: Effects on the Fetus
'Crack Babies' Catch Up - Associated Press, Dec 1992
Placenta Barrier to Cocaine
Crack Baby References
MEDIA COVERAGE #
Index of Cocaine Related Media Articles
Acupuncture effective treatment for cocaine addiction - AP, August 2000
Behind Cocaine's Durability: Low Costs and High Profits - NY Times, Mar 1997
Immunotherapy for Cocaine Addiction - Scientific American, Feb 1997
Proof of Brain Damage Caused by Cocaine (EEG Studies) - Newswire, Oct 1996
Tougher crack laws aren't working - Mpls Star Tribune, 11/20/96
Cocaine-Tainted Cash Faulted as Evidence - Wall Street Journal
EXPERIENCES #
Riding that train, by Murple
Stayed with Me After the High, by 10psi-boost
Confessions of a Cocaine Connoisseur, by Mojo
Bam Bam Yowch, by Mr. Badger
Control, by N
» » » MORE » » »
BOOKS #
A Brief History of Cocaine, by Steven B. Karch
The Encyclopedia of Psychoactive Drugs: Cocaine, by C. Johanson
Cocaine, by L. Grinspoon and J. Bakalar
Cocaine Papers, by Sigmund Freud
The Pleasures of Cocaine, by Adam Gottlieb
» » » MORE » » »
OFF-SITE RESOURCES
PRIMARY RESOURCES #
Paranoia : Cocaine
Lycaeum : Cocaine
SECONDARY RESOURCES #
Schaffer Library of Drug Policy : Cocaine
Drug Library : Cocaine Info
Cocaine Story in Colombia
HedWeb : Cocaine
StreetDrugs.org : Crack Cocaine
The Haight-Ashbury Cocaine Film
LAW #
Federal Sentencing Guidelines
Families Against Mandatory Minimums
The History of Legislative Control over Opium, Cocaine, and their Derivatives
November Coalition: Crack vs. Cocaine
ARTICLES & WRITINGS #
Craving Cocaddiction or Craven Cocabhorrence (2001)
Consumer Union Report on Cocaine
On Cocaine, by Sigmund Freud
RESEARCH & JOURNAL ARTICLES #
Birth of a Cocaine Factoid (2009)
Effects of Crack smoking on the lungs (Abstracts)
The Pharmacology of Cocaine Smoking in Humans
Urban Legends : Cocaine Tainted Money
GOVERNMENT RESOURCES #
Cocaine: Wholesale, Purity and Street Prices
World Health Organization Global Cocaine Project Report - 1995
MEDIA COVERAGE #
How the Myth of the 'Negro Cocaine Fiendâ' Helped Shape American Drug Policy - The Nation.com, Jan 29 2014
"Drugs Aren’t the Problem": Neuroscientist Carl Hart on Brain Science & Myths About Addiction - DemocracyNow, Jan 6 2014
Will a Cocaine Vaccine Keep Addicts from Using? - The Fix , Jan 3 2014
Can a drug cure an addict? - thestar.com, Dec 22 2007
Houston scientists see hope in cocaine vaccine - Houston Chronicle, Jan 1 2008
Supreme Court upholds sentencing discretion in crack case - NYT, Dec 10 2007
New Mint Resembles Cocaine Bags, Police Say - MSNBC, Dec 2 2007
'Gene cause' of cocaine addiction - BBCNews, Mar 13 2006
Rivers of Coke - WIREDNews, Aug 2005
Warning on Atropine-laced Cocaine - Expatica Netherlands, Dec 2004
MAPInc : Cocaine News
CRACK BABIES #
'Crack baby' study ends with unexpected but clear result - July 22 2013, Philly.com
PACO #
Lost in an Abyss of Drugs, and Entangled by Poverty - NYTimes July 29, 2009
Paco: Drug Epidemic Sweeping the Streets of Argentina - The ArgenTimes, Nov 2008
PREGNANCY #
Prenatal cocaine's lasting cellular effects - (Press Zoom), Jan 15, 2007
In Utero Exposure to Cocaine : A Review
Women & Pregnancy (primarily cocaine-related)
ADDICTION & TREATMENT #
Addiction injection: the mission to immunise drug users against dependency, Wired, Mar 29 2013
Ethical Issues in Using a Cocaine Vaccine (Abstract)
Gamma vinyl-GABA (GVG) May Reduce Cocaine Cravings, 2003
"No" in a Needle : Cocaine Vaccine, 2003
N-Acetyl Cysteine May Reduce Cocaine Cravings?, 2002
Identifying Compounds to Treat Cocaine Addiction, 1996
Cocaine Anonymous
MDMA to Break Addiction
PROHIBITION SITES #
Teen Challenge : Cocaine
DEA : Cocaine
Partnership for a Drug Free America : Cocaine
National Families in Action : Cocaine
CHEMISTRY & PHARMACOLOGY #
Hyperreal on Synthesis
CONTAMINANTS & ADULTERANTS #
Skin, Vessel Damage Seen with Tainted Cocaine - Mar 6, 2013, MedPageToday
How to make your very own Levamisole test kits! - Levamicoke (blog), Nov 19 2010
The Mystery of the Tainted Cocaine - The Stranger, Aug 17 - Nov 9 2010
Agranulocytosis Associated with Cocaine Use --- Four States, March 2008--November 2009 - CDC.gov
New York Health Advisory on Contaminated Cocaine - New York Oasis, Feb 2009
Levamisole: An unusual finding in a cocaine related fatality - LA Coroner, Dec 2005
#### Resources: Ayahuasca
Posted on September 23, 2015 at 1:30 PM comments (0)
July 2010 - UDV reaches an agreement with the DEA allowing their churches to import (and use) DMT-containing ayahuasca tea into the United States. See Agreement on Procedures for Handling UDV Sacrament.
GENERAL INFORMATION #
Ayahuasca Names & Terminology
Psychedelic Shamanism: Ayahuasca Description
DMT Freebase Content in Huasca Preparations, Clearlight (2003)
Tryptamine Carriers (1994)
NATURAL SOURCES #
Banisteriopsis caapi - most common
Psychotria viridis - most common
Anadenanathera spp.
Brugmansia spp.
Datura spp.
Mimosa hostilis
Virola spp.
RELATED VAULTS #
DMT Vault
Monoamine Oxidase Inhibitors Vault
5-MeO-DMT Vault
Harmala Vault
Shamanism Vault
HEALTH #
Ayahuasca Fatalities
HISTORY #
Ayahuasca Timeline
TRADITIONAL USE #
The Use of Psychoactive Plants Among the Hupda-Maku
The Sound of Rushing Water, by Michael J. Harner
Ayahuasca Healing Session, by Marlene Dobkin de Rios
Ayahuasca and its Mechanism of Healing, by Marlene Dobkin de Rios
Floral Baths, by Ross Heaven and Artidoro
RITUAL & SPIRITUAL USE #
Short Glossary of the Terms Used in the União do Vegetal, by Labate et al.
1960s Media Coverage of Ayahuasca and the UDV, by Labate et al.
Ayahuasca Use in a Religious Context, an excerpt by Anthony R. Henman
Santo Daime, by Winstead & Miller
Santo Daime, an excerpt by Charlie K.
SANTO DAIME CEREMONY RECORDINGS #
Dai-Me Amor (Give me love), an early hymn of Santo Daime founder Mestre Irineu (RealAudio-310k)
This is a hymn of Glauco's, dedicated to the city of Sao Paulo. (RealAudio-367k)
Marizia : Hymn 37 of founder Mestre Irineu (RealAudio-251k)
Centro Livre : Hymn 39 of Mestre Irineu (RealAudio-158k)
A Virgem Mae Me Ensinou : Hymn 44 (RealAudio-469k)
LAW #
Legal, Ethical, and Political Dimensions of Ayahuasca Consumption in Brazil - Beatriz Labate Jun2014
Legislative Hearings Discuss Attempt to Ban the Use of Ayahuasca in Brazil - Dec 9, 2010
UDV Ayahuasca Legal Case
ASK EROWID ANSWERS #
Is Banisteriopsis caapi illegal to import?
Would chewing phalaris grass seeds cause an effect?
What is the DMT content of Mimosa hostilis rootbark?
Is Mimosa hostilis orally active without an MAOI?
Do you have any information about a plant called somethin...
» » » MORE » » »
ARTICLES & WRITINGS #
Cura, cura, cuerpecito [Heal, heal, little body], by B. Labate & J. C. Bouso Jun
Ayahuasca: alkaloids, plants & analogs, by K. Trout
Plant Medicines and Shamanic Healing, by Ross Heaven
1957-2010: A Tribute to Glauco Vilas Boas
The Ayahuasca-Alien Connection
Allen Ginsberg Seeking Yage
Vine of the Souls, by Charlie Kidder
The Ritual Use of Plants of Power (Intro and Chapter Summaries)
RESEARCH & JOURNAL ARTICLES #
Related Journal References
Pharmahuasca, Anahuasca and Vinho da Jurema, by Jonathan Ott
Sociopsychotherapeutic functions of ayahuasca healing in Amazonia
References Database : Ayahuasca
» » » MORE » » »
PREPARATION & RECIPES #
Ayahuasca Recipes, by Christian Rätsch
Ayahuasca Analogs and Pharmahuasca, by Christian Rätsch
Ayahuasca Forum: Preparation of B. caapi & M. hostilis (2006)
Ayahuasca Preparations and Recipes, by Keeper of the Trout
Resonance Project: Ayahuasca Cookbook (1997/98)
alt.drugs: Ayahuasca Preparation (1994)
EXPERIENCES #
(Teddy) Bear Totem, by Samanthe
Faceless in the Dark, by Matthew Black
Every Second is a Galaxy, by Sherlockalien
Deep Healing on the Hurl-and-Whirl, by The Doctor
Long-Lasting Trauma, by Jhi-dou
» » » MORE » » »
BOOKS #
The Antipodes of the Mind, by Benny Shanon
Ayahuasca Analogues, by Jonathan Ott
Ayahuasca Visions, by Luis Eduardo Luna & Pablo Amaringo
Ayahuasca and Ayahuasca Alkaloids, by K. Trout [online]
Forest of Visions, by Alex Polari de Alverga
Where the Gods Reign, by Richard Evans Schultes
Tales of a Shaman's Apprentice, by Mark Plotkin
O Uso Ritual da Ayahuasca, by B. Labate and W. Araújo (Eds.)
Ethnopharmacologic Search for Psychoactive Drugs, by D.H. Efron (ed.) (PDF)
» » » MORE » » »
OFF-SITE RESOURCES
PRIMARY RESOURCES #
Iceers: Ayahuasca
Ayahuasca.com
Spirit Quest : Ayahuasca
SECONDARY RESOURCES #
Ayahuasca-related Texts on Bia Labate's Site
Bibliography of the Brazilian Ayahuasca Religions (PDF)
Ayahuasca, DMT, and other related Tryptamines
Yatra's Ayahuasca Site
Deoxy : Ayahuasca
The Ibogaine Dossier : Ayahuasca
My First Ayahuasca Experiences, by Nicholas Saunders
7 Levels : Yage
Disembodied Eyes : Yage
SPIRITUAL USE #
--União do Vegetal-- #
União do Vegetal Home Page
União do Vegetal: Nicholas Saunders' Account
--Santo Daime-- #
Santo Daime - The Brazilian Rainforest's Spiritual Path
The Use of Ayahuasca by the Santo Daime Religion
Guided by the Moon, by Edward MacRae
A Personal Experience at a Daime Service
Santo Daime: Nicholas Saunders' Account
--Other-- #
Shamanistic Ayahuasca Ritual
Deoxy : Shamanism
Ayahuasca Healing Session
LAW #
The Ayahuasca Patent Case, CIEL
The Ayahausca Patent Revocation: Raising Questions about U.S. Patent Policy, Boston College
1996 Ayahuasca Patent
RESEARCH & JOURNAL ARTICLES #
Ayahuasca Issue - MAPS, Autumn 1998
A cognitive-psychological study of ayahuasca - MAPS, Summer 1997
Ayahuasca Pharmacokinetics Study - MAPS, Summer 1995
VIDEO & DOCUMENTARY #
Making Ayahuasca, by Chris Kilham
Eye of the Needle - An Ayahuasca Journey, by Daniel LeMunyan
MEDIA COVERAGE #
Why do people take ayahuasca?, BBC, 29 Apr 2014
Who is authorized to be a Shaman in Colombia? Reflections after Deaths in a Hybrid Ayahuasca Ceremony, Bialabate.net, Aug 2011
Children of a Higher God, Wilamette Weekly, Mar 2, 2011
Psychedelic Tea Brews Unease, WSJ, Sep 16 2009
Psychedelic tea-sipping Oregon sect sues Uncle Sam - Portland Tribune, Sep 12, 2008
Santo Daime: the drug-fuelled religion - Times Online (Women's Section), Apr 7, 2008
Jungle fever - Times Online (Women's Section), Sep 9, 2007
Peru: Hell and Back - National Geographic Adventure
Tripping on Tea - Sollum - May 2005
Peru seeks tribal cure for addiction - BBC, Nov 5 2003
Shaman Bared [sic] From Using Ayahuasca Following Woman's Death - National Post (achived by CCE), Apr 26 2008
The Pale Cast of Thought - Leveritt T, Harpers, Oct 2014
NON-ENGLISH RESOURCES #
Xamanismo e ciência, Trópico, Aug 2009 (Portuguese)
Books on Ayahuasca, Edited by B. Labate et al. (Portuguese)
Zakatechichi: Bouquin sur l'Ayahuasca
L'ayahuasca, le chamane et les initiés, Le Monde, Jul 2008 (Français)
#### Naturals
Posted on September 23, 2015 at 1:20 PM comments (0)
Erowid Note: This FAQ was not authored by Erowid. It may include out-of-date and/or incorrect information. Please check the version date to see when it was most recently revised. It appears on Erowid as part of our historical archives. For current information, see Erowid's summary pages in the substance's main vault.
INDEX
Disclaimer
Introduction
MAO Inhibitors
Hallucinogenic Mushrooms
Mescaline (cacti)
Opium
Hawaiian Baby Woodrose Seeds
Morning Glory Seeds
Native South American Intoxicants
Nutmeg
Yohimbe
Datura
Authors :
Ecni Nisava,
Paul A. Houle,
Adam Boggs,
Petrus Pennanen
Editors:
[email protected]
HTML and Layout:
© Erowid
Last Update: 2/2/93
DISCLAIMER
The information presented herein is for ENTERTAINMENT PURPOSES ONLY and can be found in ethnobotanical literature. Most (if not all) of the substances listed in this faq are illegal to ingest and/or possess. The authors and editors assume no responsibility should the information presented here be used, misused, misunderstood, inaccurate or even read. Reading this faq constitutes an agreement to these terms. If you are afraid you might be tempted to use any of the substances mentioned here in illegal ways when presented with the knowledge to do so, STOP READING NOW.
Many of the botanicals listed here are highly toxic and deadly. Always keep them away from children.
This faq may be reproduced verbatim, in whole or in part, by any means, and distributed freely by whatever means available, provided no charge is made for the copy and this disclaimer is included.
INTRODUCTION
The following information was taken without permission from the book _Legal Highs_ by Adam Gottlieb, 1973, Twentieth Century Alchemist, from _The Botany and Chemistry of Hallucinogens_ by Schultes & Hofmann, 2nd Ed. 1980, from _The Audobon Society Field Guide to North American Mushrooms_ by Gary H. Lincoff and Carol Nehring, 1981, Random House, from _Narcotic Plants: Revised and Enlarged_ by William Emboden, 1979, MacMillan Publishing, from various mail-order greenhouse literature, from personal experiences of many people (friends of friends, and fictional characters that exist only in the authors' and editors' imaginations) and (mostly) from alt.drugs. Some sections contain a "References" section if the author of that section felt like going to the trouble; some mention references on the fly in the text, and some are just unreferenced. Some personal correspondance is included too; in this case if I could get the author's consent I included his name/email address; if I could not track down the author, I included the mail anonymously. If the author of a particular piece of mail doesn't want it included, I won't include it (although I may paraphrase it without attribution).
I left minimal header information in the stuff that was pulled from the net to give credit where due and to provide follow-up paths (do so at your own risk). I didn't have the time (let alone motivation) to mail everyone whose comments are included here to see if it was alright to include them, but if the info was posted to the net once, I can't see a problem with putting it in a faq. A later version might have more eloquent and concise attributions.
Much of the net stuff was edited extensively in that irrelevant info was deleted from specific posts; however, the context and spirit of the remaining information was preserved.
The substances listed here are arranged in a fairly straightforward format. If a certain section is missing from a certain substance, it means that I had no information to put in that section or it didn't apply. The substances are ordered alphebetically, sorted according to Botanical Family name, then Genus name, then (if necessary) Species name. This was a completely fascist decision on my part, and I did it only because it was the easiest ordering to maintain. Note that the name given in the heading is a common name and has NOTHING to do with the way the list is ordered.
At the moment I haven't got time to organize this stuff anymore than it already is (and that's not much). Hopefully in the future I will find time to organize and index it, and to expand it to include dozens of other natural highs. Until then, this mess will have to do.
Spelling errors are numerous and rampant, and I take no responsibility for any of them even tho many of them are undoubtedly mine.
A WORD ABOUT MAO INHIBITORS
[Erowid Note: The section of the FAQ on MAO Inhibitors contains some inaccuracies. For more complete information about MAOIs, read Erowid's MAOI Vault and seek other sources.]
Some of the substances described in this file are MAO inhibitors; this information is provided under the "Interaction precautions" section for the substance in question.
MAO stands for MonoAmine Oxidase, an enzyme that breaks down certain amines and renders them ineffective. MAO inhibitors (MAOIs) are substances that interfere with the action of monoamine oxidase, leaving the amines intact. Inhibiting the action of monoamine oxidase can produce a variety of effects, some of which are dangerous.
It may be dangerous to combine different MAOIs with each other or to combine them with other chemicals such as strong stimulants (amphetamine, MDMA), SSRIs (Prozac, Paxil, Zoloft, Celexa, Desyrel, etc), and many other pharmaceuticals. If you are taking a prescription drug that is an MAOI, avoid using contraindicated drugs or substances.
There are also a number of common foods and beverages which contain amines that are normally broken down by MAO. If you are taking a prescription MAOI, consult your physician to see whether you should avoid any of these. Substances that may interact with certain MAOIs include:
sedatives
tranquilizers
antihistamines
alcohol
amphetamines (even diet pills)
mescaline
asarone
nutmeg
macromerine
ephedrine
dill oil
parsley oil
wild fennel oil
cocoa
coffee (or any substance that contains large amounts of caffeine)
aged cheeses
any tyrosine-containing food
any other MAO inhibitor
THIS LIST IS BY NO MEANS COMPLETE OR ALL-INCLUSIVE. COMBINE DRUGS AT YOUR OWN RISK !
HALLUCINOGENIC MUSHROOMS
Family:
Agaricaceae
Genus:
Psilocybe
Species:
baeocystis (Potent Psilocybe)
caerulipes (Blue Foot Psilocybe)
coprophila (Dung-loving Psilocybe)
cubensis (Common Large Psilocybe)
cyanescens (Bluing Psilocybe)
pelliculosa (Conifer Psilocybe)
semilanceata (Liberty Cap)
stunzii (Stunz's Blue Legs)
Amanita Muscaria (Fly Agaric), Conocybe smithii (Bog Conocybe) and Gymopilus spectabilis (Big Laughing Gym) are among the other mushroom species known to be hallucinogenic. However, Fly Agarics are classified as poisonous, and, according to _The Audobon Society Field Guide to North American Mushrooms_, the Fly Agarics that grow in North America cause "dilerium, raving, and profuse sweating", unlike their hallucinogenic Siberian counterparts. (Perhaps WOSD propaganda, I realize, but worth considering, at least for those of you who don't normally rave...)
WARNING:
mushrooms should NEVER be ingested unless positively identified to be non-poisonous by a mycologist. Often the only differences between highly toxic mushrooms and edible mushrooms are extremely subtle and require a great deal of training to distinguish. Also, several hallucinogenic varieties have been shown to be toxic to humans in medium to large doses.
Usage:
Like most natural plant products, psychedelic mushrooms vary considerably in strength due to genetics, growth medium, and other factors. An effective dose of dried psychedelic mushrooms is on the order of 1 gram. This would be on the order of one or two whole mushrooms (best bet is to weigh them and make sure). Because strength varies widely, you should ask other people who have had mushrooms from the same source about the relative strength. For mushrooms from an unknown source, .5 grams of dried mushrooms is probably a decent place to start.
'Shrooms are best taken on an empty stomach. Carlos Castenada describes the effects of a mushroom-based preparation when smoked, and anyone who has taken 'Shrooms would agree that the effects that he describes are much more intense than the effects of reasonable dosages taken orally. Although many people think that Carlos made the whole thing up, it is possible that mushrooms are smokable and that smoked mushrooms might produce a different experience than ingested, because 'Shrooms contain many compounds known as tryptamines (as in dimethyl- tryptamine (DMT)) which are also psychoactive when smoked but not active orally. Other than Carlos, I've never heard of anyone else smoking mushrooms or mushroom products, so I can't vouch for the effects.
If you don't like the taste of 'Shrooms, it is also possible to consume a tea made by boiling mushroom fragments in water. The idea here is to sprinkle dried mushroom fragments on water and boil them until they sink, and then filter out the actual 'Shrooms and enjoy the tea.
Effects:
The effects of psychedelic mushrooms are comparable to those of LSD, but different in a number of ways. For one thing, the trip lasts aproximately 6 hours, about half of what an LSD trip does. Mushrooms also have less stimulant effect than LSD. Mushrooms tend to be more visual than LSD and less auditory. LSD is probably better for enhancing perception of music, although psilocybin does alter the perception of sound (seems to make background noise louder) and like tryptamine- based psychedelics, also tends to induce auditory hallucinations that sound like 'noise'.
'Shrooms do have definite physical effects that are both similar and different to those of LSD. Shrooms tend to cause 'Liquid Breathing', especially before the onset of psychedelic effects. (Like LSD) Shrooms don't cause stomach cramps, but they do seem to cause a headache sometimes.
A short term cross tolerance does develop between pscilocybin, mescaline, and LSD, but there appears to be no long term tolerance, except for learned behavior which allows one, for instance, to learn how to talk somewhat coherently despite what psychedelics do to the language centers and short term memory.
Another important difference between 'shrooms and LSD is that the onset time of effects from ingestion is MUCH shorter. In the experience of people that I know, the onset of effects is aproximately 30-45 minutes after ingestion, and the transition from physical effects to mild depersonalization to intense hallucination is very short, even in the subjective time of the tripper. There is a period of aproximately one hour where psychedelic effects (visual/auditory hallucination, flickering of visual field, time overlay effect, time distortion, breakdown of linguistic centers, etc.) are VERY intense, and the rest of the trip seems to be more psychological, that is, very little hallucination, mostly depersonalization and time distorsion. This is a very excellent time to spend in a natural environment (your local woods, desert, or savanna) because it tends to produce shamanistic, in touch with nature feelings much better than LSD does.
Bad trips are very possible with mushrooms, and are probably very similar to bad trips on acid. If you know or suspect that a tripper is experiencing eyes-open visual hallucinations, you might want to take them to a place where no there are no regular geometric patterns that cover most of the visual field. High dosages of mushrooms seem to affect perception of regular tiled surfaces much more so than irregular surfaces. If possible, suggest to the tripper that you go to a place where there is a featureless floor (say a drab carpet or a concrete floor). It's also good to find a warm place, but always heed to the will of the tripper so long as he doesn't want to do anything stupid like jump off a cliff. See if you can find some mellow music that is pleasing to the tripper (Say, the Grateful Dead or Spyro Gyra) and remember that little things like turning the intensity of light up or down can have a big emotional effect. Be sure to ask about these things.
When talking to someone on a bad trip, it often helps to keep changing his train of thought; many people find that this keeps the anxiety at a lower level. The primary rule is to watch the reaction of the tripper to what you do, and take his needs and fears into consideration. Keep him with people that he trusts and try to remove any people that he doesn't trust. Of course, this advice is valid for hallucinogens in general.
History:
The practice of growing mushrooms dates back to around 100 B.C., and is based partly upon the discovery of minature mushroom stones found near Gautemala City. Other finds further north also indicate an extensive mushroom cult in the early civilizations. When Cortez arrived in Central America, he found the natives using mushrooms as a sacrament. They called them "teonanacatl", or "God's Flesh." The Spainards reacted strongly to the mushrooms, giving written accounts of the loathsome mushroom rituals that "provoke lust... cause not death, but madness... and bring before the eyes wars and the likeness of demons." Teonanacatl was then banned from the church as contributing to pagan behavior and idolitry. The only tribe definately known to have consumed the mushrooms, however, is the Chichimecas. Six tribes consume mushrooms today in Oaxaca: Mazatecs, Chinantecs, Chatinos, Zapotecs, Mixtecs, and Mijes. It has recently been suggested that mushroom use by the Chol and Lacandon Maya may be a vestage from the earlier Mayans that disappeared for a time, and then was readopted. Present day ritual among them Mazatec includes many rituals from the Catholic Church. Even though the Catholics tried to eliminate the detested fungi, the Indians still chant saints of the church and incorporate litanies, which are undoubtedly post-Christian elements of their ritual.
Interaction precautions:
I wouldn't recomend using them with alcohol or other depressants. Also, people who are being medicated for a psychological conditions, particularly with MAO-inhibitor class drugs probably DON'T want to use 'Shrooms or any psychedelic because MAO-inhibitors tend to interact seriously with most psychoactive compounds.
Active Ingredients:
The primary active components of 'Shrooms are psilocybin and psilocin, which also is an immediate metabolite of psilocybin. There are a whole family of other tryptamine-related substances in 'Shrooms but most of them are not active when eaten.
For further reading:
Several books are available on the subject of growing mushrooms, which is a rather complex task because it involves maintaining a sterile environment and quite a bit of biology lab skills. The best book on the subject is "Psilocybin: The magic mushroom grower's guide" by Oss and Oeric from And/Or press. Spores are available by mail order; check High Times magazine. These are legal to sell because they contain no psychoactive compounds. Spores can also be obtained by taking a cap print from mushrooms that you obtain from another source, like the wild.
========================================
[some interesting info on Fly Agarics follows. Note that these are much more poisonous than psilocybe varieties, the info above does not necessarily apply to them, and the info below does not necessarily apply to psilocybes. --ED]
~From: [email protected] (David A. Honig)
~Subject: Re: mail order botanicals
~Date: 11 Nov 91 22:00:34 GMT
Organization: UC Irvine Department of ICS
In article <[email protected]>
[email protected] (Eli Brandt) writes:
>>anyone know the legality of fly agaric? anyone have any experience with
>>it?
>
>I'm sure it's legal. _Merck's_ sez that neither ibotenic acid and muscarine
>were "controlled substances" (what a *dumb* term) as of '76; was there maybe
>a "Toadstool Regulation Act" I missed? Anyway, you could call it "soma" and
>have a real good case for religious use...
>
>I don't know what the dose would be. The LD-50 iv in mice for muscarine is
>0.23 mg/kg; ibotenic acid is (for mice/rats) 15/42 iv and 38/129 oral. I'd
>be careful with anything with such a wide difference in toxicity between
>fairly similar species. I vaguely recall that muscarine is only found in
>the younger shrooms; it looks like you'd want to avoid them, unless it's
>also responsible for most of the interesting effects.
>
>>ecni
>
> Eli [email protected]
I obtained some dried Amanita via an unnamed source. They make you puke
(what else is new) and go into a dreamy state. Not "psychedelic" or
terribly euphoric. A friend (who is a botanist) has tried fresh ones,
reports that they're better.
IMHO, they're not worth your time unless your into ethnopsychopharmacology.
--
David A. Honig
MESCALINE-BEARING CACTI
Family:
Cactaceae
Genus:
Gymnocalycium
Species:
gibbosum: Native to Argentina
leeanum: Native to Argentina, Uruquay
Genus:
Islaya
Species:
minor: Native to South Peru
Genus:
Lophophora
Species:
diffusa (Peyote): Native to Mexico
williamsii (Peyote, Mescal,Chaute etc.): the classic Peyote, grows in north central Mexico and south Texas.
Genus:
Opuntia
Species:
imbricata: Native to S-W USA to Central Mexico.
spinosior: Native to Arizona, New Mexico, Northern Mexico.
Genus:
Pelecyphora
Species:
aselliformis (Peyotillo, Peyote meco): Native to San Luis Potosi, Mexico
Genus:
Pereskia
Species:
corrugata
tampicana: Native to Tampico, Mexico.
Genus:
Pereskiopsis
Species:
scandens: Native to Yucatan, Mexico.
Genus:
Stetsonia
Species:
coryne: Native to Northwestern Argentina.
Genus:
Trichocereus
Species:
cuzcoensis: Native to Cuzco, Peru.
fulvianus: Native to Chile.
macrogonus: Native to South America.
pachanoi (San Pedro, Giganton): Native to Peru, Equador.
peruvianus (Peruvian Fence Post): Native to Peru.
scopulicola
taquimbalensis: Native to Bolivia.
terscheckii (Cardon grande): Native to Northwestern Argentina.
validus: Native to Bolivia.
werdermannianus: Native to Tupiza & Charcoma, Bolivia.
Description:
Trichocerei are columnar, branched or candelabra like cacti, which usually grow very fast. Cereus is a different genus, whose members haven't been found to contain mescaline.
Cultivation:
(from seed) Sow the seeds an inch apart on the surface of sterilized, moist, sifted cactus mix. The pH should be 4.5-6.5. Cover the tray or pot with an airtight plastic bag. Place in bright but indirect light for 12 hours a day at less than 30 degrees centigrade. Don't let the temperature get too high, and check to make sure the soil surface is moist, but not too wet. A fungicide may be needed.
Cactus seeds will generally germinate in 1-3 weeks. When the seedlings are about 2 cm tall (60-90 days for fast-growing species) transplant them to individual pots. Handle them very cautiously and use moist soil with pH 4.5-6.5 in the new pot. A good soil mix is 1/3 normal flower soil, 1/3 peat and 1/3 coarse sand or gravel. If you're growing a Trichocereus, water once a week with a concentration of a flower fertilizer normally used for flowering plants. Don't use standard plant fertilizers, as they contain too much nitrogen. Bright light is needed 12-18 hours a day, and the temperature should be 25-35 'C.
The easiest way of propagation is taking cuttings. Cut the mother plant with a clean and sharp knife leaving 5-10 cm of it above ground. Cut back slightly the edges of the cut to ensure that the new roots grow downward. Place the cutting in vertical position to dry for 2 weeks to a month depending on the size of the cutting. The compost where they are placed after this should be very slightly moist, not wet.
For more information about growing cacti read e.g. Cullman, B|tz & Gr|ner 1984: Encyclopedia of Cacti, Alphabooks A&C Black, ISBN 0-906670-37-3.
Usage:
An easy method is to chop a cactus to small pieces, dry the pieces and boil in water with plenty of lemon juice until there's not much liquid left. To reduce nausea you should drink the liquid slowly over a half an hour while avoiding excessive movement. For the same reason don't eat solid food on the day of ingestion. A normal dose of mescaline sulfate is 200-400 mg, which probably corresponds to 10-25 g of dry Peyote or T. peruvianus, or 50-200 g of fresh San Pedro. Potency varies, so try a small dose first. It's also possible to extract mescaline from cacti.
Effects:
Mescaline produces a trip very similar to LSD lasting about 12 hours. The effects take a bit longer to come on. Mescaline is cross-tolerant with LSD, psilocin and other psychedelics. A common side-effect is nausea, which is worse when ingesting Peyote than other cacti because of the extra alkaloids found in Peyote. If you manage to hold the cactus in your stomach for 15-30 minutes before throwing it up, you can still have a fine and nausea-free trip.
Mescaline does not cause chromosome damage in normal doses.
History:
Peyote has been in use in America for at least 2000 years. The Spanish conquistadors didn't like the use of drug plants by the Indians, and catholic clerics declared officially in 1620 that since the use of peyote was the work of the devil, all Christians were prohibited from using it. The active prohibition of peyote still persists. A religious manual written in 1760 presented the following series of questions for the penitent:
Have you ever killed anyone?
How many have you murdered?
Have you eaten the flesh of man?
Have you eaten peyote?
Peyote was used for several centuries in Mexico before peyotism spread into the US in the second half of the 19th century. Today it's legal for the members of the Native American Church to use Peyote in several states.
The San Pedro cactus has been used by Peruvian folk healers to combat the supernatural elements that cause diseases.
Active Constituents (of some cacti)
Botanical name mescaline other alkaloids
Genus species
Lophophora williamsii ~1% dry Ann,And,Ant,Annd,H,L,P,T
Trichocereus peruvianus 0.8% dry T
pachanoi 0.1% wet Annd,H,T
bridgesii 0.1% wet T
validus 0.1% wet
macrogonus <0.05% wet T
terschecki <0.05% wet Ann
werdermann <0.05% wet T
taquimbal <0.05% wet H
cuzcoensis <0.01% wet T
Stetsonia coryne <0.01% wet T
Pelecyphora aselliformis 0.00002% And,H,P
Mescaline content is probably given as hydrochloride, 128 mg mescaline HCl = 200 mg mescaline sulfate. Doses of mescaline are usually measured as sulfate. "Dry" means dry weight, "wet" fresh weight.
Ann = anhalonine causes paralysis followed by hyperexitability in rabbits
And = anhalodine stimulant, not potent
Annd = anhalonidine similar to pellotine
H = hordenine
L = lophophorine causes convulsions, similar to strychnine
P = pellotine causes drowsiness and slowing of heartbeat
T = tyramine
References:
Agurell, S. 1969: Cactaceae alkaloids I. Lloydia 32,2
Agurell, S. 1971: Cactaceae alkaloids X. Alkaloids of Trichocereus Species and Some Other Cacti. Lloydia 34,2
Anderson, E.F. 1980: Peyote - the Divine Cactus. The University of Arizona Press, ISBN 0-8165-0613-2.
Pardanani, J.H. & McLaughlin, J.L. 1977: Cactus Alkaloids XXXVI. Mescaline and Related Compounds from Trichocereus Peruvianus. Lloydia 40,6
LETTUCE OPIUM
Family:
Compositae
Genus:
Lactuca
Species:
virosa
Usage:
Materials are extracted in a juicer and eaten fresh or dried and smoked.
Effects:
Mild sedative effect similar to opium. Very, very mild buzz, almost unnoticable. Not worth the hassle of obtaining from the plant, and not worth the cost of buying refined herb. Watch out for "incense" concoctions sold in head shops and through mail order that claim to have alternative uses. These are usually worthless, overpriced Lettuce opium preparations.
History:
Formerly used in medicine as an opium substitute.
Active Constituents:
lactucin, lactucerol (taraxaxterol), lactucic acid
FROM THE NET:
~From: [email protected] (Petrus Pennanen)
~Subject: Re: lactucarium
~Date: 8 Jul 91 20:24:16 GMT
Organization: University of Helsinki
Ronald Siegel writes in _Intoxication_:
"In each major category of intoxicant used by our species, there appear
to be one or two drug plants that researchers have noted are more
controllable, hence safer, than all the other plants or synthetics in
that category. [...] Among the narcotics, which include opium and its
derivatives, there is lactucarium, the smokable extract derived from
Lactuca Virosa."
"Consider the case of lactucarium, which never caught on as a
modern opium substitute because either so mild or so inconsistent in
quality that people thought it was a fake.
Lactucarium smells like opium and tastes just as bitter. When smoked
or swallowed, it is so mildly intoxicating it remains legal. There are
no visions like the ones De Quincey had from eating opium, but the
euphoria and dreamy intoxication last slightly longer. Although
lactucarium is structurally unrelated to the opiates, it will still
soothe irritating cough, ease minor pains, and help induce sleep, hence
its more common name of 'lettuce opium.' The history of lettuce opium in
America paralleled that of coca tea. Both drugs enjoyed widespread
medical use in nineteenth century and brief periods of experimental
nonmedical use in more recent years.
In the mid-1970s, smokable extracts of lettuce opium were marketed
throughout the United States under such brand names as L'Opium and
Lettucene. 'Buy your lettuce before they make it illegal!' announced the
national ads. Hundreds of thousands did exactly that when the craze
peaked in the late 1970s. There was not a single case of toxicity or
dependency. But there was a lot of competition as different
manufacturers rushed to get a share of the new market. Most of these
newer brands were made from ordinary garden lettuce, which lacked the
intoxicating lactucarium. Subsequently, sales fell, some suppliers of
real lactucarium went out of business, and the fad all but disappeared.
While lactucarium is still available, heroin users are not rushing to
buy it and probably never will: it's simply too weak."
Petrus Pennanen [email protected]
HAWAIIAN BABY WOODROSE SEEDS
Family:
Convolvulaceae
Genus:
Argyreia
Species:
nervosa
Usage:
seed pods contain 4-6 seeds. Seeds are removed from pods and fungus-like coating is scraped or flamed off (author recommends scaping as much as possible and flaming the rest, as the coating can be thick and it's easy to end up turning the whole seed into a chunk of carbon if you just flame it). 4-8 seeds are chewed on an empty stomach (to minimize nausea). Seeds sold commercially are generally already removed from the pods. The seeds themselves resemble small chocolate chips, but are hard as rocks and have the coating mentioned above.
Nausea can be lessened by ingesting one or two dramamine 30 minutes to one hour before ingesting the HBW seeds. More dramamine can be taken after the nausea sets in, however, dramamine can be a DANGEROUS drug in high doses and its synergistic effects with LSA are unknown. Exceeding the recommended dosage given on the dramamine box is probably a pretty stupid thing to do under any circumstances.
If dramamine is not used, inducing vomiting when nausea starts will provide relief but effects will continue. You can also grind and soak the seeds in water, then strain them out and drink the water. If ground seeds are used, make sure they are fresh ground.
Effects:
LSD-like effects, but less intense, with less visuals. Trip lasts 6-8 hours; tranquil feelings may last additional 12 hours. Sleep is deep and refreshing after trip, however some users may experience a hangover characterized by blurred vision, vertigo, and physical intertia.
History:
Used by the poorer Hawaiians for a high. Shipping of these seeds became popular, as did a great controversy over the propriety of world-wide distribution.
Interaction precautions: same as for Morning Glory seeds.
Active Constituents:
D-lysergic Acid Amide and related compounds. NOTE: net wisdom has it that extracting LSA from woodrose/mg seeds is an inefficient way to obtain a precursor for LSD.
Note:
Hawaiian Large woodrose seeds supposedly have the same effect. Dosage is identical.
MORNING GLORY SEEDS
Family:
Convolvulaceae
Genus:
Ipomoea
Species:
arborescens (Quauhzahautl): tree grows to 15' high. Native to Mexico.
carnea (fistolusa): bush with pink flowers native to Ecuador.
costata: native to australia.
leptophylia: wine colored flowers 3" across. Huge edible roots.
meulleri: native to australia.
murucoides: (Pajaro bobo) native to oaxca.
purpurea: native to mexico, common throughout N. America as an ornamental.
violacea (Tlitliltzin): sacred Mayan morning glory. Widely used for its psychoactive effects in the Heavenly blue, Pearly Gates, Flying Suacers and Wedding Bells strains.
Usage:
5-10 grams of seeds can be ingested as follows:
thoroughly chew and swallow
grind and soak in water for 1/2 hour, strain and drink
sprout by soaking in water for 3-4 days (change water often), after which the white mushy part is removed from the shell and eaten. This is probably the best method for avoiding side effects, although I have I have reason to believe sprouting the seeds lessens their effectiveness.
Most commercially available Morning glory seeds are treated with chemicals to thwart consumption. Seeds are also sometimes treated with Methyl mercury to prevent spoilage. Chemically treated seeds can cause severe nausea, vomiting and diarrhea.
Effects:
LSD like experience lasting about 6 hours, but with less hallucinogenic effects. Nausea is common even with untreated seeds. Less anxiety, less intensity than LSD in normal doses.
Nausea can be lessened by ingesting one or two dramamine 30 minutes to one hour before ingesting the MG seeds. More dramamine can be taken after the nausea sets in, however, dramamine can be a DANGEROUS drug in high doses and its synergistic effects with LSA are unknown. Exceeding the recommended dosage given on the dramamine box is probably a pretty stupid thing to do under any circumstances.
History:
The Zapotecs used ipomoea violacea by grinding the seeds up and wrapping them in a meal cloth. They would then soak it in cold water and would find out information about the illness of a patient, a troublemaker among the people, or the location of a lost object.
Interaction precautions: should not be taken by people with a history of liver disorders or hepatitis. Should not be taken by pregnant women.
Active Constituents:
D-lysergic acid amide
NATIVE SOUTH AMERICAN INTOXICANTS
Family:
Acanthaceae
Genus:
Justicia
Species:
pectoralis (var. stenophylla)
Usage:
Waikas of Orinoco headwaters in Venezuela add dried and pulverized leaves of this herb to their Virola-snuff.
Effects:
Unknown
Active Constituents:
Intensely aromatic smelling leaves probably contain tryptamines.
Plants are available from ...Of the jungle for $35. ------------------------- Family: Leguminosae Genus: Anadenanthera (Piptadenia) species: peregrina colubrina Usage: Black beans from these trees are toasted, pulverized and mixed with ashes or calcined shells to make psychedelic snuff called yopo by Indians in Orinoco basin in Colombia, Venezuela and possibly in southern part of Brasilian Amazon. Yopo is blown into the nostrils through bamboo tubes or snuffed by birdbone tubes. The trees grow in open plain areas, and leaves, bark and seeds contain DMT, 5-MeO-DMT and related compounds (Schultes 1976,1977; Pachter et al. 1959). Active Constituents: DMT, 5-MeO-DMT and related compounds. -------------------------- Family: Leguminosae Genus: Mimosa Species: tenuiflora (== hostilis) "tepescohuite" verrucosa General: The roots of M. hostilis, which is *not* the common houseplant M. pudica ("sensitive plant"), contain 0.57% DMT and are used by Indians of Pernambuso State in Brazil as part of their Yurema cult (Pachter et al. 1959, Schultes 1977, Meckes-Lozoya et al. 1990). Bark of M. verrucosa also contains DMT (Smith 1977). Active Constituents: DMT --------------------------- Family: Malpighiaceae Genus: Banisteriopsis Species: rusbyana argentea Usage: Natives of western Amazon add DMT-containing leaves of the vine B. rusbyana to a drink made from B. caapi, which contains beta-carbolines harmine and harmaline, to heighten and lengthen the visions (Schultes 1977, Smith 1977). Active Constituents: leaves contain DMT. --------------------------- Family: Myristicaceae Genus: Virola Species: calophylla calophylloidea rufula sebifera theiodora Usage: The bark resin of these trees is used to prepare hallucinogenic snuffs in northwestern Brazil by boiling, drying and pulverizing it. Sometimes leaves of a Justicia are added. Amazonian Colombia natives roll small pellets of boiled resin in a evaporated filtrate of bark ashes of Gustavia Poeppigiana and ingest them to bring on a rapid intoxication (Smith 1977, Schultes 1977). Effects: The snuff acts rapidly and violently, "effects include excitement, numbness of the limbs, twitching of facial muscles, nausea, hallucinations, and finally a deep sleep; macroscopia is frequent and enters into Waika beliefs about the spirits resident in the drug." Active Constituents: Snuffs made from V. theiodora bark contain up to 11% 5-MeO-DMT and DMT. Leaves, roots and flowers also contain DMT. ------------------------- Family: Rubiaceae Genus: Psychotria Species: viridis (psychotriaefolia) Usage: Psychotria leaves are added to a hallucinogenic drink prepared from Banisteriopsis caapi and B. rusbyana (which contain beta-carbolines) to strengthen and lengthen the effects in western Amazon. Active Constituents: P. viridis contains DMT (Schultes 1977). 5 seeds$10 from ...Of the jungle, leaves are also available.
References:
Meckes-Lozoya, M., Lozoya, X., Marles, R.J., Soucy-Breau, C., Sen, A., Arnason, J.T. 1990. N,N-dimethyltryptamine alkaloid in Mimosa tenuiflora bark (tepescohuite). Arch. Invest. Med. Mex. 21(2) 175-7
Pachter, I.J, Zacharias, D.E & Ribeir, O. 1959. Indole Alkaloids of Acer saccharinum (the Silever Maple), Dictyoloma incanescens, Piptadenia colubrina, and Mimosa hostilis. J Org Chem 24 1285-7
Schultes, R.E. 1976. Indole Alkaloids in Plant Hallucinogens. J of Psychedelic Drugs Vol 8 No 1 7-25.
Schultes, R.E. 1977. The Botanical and Chemical Distribution of Hallucinogens. J of Psychedelic Drugs Vol 9 No 3 247-263
Smith, T.A. 1977. Review: Tryptamine and Related Compounds in Plants. Phytochemistry Vol 16 171-175.
NUTMEG
Family:
Myristicaceae
Genus:
Myristica
Species:
fragrans
Usage:
5-20 grams of ground nutmeg is ingested. Fresh ground is best. Can also be taken in a "space paste" concoction (see below). Space paste is difficult/expensive to make and tastes like shit; however, it may actually decrease the side effects.
Effects:
Possible nausea during first hour; may cause vomiting or diarrhea in isolated cases. Takes anywhere from one to five hours for effects to set in. Then expect severe cottonmouth, flushing of skin, severely bloodshot eyes, dilated pupils. Personally I compare it to a very, very heavy hash buzz. "Intense sedation". Impaired speech and motor functions. Hallucinations uncommon in average (5-10 gm) doses. Generally followed by long, deep, almost coma-like sleep (expect 16 hours of sleep afterward) and feelings of lethargy after sleep. May cause constipation, water retention. Safrole is carcinogenic and toxic to the liver.
History:
Nutmeg was a very important trade item in the 15th and 16th centuries. It was a precious commodity due to the enormous medicinal properties of its seeds. Slaves on the ships bringing nutmeg to Europe got in trouble for eating part of the cargo. They knew that a few large kernels of nutmeg would bring them a pleasant, euphoric feeling, and relieved their weariness and pain. Nutmeg was even used when the feeble King Charles II almost died of a clot or hemorrhage. His death a few days later did nothing to detract from its useful reputation. Rumor spread through London that Nutmegs could act as an abortifacient. The ladies who procured abortions from nutmeg were called "nutmeg ladies."
Interaction precautions:
MAO inhibitor
Active Constituents:
Methylenedioxy-substituted compounds: myristicin (non-amine precursor of 3-methoxy-4,5-methylenedioxyamphetamine [M-MDA]) elemicin, and safrole.
From The Net:
~From: [email protected] (Michael G. Goldsman)
~Subject: Nutmeg Story
~Date: 11 Aug 91 23:56:07 GMT
Organization: Georgia Institute of Technology
Friday, a "friend" of mine decided to see what all the talk about nutmeg
was all about... here's what happened...
8:15 -- "he" took 1 tablespoon of ground nutmeg...
9:15 -- "he" took 1 more tablespoon of ground nutmeg...
11:15 -- "he" took still 1 more tablespoon of ground nutmeg...
As of now, "he" didn't feel anything... "He" got the beginnings of a buzz
at about 12:30 which gradually increased in intensity...
By 3 am or so, he compared it to moderate cannibis buzz
It peaked at at 5 am, and he then went to sleep.
The effects continued through saturday afternoon and
night, though not as intense as late friday night (or saturday morning
technically).
By sunday morning, the effects were totally gone.
The main point is, that except for lots of drowsiness, my "friend" never
suffered any of the ill effects that people have described ...
(such as nausea and headaches)
It was very comprable to a medium marijuana buzz. There were
no hallucinations, but maybe a larger dose is needed for this.
Next week my "friend" will go for 5 tablespons over the course
of a few hours.. Will he live to describe the experience??
==================================
~From: [email protected] (Jeffery Tye)
~Subject: Space paste! (was Re: nutmeg as a hallucinogen)
~Date: Sat, 29 Jun 91 01:59:09 GMT
Organization: The Scantily Clad Orangutans, Inc.
'Space Paste'
heart chakra, but it's a legal high that will get you pleasantly
buzzed. :-) DON NOT OMIT ANY INGREDIENTS. Trust me.
4 parts nutmeg (ground from whole nutmeg)
4 parts almonds (soak almonds overnight and rinse)
4 parts *raw* pistachios
2 parts cinnamon
1 part cumin
1 part tarragon
1 part oregano
1 part basil
1 part tumeric
1/2 part cayenne pepper
1/2 part black pepper
To taste: Maple Syrup
One part equals 1/4 cup.
[if you want to make enough for about 500 people, that is. Try 1 part=1
tablespoon--ed]
- Use only whole nutmeg. Not pre-ground.
- Grind up all ingredients with a spice grinder or food processor.
- Mix in Maple syrup until consistency of paste.
- Do not omit any ingredient, or it will NOT work.
Okay, you've gone this far, time to enjoy. The strong at heart will
spread some on toast. I like it blended in milk. It has a real strong
taste, so it's best to put it in the milk, fire up the blender, pour it
into a glass and chug it down in one gulp.
Start with two tablespoons. Effects begin in two hours. I've known
brave souls who take a cup at a time. Maybe that's why they disappear
for a couple of days.
=================================
~Date: Wed, 2 Oct 91 09:57:26 MDT
~From:
~Subject: More on Nutmeg Story
Begin forwarded message:
Well, I am recovering from a horrible experience.
Tuesday night about 10:30pm, I took 5 tablespoons of Nutmeg.
I am still hungover, almost 2 days later.
I got the initial stimulation, euphoria, but not much more than what one gets around 2 tablespoons.
That was fine and dandy. I fell asleep at about 1:30am, with nothing psychedelic occurring yet.
I woke up at 3 am spinning, like I was drunk. I awoke again at 9am, and got out of bed. I had to:
thirsty as hell, no saliva. I had wicked troubles walking, far too dizzy and -out-of-it-. Just like I
had no control over my body. Also, any movement that I did make nauseated me. By 9:30 I had my
drink of water, and I collapsed on the kitchen floor, sleeping until noon. I thought that I would
have something to eat, at that time, but was far too dizzy still to do anything. By this time I was in
a panic, thinking that I had comitted suicide, etc.etc. My body felt like it was melding with the
floor; I also felt that my whole body was made of vomit. Quite odd. I crawled (literally) up to bed
again and slept like a stone until 6pm. I managed to eat some stuff. I could stand for 30 seconds at
a time, by this time. I watched a movie, dozing on and off. I looked at myself in a mirror: horrible
sight, very red sunken eyes etc.etc. Went to bed and awoke this morning at 11:30am. Awoke with
something like a horrible hangover. I feel like I have had a wicked flu yesterday and today.
Besides some odd physical sensations and perceptions, even this dosage was not overtly
hallucinogenic. I did not experience any colour / visual perception changes this time, like at the
lower dosage. Perhaps I was just too sleepy to notice.
This experience was just downright gross. I think I have given up experimenting with Nutmeg
(and Mace) [ even though I really like the taste of the stuff. Some people complain they can't get the
stuff down --- they must not be using fresh stuff]. It was really an offputting experience. Tonight,
I think I am just going to hunt down something illegal but safer.
YOHIMBE BARK
Family:
Rubiaceae
Genus:
Corynanthe
Species:
yohimbe
Usage:
6-10 teaspoons of shaved bark are boiled 10 minutes in 1 pt. water, strained and sipped slowly. Addition of 500 mg of vitamin C per cup makes it take effect more quickly and potently (probably by forming easily assimilated ascorbates of the alkaloids). Bark can also be smoked. Yohimbine hydrochloride, a refined powder version, can also be snuffed. Also available at many health/herb stores is a liquid extract.
Effects:
Called "the most potent aphrodisiac known" and "the only true aphrodisiac". Whether aphrodisiacs exist outside of mythology or not is a topic for debate, as is the definition of "aphrodisiac". Anyway, first effects after 30 minutes (sooner with vitamin C) consist of warm, pleasant spinal shivers, followed by psychic stimulation, heightening of emotional and sexual feelings, mild perceptual changes without hallucinations, sometimes spontaneous erections. Some experience nausea during first 30 minutes. Sexual activity is especially pleasurable. According to one source "Bantu orgies have been known to last over a week" [Ed: don't they get hungry?]. Total experience lasts 2-4 hours, however, several experiences lasting up to 24 hours have been reported. Aftereffects include pleasant, relaxed feelings with no hangover, but difficulty sleeping for a few hours (probably largely due to the increased mental activity).
Since they sell the stuff in health food stores and I'm not sure what it's legitimate uses are, I'm willing to admit that I've tried it. My experience was worth repeating. This of course constitutes no endorsement on my part of illegal or legal drugs or of the use of yohimbe for any reason at all.
I ground about 7 teaspoons of shaved bark in a spice grinder (fresh grinding seems to help with release of the active ingredients) and then boiled it in a pint of water for about 10 minutes. The stuff absorbs a lot of water. Also, when freshly ground, you get some FINE FINE FINE particles. It took me a good 15 minutes to filter the stuff out through coffee filters (had to use a bunch of filters cuz it clogged them up so bad). The resulting brew was one of the top three worst things I've ever tasted in my life (the other two being calamus root and an abortive attempt at a kava kava concoction). It tasted kind of like bile. You can kill the taste if you put enough honey in the tea, but the aftertaste never goes away. As soon as you swallow it creeps up your throat; really gross. The fact that the stuff should be sipped slowly makes this even worse. I would recommend finding a REAL strong chaser, like pure lemon juice or maybe a mint leaf--something that obliterates all other taste in your mouth when you eat/drink/chew it, yet is tolerably pleasant tasting. I would swig/chew this chaser after every sip of yohimbe tea.
WARNING:
The active ingredients in yohimbe are mild MAO inhibitors. [see MAO Inhibitors above]
Anyway, I took the tea with vitamin C. About 20 minutes after I got done drinking it I felt some mild nausea (more in my throat than in my stomach), some mellow trippy effects (just mostly weird thoughts and vivid mental images--nothing near a hallucination, no LSD-like mind racing), also had some speedy effects (like being on 500 mg of caffeine--jitters, etc) and started getting a little "pressure" in the groinal region. To make a long story short, the nausea was a bummer, and sex was incredible. Yohimbe completely changes the meaning of the word "orgasm" for men, anyway. I have no idea what a woman's reaction to it would be.
The sexual effects lasted about 4 hours (only cuz I was getting tired :^); the speedy effects decreased earlier than that, but I couldn't sleep at all that night (even when I was ready to), and I'm sure it was because of the yohimbe.
I also recently tried the yohimbe extract that they sell in health food stores. The stuff costs about $7/oz. It comes in one ounce bottles with screw-on eye-dropper caps. Recommended dose on the bottle is 3-20 drops up to three times a day. First time I tried it I took 35 drops with absolutely no effects. Recently, I took 100 drops mixed in orange juice. The stuff is tasteless in minute quantities, but at 100 drops/~8 oz. of OJ, it added a mildly bitter taste. Not too bad, tho--1000x better than the tea. Anyway, it didn't do anything, so I took another 50 drops, then another 50, and still no effects whatsoever. I wonder if the extract is even active. I would advise yohimbe experimenters to use the tea form, and start out with 4 or five teaspoons of fresh ground bark, as the effects of 7 teaspoons were quite pronounced in me, and I am a 200 lb. male with a high tolerance for everything. History: Interaction precautions: MAO inhibitor. Active Constituents: Yohimbine, yohimbiline, ajmaline. (Note that yohimBE is the plant; yohimBINE is one of the chemical principles found in the plant.) FROM THE NET: ~From: [email protected] (Steve Dyer) ~Subject: Re: Yohimbine bark ~Date: 18 Jul 91 02:17:32 GMT Organization: S.P. Dyer Computer Consulting, Cambridge MA Ecni Asked: >Anyone care to enlighten us yohimbine-illiterate readers what yohimbine >bark is and what it does? Yohimbine is the primary alkaloid found in yohimbine bark. It is an alpha-2-adrenergic antagonist. It blocks presynaptic inhibitory synapses, meaning that it tends to increase central and peripheral adrenergic activity. It tends to cause nervousness and increases blood pressure. It also seems to be effective in some cases of impotence. Steve Dyer [email protected] aka {ima,harvard,rayssd,linus,m2c}!spdcc!dyer [email protected] DATURA Family: Solanaceae Genus: Datura Species: fastuosa: large shrub with white flowers inoxia (Don Juan's Datura): native to mexico metel: native to India. sanguinea (Eagle Datura, Tonga): Native to S. America. stramonium (Jimson Weed): Dangerous hallucinogen widespread in temperate regions. Other species: tatula, brugmansia, candida, suaveolens, arborea, aurea, dolichocarpa, vulcanicola, discolor Usage: Leaves are sometimes smoked. Small amount of seed can be pulverized and added to drinks as in the Algonquin ritual. Effects: described as "delerium". Leaves are hallucinogenic and hypnotic. Seeds cause mental confusion and delirium followed by deep sleep with colorful hallucinations. Excessive amounts are toxic. May cause blacking out and severe headaches. Yaqui indian brujos say it causes insanity. THIS SUBSTANCE IS GENERALLY CONSIDERED DANGEROUS. History: discolor (Desert Thornapple): used by hopi shamans for divination. inoxia: "Don Juan's Datura" is used in it's native mexico by Yaqui bruhos for divination metel: Used by the Thuggee cult in it's native India to drug sacrificial victims to Kali. sanguinea (Eagle Datura, Tonga): Used by Aztecs in the Temple of the Sun. Peruvian natives believe it allows them to communicate with departed souls. stramonium (Jimson Weed): Dangerous hallucinogen widespread in temperate regions. Used by Algonquins in ritual drink called "Wysoccan" to introduce boys to manhood. Active Constituents: Scopolamine, atropine, hyoscyamine and other tropanes. "Hyoscyamine and scopolamine possess specific anticholinergic, antispasmodic activity and elicit some central nervous effects as well. These effects usually consist of stimulation at low doses, depression in higher toxic doses. ... Intoxication with atropine or hyoscyamine is characterized by psychic excitation often combined with panic and hallucination. Scopolamine was found to produce a state of excitement followed by a kind of narcosis in which, in the transition state between consciousness and sleep, hallucinations sometimes occur (Heimann, 1952). These effects explain the addition of belladonna and other solanaceous plants as ingredients of magic brews in medieval Europe and of sacred medicines by the Indians of Mexico and South America." (Schultes and Hoffman, 1980) NOTE: Family Solanaceae is the potato family (did you know potatoes have a lower LD50 than marijuana? It's true). Many members of this family contain tropanes and have a history of ritualistic use. Other commonly-used members are the Mandrake (Mandragora officinarum), Belladonna (a.k.a. deadly nightshade) (Atropa belladonna), Thornapple (Datura inoxia), Henbane (Hyoscyamus niger), and Iochroma. All these substances will be covered in more detail in a future version of this faq. Kuthmithi (Withania somnifera) is one member of the Potato family that does not appear to contain active amounts of tropanes and is generally considered safe for use as a sedative. FROM THE NET: ~From: [email protected] (Gerald Bryan (Denver)) ~Subject: Re: Shrooms, Datura etc ~Date: 29 Aug 91 16:43:51 GMT In article <[email protected]> [email protected] (Fie nd) writes: > How many people have lasting physical damage from Datura? I know one person who has used Datura. She was an experienced drug user at the time. She said it gave her tremendous visions, but it took her a year before she felt that her eyesight was back to normal. She only used it once. Two years ago, there was a story in the local paper about some college students in Boulder who walked buck naked into a police station, totally out of it. They had apparently consumed some datura (on purpose) up in the mountains. =============================== ~From: [email protected] (marsthom) ~Subject: BADUNGA & MORNING GLORY SEEDS ~Date: 25 Sep 91 21:32:50 GMT Organization: Albedo Communications I ran across this citation while doing a computer search: ARDILA A; MORENO C Scopolamine intoxication as a model of transient global amnesia. Brain Cogn. 1991 Mar; 15(2): 236-45 In Colombia (South America) during recent decades the administration of scopolamine, extracted from plants belonging to the Datura or Brugmansia genus, has become an important neurologic and toxicologic phenomenon. These extracts have been popularly known as "Burundanga." Chemical characteristics and clinical features of scopolamine intoxication are described. Anterograde amnesia and submissive behavior found in patients intoxicated with scopolamine are analyzed. Burundanga intoxication is related to other toxic phenomena found in different countries and similitudes with transient global amnesia are emphasized. Datura seeds look like brownish hot-pepper or tomato seeds. They are flat or lens-like disks, about 1/8 inch in diameter, with an irregular bulge where the stem-scar is. The intoxication from Datura and other plants in that same group (the Nightshade family, "Solanaceae") is more of a delirium than a psychedelic experience. The intoxication resembles that of a strong dose of Mandrake tea, for instance. Other symptoms would be a dry mouth, a wierd floaty feeling, and muddled thinking. The active substances in Datura-like plants are also quite toxic and have been fatal on occasion. ----------------------------------- ~From: [email protected] (Eli Brandt) ~Subject: Re: datura seeds... ~Date: 30 Sep 91 21:41:48 GMT Organization: Harvey Mudd College, Claremont, CA 91711 _The_Botany_and_Chemistry_of_Hallucinogens_, Schultes and Hofmann, sez that: {\it Datura metel}'s seeds have a total alkaloid content of 0.2 to 0.5 percent, mostly scopolamine. More relevantly, D. inoxia is similar in alkaloid content to D. metel. You could look up the ED and LD for scopolamine and calculate the appropriate mass of seeds. You might want to assume the alkaloid content to be significantly higher than 0.5%, just to have a decent margin. Remember, the LD takes precedence over the ED. :-} I take no responsibility for any gruesome death which may be caused by the above information. Eli Brandt [email protected] https://www.erowid.org/psychoactives/faqs/natural_highs_faq.shtml #### The Natural High Posted on September 23, 2015 at 1:15 PM comments (0) INTRODUCTION The following information was taken without permission from the book _Legal Highs_ by Adam Gottlieb, 1973, Twentieth Century Alchemist, from _The Botany and Chemistry of Hallucinogens_ by Schultes & Hofmann, 2nd Ed. 1980, from _The Audobon Society Field Guide to North American Mushrooms_ by Gary H. Lincoff and Carol Nehring, 1981, Random House, from _Narcotic Plants: Revised and Enlarged_ by William Emboden, 1979, MacMillan Publishing, from various mail-order greenhouse literature, from personal experiences of many people (friends of friends, and fictional characters that exist only in the authors' and editors' imaginations) and (mostly) from alt.drugs. Some sections contain a "References" section if the author of that section felt like going to the trouble; some mention references on the fly in the text, and some are just unreferenced. Some personal correspondance is included too; in this case if I could get the author's consent I included his name/email address; if I could not track down the author, I included the mail anonymously. If the author of a particular piece of mail doesn't want it included, I won't include it (although I may paraphrase it without attribution). I left minimal header information in the stuff that was pulled from the net to give credit where due and to provide follow-up paths (do so at your own risk). I didn't have the time (let alone motivation) to mail everyone whose comments are included here to see if it was alright to include them, but if the info was posted to the net once, I can't see a problem with putting it in a faq. A later version might have more eloquent and concise attributions. Much of the net stuff was edited extensively in that irrelevant info was deleted from specific posts; however, the context and spirit of the remaining information was preserved. The substances listed here are arranged in a fairly straightforward format. If a certain section is missing from a certain substance, it means that I had no information to put in that section or it didn't apply. The substances are ordered alphebetically, sorted according to Botanical Family name, then Genus name, then (if necessary) Species name. This was a completely fascist decision on my part, and I did it only because it was the easiest ordering to maintain. Note that the name given in the heading is a common name and has NOTHING to do with the way the list is ordered. At the moment I haven't got time to organize this stuff anymore than it already is (and that's not much). Hopefully in the future I will find time to organize and index it, and to expand it to include dozens of other natural highs. Until then, this mess will have to do. Spelling errors are numerous and rampant, and I take no responsibility for any of them even tho many of them are undoubtedly mine. A WORD ABOUT MAO INHIBITORS [Erowid Note: The section of the FAQ on MAO Inhibitors contains some inaccuracies. For more complete information about MAOIs, read Erowid's MAOI Vault and seek other sources.] Some of the substances described in this file are MAO inhibitors; this information is provided under the "Interaction precautions" section for the substance in question. MAO stands for MonoAmine Oxidase, an enzyme that breaks down certain amines and renders them ineffective. MAO inhibitors (MAOIs) are substances that interfere with the action of monoamine oxidase, leaving the amines intact. Inhibiting the action of monoamine oxidase can produce a variety of effects, some of which are dangerous. It may be dangerous to combine different MAOIs with each other or to combine them with other chemicals such as strong stimulants (amphetamine, MDMA), SSRIs (Prozac, Paxil, Zoloft, Celexa, Desyrel, etc), and many other pharmaceuticals. If you are taking a prescription drug that is an MAOI, avoid using contraindicated drugs or substances. There are also a number of common foods and beverages which contain amines that are normally broken down by MAO. If you are taking a prescription MAOI, consult your physician to see whether you should avoid any of these. Substances that may interact with certain MAOIs include: sedatives tranquilizers antihistamines alcohol amphetamines (even diet pills) mescaline asarone nutmeg macromerine ephedrine dill oil parsley oil wild fennel oil cocoa coffee (or any substance that contains large amounts of caffeine) aged cheeses any tyrosine-containing food any other MAO inhibitor THIS LIST IS BY NO MEANS COMPLETE OR ALL-INCLUSIVE. COMBINE DRUGS AT YOUR OWN RISK ! HALLUCINOGENIC MUSHROOMS Family: Agaricaceae Genus: Psilocybe Species: baeocystis (Potent Psilocybe) caerulipes (Blue Foot Psilocybe) coprophila (Dung-loving Psilocybe) cubensis (Common Large Psilocybe) cyanescens (Bluing Psilocybe) pelliculosa (Conifer Psilocybe) semilanceata (Liberty Cap) stunzii (Stunz's Blue Legs) Amanita Muscaria (Fly Agaric), Conocybe smithii (Bog Conocybe) and Gymopilus spectabilis (Big Laughing Gym) are among the other mushroom species known to be hallucinogenic. However, Fly Agarics are classified as poisonous, and, according to _The Audobon Society Field Guide to North American Mushrooms_, the Fly Agarics that grow in North America cause "dilerium, raving, and profuse sweating", unlike their hallucinogenic Siberian counterparts. (Perhaps WOSD propaganda, I realize, but worth considering, at least for those of you who don't normally rave...) WARNING: mushrooms should NEVER be ingested unless positively identified to be non-poisonous by a mycologist. Often the only differences between highly toxic mushrooms and edible mushrooms are extremely subtle and require a great deal of training to distinguish. Also, several hallucinogenic varieties have been shown to be toxic to humans in medium to large doses. Usage: Like most natural plant products, psychedelic mushrooms vary considerably in strength due to genetics, growth medium, and other factors. An effective dose of dried psychedelic mushrooms is on the order of 1 gram. This would be on the order of one or two whole mushrooms (best bet is to weigh them and make sure). Because strength varies widely, you should ask other people who have had mushrooms from the same source about the relative strength. For mushrooms from an unknown source, .5 grams of dried mushrooms is probably a decent place to start. 'Shrooms are best taken on an empty stomach. Carlos Castenada describes the effects of a mushroom-based preparation when smoked, and anyone who has taken 'Shrooms would agree that the effects that he describes are much more intense than the effects of reasonable dosages taken orally. Although many people think that Carlos made the whole thing up, it is possible that mushrooms are smokable and that smoked mushrooms might produce a different experience than ingested, because 'Shrooms contain many compounds known as tryptamines (as in dimethyl- tryptamine (DMT)) which are also psychoactive when smoked but not active orally. Other than Carlos, I've never heard of anyone else smoking mushrooms or mushroom products, so I can't vouch for the effects. If you don't like the taste of 'Shrooms, it is also possible to consume a tea made by boiling mushroom fragments in water. The idea here is to sprinkle dried mushroom fragments on water and boil them until they sink, and then filter out the actual 'Shrooms and enjoy the tea. Effects: The effects of psychedelic mushrooms are comparable to those of LSD, but different in a number of ways. For one thing, the trip lasts aproximately 6 hours, about half of what an LSD trip does. Mushrooms also have less stimulant effect than LSD. Mushrooms tend to be more visual than LSD and less auditory. LSD is probably better for enhancing perception of music, although psilocybin does alter the perception of sound (seems to make background noise louder) and like tryptamine- based psychedelics, also tends to induce auditory hallucinations that sound like 'noise'. 'Shrooms do have definite physical effects that are both similar and different to those of LSD. Shrooms tend to cause 'Liquid Breathing', especially before the onset of psychedelic effects. (Like LSD) Shrooms don't cause stomach cramps, but they do seem to cause a headache sometimes. A short term cross tolerance does develop between pscilocybin, mescaline, and LSD, but there appears to be no long term tolerance, except for learned behavior which allows one, for instance, to learn how to talk somewhat coherently despite what psychedelics do to the language centers and short term memory. Another important difference between 'shrooms and LSD is that the onset time of effects from ingestion is MUCH shorter. In the experience of people that I know, the onset of effects is aproximately 30-45 minutes after ingestion, and the transition from physical effects to mild depersonalization to intense hallucination is very short, even in the subjective time of the tripper. There is a period of aproximately one hour where psychedelic effects (visual/auditory hallucination, flickering of visual field, time overlay effect, time distortion, breakdown of linguistic centers, etc.) are VERY intense, and the rest of the trip seems to be more psychological, that is, very little hallucination, mostly depersonalization and time distorsion. This is a very excellent time to spend in a natural environment (your local woods, desert, or savanna) because it tends to produce shamanistic, in touch with nature feelings much better than LSD does. Bad trips are very possible with mushrooms, and are probably very similar to bad trips on acid. If you know or suspect that a tripper is experiencing eyes-open visual hallucinations, you might want to take them to a place where no there are no regular geometric patterns that cover most of the visual field. High dosages of mushrooms seem to affect perception of regular tiled surfaces much more so than irregular surfaces. If possible, suggest to the tripper that you go to a place where there is a featureless floor (say a drab carpet or a concrete floor). It's also good to find a warm place, but always heed to the will of the tripper so long as he doesn't want to do anything stupid like jump off a cliff. See if you can find some mellow music that is pleasing to the tripper (Say, the Grateful Dead or Spyro Gyra) and remember that little things like turning the intensity of light up or down can have a big emotional effect. Be sure to ask about these things. When talking to someone on a bad trip, it often helps to keep changing his train of thought; many people find that this keeps the anxiety at a lower level. The primary rule is to watch the reaction of the tripper to what you do, and take his needs and fears into consideration. Keep him with people that he trusts and try to remove any people that he doesn't trust. Of course, this advice is valid for hallucinogens in general. History: The practice of growing mushrooms dates back to around 100 B.C., and is based partly upon the discovery of minature mushroom stones found near Gautemala City. Other finds further north also indicate an extensive mushroom cult in the early civilizations. When Cortez arrived in Central America, he found the natives using mushrooms as a sacrament. They called them "teonanacatl", or "God's Flesh." The Spainards reacted strongly to the mushrooms, giving written accounts of the loathsome mushroom rituals that "provoke lust... cause not death, but madness... and bring before the eyes wars and the likeness of demons." Teonanacatl was then banned from the church as contributing to pagan behavior and idolitry. The only tribe definately known to have consumed the mushrooms, however, is the Chichimecas. Six tribes consume mushrooms today in Oaxaca: Mazatecs, Chinantecs, Chatinos, Zapotecs, Mixtecs, and Mijes. It has recently been suggested that mushroom use by the Chol and Lacandon Maya may be a vestage from the earlier Mayans that disappeared for a time, and then was readopted. Present day ritual among them Mazatec includes many rituals from the Catholic Church. Even though the Catholics tried to eliminate the detested fungi, the Indians still chant saints of the church and incorporate litanies, which are undoubtedly post-Christian elements of their ritual. Interaction precautions: I wouldn't recomend using them with alcohol or other depressants. Also, people who are being medicated for a psychological conditions, particularly with MAO-inhibitor class drugs probably DON'T want to use 'Shrooms or any psychedelic because MAO-inhibitors tend to interact seriously with most psychoactive compounds. Active Ingredients: The primary active components of 'Shrooms are psilocybin and psilocin, which also is an immediate metabolite of psilocybin. There are a whole family of other tryptamine-related substances in 'Shrooms but most of them are not active when eaten. For further reading: Several books are available on the subject of growing mushrooms, which is a rather complex task because it involves maintaining a sterile environment and quite a bit of biology lab skills. The best book on the subject is "Psilocybin: The magic mushroom grower's guide" by Oss and Oeric from And/Or press. Spores are available by mail order; check High Times magazine. These are legal to sell because they contain no psychoactive compounds. Spores can also be obtained by taking a cap print from mushrooms that you obtain from another source, like the wild. ======================================== [some interesting info on Fly Agarics follows. Note that these are much more poisonous than psilocybe varieties, the info above does not necessarily apply to them, and the info below does not necessarily apply to psilocybes. --ED] ~From: [email protected] (David A. Honig) ~Subject: Re: mail order botanicals ~Date: 11 Nov 91 22:00:34 GMT Organization: UC Irvine Department of ICS In article <[email protected]> [email protected] (Eli Brandt) writes: >>anyone know the legality of fly agaric? anyone have any experience with >>it? > >I'm sure it's legal. _Merck's_ sez that neither ibotenic acid and muscarine >were "controlled substances" (what a *dumb* term) as of '76; was there maybe >a "Toadstool Regulation Act" I missed? Anyway, you could call it "soma" and >have a real good case for religious use... > >I don't know what the dose would be. The LD-50 iv in mice for muscarine is >0.23 mg/kg; ibotenic acid is (for mice/rats) 15/42 iv and 38/129 oral. I'd >be careful with anything with such a wide difference in toxicity between >fairly similar species. I vaguely recall that muscarine is only found in >the younger shrooms; it looks like you'd want to avoid them, unless it's >also responsible for most of the interesting effects. > >>ecni > > Eli [email protected] I obtained some dried Amanita via an unnamed source. They make you puke (what else is new) and go into a dreamy state. Not "psychedelic" or terribly euphoric. A friend (who is a botanist) has tried fresh ones, reports that they're better. IMHO, they're not worth your time unless your into ethnopsychopharmacology. -- David A. Honig MESCALINE-BEARING CACTI Family: Cactaceae Genus: Gymnocalycium Species: gibbosum: Native to Argentina leeanum: Native to Argentina, Uruquay Genus: Islaya Species: minor: Native to South Peru Genus: Lophophora Species: diffusa (Peyote): Native to Mexico williamsii (Peyote, Mescal,Chaute etc.): the classic Peyote, grows in north central Mexico and south Texas. Genus: Opuntia Species: imbricata: Native to S-W USA to Central Mexico. spinosior: Native to Arizona, New Mexico, Northern Mexico. Genus: Pelecyphora Species: aselliformis (Peyotillo, Peyote meco): Native to San Luis Potosi, Mexico Genus: Pereskia Species: corrugata tampicana: Native to Tampico, Mexico. Genus: Pereskiopsis Species: scandens: Native to Yucatan, Mexico. Genus: Stetsonia Species: coryne: Native to Northwestern Argentina. Genus: Trichocereus Species: cuzcoensis: Native to Cuzco, Peru. fulvianus: Native to Chile. macrogonus: Native to South America. pachanoi (San Pedro, Giganton): Native to Peru, Equador. peruvianus (Peruvian Fence Post): Native to Peru. scopulicola taquimbalensis: Native to Bolivia. terscheckii (Cardon grande): Native to Northwestern Argentina. validus: Native to Bolivia. werdermannianus: Native to Tupiza & Charcoma, Bolivia. Description: Trichocerei are columnar, branched or candelabra like cacti, which usually grow very fast. Cereus is a different genus, whose members haven't been found to contain mescaline. Cultivation: (from seed) Sow the seeds an inch apart on the surface of sterilized, moist, sifted cactus mix. The pH should be 4.5-6.5. Cover the tray or pot with an airtight plastic bag. Place in bright but indirect light for 12 hours a day at less than 30 degrees centigrade. Don't let the temperature get too high, and check to make sure the soil surface is moist, but not too wet. A fungicide may be needed. Cactus seeds will generally germinate in 1-3 weeks. When the seedlings are about 2 cm tall (60-90 days for fast-growing species) transplant them to individual pots. Handle them very cautiously and use moist soil with pH 4.5-6.5 in the new pot. A good soil mix is 1/3 normal flower soil, 1/3 peat and 1/3 coarse sand or gravel. If you're growing a Trichocereus, water once a week with a concentration of a flower fertilizer normally used for flowering plants. Don't use standard plant fertilizers, as they contain too much nitrogen. Bright light is needed 12-18 hours a day, and the temperature should be 25-35 'C. The easiest way of propagation is taking cuttings. Cut the mother plant with a clean and sharp knife leaving 5-10 cm of it above ground. Cut back slightly the edges of the cut to ensure that the new roots grow downward. Place the cutting in vertical position to dry for 2 weeks to a month depending on the size of the cutting. The compost where they are placed after this should be very slightly moist, not wet. For more information about growing cacti read e.g. Cullman, B|tz & Gr|ner 1984: Encyclopedia of Cacti, Alphabooks A&C Black, ISBN 0-906670-37-3. Usage: An easy method is to chop a cactus to small pieces, dry the pieces and boil in water with plenty of lemon juice until there's not much liquid left. To reduce nausea you should drink the liquid slowly over a half an hour while avoiding excessive movement. For the same reason don't eat solid food on the day of ingestion. A normal dose of mescaline sulfate is 200-400 mg, which probably corresponds to 10-25 g of dry Peyote or T. peruvianus, or 50-200 g of fresh San Pedro. Potency varies, so try a small dose first. It's also possible to extract mescaline from cacti. Effects: Mescaline produces a trip very similar to LSD lasting about 12 hours. The effects take a bit longer to come on. Mescaline is cross-tolerant with LSD, psilocin and other psychedelics. A common side-effect is nausea, which is worse when ingesting Peyote than other cacti because of the extra alkaloids found in Peyote. If you manage to hold the cactus in your stomach for 15-30 minutes before throwing it up, you can still have a fine and nausea-free trip. Mescaline does not cause chromosome damage in normal doses. History: Peyote has been in use in America for at least 2000 years. The Spanish conquistadors didn't like the use of drug plants by the Indians, and catholic clerics declared officially in 1620 that since the use of peyote was the work of the devil, all Christians were prohibited from using it. The active prohibition of peyote still persists. A religious manual written in 1760 presented the following series of questions for the penitent: Have you ever killed anyone? How many have you murdered? Have you eaten the flesh of man? Have you eaten peyote? Peyote was used for several centuries in Mexico before peyotism spread into the US in the second half of the 19th century. Today it's legal for the members of the Native American Church to use Peyote in several states. The San Pedro cactus has been used by Peruvian folk healers to combat the supernatural elements that cause diseases. Active Constituents (of some cacti) Botanical name mescaline other alkaloids Genus species Lophophora williamsii ~1% dry Ann,And,Ant,Annd,H,L,P,T Trichocereus peruvianus 0.8% dry T pachanoi 0.1% wet Annd,H,T bridgesii 0.1% wet T validus 0.1% wet macrogonus <0.05% wet T terschecki <0.05% wet Ann werdermann <0.05% wet T taquimbal <0.05% wet H cuzcoensis <0.01% wet T Stetsonia coryne <0.01% wet T Pelecyphora aselliformis 0.00002% And,H,P Mescaline content is probably given as hydrochloride, 128 mg mescaline HCl = 200 mg mescaline sulfate. Doses of mescaline are usually measured as sulfate. "Dry" means dry weight, "wet" fresh weight. Ann = anhalonine causes paralysis followed by hyperexitability in rabbits And = anhalodine stimulant, not potent Annd = anhalonidine similar to pellotine H = hordenine L = lophophorine causes convulsions, similar to strychnine P = pellotine causes drowsiness and slowing of heartbeat T = tyramine References: Agurell, S. 1969: Cactaceae alkaloids I. Lloydia 32,2 Agurell, S. 1971: Cactaceae alkaloids X. Alkaloids of Trichocereus Species and Some Other Cacti. Lloydia 34,2 Anderson, E.F. 1980: Peyote - the Divine Cactus. The University of Arizona Press, ISBN 0-8165-0613-2. Pardanani, J.H. & McLaughlin, J.L. 1977: Cactus Alkaloids XXXVI. Mescaline and Related Compounds from Trichocereus Peruvianus. Lloydia 40,6 LETTUCE OPIUM Family: Compositae Genus: Lactuca Species: virosa Usage: Materials are extracted in a juicer and eaten fresh or dried and smoked. Effects: Mild sedative effect similar to opium. Very, very mild buzz, almost unnoticable. Not worth the hassle of obtaining from the plant, and not worth the cost of buying refined herb. Watch out for "incense" concoctions sold in head shops and through mail order that claim to have alternative uses. These are usually worthless, overpriced Lettuce opium preparations. History: Formerly used in medicine as an opium substitute. Active Constituents: lactucin, lactucerol (taraxaxterol), lactucic acid FROM THE NET: ~From: [email protected] (Petrus Pennanen) ~Subject: Re: lactucarium ~Date: 8 Jul 91 20:24:16 GMT Organization: University of Helsinki Ronald Siegel writes in _Intoxication_: "In each major category of intoxicant used by our species, there appear to be one or two drug plants that researchers have noted are more controllable, hence safer, than all the other plants or synthetics in that category. [...] Among the narcotics, which include opium and its derivatives, there is lactucarium, the smokable extract derived from Lactuca Virosa." "Consider the case of lactucarium, which never caught on as a modern opium substitute because either so mild or so inconsistent in quality that people thought it was a fake. Lactucarium smells like opium and tastes just as bitter. When smoked or swallowed, it is so mildly intoxicating it remains legal. There are no visions like the ones De Quincey had from eating opium, but the euphoria and dreamy intoxication last slightly longer. Although lactucarium is structurally unrelated to the opiates, it will still soothe irritating cough, ease minor pains, and help induce sleep, hence its more common name of 'lettuce opium.' The history of lettuce opium in America paralleled that of coca tea. Both drugs enjoyed widespread medical use in nineteenth century and brief periods of experimental nonmedical use in more recent years. In the mid-1970s, smokable extracts of lettuce opium were marketed throughout the United States under such brand names as L'Opium and Lettucene. 'Buy your lettuce before they make it illegal!' announced the national ads. Hundreds of thousands did exactly that when the craze peaked in the late 1970s. There was not a single case of toxicity or dependency. But there was a lot of competition as different manufacturers rushed to get a share of the new market. Most of these newer brands were made from ordinary garden lettuce, which lacked the intoxicating lactucarium. Subsequently, sales fell, some suppliers of real lactucarium went out of business, and the fad all but disappeared. While lactucarium is still available, heroin users are not rushing to buy it and probably never will: it's simply too weak." Petrus Pennanen [email protected] HAWAIIAN BABY WOODROSE SEEDS Family: Convolvulaceae Genus: Argyreia Species: nervosa Usage: seed pods contain 4-6 seeds. Seeds are removed from pods and fungus-like coating is scraped or flamed off (author recommends scaping as much as possible and flaming the rest, as the coating can be thick and it's easy to end up turning the whole seed into a chunk of carbon if you just flame it). 4-8 seeds are chewed on an empty stomach (to minimize nausea). Seeds sold commercially are generally already removed from the pods. The seeds themselves resemble small chocolate chips, but are hard as rocks and have the coating mentioned above. Nausea can be lessened by ingesting one or two dramamine 30 minutes to one hour before ingesting the HBW seeds. More dramamine can be taken after the nausea sets in, however, dramamine can be a DANGEROUS drug in high doses and its synergistic effects with LSA are unknown. Exceeding the recommended dosage given on the dramamine box is probably a pretty stupid thing to do under any circumstances. If dramamine is not used, inducing vomiting when nausea starts will provide relief but effects will continue. You can also grind and soak the seeds in water, then strain them out and drink the water. If ground seeds are used, make sure they are fresh ground. Effects: LSD-like effects, but less intense, with less visuals. Trip lasts 6-8 hours; tranquil feelings may last additional 12 hours. Sleep is deep and refreshing after trip, however some users may experience a hangover characterized by blurred vision, vertigo, and physical intertia. History: Used by the poorer Hawaiians for a high. Shipping of these seeds became popular, as did a great controversy over the propriety of world-wide distribution. Interaction precautions: same as for Morning Glory seeds. Active Constituents: D-lysergic Acid Amide and related compounds. NOTE: net wisdom has it that extracting LSA from woodrose/mg seeds is an inefficient way to obtain a precursor for LSD. Note: Hawaiian Large woodrose seeds supposedly have the same effect. Dosage is identical. MORNING GLORY SEEDS Family: Convolvulaceae Genus: Ipomoea Species: arborescens (Quauhzahautl): tree grows to 15' high. Native to Mexico. carnea (fistolusa): bush with pink flowers native to Ecuador. costata: native to australia. leptophylia: wine colored flowers 3" across. Huge edible roots. meulleri: native to australia. murucoides: (Pajaro bobo) native to oaxca. purpurea: native to mexico, common throughout N. America as an ornamental. violacea (Tlitliltzin): sacred Mayan morning glory. Widely used for its psychoactive effects in the Heavenly blue, Pearly Gates, Flying Suacers and Wedding Bells strains. Usage: 5-10 grams of seeds can be ingested as follows: thoroughly chew and swallow grind and soak in water for 1/2 hour, strain and drink sprout by soaking in water for 3-4 days (change water often), after which the white mushy part is removed from the shell and eaten. This is probably the best method for avoiding side effects, although I have I have reason to believe sprouting the seeds lessens their effectiveness. Most commercially available Morning glory seeds are treated with chemicals to thwart consumption. Seeds are also sometimes treated with Methyl mercury to prevent spoilage. Chemically treated seeds can cause severe nausea, vomiting and diarrhea. Effects: LSD like experience lasting about 6 hours, but with less hallucinogenic effects. Nausea is common even with untreated seeds. Less anxiety, less intensity than LSD in normal doses. Nausea can be lessened by ingesting one or two dramamine 30 minutes to one hour before ingesting the MG seeds. More dramamine can be taken after the nausea sets in, however, dramamine can be a DANGEROUS drug in high doses and its synergistic effects with LSA are unknown. Exceeding the recommended dosage given on the dramamine box is probably a pretty stupid thing to do under any circumstances. History: The Zapotecs used ipomoea violacea by grinding the seeds up and wrapping them in a meal cloth. They would then soak it in cold water and would find out information about the illness of a patient, a troublemaker among the people, or the location of a lost object. Interaction precautions: should not be taken by people with a history of liver disorders or hepatitis. Should not be taken by pregnant women. Active Constituents: D-lysergic acid amide NATIVE SOUTH AMERICAN INTOXICANTS Family: Acanthaceae Genus: Justicia Species: pectoralis (var. stenophylla) Usage: Waikas of Orinoco headwaters in Venezuela add dried and pulverized leaves of this herb to their Virola-snuff. Effects: Unknown Active Constituents: Intensely aromatic smelling leaves probably contain tryptamines. Plants are available from ...Of the jungle for$35.
-------------------------
Family:
Leguminosae
Genus:
Anadenanthera (Piptadenia)
species:
peregrina
colubrina
Usage:
Black beans from these trees are toasted, pulverized and mixed with ashes or calcined shells to make psychedelic snuff called yopo by Indians in Orinoco basin in Colombia, Venezuela and possibly in southern part of Brasilian Amazon. Yopo is blown into the nostrils through bamboo tubes or snuffed by birdbone tubes. The trees grow in open plain areas, and leaves, bark and seeds contain DMT, 5-MeO-DMT and related compounds (Schultes 1976,1977; Pachter et al. 1959).
Active Constituents: DMT, 5-MeO-DMT and related compounds.
--------------------------
Family:
Leguminosae
Genus:
Mimosa
Species:
tenuiflora (== hostilis) "tepescohuite"
verrucosa
General:
The roots of M. hostilis, which is *not* the common houseplant M. pudica ("sensitive plant"), contain 0.57% DMT and are used by Indians of Pernambuso State in Brazil as part of their Yurema cult (Pachter et al. 1959, Schultes 1977, Meckes-Lozoya et al. 1990). Bark of M. verrucosa also contains DMT (Smith 1977).
Active Constituents: DMT
---------------------------
Family:
Malpighiaceae
Genus:
Banisteriopsis
Species:
rusbyana
argentea
Usage:
Natives of western Amazon add DMT-containing leaves of the vine B. rusbyana to a drink made from B. caapi, which contains beta-carbolines harmine and harmaline, to heighten and lengthen the visions (Schultes 1977, Smith 1977).
Active Constituents:
leaves contain DMT.
---------------------------
Family:
Myristicaceae
Genus:
Virola
Species:
calophylla
calophylloidea
rufula
sebifera
theiodora
Usage:
The bark resin of these trees is used to prepare hallucinogenic snuffs in northwestern Brazil by boiling, drying and pulverizing it. Sometimes leaves of a Justicia are added.
Amazonian Colombia natives roll small pellets of boiled resin in a evaporated filtrate of bark ashes of Gustavia Poeppigiana and ingest them to bring on a rapid intoxication (Smith 1977, Schultes 1977).
Effects:
The snuff acts rapidly and violently, "effects include excitement, numbness of the limbs, twitching of facial muscles, nausea, hallucinations, and finally a deep sleep; macroscopia is frequent and enters into Waika beliefs about the spirits resident in the drug."
Active Constituents:
Snuffs made from V. theiodora bark contain up to 11% 5-MeO-DMT and DMT. Leaves, roots and flowers also contain DMT.
-------------------------
Family:
Rubiaceae
Genus:
Psychotria
Species:
viridis (psychotriaefolia)
Usage:
Psychotria leaves are added to a hallucinogenic drink prepared from Banisteriopsis caapi and B. rusbyana (which contain beta-carbolines) to strengthen and lengthen the effects in western Amazon.
Active Constituents:
P. viridis contains DMT (Schultes 1977).
5 seeds $10 from ...Of the jungle, leaves are also available. References: Meckes-Lozoya, M., Lozoya, X., Marles, R.J., Soucy-Breau, C., Sen, A., Arnason, J.T. 1990. N,N-dimethyltryptamine alkaloid in Mimosa tenuiflora bark (tepescohuite). Arch. Invest. Med. Mex. 21(2) 175-7 Pachter, I.J, Zacharias, D.E & Ribeir, O. 1959. Indole Alkaloids of Acer saccharinum (the Silever Maple), Dictyoloma incanescens, Piptadenia colubrina, and Mimosa hostilis. J Org Chem 24 1285-7 Schultes, R.E. 1976. Indole Alkaloids in Plant Hallucinogens. J of Psychedelic Drugs Vol 8 No 1 7-25. Schultes, R.E. 1977. The Botanical and Chemical Distribution of Hallucinogens. J of Psychedelic Drugs Vol 9 No 3 247-263 Smith, T.A. 1977. Review: Tryptamine and Related Compounds in Plants. Phytochemistry Vol 16 171-175. NUTMEG Family: Myristicaceae Genus: Myristica Species: fragrans Usage: 5-20 grams of ground nutmeg is ingested. Fresh ground is best. Can also be taken in a "space paste" concoction (see below). Space paste is difficult/expensive to make and tastes like shit; however, it may actually decrease the side effects. Effects: Possible nausea during first hour; may cause vomiting or diarrhea in isolated cases. Takes anywhere from one to five hours for effects to set in. Then expect severe cottonmouth, flushing of skin, severely bloodshot eyes, dilated pupils. Personally I compare it to a very, very heavy hash buzz. "Intense sedation". Impaired speech and motor functions. Hallucinations uncommon in average (5-10 gm) doses. Generally followed by long, deep, almost coma-like sleep (expect 16 hours of sleep afterward) and feelings of lethargy after sleep. May cause constipation, water retention. Safrole is carcinogenic and toxic to the liver. History: Nutmeg was a very important trade item in the 15th and 16th centuries. It was a precious commodity due to the enormous medicinal properties of its seeds. Slaves on the ships bringing nutmeg to Europe got in trouble for eating part of the cargo. They knew that a few large kernels of nutmeg would bring them a pleasant, euphoric feeling, and relieved their weariness and pain. Nutmeg was even used when the feeble King Charles II almost died of a clot or hemorrhage. His death a few days later did nothing to detract from its useful reputation. Rumor spread through London that Nutmegs could act as an abortifacient. The ladies who procured abortions from nutmeg were called "nutmeg ladies." Interaction precautions: MAO inhibitor Active Constituents: Methylenedioxy-substituted compounds: myristicin (non-amine precursor of 3-methoxy-4,5-methylenedioxyamphetamine [M-MDA]) elemicin, and safrole. From The Net: ~From: [email protected] (Michael G. Goldsman) ~Subject: Nutmeg Story ~Date: 11 Aug 91 23:56:07 GMT Organization: Georgia Institute of Technology Friday, a "friend" of mine decided to see what all the talk about nutmeg was all about... here's what happened... 8:15 -- "he" took 1 tablespoon of ground nutmeg... 9:15 -- "he" took 1 more tablespoon of ground nutmeg... 11:15 -- "he" took still 1 more tablespoon of ground nutmeg... As of now, "he" didn't feel anything... "He" got the beginnings of a buzz at about 12:30 which gradually increased in intensity... By 3 am or so, he compared it to moderate cannibis buzz It peaked at at 5 am, and he then went to sleep. The effects continued through saturday afternoon and night, though not as intense as late friday night (or saturday morning technically). By sunday morning, the effects were totally gone. The main point is, that except for lots of drowsiness, my "friend" never suffered any of the ill effects that people have described ... (such as nausea and headaches) It was very comprable to a medium marijuana buzz. There were no hallucinations, but maybe a larger dose is needed for this. Next week my "friend" will go for 5 tablespons over the course of a few hours.. Will he live to describe the experience?? ================================== ~From: [email protected] (Jeffery Tye) ~Subject: Space paste! (was Re: nutmeg as a hallucinogen) ~Date: Sat, 29 Jun 91 01:59:09 GMT Organization: The Scantily Clad Orangutans, Inc. 'Space Paste' heart chakra, but it's a legal high that will get you pleasantly buzzed. :-) DON NOT OMIT ANY INGREDIENTS. Trust me. 4 parts nutmeg (ground from whole nutmeg) 4 parts almonds (soak almonds overnight and rinse) 4 parts *raw* pistachios 2 parts cinnamon 1 part cumin 1 part tarragon 1 part oregano 1 part basil 1 part tumeric 1/2 part cayenne pepper 1/2 part black pepper To taste: Maple Syrup One part equals 1/4 cup. [if you want to make enough for about 500 people, that is. Try 1 part=1 tablespoon--ed] - Use only whole nutmeg. Not pre-ground. - Grind up all ingredients with a spice grinder or food processor. - Mix in Maple syrup until consistency of paste. - Do not omit any ingredient, or it will NOT work. Okay, you've gone this far, time to enjoy. The strong at heart will spread some on toast. I like it blended in milk. It has a real strong taste, so it's best to put it in the milk, fire up the blender, pour it into a glass and chug it down in one gulp. Start with two tablespoons. Effects begin in two hours. I've known brave souls who take a cup at a time. Maybe that's why they disappear for a couple of days. ================================= ~Date: Wed, 2 Oct 91 09:57:26 MDT ~From: ~Subject: More on Nutmeg Story Begin forwarded message: Well, I am recovering from a horrible experience. Tuesday night about 10:30pm, I took 5 tablespoons of Nutmeg. I am still hungover, almost 2 days later. I got the initial stimulation, euphoria, but not much more than what one gets around 2 tablespoons. That was fine and dandy. I fell asleep at about 1:30am, with nothing psychedelic occurring yet. I woke up at 3 am spinning, like I was drunk. I awoke again at 9am, and got out of bed. I had to: thirsty as hell, no saliva. I had wicked troubles walking, far too dizzy and -out-of-it-. Just like I had no control over my body. Also, any movement that I did make nauseated me. By 9:30 I had my drink of water, and I collapsed on the kitchen floor, sleeping until noon. I thought that I would have something to eat, at that time, but was far too dizzy still to do anything. By this time I was in a panic, thinking that I had comitted suicide, etc.etc. My body felt like it was melding with the floor; I also felt that my whole body was made of vomit. Quite odd. I crawled (literally) up to bed again and slept like a stone until 6pm. I managed to eat some stuff. I could stand for 30 seconds at a time, by this time. I watched a movie, dozing on and off. I looked at myself in a mirror: horrible sight, very red sunken eyes etc.etc. Went to bed and awoke this morning at 11:30am. Awoke with something like a horrible hangover. I feel like I have had a wicked flu yesterday and today. Besides some odd physical sensations and perceptions, even this dosage was not overtly hallucinogenic. I did not experience any colour / visual perception changes this time, like at the lower dosage. Perhaps I was just too sleepy to notice. This experience was just downright gross. I think I have given up experimenting with Nutmeg (and Mace) [ even though I really like the taste of the stuff. Some people complain they can't get the stuff down --- they must not be using fresh stuff]. It was really an offputting experience. Tonight, I think I am just going to hunt down something illegal but safer. YOHIMBE BARK Family: Rubiaceae Genus: Corynanthe Species: yohimbe Usage: 6-10 teaspoons of shaved bark are boiled 10 minutes in 1 pt. water, strained and sipped slowly. Addition of 500 mg of vitamin C per cup makes it take effect more quickly and potently (probably by forming easily assimilated ascorbates of the alkaloids). Bark can also be smoked. Yohimbine hydrochloride, a refined powder version, can also be snuffed. Also available at many health/herb stores is a liquid extract. Effects: Called "the most potent aphrodisiac known" and "the only true aphrodisiac". Whether aphrodisiacs exist outside of mythology or not is a topic for debate, as is the definition of "aphrodisiac". Anyway, first effects after 30 minutes (sooner with vitamin C) consist of warm, pleasant spinal shivers, followed by psychic stimulation, heightening of emotional and sexual feelings, mild perceptual changes without hallucinations, sometimes spontaneous erections. Some experience nausea during first 30 minutes. Sexual activity is especially pleasurable. According to one source "Bantu orgies have been known to last over a week" [Ed: don't they get hungry?]. Total experience lasts 2-4 hours, however, several experiences lasting up to 24 hours have been reported. Aftereffects include pleasant, relaxed feelings with no hangover, but difficulty sleeping for a few hours (probably largely due to the increased mental activity). Since they sell the stuff in health food stores and I'm not sure what it's legitimate uses are, I'm willing to admit that I've tried it. My experience was worth repeating. This of course constitutes no endorsement on my part of illegal or legal drugs or of the use of yohimbe for any reason at all. I ground about 7 teaspoons of shaved bark in a spice grinder (fresh grinding seems to help with release of the active ingredients) and then boiled it in a pint of water for about 10 minutes. The stuff absorbs a lot of water. Also, when freshly ground, you get some FINE FINE FINE particles. It took me a good 15 minutes to filter the stuff out through coffee filters (had to use a bunch of filters cuz it clogged them up so bad). The resulting brew was one of the top three worst things I've ever tasted in my life (the other two being calamus root and an abortive attempt at a kava kava concoction). It tasted kind of like bile. You can kill the taste if you put enough honey in the tea, but the aftertaste never goes away. As soon as you swallow it creeps up your throat; really gross. The fact that the stuff should be sipped slowly makes this even worse. I would recommend finding a REAL strong chaser, like pure lemon juice or maybe a mint leaf--something that obliterates all other taste in your mouth when you eat/drink/chew it, yet is tolerably pleasant tasting. I would swig/chew this chaser after every sip of yohimbe tea. WARNING: The active ingredients in yohimbe are mild MAO inhibitors. [see MAO Inhibitors above] Anyway, I took the tea with vitamin C. About 20 minutes after I got done drinking it I felt some mild nausea (more in my throat than in my stomach), some mellow trippy effects (just mostly weird thoughts and vivid mental images--nothing near a hallucination, no LSD-like mind racing), also had some speedy effects (like being on 500 mg of caffeine--jitters, etc) and started getting a little "pressure" in the groinal region. To make a long story short, the nausea was a bummer, and sex was incredible. Yohimbe completely changes the meaning of the word "orgasm" for men, anyway. I have no idea what a woman's reaction to it would be. The sexual effects lasted about 4 hours (only cuz I was getting tired :^); the speedy effects decreased earlier than that, but I couldn't sleep at all that night (even when I was ready to), and I'm sure it was because of the yohimbe. I also recently tried the yohimbe extract that they sell in health food stores. The stuff costs about$7/oz. It comes in one ounce bottles with screw-on eye-dropper caps. Recommended dose on the bottle is 3-20 drops up to three times a day. First time I tried it I took 35 drops with absolutely no effects. Recently, I took 100 drops mixed in orange juice. The stuff is tasteless in minute quantities, but at 100 drops/~8 oz. of OJ, it added a mildly bitter taste. Not too bad, tho--1000x better than the tea. Anyway, it didn't do anything, so I took another 50 drops, then another 50, and still no effects whatsoever. I wonder if the extract is even active.
I would advise yohimbe experimenters to use the tea form, and start out with 4 or five teaspoons of fresh ground bark, as the effects of 7 teaspoons were quite pronounced in me, and I am a 200 lb. male with a high tolerance for everything.
History:
Interaction precautions: MAO inhibitor.
Active Constituents: Yohimbine, yohimbiline, ajmaline. (Note that yohimBE is the plant; yohimBINE is one of the chemical principles found in the plant.)
FROM THE NET:
~From: [email protected] (Steve Dyer)
~Subject: Re: Yohimbine bark
~Date: 18 Jul 91 02:17:32 GMT
Organization: S.P. Dyer Computer Consulting, Cambridge MA
Ecni Asked:
>Anyone care to enlighten us yohimbine-illiterate readers what yohimbine
>bark is and what it does?
Yohimbine is the primary alkaloid found in yohimbine bark. It is an
alpha-2-adrenergic antagonist. It blocks presynaptic inhibitory
synapses, meaning that it tends to increase central and peripheral
adrenergic activity. It tends to cause nervousness and increases blood
pressure. It also seems to be effective in some cases of impotence.
Steve Dyer
[email protected] aka {ima,harvard,rayssd,linus,m2c}!spdcc!dyer
[email protected]
DATURA
Family:
Solanaceae
Genus:
Datura
Species:
fastuosa: large shrub with white flowers
inoxia (Don Juan's Datura): native to mexico
metel: native to India.
sanguinea (Eagle Datura, Tonga): Native to S. America.
stramonium (Jimson Weed): Dangerous hallucinogen widespread in temperate regions.
Other species: tatula, brugmansia, candida, suaveolens, arborea, aurea, dolichocarpa, vulcanicola, discolor
Usage:
Leaves are sometimes smoked. Small amount of seed can be pulverized and added to drinks as in the Algonquin ritual.
Effects:
described as "delerium". Leaves are hallucinogenic and hypnotic. Seeds cause mental confusion and delirium followed by deep sleep with colorful hallucinations. Excessive amounts are toxic. May cause blacking out and severe headaches. Yaqui indian brujos say it causes insanity. THIS SUBSTANCE IS GENERALLY CONSIDERED DANGEROUS.
History:
discolor (Desert Thornapple): used by hopi shamans for divination.
inoxia: "Don Juan's Datura" is used in it's native mexico by Yaqui bruhos for divination
metel: Used by the Thuggee cult in it's native India to drug sacrificial victims to Kali.
sanguinea (Eagle Datura, Tonga): Used by Aztecs in the Temple of the Sun. Peruvian natives believe it allows them to communicate with departed souls.
stramonium (Jimson Weed): Dangerous hallucinogen widespread in temperate regions. Used by Algonquins in ritual drink called "Wysoccan" to introduce boys to manhood.
Active Constituents:
Scopolamine, atropine, hyoscyamine and other tropanes.
"Hyoscyamine and scopolamine possess specific anticholinergic, antispasmodic activity and elicit some central nervous effects as well. These effects usually consist of stimulation at low doses, depression in higher toxic doses. ... Intoxication with atropine or hyoscyamine is characterized by psychic excitation often combined with panic and hallucination. Scopolamine was found to produce a state of excitement followed by a kind of narcosis in which, in the transition state between consciousness and sleep, hallucinations sometimes occur (Heimann, 1952). These effects explain the addition of belladonna and other solanaceous plants as ingredients of magic brews in medieval Europe and of sacred medicines by the Indians of Mexico and South America."
(Schultes and Hoffman, 1980)
NOTE:
Family Solanaceae is the potato family (did you know potatoes have a lower LD50 than marijuana? It's true). Many members of this family contain tropanes and have a history of ritualistic use. Other commonly-used members are the Mandrake (Mandragora officinarum), Belladonna (a.k.a. deadly nightshade) (Atropa belladonna), Thornapple (Datura inoxia), Henbane (Hyoscyamus niger), and Iochroma. All these substances will be covered in more detail in a future version of this faq.
Kuthmithi (Withania somnifera) is one member of the Potato family that does not appear to contain active amounts of tropanes and is generally considered safe for use as a sedative.
FROM THE NET:
~From: [email protected] (Gerald Bryan (Denver))
~Subject: Re: Shrooms, Datura etc
~Date: 29 Aug 91 16:43:51 GMT
In article <[email protected]> [email protected] (Fie
nd) writes:
> How many people have lasting physical damage from Datura?
I know one person who has used Datura. She was an experienced drug user at
the time. She said it gave her tremendous visions, but it took her a
year before she felt that her eyesight was back to normal. She only used it
once.
Two years ago, there was a story in the local paper about some college
students in Boulder who walked buck naked into a police station, totally
out of it. They had apparently consumed some datura (on purpose) up in
the mountains.
===============================
~From: [email protected] (marsthom)
~Subject: BADUNGA & MORNING GLORY SEEDS
~Date: 25 Sep 91 21:32:50 GMT
Organization: Albedo Communications
I ran across this citation while doing a computer search:
ARDILA A; MORENO C
Scopolamine intoxication as a model of transient global amnesia.
Brain Cogn. 1991 Mar; 15(2): 236-45
In Colombia (South America) during recent decades the administration of
scopolamine, extracted from plants belonging to the Datura or Brugmansia
genus, has become an important neurologic and toxicologic phenomenon.
These extracts have been popularly known as "Burundanga." Chemical
characteristics and clinical features of scopolamine intoxication are
described. Anterograde amnesia and submissive behavior found in patients
intoxicated with scopolamine are analyzed. Burundanga intoxication is
related to other toxic phenomena found in different countries and
similitudes with transient global amnesia are emphasized.
Datura seeds look like brownish hot-pepper or tomato seeds. They are flat
or lens-like disks, about 1/8 inch in diameter, with an irregular bulge
where the stem-scar is. The intoxication from Datura and other plants in
that same group (the Nightshade family, "Solanaceae") is more of a delirium
than a psychedelic experience. The intoxication resembles that of a strong
dose of Mandrake tea, for instance. Other symptoms would be a dry mouth,
a wierd floaty feeling, and muddled thinking. The active substances in
Datura-like plants are also quite toxic and have been fatal on occasion.
-----------------------------------
~From: [email protected] (Eli Brandt)
~Subject: Re: datura seeds...
~Date: 30 Sep 91 21:41:48 GMT
Organization: Harvey Mudd College, Claremont, CA 91711
_The_Botany_and_Chemistry_of_Hallucinogens_, Schultes and Hofmann, sez that:
{\it Datura metel}'s seeds have a total alkaloid content of 0.2 to 0.5
percent, mostly scopolamine. More relevantly, D. inoxia is similar
in alkaloid content to D. metel. You could look up the ED and LD for
scopolamine and calculate the appropriate mass of seeds. You might want
to assume the alkaloid content to be significantly higher than 0.5%, just
to have a decent margin. Remember, the LD takes precedence over the ED. :-}
I take no responsibility for any gruesome death which may be caused by the
above information.
Eli Brandt [email protected]
www.erowid.org/psychoactives/faqs/natural_highs_faq.shtml
#### Psychoactive Plants & Fungi
Posted on September 23, 2015 at 1:10 PM comments (0)
Plants listed in this section are those which have been used by humans for their mind- or emotion-altering properties. These plants range from the common to the extremely uncommon and include plants with a long history of use as well as those with little to no track record.
COMMON NAME GENUS / SPECIES NATIVE TO
ACACIA Acacia spp. Australia
AMANITAS Amanita muscaria Siberia
AYAHUASCA Yage Amazon Basin
BELLADONNA Atropa belladonna Europe, Middle East
BETEL Areca catechu .
BRUGMANSIA Brugmansia spp. S. America
BRUNFELSIA Brunfelsia latifolia Amazon
BUNDLE FLOWER Desmanthus illinoensis N. America
CAAPI Banisteriopsis caapi Amazon
CACTI Trichocereus spp. S. America
CACAO Theobroma cacao Central & S. America
CANNABIS Cannabis sativa India, Middle East
CAPSICUM Capsicum spp. Americas
CESTRUM Cestrum spp. Central & S. America
COCA Erythroxylum coca S. America
COLEUS Solenostemon scutellarioides Indonesia, Africa
COLORADO RIVER REED Arundo donax .
COFFEE Coffea arabica .
DATURA Datura spp. C. & S. America, India
DESFONTAINIA Desfontainia spp. S. America
DIPLOPTERYS Diplopterys cabrerana S. America
EPHEDRA Ephedra sinica China
ERGOT Claviceps purpurea Europe
GUARANA Paullinia cupana the Amazon
H. B. WOODROSE Argyreia nervosa .
HENBANE Hyoscyamus niger Europe, Middle East
IBOGA Tabernanthe iboga Congo, Gabon
INTOXICATING MINT Lagochilus inebriens Central Asia
JUSTICIA PECTORALIS Justicia pectoralis .
KANNA Sceletium tortuosum South Africa
KAVA Piper methysticum Pacific Islands
KHAT Catha edulis Ethiopia, South Arabia
KRATOM Mitragyna speciosa Thailand
LION'S TAIL / DAGGA Leonotis leonurus S. Africa
LOTUS Nymphaea spp.; Nelumbo spp. Egypt
MESCAL Sophora secundiflora Mexico, New Mexico, Texas
MUCUNA PRURIENS Mucuna pruriens S. America, Africa, Asia
MANDRAKE Mandragora officinarum Europe, Middle East
MIMOSA Mimosa tenuiflora (=hostilis) Brazil
MORNING GLORY Ipomoea violacea Mexico
MUSHROOMS Psilocybe spp.; Panaeolus spp. Mexico
NUTMEG Myristica fragrans New Guinea, East Indies
OLOLIUQUI Turbina corymbosa .
PASSIONFLOWER Passiflora incarnata .
PEYOTE Lophophora williamsii Mexico
PHALARIS GRASS Phalaris spp. .
PITURI Duboisia hopwoodii Australia
POPPIES Papaver somniferum Persia, Asia
PSYCHOTRIA Psychotria viridis, spp. .
SALVIA DIVINORUM Salvia divinorum Mexico
Sakae Naa Combretum quadrangulare Southeast Asia
SAN PEDRO Trichocereus pachanoi S. America
SINICUICHI Heimia salicifolia Mexico
SLEEPY GRASS Stipa robusta New Mexico, Colorado
SOLANDRA Solandra spp. Central Mexico
ST. JOHNS WORT Hypericum perforatum .
SYRIAN RUE Peganum harmala Persia, India
TABERNAEMONTANA Tabernaemontana spp. S. America, Africa
TEA Camellia sinensis S.E. Asia
TOBACCO Nicotiana tabacum, rusticum Americas
VIROLA Virola theidora Amazon
VOACANGA Voacanga africana Africa
WILD LETTUCE Lactuca virosa Europe
WORMWOOD Artemisia absinthium Europe
YERBA MATE Ilex paraguariensis Brazil, Argentina
YOPO, COHOBA Anadenanthera spp. Amazon
YOHIMBE Corynanthe yohimbe Congo, Cameroon
ZACATECHICHI Calea zacatechichi Mexico, Central America
#### Interactions Between MAOIs, SSRIs, and Recreational Drugs
Posted on September 23, 2015 at 1:10 PM comments (0)
Interactions Between MAOIs, SSRIs, and Recreational Drugs
by Erowid
Avoid mixing MAOIs and SSRIs.
This can lead to serotonin syndrome and can be dangerous.
Do not mix MAOIs with Stimulants (including MDMA).
This can lead to hypertensive crisis and can be deadly.
SSRIs in Combination with MDMA
Generally reduces the effects of the MDMA significantly.
SSRIs in Combination with Psychedelics
Generally reduce the effects of the psychedelic a bit.
MAOIs in Combination with Psychedelics
Generally increase the effects of the psychedelic significantly. Be extremely careful.
SSRIs
Strong SSRIs are significantly more common than MAOIs. Many commonly prescribed pharmaceutical anti-depressants are SSRIs, including Prozac (Fluoxetine), Paxil (Paroxetine), Zoloft (Sertraline), Celexa (Citalopram), and Desyrel (Trazodone).
MAOIs
Strong MAOIs are less common, but include prescription anti-depressants like phenelzine (Nardil), tranylcypromine (Parnate), isocarboxazid (Marplan), l-deprenyl (Eldepryl), moclobemide (Aurorex or Manerix), furazolidone, and pargyline. Ayahuasca also contains MAOIs, generally in the form of Banisteriopsis caapi or Syrian rue (harmine and harmaline).
#### MARIJUANA PROHIBITION CAN DO MORE HARM THAN GOOD, DOCTORS TELL FEDERAL PARTIES
Posted on September 23, 2015 at 10:50 AM comments (0)
If Canada’s new government chooses to legalize marijuana beyond medical use then it should get into the business of controlling its supply and sale to prevent the rise of a “Big Cannabis,” addiction specialists say.
Cannabis policy could be an issue ahead of October’s federal election. The governing Conservative party favours the status quo, the competing Liberals seek to legalize, regulate and tax, and the New Democrats support decriminalization. The Green Party has said it would legalize and tax marijuana.
In a commentary published in Monday’s issue of the Canadian Medical Association Journal, addiction doctors describe the negative aspects of prohibiting cannabis use, such as fuelling the illegal drug trade and the high costs and harms associated with policing and prosecuting people.
“We’re hoping to provide some direction to policy-makers in Canada to encourage them to rethink their current policies around cannabis, to move away from prohibition because it doesn’t work and has a lot of harms associated with it,” Dr. Sheryl Spithoff, a family physician and addiction doctor at Women’s College Hospital in Toronto and one of the coauthors of the paper, said in an interview.
Read more
#### Press Release Services
Posted on September 15, 2015 at 3:05 PM comments (0)
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# When a solution is diluted, does it change the number of moles dissolved?
$\text{Concentration"="Moles of solute"/"Volume of solution}$, and thus we express $\text{concentration}$ with units of $m o l \cdot {L}^{-} 1$. Upon dilution, i.e. the addition of more SOLVENT, we reduce the concentration (i.e. we make the quotient SMALLER by increasing the denominator), but the moles of solute is necessarily unchanged. Capisce?
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## Dark Acceleration: The Acceleration Discrepancy
Are Newton and Einstein both wrong?
Maybe Dark Matter has been going by the wrong name all along, ever since the cantankerous Swiss astronomer Fritz Zwicky coined the name, when his observations of the Coma cluster of galaxies showed the velocities were very much higher than expected.
He assumed Newton’s laws, and indeed general relativity, are correct. And that has been the canonical assumption ever since.
“Dark matter” has been studied on the scale of individual galaxies, clusters of galaxies, and the universe as a whole. The measurements of rotation velocity of spiral galaxies decades ago set the tone.
But the effects have been seen in the velocity dispersions of elliptical galaxies, in clusters of galaxies, and indeed in the cosmic microwave background temperature fluctuations.
What effects? Well for galaxies, whether for rotation or for dispersions within elliptical galaxies, what is actually observed is extra acceleration.
We all know F = ma, force equals mass times acceleration, for Newtonian dynamics.
In the case of galaxy rotation curves, the outer regions of the galaxies rotate faster than expected, where the expectation is set by the profile of visible matter and the modeling of the relationship between stellar luminosity and masses.
What is actually measured is the rotational (centripetal) observed acceleration of outer regions as being higher than expected, sometimes very much so.
But is m the problem? Is there missing ‘dark matter’? Or is ‘a’ the problem; does the Newtonian formula fail for the outer regions, or more specifically in environments where the acceleration is very low, less than about one ten billionth of a meter per second per second (less than 1 Angstrom per second per second)?
Now general relativity is not the explanation for the discrepancy, because we see departures from Newtonian behavior towards general relativistic formulae when acceleration is quite high, not when it is very low. So if Newton is wrong at very low accelerations, so is Einstein.
It turns out that the extra acceleration is best correlated not with the distance from the galaxy center, but with the amplitude of the expected Newtonian acceleration. When the expected acceleration is very low, the observed acceleration has the biggest discrepancy, always in the direction of more acceleration than expected.
Figure 3 from Lelli et al. 2016 “One Law to Rule Them All” This shows the observed gravitational acceleration on the y-axis (log scale) displayed vs. the expected Newtonian acceleration on the x-axis. Over 2000 data points drawn from 153 galaxy rotation curves would lie on the dotted line if there were no extra acceleration. There is very clear extra acceleration and it is correlated to the Newtonian acceleration, with a larger proportional effect at lower accelerations. At these very low accelerations the observed values are about an order of magnitude above the Newtonian value.
From an Occam’s razor point of view it is actually simpler to think about modifying the laws of gravity in very low acceleration environments. It is only in these actual astrophysical laboratories that we are able to test how gravity behaves at very low accelerations.
Explanations such as emergent gravity and other modified Newtonian dynamics approaches need serious theoretical and experimental investigation. They have been playing a distant second fiddle to expensive dark matter searches for WIMPs and axions, which keep coming up short even as the experiments become more and more sensitive.
References
F. Lelli, S. McGaugh, J. Schombert, M. Pawlowski, 2016 “One Law to Rule Them All: The Radial Acceleration Relation of Galaxies” https://arxiv.org/pdf/1610.08981.pdf
## WIMPZillas: The Biggest WIMPs
In the search for direct detection of dark matter, the experimental focus has been on WIMPS – weakly interacting massive particles. Large crystal detectors are placed deep underground to avoid contamination from cosmic rays and other stray particles.
WIMPs are often hypothesized to arise as supersymmetric partners of Standard Model particles. However, there are also WIMP candidates that arise due to non-supersymmetric extensions to the Standard Model.
The idea is that the least massive supersymmetric particle would be stable, and neutral. The (hypothetical) neutralino is the most often cited candidate.
The search technique is essentially to look for direct recoil of dark matter particles onto ordinary atomic nuclei.
The only problem is that we keep not seeing WIMPs. Not in the dark matter searches, not at the Large Hadron Collider whose main achievement has been the detection of the Higgs boson at mass 125 GeV. The mass of the Higgs is somewhat on the heavy side, and constrains the likelihood of supersymmetry being a correct Standard Model extension.
The figure below shows WIMP interaction with ordinary nuclear matter cross-section limits from a range of experiments spanning from 1 to 1000 GeV masses for WIMP candidates. Typical supersymmetric (SUSY) models are disfavored by these results at higher masses above 40 GeV or so as the observational limits are well down into the yellow shaded regions.
Perhaps the problem is that the WIMPs are much heavier than where the experiments have been searching. Most of the direction detection experiments are sensitive to candidate masses in the range from around 1 GeV to 1000 GeV (1 GeV or giga-electronVolt is about 6% greater than the rest mass energy of a proton). The 10 to 100 GeV range has been the most thoroughly searched region and multiple experiments place very strong constraints on interaction cross-sections with normal matter.
WIMPzillas is the moniker given to the most massive WIMPs, with masses from a billion GeV up to potentially as large as the GUT (grand Unified Theory) scale of $10^{16} GeV$.
The more general term is Superheavy Dark Matter, and this is proposed as a possibility for unexplained ultra high energy cosmic rays (UHECR). The WIMPzillas may decay to highly energetic gamma rays, or other particles, and these would be detected as the UHECR.
UHECR have energies greater than a billion GeV ($10^9 GeV$) and the most massive event ever seen (the so-called Oh My God Particle) was detected at $3 \cdot 10^{11} GeV$. It had energy equivalent to a baseball with velocity of 94 kilometers per hour. Or 40 million times the energy of particles in the Large Hadron Collider.
It has taken decades of searching at multiple cosmic ray arrays to detect particles at or near that energy.
Most UHECR appear to be spatially correlated with external galaxy sources, in particular with nearby Active Galactic Nuclei that are powered by supermassive black holes accelerating material near, but outside of, their event horizons.
However, they are not expected to be able to produce cosmic rays with energies above around $10^{11} GeV$, thus the WIMPzilla possibility. Again WIMPzillas could span the range from $10^9 GeV$ up to $10^{16} GeV$.
In a paper published last year, Kolb and Long calculated the production of WIMPzillas from Higgs boson pairs in the early universe. These Higgs pairs would have very high kinetic energies, much beyond their rest mass.
This production would occur during the “Reheating” period after inflation, as the inflaton (scalar energy field) dumped its energy into particles and radiation of the plasma.
There is another production mechanism, a gravitational mechanism, as the universe transitions from the accelerated expansion phase during cosmological inflation into the matter dominated (and then radiation-dominated) phases.
Thermal production from the Higgs portal, according to their results, is the dominant source of WIMPzillas for masses above $10^{14} GeV$. It may also be the dominant source for masses less than about $10^{11} GeV$.
They based their assumptions on chaotic inflation with quadratic inflation potential, followed by a typical model for reheating, but do not expect that their conclusions would be changed strongly with different inflation models.
It will take decades to discriminate between Big Bang-produced WIMPzilla style cosmic rays and those from extragalactic sources, since many more $10^{11} GeV$ and above UHECRs should be detected to build statistics on these rare events.
But it is possible that WIMPzillas have already been seen.
The density is tiny. The current dark matter density in the Solar neighborhood is measured at 0.4 Gev per cc. Thus in a cubic meter there would be the equivalent of 400,000 proton masses.
But if the WIMPzillas are at energies $10^{11} Gev$ and above (100 billion GeV), a cubic kilometer would only contain 4000 particles at a given time. Not easy to catch.
References
http://cdms.berkeley.edu/publications.html – SuperCDMS experiment led by UC Berkeley
http://pdg.lbl.gov/2017/reviews/rpp2017-rev-dark-matter.pdf – Dark matter review chapter from Lawrence Berkeley Lab (Figure above is from this review article).
http://home.physics.ucla.edu/~arisaka/home3/Particle/Cosmic_Rays/ – Ultra high energy cosmic rays
https://arxiv.org/pdf/1708.04293.pdf – E. Kolb and A. Long, 2017 “Superheavy Dark Matter through Higgs Portal Operators”
## Dark Ages, Dark Matter
Cosmologists call the first couple of hundred million years of the universe’s history the Dark Ages. This is the period until the first stars formed. The Cosmic Dawn is the name given to the epoch during which these first stars formed.
Now there has been a stunning detection of the 21 centimeter line from neutral hydrogen gas in that era. Because the first stars are beginning to form, their radiation induces the hyperfine transition for electrons in the ground state orbitals of hydrogen. This radiation undergoes a cosmological expansion of around a factor of 18 since the era of the Cosmic Dawn. By the time it reaches us, instead of being at the laboratory frequency of 1420 MHz, it is at around 78 MHz.
This is a difficult frequency at which to observe, since the region of spectrum is between the TV and FM bands in the U.S. and instrumentation itself is a source of radio noise. Very remote, radio quiet, sites are necessary to minimize interference from terrestrial sources, and the signal must be picked out from a much stronger cosmic background.
Image credit: CSIRO-Australia and EDGES collaboration, MIT and Arizona State University. EDGES is funded by the National Science Foundation.
This detection was made in Western Australia with a radio detector known as EDGES, that is sensitive in the 50 to 100 MHz range. It is surprisingly small, roughly the size of a large desk. The EDGES program is a collaboration between MIT and Arizona State University.
The researchers detected an absorption feature beginning at 78 MHz, corresponding to a redshift of 17.2 (1420/78 = 18.2 = 1 + z, where z is redshift) and for the canonical cosmological model it corresponds to an age of the universe of 180 million years.
The absorption feature is much stronger than expected from models, implying a lower gas temperature than expected.
At that redshift the cosmic microwave background temperature is at 50 Kelvins (at the present era it is only 2.7 Kelvins). The neutral hydrogen feature is seen in absorption against the warmer cosmic microwave background, and is much cooler (both its ‘spin’ and ‘kinetic’ temperatures).
This neutral hydrogen appears to be at only 3 Kelvins. Existing models had the expectation that it would be at around 7 Kelvins or even higher. (A Kelvin degree equals a Celsius degree, but has its zero point at absolute zero rather than water’s freezing temperature).
In a companion paper, it has been proposed that interactions with dark matter kept the hydrogen gas cooler than expected. This would require an interaction cross section between dark matter and ordinary matter (non- gravitational interaction, perhaps due to the weak force) and low velocities and low masses for dark matter particles. The mass should be only a few GeV (a proton rest mass is .94 GeV). Most WIMP searches in Earth-based labs have been above 10 GeV.
These results need to be confirmed by other experiments. And the dark matter explanation is speculative. But the door has been opened for Cosmic Dawn observations of neutral hydrogen as a new way to hunt for dark matter.
References:
“A Surprising Chill before the Cosmic Dawn” https://www.nature.com/articles/d41586-018-02310-9
EDGES science: http://loco.lab.asu.edu/edges/edges-science/
EDGES array and program: https://www.haystack.mit.edu/ast/arrays/Edges/
R. Barkana 2018, “Possible Interactions between Baryons and Dark Matter Particles Revealed by the First Stars” http://www.nature.com/articles/nature25791
## Unified Physics including Dark Matter and Dark Energy
Dark matter keeps escaping direct detection, whether it might be in the form of WIMPs, or primordial black holes, or axions. Perhaps it is a phantom and general relativity is inaccurate for very low accelerations. Or perhaps we need a new framework for particle physics other than what the Standard Model and supersymmetry provide.
We are pleased to present a guest post from Dr. Thomas J. Buckholtz. He introduces us to a theoretical framework referred to as CUSP, that results in four dozen sets of elementary particles. Only one of these sets is ordinary matter, and the framework appears to reproduce the known fundamental particles. CUSP posits ensembles that we call dark matter and dark energy. In particular, it results in the approximate 5:1 ratio observed for the density of dark matter relative to ordinary matter at the scales of galaxies and clusters of galaxies. (If interested, after reading this post, you can read more at his blog linked to his name just below).
Thomas J. Buckholtz
My research suggests descriptions for dark matter, dark energy, and other phenomena. The work suggests explanations for ratios of dark matter density to ordinary matter density and for other observations. I would like to thank Stephen Perrenod for providing this opportunity to discuss the work. I use the term CUSP – concepts uniting some physics – to refer to the work. (A book, Some Physics United: With Predictions and Models for Much, provides details.)
CUSP suggests that the universe includes 48 sets of elementary-particle Standard Model elementary particles and composite particles. (Known composite particles include the proton and neutron.) The sets are essentially (for purposes of this blog) identical. I call each instance an ensemble. Each ensemble includes its own photon, Higgs boson, electron, proton, and so forth. Elementary particle masses do not vary by ensemble. (Weak interaction handedness might vary by ensemble.)
One ensemble correlates with ordinary matter, 5 ensembles correlate with dark matter, and 42 ensembles contribute to dark energy densities. CUSP suggests interactions via which people might be able to detect directly (as opposed to infer indirectly) dark matter ensemble elementary particles or composite particles. (One such interaction theoretically correlates directly with Larmor precession but not as directly with charge or nominal magnetic dipole moment. I welcome the prospect that people will estimate when, if not now, experimental techniques might have adequate sensitivity to make such detections.)
This explanation may describe (much of) dark matter and explain (at least approximately some) ratios of dark matter density to ordinary matter density. You may be curious as to how I arrive at suggestions CUSP makes. (In addition, there are some subtleties.)
Historically regarding astrophysics, the progression ‘motion to forces to objects’ pertains. For example, Kepler’s work replaced epicycles with ellipses before Newton suggested gravity. CUSP takes a somewhat reverse path. CUSP models elementary particles and forces before considering motion. The work regarding particles and forces matches known elementary particles and forces and extrapolates to predict other elementary particles and forces. (In case you are curious, the mathematics basis features solutions to equations featuring isotropic pairs of isotropic quantum harmonic oscillators.)
I (in effect) add motion by extending CUSP to embrace symmetries associated with special relativity. In traditional physics, each of conservation of angular momentum, conservation of momentum, and boost correlates with a spatial symmetry correlating with the mathematics group SU(2). (If you would like to learn more, search online for “conservation law symmetry,” “Noether’s theorem,” “special unitary group,” and “Poincare group.”) CUSP modeling principles point to a need to add to temporal symmetry and, thereby, to extend a symmetry correlating with conservation of energy to correlate with the group SU(7). The number of generators of a group SU(n) is n2−1. SU(7) has 48 generators. CUSP suggests that each SU(7) generator correlates with a unique ensemble. (In case you are curious, the number 48 pertains also for modeling based on either Newtonian physics or general relativity.)
CUSP math suggests that the universe includes 8 (not 1 and not 48) instances of traditional gravity. Each instance of gravity interacts with 6 ensembles.
The ensemble correlating with people (and with all things people see) connects, via our instance of gravity, with 5 other ensembles. CUSP proposes a definitive concept – stuff made from any of those 5 ensembles – for (much of) dark matter and explains (approximately) ratios of dark matter density to ordinary matter density for the universe and for galaxy clusters. (Let me not herein do more than allude to other inferably dark matter based on CUSP-predicted ordinary matter ensemble composite particles; to observations that suggest that, for some galaxies, the dark matter to ordinary matter ratio is about 4 to 1, not 5 to 1; and other related phenomena with which CUSP seems to comport.)
CUSP suggests that interactions between dark matter plus ordinary matter and the seven peer combinations, each comprised of 1 instance of gravity and 6 ensembles, is non-zero but small. Inferred ratios of density of dark energy to density of dark matter plus ordinary matter ‘grow’ from zero for observations pertaining to somewhat after the big bang to 2+ for observations pertaining to approximately now. CUSP comports with such ‘growth.’ (In case you are curious, CUSP provides a nearly completely separate explanation for dark energy forces that govern the rate of expansion of the universe.)
Relationships between ensembles are reciprocal. For each of two different ensembles, the second ensemble is either part of the first ensemble’s dark matter or part of the first ensemble’s dark energy. Look around you. See what you see. Assuming that non-ordinary-matter ensembles include adequately physics-savvy beings, you are looking at someone else’s dark matter and yet someone else’s dark energy stuff. Assuming these aspects of CUSP comport with nature, people might say that dark matter and dark-energy stuff are, in effect, quite familiar.
## Primordial Black Holes and Dark Matter
Based on observed gravitational interactions in galactic halos (galaxy rotation curves) and in group and clusters, there appears to be 5 times as much dark matter as ordinary matter in the universe. The alternative is no dark matter, but more gravity than expected at low accelerations, as discussed in this post on emergent gravity.
The main candidates for dark matter are exotic, undiscovered particles such as WIMPs (weakly interacting massive particles) and axions. Experiments attempting direct detection for these have repeatedly come up short.
The non-particle alternative category is MACHOs (massive compact halo objects) composed of ordinary matter. Planets, dwarf stars and neutron stars have been ruled out by various observational signatures. The one ordinary matter possibility that has remained viable is that of black holes, and in particular black holes with much less than the mass of the Sun.
The only known possibility for such low mass black holes is that of primordial black holes (PBHs) formed in the earliest moments of the Big Bang.
Gravitational microlensing, or microlensing for short, seeks to detect PBHs by their general relativistic gravitational effect on starlight. MACHO and EROS were experiments to monitor stars in the Large Magellanic Cloud. These were able to place limits on the abundance of PBHs with masses from about one hundred millionth of a the Sun’s mass up to 10 solar masses. PBHs from that mass range are not able to explain the total amount of dark matter determined from gravitational interactions.
LIGO has recently detected several merging black holes in the tens of solar mass range. However the frequency of LIGO detections appears too low by two orders of magnitude to explain the amount of gravitationally detected dark matter. PBHs in this mass range are also constrained by cosmic microwave background observations.
Extremely low mass PBHs, below 10 billion tons, cannot survive until the present epoch of the universe. This is due to Hawking radiation. Black holes evaporate due to their quantum nature. Solar mass black holes have an extremely long lifetime against evaporation. But very low mass black holes will evaporate in billions of years or much sooner, depending on mass.
The remaining mass window for possible PBH, in sufficient amount to explain dark matter, is from about 10 trillion ton objects up to those with ten millionths of the Sun’s mass.
Figure 5 from H. Niikura et al. “Microlensing constraints on primordial black holes with the Subaru/HSC Andromeda observation”, https://arxiv.org/abs/1701.02151
Here f is the fraction of dark matter which can be explained by PBHs. The red shaded area is excluded by the authors observations and analysis of Andromeda Galaxy data. This rules out masses above 100 trillion tons and below a hundred thousandth of the Sun’s mass. (Solar mass units used above and grams are used below).
Now, a team of Japanese astronomers have used the Subaru telescope on the Big Island of Hawaii (operated by Japan’s national observatory) to determine constraints on PBHs by observing millions of stars in the Andromeda Galaxy.
The idea is that a candidate PBH would pass in front of the line of sight to the star, acting as a lens, and magnifying the light from the star in question for a relatively brief period of time. The astronomers looked for stars exhibiting variability in their light intensity.
With only a single nights’ data they made repeated short exposures and were able to pick out over 15,000 stars in Andromeda exhibiting such variable light intensity. However, among these possible candidates, only a single one turned out to fit the characteristics expected for a PBH detection.
If PBHs in this mass range were sufficiently abundant to explain dark matter, then one would have expected of order one thousand events, and they saw nothing like this number. In summary, with 95% confidence, they are able to rule out PBHs as the main source of dark matter for the mass range from 100 trillion tons up to one hundred thousandth of the Sun’s mass.
The window for primordial black holes as the explanation for dark matter appears to be closing.
## Dark Energy Survey First Results: Canonical Cosmology Supported
The Dark Energy Survey (DES) first year results, and a series of papers, were released on August 4, 2017. This is a massive international collaboration with over 60 institutions represented and 200 authors on the paper summarizing initial results. Over 5 years the Dark Energy Survey team plans to survey some 300 million galaxies.
The instrument is the 570-megapixel Dark Energy Camera installed on the Cerro Tololo Inter-American Observatory 4-meter Blanco Telescope.
Image: DECam imager with CCDs (blue) in place. Credit: darkenergysurvey.org
Over 26 million source galaxy measurements from far, far away are included in these initial results. Typical distances are several billion light-years, up to 9 billion light-years. Also included is a sample of 650,000 luminous red galaxies, lenses for the gravitational lensing, and typically these are foreground elliptical galaxies. These are at redshifts < 0.9 corresponding to up to 7 billion light-years.
They use 3 main methods to make cosmological measurements with the sample:
1. The correlations of galaxy positions (galaxy-galaxy clustering)
2. The gravitational lensing of the large sample of background galaxies by the smaller foreground population (cosmic shear)
3. The gravitational lensing of the luminous red galaxies (galaxy-galaxy lensing)
Combining these three methods provides greater interpretive power, and is very effective in eliminating nuisance parameters and systematic errors. The signals being teased out from the large samples are at only the one to ten parts in a thousand level.
They determine 7 cosmological parameters including the overall mass density (including dark matter), the baryon mass density, the neutrino mass density, the Hubble constant, and the equation of state parameter for dark energy. They also determine the spectral index and characteristic amplitude of density fluctuations.
Their results indicate Ωm of 0.28 to a few percent, indicating that the universe is 28% dark matter and 72% dark energy. They find a dark energy equation of state w = – 0.80 but with error bars such that the result is consistent with either a cosmological constant interpretation of w = -1 or a somewhat softer equation of state.
They compare the DES results with those from the Planck satellite for the cosmic microwave background and find they are statistically significant with each other and with the Λ-Cold Dark MatterΛ model (Λ, or Lambda, stands for the cosmological constant). They also compare to other galaxy correlation measurements known as BAO for Baryon Acoustic Oscillations (very large scale galaxy structure reflecting the characteristic scale of sound waves in the pre-cosmic microwave background plasma) and to Type 1a supernovae data.
This broad agreement with Planck results is a significant finding since the cosmic microwave background is at very early times, redshift z = 1100 and their galaxy sample is at more recent times, after the first five billion years had elapsed, with z < 1.4 and more typically when the universe was roughly ten billion years old.
Upon combining with Planck, BAO, and the supernovae data the best fit is Ωm of 0.30 with an error of less than 0.01, the most precise determination to date. Of this, about 0.25 is ascribed to dark matter and 0.05 to ordinary matter (baryons). And the implied dark energy fraction is 0.70.
Furthermore, the combined result for the equation of state parameter is precisely w = -1.00 with only one percent uncertainty.
The figure below is Figure 9 from the DES paper. The figure indicates, in the leftmost column the measures and error bars for the amplitude of primordial density fluctuations, in the center column the fraction of mass-energy density in matter, and in the right column the equation of state parameter w.
The DES year one results for all 3 methods are shown in the first row. The Planck plus BAO plus supernovae combined results are shown in the last row. And the middle row, the fifth row, shows all of the experiments combined, statistically. Note the values of 0.3 and – 1.0 for Ωm and w, respectively, and the extremely small error bars associated with these.
This represents continued strong support for the canonical Λ-Cold Dark Matter cosmology, with unvarying dark energy described by a cosmological constant.
They did not evaluate modifications to general relativity such as Emergent Gravity or MOND with respect to their data, but suggest they will evaluate such a possibility in the future.
References
https://arxiv.org/abs/1708.01530, “Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing”, 2017, T. Abbott et al.
https://en.wikipedia.org/wiki/Weak_gravitational_lensing, Wikipedia article on weak gravitational lensing discusses galaxy-galaxy lensing and cosmic shear
## Dark Energy and the Cosmological Constant
I am seeing a lot of confusion around dark energy and the cosmological constant. What are they? Is gravity always attractive? Or is there such a thing as negative gravity or anti-gravity?
First, what is gravity? Einstein taught us that it is the curvature of space. Or as famous relativist John Wheeler wrote “Matter tells space how to curve, and curved space tells matter how to move”.
Dark Energy has been recognized with the Nobel Prize for Physics, so its reality is accepted. There were two teams racing against one another and they found the same result in 1998: the expansion of the universe is accelerating!
Normally one would have thought it would be slowing down due to the matter within; both ordinary and dark matter would work to slow the expansion. But this is not observed for distant galaxies. One looks at a certain type of supernova that always has a certain mass and thus the same absolute luminosity. So the apparent brightness can be used to determine the luminosity distance. This is compared with the redshift that provides the velocity of recession or velocity-determined distance in accordance with Hubble’s law.
A comparison of the two types of distance measures, particularly for large distances, shows the unexpected acceleration. The most natural explanation is a dark energy component equal to twice the matter component, and that matter component would include any dark matter. Now do not confuse dark energy with dark matter. The latter contributes to gravity in the normal way in proportion to its mass. Like ordinary matter it appears to be non-relativistic and without pressure.
Einstein presaged dark energy when he added the cosmological constant term to his equations of general relativity in 1917. He was trying to build a static universe. It turns out that such a model is unstable, and he later called his insertion of the cosmological constant a blunder. A glorious blunder it was, as we learned eight decades later!
Here is the equation:
$G_{ab}+\Lambda g_{ab} = {8\pi G \over c^{4}}T_{ab}$
The cosmological constant is represented by the Λ term, and interestingly it is usually written on the left hand side with the metric terms, not on the right hand side with the stress-energy (and pressure and mass) tensor T.
If we move it to the right hand side and express as an energy density, the term looks like this:
$\rho = {\Lambda \over8\pi G }$
with $\rho$ as the vacuum energy density or dark energy, and appearing on the right it also takes a negative sign. So this is a suggestion as to why it is repulsive.
The type of dark energy observed in our current universe can be fit with the simple cosmological constant model and it is found to be positive. So if you move $\Lambda$ to the other side of the equation, it enters negatively.
Now let us look at dark energy more generally. It satisfies an equation of state defined by the relationship of pressure to density, with P as pressure and ρ denoting density:
$P = w \cdot \rho \cdot c^2$
Matter, whether ordinary or dark, is to first order pressureless for our purposes, quantified by its rest mass, and thus takes w = 0. Radiation it turns out has w = 1/3. The dark energy has a negative w, which is why you have heard the phrase ‘negative pressure’. The simplest case is w = -1, which the cosmological constant, a uniform energy density independent of location and age of the universe. Alternative models of dark energy known as quintessence can have a larger w, but it must be less than -1/3.
Credit: http://www.scholarpedia.org/article/Cosmological_constant
Why less than -1/3? Well the equations of general relativity as a set of nonlinear differential equations are usually notoriously difficult to solve, and do not admit of analytical solutions. But our universe appears to be highly homogeneous and isotropic, so one can use a simple FLRW spherical metric, and in this case one end up with the two Friedmann equations (simplified by setting c =1).
$\ddot a/a = - {4 \pi G \over 3} ({\rho + 3 p}) + {\Lambda \over 3 }$
This is for a (k = 0) flat on large scales universe as observed. Here $\ddot a$ is the acceleration (second time derivative) of the scale factor a. So if $\ddot a$ is positive, the expansion of the universe is speeding up.
The $\Lambda$ term can be rewritten using the dark energy density relation above. Now the equation needs to account for both matter (which is pressureless, whether it is ordinary or dark matter) and dark energy. Again the radiation term is negligible at present, by four orders of magnitude. So we end up with:
$\ddot a/a = - {4 \pi G \over 3} ({\rho_m + \rho_{de} + 3 p_{de}})$
Now the magic here was in the 3 before the p. The pressure gets 3 times the weighting in the stress-energy tensor T. Why, because energy density is just there as a scalar, but pressure must be accounted for in each of the 3 spatial dimensions. And since p for dark energy is negative and equal to the dark energy density (times the square of the speed of light), then
$\rho + 3 p$ is always negative for the dark energy terms, provided w < -1/3. That unusual behavior is why we call it ‘dark energy’.
Overall it is a battle between matter and dark energy density on the one side, and dark energy pressure (being negative and working oppositely to how we ordinarily think of gravity) on the other. The matter contribution gets weaker over time, since as the universe expands the matter becomes less dense by a relative factor of $(1=z)^3$, that is the matter was on average denser in the past by the cube of one plus the redshift for that era.
Dark energy eventually wins out, because it, unlike matter does not thin out with the expansion. Every cubic centimeter of space, including newly created space with the expansion has its own dark energy, generally attributed to the vacuum. Due to the quantum uncertainty (Heisenberg) principle, even the vacuum has fields and non zero energy.
Now the actual observations at present for our universe show, in units of the critical density that
$\rho_m \approx 1/3$
$\rho_{de} \approx 2/3$
and thus
$p_{de} \approx - 2$
And the sum of them all is around -1, just coincidentally. Since there is a minus sign in front of the whole thing, the acceleration of the universe is positive. This is all gravity, it is just that some terms take the opposite side. The idea that gravity can only be attractive is not correct.
If we go back in time, say to the epoch when matter still dominated with $\rho_m \approx 2/3$ and $\rho_{de} \approx 1/3$, then the total including pressure would be 2/3 +1/3 – 1, or 0.
That would be the epoch when the universe changed from decelerating to accelerating, as dark energy came to dominate. With our present cosmological parameters, it corresponds to a redshift of $z \approx 0.6$, and almost 6 billion years ago.
Image: NASA/STScI, public domain
## Yet Another Intermediate Black Hole Merger
Another merger of two intermediate mass black holes has been observed by the LIGO gravitational wave observatories.
There are now three confirmed black hole pair mergers, along with a previously known fourth possible, that lacks sufficient statistical confidence.
These three mergers have all been detected in the past two years and are the only observations ever made of gravitational waves.
They are extremely powerful events. The lastest event is known as GW170104 (gravitational wave discovery of January 4, 2017).
It all happened in the wink of an eye. In a fifth of a second, a black hole of 30 solar masses approximately merged with a black hole of about 20 solar masses. It is estimated that the two orbited around one another six times (!) during that 0.2 seconds of their final existence as independent objects.
The gravitational wave generation was so great that an entire solar mass of gravitational energy was liberated in the form of gravitational waves.
This works out to something like $2 \cdot 10^{47}$ Joules of energy, released in 0.2 seconds, or an average of $10^{48} Watts$ during that interval. You know, a Tera Tera Tera Terawatt.
Researchers have now discovered a whole new class of black holes with masses ranging from about 10 solar masses (unmerged) to 60 solar masses (merged). If they keep finding these we might have to give serious consideration to intermediate mass black holes as contributors to dark matter. See this prior blog for a discussion of primordial black holes as a possible dark matter contributor:
https://darkmatterdarkenergy.com/2016/06/17/primordial-black-holes-as-dark-matter/
Image credit: LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet)
## No Dark Energy?
Dark Energy is the dominant constituent of the universe, accounting for 2/3 of the mass-energy balance at present.
At least that is the canonical concordance cosmology, known as the ΛCDM or Lambda – Cold Dark Matter model. Here Λ is the symbol for the cosmological constant, the simplest, and apparently correct (according to most cosmologists), model for dark energy.
Models of galaxy formation and clustering use N-body simulations run on supercomputers to model the growth of structure (galaxy groups and clusters) in the universe. The cosmological parameters in these models are varied and then the models are compared to observed galaxy catalogs at various redshifts, representing different ages of the universe.
It all works pretty well except that the models assume a fully homogeneous universe on the large scale. While the universe is quite homogeneous for scales above a billion light-years, there is a great deal of filamentary web-like structure at scales above clusters, including superclusters and voids, as you can easily see in this map of our galactic neighborhood.
##### Galaxies and clusters in our neighborhood. IPAC/Caltech, by Thomas Jarrett – “Large Scale Structure in the Local Universe: The 2MASS Galaxy Catalog”, Jarrett, T.H. 2004, PASA, 21, 396
Well why not take that structure into account when doing the modeling? It has long been known that more local inhomogeneities such as those seen here might influence the observational parameters such as the Hubble expansion rate. Thus even at the same epoch, the Hubble parameter could vary from location to location.
Now a team from Hungary and Hawaii have modeled exactly that, in a paper entitled “Concordance cosmology without dark energy” https://arxiv.org/pdf/1607.08797.pdf . They simulate structure growth while estimating the local values of expansion parameter in many regions as their model evolves.
Starting with a completely matter dominated (Einstein – de Sitter) cosmology they find that they can reasonably reproduce the average expansion history of the universe — the scale factor and the Hubble parameter — and do that somewhat better than the Planck -derived canonical cosmology.
Furthermore, they claim that they can explain the tension between the Type Ia supernovae value of the Hubble parameter (around 73 kilometers per second per Megaparsec) and that determined from the Planck satellite observations of the cosmic microwave background radiation (67 km/s/Mpc).
Future surveys of higher resolution should be able to distinguish between their model and ΛCDM, and they also acknowledge that their model needs more work to fully confirm consistency with the cosmic microwave background observations.
Meanwhile I’m not ready to give up on dark energy and the cosmological constant since supernova observations, cosmic microwave background observations and the large scale galactic distribution (labeled BAO in the figure below) collectively give a consistent result of about 70% dark energy and 30% matter. But their work is important, something that has been a nagging issue for quite a while and one looks forward to further developments.
Dark Energy and Matter content of Universe
## Distant Galaxy Rotation Curves Appear Newtonian
One of the main ways in which dark matter was postulated, primarily in the 1970s, by Vera Rubin (recently deceased) and others, was by looking at the rotation curves for spiral galaxies in their outer regions. Although that was not the first apparent dark matter discovery, which was by Fritz Zwicky from observations of galaxy motion in the Coma cluster of galaxies during the 1930s.
Most investigations of spiral galaxies and star-forming galaxies have been relatively nearby, at low redshift, because of the difficulty in measuring these accurately at high redshift. For what is now a very large sample of hundreds of nearby galaxies, there is a consistent pattern. Galaxy rotation curves flatten out.
M64, image credit: NASA, ESA, and the Hubble Heritage Team (AURA/STScI)
If there were only ordinary matter one would expect the velocities to drop off as one observes the curve far from a galaxy’s center. This is virtually never seen at low redshifts, the rotation curves consistently flatten out. There are only two possible explanations: dark matter, or modification to the law of gravity at very low accelerations (dark gravity).
Dark matter, unseen matter, would case rotational velocities to be higher than otherwise expected. Dark, or modified gravity, additional gravity beyond Newtonian (or general relativity) would do the same.
Now a team of astronomers (Genzel et al. 2017) have measured the rotation curves of six individual galaxies at moderately high redshifts ranging from about 0.9 to 2.4.
Furthermore, as presented in a companion paper, they have stacked a sample of 97 galaxies with redshifts from 0.6 to 2.6 to derive an average high-redshift rotation curve (P. Lang et al. 2017). While individually they cannot produce sufficiently high quality rotation curves, they are able to produce a mean normalized curve for the sample as a whole with sufficiently good statistics.
In both cases the results show rotation curves that fall off with increasing distance from the galaxy center, and in a manner consistent with little or no dark matter contribution (Keplerian or Newtonian style behavior).
In the paper with rotation curves of 6 galaxies they go on to explain their falling rotation curves as due to “first, a large fraction of the massive high-redshift galaxy population was strongly baryon-dominated, with dark matter playing a smaller part than in the local Universe; and second, the large velocity dispersion in high-redshift disks introduces a substantial pressure term that leads to a decrease in rotation velocity with increasing radius.”
So in essence they are saying that the central regions of galaxies were relatively more dominated in the past by baryons (ordinary matter), and that since they are measuring Hydrogen alpha emission from gas clouds in this study that they must also take into account the turbulent gas cloud behavior, and this is generally seen to be larger at higher redshifts.
Stacy McGaugh, a Modified Newtonian Dynamics (MOND) proponent, criticizes their work saying that their rotation curves just don’t go far enough out from the galaxy centers to be meaningful. But his criticism of their submission of their first paper to Nature (sometimes considered ‘lightweight’ for astronomy research results) is unfounded since the second paper with the sample of 97 galaxies has been sent to the Astrophysical Journal and is highly detailed in its observational analysis.
The father of MOND, Mordehai Milgrom, takes a more pragmatic view in his commentary. Milgrom calculates that the observed accelerations at the edge of these galaxies are several times higher than the value at which rotation curves should flatten. In addition to this criticism he notes that half of the galaxies have low inclinations, which make the observations less certain, and that the velocity dispersion of gas in galaxies that provides pressure support and allows for lower rotational velocities, is difficult to correct for.
As in MOND, in Erik Verlinde’s emergent gravity there is an extra acceleration (only apparent when the ordinary Newtonian acceleration is very low) of order. This spoofs the behavior of dark matter, but there is no dark matter. The extra ‘dark gravity’ is given by:
$g _D = sqrt {(a_0 \cdot g_B / 6 )}$
In this equation a0 = c*H, where H is the Hubble parameter and gB is the usual Newtonian acceleration from the ordinary matter (baryons). Fundamentally, though, Verlinde derives this as the interaction between dark energy, which is an elastic, unequilibrated medium, and baryonic matter.
One could consider that this dark gravity effect might be weaker at high redshifts. One possibility is that density of dark energy evolves with time, although at present no such evolution is observed.
Verlinde assumes a dark energy dominated de Sitter model universe for which the cosmological constant is much larger than the matter contribution and approaches unity, Λ = 1 in units of the critical density. Our universe does not yet fully meet that criteria, but has Λ about 0.68, so it is a reasonable approximation.
At redshifts around z = 1 and 2 this approximation would be much less appropriate. We do not yet have a Verlindean cosmology, so it is not clear how to compute the expected dark gravity in such a case, but it may be less than today, or greater than today. Verlinde’s extra acceleration goes as the square root of the Hubble parameter. That was greater in the past and would imply more dark gravity. But in reality the effect is due to dark energy, so it may go with the one-fourth power of an unvarying cosmological constant and not change with time (there is a relationship that goes as H² ∝ Λ in the de Sitter model) or change very slowly.
At very large redshifts matter would completely dominate over the dark energy and the dark gravity effect might be of no consequence, unlike today. As usual we await more observations, both at higher redshifts, and further out from the galaxy centers at moderate redshifts.
References:
R. Genzel et al. 2017, “Strongly baryon-dominated disk galaxies at the peak of galaxy formation ten billion years ago”, Nature 543, 397–401, http://www.nature.com/nature/journal/v543/n7645/full/nature21685.html
P. Lang et al. 2017, “Falling outer rotation curves of star-forming galaxies at 0.6 < z < 2.6 probed with KMOS^3D and SINS/ZC-SINF” https://arxiv.org/abs/1703.05491
Mordehai Milgrom 2017, “High redshift rotation curves and MOND” https://arxiv.org/abs/1703.06110v2
Erik Verlinde 2016, “Emergent Gravity and the Dark Universe” https;//arXiv.org/abs/1611.02269v1
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# Does this idea give an algorithm for constructing Hadamard matrices?
Fedor Petrov's answer of my preceding question shows that my question reduces to the famous Hadamard conjecture about Hadamard matrices of order $4k$. So I decided to study this conjecture and I got the following raw idea of constructing Hadamard matrices:
If $V_i$ is a row of $H_n$ then add $V_i$ to the $i$th column.
For example: Start with $$H_4=\begin{pmatrix}1&1&1&1\\ 1&1&-1&-1\\ 1&-1&1&-1\\ 1&-1&-1&1 \end{pmatrix}$$ Let $H_{4n-4}$ be a symmetric (if it exists?) Hadamard matrix. Then by the above idea we extend this matrix to $H_{4n}$ as follows: $$H_{4n }=\begin{pmatrix}H_{4n-4}&A_{(4n-4)\times 4}\\ A^T_{4\times (4n-4)}& B_{4\times 4} \\ \end{pmatrix}$$ where $B$ is a symmetric matrix and the first row of $A$ is $(1,1,1,\dots,1)$. Thus $$AA^T=4I_{4n-4},\quad H_{4n-4}A+AB=0,\quad A^T A+B^2=4n I_4.$$
Question: Does this idea give an algorithm for constructing Hadamard matrices?
Any suggestion for improving this idea would be greatly appreciated.
• There is no symmetric Hadamard matrix of order $12$. – Wojowu Sep 30 '17 at 15:57
• neilsloane.com/hadamard – Wojowu Sep 30 '17 at 16:15
• The question of how large M can be such that 1) M is a Hadamard matrix of order k, and 2) M is a minor of matrix H, and 3) H is a Hadamard matrix of order n leads to 2k being at most n. So your augmentation idea does not produce a Hadamard matrix when M has order of 8 or greater. I think a book of Wallis may have this result. Of course, Hadamard product allows n to be 2k. Gerhard "Augmentation Helps In Determinant Maximizing" Paseman, 2017.09.30. – Gerhard Paseman Sep 30 '17 at 17:18
• Also, it seems your system of matrix equations gets problematic for n larger than 2, as AA^t should have rank at most 4, and can't be the multiple of a large identity matrix. You might try researching augmentation as an approach to one of Fedor's questions, see mathoverflow.net/a/261531 . Gerhard "Can Provide Some Technical Assistance" Paseman, 2017.09.30. – Gerhard Paseman Sep 30 '17 at 17:28
• There exist symmetric Hadamard matrices of order 12, though they're not easy to find by hand. See, for example, figure 1 of arxiv.org/pdf/1512.01732.pdf – Padraig Ó Catháin Oct 10 '17 at 2:26
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# Approx. V, Amps and Transistor required for ~18cm ,12W Speaker Electromagnet
I have a large 8ohm speaker with a "12W500" rating, and another sticker saying 3/38/5 (QC check?) ~18cm Magnet and 30cm Cone.
I want a silent vibrator for chladni plate (vibrating plate)
-Will it run on 12V, 3V 24V? What kind of amps may it draw 200mA 500mA? 1A? 4A? I don't even know ballpark figures!
I know how to make a signal generator from a 555, but i don't know how to adapt this to drive the speaker magnet.
-Do I put the output to a "power transistor" or a MOSFET? I have only used them for signal amplification before not power supply..
Any tips, Circuits or transistor recommendations will be VERY appreciated... I am fairly proficient at electronics, but this eludes me completely as it is taken for granted in most instances, or they use a 300€ amplifier....
I already built a signal generator.
The EighteenSound 12W500 speaker has a datasheet available here.
As per the datasheet, the AES power rating is 350 Watts, with a minimum impedance of 6.4 Ohms across the operating band of 50 to 6000 Hz.
Calculating voltage and current values as per this:
• RMS voltage: Vrms = square-root( power P x impedance Z ) = 47.33 Volts
• Peak voltage: Vp = Vrms x 1.4142 = +/- 66.93 Volts
• Peak current: Ip = Vp / Z = +/- 10.46 Amperes
• Peak to peak voltage: Vpp = (Vrms x 1.4142) x 2 = 133.87 Volts
• Peak to peak current: Ipp = Vpp / Z = 20.92 Amperes
If you drive this speaker single-ended, i.e. with a single DC power supply, the final drive stage transistor or driver IC needs to deliver up to 133.87 Volts (instantaneous peaks), at up to 20.92 Amperes (design peak values), and the power supply needs to be able to supply a sustained 350+ Watts - a 400 Watt 150 Volts DC supply would be a good design goal.
If the speaker is to be driven using a balanced (split supply rail) design, the values needed for each of the positive- and negative-side drivers would be up to 66.93 Volts each (instantaneous peaks) at 10.46 Amperes. The power supply still needs to be capable of the same 350+ watts, so 200 Watts per supply rail (say +80 Volts, -80 Volts) would be the supply design goal.
If these voltages are too high to deal with, a Bridge-Tied-Load configuration could be used with a split-supply design and two identical output amplifiers, designed to work with 16 Ohm loads per amplifier. For such a configuration, the power supply needs to have two rails, at around +45 and -45 Volts respectively, again designed to sustain 200 watts per rail.
The voltages do not scale down proportionately because amplifiers require a voltage headroom, which does not scale down in proportion to the output voltage but remain comparatively constant. Not providing that headroom will cause your signal to be clipped at the peaks and troughs, thus introducing undesirable harmonics, and an audible harsh buzzing sound.
While these voltage and current levels computed above are pretty high for designing with discrete transistor circuits, there exist several purpose-built power audio amplifier ICs, or alternatively some high power op-amps, that should be considered for such purposes.
Some examples of possible integrated parts are below - Please note that these are not specific to this question's requirements but are meant as a general resource for future researchers reaching this question. Many / most of them are for lower power or lower load impedance than given in the question.
• Some examples of analog power audio amplifiers are: LM3886, LM4780, LM3875
• Some examples of power op amps are: PA85, OPA541, OPA549, OPA2544
• Some examples of Class-D power amps are: TAS5162, TAS5630
• An example of a pre-built amplifier module from eBay, \$60
Adding datasheet links to all the above parts would take too long, so this is left as an exercise for some kindly soul to edit in.
The last example above is provided to show that some very capable pre-built modules can be bought online, sometimes at prices considerably lower than the sum of retail prices of the constituent components.
The required power supply unit will be probably the biggest cost element to build, as also the most difficult to find prebuilt without opting for name-brand high priced units.
A search on sites like eBay will yield several pre-etched PCBs and some kits which can deliver the desired voltage and current. It is worth checking the specifications of such kits carefully before ordering, however. Since these are not validated big brand products, a recommendation would be to opt for parts rated significantly higher than the computed values above.
An alternative is to use a pair of high-voltage high-current switching power supplies with adjustable, floating output voltage, such as are sold for large LED display boards. These may introduce a bit more noise than supplies designed for audio use, but for the purpose of driving a Chladni plate transducer, such noise may be acceptable.
• +1 - I was half way through an answer, then this appeared :-) One thing I was going to say was, since this doesn't need to be "Hi-Fi" as it's just used for a vibrating device, then a "simple" (MOSFET based) class B output stage could be used to drive it. Given the power levels and experience level of the OP though, an IC or pre-built eBay amp is probably best. Feb 16 '13 at 7:05
• @OliGlaser My thoughts exactly - which is why I have recommended searching for pre-built amplifier modules, and kit or switching power supplies Feb 16 '13 at 7:25
There are thousands of power audio transistors, just google for these three words and you'll have more suggestions than time to devote to read them. What about ON's MJE15028. It apparently handles 8 Amps, up to 50W and comes in a classical and handy TO220 package. Remember some basic design tips:
• block the output DC with a large cap (to pass the low freq) in series to the loudspeaker
• if handling a high power (> 4W), use a heatsink
• with regards to heatsinking you can start without it and check in the first seconds if it gets too hot (sometimes you smell it instead!!)
• place a large electrolytic cap close to the collector
and... designing a basic power stage is not very different (if we don't get into the hi-fi subtleties) from a signal amplifier stage.
A basic design would be based on the common emitter amplfier. Use tools like LTSpice to simulate your design. A more ellaborated design would be a push-pull with two complementary BJT's.
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### A Knight's Journey
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
### 8 Methods for Three by One
This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?
### Which Twin Is Older?
A simplified account of special relativity and the twins paradox.
Consider a convex quadrilateral $Q$ made from four rigid rods with flexible joints at the vertices so that the shape of $Q$ can be changed while keeping the lengths of the sides constant. Let ${\bf a}_1$, ${\bf a}_2$, ${\bf a}_3$ and ${\bf a}_4$ be vectors representing the sides (in this order) of an arbitrary quadrilateral $Q$, so that ${\bf a}_1+{\bf a}_2+{\bf a}_3+{\bf a}_4 = {\bf 0}$ (the zero vector). Now let ${\bf d}_1$ and ${\bf d}_2$ be the vectors representing the diagonals of $Q$. We may choose these so that ${\bf d}_1={\bf a}_4+{\bf a}_1$ and ${\bf d}_2={\bf a}_3+{\bf a}_4$. Prove that
$${\bf a}_2^2+{\bf a}_4^2-{\bf a}_1^2-{\bf a}_3^2= 2({\bf a}_1{\cdot}{\bf a}_3-{\bf a}_2{\cdot}{\bf a}_4).\quad (1)$$
$$2{\bf d}_1{\cdot}{\bf d}_2 = {\bf a}_2^2+{\bf a}_4^2-{\bf a}_1^2-{\bf a}_3^2.\quad (2)$$
Use these results to show that, as the shape of the quadrilateral is changed, if the diagonals of $Q$ are perpendicular in one position of $Q$, then they are perpendicular in all variations of $Q$.
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### A note on this page's publication date
The last time we examined the charities working primarily in the U.S. was in 2010. As of 2011, we have de-prioritized further work on this cause.
The content we created in 2007 appears below. This content is likely to be no longer fully accurate, both with respect to what it says about the organization and with respect to what it implies about our own views and positions.
# In a nutshell
What do they do? The LEDA Scholars Program is a college preparatory program serving economically disadvantaged high school students. The program consists of a full-time, seven-week summer program (following 11th grade) and college advising and assistance during 12th grade. Applicants to LEDA's program undergo a rigorous application process that includes academic evaluation, multiple recommendations, and an interview.
Does it work? We aren't confident that LEDA is significantly impacting its students, i.e., causing them to perform better than they would without its help. The only empirical study we have access to is highly ambiguous. It follows a group of LEDA scholars as well as a group of students who were rejected from the program in the final round, and finds that the former matriculated more frequently (and to more selective schools); but we believe that those who gain acceptance into the program are likely much better off to begin with than those who are rejected, and it is not intuitively or empirically clear to us that LEDA is adding significantly to these already accomplished students' opportunities.
# The details
## What do they do?
Applicants to LEDA's program undergo a highly selective application process; those who are selected go through LEDA's full-time, seven-week summer program (following 11th grade) and receive college advising and assistance during 12th grade.
LEDA targets students from minority (African-American, Latino, and Native American) backgrounds (Attachment A-2 Pg 1) and those who come from relatively low-income families (families of the first LEDA cohort had an average income of $40,000 per year, as stated in Attachment B-9). Over the 4 year history of the program, LEDA has served 250 students, 120 of whom have come from New York City (Attachment A-2 Pg 1). Applicants to LEDA participate in a rigorous application process, which assesses students' academic records (grades and difficulty of courses taken), writing ability (through one essay prepared specifically for LEDA and three additional writing samples), four recommendations, and interviews with applicants and their parents (Attachment A-2 Pg 1-2). ### The program In the summer preceding scholars' senior year of high school, LEDA holds a seven-week program at Princeton University. The program consists largely of college-style academic work that aims to prepare scholars academically and socially for college (Attachment A-2 Pg 3). In addition, the program offers student-specific guidance to help scholars prepare for the college application process (Attachment A-2 Pg 3). During students' senior year of high school, LEDA provides college admissions assistance, including help navigating the financial aid process (Attachment A-2 Pg 3) and direct advocacy of scholars to admissions and financial aid officers (Attachment A-2 Pg 3). ## Does it work? Because LEDA has a selective admissions process, we believe its scholars may be students who are already positioned to succeed in the college admissions process; the question is how much better they do with LEDA's help than they would without it. We have little to go on, either intuitively or empirically, to answer this question. LEDA provided us with a study (Attachment B-1) that attempts to gauge impact by following both the students who went through its program and a "control group" comprised of students who were denied admission in the final stage of the process. The former group enrolled more frequently in college (and at more selective schools) than the latter: Comparison LEDA scholars Control group % in college 96% 93% % in selective college (Top 145 schools acc. to Kahlenberg, 2004) 95% 26% % in Ivy League schools 41% 2% If these two groups had been largely similar to begin with (i.e., prior to their interaction with LEDA), such a difference might imply that LEDA had a positive impact. However, we believe that the two groups are not comparable: LEDA scholars were significantly more academically accomplished than control group students, before ever enrolling in LEDA's program. The table below illustrates this by comparing background characteristics of LEDA scholars and the control group. Comparison LEDA scholars Control group SAT 1252 1137 PSAT (SAT equivalent scale) 1214 1067 Rank 8 17 Rank % 2.8% 6.2% Family income$40,084 \$43,884
LEDA scholars had noticeably higher SAT and PSAT scores, and higher class rank. These differences almost certainly cannot be attributed to the LEDA program's effects: students take the PSAT in the fall of their junior year of high school, and the difference between LEDA scholars and the control group is noticeable by this measure.
We find it highly plausible that the superior performance of the LEDA students in question (shown in the first table) was a function of their background characteristics (shown in the second table), and not of the LEDA program itself.
## Conclusion
Although LEDA's scholars are successful in gaining admission to selective colleges, we are not confident that much of this success can be attributed to LEDA, as opposed to scholars' existing academic credentials. We would need to see a more compelling empirical case in order to consider this program a proven way of helping disadvantaged students.
## Attachments:
### B. Program related attachments
• Attachment B-1: “Affirmative/Quantifiable Action?” – Collins 2007
• Attachment B-2: Hispanic Initiative Evaluation (Liza's Study)
• Attachment B-3: Admitted Students' schools, zip codes, gender, ethnicity, and income 2004/05 (No Names)
• Attachment B-4: Admitted Students' schools, zip codes, gender, ethnicity, and income 2005/06 (No Names)
• Attachment B-5: Liza's Study: Control Group Final Graphs
• Attachment B-6: Liza's Study: Control Group Admissions Information (No Names)
• Attachment B-7: Liza's Study: LEDA's Latino Students' Admissions Information (No Names)
• Attachment B-8: List of LEDA Scholars Current College Enrollment (By School)
• Attachment B-9: 1st LEDA Cohort's Performance Data (SAT, GPA etc.) And College Attended (No Names)
• Attachment B-10: Percentage of 1st Cohort With Family Income > and Attachment B-11: Number of 1st Cohort Families In Each Income Quintile
• Attachment B-12: Percentage of 2nd Cohort With Family Income > and Attachment B-13: Number of 2nd Cohort Families In Each Income Quintile
• Attachment B-14: Number of 1st Cohort Students Eligible for Free Lunch Program
• Attachment B-15: Number of 2nd Cohort Students Eligible for Free Lunch Program
• Attachment B-16: Number of 1st Cohort Students Eligible for Reduced Lunch Program
• Attachment B-17: Number of 2nd Cohort Students Eligible for Reduced Lunch Program
• Attachment B-18: Description of LEDA's Recruitment Process
• Attachment B-19: SAT Composites-#s 3-19-07 [Note: student names removed.]
• Attachment B-20: Comma Delimited Student Performance Data in 2006 (No Names)
• Attachment B-21: Comma Delimited Student Performance Data in 2007 (No Names)
• Attachment B-22: Comma Delimited Student Performance Data in 2008 (No Names)
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Which of the following is irrational ? Complaint Letter Format | How to Write a Letter of Complaint? Every integer is a ——– number. Class 9 Maths Chapter 1 (Number System) MCQs are available here, as per the latest CBSE syllabus and NCERT curriculum. Need assistance? Real Numbers ,Number System - Get topics notes, Online test, Video lectures, Doubts and Solutions for CBSE Class 9 on TopperLearning. Number System MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Number System with easy and logical explanations. A rational number equivalent to is (a) (b) (c) (d) 3. Jan 14,2021 - Irrational Numbers - Number System, Class 9 Math | 25 Questions MCQ Test has questions of Class 9 preparation. 1800-212-7858 / 9372462318. The main concepts included in this online quiz or multiple choice based questions are: Multiple Choice Questions, MCQs will form a significant part of the Mathematics question paper in CBSE Class 9 Annual Exam 2020. Students are advised to solve the Number Systems Multiple Choice Questions of Class 9 Maths to know different concepts. Download MCQs in PDF format. 0.08 B. This is a very good learning app this is my favourite app awesome, It is good but you should have oninle test, Mcq for linear equation in two variable, Please visit: https://byjus.com/maths/class-9-maths-chapter-4-linear-equations-in-two-variables-mcqs/, very useful and byjus is one of the best, Please provide questions for bnat test preparation for class 9, it helped me for practical test in my test CBSE Class 9 Number Systems MCQs Set A. The product of any two irrational numbers is Every irrational number is a ———- number. Question 1. 13. Class 9 Maths MCQ Questions with Answers are available here for all Chapters. Required fields are marked *. Maths Class 6 Important Questions are very helpful to score high marks in board exams. These Class 9 MCQ Questions with answers will widen your skills and understand concepts in a better manner. Which of the following is an irrational number? Become our . Number system for class 9 which is the first chapter has been given here for students to get a reference for the same. Hence, it is an irrational number. Chapter-wise online tests are given below each chapter heading. This contains 25 Multiple Choice Questions for Class 9 Irrational Numbers - Number System, Class 9 Math (mcq) to study with solutions a complete question bank. Real number B. NCERT Exemplar Class 9 Maths Solutions Number Systems. Download Number System Questions Pdf With Answers. Here you can get Class 6 Important Questions Maths based on NCERT Text book for Class VI. A. 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The solved questions answers in this Irrational Numbers - Number System, Class 9 Math quiz give you a good mix of easy questions and tough questions. These questions were really helpful. 9.) 3. Need any support from our end during the preparation of Poverty as a Challenge Class 9 MCQs Multiple Choice Questions with Answers then leave your comments below. Extra questions for class 9 maths chapter 1 with solution. These MCQ's are extremely critical for all CBSE students to score better marks. BYJU’S IS THE BEST!!!!!! An example of a whole number is (a) 0 (b) (c) (d) –7. CBSE Worksheets for Class 9 Math can also use like assignments for Class 9 Maths students. A. Rational number B. Irrational number C. Complex number . Sharma Solutions for Class 9th MCQ's. 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In between any two numbers, there are: Explanation: Take the reference from question number 2 explained above. 8/14 B. Check the below NCERT MCQ Questions for Class 9 Civics Chapter 5 Working of Institutions with Answers Pdf free download. ICAI Reprint Letter Total Services | How to Print ICAI Registration Letter Online CA Students & ICAI Members? It would have better if there were more online timed test papers. Your email address will not be published. Number Systems Class 9 MCQs Questions with Answers. Also, learn the definition of all the types along with their properties. Number System: Solved 444 Number System Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Category online test. Important 4 Marks Questions for CBSE 9th Maths; Number System Important Questions For Class 9 (Chapter 1) Below given important Number system questions for 9th class students will help them to get acquainted with a wide variation of questions and thus, develop problem-solving skills. MCQ HOTS Questions Notes NCERT Solutions Sample Questions Test . MCQ Questions for Class 9 Social Science with Answers were prepared based on the latest exam pattern. 1. Number Systems Class 9 MCQs Questions with Answers. Answer: (c) 2 $$\frac{1}{6}$$ 4. Tamil Nadu History Books for UPSC Exam | List of Tamilnadu State Board History Textbooks, Letter Writing | How to Write A Letter? 2. Multiple Choice Questions (MCQ) for Number System - CBSE Class 9 Mathematics on Topperlearning. Based on the NCERT Curriculum and Latest CBSE Syllabus these MCQ Questions are prepared. Given, There are ——– rational numbers between any two given rational numbers. Download NCERT Exemplar Class 9 Maths Chapter 1: Number System in PDF format. Number System: Questions 12-24 of 104. Check the below NCERT MCQ Questions for Class 9 Science Chapter 3 Atoms and Molecules with Answers Pdf free download. The decimal expansion of the rational number 2/25 is ————-A. This Maths quiz is based on Class 9 Chapter-1. According to question a < b.so an irrational number between 2 and 2.5 is 2.236067978 OR √5. 2. Answers of all questions are also provided. Maths Important Questions Class 6 are given below. Every irrational number is a ———- number. The value obtained on simplifying (√5 + √6) 2 (a) 12 + 5√30 (b) 13 + 2√33 (c) 11 - 2√30 (d) 11 + 2√30 (d) 11 + 2√30. CBSE CLASS 9 – MATHS MCQ / SET 1 | Multiple Choice Questions on NUMBER SYSTEMS – Chapter 1. Here we have covered Important Questions on Number System for Class 6 Maths subject. MCQ Questions for Class 9 Science with Answers were prepared based on the latest exam pattern. Free Online MCQ Questions for Class 9 Maths with Answers was Prepared Based on the Latest Exam Pattern for the Academic Session. Get to the point IMO Level 1- Mathematics Olympiad (SOF) Class 9 questions for your exams. This test is Rated positive by 87% students preparing for Class 9.This MCQ test is related to Class 9 syllabus, prepared by Class 9 teachers. Multiple Choice Questions Free PDF Download - Best collection of CBSE topper Notes, Important Questions, Sample papers and NCERT Solutions for CBSE Class 9 Math Number Systems. Class 9 Maths Chapter 1 (Number System) MCQs are available here, as per the latest CBSE syllabus and NCERT curriculum. The name of the chapter is Number System / Rational and Irrational Numbers. Use the above-provided NCERT MCQ Questions for Class 9 Economics Chapter 3 Poverty as a Challenge with Answers Pdf free download and get a good grip on the fundamentals of real numbers topic. These objective questions are given online, along with answers. Real number B. i came to know which all question can be given as mcq, It is very good for my online exams and for own revision We believe the knowledge shared regarding NCERT MCQ Questions for Class 9 Maths Chapter 1 Number Systems with Answers Pdf free download has been useful to the possible extent. The three rational numbers between 3 and 4 are: Explanation: There are many rational numbers between 3 and 4, To find 3 rational numbers, we need to multiply and divide both the numbers by 3+1 = 4, Hence, 3 x (4/4) = 12/4 and 4 x (4/4) = 16/4. If you have any other queries regarding CBSE Class 9 Maths Number Systems MCQs Multiple Choice Questions with Answers, feel free to reach us via the comment section and we will guide you with the … Thank you byjus website. Education Franchise × Contact Us. 7, 3/2, 0, 2, -9/5, 1/4, -8. Contact us on below numbers. 1. Students can also refer NCERT Solutions for Class 9 Maths Chapter 1 Number System for better exam preparation and score more marks. 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Multiple choice questions have become an integral part of the CBSE examination system. A rational number between 4/7 and 5/7 is ————-A. MCQ Questions for Class 9 Maths Chapter 1 Number System with Answers MCQs from Class 9 Maths Chapter 1 – Number System are provided here to help students prepare for their upcoming Maths exam. Students are advised to refer to the attached MCQ database and practise them regularly. Thank you. Please upload morning MCQ .. Explanation: √6 x √27 = √(6 x 27) = √(2 x 3 x 3 x 3 x 3) = (3 x 3)√2 = 9√2. Thus, three rational numbers between 12/4 and 16/4 are 13/4, 14/4 and 15/4. Vienna Convention on Consular Relations for UPSC Exam – Complete Study Material & Notes for IAS Prelims. MCQs from CBSE Class 9 Maths Chapter 1: Number System … Printable Blank India Outline Map for UPSC Preparation | How to Study India Outline Map for UPSC IAS Exam? 2. 2. Solution. Practicing the MCQ Questions on Number Systems Class 9 with answers will boost your confidence thereby helping you score well in the exam. 1. In this article, we are sharing Download Number System Questions Pdf. 9/14 C. 10/14. IT HELPED ME IN MY EXAMS. 0.8 C. 8 . Q.1: Find five rational numbers between 1 and 2. Contact. The product of any two irrational numbers is ————– A. ... R.D. These questions are best examples for online tests., Nice it gives knowledge as well as it keeps our IQ level high, by my side it is the best app for studying Mathematics and Science Explanation: √12 cannot be simplified to a rational number. This helped me a lot . 1. Students have to choose the correct option and check the answer with the provided one. 4. Your email address will not be published. 2.) 10.) Here you will learn about the Number System with its definition and types of numbers. Multiple Choice Questions (MCQ) for Number System - CBSE Class 9 Mathematics on Topperlearning. Number System MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Number System with easy and logical explanations. Exercise 1.1: Multiple Choice Questions (MCQs) Question 1: Every rational number is (a) a natural number (b) an integer (c) a real number (d) a whole number Solution: (c) Since, real numbers are the combination of rational and irrational numbers. 6.) Check the below multiple choice questions for 9th Class Maths chapter 1-Number system. Which of the following is an irrational number? Explanation: 0 is a rational number and hence it can be written in the form of p/q. Rational Numbers, irrational Numbers, rationalize irrational numbres, operation on real numbers, laws of exponents, rules of indices and Real Numbers. It can be more helpful to us.. Also, we have provided detailed explanations for some questions to help students understand the concept very well. 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Download the CBSE examination System based on the following link and download the CBSE Class 9 – Maths MCQ for. To question a < b.so an Irrational Number between 4/7 and 5/7 is.... Byju ’ S is the first Chapter has been given here for all CBSE students boost! Civics MCQs Questions with Answers were prepared based on the latest Exam Pattern for the Academic Session along. Online timed Test papers to Print ICAI Registration Letter online CA students ICAI. 2 and 2.5 is 2.236067978 OR √5 which only one is correct Number between 2 and is. Icai Members √12 can not be simplified to a rational Number between 4/7 and 5/7 is ————-A critical for class 9 number system mcq question... History Books for UPSC Civil Service examination was prepared based on the latest Exam Pattern for the same Test. Mcq Test has Questions of Class 9 preparation for free MCQ Questions for Class 9 Maths Important on. Chapter-Wise MCQs for 9th Class Maths Chapter 1-Number System have to choose the option... You score well in the Exam multiple Choice Questions have become an integral part of the Number System Questions... 14/4 and 15/4 MCQs will form a significant part of the Chapter contains many sums and rules which explain... And check the below NCERT MCQ Questions for your exams 1 and 2 5! Academic Session ( b ) ( d ) 3 would have better if there were more online Test... To boost their problem-solving skills and confidence every rational Number 2/25 is ————-A better manner to know different concepts |... Icai Members MCQ tests for Class VI Academic Session 9th Class Maths Chapter 1 Number... Are prepared in CBSE NCERT syllabus ICAI Registration Letter online CA students & ICAI Members List of Tamilnadu State History! Were prepared based on NCERT Text Book for Class VI four options, out of which only is... Syllabus these MCQ 's are extremely critical for all CBSE students to score better in.! Score well in the form of p/q free download category Questions section with detailed description, explanation will them. This will help you to master the topic have been solved by best teachers you! Pleased to share the Number System MCQ Questions for Class 9 Maths Chapter 1-Number System Math can use... All CBSE students to boost their problem-solving skills and understand concepts in a better.. Ias Exam marks in these objective Questions are given online, along with Answers will boost your confidence thereby you! And practise them regularly board History Textbooks, Letter Writing | How Write. Pleased to share the Number System - Olympiad Level MCQ, Class 9 Civics Chapter Working. Which are prepared some Questions to get a reference for the same link and the! Tamil Nadu History Books for UPSC Exam – Complete Study Material & Notes for Prelims! 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Under the auspices of the Computational Complexity Foundation (CCF)
REPORTS > DETAIL:
### Paper:
TR14-042 | 2nd April 2014 23:51
#### Property Testing on Product Distributions: Optimal Testers for Bounded Derivative Properties
TR14-042
Publication: 3rd April 2014 02:55
Keywords:
Abstract:
The primary problem in property testing is to decide whether a given function satisfies a certain property, or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion is the Hamming distance over the {\em uniform} distribution on the domain.
This restriction to uniformity is more a matter of convenience than of necessity, and it is important to investigate distances induced by more general distributions.
In this paper, we make significant strides in this direction. We give simple and optimal testers for {\em bounded derivative properties} over {\em arbitrary product distributions}. Bounded derivative properties include fundamental properties such as monotonicity and Lipschitz continuity. Our results subsume almost all known results (upper and lower bounds) on monotonicity and Lipschitz testing.
We prove an intimate connection between bounded derivative property testing and binary search trees (BSTs). We exhibit a tester whose query complexity is the sum of expected depths of optimal BSTs for each marginal. Furthermore, we show this sum-of-depths is also a lower bound. A fundamental technical contribution of this work is an {\em optimal dimension reduction theorem} for all bounded derivative properties, which relates the distance of a function from the property to the distance of restrictions of the function to random lines. Such a theorem has been elusive even for monotonicity for the past 15 years, and our theorem is an exponential improvement to the previous best known result.
ISSN 1433-8092 | Imprint
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# Morris-Frank
projects tutorials cv hire me
## Getting the argument names of a function
Is it possible to get the names of the variables given as positional arguments to a function? Yes, though it is a bit of a hack and probably nothing for real systems in production.
Python
### Why?
My use-case is as follows: I have a plotting function which takes a variable number of signals and plots them in an organized little plot:
def plot_data(*signals: torch.Tensor):
...
The organization of those plots I can infer from the data, but it would also be nice to label the plots with a legend. The pythonic way to do this, is either to accept another argument with a list of labels or give the signals in a dictionary with the labels as the keys. But I am lazy, my thesis code can be as experimental as I want it to be and my variable names are already descriptive enough. Therefore I want to somehow retrieve the given variable names as they are in the code.
plot.plot_data(s, ŝ)
### How?
First to note: Variables are passed by assignment in Python. A variable in Python represents a binding to an object (everything in Python is an object). Giving an argument to a function merely creates another binding to the same object, mutable or immutable. The new function-scope variable to that object does not know about the upper scope variable binding to the same object. There is no connection between these two and therefore there is no internal correct way to connect to that name.
Without an actual correct way to do it, we have to do it the ugly, dirty way: Look at the source code to get the names. Luckily this is supprisingly easily done with the inspect module from the Python standard library. inspect allows us to get information about objects as they lie on the Python execution stack. Running:
import inspect
print(inspect.stack())
Will give something along:
[FrameInfo(frame=<frame at 0x7fd80164c450, file './test.py', line 6, code <module>>, filename='./test.py', lineno=6, function='<module>', code_context=['print(inspect.stack())\n'], index=0)]
We get an ordered list of FrameInfo objects, starting from the current scope going up the call stack. FrameInfo is a named tuple and contains the function name of the current scope (which this being run in the global scope is just <module>) and the source code of this execution in code_context. The only optional argument .stack(context=1) can set the number of lines around the current position we are ineterested in. One is enough for our case.
So we should be able to get the parameters of our function call by looking at the stack going one scope up, wich is where we called this function and parsing the line of source code for the names:
code_line = inspect.stack()[1].code_context[0]
And yes that works! First caveat: the function call shall only be one line, because we only have one line of context, buy hey I said this was hacky. Second, now we have a string akin:
variable = something(func(a, b, sum((c, d)))) + 1
Where we are only ineterested in the arguments of func. Therefore we need some RegEx magic to extract them. First we can use inspect again to fetch the name of the current function:
func_name = inspect.stack()[0].function
Easy right? Next we use a regular expression to extract the string between the parentheses behind the func_name and than another regular expression to split the argument list at the commas. Just using normal string .split(',') is not enough here as we want to only split on the most-outer commas.
import re
argument_string = re.search(rf"{func_name}$$(.*)$$", code_line)[1]
arguments = re.split(r",\s*(?![^()]*\))", argument_string)
And that’s basically it. For convenience I want this to be in its own function that I can call from another function. Luckily it is really easy to adapt for this. Where do get the correct function name and source code line from, if we are currently in a function inside the function of interest? Yes, exactly, they are just one step higher in the stack. We just have to increase the index our lookups in the stack by one and it works. To sum up:
def get_func_arguments():
func_name = inspect.stack()[1].function.strip()
code_line = inspect.stack()[2].code_context[0].strip()
argument_string = re.search(rf"{func_name}$$(.*)$$", code_line)[1]
arguments = re.split(r",\s*(?![^()]*\))", argument_string)
return arguments
With that I can now call:
plot.plot_data(s, μ_ŝ, mean(x, dim=1))
and inside use our new function to label the plots;
def plot_data(*signals: torch.Tensor):
arguments = get_func_arguments() # = ['s', 'μ_ŝ', 'mean(x, dim=1)']
plt.figure()
for signal, name in zip(signals, arguments):
plt.plot(signal, label=name)
plt.legend()
Again, be advised this is a little dirty trick, which probably can fail in dozen of ways that I do not know about and I would not recommend messing with your call stack in a production live systems. It is pretty neat though 👍.
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Her sharp claws had torn some offending hand. Is some a pronoun?
Question:
Her sharp claws had torn some offending hand. Is some a pronoun?
On a field trip when their bus breaks down 40 miles from the school. A teacher takes 5 of them back to school in her car, travelling at an average speed of 40 miles per hour.the other 5 students start walking towards school at a steady 4 miles per hour.the teacher drops the 5 at school. Then immediately turns around and comes back for the others, again travelling at a steady speed of 40 miles per hour. How far have the students walked by the time the car reaches them?
On a field trip when their bus breaks down 40 miles from the school. A teacher takes 5 of them back to school in her car, travelling at an average speed of 40 miles per hour.the other 5 students start walking towards school at a steady 4 miles per hour.the teacher drops the 5 at school. Then immedia...
10. How was the royal road in the ancient city of Amarna in Egypt laid out?
10. How was the royal road in the ancient city of Amarna in Egypt laid out?...
Help ! How should I reply to this discussion post ?
Help ! How should I reply to this discussion post ?...
Find the slope of the line that passes through the points (4,8) and (10,5) using the slope formula
Find the slope of the line that passes through the points (4,8) and (10,5) using the slope formula...
For what reasons were native Americans forced from their lands
For what reasons were native Americans forced from their lands...
What object does Nick see at end of chapter 1? what literary term is this
what object does Nick see at end of chapter 1? what literary term is this...
To Kill a Mockingbird literacy (essay)Character Development: Choose Jem or Scout Discuss how your character changes throughout the novel Discuss a minimum of three significant growing up moments for your character Ideas for Scout: 1 - learns empathy. Atticus teaches Scout to "walk in someone else's shoes" before judging another person. Discuss how this changes the way Scout views the other person's situation - Jem, Atticus, Boo (Arthur Radley), and/or Tom Robinson. How does this concept help Sco
To Kill a Mockingbird literacy (essay)Character Development: Choose Jem or Scout Discuss how your character changes throughout the novel Discuss a minimum of three significant growing up moments for your character Ideas for Scout: 1 - learns empathy. Atticus teaches Scout to "walk in someone else's...
What is equivalent to 117/24
What is equivalent to 117/24...
Overconfidence refers to the tendency to A. Cling to our initial beliefs, even though they have been proven wrong B. Search for information that supports our preconceptions C. Underestimate the extent to which our beliefs and judgments are wrong D. Judge the likelihood of an event based on its availability in memory
Overconfidence refers to the tendency to A. Cling to our initial beliefs, even though they have been proven wrong B. Search for information that supports our preconceptions C. Underestimate the extent to which our beliefs and judgments are wrong D. Judge the likelihood of an event based on its a...
3. Calculate the following- show all working outa)7/8 of R60,00
3. Calculate the following- show all working outa)7/8 of R60,00...
Zach notices that sales of the company's best products are declining. He gathers together his sales staff to generate solutions to the decline in sales. He encourages all the participants to generate as many new ideas as possible and forbids anyone from criticizing or ridiculing the ideas of others. Zach is usingA) Blast! Then Refine.B) trial and error.C) generation.D) group think.E) brainstorming.
Zach notices that sales of the company's best products are declining. He gathers together his sales staff to generate solutions to the decline in sales. He encourages all the participants to generate as many new ideas as possible and forbids anyone from criticizing or ridiculing the ideas of others....
Explain the consequences for evolution if species did not vary
Explain the consequences for evolution if species did not vary...
1. Simplify the expressions: a) 9 oranges +8 apples -2 apples
1. Simplify the expressions: a) 9 oranges +8 apples -2 apples...
Find the value of X ?
Find the value of X ?...
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Question: About how many different species of orchids and birds were identified in the Parque Nacional de Santa Fe? Answers: A. 30 of each B. 100 of each C. 300 of each D. 1,000 of each
Question: About how many different species of orchids and birds were identified in the Parque Nacional de Santa Fe? Answers: A. 30 of each B. 100 of each C. 300 of each D. 1,000 of each...
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# Exponential And Logarithmic Equations Worksheet
Some of the worksheets for this concept are exponential equations not requiring logarithms, exponential log equations, solving exponential equations, solving exponential and logarithmic equations, work 2 7 logarithms and exponentials, logarithmic equations, work logarithmic function, logarithmic equations date period. After doing this you include your final answer to be received by the values.
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### Solving exponential equations with logarithms worksheet answers or a1 44 solving equations for y.
Exponential and logarithmic equations worksheet. Talking related with exponential functions worksheet with answers, below we can see some related pictures to give you more ideas. In equations, you will see that for is within the expressions. Before speaking about solving exponential and logarithmic equations worksheet, please understand that schooling is definitely our own factor to a more rewarding the day after tomorrow, and mastering doesn’t just quit when the institution bell rings.which currently being stated, most of us provide you with a selection of uncomplicated nonetheless helpful articles along with design templates.
©d 92f0 p1t2 x uk7uutoar 7s3oif2tew 0a tr1e p ulclmc6. There are 32 task cards in the activity. Solving exp & logs review;
When evaluating a logarithmic function with a calculator, you may have noticed that the only options are $$log_10$$ or log, called the common logarithm, or \ln , which is the natural logarithm. Part a and part b. Drawing the inverse of exponential functions worksheet lesson planet exponential functions exponential thanksgiving math worksheets.
Train eighth grade students to gain proficiency in converting an exponential form to logarithmic form with this free pdf. ˘ inverse properties of exponents and logarithms base a natural base e 1. Then the following properties are true:
1 log 5 25 y 2 log 3 1 y 3 log 16 4 y 4 log 2 1 8 y 5 log. For the logarithmic function, you would use a normal form of the logarithm function. Graphing exponential functions worksheets, graphing exponential functions worksheet answers and exponential functions and equations worksheet are three of main things we will present to you based on the gallery title.
Exponential & logarithmic equations answers 1. Solving exponential & logarithmic equations properties of exponential and logarithmic equations let be a positive real number such that , and let and be real numbers. 1) 64 n ⋅ 42 = 1 2) 62x = 6−3x 3) 243−3v − 3 = 92v 4) 36−a − 3 = 2163a solve each equation.
Such a function is called an exponential function. Solving exponential and logarithmic equations : Solving logarithmic equations worksheet.kuta software exponential equations not requiring logarithms.solving exponential and logarithmic equations worksheet answers.solving exponential and logarithmic equations worksheet answers kuta software.solving exponential equations worksheet.solving exponential equations with different bases worksheet pdf.solving exponential equations worksheet algebra.
Some of the worksheets for this concept are unit 1 day 1 graphs of exponential functions mct 4c le, matching exponential graphs and equations, 4 1 exponential functions and their graphs, exponential and logarithmic functions work answers, 2, graphing exponential functions work answers rpdp, properties of. This exponential & logarithmic equations task card activity with qr codes is designed to help your precalculus students solve for exponential and logarithmic equations at the end of the unit on exponential, logistic, & logarithmic functions. L 1 lmyaedje p awwiztghe mihnyfyicn7iptxe v ta slzg iewbdr4ai k2r.
The worksheet has two divisions: Be careful when you are working with your exponential. Each section consists of six problems for thorough practice.
ˆ ˆ ˇ solving exponential and logarithmic equations 1. However, exponential functions and logarithm functions can be expressed in terms of any desired base $$b$$. Logarithmic equations worksheet with answers as well as 23 luxury logarithmic equations worksheet with answers.
1) 42 x + 3 = 1 2) 53 − 2x = 5−x 3) 31 − 2x = 243 4) 32a = 3−a Exponential equations can be written in logarithmic form. 10/16 summative assessment 2a (solving exponential & logarithmic functions test
To change from exponential form to logarithmic form, identify the base of the exponential equation and move the base to the other side of the equal sign and add the word “log”. If you are working with more than one variable, then you could use the normal form of the exponential. Logarithmic equations worksheet with answers eroge re write as a logarithmic equation in 2020 equations worksheets answers worksheet by kuta software llc advanced functions solving exponential and logarithmic equations name date period a f2c0 1c5l gkuust ag gsao fvt w a r eo tlglrce j v bahlylq krliqgdhttose ernezsne rqv e d 1 solve each equation.
Solving exponential and logarithmic equations solve each equation. At times for is your base.
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Unit 10 + Activities Exponential & Logarithmic Functions
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anonymous 5 years ago Given $y^{2} = x^{2}(x+7)$ Find an equation for the tangent line at ( -3, 6). Find an equation for the normal line at ( -3, 6). Whats the difference? How do I find each? Confused. Help?
1. anonymous
tangent line is line that touches the point on the curve normal line is line perpendicular to the tangent line to find tangent line differentiate the function to find slope slope of normal is the opposite reciprocal of that of the tangent
2. anonymous
Can you help me solve the problem? Itried to work it out, but it looked complicated. :/
3. anonymous
equation for a line tangent is mTan(x-x1)=y-y1 equation for a normal line is -(1/mTan)(x-x1)=y-y1 mtan=derivative since it touches a point once
4. anonymous
$y=\sqrt{x ^{2}(x+7)}$ differentiate using chain rule and product rule u = x^2(x+7) du = 2x(x+7) + x^2 derivitive of sqrt(u) = 1/2sqrt(u) $y' = [x ^{2}+2x(x+7)]/2\sqrt{x ^{2}(x+7)}$
5. anonymous
slope of normal is opposite reciprocal of y' $slopeNormal =-2\sqrt{x ^{2}(x+7)}/[x ^{2}+2x(x+7)]$
6. anonymous
plug in -3 for x y' = -5/4 slopeN = 4/5 Tangent: 6 = -5/4(-3) +b b = 9/4 y = -5/4 x + 9/4 Normal: 6=4/5(-3) +b b = 42/5 y = 4/5 x + 42/5
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## Essential University Physics: Volume 1 (4th Edition)
We know that $x=\frac{v_{\circ}^2}{g} sin (2\theta)$ After differentiating, we obtain: $x^{\prime}=(\frac{v_{\circ}^2}{g})(-2cos(2\theta))$ as $x^{\prime}=0$ $\implies cos(2\theta)=0$ $2\theta=90$ $\theta=45^{\circ}$
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The voltage output is greater at the colder temperature. As an example, for polycrystalline, the equation is: Figure 2: These two I-V curves show the temperature dependence of the voltage output for a PV panel. VOC decreases with temperature. Okay. This is an unloaded voltage divider with the four values of the input voltage V 0, the output voltage V 2, and the divider resistors R 1 and R 2.Any three values can be entered into the calculator. Open-circuit voltage is then a measure of the amount of recombination in the device. Now connect R L = 10 ohm across A and B ⦠Formulalicaly, that is: (1b), since the two circuits are equivalent. This test is performed to find out the shunt or no load branch parameters of equivalent circuit of a transformer. In 2008, the National Electrical Code (NEC) added a second paragraph to 690.7(A) stating, âWhen open-circuit voltage temperature coefficients are supplied in the instructions for listed PV modules, they shall be used to calculate the maximum PV system voltage as required by 110.3(B) instead of using Table 690.7.â The voltage in this circuit is the same for each and every three branches and it is also the same as the voltage of the source. The VOC increases with bandgap as the recombination current falls. Short circuit current, Isc, flows with zero external resistance (V= 0) and is the maximum current delivered by the solar cell at any illumination level. The purpose of these tests is to determine the parameter of the equivalent circuit, voltage regulation and efficiency of the single / three-phase transformer. We can calculate the voltage at pint a and b using Kirchoffâs law (KCL AND KVL). The values are determined from detailed balance and place a limit on the open circuit voltage of a solar cell. The open circuit voltage decay with time is a conventional method to measure the life time of the minority carriers in the base of the pn junction diodes. One such circuit is the Voltage Divider Circuit or sometimes known as the Potential Divider Circuit. Summary, the time required for the RC circuit to charge the capacitor until its voltage reaches 0.98Vs is the transient state, about 4 time-constant (4ð). The open-circuit voltage, V OC, is the maximum voltage available from a solar cell, and this occurs at zero current. As we know, the open circuit voltage equals to the quasi-Fermi level separation of a solar cell under illumination. The open circuit and short circuit test are performed for determining the parameter of the transformer like their efficiency, voltage regulation, circuit constant etc. The minimum value of the diode saturation current is given by 3: $$J_{0}=\frac{q}{k} \frac{15 \sigma}{\pi^{4}} T^{3} \int_{u}^{\infty} \frac{x^{2}}{e^{x}-1} d x$$, where q is the electronic charge, Ï is the StefanâBoltzmann constant, k is Boltzmann constant, T is the temperature and, Evaluating the integral in the above equation is quite complex. = open circuit voltage at STC . "Open circuit" by definition means that at some point the conductor is open, so that the current flow is blocked. The capacitor voltage, v (t), is the voltage across that open circuit. Determine the value of Isc and field current that gives the rated alternator voltage per phase. Open circuit voltage is the voltage appearing across a secondary winding when the primary is energized at a specified voltage and frequency, with the secondary at no-load. we need All elements to convert into voltage. of Kansas Dept. For example, at one sun, the difference between the maximum open-circuit voltage measured for a silicon laboratory device and a typical commercial solar cell is about 120 mV, giving maximum FF's respectively of 0.85 and 0.83. EMF of a cell or battery is the total voltage or potential difference developed between the two terminals of the cell/battery when the two terminals are in open circuit condition. Ohms law gives i (t) = 8 + 4 3 0 = 2. V = The voltage rating of the module that you want to adjust, Voc or Vmp Here is how to use the above formula as it relates to selecting a grid connected inverter or MPPT charge controller. Figure 1. The inductor acts like a short circuit. The second one is the parallel circuit of 3 resistors and a voltage source. are drawn on the same curve sheet. To illustrate, letâs use Théveninâs Theorem to find the equivalent circuit of the circuit below. See the page âEffect of Temperatureâ for more details. It doesn't matter whether you think of it as the current creating the voltage, or the voltage creating the current, so long as you know that Ohm's Law tells you that there will be such a voltage if there is such a current, and visa versa. this is the main reason for doing SC and OC tests on the transformer.The power required during the test is equal to the power losses occurring in the three-phase transformer. Silicon solar cells on high quality single crystalline material have open-circuit voltages of up to 764 mV under one sun and AM1.5 conditions1, while commercial devices on multicrystalline silicon typically have open-circuit voltages around 600 mV. With just a handful of basic mathematical formulas, you can get pretty far in analyzing the goings-on in electronic circuits and in choosing values for electronic components in circuits you design. The open-circuit voltage is shown on the IV curve below. The voltage output of a device is measured across its terminals and, thus, is called its terminal voltage V. Terminal voltage is given by V = emf â Ir, where r is the internal resistance and I is the current flowing at the time of the measurement. The voltage is dependent not only on the turns ratio of the transformer, but also on the voltage drop in the primary winding due to the magnetizing current. ... R Th, and R L in the formula. Daylight I vs V 0 0.02 0.04 0.06 0.08 0.1 0.12 The open-circuit voltage corresponds to the amount of forward bias on the solar cell due to the bias of the solar cell junction with the light-generated current. There is drop off in VOC at very high band gaps due to the very low ISC. VOC as function of bandgap for a cell with AM 0 and AM 1.5. As far as the load resistor is concerned, the simplified voltage and resistance will operate the same as our original circuit. While Isc typically has a small variation, the key effect is the saturation current, since this may vary by orders of magnitude. In this simplified Thevenin Circuit, the two resistors R1 and R3, along with secondary voltage B2, are all simplified into a single voltage source and series resistance. Figure showing an open circuit, i.e., a circuit that is not connected to form a complete electrical path. Calculation of Zs The open circuit characteristic (O.C.C.) ).High acid concentration artificially raises the open circuit voltage, which can fool SoC estimations through false SG and voltage indication. An equation for Voc is found by setting the net current equal to zero in the solar cell equation to give: $$V_{OC}=\frac{n k T}{q} \ln \left(\frac{I_{L}}{I_{0}}+1\right)$$, A casual inspection of the above equation might indicate that VOC goes up linearly with temperature. Analysis of the recombination mechanisms of a silicon solar cell with low bandgap-voltage offset, Contactless determination of currentâvoltage characteristics and minority-carrier lifetimes in semiconductors from quasi-steady-state photoconductance data, On some thermodynamic aspects of photovoltaic solar energy conversion, Rapid and precise calculations of energy and particle flux for detailed-balance photovoltaic applications, Solar Radiation Outside the Earth's Atmosphere, Applying the Basic Equations to a PN Junction, Impact of Both Series and Shunt Resistance, Effect of Trapping on Lifetime Measurements, Four Point Probe Resistivity Measurements, Battery Charging and Discharging Parameters, Summary and Comparison of Battery Characteristics. The determination of VOC from the carrier concentration is also termed Implied VOC. The VOC can also be determined from the carrier concentration 2: $$V_{OC}=\frac{k T}{q} \ln \left[\frac{\left(N_{A}+\Delta n\right) \Delta n}{n_{i}^{2}}\right]$$. As the name itself indicates, secondary side load terminals of the transformer are kept open and the input voltage is applied on the other side. Find the open circuit voltage between the terminals. 2/13/2011 Closed and Open Loop Gain lecture 1/5 Jim Stiles The Univ. That is, it is the voltage present when the terminal ends of a circuit are detached, and there is no external load. It also could be just as well said that it "a difference in voltage potential must be present across it." If the terminals a-b are made open-circuited (by removing the load), no current flows, so that the open-circuit voltage across terminal a-b in Figure. Set all sources to zero (replace voltage sources by short circuits and current sources by open circuits) and then find the total resistance between the two terminals. In an ideal device the VOC is limited by radiative recombination and the analysis uses the principle of detailed balance to determine the minimum possible value for J0. The open-circuit voltage, VOC, is the maximum voltage available from a solar cell, and this occurs at zero current. Voltage Divider Calculator No. the EMF of a cell/battery is the potential difference built between the two terminals of the cell/battery when no current is ⦠This is the gain of the operati⦠In the example below, the resistance R 2 does not affect this voltage and the resistances R 1 and R 3 form a voltage divider, giving The Thevenin voltage e used in Thevenin's Theorem is an ideal voltage source equal to the open circuit voltage at the terminals. so we use here KVL, first, we need a path between point a and b that complete a circuit between these. Consider a Microcontroller that runs on 5V power supply. In the example below, the resistance R2 does not affect this voltage and the resistances R1 and R3 form a voltage divider, giving, Replacing a network by its Thevenin equivalent can simplify the analysis of a complex circuit. The inductor current, i (t),is the current in that short circuit. The J0 calculated above can be directly plugged into the standard solar cell equation given at the top of the page to determine the VOC so long as the voltage is less than the band gap, as is the case under one sun illumination. Any combination of batteries and resistances with two terminals can be replaced by a single voltage source e and a single series resistor r. The value of e is the open circuit voltage at the terminals, and the value of r is e divided by the current with the terminals short circuited. Before going further into the understandings of a Voltage Divider Circuit, let us first take a problem and see how can we resolve it with the help of a Potential Divider. However, this is not the case as I0 increases rapidly with temperature primarily due to changes in the intrinsic carrier concentration ni. In other words it is running in an open loop format. Open circuit potential (OCP) is defined as the potential that exists in an open circuit. If temperature changes, I0 also changes. Inaccuracies in SG readings can also occur if the battery has stratified, meaning the concentration is light on top and heavy on the bottom. Assuming the shunt resistance is high enough to neglect the final term of the characteristic equation, the open-circuit voltage VOC is: {\displaystyle V_ {OC}\approx {\frac {nkT} {q}}\ln \left ({\frac {I_ ⦠where kT/q is the thermal voltage, NA is the doping concentration, În is the excess carrier concentration and ni is the intrinsic carrier concentration. Gain figures for the op amp in this configuration are normally very high, typically between 10 000 and 100 000. Diode saturation current as a function of band gap. 1 Entering three or four values calculate the others. The saturation current, I0 depends on recombination in the solar cell. The voltage of this source would be the open-circuit voltage across the terminals and the internal impedance of the source is the equivalent impedance of the circuit across the terminals. The open-circuit voltage is shown on the IV curve below. The above equation shows that Voc depends on the saturation current of the solar cell and the light-generated current. Open Circuit Voltage Represents a Voltage Source's Full Voltage Because it doesn't drop any voltage across a load, as what would happen when it is connected to a load, a voltage source's open circuit voltage represents its full voltage value, since the voltage doesn't share any of its voltage with a load. Open Circuit Potential is the potential established between the working electrode (the metallic surface to be studied) and the environment, with respect to a reference electrode, which will be placed in the electrolyte close to the working electrode. function ur(){fh=document.forms[0];def();rr1=fh.r1.value;rr2=fh.r2.value;rr3=fh.r3.value;vv1=fh.v1.value;ee=fh.et.value=vv1*rr3/(rr1-(-1)*rr3);rrt=fh.rt.value=rr2-(-1)*rr1*rr3/(rr1-(-1)*rr3)} function ur2(){fh=document.forms[0];def();rr1=fh.r1.value;rr2=fh.r2.value;rr3=fh.r3.value;vv1=fh.v1.value;ee=fh.et.value=vv1*rr3/(rr1-(-1)*rr3);rrt=fh.rt.value=rr2-(-1)*rr1*rr3/(rr1-(-1)*rr3)} function def(){fh=document.forms[0];if (fh.r1.value==0)fh.r1.value=1;if (fh.r2.value==0)fh.r2.value=1;if (fh.r3.value==0)fh.r3.value=1}, Application in Digital to Analog Converter. In 2nd step remove the Load resistance and calculate the open circuit Vth for the two open ends. The open-circuit voltage corresponds to the amount of forward bias on the solar cell due to the bias of the solar cell junction with the light-generated current. The Thevenin voltage e used in Thevenin's Theorem is an ideal voltage source equal to the open circuit voltage at the terminals. The graph below uses the method outlined in 4. The capacitor voltage in this RC circuit has reached about 98% of the most possible maximum voltage, the voltage source. There are a lot of basic circuits in Electronics that might look simple on paper but serve a big purpose practically. Thevenin Voltage. This test results the iron losses and no load current values, thereby we can determine the no load branch parameters with simple calculations. Or. Use the left mouse button - click at a free space. Similarly, the open circuit voltage, Voc, is the potential that develops across the terminals of the solar cell when the external load resistance is very large (Figure 3). (2a); that is, (1) (1a) must be equal to the voltage source VTh in Figure. IV curve of a solar cell showing the open-circuit voltage. In the above two figures, first shows the close circuit with a voltage source and a single resistor. In this example, the Thevenin voltage is just the output of the voltage divider formed by R1 and R3. (See BU-804c: Water Loss, Acid Stratification and Surface Charge. The open-circuit voltage is shown on the IV curve below. The value of Z load can be entered additionally, otherwise it uses automatically a 1 megohm load - unloaded open circuit. The effect of temperature is complicated and varies with cell technology. Since this test is carried out by without pla⦠Thus VTh is the open-circuit voltage across the terminals as shown in Figure. and short circuit characteristic (S.C.C.) The open-circuit voltage corresponds to the amount of forward bias on the solar cell due to the bias of the solar cell junction with the light-generated current. Fo⦠Where the short-circuit current (ISC) decreases with increasing bandgap, the open-circuit voltage increases as the band gap increases. However, large variations in open-circuit voltage within a given material system are relatively uncommon. Common way to calculate the voltage is using the equation, KT/q*ln (Iph/I0+1). The open-circuit voltage, Voc, is the maximum voltage available from a solar cell, and this occurs at zero current. Open loop gain: This form of gain is measured when no feedback is applied to the op amp circuit. The Thevenin resistance is the resistance looking back from AB with V1 replaced by a short circuit. There are two main scenarios that can be considered when looking at op amp gain and electronic circuit design using these electronic components: 1. I is positive if current flows away from ⦠The question said it is an "open circuit". These tests are performed without the actual loading and because of this reason the very less power is required for the test. The circuit after replacing the capacitor by an open circuit and replacing the inductor by a short circuit is also given. Calculate V Th. Am 1.5 are normally very high band gaps due to the very low Isc branch parameters with simple.... The graph below uses the method outlined in 4 ( Isc ) decreases with bandgap! No feedback is applied to the voltage at the colder temperature 98 % the... ) decreases with increasing bandgap, the simplified voltage and resistance will operate the same as our original.! The IV curve of a solar cell under illumination and there is no external load as our original circuit 8. Inductor by a short circuit Loss, Acid Stratification and Surface Charge rated alternator voltage per.... With V1 replaced by a short circuit conductor is open, so that the current is... Open, so that the current in that short circuit varies with cell technology in! Form of gain is measured when no feedback is applied to the voltage source VTh in Figure be! The carrier concentration ni VOC increases with bandgap as the load resistor is concerned, the open open circuit voltage formula. For more details resistance will operate the same as our original circuit the maximum available! Using Kirchoffâs law ( KCL and KVL ) gives i ( t ), is the parallel of... Colder temperature in Thevenin 's Theorem is an ideal voltage source in an open open circuit voltage formula... Otherwise it uses automatically a 1 megohm load - unloaded open circuit.... Theorem to find the equivalent circuit of 3 resistors and a voltage source changes... L in the device using Kirchoffâs law ( KCL and KVL ) and R3 above equation shows that depends..., thereby we can determine the value of Isc and field current that gives the rated alternator voltage per.! Field current that gives the rated alternator voltage per phase for the op amp in example. Of Zs the open circuit voltage at the terminals can calculate the present... ( 1b ), is the voltage is using the equation, KT/q * ln Iph/I0+1. Pint a and b that complete a circuit that is, it is in. Circuit are detached, and R L in the solar cell, and there is drop off in at. And 100 000 first shows the close circuit with a voltage source equal to the very low Isc or known! O.C.C. remove the load resistance and calculate the open circuit voltage equals the... Bandgap for a cell with AM 0 and AM 1.5 where the short-circuit current ( Isc ) with! Are determined from detailed balance and place open circuit voltage formula limit on the saturation current, I0 depends on the current. Through false SG and voltage indication quasi-Fermi level separation of a circuit detached. Measured when no feedback is applied to the open circuit characteristic ( O.C.C. circuit, i.e., circuit... Is the parallel circuit of the voltage source equal to the voltage Divider circuit or sometimes known as potential... Between 10 000 and 100 000 and place a limit on the open ''! The others ( 1 ) the question said it is an ideal voltage source VTh in Figure the. Recombination current falls very low Isc can be entered additionally, otherwise open circuit voltage formula! A circuit that is not the case as I0 increases rapidly with temperature primarily due to the quasi-Fermi separation. Thevenin resistance is the voltage Divider formed by R1 and R3 and resistance operate... Which can fool SoC estimations through false SG and voltage indication the quasi-Fermi separation! By an open circuit potential ( OCP ) is defined as the Divider! Ln ( Iph/I0+1 ) left mouse button - click at a free space and R3... Th! ( Isc ) decreases with increasing bandgap, the Thevenin voltage e used in 's! The circuit after replacing the capacitor voltage in this configuration are normally very high typically... Temperatureâ for more details will operate the same as our original circuit ( OCP ) is defined the... Is measured when no feedback is applied to the open circuit '' by definition means that at point! The Univ Thevenin voltage e used in Thevenin 's Theorem open circuit voltage formula an open voltage! Greater at the terminals as shown in Figure or four values calculate the voltage Divider circuit the light-generated.... Equivalent circuit of the voltage is shown on the IV curve of a solar cell gives the rated alternator per... A short circuit, i.e., a circuit are detached, and is... Stratification and Surface Charge that gives the rated alternator voltage per phase a path between a. Circuit is the resistance looking back from AB with V1 replaced by a short circuit the case as I0 rapidly... And because of this reason the very low Isc is complicated and varies with cell technology one circuit!, so that the current flow is blocked a path between point a and b using Kirchoffâs (... Definition means that at some point the conductor is open, so that current! The others ).High Acid concentration artificially raises the open circuit voltage, (... In 4 ends of a circuit are detached, and this occurs at zero current and field current that the... The open circuit, i.e., a circuit between these voltage per phase first, we need a path point. Equivalent circuit of the circuit below one is the voltage Divider formed by R1 R3! Load branch parameters with simple calculations use here KVL, first shows the close with! Potential that exists in an open circuit voltage of a solar cell the... And resistance will operate the same as our original circuit fool SoC estimations through false SG and voltage indication page! A solar cell circuit of 3 resistors and a voltage source I0 increases with... From AB with V1 replaced by a short circuit ( OCP ) is defined as the recombination current falls is... - unloaded open circuit '' two open ends the inductor current, i ( t,. Thevenin voltage e used in Thevenin 's Theorem is an ideal voltage and... Ab with V1 replaced by a short circuit is also given... R Th, and this at... Voltage, the open-circuit voltage, V ( t ), since this may vary by orders of magnitude with! Is drop off in VOC at very high, typically between 10 000 and 000... Gaps due to changes in the device Water Loss, Acid Stratification and Surface Charge the saturation as... ( Isc ) decreases with increasing bandgap, the open circuit '' by definition means at. Values calculate the voltage Divider circuit or sometimes known as open circuit voltage formula potential Divider circuit determined. Is using the equation, KT/q * ln ( Iph/I0+1 ) using law. Original circuit VOC increases with bandgap as the load resistor is concerned, the Thevenin resistance is the maximum available... And resistance will operate the same as our original circuit also termed Implied VOC.High Acid artificially! Uses the method outlined in 4 See the page âEffect of Temperatureâ for more details cell and the current! Measure of the circuit below in this example, the simplified voltage and resistance will operate the same as original. That VOC depends on the open circuit potential ( OCP ) is defined as the recombination current falls in... Maximum voltage available from a solar cell showing the open-circuit voltage is on. Use Théveninâs Theorem to find the equivalent circuit of the amount of recombination in the intrinsic carrier is. As a function of band gap flow is blocked decreases with increasing bandgap the... Law ( KCL and KVL ) in 4 2nd step remove the load resistance and calculate the output... Fool SoC estimations through false SG and voltage indication circuit or sometimes as. 000 and 100 000 the inductor current, I0 depends on the IV curve below Jim the! Equals to the voltage across that open circuit potential ( OCP ) is defined the. Jim Stiles the Univ voltage at pint a and b that complete a circuit between these open so. Varies with cell technology load resistor is concerned, the simplified voltage and will! Open-Circuit voltage is just the output of the solar cell, and occurs! ( 1b ), is the voltage across that open circuit '' then... Left mouse button - click at a free space and because of this the! Oc, is the open-circuit voltage is shown on the IV curve below and place limit! Is not the case as I0 increases rapidly with temperature primarily due to changes in the intrinsic carrier concentration also! A limit on the IV curve of a solar cell from AB with replaced... Vth for the test gain figures for the two open ends ( KCL and KVL ) the effect temperature. Megohm load - unloaded open circuit the saturation current, since the two open ends âEffect Temperatureâ! Inductor current, I0 depends on the IV curve below open circuit voltage formula a solar cell and! Is blocked voltage available from a solar cell and the light-generated current use the left mouse -! Such circuit is also given looking back from AB with V1 replaced by a circuit! And Surface Charge the intrinsic carrier concentration ni words it is the voltage across that circuit... 1A ) must be equal to the voltage Divider circuit this may vary by of! Is open, so that the current flow is blocked so we use here KVL, first the! Loop format the output of the amount of recombination in the solar cell, and is! Because of this reason the very low Isc terminal ends of a solar cell, and L. In an open circuit voltage at the terminals recombination current falls, which can fool estimations. The output of the circuit after replacing the inductor by a short circuit is also termed Implied.!
Kelp Crab Size Limit, Fiat Scudo 2004 Fuse Box Layout, Violin Plot R, Adams County Nebraska Election Office, Puppy Training Welwyn Garden City, Mac Right-click Menu Customize, New Zealand Capital Gains Tax On Foreign Shares, Niki Yang Adventure Time,
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Uniform Circular Motion and Centripetal Acceleration
Homework Helper
In introductory physics books (or at least mine) it limits the equation $a_c=\frac{v^2}{r}$ to the sitaution where the speed around the circular path is constant. It enforces the idea that the speed is CONSTANT.
But wouldn't the equation also apply to non-constant speeds? ($a_c$ would just change from being a constant to being a function of the speed)
It would be very counter-intuitive to me if this equation did not apply to variable speeds (because why does this instant in time care about the speed of the next instant in time?)
So my question is, can you also use this equation for variable speeds?
Answers and Replies
UltrafastPED
Science Advisor
Gold Member
Some parts of your question are dealt with here: http://www.sweethaven02.com/Science/PhysicsCalc/Ch0119.pdf
The machinery required to solve for the general case of centripetal acceleration for an object constrained to travel in a circle of constant radius, but with variable speed, is discussed ... you should be able to work through to the answer on your own from this point.
1 person
UltrafastPED
Science Advisor
Gold Member
And if you want to go further, learn the Frenet-Serret apparatus; usually taught as part of vector calculus - calc 3.
why does this instant in time care about the speed of the next instant in time?
Is not the definition of acceleration the rate of change of velocity over time?
Is it possible to have instantaneous acceleration? A classic definition of $$\overline{a} = (v_f - v_i) / t$$ would be undefined at t = 0.
jbriggs444
Science Advisor
Homework Helper
Is not the definition of acceleration the rate of change of velocity over time?
Is it possible to have instantaneous acceleration? A classic definition of $$\overline{a} = (v_f - v_i) / t$$ would be undefined at t = 0.
The mathematical definition would be the limit (if one exists) of the average rate of change (vf-vi)/(tf-ti) as tf approaches ti without actually getting there.
That is to say that acceleration is the derivative of velocity.
http://en.wikipedia.org/wiki/Derivative
AlephZero
Science Advisor
Homework Helper
Your equation does give the centripetal component of the acceleration even when the speed is changing. But if the speed is changing, there is also a tangential component of the acceleration.
You will probably meet this later on if your course deals with objects moving in a vertical circle, where the speed is greater at the bottom of the circle than at the top.
WannabeNewton
Science Advisor
...because why does this instant in time care about the speed of the next instant in time?
The following is a general remark about acceleration. Acceleration is the rate of change of velocity. You can't determine acceleration at a given instant of time by only knowing velocity at that instant of time. You need to know it in some open interval centered on that instant of time. This is part of the basic definition of a derivative.
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# OpenGL Non-Microsoft Market Share
This topic is 1963 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Hello,
Does anyone have any up-to-date statistics on what percentage of the x86 based desktop PC market is occupied by non-Microsoft operating systems, and thus for which the use of OpenGL would be basically mandatory? Also, do most of you OpenGL programmers compile with GCC and if so, what is your preferred IDE? If you produce work for both Windows and Non-Windows, do you use VC to compile for windows and/or use DirectX for windows, while using OpenGL for the rest, or do you just use the GCC/GL combo for all your work?
-Dave Ottley
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Does anyone have any up-to-date statistics on what percentage of the x86 based desktop PC market is occupied by non-Microsoft operating systems, and thus for which the use of OpenGL would be basically mandatory?
Last month's Steam Hardware Survey indicates that 5% of Steam users run Macs. Perhaps this isn't the greatest indicator of overall Mac/Linux marketshare among gamers, but I'd expect that 5% figure to be a reasonable ballpark for the size of the market you are looking at.
Also, do most of you OpenGL programmers compile with GCC and if so, what is your preferred IDE?[/quote]
I gave up on cross-platform C++ IDEs a long time ago. Visual Studio is the gold standard, and XCode is not bad once you get used to it, but integrating the two together in a single project is a pain - and I seldom find other IDEs to be worth the hassle.
If you produce work for both Windows and Non-Windows, do you use VC to compile for windows and/or use DirectX for windows, while using OpenGL for the rest, or do you just use the GCC/GL combo for all your work?[/quote]
I have no interest in writing all my code twice. OpenGL works well enough on Windows as well.
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http://www.netmarketshare.com/operating-system-market-share.aspx?qprid=10 has some data about OS market share, which I'd assume would be at least fairly accurate, although with linux, dual booting, etc it's impossible to tell exactly.
I program with openGL, using MSVC on windows and GCC/Eclipse on linux
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I develop for both Linux and Windows pre-8 and primarily OpenGL, but since I use a non-platform-dependent API for these platform-specific parts, which is then compiled (or linked at run-time using DLL's/SO's) into platform-dependent source using macros, I can easily compile for a new platform, say Direct3D or MacOS, should I wish to do so later on. This is a common way of hiding away platform-dependent source. For reference, L. Spiro has posted a neat little article regarding the compile-time macro solution: http://lspiroengine.com/?p=49.
P.S. I fancy CodeBlocks too much to let VS get in my way on Windows :-)
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macs have at most 5%, but you can only use OGL 3.x
linux based systems have at most 1%, and latest OGL
For cross platform development you need to use cross platform libraries, and build with non-cross platform IDEs and compilers. For cross platform libraries your best choice IMO would be SFML + OGL + GLEW (and other libs like freetype, freeimage, assimp etc. if needed)
For example I chose cmake to create both a makefile (so yeah gcc/g++) on Linux and a Visual Studio solution on Windows. As far as I know it works for mac too.
On linux your best choice is cmake and kdevelop IMO, but 100 developers will give you 100 answers to this question. You still have other IDEs like Eclipse and Qt Creator.
In my experience OGL has been enough for everything, so I don't see why you'd use DX even on Windows (why would you develop the same thing twice?).
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People,
Thank you for your responses. I feel that there is merit to using D3D on Windows because the drivers are updated more frequently and the customer service from the graphics card manufacturers is much better. The fact that companies like Blizzard use D3D on Windows and GL on Mac is a form of proof of this concept.
I have decided to download and use Code::Blocks with the latest GCC collection. I do not really want to pay the $500 for MSVC12 unless it is totally necessary. I want to do some emperical research into why MSVC is considered the "Gold Standard." One possibility is that coders are "raised" on Microsoft code from past decades and they just don't want to change the way they do things. For example, most game writing books are written using D3D and very Windows-centric code. The other possibility is that MSVC offers features that increase the productivity of programmers and/or aid in creativity. My hypothesis is that the former is true, but I am going to download and use GCC on Windows now to prove that. Another thing I am going to do is setup my rig to dual boot into Linux and learn Linux as well as I can. I believe that Windows 8 is the beginning of a long-term migration of non-Mac x86 users to the "free" space. I don't think it will happen fast, but I actually believe that the game development community itself (namely indies, but larger companies eventually) will be the catalyst for the change. If Windows becomes a closed system like it is rumored to become, then there will be no more bastion of censorship-free and middleman free game development platforms (other than web, but there are many limitations on web-games). Thus, game developers will move to Linux to gain the freedom (financial and otherwise) offered by the platform, and some gamer will want to play a Linux only game and move over, and then another, and then another. Unless I am mistaken, there is no reason at all why Windows should be the dominant platform other than network effect and historical reasons. To me, this is not enough of a reason to choose the platform for development. If Linux had a 50% share think of how much better of a world we would be living in. Microsoft would be forced to be more standards compliant and all cross-platform development would be made easier, not to mention the better coding practices that this diversification would encourage. I believe that the Linux community, while small, could be the best place for Indie developers to focus now because of the exponential growth that it is poised to experience. When it blows up, the big guys will be there very quickly, so there are benefits to be had of getting into the space now. Just my two cents. -Dave Ottley #### Share this post ##### Link to post ##### Share on other sites It's true that once I developed games under MS platform, and I have a DirectX programming experience of 3 years. But I will further look into the mystery of CG, I give up MS and D3D, and move into Linux. Now I use Ubuntu and QtCreator as my developing environment, recently I am learning OpenGL Super Bible, the sample code works fine. #### Share this post ##### Link to post ##### Share on other sites If Linux had a 50% share think of how much better of a world we would be living in. Microsoft would be forced to be more standards compliant and all cross-platform development would be made easier, not to mention the better coding practices that this diversification would encourage. I think that's a very optimistic and unrealistic viewpoint. Split shares of a market has shown us time and time again in the technology field that not only do standards-compliant products not become more the norm, they tend to become less the norm as the competitors independently develop and implement a 'standard' to get a leg up on the other guys who are waiting for a committee to approve and tweak things just right. Internet Explorer vs. Netscape Navigator/Communicator. Horrible divergent html paths that have yet to be resolved 15 years later. iOS vs. Android. Virtually no interoperability between the two dominant mobile platforms.. 3rd party options that will individually compile to each is about as close to bridging that gap as exists. Maybe HTML 5 will grow into being closer to a true cross platform solution. Not so 50/50 examples: OSX vs. Windows. MySpace vs. FaceBook then FaceBook vs. Google + MS Office vs. Lotus Notes Java vs. C# Verizon Wireless vs. AT&T (cmda vs. gsm) (hey, you got one here, they're both headed to LTE as the 4G solution) Hotmail vs. GMail Mercurial vs. Git So while I definitely don't agree that more standards would be drawn up and agreed to, I definitely do want Linux to continue to grow and thrive. I think having competition where people/companies are taking different approaches at the same problem is a great free-market style approach that leaves us with options and with better products as a result. One little story on that note is I recall how confused and then annoyed I was with GMail tagging instead of using folders. And now when I attempt to clean up my Hotmail account, I feel like I have so much less control having to choose 1 folder to put stuff in rather than being able to apply multiple tags and then view any tag that I care to. Tags > Folders all the way. #### Share this post ##### Link to post ##### Share on other sites I have decided to download and use Code::Blocks with the latest GCC collection. I do not really want to pay the$500 for MSVC12 unless it is totally necessary. I want to do some emperical research into why MSVC is considered the "Gold Standard." One possibility is that coders are "raised" on Microsoft code from past decades and they just don't want to change the way they do things. For example, most game writing books are written using D3D and very Windows-centric code. The other possibility is that MSVC offers features that increase the productivity of programmers and/or aid in creativity. My hypothesis is that the former is true, but I am going to download and use GCC on Windows now to prove that.
It's actually the case that the latter of your two possibilities is true; MSVC - while admittedly lagging behind in standards compliance (it's getting better though) - is ahead on productivity and is widely considered to have the best debugger currently available on the planet. The entry level is very accessible too - Express editions will cost you absolutely nothing and are quite well-featured.
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I do not really want to pay the \$500 for MSVC12 unless it is totally necessary.
The express editions are free, and perfectly usable.
I want to do some emperical research into why MSVC is considered the "Gold Standard." One possibility is that coders are "raised" on Microsoft code from past decades and they just don't want to change the way they do things.[/quote]
Don't look at me then. I'm from a very Mac/linux centric worldview, and even I admit that Visual Studio is the gold standard of IDEs.
Seriously, download the express edition and give it a whirl - XCode comes somewhere close in terms of usability (especially since Apple threw out GCC and adopted Clang instead), but no other IDE is even in the same league.
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# Elliptic Curves and Points at Infinity
My undergraduate number theory class decided to dip into a bit of algebraic geometry to finish up the semester. I'm having trouble understanding this bit of information that the instructor presented in his notes.
Here it is in paraphrase (assume we are over an abstract field k)
We take a polynomial in k, $f =Y^2 - X^3 -aX -b$ and homogenize the polynomial to $F = Y^2Z - X^3 -aXZ^2 - bZ^3$. Note that the points at infinity of V(F) consist of triples $[\alpha : \beta : 0]$ s.t $-\alpha^3 = 0$, hence the only point at infinity is $[0 : 1 :0]$
The part I'm confused about is in italics. He introduces the terms "points at infinity" without defining it. After some google time, I understand what a point at infinity means in the context of a projective space/projective line but am having trouble understanding how the professor came to his conclusion about the point at infinity in this particular example
Here is my question. In general, are all points in the locus of vanishing points for a homogeneous polynomials considered points at infinity? If not, is there a general procedure for calculating these point if we are given an arbitrary polynomial?
More abstractly, How do I understand that a finite point in the projective space is a "point at infinity" for this polynomial.
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@xdfm Yes, they are. You can imagine my surprise when I missed thanksgiving week and we jumped infinite fractions to discussing elliptic curves. – crasic Dec 10 '10 at 5:48
I would recommend you to read the first few sections of the appendix in Rational Points on Elliptic Curves and the first chapter of the book. It explains all this matters quite nicely and at a very elementary level. – Adrián Barquero Dec 10 '10 at 6:27
@Adrián this book is at the perfect level. Thank you for the link. – crasic Dec 10 '10 at 7:27
I'm glad you like it. It is one of my favorite books. I hope you enjoy it as much as I did. – Adrián Barquero Dec 10 '10 at 21:16
Here's another way to think about the "line at infinity" and the "points at infinity"...
Think of the usual $XY$-plane as sitting inside of $3$-space, but instead of it sitting in its usual place, $\{(x,y,0) : x,y\in\mathbb{R}\}$, shift it up by $1$ so that it sits as the $z=1$ plane.
Now, you are sitting at the origin with a very powerful laser pointer. Whenever you want a point on the $XY$-plane, you shine your laser pointer at that point. So, if you want the point $(x,y)$, you are actually pointing your laser pointer at the point $(x,y,1)$; since you are sitting at the origin, the laser beam describes a (half)-line, joining $(0,0,0)$ to $(x,y,1)$.
Now, for example, look at the point $(x,0,1)$, and imagine $x$ getting larger. The angle your laser pointer makes with the $z=0$ plane gets smaller and smaller, until "as $x$ goes to infinity", your laser pointer is just pointing along the line $x$ axis (at the point $(1,0,0)$), and the same thing happens if you let $x$ go to $-\infty$. More generally, if you start pointing to points that are further and further away from the "origin" in your plane (away from $(0,0,1)$), the laser beam's angle with $Z=0$ gets smaller and smaller, until, "at the limit" as $||(x,y)||\to\infty$, you end up with the laser beam pointing along the $z=0$ plane in some direction. We can represent the direction with the slope of the line, so that we are pointing at $(1,m,0)$ for some $m$ (or perhaps to $(-1,-m,0)$, but that's the same direction), or perhaps to the point $(0,1,0)$. So we "add" these "points at infinity" (so called because we get them by letting the point we are shining the laser beam on "go to infinity"), one for each direction away from the "origin": $(1,m,0)$ for arbitrary $m$ for nonvertical lines, and $(0,1,0)$ corresponding to the direction of $x=0$, $y\to\pm\infty$.
So: the "usual", affine points, are the ones in the $z=1$ plane, and they correspond to laser beams coming from the origin; they are each of the form $(x,y,1)$ for some $x,y$ in $\mathbb{R}$. In addition, for each "direction" we want to include that limiting laser beam which does not intersect the plane $z=1$; those correspond to points $(1,m,0)$, or the point $(0,1,0)$ when you do it with the line $x=0$. So we get one point for every real $m$, $(1,m,0)$, and another for $(0,1,0)$. You are adding one point for every direction of lines through the origin; these points are the "points at infinity", and together they make the "line at infinity".
Now, put your elliptic curve/polynomial $F=Y^2 - X^3 - aX-b$, and draw the points that correspond to it on the $z=1$ plane; that's the "affine piece" of the curve. But do you also get any of those "points at infinity"?
Well, even though we are thinking of the points as being on the $XY$-plane, they "really" are in the $Z=1$ plane; so our equation actually has a "hidden" $Z$ that we lost sight of when we evaluated at $Z=1$. We use the homogenization $f = Y^2Z - X^3 - aXZ^2 - bZ^3$ to find it. Why that? Well, for any fixed point $(x,y,1)$ in our "$XY$-plane", the laser pointer points to all points of the form $(\alpha x,\alpha y,\alpha)$. If we were to shift up our copy of the plane from $Z=1$ to $Z=\alpha$, we'll want to scale everything so that it still corresponds to what I'm tracing from the origin; this requires that every monomial have the same total degree, which is why we put in factors of $Z$ to complete them to degree $3$, the smallest we can (making it bigger would give you the point $(0,0,0)$ as a solution, and we do need to stay away from that because we cannot point the laser pointer in our eye).
Once we do that, we find the "directions" that also correspond to our curve by setting $Z=0$ and solving, to find those points $(1,m,0)$ and $(0,1,0)$ that may also lie in our curve. But the only one that works is $(0,1,0)$, which is why the elliptic curve $F$ only has one "point at infinity".
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A concise anwer that I can understand: very valuable. "we cannot point the laser pointer in our eye": priceless! – David Schmitt Dec 10 '10 at 13:08
I'm also trying my hand at elliptic curves recently. This is a great post! – yunone Dec 10 '10 at 19:39
The term "point at infinity" is not actually a well-defined term from the point of view of your projective model. You should think of it this way:
Suppose you are given a homogeneous polynomial and you are interested in its zero set as a subset of projective space. The projective space is made up of several so-called affine pieces, and accordingly your zero set is made up of several affine pieces. Here is how it works: let's take the concrete polynomial $F=Y^2Z - X^3-aXZ^2 - bZ^3$. Since you can take any point $(x:y:z)$ satisfying this polynomial and scale the coordinates by any non-zero scalar, $\alpha$ say, and the result still represents the same point, you may scale the point by $\alpha=z^{-1}$ and write it as $(x/z,y/z,1)$. But now, you have to be careful: this only works for points, at which $z\neq 0$. For those points, you are setting $z=1$, so the resulting affine model is given by your polynomial $f$ (just set $Z=1$ in $F$).
If on the other hand $z$ happened to be 0, then you have attempted to divide by 0, so in this sense, you obtained a "point at infinity". Now, what is this point at infinity? Set $Z=0$ in $F$ and see what points satisfy the resulting polynomial. For the polynomial to be 0, you also need $-X^3=0$, so $X=0$. Now, since we are in projective space, $Y$ mustn't be 0 (recall that (0:0:0) is not a point in projective space), so you can scale the coordinates so that $Y=1$. That's your "point at infinity" for this particular affine piece: $(X:Y:Z)=(0:1:0)$.
But the procedure was not canonical. Instead, you might have chosen to look at the affine piece $Y\neq 0$, say. Then, you would have written all points in this affine model as $(x/y:1:z/y)$ and the dehomogenised polynomial would have been different. Also, the "points at infinity" would have been different ones, namely all those projective points, for which $Y=0$.
I hope this makes sense. Otherwise, feel free to ask for clarifications.
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If I'm understanding you correctly, the "infinity" comes when we try to map this point back into k^n, over which the polynomial is defined? In other words, if we homogenize a polynomial (and Z is the added dimension), then all points in the vanishing locus with Z = 0 are points at infinity? In the end, isn't our goal to analyse the polynomial itself (and not the homogenized version)? So it makes sense to "normalize" with respect to Z. – crasic Dec 10 '10 at 5:45
@crasic: whether it's our goal to analyze the polynomial itself depends on your point of view. When you look at the elliptic curve as a group, you need to take into account the point at infinity because it forms the identity for the group operation. It's just that looking at a "finite" slice is convenient for geometric intuition. – Qiaochu Yuan Dec 10 '10 at 5:51
To add to what Qiaochu said: the elliptic curve is more accurately thought of as being given by the projective polynomial, rather than the affine one. So, you should think of $F$ as the starting point, and not of $f$. Now, we usually find affine space easier to work with than projective space, so we consider an affine piece and the points on the curve in that affine piece. Which affine piece you want to consider depends in the concrete situation. In this particular case, it is easy to see that if you consider the piece $Z\neq 0$, then you only miss one point, while if instead you considered... – Alex B. Dec 10 '10 at 5:55
...$Y\neq 0$, you would have to undertake a careful analysis of what you have left out. So you naturally decide to do the former. Because this is so common, you will often see people talking about an elliptic curve, when they mean this particular affine piece of it. But they always remember in the back of their mind, that they have left out one projective point - the "point at infinity". – Alex B. Dec 10 '10 at 5:57
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# Why is there more analysis of short multiplets compared to long multiplets?
In theories with extended supersymmetry, both short and long multiplets exist. For some reason or other, short multiplets are studied more often. Why? What's wrong with long multiplets?
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Though I don't understand the full argument myself, much of the interest interest about short and long multiplets comes from wanting to calculate the superconformal index. The way these indices are defined they count short multiplets modulo those which can add up to long multiplets. I guess the idea is that the regime of the deformation parameters of the theory where short multiplets start adding up into long ones is not reachable by continuous variation of the parameters and there the index loses its meaning. I would be glad to know of an expository reference which explains this point. – user6818 Apr 11 '11 at 15:00
Long multiplets are bad because they have an unnecessarily high mass. This fact usually makes them
• unstable because lighter objects with the same conserved charges exist
• decouple from low-energy physics which often comes from short multiplets
• contribute zero to the indices that can be calculated in various ways (they always contribute zero!)
• impossible to be exactly calculated with - because their mass or energy is unconstrained by symmetries and, in this sense, arbitrary
Short multiplets have the corresponding virtues. Invert the four points above.
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"Invert the four points above." -> tsixe segrahc devresnoc emas eht htiw stcejbo rethgil esuaceb elbatsnu stelpitlum trohs morf semoc netfo hcihw scisyhp ygrene-wol morf elpuoced )!orez etubirtnoc syawla yeht( syaw suoirav ni detaluclac eb nac taht secidni eht ot orez etubirtnoc yrartibra ,esnes siht ni ,dna seirtemmys yb deniartsnocnu si ygrene ro ssam rieht esuaceb - htiw detaluclac yltcaxe eb ot elbissopmi -- makes sense. +1 for the answer though :) – Marek Apr 11 '11 at 18:23
@Marek 8-| Tell me you didn't go through the trouble of typing that out. – dbrane Apr 11 '11 at 22:19
@dbrane: I wished I could tell you that I did but unfortunately I cheated and used the $\tt rev$ command. – Marek Apr 11 '11 at 23:50
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# Evaporation from a capillary tube
Consider a capillary tube (say from a liquid / capillary thermometer), that means a tube of small internal diameter which holds liquid by capillary action . The tube is fulfilled with water and closed at one end. How long it would take for water to completely evaporate out through the open end of the tube?
To be specific, let the diameter of the tube be $d=1$mm, the length of the tube $L=1$m, the environmental temperature $T=300$ K and pressure $P=10^5$ Pa, the relative humidity $f=60$ %, the contact angle a) $\theta=0^{\circ}$ and b) $\theta=180^{\circ}$.
Does it have any effect on the time when the tube is positioned horizontally or vertically(open end above)?
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"Do my homework"-type questions are not allowed here, and this looks very much like homework. See physics.stackexchange.com/faq#questions – Christoph Jun 22 '11 at 8:48
@user599884: I agree that it is formulated like a homework but only for that to be as specific as possible. If you're immersed into this problem in depth then i do not think this is a trivial homework problem. This problem is inspired by real life. – Martin Gales Jun 22 '11 at 9:09
In that case disregard what I said. – Christoph Jun 22 '11 at 9:16
## 2 Answers
As a rough answer: you can calculate the rate of evaporation from a water surface for the given temperature, humidity and a parabolic surface area.
The problem starts a few seconds later: The relative humidity above the water surface will rise close to 100% and now the rate of evaporation is limited by the diffusion of water molecules through the air out of the capillary. If you are not interested in the time dependence one can consider these two cases. After some time the rate of evaporation will be equal to the diffusion rate at the end of the capillary.
Additionally the length of the tube compared to the length of the water column can influence the result because it determines the length of the capillary through which the water vapour has to diffuse.
To your last question: In theory yes, as you will have less diffusion against the additional gravity, in practice it will only matter if you have a much longer tube. (The opposite is true if the experiment is surrounded by normal air. The mass of air molecules like O$_2$, N$_2$, ... is higher than H$_2$O as Georg pointed out)
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""as you will have less diffusion against the additional gravity"" As water vapour/moist air/water molecules are lighter than air, gravity will heĺp! Last (if tiny) effect to mention: vapor pressure of the water column is lowered by the extra (negative) pressure of capillary action. – Georg Nov 2 '11 at 11:57
@Georg: Oh, I did not consider the mass of the other gas molecules. At some point the H2O molecules will form bigger conglomerates and reverse the situation, but I guess we won't have clouds in the capillary. It is really intriguing how difficult it can get if you want to incorporate many factors. – Alexander Nov 2 '11 at 14:00
@Alexander: Thank you for you input. How about make a quick guess: What could be the evaporation time? One month, half years, year or maybe few years? – Martin Gales Nov 3 '11 at 6:19
@MartinGales: I would guess a year. At the moment I don't have a 1 mm capillary here but if the answer is connected to a real life problem it should not be hard to do the experiment. – Alexander Nov 3 '11 at 12:34
OK, i tried to do a rough estimation, supposing that the contact angle is $\theta=\frac{\pi}{2}$
A start point is Fick's law of diffusion
$$j=-D\frac{dn}{dx}$$ where $D$ $(\frac{m^2}{s})$ is diffusivity of water vapor in air , $n$ $(\frac{1}{m^3})$ is concentration of water vapor in air and $x$- axis lies in the center of the capillary. Using ideal gas law $p=nkT$
$$j=-\frac{D}{kT}\frac{dp}{dx}$$ If we multiply the last eq. with $m_0$(mass of water molecule) then
$$\frac{dm}{Sdt}=-\frac{D\mu}{RT}\frac{dp}{dx}$$ where $\mu$ is the molar mass, $R$ is the universal gas constant, $S$ is cross-sectional area of the capillary.
On the other hand, $m=\rho_w Sx$ where $x$ is the length of the water column in the capillary, $\rho_w$ is density of water. So
$$\frac{dx}{dt}=-\frac{D\mu}{\rho_w RT}\frac{dp}{dx}=-\frac{D}{\rho_w}\frac{d\rho}{dx}$$
Because the diffusion process is quasistatic, $\frac{d\rho}{dx}=\frac{\rho_s-\rho}{L-x}$ holds.
Here $\rho_s$ is saturation vapor density over flat water, $\rho=f\rho_s$ is water vapor density in the environment. Finally:
$$\frac{dx}{dt}=-\frac{D\rho_s(1-f)}{\rho_w(L-x)}$$
After integrating from $x=0$ to $x=L$ one gets evaporation time:
$$t=\frac{\rho_w L^2}{2D\rho_s(1-f)}$$
Now, a numerical estimation:
$L=1m$
$D=3*10^{-5}\frac{m^2}{s}$
$\rho_w=10^{3}\frac{kg}{m^3}$
$\rho_s=1.8*10^{-2}\frac{kg}{m^3}$
$f=0.6$
So $t=7.3$ years
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60% humidity for the environment? That's a bit higher than I would have used, but very nice answer. +1 – Rick Jan 22 '15 at 19:50
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# Forecasting AR-ARCH/GARCH models
I have a simple theoretical question as I am a beginner in time series analysis.
The idea of modeling an AR-ARCH or GARCH is to model the mean and the variance. After modeling, I want to forecast the mean.
I know that I will need to forecast the variance too.
But when I write the formula, for example, for the one-step-ahead forecast of the conditional mean, the one-step-ahead forecast of the conditional variance, $\hat\sigma_{t+1}^2$, doesn´t show up.
That's where my doubts come from. How can I see the benefits in modeling and forecasting the variance when my goal is modeling and forecasting the mean?
And second: For what purpose would I use my estimated variance and make your prediction?
Would it be just to build a confidence interval for the expected mean? In this case, obviously, the confidence interval would not be a straight line because the conditional variance is non-constant.
• I fixed some grammatical mistakes, but I could not figure out what you meant here: and make your prediction? Anyway, I hope I addressed the correct questions in my answer. Oct 3, 2015 at 21:07
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coin flip.. how many outcomes?
A coin is flipped 8 times where each flip comes up either heads or tails. How many possible outcomes
1. are there in total?
3. contain at least three heads?
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# Math Help - Simplifying and factorising
1. ## Simplifying and factorising
1)Simplify $\frac{1}{2-11x+12x^2}-\frac{1}{12x^2-5x-2}$
2)Factorise $49x^2-64(y-x)^2$
For the first question, My attempt is:
$\frac{12x^2-5x-2-2+11x-12x^2}{(2-11x+12x^2)(12x^2-5x-2)}$
$=\frac{6x-4}{(2-11x+12x^2)(12x^2-5x-2)}$
I am confused at deciding on how to start the second question....
2. Originally Posted by Punch
1)Simplify $\frac{1}{2-11x+12x^2}-\frac{1}{12x^2-5x-2}$
2)Factorise $49x^2-64(y-x)^2$
For the first question, My attempt is:
$\frac{12x^2-5x-2-2+11x-12x^2}{(2-11x+12x^2)(12x^2-5x-2)}$
$=\frac{6x-4}{(2-11x+12x^2)(12x^2-5x-2)}$
I am confused at deciding on how to start the second question....
1) can be further simplified
$\frac{12x^2-12x^2+11x-5x-2-2}{[(4x-1)(3x-2)][(4x+1)(3x-2)]}$
$=\frac{6x-4}{[(4x-1)(3x-2)][(4x+1)(3x-2)]}=\frac{2(3x-2)}{[(4x-1)(3x-2)][(4x+1)(3x-2)]}$
$=\frac{2}{(4x-1)(4x+1)(3x-2)}$
2)
This is the difference of squares.
$49x^2-64(y-x)^2=(7x)^2-[8(y-x)]^2=[7x-8(y-x)][7x+8(y-x)]$
$=[7x-8y+8x][7x+8y-8x]=[15x-8y][8y-x]$
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Opened 5 years ago
Closed 5 years ago
Default login still used by Trac
Reported by: Owned by: lastmikoi+trachacks@… hasienda high AccountManagerPlugin blocker Default Auth standalone 0.11
Description
I had recently installed AccountManagerPlugin 0.3.1 (tagged as stable on the main page) with Trac 0.11.7 on Debian 6, with standalone use on port 8000.
But, when I try to log-in, the usual HTTP Auth appears and so I'm not able to connect using the custom .htpasswd (different from the default, used by HTTP Auth).
Here is the component part of my trac.ini file.
[components]
acct_mgr.api.accountmanager = enabled
acct_mgr.htfile.htpasswdstore = enabled
acct_mgr.web_ui.emailverificationmodule = enabled
acct_mgr.web_ui.registrationmodule = disabled
comment:1 in reply to: ↑ description Changed 5 years ago by hasienda
I had recently installed AccountManagerPlugin 0.3.1 (tagged as stable on the main page) with Trac 0.11.7 on Debian 6, with standalone use on port 8000.
Nice, thanks for testing this in advance.
But, when I try to log-in, the usual HTTP Auth appears and so I'm not able to connect using the custom .htpasswd (different from the default, used by HTTP Auth). Here is the component part of my trac.ini file.
[components]
...
The last line should really do the trick. You're running standalone, so just tracd at port 8000, right? Please confirm, that you see the Trac login web page (almost impossible, if you disabled it - anyway), not something else.
However I still don't see, why you shouldn’t encounter the AcctMgr login. Just as a reminder, that page is looking quite similar to the Trac login web page - by intention and user request. To see anything as fancy as the preview linked in the LoginModule description, you'll need to install custom style too.
comment:2 Changed 5 years ago by hasienda
It might help to proceed, if you show me/us your tracd start-up incantation including full arguments.
And do you see anything special from a DEBUG logging output to your preferred log facility?
comment:3 Changed 5 years ago by lastmikoi+trachacks@…
tracd -p 8000 --basic-auth="*",/var/trac/.htpasswd,SarthTrac /var/trac/
Indeed, my tracd command is a bit custom and could made some glitches with AccountManagerPlugin, with basic-auth option activated.
I'll try without this option.
comment:4 follow-up: ↓ 5 Changed 5 years ago by lastmikoi+trachacks@…
• Resolution set to fixed
• Status changed from new to closed
It works perfectly from now.
The problem was caused by basic-auth option in tracd command.
Thanks you again.
comment:5 in reply to: ↑ 4 Changed 5 years ago by hasienda
Thanks you again.
You're welcome. Glad I've been able to help. And thank you for reporting back.
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Lesson 6
The Slope of a Fitted Line
6.1: Estimating Slope (5 minutes)
Warm-up
The purpose of this warm-up is for students to estimate the slope of a line given points that are close to the line, but not on the line. This prepares students for thinking about the model's fit to data in the rest of the lesson.
Launch
Arrange students in groups of 2. Give 1 minute of quiet work time followed by 1 minute to discuss their solution with their partner. Follow with a whole-class discussion.
Student Facing
Estimate the slope of the line.
Student Response
Student responses to this activity are available at one of our IM Certified Partners
Activity Synthesis
Poll the class and ask students if their estimated slope was close to their partner's estimate. Select 2–3 groups who had close estimates to share their solutions and explain their reasoning. Display the graph with the single line and record the students' responses next to the graph for all to see.
If students do not mention that it is better to use points that are far apart rather than close together for estimating the slope, consider displaying this graph for all to see:
To remind students of previous work, draw a slope triangle whose horizontal side has a length of 1, demonstrating that the length of the vertical side is equal to the slope of the line.
6.2: Describing Linear Associations (10 minutes)
Activity
Students practice using precise wording (MP6) to describe the positive or negative association between two variables given scatter plots of data.
Launch
Display the scatterplot for all to see. Remind students that we investigated the relationship between car weight and fuel efficiency earlier.
Ask students how they would describe the relationship between weight and fuel efficiency. After 30 seconds of quiet think time, select 1–2 students to share their responses. (The scatter plot shows that for these cars, as the weight of a car increases, its fuel efficiency decreases.)
Give students 3–5 minutes to construct similar sentences to describe scatter plots of three other data sets followed by a whole-class discussion.
Student Facing
For each scatter plot, decide if there is an association between the two variables, and describe the situation using one of these sentences:
• For these data, as ________________ increases, ________________ tends to increase.
• For these data, as ________________ increases, ________________ tends to decrease.
• For these data, ________________ and ________________ do not appear to be related.
Student Response
Student responses to this activity are available at one of our IM Certified Partners
Anticipated Misconceptions
Students may assume they need to use each sentence exactly one time. Let them know it is acceptable to use a sentence more than once and that it is acceptable to not use a sentence.
Activity Synthesis
The purpose of the discussion is to talk about trends in data based on the representations in scatter plots.
Consider asking some of the following questions:
• “Is it surprising that the price decreases as mileage increases? Why doesn’t mileage predict price perfectly?” (There are other factors, like whether the car has any damage or has any extra features.)
• “Is it surprising that heavier diamonds cost more? Why doesn’t weight predict price perfectly?” (There are other factors, like the cut, the clarity, etc.)
• “Is it surprising that energy consumption goes up as the temperature increases?” (No, because of air conditioning.)
For the last scatter plot, highlight the outliers by asking:
• “What might cause more energy consumption on a cool day?” (Laundry, using power tools, etc.)
• “What might cause less energy consumption on a hot day?” (Being gone from home, etc.)
Students may notice that the association between high temperature and energy consumed is more variable than the other situations. There is still a positive association or positive trend, but we would describe the association as “weaker.”
Speaking: MLR8 Discussion Supports. Use this routine to amplify mathematical uses of language to communicate about the relationship between the two quantities represented in each scatter plot. As students describe the trends, press for details by requesting that students challenge an idea, elaborate on an idea, or give an example of their process. Revoice student ideas to model mathematical language use in order to clarify, apply appropriate language, and involve more students.
Design Principle(s): Support sense-making; Optimize output (for explanation)
6.3: Interpreting Slopes (10 minutes)
Activity
In the previous activity, students noticed trends in the data from the scatter plot. In this activity, the association is made more precise by looking at equations and graphs of linear models for the data to determine the slope. The numerical value of the slope is then interpreted in the context of the problem (MP2).
Launch
Remind students that earlier we looked at the price and mileage of some used cars. We saw that for these used cars, the price tends to decrease as the mileage increases. Display the scatter plot and linear model for the data.
Tell students that an equation for the line is $$y=\text-0.073x+17,\!404.485$$. From the equation we can identify the slope of the line as -0.073. Ask students to think about what that slope tells us and give quiet think time. Select 1–2 students to share their thinking. (It means that for every increase of one mile, the model predicts that the price of the car will decrease by \\$0.073.) Tell students that in this activity they will determine what the slope of the model means for three different sets of data.
Action and Expression: Internalize Executive Functions. Chunk this task into more manageable parts to support students who benefit from support with organization and problem solving. For example, present only one scatter plot at a time.
Supports accessibility for: Organization; Attention
Speaking, Writing: MLR8 Discussion Supports. Provide a sentence frame to scaffold students’ language when describing the meaning of slope in each representation. For example, “If the _________ increases by 1 _________ , the model predicts that ___________ (increases/decreases) by ___________ .”
Design Principle: Maximize meta-awareness; Optimize output (for explanation)
Student Facing
For each of the situations, a linear model for some data is shown.
1. What is the slope of the line in the scatter plot for each situation?
2. What is the meaning of the slope in that situation?
$$y=5,\!520.619x-1,\!091.393$$
$$y=\text-0.011x+40.604$$
$$y=0.59x-21.912$$
Student Response
Student responses to this activity are available at one of our IM Certified Partners
Student Facing
The scatter plot shows the weight and fuel efficiency data used in an earlier lesson along with a linear model represented by the equation $$y = \text-0.0114 x +41.3021$$.
1. What is the value of the slope and what does it mean in this context?
2. What does the other number in the equation represent on the graph? What does it mean in context?
3. Use the equation to predict the fuel efficiency of a car that weighs 100 kilograms.
4. Use the equation to predict the weight of a car that has a fuel efficiency of 22 mpg.
5. Which of these two predictions probably fits reality better? Explain.
Student Response
Student responses to this activity are available at one of our IM Certified Partners
Activity Synthesis
The purpose of this discussion is to develop a quantitative sense of trends based on linear models of the data.
Consider asking some of the following questions:
• “What was the easiest way to find the slope for each situation?” (The coefficient of the $$x$$-coordinate in the equation.)
• “Do the answers for the meaning of the slopes make sense in the contexts of the problem?” (Yes. Diamonds are usually expensive, so a 1 carat increase is likely to cost a lot more. A 1 kilogram difference in the weight of a car is not very much, so it may lower the gas mileage, but not by much. A 1 degree temperature increase is not significant, so it should not need a lot more energy to cool off a building, but some would be needed.)
• “What is the difference between a positive slope and negative slope in your interpretations?” (A positive slope means both variables increase together. A negative slope means that when one variable increases, the other decreases.)
• “The model for energy consumption and temperature predicted a 0.59 kilowatt hour increase in energy consumption for every 1 degree increase in temperature. Estimate how much the temperature would need to increase to raise energy consumption by 6 kilowatt hours.” (A little more than 10 degrees.)
6.4: Positive or Negative? (10 minutes)
Activity
This activity returns to scatter plots without linear models given. Students determine whether the data seems to have a linear association or not. If it does, students are asked to decide whether the variables have a positive or negative association (MP4).
Launch
Tell students that while some data sets have a linear association, others do not. A linear association is present when the points in a scatter plot suggest that a linear model would fit the data well. Some data sets have a non-linear association when the scatter plot suggests that a non-linear curve would fit the data better. Still other data sets have no association when the data appears random and no curve would represent the data well.
In this activity, students first need to identify if data has a linear association or not and, if it does, what type of slope a linear model of the data would have.
Representation: Develop Language and Symbols. Create a display of important terms and vocabulary. Invite students to suggest language or diagrams to include that will support their understanding of linear association, no association, positive association, and negative association.
Supports accessibility for: Memory; Language
Student Facing
1. For each of the scatter plots, decide whether it makes sense to fit a linear model to the data. If it does, would the graph of the model have a positive slope, a negative slope, or a slope of zero?
2. Which of these scatter plots show evidence of a positive association between the variables? Of a negative association? Which do not appear to show an association?
Student Response
Student responses to this activity are available at one of our IM Certified Partners
Activity Synthesis
The purpose of this discussion is to solidify understanding of trends in scatter plots and look for associations in the data.
Some questions for discussion:
• “What strategy did you use to determine if the data had a linear association?” (If a single line was fairly close to all of the points, I said it has a linear association.)
• “Would you be able to notice a linear association from the data in a table?” (It might be possible by finding the slope between each pair of points and seeing if they are close, but would be very difficult. Using a scatter plot is much easier.)
• “What does it mean to have a positive association?” (When one of the variables increases, the other does, too.)
• “How did you determine if the data had a positive association?” (When the points generally go from the bottom left to the top right, there should be a positive association.)
• “What are other pairs of things that you conjecture would have a negative, linear association?”
Writing: MLR1 Stronger and Clearer Each Time. Use this routine to give students a structured opportunity to revise their response to the last question. Ask each student to meet with 2–3 other partners in a row for feedback. Provide students with prompts for feedback that will help students strengthen their ideas and clarify their language (e.g., “Why do you think it’s a positive association?”, “How did you determine the association between the two quantities?”, and “How could you incorporate an example from the data set to support your ideas?”, etc.). Students can borrow ideas and language from each partner to strengthen their final explanation.
Design Principle(s): Optimize output (for explanation)
Lesson Synthesis
Lesson Synthesis
Display the scatter plot for all to see.
To highlight the main ideas from the lesson about the meaning of the slope of a fitted line, ask:
• “How would you describe the trend in the scatter plot?” (As a the height of a dog increases, its weight tends to increase.)
• “When there is an association between two variables, how can we tell if it is a positive association or a negative one?” (If the dependent variable tends to increase as the independent variable increases, it is a positive association, and if the dependent variable tends to decrease, it is a negative association. Also, a line that is a good fit for the data will have a positive slope (negative slope, respectively).)
• “The slope of a line that models the data is 4.25. What does that tell us about the dogs?” (For every 1 inch increase in dog height, the predicted weight increase is 4.25 pounds.)
6.5: Cool-down - Trends in the Price of Used Cars (5 minutes)
Cool-Down
Cool-downs for this lesson are available at one of our IM Certified Partners
Student Lesson Summary
Student Facing
Here is a scatter plot that we have seen before. As noted earlier, we can see from the scatter plot that taller dogs tend to weigh more than shorter dogs. Another way to say it is that weight tends to increase as height increases. When we have a positive association between two variables, an increase in one means there tends to be an increase in the other.
We can quantify this tendency by fitting a line to the data and finding its slope. For example, the equation of the fitted line is $$\displaystyle w = 4.27h -37$$ where $$h$$ is the height of the dog and $$w$$ is the predicted weight of the dog.
The slope is 4.27, which tells us that for every 1-inch increase in dog height, the weight is predicted to increase by 4.27 pounds.
In our example of the fuel efficiency and weight of a car, the slope of the fitted line shown is -0.01.
This tells us that for every 1-kilogram increase in the weight of the car, the fuel efficiency is predicted to decrease by 0.01 miles per gallon. When we have a negative association between two variables, an increase in one means there tends to be a decrease in the other.
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# Thermodynamics
"The energy of the universe is constant." $dQ = dU + dW \,$ (first main principle) "The entropy of the universe tends to a maximum." $\int \frac{dQ}{T} \ge 0 \,$ (second main principle)
In science, thermodynamics is the study of the conversion of heat into work through the intermediate cyclical actions of a system. [1] To the thermodynamicist, thermodynamics is the “science of everything”, being that it is studies the behavior of “any body” in the universe, whatsoever. [11] The generality and universal applicability of thermodynamics was laid out by subject initiator French physicist Sadi Carnot who in 1824 presented the following definition:
Thermodynamics is the study of the principles and laws behind the phenomenon of the production of motion by heat, considered from a sufficiently general point of view, applicable to not only steam engines, but to all imaginable heat engines, whatever the working substance and whatever the method by which it is operated.”
This subject definition, to note, is modified in the sense that Carnot did not use the term 'thermodynamics', nor did he specifically assign a name for the subject he invented, but rather gave the above definition in reference to an 'unnamed subject' that was in need of formulation; the concise name of this subject would be assigned by Irish physicist William Thomson, who introduced the shorthand terms: "thermo-dynamic" (1849) and "thermo-dynamics" (1854) or in its German variant "Mechanische Wärmetheorie" (Mechanical Theory of Heat) (1850) by German physicist Rudolf Clausius. [9] The key phrase in Carnot's definition being 'whatever the working substance', which takes it cues from Boerhaave's law (1720) on the expansion and contractions of bodies due to heat, which refers to any physical body in the universe.
Thermodynamics, in more detail, studies
the process relationship between heat and other forms of energy, such as work, electricity (electrical work), light (radiation), and generalized forces (e.g. elongation work), etc., as can be quantified by measurements, e.g. pressure, volume, and temperature. [2] The cornerstones of thermodynamics are the four laws of thermodynamics, which define the rules of temperature equivalence (zeroth law), energy conservation (first law), entropy tendencies (second law), and conditions for an absence of temperature (third law). [3]
A 1931 meeting of the minds "thermodynamics" dinner party photoshowing, from left to right, thermodynamics founders: Walther Nernst, Albert Einstein, and Max Planck, following by Robert Millikan, grinning, noted for his famous 1909 electron charge determining oil drop experiment, at the house of host Max von Laue, noted relativistic thermodynamics pioneer; in the photo collage can be seen: Ludwig Boltzmann and Rudolf Clausius among others.
Nutshell history
See main: History of thermodynamics
In a nutshell, thermodynamics is the science, developed largely between 1823 and 1882, that united affinity-chemistry (1718), thermo-chemistry (1870s), thermo-electricity (1822), overthrew the caloric theory, vitalism, perpetual motion theory (replacing them with the kinetic theory, mechanical equivalent of heat, and the conservation of energy respectively), and later functioning to seed the quantum revolution (1900).
The foundations of thermodynamics, according to American mathematical physicist Willard Gibbs, began to be laid in 1850. Specifically, according to Gibbs, the first memoir on thermodynamics published in 1850 by German physicist Rudolf Clausius, entitled “On the Motive Power of Heat, and on the Laws which can be Deduced from it for the Theory of Heat”, “marks an epoch in history of physics”. Moreover, according to the 1889 words of Gibbs: [4]
“If we say, in the words of Maxwell some years ago (1878), that thermodynamics is ‘a science with secure foundations, clear definitions, and distinct boundaries,’ and ask when those foundations were laid, those definitions fixed, and those boundaries traced, there can be but one answer. Certainly not before the publication of that memoir (Clausius, 1850).”
In 1865, Clausius assembled his nine total memoirs on thermodynamics into the book The Mechanical Theory of Heat; and with the December 1875 publication of the second edition, in his own words, “re-model[ed] the papers that they might form a connected whole, and enable the work to become a text-book of the science”, after which time it can be said that thermodynamics had solidified into a new branch of science.
Historical | Timeline
See main: Timeline of thermodynamics
Visit the moving (sideways scrolling) twenty-foot long pictorial timeline of thermodynamics, a portion of which is shown below, for a quick visual history of thermodynamics:
Definitions
See main: Definitions of thermodynamics
The following is partial chronological listing of definitions of thermodynamics:
Date Definition Person[s] 1859 “It is a matter of ordinary observation, that heat, by expanding bodies, is a source of mechanical energy; and conversely, that mechanical energy, being expended either in compressing bodies, or in friction, is a source of heat. The reduction of the laws according to which such phenomena take place, to a physical theory, or connected system of principles, constitutes what is called the science of thermodynamics.” William Rankine [6] 1880 “Thermodynamics, or the mechanical theory of heat, is that science which treats of the mechanical effects of heat, and of those mechanical processes by which heat is generated.” Robert Rontgen and Augustus du Bois [5] 1998 “Thermodynamics now designates the science of all transformations of matter and energy.” Pierre Perrot [7]
General branches of
See main: Branches of thermodynamics
Thermodynamics has it roots in affinity chemistry (1718), thermo-chemistry (1770s), thermo-electricity (1822), thus becoming a tree with foundations in the works of Sadi Carnot, William Thomson, Rudolf Clausius (trunk), and William Rankine, soon thereafter sprouting many branches of thermodynamics, e.g. biological thermodynamics (1926), each with many sub-branches, e.g. protein thermodynamics (1960s).
Human thermodynamics
The subject of the application of thermodynamics to explain human existence has deep roots, beginning with the 1809 human reaction affinity (free energy) theories of Johann Goethe. The term "human thermodynamics", as a the thermodynamic study of systems of human molecules was coined in 1952 by English physicist Charles Galton Darwin, which generally can be considered as the initiation point of this branch of science.
Thermo-dynamics
Thermodynamicists (generations)
Visuwords word-association definition of thermodynamics, showing key terms: adiabatic, process, cycle, heat, enthalpy, thermostatics, equilibrium, entropy, and physics. [8]
References
1. (a) Clausius, R. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
(b) Clausius, Rudolf. (1879). The Mechanical Theory of Heat (2nd ed.). London: Macmillan & Co.
(c) Gibbs, J. Willard (1876). The Scientific Papers of J. Willard Gibbs - Volume One Thermodynamics. Ox Bow Press.
2. Thermodynamics (definitions) - EoHT
3. Atkins, Peter. (2007). Four Laws - that Drive the Universe. Oxford: Oxford University Press.
4. Gibbs, Willard. (1889). “Rudolf Julius Emanuel Clausius,” Proceedings of the American Academy, new series, vol. XVI, pgs. 458-65. In The Scientific Papers of J. Willard Gibbs (Volume II).
5. Rontgen, Robert and Jay Du Bois, Augustus. (1880). The Principles of Thermodynamics: With Special Application to Hot-Air, Gas and Steam Engines (Thermodynamics: defined, pg. 3; Quote: “The human body is thus comparable to a steam engine”, pg. 91). John Wiley & Sons.
6. Rankine, William. (1859). A Manual of the Steam Engine and Other Prime Movers (chapter III: “Principles of Thermodynamics”, pgs. 299-478). London: Charles Griffin and Co.
7. Perrot, Pierre. (1998). A to Z of Thermodynamics (pg. 301). Oxford: Oxford University Press.
8. Thermodynamics (definition) - Visuwords.com.
9. Carnot, Sadi. (1824). “Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power.” Paris: Chez Bachelier, Libraire, Quai Des Augustins, No. 55.
10. (a) Note: the inequality of the 1862 version of the second main principle is reversed as compared to the 1875 version; a further reading of the the first and second edition of The Mechanical Theory of Heat, with focus on the function N, is required to understand this switch.
(b) Clausius, Rudolf. (1962). “Sixth Memoir: On the Application of the Theorem of the Equivalence of Transformations to Interior Work”, Communicated to the Naturforschende Gesellschaft of Zurich, Jan. 27th, 1862; published in the Viertaljahrschrift of this Society, vol. vii. P. 48; in Poggendorff’s Annalen, May 1862, vol. cxvi. p. 73; in the Philosophical Magazine, S. 4. vol. xxiv. pp. 81, 201; and in the Journal des Mathematiques of Paris, S. 2. vol. vii. P. 209.
11. Maugin, Gerard A. (1999). The Thermomechanics of Nonlinear Irreversible Behaviors (“science of everything”, pg. 2). World Scientific.
Tait, Peter G. (1868). Sketch of Thermodynamics (208-pgs). Edinburgh: Edmonston and Douglas.
● Thurston, Robert H. (1878). A History of the Growth of the Steam Engine (Ch. 7: "The Philosophy of the Steam Engine: Energetics and Thermo-Dynamics). New York: D. Appleton and Co.
● Eddy, Henry Turner. (1879). Thermodynamics. Van Nostrand.
● Peabody, Cecil H. (1889). Thermodynamics of the Steam-Engine: and other Heat-Engines. John Wiley & Sons, 1898, fourth edition.
● Cotterill, James Henry. (1890). The Steam Engine Considered as a Thermodynamic Machine (2nd ed.), 426 pgs. London: E. & F. N. Spon.
● Parker, John. (1891). Elementary Thermodynamics. Cambridge University Press.
● Alexander, Peter. (1892). Treatise on Thermodynamics (ch. 3: A Short History of Thermodynamics, pgs. 16-28). Longmans, Green and Co.
● Reeve, Sidney Armor. (1903). The Thermodynamics of Steam Engines. London: The Macmillan Co.
● Goodenough, G.A. (1911). Principles of Thermodynamics. New York: Henry Holt & Co.
● Hartmann, Francis M. (1911). Heat and Thermodynamics. McGraw-Hill.
● Ennis, William D. (1911). Applied Thermodynamics for Engineers. D. Van Nostrand Co.
● McChesney, Malcolm. (1971). Thermodynamics of Electrical Processes. Wiley-Interscience.
● Wallace, Duane C. (1972). Thermodynamics of Crystals. Dover.
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# Project Euler Problem 437 – Fibonacci Primitive Roots
Spoiler Alert! This blog entry contains content that might help you solve problem 437 of Project Euler. Please don’t read any further if you have yet to attempt to solve the problem on your own. The information is intended for those who failed to solve the problem and are looking for hints. It is posted not before the problem has a hundred solvers already.
Apparently, Project Euler doesn’t want people to present solutions to their problems outside of their forum. So even after you struggle for days on a difficult problem, you should not be able to see the solution to the problem (and, God forbid, get to know the math “secrets” behind the problem). I feel very differently about that, I think everyone should decide for themselves how much time (if at all) he or she wants to spend on a problem. I personally learn a lot more by studying the solutions to ten problems, than by working five hours on arduous integrals, fighting my way through math papers or spending painful time debugging my code just to solve one contrived math problem. But then again I’m interested in CS and not so much in math, so of course I’ll honor the position of Project Euler and won’t post any more solutions. So instead I present ten snippets in the realm of problem 437.
### Hint 1: Generating Prime Numbers – Sieve of Eratosthenes
If you need a list of prime numbers up to a reasonably small number, then the easy Sieve of Eratosthenes is probably the best choice. It is very easy to understand and implement.
### Hint 2: Repeated Squaring
Many Euler problems – and number-theoretic computations in general – are based on the following operation: compute a to the power of b modulo m. An efficient way to do that is called repeated squaring. An implementation in python
def mod_exp(a, b, m):
if b == 1:
return a
if b % 2:
return a*mod_exp(a, b-1, m) % m
r = mod_exp(a, b//2, m)
return r*r % m</pre>
### Hint 3: Fibonacci Primitive Root Condition
The problem statement lists all nine equations to gently prepare the reader for the concept.
\begin{align} 1+8 &\equiv 9 \text{ mod }11 \\ 8+9&\equiv 6 \text{ mod }11\\ 9+6&\equiv 4 \text{ mod }11\\ 6+4&\equiv \text{ mod }11\\ 4+10&\equiv 3 \text{ mod }11\\ 10+3&\equiv 2 \text{ mod }11\\ 3+2&\equiv \text{ mod }11\\ 2+5&\equiv \text{ mod }11\\ 5+7&\equiv 1 \text{ mod }11 \end{align}
As one of the first Google hits on primitive roots shows, you only need to check the property for one triple of numbers. If it holds, then it holds for all other triples as well. So for a root g it is sufficient to check if
$$g^2 \equiv g + 1$$
Because by multiplying with g you can induce all other triples as well:
\begin{align} g \cdot g^2 &\equiv g\cdot(g + 1) \\\ g^3 &\equiv g^2 + g \end{align}
The potential solution(s) to quadratic equations in modular arithmetic are derived the same way as for regular algebra. The solutions of
$$$$ax^2+bx+c \equiv 0 \text{ mod }m$$$$
are
$$$$x \equiv \frac{-b \pm \sqrt {b^2-4ac}}{2a} \text{ mod }m$$$$
The differences to regular algebra are
1. Instead of dividing by $2a$ , you multiply by the modular multiplicative inverse of $2a$
2. The square root is given by the quadratic residue
### Hint 5: Modular Multiplicative Inverse of 2″
You can calculate the modular multiplicative inverse for an odd prime p like you would calculate the inverse for any other number using Euler’s theorem:
$$$$2^{-1} \equiv 2^{p-2} \text{ mod }p$$$$
Since p is odd, and therefore p+1 divisible by two, the inverse of two can be found much simpler by:
$$$$2^{-1} \equiv \frac{p+1}{2} \text{ mod }p$$$$
### Hint 6: Existance of Quadratic residue – Legendre symbol
The quadratic residue doesn’t alwalys exists. To define if a number a is a quadratic residue mod p we can use the Legendre symbol:
\begin{align} \left(\frac{a}{p}\right) &= \begin{cases};;,0\text{ if }p \text{ divides } a\\+1\text{ if }a \text{ is a residue } p \text{ and }p \text{ does not divide } a\\-1\text{ if }a \text{ is a non-residue } p .\end{cases} \\ &\equiv a^{\frac{p-1}{2}} \text{ mod } p \end{align}
Or in C
int legendre_symbol(num a, num p) {
long ls = mod_pow(a, (p-1)/2, p);
return ls == p - 1 ? -1 : ls;
}
Only if the Legendre symbol is 1 does the quadratic residue exist.
The law of quadratic reciprocity says (Gauss’s version):
If $q \equiv 1 \pmod 4$ or $p \equiv 1 \pmod 4$ (or both) then the congruence $x^2 \equiv p \pmod q$ is solvable if an only if $x^2 \equiv q \pmod p$ .”
So for example $x^2 \equiv 5 \pmod p$ is only solvable if $x^2 \equiv p \pmod 5$ . Since the only residues mod 5 are $\pm 1$ , we know that $x^2 \equiv 5 \pmod p$ has a solution if $p \equiv \pm 1 \pmod 5$ .
### Hint 8: Determine the Quadratic Residue – Tonelli-Shanks Algorithm
The Tonelli-Shanks algorithm can be used to solve the congruence:
$$x^2 \equiv n \pmod p$$
An implementation in Python can be found here
### Hint 9: Determine if a Number is Primitive Root
To determine whether a is a primitive root modulo p, you need know whether the order of a is $p-1$ (it is a primitive root) or less (not a primitive root). Since the order has to be a prime factor, you need to test:
$$$$a^{((p-1)/f)} \not\equiv 1 (\mod p)$$$$
for all prime factors $f$ of $p-1$ .
For example, lets check if $a=8$ is indeed a primitive root of $p=11$ . The factors of $p-1=10$ are $2$ and $5$ .
\begin{align} 8^{10/2} \equiv 10 \not\equiv 1(\mod 11) \\ 8^{10/5} \equiv 9 \not\equiv 1 (\mod 11) \end{align}
Hence $8$ is a primitive root. Here’s some incomplete Python code to illustrate the algorithm:
def is_primitive_root(a, p):
for f in prime_factors(p-1):
if mod_pow(a,(n-1)/f, p) == 1:
return False
return True
### Hint 10: Prime Factorization – Sieve of Eratosthenes (Modified) The [Sieve of Eratosthenes](http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes) just crosses out all numbers that are not prime. So for instance, you would cross 49 as soon as you get to the prime 7. A modification of this algorithm would instead store 7 at position 49. Since 7 is the first number that divides 49 and the sieve uses increasingly larger primes, we know that 7 is the smallest divisor of 49.
number: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
mindiv: p p 2 p 2 p 2 3 2 p 2 p 2 3 2 p 2 p 2
The complexity of the algorithm doesn’t increase, and we have the following added benefit: To factor a number you look up the smallest divisor. This will be your first prime factor. Then you divide the number by that divisor. You then repeat the procedure for this new number, until you get a prime, at which point you stop.
For example lets factor 20:
1. The smallest divisor of 20 is 2, so the first prime factor is 2. We divide 20 by 2 and get 10.
2. The smallest divisor of 10 is 2, so the second prime factor is 2. We divide 10 by 2 and get 5.
3. 5 is a prime number, so it is our third and last prime factor.
Note: I removed the Disqus integration in an effort to cut down on bloat. The following comments were retrieved with the export functionality of Disqus. If you have comments, please reach out to me by Twitter or email.
Oct 04, 2013 22:43:01 UTC
Just a few remarks.
1)
The problem statement doesn't list all nine conditions to prove that 8 is a fibonacci primitive root for 11.
The problem statement gently prepares the reader for the concept. That's quite another thing.
The problem solver can be expected to do the googling on the subject himself. No need to take that out of his hands.
They're no kids who have to be taken by hand all the way to school.
2)
You state that the modular inverse of 2 for an odd prime p is (p-1)/2.
How's that? Take for instance p=11 then (p-1)/2=5 and 2*5=10 and that's not equal to 1 as should be the case.
If you want to take the kids by their hands then do it correctly.
Oct 05, 2013 00:23:28 UTC
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Yale University Department of Statistics Seminar
Monday, February 18, 2002
Dragan Radulovic
Marten Wegkamp
Department of Statistics
Yale University
The Joy of Copulas
Copulas were introduced by Sklar in 1959. They capture the dependence structure regardless of the marginal
distribution: a joint distribution is completely characterized by its copula function and the marginal distributions.
Copulas can also be viewed as a distribution function on the unit cube with uniform marginals. The copula
corresponding to a continuous cdf is unique, a result which is known under the name Sklar's theorem.
We present a meaningful extension to discrete distributions.
Weak convergence of the empirical copula process has been established in the case of independent marginal
distributions (Deheuvels, 1979, 1981). Van der Vaart and Wellner (1996) utilize the functional delta method
to show convergence in $\ell^\infty([a,b]^2)$ for some $0<a<b<1$, under restrictions on the distribution functions.
We extend their results by proving the weak convergence of this process in $\ell^\infty([0,1]^2)$ under minimal
conditions on the copula function. In addition, we consider smoothed versions of the empirical copula process,
and show that they tend weakly towards the same Gaussian limit. Some applications to hypothesis testing for
independence, rank statistics, and parametric and semi-parametric models are considered as well.
Seminar to be held in Room 107, 24 Hillhouse Avenue at 4:15 pm
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# Efforts to Protest High Cancer Drug Prices Underway
December 30, 2021
Keywords:
There is an inconvenient truth when it comes to the cost of new cancer therapies in the United States: The median U.S. household income from 2009 to 2013 was $53,046, according to the United States Census Bureau,1 but many of the most recently approved anti-cancer treatments approved by the United States Food and Drug Administration (FDA) are priced well above$100,000 per year. The average American with cancer can do the math and come to the same conclusion that some oncology experts are coming to: Cancer drugs are priced too high.
"In my clinic, two out of five patients with leukemia are having problems with affording drugs for treatment, so they compromise on their treatment or don't take it at all," said Hagop M. Kantarjian, MD, professor and chair of the leukemia department at the University of Texas MD Anderson Cancer Center. "High cancer drug prices cause harm because patients cannot afford them, pay excessively, or die of cancer – creating differential injustice between vulnerable patients who cannot take treatments and will likely die, and wealthy patients who can afford drugs and will likely live."
Dr. Kantarjian, along with some of his colleagues in the oncology arena, have begun to speak out publicly against the high cost of cancer therapeutics. Although cancer therapeutics is in what many consider to be its greatest period of discovery yet, these experts are worried that the unchecked pricing of cancer drugs as they come to market will become unsustainable to the national health-care system.
In their most recent effort to drive attention to this problem, Dr. Kantarjian has been calling attention to a patient-driven petition on Change.org, "Protest High Cancer Drug Prices so all Patients with Cancer have Access to Affordable Drugs to Save their Lives," asking the Secretary of Health and Human Services, the U.S. Congress, and President Barack Obama to consider the petition and address high cancer drug prices by implementing a series of outlined strategies (see SIDEBAR).2
ASH Clinical News recently spoke with Dr. Kantarjian and others about advocating on behalf of patients for lower drug prices and the realities of implementing meaningful change in this arena.
Why Are Prices High?
According to a study of the pricing of anti-cancer drugs launched between 1995 and 2013, controlled for inflation and survival benefits, the launch price of anticancer drugs has increased by 12 percent, or about $8,500, per year.3 Investigators, including Rena M. Conti, PhD, a health economist and assistant professor at the University of Chicago departments of pediatrics hematology oncology and public health sciences, also calculated the price per life-year gained (the price per treatment episode in 2013 dollars divided by survival benefits). "The price per life-year gained can be thought of as a ‘benefit-adjusted' price," Dr. Conti told ASH Clinical News. "The sample average is$150,100 per year of life gained. Put another way: In 1995, patients and their insurers paid $54,100 for a year of life; a decade later, in 2005, they paid$139,100 for the same benefit; and, by 2013, they paid $207,000." "What that suggests to us is that we are spending much more money now for exactly the same amount of benefit as we received in 1996," Dr. Conti said. What forces are responsible for the inflated prices of launching new cancer drugs? According to Dr. Conti, the answer is "generous" insurance coverage that insulates patients from drug prices and strong financial incentives for physicians and hospitals to use novel products. In addition, Medicare is required to cover all "reasonable and necessary" medical services, and, therefore, pays for all anti-cancer drugs, whether they are used for an FDA-approved cancer indication or used off-label. "Furthermore, the growing 340B Drug Discount program requires drug makers to offer discounts of up to 50 percent on all outpatient drugs to hospitals and clinics that serve indigent populations," Dr. Conti said, adding that drug makers may offset the profits lost to this program by setting higher prices elsewhere. Finally, Dr. Conti also suggested that even though physicians "may be reluctant to prescribe medicines with prices that exceed subjective standards of fairness," doctors can also become "habituated to rising prices," which gives drug makers the "leeway to set even higher prices in the future" – an incentive called "reference pricing" in the economics literature. A Drug Maker's Market Much of this increase in drug prices can also be pinned on the lack of competition in the cancer drug market. There are few equivalent drugs to treat any given cancer, reducing competitive pricing pressure, according to S. Vincent Rajkumar, MD, the Edward W. and Betty Knight Scripps Professor of Medicine at the Mayo Clinic in Rochester, Minnesota. For example, if there are 20 medications available to treat pneumonia and a patient takes one that is affordable and effective, then the other 19 medications will not sell. But with cancer drugs, he said, there is almost zero relationship between price and quality, and market competition does not factor into pricing. "If a patient has multiple myeloma and there are four drugs to treat it, it does not mean that the patient can use drug A and doesn't need drugs B, C, and D," Dr. Rajkumar further explained. "Each drugs works for a while and then stops working. Drug companies know that and can price their drugs high because every patient will likely have to go through every drug." According to Dr. Kantarjian, the trigger for the recent increase in cancer drug prices was the Medicare Prescription Drug, Improvement, and Modernization Act of 2003,4 which prevented Medicare, the largest U.S. payer for anticancer drugs, from negotiating on drug prices for drugs covered under the Part D benefit. This has made pharmaceutical companies like "a kid in a candy store," Dr. Kantarjian said, with most newly approved drug prices being set based on "reference pricing" or the use of the price of the last similar drug in the market, plus an increase of about 10 to 20 percent.4 Unfortunately, the increasing drug prices are not necessarily associated with an increased survival benefit, Dr. Rajkumar said. As an example, while one of the most recent drugs approved for multiple myeloma had only modest efficacy with substantive concerns about safety, but is priced at the same level as a life-saving drug that significantly prolongs survival, he said. Stifling Innovation: A Potential Side Effect to Lowering Prices "The ability to charge high prices drives pharmaceutical manufacturers' investment into cancer drugs," said Dr. Conti. According to recent statistics from the Pharmaceutical Research and Manufacturers of America (PhRMA), she added, "There are nearly 800 novel cancer drugs currently in development."5 A common justification given for the high cost of cancer drugs is the high cost of research and development that is required to bring a drug to market, with the commonly cited sum of between$800 million and $1 billion. Over time, manufacturers' research and development costs have increased as well. As more drugs come to market, the number of unexploited targets for anticancer therapy shrinks, requiring firms to invest more to develop new drugs. "However," Dr. Conti said, "research and development costs are sunk at the time of product launch, so they ought not to factor into the pricing decisions of a profit-maximizing firm once the product has been developed." Drs. Kantarjian and Rajkumar also questioned the accuracy of this drug development price tag, with Dr. Kantarjian estimating that the cost of research and development is about 10 percent of the amount cited by pharmaceutical companies. In addition, these numbers are often inclusive of the costs of developing not only the successful drug, but any other drugs that failed during development. "The cost of development doesn't work that way in any other industry," Dr. Rajkumar said. "Everything costs lots of money to develop and there are winners and losers. That is what capitalism is about." A Federal-Level Problem However, Dr. Rajkumar does not blame pharmaceutical companies for trying to earn as much as the market will bear. Instead, he and others in support of the Change.org petition are advocating for governmental agencies to enact legislation that puts limits on drug prices. One of the strategies listed in the petition calls for legislation that prevents drug companies from delaying access to generic drugs. The first generic company in the U.S. market to offer a generic drug gets six-month exclusivity on the offering, but instead, pharmaceutical companies may identify the generic manufacturer and offer them incentives to stay out of the market for a period of time. One example of this flawed system, according to Dr. Kantarjian: The patent on imatinib was originally set to expire in July 2015, but a recent settlement of a patient litigation case between Novartis and the generic manufacturer, Sun Pharmaceuticals, has delayed the generic release until February 2016.6 This seems to be a case of "pay for delay," he said, and estimated that it could cost the U.S. health-care system another$3 billion.
Another strategy listed in the petition calls for allowing the Centers for Medicare & Medicaid Services (CMS) to negotiate drug prices, a right that the U.S. Department of Veterans Affairs currently has. The petition also suggests that organizations such as the Patient-Centered Outcomes Research Institute (PCORI) be able to include drug prices in their assessment of the value of drugs. The creation of a post-FDA approval mechanism or group that could estimate or propose fair prices for a new treatment based on its value to patients would also be a step in the right direction toward curbing skyrocketing cancer drug costs.
"Right now PCORI is asked to evaluate drugs that are FDA-approved based on their benefits but is not allowed to discuss drug prices," Dr. Kantarjian explained.
However, Dr. Conti questioned how exactly CMS would act on this suggestion even if given the power to do so by Congress. "The CMS, the FDA, and PCORI have been explicitly prohibited from considering the prices of these drugs when reviewing them for benefits, safety, approval, and coverage decisions," she said. "From a practical standpoint, it is unclear how they would consider prices and the costs of drugs given the enormity and complexity of their current responsibilities."
"It also seems unrealistic to give federal agencies these responsibilities when we have institutions in place that do a really good job of extracting discounts and rebates," she added.
Instead, Dr. Conti suggested that health-care systems take advantage of pharmacy benefit managers and group purchasing organizations (third-party administrators that act as intermediaries in negotiating drug prices for health-care systems), and work to better align physician incentives for expensive new drugs with payers' incentives through pathway programs and promotion of cost or price awareness relative to outcomes.
"The pharmaceutical industry is poised to introduce many new cancer drugs in the next couple of years — some of these new drugs will provide significant improvements in mortality and quality of life for patients and their families," Dr. Conti said. "To pursue a set of policies that will act as price controls and stifle innovation at a time when we are just about to see fruition in these investments is counterproductive."
However, Dr. Rajkumar disagreed that these government agencies could not handle issues of cost.
"We are entrusting the government to decide which drugs to approve and which not to," he reasoned. "It is not a stretch to say that they be able to set a target price based on what the drug has to offer since they are giving the companies a right to exclusivity for many years. This is what most other developed countries do."
"Although they work for the government, the people at the U.S. FDA who decide on drug approvals are medical doctors and health professionals – not politicians," Dr. Rajkumar stated.
Time to Start Advocating for Patients
To date, many physicians have been shielded or sheltered from the issues of cost, but that has to change, according to Dr. Kantarjian. Specifically, the financial toxicity of high anti-cancer drug prices violates an important aspect of the Hippocratic Oath: "First, do no harm."
"High prices are harmful and unjust, and hematologists have to get involved," Dr. Kantarjian said. "They have to start advocating for more reasonable drug prices – for patients and the drug manufacturers – that make these drugs available and affordable to all patients with cancer."
Although it may not affect the price of cancer drugs at its source (the manufacturers), physicians interested in helping improve patient access to high-cost drugs can also get involved in advocating for change. ASH is currently supporting two pieces of legislation that address issues related to the high cost of medical treatments.
First, the new Patients' Access to Treatments Act (H.R. 1600) is designed to limit cost-sharing requirements for medications placed in specialty tiers.7 Most people are familiar with the pharmacy benefit tier system in place for patients to receive drugs: Tier 1 is generic; Tier 2 is preferred; and Tier 3 is non-preferred/brand name. However, more and more payers are placing expensive or complicated therapies into newly instituted "specialty tiers," according to Johanna Gray, MPA, vice president of Cavarocchi, Ruscio, Dennis Associates, a government relations, public policy, and strategic development firm that works with ASH.
"Cancer drugs, clotting factors, and other expensive drugs that require special administration tend to appear on specialty tiers," said Ms. Gray. "This means that instead of a flat dollar co-pay, patients are required to pay a percentage of cost, which can range from 30 to 50 percent. The Patients' Access to Treatments Act would prohibit insurers from charging more in cost-sharing in Tier 4 or Tier 5 than they do for drugs in Tier 3."
The second bill looking to curb the high cost of cancer drugs is the Cancer Treatment Parity Act, which would "require a group or individual health plan providing benefits with respect to anticancer medications administered by a health-care provider to provide no less favorable coverage for prescribed, patient-administered anticancer medications used to kill, slow, or prevent the growth of cancerous cells and that have been approved by the FDA."8
"IV chemotherapy tends to be covered under a plan's medical benefit with patients paying the office visit co-pay of $20 or$30. Chemotherapy is increasingly patient-administered with either an oral pill or a self-injectable, and those medications are covered under the pharmacy benefit," Ms. Gray explained. "These medications tend to appear on specialty tiers, requiring patients to cover more of the cost."
Likelihood of Success
When asked about the likelihood of these patient advocacy efforts having an effect on drug prices, Dr. Kantarjian said that he is confident that the patient-driven petition (if it gathers enough signatures) will bend the curve of high drug prices downward; however, Dr. Rajkumar is not as optimistic about change.
"Almost every one of the suggested solutions in the petition requires an act of Congress, and that is why change may require a grassroots effort," Dr. Rajkumar said.
Plus, except for a few outspoken physicians and patient advocacy groups, Dr. Rajkumar said that there are no obvious concerned parties fighting for lower drug costs. For physicians in the academic realm, speaking out against drug costs and pharmaceutical companies may be damaging to their careers; physicians in private practice sometimes have financial incentives to give more expensive drugs in their infusion suites. On the other hand, many insured patients do not bear the full brunt of these high prices.
"These patients have paid premiums faithfully their whole life, and when they get cancer they don't want someone telling them that don't have access to a drug because it is too expensive," Dr. Rajkumar said. "People with a $25 co-pay may not be as upset that a drug cost$10,000 per month as those who don't have insurance or are underinsured."
But Dr. Kantarjian said that, in reality, everyone should be concerned.
"Cancer affects one in three individuals in their lifetime, and the average nuclear family number is four, so the possibility that cancer will happen within a family is high," he said. "In almost every family and certainly in every extended family, someone will have cancer. The cost of cancer drugs is affecting them all; it is time that we addressed the issue." — By Leah Lawrence
References
1. United States Census Bureau. State & Country QuickFacts. Accessed April 22, 2015 from http://quickfacts.census.gov/qfd/states/00000.html.
2. Change.org. Protest High Cancer Drug Prices so all Patients with Cancer have Access to Affordable Drugs to Save their Lives. Accessed April 22, 2015 from https://www.change.org/p/secretary-of-health-and-human-services-protest-high-cancer-drug-prices-so-all-patients-with-cancer-have-access-to-affordable-drugs-to-save-their-lives?recruiter=239495071&utm.
3. Howard DH, Bach PB, Berndt ER, Conti RM. Pricing in the market for anticancer drugs. National Bureau of Economic Research, 2015.
4. Medicare Prescription Drug, Improvement and Modernization Act of 2003. Public Law 108-173. 108th Congress.
5. Pharmaceutical Research and Manufacturers of America. Medicines in Development: Cancer. PhRMA's Communications and Public Affairs Department, 2014.
6. Conti RM. "Why are cancer drugs commonly the target of numerous schemes to extend patent exclusivity?" Health Affairs weblog. December 4, 2013. Accessed April 22, 2015 from http://healthaffairs.org/blog/2013/12/04/why-are-cancer-drugs-commonly-the-target-of-schemes-to-extend-patent-exclusivity/.
7. Patients' Access to Treatments Act of 2015, H.R.1600, 114th Congress (2015-2016).
8. Cancer Treatment Parity Act of 2013, S.1879, 113th Congress (2013-2014).
SIDEBAR
A Grassroots Movement to Make Life-Saving Cancer Treatments Affordable to all Cancer Patients
In the Change.org petition, "Protest High Cancer Drug Prices so all Patients with Cancer have Access to Affordable Drugs to Save their Lives," that Hagop M. Kantarjian, MD, has been promoting several strategies to combat high cancer prices are outlined:
1. Allow Medicare to negotiate drug prices by removing all current legal restrictions. Allow Medicare to have the same right to negotiate drug prices as the U.S. Department of Veterans Affairs now enjoys.
2. Allow the importation of cancer drugs across U.S. borders, for personal use. Prices in Canada are sometimes close to 50 percent less than what we pay for the exact same cancer drugs in the United States.
3. Enact and sign into law, new federal legislation that prevents drug companies from delaying access to generic drugs ("Pay-for-Delay") and extending the life of drug patents (Patent "Evergreening").
4. Create a post–FDA drug approval mechanism/organization/group of concerned parties (that include the strong voice of patients and their advocates) to estimate/propose a fair price for the new treatment, based on its value to patients and health care.
5. Allow organizations such as the PCORI – the Patient-Centered Outcomes Research Institute (a nonprofit, nongovernmental organization located in Washington, DC created by the Patient 6. Protection and Affordable Care Act) – to include drug prices in their assessments of the value of drugs and treatments.
6. Request that nonprofit organizations that represent cancer specialists and their patients develop guidelines to incorporate prices of drugs relative to treatment value.
Source: Change.org petition
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# Marginal cost
#### Did you know...
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In economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. Mathematically, the marginal cost (MC) function is expressed as the derivative of the total cost (TC) function with respect to quantity (Q). Note that the marginal cost may change with volume, and so at each level of production, the marginal cost is the cost of the next unit produced.
A typical Marginal Cost Curve
$MC=\frac{dTC}{dQ}$
In general terms, marginal cost at each level of production includes any additional costs required to produce the next unit. If producing additional vehicles requires, for example, building a new factory, the marginal cost of those extra vehicles includes the cost of the new factory. In practice, the analysis is segregated into short and long-run cases, and over the longest run, all costs are marginal. At each level of production and time period being considered, marginal costs include all costs which vary with the level of production, and other costs are considered fixed costs.
It is a general principle of economics that a (rational) producer should always produce (and sell) the last unit if the marginal cost is less than the market price. As the market price will be dictated by supply and demand, it leads to the conclusion that marginal cost equals marginal revenue. These general principles are subject to a number of other factors and exceptions, but marginal cost and marginal cost pricing play a central role in economic definitions of efficiency.
Marginal cost pricing is the principle that the market will, over time, cause goods to be sold at their marginal cost of production. Whether goods are in fact sold at their marginal cost will depend on competition and other factors, as well as the time frame considered. In the most general criticism of the theory of marginal cost pricing, economists note that monopoly power may allow a producer to maintain prices above the marginal cost; more specifically, if a good has low elasticity of demand (consumers are insensitive to changes in price) and supply of the product is limited (or can be limited), prices may be considerably higher than marginal cost. Since this description applies to most products with established brands, marginal pricing may be relatively rare; an example would be in markets for commodities.
A number of other factors can affect marginal cost and its applicability to real world problems. Some of these may be considered market failures. These may include information asymmetries, the presence of negative or positive externalities, transaction costs, price discrimination and others.
## Cost functions and relationship to average cost
In the most simple case, the total cost function and its derivative are expressed as follows, where Q represents the production quantity, VC represents variable costs (costs that vary with Q), and FC represents fixed costs:
$TC=FC + VC$
$MC=\frac{dTC}{dQ}=\frac{d(FC + VC)}{dQ}=\frac{dVC}{dQ}$
Since (by definition) fixed costs do not vary with production quantity, it drops out of the equation when it is differentiated. The important conclusion is that marginal cost is not related to fixed costs. This can be compared with average total cost or ATC, which is the total cost divided by the number of units produced and does include fixed costs.
$ATC=\frac{FC + VC}{Q}$
For discrete calculation without calculus, marginal cost equals the change in total (or variable) cost that comes with each additional unit produced. For instance, suppose the total cost of making 1 shoe is $30 and the total cost of making 2 shoes is$40. The marginal cost of producing the second shoe is $40 -$30 = \$10.
## Economies of scale
Production may be subject to economies of scale (or diseconomies of scale). Increasing returns to scale are said to exist if additional units can be produced for less than the previous unit, that is, average cost is falling. This can only occur if average cost at any given level of production is higher than the marginal cost. Conversely, there may be levels of production where marginal cost is higher than average cost, and average cost will rise for each unit of production after that point. This type of production function is generically known as diminishing marginal productivity: at low levels of production, productivity gains are easy and marginal costs falling, but productivity gains become smaller as production increases; eventually, marginal costs rise because increasing output (with existing capital, labour or organization) becomes more expensive. For this generic case, minimum average cost occurs at the point where average cost and marginal cost are equal (when plotted, the two curves intersect); this point will not be at the minimum for marginal cost if fixed costs are greater than zero.
## Short and long run costs and economies of scale
A textbook distinction is made between short-run and long-run marginal cost. The former takes as unchanged, for example, the capital equipment and overhead of the producer, any change in its production involving only changes in the inputs of labour, materials and energy. The latter allows all inputs, including capital items (plant, equipment, buildings) to vary.
A long-run cost function describes the cost of production as a function of output assuming that all inputs are obtained at current prices, that current technology is employed, and everything is being built new from scratch. In view of the durability of many capital items this textbook concept is less useful than one which allows for some scrapping of existing capital items or the acquisition of new capital items to be used with the existing stock of capital items acquired in the past. Long-run marginal cost then means the additional cost or the cost saving per unit of additional or reduced production, including the expenditure on additional capital goods or any saving from disposing of existing capital goods. Note that marginal cost upwards and marginal cost downwards may differ, in contrast with marginal cost according to the less useful textbook concept.
Economies of scale are said to exist when marginal cost according to the textbook concept falls as a function of output and is less than the average cost per unit. This means that the average cost of production from a larger new built-from-scratch installation falls below that from a smaller new built-from-scratch installation. Under the more useful concept, with an existing capital stock, it is necessary to distinguish those costs which vary with output from accounting costs which will also include the interest and depreciation on that existing capital stock, which may be of a different type from what can currently be acquired in past years at past prices. The concept of economies of scale then does not apply.
## Externalities
Externalities are costs (or benefits) that are not borne by the parties to the economic transaction. A producer may, for example, pollute the environment, and others may bear those costs. A consumer may consume a good which produces benefits for society, such as education; because the individual does not receive all of the benefits, he may consume less than efficiency would suggest. Alternatively, an individual may be a smoker or alcoholic and impose costs on others. In these cases, production or consumption of the good in question may differ from the optimum level.
### Negative externalities of production
Negative Externalities of Production
Much of the time, private and social costs do not diverge from one another, but at times social costs may be either greater or less than private costs. When marginal social costs of production are greater than that of the private cost function, we see the occurrence of a negative externality of production. Productive processes that result in pollution are a textbook example of production that creates negative externalities.
Such externalities are a result of firms externalising their costs onto a third party in order to reduce their own total cost. As a result of externalising such costs we see that members of society will be negatively affected by such behaviour of the firm. In this case, we see that an increased cost of production on society creates a social cost curve that depicts a greater cost than the private cost curve.
In an equilibrium state we see that markets creating negative externalities of production will overproduce that good. As a result, the socially optimal production level would be lower than that observed.
### Positive externalities of production
Positive Externalities of Production
When marginal social costs of production are less than that of the private cost function, we see the occurrence of a positive externality of production. Production of public goods are a textbook example of production that create positive externalities. An example of such a public good, which creates a divergence in social and private costs, includes the production of education. It is often seen that education is a positive for any whole society, as well as a positive for those directly involved in the market.
Examining the relevant diagram we see that such production creates a social cost curve that is less than that of the private curve. In an equilibrium state we see that markets creating positive externalities of production will under produce that good. As a result, the socially optimal production level would be greater than that observed.
### Social costs
Of great importance in the theory of marginal cost is the distinction between the marginal private and social costs. The marginal private cost shows the cost associated to the firm in question. It is the marginal private cost that is used by business decision makers in their profit maximization goals, and by individuals in their purchasing and consumption choices. Marginal social cost is similar to private cost in that it includes the cost functions of private enterprise but also that of society as a whole, including parties that have no direct association with the private costs of production. It incorporates all negative and positive externalities, of both production and consumption.
Hence, when deciding whether or how much to buy, buyers take account of the cost to society of their actions if private and social marginal cost coincide. The equality of price with social marginal cost, by aligning the interest of the buyer with the interest of the community as a whole is a necessary condition for economically efficient resource allocation.
## Other cost definitions
• Fixed costs are costs which do not vary with output, for example, rent. In the long run all costs can be considered variable.
• Variable cost also known as, operating costs, prime costs, on costs and direct costs, are costs which vary directly with the level of output, for example, labour, fuel, power and cost of raw material.
• Social costs of production are costs incurred by society, as a whole, resulting from private production.
• Average total cost is the total cost divided by the quantity of output.
• Average fixed cost is the fixed cost divided by the quantity of output.
• Average variable cost are variable costs divided by the quantity of output.
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Article | Open | Published:
# Comparison of graphical optimization or IPSA for improving brachytheraphy plans associated with inadequate target coverage for cervical cancer
## Abstract
Many studies have reported that inverse planning by simulated annealing (IPSA) can improve the quality of brachytherapy plans, and we wanted to examine whether IPSA could improve cervical cancer brachytherapy plans giving D90 < 6 Gy (with 7 Gy per fraction) at our institution. Various IPSA plans involving the tandem and ovoid applicators were developed for 30 consecutive cervical cancer patients on the basis of computed tomography: IPSA1, with a constraint on the maximum dose in the target volume; IPSA1-0, identical to IPSA1 but without a dwell-time deviation constraint; IPSA2, without a constraint on the maximum dose; and IPSA2-0, identical to IPSA2 but without a dwell-time deviation constraint. IPSA2 achieved similar results as graphical optimization, and none of the other IPSA plans was significantly better than graphical optimization. Therefore, other approaches, such as combining interstitial and intracavitary brachytherapy, may be more appropriate for improving the quality of brachytherapy plans associated with inadequate target coverage.
## Introduction
Cervical cancer is very common in China, and brachytherapy plays an important role in its treatment1. Brachytherapy plans were historically developed using radiographs and point dosimetry systems2, and today 3-D image-guided brachytherapy is used to optimize the dose distribution to the target volume and avoid high doses to organs at risk3,4,5. Inverse planning by simulated annealing (IPSA) can allow the use of lower radiation doses while maintaining or improving target coverage when planning brachytherapy involving tandem and ovoid applicators in cervical cancer6. Other studies have reported similar results when comparing IPSA with dose point optimization, manual optimization of dwell weights/times and geometric optimization for planning brachytherapy involving a tandem and ovoid7,8,9,10,11.
In our hospital, some brachytherapy plans based on the graphical optimization (GrO) algorithm do not give adequate target coverage (providing D90 < 6 Gy and 7 Gy per fraction) when the dose to organs at risk is kept within recommended limits routinely used at our institution. Here we investigated whether such plans could be improved using IPSA. Our primary criterion for improvement was D90, and secondary criteria were V150, V200 and dwell time.
## Results
### Comparison of IPSA1, IPSA2 and GrO
Mean D90 was 0.2 Gy smaller with IPSA1 than with GrO (3.8%, p = 0.031; Table 1 and Fig. 1), while D90 was 0.4 Gy higher with IPSA2 than with IPSA1 (8.0%, p = 0.002), illustrating the effect of removing the Vmax restriction. Of the three planning algorithms, IPSA1 had the smallest V150 and V200 (p = 0.036 and 0.030 vs. GrO; p = 0.037 and 0.032 vs. IPSA2).
A direct linear relationship was observed between high-risk clinical target volume (HR-CTV) D90 and high dose in the target (Fig. 2). The IPSA2 line lies beneath the two straight lines of IPSA1 and GrO indicating that IPSA2 may be associated with smaller V150 than IPSA1 or GrO for the same HR-CTV D90. The length of each line represents the range of the HR-CTV D90, and a considerable part of the line in the case of IPSA1 is biased towards the left side of the x axis, indicating that it provided the smallest average high-dose volume. Lines for the various IPSA algorithms nearly coincide for V200.
Figures 35 show that the concentration of D2cc points near the dose limit is greater at the bladder than at other organs at risk. This indicates that all the plans tested expose the bladder to a similar dose, implying that the bladder may be the organ at risk that most limits target coverage. GrO offered significantly lower dose to the bladder than the IPSA plans (p = 0.012), whereas IPSA1 offered significantly lower dose to the rectum (p = 0.001).
The conformity index (CI) of GrO was 0.94; IPSA1, 0.91; and IPSA2, 0.87 (p = 0.002; Table 1). The corresponding values of the conformal index (COIN) were 0.62, 0.57 and 0.59 (p = 0.000). There was no significant difference in maximum dwell time among the three plans (p = 0.526), although IPSA2 showed significantly longer total dwell time and greater dwell-time standard deviation than the two other methods (p = 0.002, p = 0.003).
### Comparing IPSA plans with and without dwell-time deviation constraint
There was significant difference in D90 between IPSA1 and IPSA1-0 (p = 0.047) while there was no significant difference between IPSA2 and IPSA2-0 (p = 0.781). The V150 and V200 of IPSA1-0 were significantly higher than those of IPSA1 (34.7% vs 33.4%, p = 0.001; 20.7% vs 19.6%, p = 0.013). COIN and CI were also significantly different between IPSA1-0 and IPSA1 (p = 0.026, p = 0.001).
Total dwell time, maximum dwell time and dwell-time standard deviation were significantly larger with IPSA1-0 than with IPSA1 (p = 0.003, p = 0.000, p = 0.000), reflecting the lack of a constraint on dwell-time deviation. These three parameters did not differ significantly between IPSA2-0 and IPSA2 (p = 0.642, p = 0.574, p = 0.663).
## Discussion
The IPSA1 plan did not provide better target coverage than GrO. The IPSA2 plan improved D90 by 0.4 Gy (8%) relative to IPSA1, reflecting the effect of removing the Vmax restriction; however, this improved D90 by only 0.2 Gy relative to GrO. Further removing the dwell-time deviation constraint led to increases in V150, V200, total dwell time, maximum dwell time and dwell-time standard deviation.
We found a linear relationship between D90 and high dose at the target (Fig. 2). This likely reflects a fundamental limitation of the tandem and ovoid applicators: since only one catheter lies within the uterine cavity, the isodose lines form concentric circles around it, reflecting the fact that dose falls off by the inverse square law. As a result, achieving the prescribed dose on the surface of a large target necessarily implies a large high-dose volume at the target.
The optimization parameter Vmax in IPSA1 may not be the most effective guide for brachytherapy planning, since it operates in opposition to the “minimum surface dose” parameter. Dose distribution is quite sensitive to Vmax, which can decrease dose to organs at risk, high-dose volume in the target as well as target coverage12. We found that removing the Vmax constraint improved target coverage while keeping the dose to organs at risk within limits. Thus, IPSA2 showed greater V150 and V200 than IPSA1 while keeping the high-dose volume similar to that with GrO. These results suggest that the “maximum surface dose” parameter used in IPSA2 may be more reasonable and effective.
At the same time, removing the Vmax restraint increased target coverage by 0.2 Gy relative to GrO, which does not substantially improve plan quality. In fact, the various IPSA plans succeeded only in optimizing dwell time and dwell position relative to GrO. In all plans, a large part of the target lies close to the bladder or rectum, or the target extends laterally into the region in the case of a tandem applicator. This suggests that dose distribution is affected mainly by the location of the target and organs at risk, the shape of the target and the placement of the catheters. If all these factors are fixed, optimization of dwell time and dwell position can, at best, merely fine-tune the dose distribution. These findings are consistent with other studies showing that IPSA can minimize dose to organs at risk and maximize target coverage without substantially altering the dose distribution in brachytherapy for prostate cancer13,14 or gynecologic cancers7,8,10.
Using different applicators may substantially improve plan quality. In contrast to our increase of 0.2 Gy in mean D90 achieved through plan optimization, the combination of interstitial and intracavitary brachytherapy can increase D90 by about 1 Gy (17.5%) relative to intracavitary brachytherapy alone11. Similarly, using Vienna applicators rather than tandem and ovoid applicators increased D90 by 1.7 Gy (27.9%)9, and interstitial brachytherapy has been shown to give higher mean D90 than intracavitary brachytherapy15.
We found that removing the dwell-time deviation constraint from IPSA1 and IPSA2 increased target coverage and dwell-time deviation, consistent with a previous report16. However, the change in D90 was relatively small in our study. In addition, the increase in dwell-time deviation can generate isolated dwell positions with long dwell times, which may increase the risk of hot spots. These hot spots may migrate onto organs at risk if the catheter shifts after computed tomography. Therefore, removing the dwell-time deviation constraint may not be an appropriate method for improving target coverage.
IPSA2 significantly increased target coverage without increasing V150 or V200 relative to GrO. At the same time, IPSA2 showed larger dwell-time deviation than GrO and IPSA1. Increasing the dwell-time deviation constraint may reduce dwell-time deviation in IPSA216.
Although our results reflect the particular approach for target delineation and plan evaluation in place at our hospital, our findings may be useful for brachytherapy planning at other institutions. We found that none of the IPSA plans substantially improved brachytherapy quality above GrO, and the IPSA2 plan achieved similar results as GrO. The “maximum surface dose” parameter may be more reasonable and effective for decreasing high dose volume of brachytherapy plans giving poor performance (D90 < 6 Gy with 7 Gy per fraction) using tandem and ovoid applicators. Removing the dwell-time deviation constraint may increase the risk of harm to normal tissue without improving target coverage.
## Methods
### Patients
Computed tomography images were used to re-plan the brachytherapy treatment plans based on tandem and ovoid applicators for 30 consecutive patients (mean age, 48 yr) with cervical cancer in stage IIB-IIIB based on the International Federation of Gynecology and Obstetrics staging system. These patients were treated at the Affiliated Cancer Hospital of Guangxi Medical University between December 2015 and June 2016. Patients were treated with external beam radiation therapy of 50 Gy in 25 fractions to the target and were concurrently given chemotherapy. This combination therapy was followed by high-dose-rate brachytherapy of 28 Gy in 4–5 fractions.
This study was approved by the Ethics Committee at the Affiliated Cancer Hospital of Guangxi Medical University. All procedures were in accordance with national and international ethical guidelines. Informed consent was obtained from all participants.
### Contouring
Each brachytherapy fraction was followed by computed tomography scanning and contour delineation. Therefore, every patient had four or five computed tomography image sets and contours of the region of interest. Only one fraction from each patient was used in this study. HR-CTVs and organs at risk (rectum, bladder and sigmoid)17 were delineated by a gynecologist.
Contouring and treatment planning were performed using Oncentra® Brachy software (version 4.3, Elekta). One GrO plan and four IPSA plans (see below) were prepared from each computed tomography image set. HR-CTV per fraction was defined to be 7 Gy, maximum bladder dose could not exceed 4.5 Gy, and maximum rectum dose could not exceed 4 Gy. In some cases, limiting the dose to organs at risk was given higher priority than target coverage. This was decided by the physician based on prognostic factors and institutional procedures. When target coverage was insufficient, an additional fraction of high-dose-rate brachytherapy was delivered in order to cover the target with an equivalent dose in 2 Gy-fractions (EQD2) of 80–90 Gy.
### Treatment planning
#### GrO plans
GrO plans were first optimized via dose points optimization. After digitizing applicators, the dwell positions, separated by a 2.5-mm step size, were determined by the extent of the HR-CTV. Dose distributions were then dose-points-optimized with 300 target points randomly placed at the surface of the HR-CTV. After dose points optimization, the GrO was applied to adjust isodose lines using the mouse to achieve the desired target coverage while keeping the doses to organs at risk below the given constraints. The GrO plans were used in actual treatments.
#### IPSA plans
Two-class solutions shown in Table 2 were used as starting points for IPSA1 and IPSA2. The main differences between IPSA1 and IPSA2 were that IPSA1 had a constraint on the maximum dose to the target volume (Vmax), and IPSA1 assigned a slightly higher weight to the “minimum surface dose” parameter. The dwell-time deviation constraint was set to 0.2 in both IPSA1 and IPSA2. To further improve target coverage, this constraint was set to 0 in these plans to generate the respective plans IPSA1-0 and IPSA2–0. The organs at risk were set to the same value in the two-class solutions. After running the optimization with the class solution, dose objectives and weighting factors were modified for individual patients when necessary in order to optimize the dose distribution. After the final results were obtained in the IPSA plans, no fine-tuning of the dose distribution using GrO was allowed.
### Plan evaluation
The following dosimetric parameters of different plans were analyzed based on the dose-volume histograms: HR-CTV D90, the dose that covered 90% of the HR-CTV; D100, the dose that covered 100% of the HR-CTV; V100, the percentage volume covered by at least 100% of the prescribed dose; V150, the volume that received at least 150% of the prescribed dose; V200, the volume that received at least 200% of the prescribed dose; and D2cc, dose covering at least 2 cm3 of organs at risk. In addition, COIN and CI7, were compared (Eqs 12).
Since we were concerned about potential hot spots, we also evaluated the differences in dwell time distributions by recording the mean and maximum dwell time and the mean standard deviation (SD) of the dwell time in each plan.
### Statistical analysis
Differences in the means of each dose parameter among the five plans (GrO, IPSA1, IPSA2, IPSA1-0, IPSA2-0) were assessed for significance using matched ANOVA. Two-group comparisons were assessed for significance using the least-squares difference test. Two-tailed values of P < 0.05 were considered statistically significant. All data analyses were performed using SPSS (IBM, Chicago, IL, USA) and GraphPad Prism 5 (Graphpad, USA).
### Data availability
The datasets analyzed in the present study are available from the corresponding author upon reasonable request.
$${\rm{COIN}}={{\rm{CTV}}}_{{\rm{target}}}\times {{\rm{CTV}}}_{{\rm{target}}}{/({\rm{V}}}_{{\rm{CTV}}}\times {{\rm{V}}}_{{\rm{total}}})$$
(1)
$${\rm{CI}}={{\rm{CTV}}}_{{\rm{target}}}/{{\rm{V}}}_{{\rm{total}}}$$
(2)
CTVtarget is the part of the HR-CTV receiving at least the prescribed dose, Vtotal is the total volume receiving at least the prescribed dose, and VCTV is the volume of the HR-CTV.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## References
1. 1.
Viswanathan, A. N. et al. American Brachytherapy Society consensus guidelines for locally advanced carcinoma of the cervix. Part II: high-dose-rate brachytherapy. Brachytherapy 11, 47–52, https://doi.org/10.1016/j.brachy.2011.07.002 (2012).
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Brooks, S., Bownes, P., Lowe, G., Bryant, L. & Hoskin, P. J. Cervical brachytherapy utilizing ring applicator: comparison of standard and conformal loading. International journal of radiation oncology, biology, physics 63, 934–939, https://doi.org/10.1016/j.ijrobp.2005.07.963 (2005).
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De Brabandere, M., Mousa, A. G., Nulens, A., Swinnen, A. & Van Limbergen, E. Potential of dose optimisation in MRI-based PDR brachytherapy of cervix carcinoma. Radiotherapy and oncology: journal of the European Society for Therapeutic Radiology and Oncology 88, 217–226, https://doi.org/10.1016/j.radonc.2007.10.026 (2008).
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Lindegaard, J. C., Tanderup, K., Nielsen, S. K., Haack, S. & Gelineck, J. MRI-guided 3D optimization significantly improves DVH parameters of pulsed-dose-rate brachytherapy in locally advanced cervical cancer. International journal of radiation oncology, biology, physics 71, 756–764, https://doi.org/10.1016/j.ijrobp.2007.10.032 (2008).
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Potter, R. et al. Clinical impact of MRI assisted dose volume adaptation and dose escalation in brachytherapy of locally advanced cervix cancer. Radiotherapy and oncology: journal of the European Society for Therapeutic Radiology and Oncology 83, 148–155, https://doi.org/10.1016/j.radonc.2007.04.012 (2007).
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Dewitt, K. D. et al. 3D inverse treatment planning for the tandem and ovoid applicator in cervical cancer. International journal of radiation oncology, biology, physics 63, 1270–1274, https://doi.org/10.1016/j.ijrobp.2005.07.972 (2005).
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Palmqvist, T. et al. Dosimetric evaluation of manually and inversely optimized treatment planning for high dose rate brachytherapy of cervical cancer. Acta oncologica (Stockholm, Sweden) 53, 1012–1018, https://doi.org/10.3109/0284186x.2014.928829 (2014).
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Chajon, E. et al. Inverse planning approach for 3-D MRI-based pulse-dose rate intracavitary brachytherapy in cervix cancer. International journal of radiation oncology, biology, physics 69, 955–961, https://doi.org/10.1016/j.ijrobp.2007.07.2321 (2007).
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Jamema, S., Mahantshetty, U., Deshpande, D., Sharma, S. & Shrivastava, S. Does help structures play a role in reducing the variation of dwell time in IPSA planning for gynaecological brachytherapy application? Journal of contemporary brachytherapy 3, 142–149, https://doi.org/10.5114/jcb.2011.24821 (2011).
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Jamema, S. V. et al. Comparison of IPSA with dose-point optimization and manual optimization for interstitial template brachytherapy for gynecologic cancers. Brachytherapy 10, 306–312, https://doi.org/10.1016/j.brachy.2010.08.011 (2011).
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Yoshio, K. et al. Inverse planning for combination of intracavitary and interstitial brachytherapy for locally advanced cervical cancer. Journal of radiation research 54, 1146–1152, https://doi.org/10.1093/jrr/rrt072 (2013).
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Lapuz, C., Dempsey, C., Capp, A. & O’Brien, P. C. Dosimetric comparison of optimization methods for multichannel intracavitary brachytherapy for superficial vaginal tumors. Brachytherapy 12, 637–644, https://doi.org/10.1016/j.brachy.2013.04.009 (2013).
13. 13.
Morton, G. C., Sankreacha, R., Halina, P. & Loblaw, A. A comparison of anatomy-based inverse planning with simulated annealing and graphical optimization for high-dose-rate prostate brachytherapy. Brachytherapy 7, 12–16, https://doi.org/10.1016/j.brachy.2007.10.001 (2008).
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Panettieri, V., Smith, R. L., Mason, N. J. & Millar, J. L. Comparison of IPSA and HIPO inverse planning optimization algorithms for prostate HDR brachytherapy. Journal of applied clinical medical physics/American College of Medical Physics 15, 5055, https://doi.org/10.1120/jacmp.v15i6.5055 (2014).
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Liu, Z. S. et al. Computed Tomography-Guided Interstitial Brachytherapy for Locally Advanced Cervical Cancer: Introduction of the Technique and a Comparison of Dosimetry With Conventional Intracavitary Brachytherapy. International journal of gynecological cancer: official journal of the International Gynecological Cancer Society 27, 768–775, https://doi.org/10.1097/igc.0000000000000929 (2017).
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Smith, R. L. et al. The influence of the dwell time deviation constraint (DTDC) parameter on dosimetry with IPSA optimisation for HDR prostate brachytherapy. Australasian physical & engineering sciences in medicine/supported by the Australasian College of Physical Scientists in Medicine and the Australasian Association of Physical Sciences in Medicine 38, 55–61, https://doi.org/10.1007/s13246-014-0317-2 (2015).
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Potter, R. et al. Recommendations from gynaecological (GYN) GEC ESTRO working group (II): concepts and terms in 3D image-based treatment planning in cervix cancer brachytherapy-3D dose volume parameters and aspects of 3D image-based anatomy, radiation physics, radiobiology. Radiotherapy and oncology: journal of the European Society for Therapeutic Radiology and Oncology 78, 67–77, https://doi.org/10.1016/j.radonc.2005.11.014 (2006).
## Acknowledgements
This work was supported in part by the Self-financing Project of Guangxi Zhuang Autonomous Region Health and Family Planning Commission (Z2016481) and the Guangxi Medical University Youth Science Foundation (GXMUYSF201627).
## Author information
### Author notes
1. ZhiJie Liu and HuanQing Liang contributed equally to this work.
### Affiliations
1. #### Department of Radiation Oncology, Cancer Institute of Guangxi Zhuang Autonomous Region, The Affiliated Cancer Hospital of Guangxi Medical University, Nanning, 530021, PR China
• ZhiJie Liu
• , HaiMing Yang
• , Ye Deng
• , TingJun Luo
• , ChaoFeng Yang
• , Min Lu
• , QingGuo Fu
• & XiaoDong Zhu
2. #### Department of Radiation Oncology, Nanfang Hospital, Southern Medical University, Guangzhou, 510515, PR China
• HuanQing Liang
• Xiao Wang
### Contributions
Liu Zhijie prepared the brachytherapy plans, participated in data collection and data analysis, and co-wrote the manuscript. Liang Huanqing participated in data collection and data analysis, and co-wrote the manuscript. Wang Xiao co-wrote the manuscript. Yang Haiming, Deng Ye, Luo Tingjun, Yang Chaofeng and Lu Min participated in data collection. Fu Qingguo and Zhu XiaoDong designed the study.
### Competing Interests
The authors declare that they have no competing interests.
### Corresponding authors
Correspondence to QingGuo Fu or XiaoDong Zhu.
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I'm using openssl library and I've a problem with RSA_private_encrypt() and RSA_public_decrypt(). I'm using a key size of 256 bit with no padding of the input message. I've noted that when my input ...
24 views
### Is there an existing authorative definition of the cryptographic term 'pepper'
I can attempt to define the term 'pepper' as: In cryptography, a pepper is a something that is added to another value (for example a password) prior to a the value being hashed using a ...
32 views
### (bfxor) BruteForcer XOR v1.2 - Data Dictionary Attack on 64-bit Keys
This is Reptor/xorcoder from Germany again. Yesterday I resumed work on bfxor, my brute-forcing tool with which it's possible to hack XOR encrypted data, mostly text, up to 64-bit keys (8 chars). The ...
17 views
### Device intercommunication with commands
I want to create a smart house project, and in that i bought some simple RF modules. Those modules don't support crypto out of the box but i want to connect them to a device that i would program to ...
36 views
### RSA, proof of correct work, if p is not a prime number [duplicate]
Is there any proof of correct work of RSA algorithm, if p is not a prime number? For example: n = p*q, p = p1*p2, where p1 and p2 are primes. Edit: I found that it's called Multiprime RSA, but i ...
65 views
### Can Poly1305-AES be used with AES-256?
I'm reading through Bernstein's The Poly1305-AES message-authentication code. The MAC is predicated on 16-byte block ciphers like AES and produces 16-byte authentication tags. However, Bernstein does ...
168 views
### Cryptography system by combining a block cipher and a stream cipher
I have to come up with a design for a cryptography system by combining a block cipher and a stream cipher. I can't seem to come up with anything on my own. Can someone point me in the right direction ...
53 views
### Prove that if we redefine the key space, we can assume Gen chooses a key uniformly
I am working on problem 2.1 in Introduction to Modern Cryptography 2nd edition by Katz and Lindell. 2.1) Prove that by redefining the key space, we may assume that the key generation algorithm ...
66 views
### Stacked LFSR - why not used?
New to cryptographic, weak in math. I have designed a PRG which consist of 33 LFSR's, each 32 bits wide. I use one of the LFSR's as "selector", using the 5 LSB from this register to select one of ...
9 views
### Keystore and configuration file
It appears that Java Keystore is often used by web server using a configuration file, with the password opening the JKS written in it and also the password protecting the specific entry. How could ...
33 views
### Assemble RSA keys from components
I'm studying openpgp cryptography and struggling to understand some things. I can't use pgp tool for generating keys and ecryption, but have to write a simple app to generate keys, encrypt and decrypt ...
60 views
### Who are cryptography programmers responsible to? [on hold]
Crypto allows privacy, governments want to preserve their power. What about the fact that cryptography programs would also be of help to the enemies of freedom.
25 views
### Attack probability of an algorithm? [on hold]
I am currently working on improvising the blow fish algorithm. Is there any method to find the attack probability of the algorithm? I am in learning stage right now so please don't mind if the ...
51 views
### In modern definition, what is Enigma, and what caused its downfall?
This question is sparked from the movie The Imitation Game. This single question will have lots of subquestions. The Germans must put the Enigma at the same settings before encrypting and decrypting ...
59 views
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## Chemistry 9th Edition
a) $T_2$ is greater than $T_1$. b) As temperature increases, the reaction rate increases.
a) The average collision energy of the reactants at $T_2$ is greater than that at $T_1$; therefore, $T_2$ must be at a higher temperature than $T_1$. b) As temperature increases, the probability that the collision of the reactants will have enough energy to overcome the activation energy of the reaction increases; therefore, more of the collisions result in reactions, and the reaction rate increases.
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# Tag Info
0
It could be the base itself. If it's made of plastic or aluminum, there's a possibility that ends of the legs where the wheels mount, are slightly bent or warped. I had the same problem with my computer chair and it would always spin counter clockwise. I've even tried positioning the wheels in the opposite direction to see if it would turn clockwise which ...
2
A good way to model the thermodynamics of a system like this (that involves sliding friction) is to treat the interface between the bodies (the sandpaper and the table) as a separate thermodynamic sub-system. The interface has no mass, so its change in internal energy is always zero. The sandpaper is exerting a frictional force in the positive x-direction ...
1
As your hand pushes the sandpaper there is negative mechanical work done on your hand and positive mechanical work done on the sandpaper. These are (in the ideal case) equal in magnitude so that there is no mechanical energy lost between the sandpaper and the hand. As the sandpaper pushes on the wall there is negative mechanical work done on the sandpaper ...
3
Heat that is generated by mechanical motion arises because of friction, as noted in the other answers given above. Note that it can also be generated on the molecular level by forcing adjacent molecules to "rub against" one another inside a chunk of solid material. Materials scientists call this internal friction and is the reason why a chunk of ...
6
In short, heating due to rubbing surfaces has the same roots as Joule heating, which induces a temperature increase in a conductor when drifting electrons interact with solid lattice ions, producing phonons, i.e., quantized sound waves. Thus, in principle, everything that generates sound waves in a body makes it hotter as new vibrational degrees of freedom ...
9
The negative work done by kinetic friction takes the macroscopic kinetic energy of the object it does work on and converts into the microscopic kinetic energy of the molecules of the sandpaper and wall materials, as reflected by an increase in the temperature of the surface of the materials. In effect, the rubbing action between materials increases molecular ...
0
$a$ is the acceleration of block A with respect to the reference frame $S$ in which the ground is at rest. We do not need to introduce a pseudo force because $S$ is an inertial frame. However, $a$ is not necessarily the same as the acceleration $\frac F {M+2m}$, which is the acceleration of the centre of mass of the whole system. We can only say that $a = \... 0 The normal force on each small segment of area may vary, depending on how the mass is distributed, but the friction force is always proportional to the normal force, so the total friction is proportional to the total normal. 0 I don't know what you mean by "size" but the angle$\theta$where both blocks begin to slide, that is, where the maximum possible static friction force occurs, only depends on the coefficient of static friction, and the coefficient of static friction equals the tangent of$\theta$. So if the coefficient of static friction is the same for both ... 0 TL;DR Whether or not the block will start moving (sliding) depends only on the inclination angle$\theta$and the static friction coefficient$\mu_s$of the inclined surface. The block will move when the following condition is satisfied $$\boxed{\theta > \arctan \mu_s}$$ Below I give detailed derivation for this condition. The magnitude of static ... 0 Nothing of the above mentioned thing matter, only the coefficient of friction between the two surfaces. 1 Every book says that friction is independent of surface area in contact. It is pretty obvious that equation for our friction doesn't have any "area term" in it. The "area term" is built into the value of the normal (perpendicular) force,$N$, between the contacting surfaces. Think about$N$being the pressure (force per unit area) on the ... 0 Friction does depend on the normal force. As the area gets bigger, the normal force per unit area and the friction per unit area get smaller: f = (f/A)A = [μ(N/A)]A = μN. 0 The reason is that the weight of the cube is now spread over a larger area of contact, so each part of every plate is now pressed more lightly in contact with the surface. 1 You have assumed that the coefficient of friction for the car is the same as that give for the trailer (0.15) so the frictional force acting on the car and the trailer is$1630 \times 9.8 \times 0.15 = 2396.1$Newtons You have also assumed that friction acts in a backwards direction on the car. But you are told that the force exerted by the car on the ground ... 1 The free-body diagram at exact collision time should look like: If I assume there is no mass loss the first equation cannot be used, otherwise, J would always be zero. I will define some parameters: e: coefficient of restitution u: coefficient of friction t_c : time collapse during collision vi: initial velocity before collision vf: final velocity after ... 0 So during a typical collision calculation with no friction, there is a single impulse$J$along the contact normal that is applied in equal and opposite measure on the colliding bodies. This impulse is calculated by $$J = (1+\epsilon)\, m^\star\, v_{\rm imp}$$ where$\epsilon$is the coefficient of restitution,$m^\star$is the reduced mass of the system ... 5 First, consider the hand: The force of friction on the hand is acting in the opposite direction of the hand’s velocity. (Specifically the velocity of the material of the hand where the force is applied) So the mechanical work is negative meaning that mechanical energy is leaving the hand. Next, consider the table: the force of friction on the table is equal ... 2 To begin with, I don't care much for the diagram you obtained as it implies a gradual transition over time between the maximum static friction friction force and the onset of the constant kinetic friction. In my view a better diagram of the friction plot is one relating friction to applied force as found here: http://hyperphysics.phy-astr.gsu.edu/hbase/... 1 I misunderstood the question with my first answer. Here's a better one. The two blocks will, when the surface underneath them starts accelerating, stay stationary, influenced by static friction, until the surface accelerates so much that they individually break free from static friction and start sliding and lagging behind, influenced by kinetic friction ... 0 The main reason why ABS shortens the braking distance, is because the static friction between the tyres and the road surface is larger than the sliding friction. By making sure the tyres are rolling, the tyres will have the larger static friction with the road surface than if they are sliding, resulting in a larger maximum deceleration of the car. A reason ... 0 ... friction is suppose[d] to be present only when there's a force pulling an object forwards ... Incorrect. Friction always acts on objects to oppose relative motion between two surfaces, regardless of whether a force is or is not applied to one or both objects. If two touching objects are in motion relative to one another then kinetic friction will always ... 0 I have always, always hated how friction is explained at the school level. The issue you are facing is that all these shenanigans about static friction, kinetic friction and even the misnomered monstrosity the rolling friction is are highly empirical. That is, given Newton's laws of motion we try to describe how objects around us behave, almost completely ... 0 Friction is not about other forces. It is not even just about speed. It is about sliding. Technically, that means that it is about relative speed. Solely and purely. Friction comes into existence in order to stop sliding. And that is why a moving object that slides over the ground comes to rest. A moving object in space wouldn't come to rest as it wouldn't ... 3 I think you are confused about differences between the static friction and kinetic friction. OBJECT IS AT REST When an object is at rest, there is a static friction on the contact surface $$F_{fs} = \mu_s n$$ where$n$is magnitude of the normal force, and$\mu_s$is coefficient of static friction. In order to move the object, the resultant force from other ... 1 The object will come to rest. Friction is "always" present. There is no frictional force if the object isn't currently moving, but when you exert a force or if the object is moving, there is a frictional force. The value of that friction is$\mu R$where$R$is the reaction force. 0 There are two main types of friction, static and dynamic friction. Static friction determines the amount of force required for a non-moving object to accelerate, and dynamic friction determines the deceleration of an object that is already in motion. Shaking or vibrating a surface simply has the effect of adding additional forces that aren't biased in any ... 2 Imagine rain falling on a landscape in which there are hills and valleys. A small lake may form in a hollow half way up the side of a hill. The water doesn't know that it's half way up the hillside, so it stays where it is. If a storm blows, or if there's an earthquake, the water in the hollow may be shaken out, and descend the hillside to the valley below. ... 0 from the free body diagram you see that the car move due to the constraint force$~F~$between the wheel axel and the car suspension, for a static case this force is equal to the force between the wheel and the road$F_T~\tau~$Engine torque (transmitted to the wheel)$~F~$constraint force$~F_T~$Tire force or constraint force (in case of no slip ... 0 Friction is a rather general word, which can mean several things here. The dissipation processes that reduce the energy of the ball when it heats the surface, by transforming a part of this energy into heat. Friction of the ball against the air, which slows it down. Sliding friction when it touches the surface: it may actually force the ball to start ... 0 Consider the system as the yo-yo and a short portion of the string attached to the yo-yo. For this system, the external forces are: gravity and the tension on the string. Friction between the yo-yo and the string is an internal force for this system. The motion of the Center of Mass (CM) of the yo-yo is determined by the net external force. (The tension ... 2 But how does the ground actually make the car move? By applying a static friction force forward on the car. The ground's static friction force acting forward on the wheel is equal and opposite to the rearward force the wheel applies to the ground, per Newton's third law. Since the static friction force acting forward on the wheel, and thus the car, is the ... 5 . . . . linear force from the wheel on the ground and the linear force from the ground on the wheel would not cancel as the two forces act on separate bodies and the wheel will spin. 0 The Newton equations of motion are $$m\,\ddot x+k\,(x-x_0)=F(t)+F_c-F_\mu\tag 1$$ $$I\,\ddot \phi+d\,\dot\phi=-F_c\,R\tag 2$$ and the kinematic equations $$x=R\,\phi\quad\Rightarrow ~,\dot x=R\,\dot\phi~,\ddot x=R\ddot\phi\tag 3$$ you have now three equations for the three unknowns$~\ddot x~,\ddot\phi~$and the constraint force$~F_c~$you obtain $$(I+m\,R^... -1 I would imagine that this problem is best solved by using a work-energy balance, but it looks like it fits a second order DE system well. Could someone provide me some guidance on how to solve for the travel function x(t) for this? Because there is friction involved kinetic energy is not conserved. So you need to set up a Newtonian Equation of Motion.$$F(t)... 57 It’s like shaking a measuring cup half full of sugar to make it level out—in both cases there’s an energetically favored configuration you’re trying to reach, but without agitation, friction prevents the grains from moving to that configuration. Each time you tap the cardboard or shake the cup, you give the grains a new opportunity to settle in a new ... 0 It's not necessary that increasing the temperature will only increase the friction on the surface it can also decrease with time which depends upon temperature difference between the heat source and surface or the mechanism which is providing heat to the surface and rising the temperature of the surface. Let's take an example that how friction can decrease ... 1 The assumption you are making that breaks everything is that static friction is required for the ball or cylinder to freely roll at constant velocity on a horizontal surface without sliding. It is not. The friction force you show would only be required to start the ball or cylinder rolling backwards without sliding from rest, for example in response to a ... 0 If i am correct, temperature cannot make frictional force increase or decrease Possible explanation: If the temperature increases then distance between the particles of the body increases due to thermal expansion which results in smoothening the surface accordingly and the frictional force between them decreases. 0 The harder material deforms and wears less than the softer one, but wears nevertheless. However the hardness relation between materials makes a lot of difference in industrial processes. For example: we can machine a part of cast iron using a tool of tungsten carbide. But after repeating the process with several other iron parts, the tool wears, and ... 2 Rolling resistance is an interesting topic. It is clear from experience that a rolling wheel does eventually slow down and stop. So clearly there is some dissipative process that removes the energy from the wheel and transfers it to the environment. However, it is more than that, momentum and angular momentum are also conserved, and you have to consider ... 3 If the energy were indeed conserved, the ball would roll without stopping. The reason why it stops is Rolling friction, which results in converting some of the mechanical energy into heat. Note that this is a type of friction that is different from more familiar static friction, which is also present in case of an object rolling, but which does not result in ... 1 In an ideal case, once rolling starts, friction stops acting as there is no relative motion at the point of contact and the ball keeps on rolling. In a real life scenario, there is some deformation at the point of contact, and the normal shifts slightly and no longer passes through the centre. On performing torque analysis at the centre of mass, you will ... 5 Yes, energy is always conserved. If not then you have to widen your definition of the system to include all relevant parts. For rolling motion, the main energy absorbers that cause slowing down is the contact with the surface and the mechanics of an axle (if its a wheel on a car e.g.). Kinetic energy might be lost as heat from friction in the axle bearings, ... 4 Energy is conserved when a real wheel or a real ball rolls along a real surface, but purely mechanical energy is not conserved. Some of the mechanical energy is converted to heat, which is considered to be another form of energy. One important mechanism of energy conversion is hysteresis. No object is truly rigid. A rolling wheel or ball is continually ... 1 Critical damping is the condition which transitions between overshoot of the static equilibrium position (under damped) and an exponential decay to the static equilibrium position (over damped). With less damping than critical damping the system will reach the static equilibrium position quicker than one which was critically damped but will overshoot and ... 0 Simplest answer is that it is just a matter of jargon. Obviously, with very little damping the system may vibrate increasingly (unstable), or the vibration may dampen out after a long time. With a lot of damping it will get to the stable position but it may take long, very long, or "forever". So somewhere in between is the amount of damping where ... 0 it begin by spinning its wheels. At first the car won't be moving, so if the wheels were to begin spinning without the car moving, there would be a relative motion between the wheels and the road. That describes a skid. It would work but be inefficient. Instead for most cars and drivers, the engine applies a torque to the wheel. The ground applies a ... 2 What the OP asks for is indeed possible but only for very specific initial conditions. There are a few things to discuss, the first being what does "returning to equilibrium faster" mean. First, we are trying to compare the behavior of two different systems (I will assume they have the same damping coefficient$\gamma\$ but different resonant ...
2
I agree with the idea that the first block provides total friction in that case. Here is an imaginary experiment, assume there are "two" equal forces pushing in obverse directions on the two blocks. In the beginning, the two blocks are "separated", and they move to each other until they are in "contact". Now, as they are in ...
Top 50 recent answers are included
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# Using one font type for text, and other type for Math
Can I make in my document so that I use one font for the text part, but other font for formulas?
I'd like to use Garamond for text, and Utopia for math.
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Have a look at the solution of tex.stackexchange.com/questions/11058/…, it should give you the right direction. – Uwe Ziegenhagen Feb 22 '13 at 19:17
Yeah, that doesn't help as it requires XeTeX, and I keep getting errors :\ – dingo_d Feb 22 '13 at 20:08
You didn't say that xeTeX wasn't an option... :-) – Uwe Ziegenhagen Feb 22 '13 at 20:22
Yeah, I should have mentioned that, sorry :| – dingo_d Feb 22 '13 at 20:24
I don't think it's a good idea: the two fonts are quite different from each other, so they don't mix at all. – egreg Feb 22 '13 at 21:35
You could use `\usepackage[utopia]{mathdesign}` or `\usepackage{fourier}` to get Utopia, and `\usepackage[osf]{garamondx}` to obtain Garamond in the text. It is also possible to load `ebgaramond`.
To use `garamondx` package you have to install it through getnonfreefonts script. And here you have the exact way to do obtain `garamond`: Can I install fonts from CTAN using TeX Live Utility? (you just have to substitute `garamond` for `garamondx` in the last command).
By the way, as a temporal solution, you can just use this (which just uses the `mathdesign`s garamond)
``````\usepackage{fourier}% or \usepackage[utopia]{mathdesign}
\renewcommand*{\rmdefault}{mdugm}
``````
But I encourage using `garamondx` as it adds small caps, old style figures and ligatures.
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This `garamondx` gives me error (.sty not found), and if I use my current one `\usepackage[urw-garamond]{mathdesign}` with `fourier` the equations end up being messed up :\ – dingo_d Feb 22 '13 at 20:02
Ouch, I forgot. You have to install them through getnonfreefonts. I'll edit my answer. – Manuel Feb 22 '13 at 20:41
And I'm on windows... if that's any help xD – dingo_d Feb 22 '13 at 20:58
@dingo_d I don't know how to use it in Windows, by the way, I added a not quite good solution. – Manuel Feb 22 '13 at 21:28
Thanks I'll see how this works :) – dingo_d Feb 22 '13 at 22:36
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# I need to reduce the fontsize of only one equation/formula because it's too long
$$\left| Y(j \omega) \right| = \sqrt{\frac{\omega^2 \left( C\ped{DC} + C\ped{eq} \right)^2 + \omega^4 \left[ \left( R\ped{eq} C\ped{eq} C\ped{DC} \right)^2 - 2 \left( C\ped{DC} + C\ped{eq} \right) \left( L\ped{eq} C\ped{eq} C\ped{DC} \right) \right] + \omega^6 \left( L\ped{eq} C\ped{eq} C\ped{DC} \right)^2}{1 + \omega^2 \left[ \left( R\ped{eq} C\ped{eq} \right)^2 - 2 L\ped{eq} C\ped{eq} \right] + \omega^4 \left( L\ped{eq} C\ped{eq} \right)^2}}. \label{eq:cmut:abs_y_w_eq}$$
Hi. This is an equation I have to write. It's too long. (I cannot show you the results because I don't have enough reputation points to post images). How can I reduce the fontsize of the equation (without reducing the fontsize of the number of the reference)? Any suggestion to solve this problem? Thank you.
• Could you provide a MWE? From the document class declaration and packages loaded through to the end of the document? For example, if I try to compile your snippet, I get a compilation error with \ped. I'm not sure whether that's a user defined macro or something else. Either way, I'm unfamiliar with it. – A.Ellett Feb 22 '13 at 15:58
• Welcome to TeX.sx! Reducing the size won't help; assuming the standard settings for 10pt article on A4 paper, even at \scriptsize the formula is too wide. With \tiny it is not overfull, but it becomes unreadable. – egreg Feb 22 '13 at 16:07
• Please, bear in mind that \ped is not a standard command, but is only provided by the italian option to babel. So you see the necessity for a minimal working example (MWE) – egreg Feb 22 '13 at 16:18
Reducing the size won't help; assuming the standard settings for 10pt article on A4 paper, even at \scriptsize the formula is too wide. With \tiny it is not overfull, but it becomes unreadable.
A possibility is to avoid the radical, squaring the left hand side, and using multlined from the mathtools package for the numerator:
\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc} % or other encoding
\usepackage[italian]{babel}
\usepackage{amsmath,mathtools}
\begin{document}
$$\lvert Y(j \omega) \rvert^2 = \frac{ \begin{multlined}[b] \omega^2 ( C\ped{DC} + C\ped{eq} )^2 \\ \qquad{} +\omega^4 [ ( R\ped{eq} C\ped{eq} C\ped{DC} )^2 - 2 (C\ped{DC} + C\ped{eq} ) ( L\ped{eq} C\ped{eq} C\ped{DC} ) ] \qquad\\ {} + \omega^6 ( L\ped{eq} C\ped{eq} C\ped{DC} )^2 \end{multlined} } { 1 + \omega^2 [ ( R\ped{eq} C\ped{eq} )^2 - 2 L\ped{eq} C\ped{eq} ] + \omega^4 ( L\ped{eq} C\ped{eq} )^2 }. \label{eq:cmut:abs_y_w_eq}$$
\end{document}
The two \qquad commands are just to widen the middle row which shouldn't be broken, but becomes the longest, spoiling the alignment.
Don't overuse \left and \right; in this formula none of them is needed.
A different strategy might be to use symbolic names for the coefficients: with the same preamble as before (but mathtools is not necessary), you can write
\begin{align}
\lvert Y(j \omega) \rvert &=
\sqrt{
\frac{X_2 \omega^2 + X_4 \omega^4 + X_6 \omega^6}
{1 + Y_2 \omega^2 + Y_4 \omega^4}
},\\[2ex]
%%%
X_2 &= ( C\ped{DC} + C\ped{eq} )^2
\notag\\
X_4 &= ( R\ped{eq} C\ped{eq} C\ped{DC} )^2 -
2 (C\ped{DC} + C\ped{eq} ) ( L\ped{eq} C\ped{eq} C\ped{DC} )
\notag\\
X_6 &= ( L\ped{eq} C\ped{eq} C\ped{DC} )^2
\notag\\
Y_2 &= ( R\ped{eq} C\ped{eq} )^2 - 2 L\ped{eq} C\ped{eq}
\notag\\
Y_4 &= ( L\ped{eq} C\ped{eq} )^2
\notag
\end{align}
and get the following result
• The OP's readers will thank you if he adopts your suggestion to name the coefficients. – Ethan Bolker Feb 22 '13 at 16:44
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A jump suit costs 125 dollars. The rate of the discount is 20 percent. What is the discount
10% of $125 is$12.50.
Now 20%=2*10%.
So 20% of $125 is$25.
If you were to receive a 20% discount, you’d only have to pay $100 to bag the jump suit. A$25 discount is what the discount is.
You could also say that 20 percent of 125 dollars is a fifth of 125 dollars. A fifth of 125 dollars is 25 dollars. So once again, if you were given 20 percent off, you’d only have to hand out out 100 dollars.
RELATED:
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# Where to store service urls for a Unity3D game
I have URL information for services (dozens of them) that I want to store in a Unity3D web player project. What is a good practice for storing it. (please don't say hard coding them)
I've recently joined a large scale Unity 3D project in the business world. I've noticed that there is no configuration file of any type. I.e. All URLs for service calls are hard coded. (among other configuration settings that are not typical for player editing)
While looking for a good solution to store/load, I'm seeing that: 1) Unity does not appear to have any kind of AppSettings. I.e. like Visual Studio dlls/exes/services might. (PlayerPrefs expressed in #3)
2) Web Player (which the project uses) does not support File IO, to store my own config.xml/config.json type file.
3) PlayerPrefs appears that it will remain isolated to the local machine. Updating the project does not replace the player prefs, and new variables are supposed to be hardcoded to populate the PlayerPrefs if those variables didn't already exist.
4) Hard Coding the values creates a hefty inconvenience, as we push our solutions from Dev to Test to Staging to Prod, we have to make sure to replace a code file. (typically systems are designed to change config files.) Additionally, once the code was built, we wouldn't be able to reasonably change the settings to experiment with different servers or other configuration changes.
What would you recommend?
• I also have this same question on the LinkedIn Unity Group, and also on the Unity Scripting forum. --> I will repost the solution from the others if they have it first. – Dan Violet Sagmiller Jan 2 '15 at 14:20
• Presently I'm leaning towards a Settings class with a dictionary. The settings will attempt to be populated from JSON, and attempt 2 paths. 1) it will try to load from a File IO, to find a JsonSettings.dat file, which works in everything but Web, and 2) it will attempt to send a JS Network message out to the page it is hosted in, to get the JSON settings from it instead, which only works in the web. In either case it is a JSON file, it has 2 locations it needs to live. but that I think might be the best solution at present. – Dan Violet Sagmiller Jan 2 '15 at 14:34
We actually got over this problem in a non-game application by using an XML file (you could also use JSON if you prefer). This is compiled into our application so we don't use IO for it, we instead use XML. This does obviously mean you have to re-compile when making changes though.
Our file looked something like this:
services.xml
<services serverURL="https://services.our-api-url.com">
<service>
<label><![CDATA[GETSTATUS]]></label>
<url><![CDATA[/status]]></url>
<method><![CDATA[GET]]></method>
<type></type>
</service>
<service>
<url><![CDATA[/session]]></url>
<method><![CDATA[POST]]></method>
<type></type>
</service>
<service>
<label><![CDATA[LOGOUT]]></label>
<url><![CDATA[/session]]></url>
<method><![CDATA[DELETE]]></method>
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# source:nscp/NSC.dist@89f1a84
0.4.00.4.10.4.2stable
Last change on this file since 89f1a84 was 89f1a84, checked in by Michael Medin <michael@…>, 8 years ago
Added some missing files tpo the CVS
• Property mode set to `100644`
File size: 4.1 KB
Line
1[modules]
2;# NSCLIENT++ MODULES
3;# A list with DLLs to load at startup.
4; You will need to enable some of these for NSClient++ to work.
5; ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
6; * *
7; * N O T I C E ! ! ! - Y O U H A V E T O E D I T T H I S *
8; * *
9; ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
10;FileLogger.dll
11;CheckSystem.dll
12;CheckDisk.dll
13;NSClientListener.dll
14;NRPEListener.dll
15;SysTray.dll
16;CheckEventLog.dll
17;CheckHelpers.dll
18
19[Settings]
21; This is the same as the password option but here you can store the password in an obfuscated manner.
22; *NOTICE* obfuscation is *NOT* the same as encryption, someone with access to this file can still figure out the
23; password. Its just a bit harder to do it at first glance.
25;
27; This is the password (-s) that is required to access NSClient remotely. If you leave this blank everyone will be able to access the daemon remotly.
29;
31; This is a comma-delimited list of IP address of hosts that are allowed to talk to the all daemons.
32; If leave this blank anyone can access the deamon remotly (NSClient still requires a valid password).
33;allowed_hosts=127.0.0.1
34
35[log]
36;# LOG DEBUG
37; Set to 1 if you want debug message printed in the log file (debug messages are always printed to stdout when run with -test)
38;debug=1
39;
40;# LOG FILE
41; The file to print log statements to
42;file=NSC.log
43;
45; The format to for the date/time part of the log entry written to file.
47
48
49[NSClient]
50;# NSCLIENT PORT NUMBER
51; This is the port the NSClientListener.dll will listen to.
52;port=12489
53
54
55[Check System]
56;# CPU BUFFER SIZE
57; Can be anything ranging from 1s (for 1 second) to 10w for 10 weeks. Notice that a larger buffer will waste memory
58; so don't use a larger buffer then you need (ie. the longest check you do +1).
59;CPUBufferSize=1h
60;
61;# CHECK RESOLUTION
62; The resolution to check values (currently only CPU).
63; The value is entered in 1/10:th of a second and the default is 10 (which means ones every second)
64;CheckResolution=10
65
66[NRPE]
67;# NRPE PORT NUMBER
68; This is the port the NRPEListener.dll will listen to.
69;port=5666
70;
71;# COMMAND TIMEOUT
72; This specifies the maximum number of seconds that the NRPE daemon will allow plug-ins to finish executing before killing them off.
73;command_timeout=60
74;
75;# COMMAND ARGUMENT PROCESSING
76; This option determines whether or not the NRPE daemon will allow clients to specify arguments to commands that are executed.
77;allow_arguments=0
78;
79;# COMMAND ALLOW NASTY META CHARS
80; This option determines whether or not the NRPE daemon will allow clients to specify nasty (as in |`&><'"\[]{}) characters in arguments.
81;allow_nasty_meta_chars=0
82;
83;# USE SSL SOCKET
84; This option controls if SSL should be used on the socket.
85;use_ssl=1
86
87[NRPE Handlers]
88;# COMMAND DEFINITIONS
89;# Command definitions that this daemon will run.
90;# Can be either NRPE syntax:
91;command[check_users]=/usr/local/nagios/libexec/check_users -w 5 -c 10
92;# Or simplified syntax:
93;test=c:\test.bat foo \$ARG1\$ bar
94;check_disk1=/usr/local/nagios/libexec/check_disk -w 5 -c 10
95;# Or even loopback (inject) syntax (to run internal commands)
96;# This is a way to run "NSClient" commands and other internal module commands such as check eventlog etc.
97;check_cpu=inject checkCPU warn=80 crit=90 5 10 15
98;check_eventlog=inject CheckEventLog Application warn.require.eventType=error warn.require.eventType=warning critical.require.eventType=error critical.exclude.eventType=info truncate=1024 descriptions
99;check_disk_c=inject CheckFileSize ShowAll MaxWarn=1024M MaxCrit=4096M File:WIN=c:\ATI\*.*
100;# But be careful:
101; dont_check=inject dont_check This will "loop forever" so be careful with the inject command...
102;# Check some escapings...
103; check_escape=inject CheckFileSize ShowAll MaxWarn=1024M MaxCrit=4096M "File: foo \" WIN=c:\\WINDOWS\\*.*"
Note: See TracBrowser for help on using the repository browser.
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show · group.permutation_gens all knowls · up · search:
For non-solvable groups $G$ we give a set of permutations that generate a minimal degree faithful permutation representation of $G$.
Authors:
Knowl status:
• Review status: beta
• Last edited by David Roe on 2020-12-08 01:21:33
Referred to by:
Not referenced anywhere at the moment.
History: Differences
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Linear Regression and Kernel Methods
Linear Regression and Kernel Methods
This tour studies linear regression method in conjunction with regularization. It contrasts ridge regression and the Lasso. It also presents its non-linear variant using kernlization.
Contents
We recommend that after doing this Numerical Tours, you apply it to your own data, for instance using a dataset from LibSVM.
Disclaimer: these machine learning tours are intended to be overly-simplistic implementations and applications of baseline machine learning methods. For more advanced uses and implementations, we recommend to use a state-of-the-art library, the most well known being Scikit-Learn
Installing toolboxes and setting up the path.
You need to unzip these toolboxes in your working directory, so that you have toolbox_general in your directory.
For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'.
Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab command you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands.
Execute this line only if you are using Matlab.
getd = @(p)path(p,path); % scilab users must *not* execute this
Then you can add the toolboxes to the path.
getd('toolbox_general/');
We test the method on the prostate dataset in $$n=97$$ samples with features $$x_i \in \RR^p$$ in dimension $$p=8$$. The goal is to predict the price value $$y_i \in \RR$$.
Helpers.
SetAR = @(ar)set(gca, 'PlotBoxAspectRatio', [1 ar 1], 'FontSize', 20);
Xm = @(X)X-repmat(mean(X,1), [size(X,1) 1]);
Cov = @(X)Xm(X)'*Xm(X);
name = 'prostate';
Randomly permute it.
A = A(randperm(size(A,1)),:);
Separate the features $$X$$ from the data $$y$$ to predict information.
X = A(:,1:end-2);
y = A(:,end-1);
c = A(:,end);
$$n$$ is the number of samples, $$p$$ is the dimensionality of the features,
[n,p] = size(X);
fprintf('n=%d, p=%d\n', n,p);
n=97, p=8
Split into training and testing.
I0 = find(c==1); % train
I1 = find(c==0); % test
n0 = length(I0); n1 = n-n0;
X0 = X(I0,:); y0 = y(I0);
X1 = X(I1,:); y1 = y(I1);
Normalize the features by the mean and std of the training set. This is optional.
RepSub = @(X,u)X-repmat(u, [size(X,1) 1]);
RepDiv = @(X,u)X./repmat(u, [size(X,1) 1]);
mX0 = mean(X0); sX0 = std(X0);
X0 = RepSub(X0,mX0); X1 = RepSub(X1,mX0);
X0 = RepDiv(X0,sX0); X1 = RepDiv(X1,sX0);
Remove the mean (computed from the test set) to avoid introducing a bias term and a constant regressor. This is optional.
m0 = mean(y0);
y0 = y0-m0;
y1 = y1-m0;
Dimenionality Reduction and PCA
In order to display in 2-D or 3-D the data, dimensionality is needed. The simplest method is the principal component analysis, which perform an orthogonal linear projection on the principal axsis (eigenvector) of the covariance matrix.
Display the covariance matrix of the training set.
clf;
imagesc(Cov(X0));
Display the covariance between the data and the regressors.
clf;
bar(X0'*y0);
axis tight;
SetAR(1/2);
Compute PCA ortho-basis and the feature in the PCA basis.
[U,D,V] = svd(Xm(X0),'econ');
Z = Xm(X0) * V;
Plot sqrt of the eigenvalues.
clf;
plot(diag(D), '.-', 'LineWidth', 2, 'MarkerSize', 30);
axis tight;
SetAR(1/2);
Display the features.
pmax = min(p,8);
k = 0;
clf;
for i=1:pmax
for j=1:pmax
k = k+1;
subplot(pmax,pmax,k);
if i==j
hist(X0(:,i),6);
axis tight;
else
plot(X0(:,j),X0(:,i), '.');
axis tight;
end
set(gca, 'XTick', [], 'YTick', [] );
axis tight;
if i==1
title(class_names{j});
end
end
end
Display the points cloud of feature vectors in 3-D PCA space.
options.disp_dim = 3;
clf; plot_multiclasses(X,ones(n,1),options);
SetAR(1);
1D plot of the function to regress along the main eigenvector axes.
col = {'b' 'g' 'r' 'c' 'm' 'y' 'k'};
clf;
for i=1:min(p,3)
subplot(3,1,i);
plot(Z(:,i), y0, '.', 'Color', col{i}, 'MarkerSize', 20);
axis tight;
end
Linear Regression
We look for a linear relationship $$y_i = \dotp{w}{x_i}$$ written in matrix format $$y= X w$$ where the rows of $$X \in \RR^{n \times p}$$ stores the features $$x_i \in \RR^p$$.
Since here $$n > p$$, this is an over-determined system, which can solved in the least square sense $\umin{ w } \norm{Xw-y}^2$ whose solution is given using the Moore-Penrose pseudo-inverse $w = (X^\top X)^{-1} X^\top y$
Least square solution.
w = (X0'*X0) \ (X0'*y0);
Prediction (along 1st eigenvector).
clf;
plot( [y1 X1*w], '.-', 'MarkerSize', 20);
axis tight;
legend('y', 'X_1 w');
Mean-square error on testing set.
E = norm(X1*w-y1) / norm(y1);
fprintf('Relative prediction error: %.3f\n', E);
Relative prediction error: 0.702
Regularization is obtained by introducing a penalty. It is often called ridge regression, and is defined as $\umin{ w } \norm{Xw-y}^2 + \lambda \norm{w}^2$ where $$\lambda>0$$ is the regularization parameter.
The solution is given using the following equivalent formula $w = (X^\top X + \lambda \text{Id}_p )^{-1} X^\top y,$ $w = X^\top ( XX^\top + \lambda \text{Id}_n)^{-1} y,$ When $$p<n$$ (which is the case here), the first formula should be prefered.
In contrast, when the dimensionality $$p$$ of the feature is very large and there is little data, the second is faster. Furthermore, this second expression is generalizable to Kernel Hilbert space setting, corresponding possibly to $$p=+\infty$$ for some kernels.
lambda = .2*norm(X0)^2;
w = (X0'*X0+lambda*eye(p)) \ (X0'*y0);
w1 = X0'*( (X0*X0'+lambda*eye(n0)) \ y0 );
fprintf('Error (should be 0): %.4f\n', norm(w-w1)/norm(w));
Error (should be 0): 0.0000
Exercice 1: (check the solution) Display the evolution of the test error $$E$$ as a function of $$\lambda$$.
exo1;
Ridge: 67.91%
Exercice 2: (check the solution) Display the regularization path, i.e. the evolution of $$w$$ as a function of $$\lambda$$.
exo2;
Sparse Regularization
In order to perform feature selection (i.e. select a subsect of the features which are the most predictive), one needs to replace the $$\ell^2$$ regularization penalty by a sparsity inducing regularizer. The most well known is the $$\ell^1$$ norm $\norm{w}_1 \eqdef \sum_i \abs{w_i} .$
The energy to minimize is $\umin{w} J(w) \eqdef \frac{1}{2}\norm{X w-y}^2 + \lambda \norm{w}_1.$
J = @(w,lambda)1/2*norm(X0*w-y0)^2 + lambda*norm(w,1);
The simplest iterative algorithm to perform the minimization is the so-called iterative soft thresholding (ISTA), aka proximal gradient aka forward-backward.
It performs first a gradient step (forward) of the smooth part $$\frac{1}{2}\norm{X w-y}^2$$ of the functional and then a proximal step (backward) step which account for the $$\ell^1$$ penalty and induce sparsity. This proximal step is the soft-thresholding operator $\Ss_s(x) \eqdef \max( \abs{x}-\lambda,0 ) \text{sign}(x).$
Soft = @(x,s)max(abs(x)-s,0).*sign(x);
The ISTA algorithm reads $w_{k+1} \eqdef \Ss_{\la\tau}( w_k - \tau X^\top ( X w_k - y ) ),$ where, to ensure convergence, the step size should verify $$0 < \tau < 2/\norm{X}^2$$ where $$\norm{X}$$ is the operator norm.
Display the soft thresholding operator.
t = linspace(-5,5,201);
clf; plot(t,Soft(t,2), 'LineWidth', 2);
axis tight;
SetAR(1/2);
Descent step size.
tau = 1.5/norm(X0)^2;
Choose a regularization parameter $$\la$$.
lambda = max(abs(X0'*y0))/10;
Initialization $$w_0$$.
w = zeros(p,1);
A single ISTA step.
C = X0'*X0;
u = X0'*y0;
ISTA = @(w,lambda,tau)Soft( w-tau*( C*w-u ), lambda*tau );
w = ISTA(w,lambda,tau);
Exercice 3: (check the solution) Implement the ISTA algorithm, display the convergence of the energy.
exo3;
Exercice 4: (check the solution) Compute the test error along the full regularization path. You can start by large $$\lambda$$ and use a warm restart procedure to reduce the computation time. Compute the classification error.
exo4;
Lasso: 65.42%
Exercice 5: (check the solution) Display the regularization path, i.e. the evolution of $$w$$ as a function of $$\lambda$$.
exo5;
Exercice 6: (check the solution) Compare the optimal weights for ridge and lasso.
exo6;
Kernelized Ridge Regression
In order to perform non-linear and non-parametric regression, it is possible to use kernelization. It is non-parametric in the sense that the number of parameter grows with the number $$n$$ of samples (while for the initial linear method, the number of parameter is $$p$$). This allows in particular to generate estimator of arbitrary complexity.
Given a kernel $$\kappa(x,z) \in \RR$$ defined for $$(x,z) \in \RR^p \times \RR^p$$, the kernelized method replace the linear approximation functional $$f(x) = \dotp{x}{w}$$ by a sum of kernel centered on the samples $f_h(x) = \sum_{i=1}^n h_i k(x_i,x)$ where $$h \in \RR^n$$ is the unknown vector of weight to find.
When using the linear kernel $$\kappa(x,y)=\dotp{x}{y}$$, one retrieves the previously studied linear method.
Generate synthetic data in 2D. Add noise to a deterministic map.
B = 3;
n = 500; p = 2;
X = 2*B*rand(n,2)-B;
rho = .5; % noise level
y = peaks(X(:,1), X(:,2)) + randn(n,1)*rho;
Display as scattered plot.
clf;
scatter(X(:,1), X(:,2), ones(n,1)*20, y, 'filled');
colormap jet(256);
axis equal; axis([-B B -B B]); box on;
Macro to compute pairwise squared Euclidean distance matrix.
distmat = @(X,Z)bsxfun(@plus,dot(X',X',1)',dot(Z',Z',1))-2*(X*Z');
The gaussian kernel is the most well known and used kernel $\kappa(x,y) \eqdef e^{-\frac{\norm{x-y}^2}{2\sigma^2}} .$ The bandwidth parameter $$\si>0$$ is crucial and controls the locality of the model. It is typically tuned through cross validation.
sigma = .3;
kappa = @(X,Z)exp( -distmat(X,Z)/(2*sigma^2) );
Once avaluated on grid points, the kernel define a matrix $K = (\kappa(x_i,x_j))_{i,j=1}^n \in \RR^{n \times n}.$
K = kappa(X,X);
The weights $$h \in \RR^n$$ are solutions of $\umin{h} \norm{Kh-y}^2 + \la \dotp{Kh}{h}$ and hence can be computed by solving a linear system $h = (K+\la \text{Id}_n)^{-1} y$
lambda = 0.01;
h = (K+lambda*eye(n))\y;
Regressor.
Y = @(x)kappa(x,X)*h;
Evaluation on a 2D grid.
q = 101;
t = linspace(-B,B,q);
[v,u] = meshgrid(t,t);
Xn = [u(:), v(:)];
Display as an image.
yn = reshape(Y(Xn),[q,q]);
clf;
imagesc(t,t,yn); axis image; axis off;
colormap jet(256);
Exercice 7: (check the solution) Display the evolution of the regression as a function of $$\sigma$$.
exo7;
Exercice 8: (check the solution) Apply the kernelize regression to a real life dataset. Study the influence of $$\la$$ and $$\si$$.
exo8;
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CTAN has a new package: pageslts
Date: June 10, 2010 7:54:14 AM CEST
This should within a day be at your local mirror. Thanks Jim Hef{}feron Saint Michael's College ...................................................................... The following information was provided by our fellow contributor: Name of contribution: pagesLTS Version number: 1.1b Author's name: Hans-Martin Münch Summary description: Puts the labels LastPage (\AtEndDocument) and VeryLastPage (\AfterLastShipout) into the .aux file, allowing the user to refer to the (very) last page of a document..number of pages in the current page numbering scheme. \thepage and \theCurrentPageLocal are different e. g. when \addtocounter{pageg}{...} or \setcounter{page}{...} were used. At the first page of the document a label pagesLTS.0 is created. This label can be referred to, too. Further labels are provided for special cases. The alphalph package is supported, i. e. page numbers alph or Alph > 26 and fnyambol > 9 can be used (with according options set). Even zero and negative page numbers can be used with ara License type: lppl Announcement text:
This package puts the labels LastPage (\AtEndDocument) and VeryLastPage (\AfterLastShipout) into the .aux file, allowing the user to refer to the (very) last page of a document. This might be particularly useful in places like headers or footers. When more than one page numbering scheme is used, these references do not give the total number of pages. For this case the label LastPages is introduced. Additionally, at the last page of each page numbering scheme a label pagesLTS.<numbering scheme> is placed, where <numbering scheme> is e. g. arabic, roman, Roman, alph, or Alph. For fnsymbol please use \lastpageref{pagesLTS.fnsymbol} instead of \pageref{pagesLTS.fnsymbol}. When the same numbering scheme is used twice, the page numbers are either reset to one or continued automatically, depending on the option given when the package is called. The command \theCurrentPage prints the current total/absolute page number - in contrast to \thepage, which gives only the page name in the current page numbering scheme. \theCurrentPageLocal gives the current number of pages in the current page numbering scheme. \thepage and \theCurrentPageLocal are different e. g. when \addtocounter{pageg}{...} or \setcounter{page}{...} were used. At the first page of the document a label pagesLTS.0 is created. This label can be referred to, too. Further labels are provided for special cases. The alphalph package is supported, i. e. page numbers alph or Alph > 26 and fnyambol > 9 can be used (with according options set). Even zero and negative page numbers can be used with arabic, alph, Alph, roman, Roman, and fnsymbol page numbering (with alphalph package and according options).
This package is located at http://tug.ctan.org/tex-archive/macros/latex/contrib/pageslts . More information is at http://tug.ctan.org/pkg/pageslts (if the package is new it may take a day for that information to appear). We are supported by the TeX Users Group http://www.tug.org . Please join a users group; see http://www.tug.org/usergroups.html .
pageslts – Variants of last page labels
The package was designed as an extension of the lastpage package — as well as that package’s LastPage label (created \AtEndDocument) it adds a VeryLastPage (created \AfterLastShipout).
When more than one page numbering scheme is in operation (as in a book class document with frontmatter), the labels above do not give the total number of pages, so the package also provides labels pagesLTS.<numbering scheme>, where the numbering scheme is arabic, roman, etc.
The package relies on the undolabl package.
Package pageslts Version 1.2f 2015-12-21 Copyright 2010–2015 H.-Martin Münch Maintainer Hans-Martin Münch
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We are very excited to join forces with MLCommons and OctoML.ai! Contact Grigori Fursin for more details!
### Improved Generalization Bound of Group Invariant / Equivariant Deep Networks via Quotient Feature Space
lib:f359b84203b05e43 (v1.0.0)
Authors: Akiyoshi Sannai,Masaaki Imaizumi
ArXiv: 1910.06552
Document: PDF DOI
Abstract URL: https://arxiv.org/abs/1910.06552v2
A large number of group invariant (or equivariant) networks have succeeded in handling invariant data such as point clouds and graphs. However, generalization theory for the networks has not been well developed, because several essential factors for generalization theory, such as size and margin distribution, are not very suitable to explain invariance and equivariance. In this paper, we develop a generalization error bound for invariant and equivariant deep neural networks. To describe the effect of the properties on generalization, we develop a quotient feature space, which measures the effect of group action for invariance or equivariance. Our main theorem proves that the volume of quotient feature spaces largely improves the main term of the developed bound. We apply our result to a specific invariant and equivariant networks, such as DeepSets (Zaheer et al. (2017)), then show that their generalization bound is drastically improved by $\sqrt{n!}$ where $n$ is a number of permuting coordinates of data. Moreover, we additionally discuss the representation power of invariant DNNs, and show that they can achieve an optimal approximation rate. This paper is the first study to provide a general and tight generalization bound for a broad class of group invariant and equivariant deep neural networks.
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# Why RSA-KEM is more secure than Textbook-RSA?
I am studying RSA-KEM but I can not see why it should be as secure as padding RSA messages (e.g with RSA-OAEP) when exchanging a key between two parties (say A and B).
It is easy to see that Textbook-RSA is problematic, as sending a key with $$k_1^{e_B} \bmod n$$ leaves the possibility for an attacker to analyze the message. Let's say that by coincidence A sends to B a second key $$k_2^{e_B} = (42 k_1)^{e_B} = 42^{e_B} k_1^{e_B}$$ (in the following $$\bmod n$$ is always omitted). An attacker could easily notice this as it could divide $$k_2^{e_B}$$ by $$42^{e_B}$$.
Now let us suppose that A and B are using RSA-KEM to exchange keys. An attacker cannot detect anymore if e.g. $$k_2 = 42 k_1$$ as a key encapsulation key is used to encrypt the shared key. However, the random integer to generate the key encapsulation key is still encrypted over Textbook-RSA.
Why is this not a problem? An attacker is still able to perform e.g. statistical analysis on the randomly exchanged integer, e.g. if A and B again perform two key exchanges and it happens that $$r_2 = 6943 r_1$$ an attacker may be able to notice this and eventually even find out the random integers, thus breaking the shared key as it depends on these integers.
• You need to explain the algorithm you are using to discover the 6943 and the r2 in your equation. Once you can explain the algorithm then we can explain why it won't work. – President James K. Polk Nov 30 '19 at 13:22
Why is this not a problem?
Because for two different encryptions the random integers are drawn independently and uniformly at random over the whole range of the multipicative group $$\mathbb Z_N^*$$ (in practice this is usually approximated as $$[1,n)$$). The RSA assumption now literally states that it's difficult to recover the random value from its textbook RSA encryption if it is sampled in this way.
if A and B again perform two key exchanges and it happens that $$r_2 = 6943 r_1$$ an attacker may be able to notice this and eventually even find out the random integers
Actually this won't happen because both $$r_1,r_2$$ are independently random, so is their group combination $$r_1/r_2$$ which has a chance of $$2^{b-n}$$ to be smaller than $$2^b$$ for $$n$$-bit RSA moduli, so for a really generous estimate suppose you are betting on $$r_1/r_2$$ to be guessable small, say smaller than $$2^{60}$$ and using weak 1024-bit RSA encryption, then you have a chance of $$2^{60-1024}\approx 2^{-940}$$ of the quotient being sufficiently small. This is a really negligible probability and likely won't ever be observed.
The standard criterion for security is indistinguishability under adaptive chosen-ciphertext attack, or IND-CCA2. What this means is that the adversary is given:
• the public key $$(n, e_B)$$, and
• an oracle that answers queries of the form: What is the plaintext for the ciphertext message $$c$$?
The adversary's task is to find any pair of messages with a pattern they can distinguish in the corresponding ciphertexts. Specifically, perhaps after interacting with the oracle, the adversary chooses two messages $$m_0 \ne m_1$$, and asks to be challenged with the ciphertext $$c_b$$ for $$m_b$$ where $$b$$ is a secret coin toss not known to the adversary; the adversary then wins the game if they guess correctly what $$b$$ was.
If ‘encryption’ is $$m \mapsto m^{e_B} \bmod n$$, then this is very easy! The adversary can furnish any pair of plaintexts $$m_0 \ne m_1$$, and check whether $$c_b \stackrel?= {m_0}^{e_B} \bmod n$$ or $$c_b \stackrel?= {m_1}^{e_B} \bmod n$$ to determine what $$b$$ was. What this illustrates is that public-key encryption must be randomized so that the adversary cannot simply confirm guesses about what the plaintext is.
‘But,’ you object, ‘I said the plaintext is a random key which the adversary cannot predict!’ Well, security in your scenario is weaker than security in the IND-CCA2 scenario, because you've added extra assumptions about how the legitimate users use the cryptosystem. But OK, let's say you add that assumption.
For example, let's say the legitimate users use RSA-2048 to encrypt AES-256 keys for AES-GCM, and let's say they pick the exponent that gives the best performance: $$e_B = 3$$. Now when you send me $$c = {k_1}^{e_B} \bmod n = {k_1}^3 \bmod n,$$ I can simply compute the real number cube root $$\sqrt[3] c$$ to recover what $$k_1$$ was, because as an integer, $$0 \leq k_1 < 2^{256}$$, so that $${k_1}^3 < 2^{768} \lll n$$, which means the $$\bmod n$$ part never kicked in with parameters of this size! Oops.
You might object that $$e = 3$$ is bad, but even with larger exponents like $$e = 65537$$ there are all manner of elaborate attacks using black magic like continued fractions or lattice algorithms on structured messages such as 256-bit strings. The problem is that the RSA trapdoor permutation $$x \mapsto x^e \bmod n$$ is bad at concealing structured messages. It's only good at concealing uniform random elements of $$\mathbb Z/n\mathbb Z$$.
What's different about RSA-KEM is that you choose a secret integer $$x$$ uniformly at random below $$n$$ independently for each message, and then hash it to derive your AES-256 key $$k_1 = H(x)$$ while transmitting the encapsulation $$y = x^e \bmod n$$ so the recipient can recover $$x$$. Note that $$x$$ is not restricted to $$0 \leq x < 2^{256}$$; it is only restricted to $$0 \leq x < n$$. This means that any adversary defined in terms of a generic hash function $$H$$ can easily be shown to be able to compute arbitrary $$e^{\mathit{th}}$$ roots modulo $$n$$, meaning that such an adversary is guaranteed to be able to solve the RSA problem.
(And the most efficient exponent 3 is just fine with RSA-KEM, as it is with any serious public-key encryption scheme built out of RSA.)
• I think 0 usually isn't allowed for RSA-KEM because we map into $\mathbb Z_n^*$? (though of course the chance of actually hitting 0 is negligible) – SEJPM Nov 29 '19 at 15:16
• It doesn't matter because the probability is so low. Same for any linear combination $\theta p + \eta q$ below $n$. Actually taking the effort to restrict $x$ to $(\mathbb Z/n\mathbb Z)^\times$ would be a mistake because it would be costly to test and likely expose you to side channel attacks, while providing utterly negligible security. Even in the (already negligible-probability!) event of detecting an element outside $(\mathbb Z/n\mathbb Z)^\times$, the conditional probability of detecting zero is still negligible, below $1/2^{1024}$. – Squeamish Ossifrage Nov 29 '19 at 15:20
RSA-KEM is not working as you described. RSA-KEM mitigates the attack that you have described, RSA-KEM simply as follows;
1. First generate a random $$x \in [2..n\hbox{-}1]$$, $$n$$ is the RSA modulus.
2. Encrypt the $$x$$, $$c \equiv x^c \bmod n$$
3. Send $$c$$
4. The other side will decrypt to get $$x = c^d \bmod n$$. Now both side has $$x$$.
5. To derive a key both sides use a Key Derivation function on $$x$$, $$key= \operatorname{KDF}(x)$$
If you send the key itself you will need a padding scheme like OAEP to prevent the attacks on textbook RSA. KEM eliminates this by using the full modulus as message.
How to use it to encrypt a message
Per message choose a new random $$x$$ and derived a new $$key$$ to encrypt messages. Use an authentication on the encryption like HMAC or better use Authenticated Encryption like AES-GCM or ChaCha20-Poly1305.
$$ciphertext = \operatorname{AES-GCM}(m, key)$$
Encapsulate the Key $$c = x^e$$
Now send the other side $$(c,ciphertext)$$
The other side, first decrypts $$c$$ to get $$x$$ then will use $$\operatorname{KDF}(x)$$ to find the encryption key and finally will decrypt AES-GCM.
• If there is an integrity error, then you know that an attacker played with the transmitted message or there is a transmission error.
• Can the attacker guess my key? If I used a bad random number generator, yes. Otherwise no since there is $$1/2^{128}$$ if you generate the key for AES-128.
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# VQSR Training
Posts: 16Member
edited October 2012
When performing VQSR, the data set has its variants overlapped with the training set, may I know if all the overlapped variants are used in the training or is it down sampled?
Post edited by Geraldine_VdAuwera on
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## Best Answer
• Posts: 122Dev ✭✭✭
Answer ✓
Hi atks,
There isn't any downsampling of the training variants however there is some filtering that is done. By looking at the 1D annotation distributions, extreme outliers are removed from the training set. This behavior is controlled with the --stdThreshold argument to VariantRecalibrator.
I hope that helps,
## Answers
• Posts: 122Dev ✭✭✭
Answer ✓
Hi atks,
There isn't any downsampling of the training variants however there is some filtering that is done. By looking at the 1D annotation distributions, extreme outliers are removed from the training set. This behavior is controlled with the --stdThreshold argument to VariantRecalibrator.
I hope that helps,
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= 6 x 5 x 4 x 3 x 2 x 1 = 720. = 8 * Factorial_Number (7) Factorial = 8 * 7 * Factorial_Number (6) = 8 * 7 * 6 * Factorial_Number (5) = 8 * 7 * 6 * 5 * Factorial_Number (4) Factorial = 8 * 7 * 6 * 5 * 4 * Factorial_Number (3) = 8 * 7 * 6 * 5 * 4 * 3 * Factorial_Number (2) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * Factorial_Number … 7!=7*6*5*4*3*2*1=5040 . In general, n objects can be arranged in n(n – 1)(n – 2) … The factorial of a positive number n is given below. For example, Factorial of 6 is 720 (1 x 2 x 3 x 4 x 5 x 6 = 720). First, note that the factorial of 8 can be written as 8 followed by an exclamation mark: 8! For n=0, 0! Factorial of 10! Calculate the Sum of Natural Numbers. Related Read: C Program To Find Factorial of a Number. Those numbers would be 6,5,4,3,2,1. The factorial of 7 is 5040. link brightness_4 code # Python 3 program to find # factorial of given number . Share on: Was this article helpful? 5! 5x4x3x2x1=120. For example, the factorial of 7 is equal to 7×6×5×4×3×2×1 = 5040. Recursive Solution: Factorial can be calculated using following recursive formula. These while loops will calculate the Factorial of a number.. was started by Christian Kramp in 1808. Learn how to write a C program for factorial.Writing a C program to find factorial can be done using various techniques like using for loop, while loop, pointers, recursion but here in this program, we show how to write a factorial program using for loop in a proper way.. Factorial definition formula n! Factorial of 7! Multiply all these numbers by 7 and the final result is the factorial of 7. The value n! And also factorial examples for numbers 5 and 7. 5! To find the factorial of any number in Java Programming, you have to ask to the user to enter the number, now find the factorial of the entered number using for loop and display the factorial result of the given number on the output screen as shown in the following program.. Java Programming Code to Find Factorial of Number However, if I put $(7/2)!$ in the calculate I get $11.631$ Am I … Factorial of a non-negative integer n is the product of all the positive integers that are less than or equal to n. For example: The factorial of 5 is 120. Example – Factorial using While Loop. Take a number of input from the user In mathematics, the factorial of a number (that cannot be negative and must be an integer) n, denoted by n!, is the product of all positive integers less than or equal to n. In this program we will find the factorial of a number where the number should be entered by the user. edit close. Factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n: For example, The value of 0! Find Factorial of a Number. I did $(7/2) \times (5/2) \times (3/2) \times (1/2) = (105/16) ^ \pi = 1.82$ (as per a little tutorial I'm doing). Start. Factorial of n is denoted by n!. There … Now you will be able to easily solve problems on n+1 factorial, the factorial of 10, the factorial of 0, combinations, and permutations. No need to get your calculator out because we calculated it for you. 5040 / … So if you want to find the factorial of 7, multiply 7 with all positive integers less than 7. Note:-Factorial of n number is 1*2*3*…n. Factorial of a number is calculated by multiplying it with all the numbers below it starting from 1. Using the concept of factorials, many complicated things are made simpler. = 5 * 4 * 3 * 2 *1 5! The factorial of n is denoted by n! The factorial is always found for a positive integer by multiplying all the integers starting from 1 till the given number. Here, we can follow some procedure to reach the completion of this program. Write a function to calculate the factorial value of any integer entered through the keyboard. Kotlin Example. Here, the number whose factorial is to be found is stored in num, and we check if the number is negative, zero or positive using if...elif...else statement. One of the most basic concepts of permutations and combinations is the use of factorial notation. = 1. and is equal to 1*2*3*4 = 24. Factorial of a number is denoted by n!, is the product of all positive integers less than or equal to n: The factorial of 8 is: 40320 In general, the factorial of a number is a shorthand way to write a multiplication expression wherein the number is multiplied by each number less than it but greater than zero. * Related Examples. = 1. 1) using for loop 2) using while loop 3) finding factorial of a number entered by user. Factorial of 6! The factorial of an integer can be found using a recursive program or a non-recursive program. Factorial of a 5=120. We shall implement the following factorial algorithm with while loop. Following picture has the formula to calculate the factorial of a number. and calculated by the product of integer numbers from 1 to n. For n>0, n! Before going through the program, lets understand what is factorial: Factorial of a number n is denoted as n! The notation for this function is !, as for instance when we say we need to find the value behind 4 factorial it should be written such 4! n! Find Factorial of a Number Using Recursion. In this example, we shall make use of Java While Loop, to find the factorial of a given number. = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800 How to Calculate Factorial in C++ Language by using the Various methods? Visit this page to learn to find factorial of a number using recursion. It's been many years since I studied maths, and I'm trying to figure out the half factorials $(7/2)!$ without a calculator. The factorial is normally used in Combinations and Permutations (mathematics). Therefore, you calculate the factorial of 8 as follows: 8 x 7 x 6 and so on until 1. Enter number for find factorial: 7 Factorial of 6 is:5040. We will write three java programs to find factorial of a number. For example: Here, 5! Kotlin Example. Finding the factorial of a number is a frequent requirement in data analysis and other mathematical analysis involving python. = 120. In maths, the factorial of a non-negative integer, is the product of all positive integers less than or equal to this non-negative integer. Factorial definition is - of, relating to, or being a factor or a factorial. We hope you enjoyed learning about Factorial with the simulations and practice questions. = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040. Factorial is sequence of a number whose multiply by all previous number. factorial of 7 is. factorial of n is. Formula of Factorial . Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720. Factorial Program in C: Factorial of n is the product of all positive descending integers. play_arrow. Solution : Now in this problem to get the solution, we have to divide the factorial of 7 with the factorial of 6. Recent Examples on the Web: Noun The exclamation point there isn’t the end of a sentence but, instead, denotes a factorial, the value obtained by multiplying the number by every number that precedes it. is called "n factorial" and is calculated by following formula: By convention, 0! return no * fact(no-1) => 7 * fact(6) => 7 * 6 * fact(5) => => 7 * 6 * 5 * fact(4) => 7 * 6 * 5 * 4 * fact(3) => 7 * 6 * 5 * 4 * 3 * fact(2) => 7 * 6 * 5 * 4 * 3 * 2 * fact(1) => 7 * 6 * 5 * 4 * 3 * 2 * 1 => 5040. is pronounced as "5 factorial", it is also called "5 bang" or "5 shriek". The user can provide numbers as they wish and get the factorial according to their input . Find factorial of a number using the do-while loop In mathematics a factorial is a function that makes the product of all positive integers less than or equal to a desired number (n). Kotlin Example. The use of !!! Here we are going to discuss how to calculate factorial in a C++ language using various methods like the if-else statement, for loop, recursion method, and function with the help of examples: About Cuemath. = 1×2×3×4×...×n. Recursive : filter_none. Factorial of 8 means that you multiply 8 by every number below it. Algorithm. Ex:- No is 5. 4! n!=n*(n-1)*....2*1. = 1 if n = 0 or n = 1 is 1, according to the convention for an empty product. Factorial of a number is the product of all the numbers preceding it. = 5 * 4 * 3 * 2 * 1 = 120 When we use the formula to find 5!, we get 120. Example of both of these are given as follows. This program intakes input (a positive integer) from the user and calculates the factorial of the given number using while loop and displays the result. Here you will get python program to find factorial of number using for and while loop. For example factorial of 4 is 24 (1 x 2 x 3 x 4). TABLE 3.17 catalogs these useful fractional factorial designs using the notation previously described in FIGURE 3.7. and the value of n! C Program For Factorial. = n * (n-1)! Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720. is: 1 * 2 * 3 * … (n-1) * n To find 5 factorial, or 5!, simply use the formula; that is, multiply all the integers together from 5 down to 1. Though they may seem very simple, the use of factorial notation for non-negative integers and fractions is a bit complicated. Below program takes a number from user as an input and find its factorial. 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Number, change the value of any integer entered through the program for a positive number n denoted... * 3 * …n previous number so on until 1 an empty product starting from 1 we can some! 1 * 2 * 1 may seem very simple, the use of Java while loop! =7 * *! From 1 integer by multiplying all the integers starting from 1 * 2 * 1=5040 6 = 720.! Non-Recursive program algorithm with while loop, to find factorial of a positive integer by multiplying the... The program, lets understand what is factorial: factorial of 7 with the factorial of a given.. We hope you enjoyed learning about factorial with the factorial of 6 given. And fractions is a bit complicated example, we have to divide the factorial 6... 4 = 24 all previous number is 24 ( 1 x 2 3. 1 * 2 * 1=5040 find the factorial of a number from as! In C: factorial of a number using the do-while loop following picture has the to. Java while loop integer entered through the factorial of 7 denoted as n! =n * ( n-1 )....! Function to calculate the factorial of an integer can be factorial of 7 as 8 followed by an exclamation mark 8! Program takes a number from user as an input and find its factorial an mark... The product of integer numbers from 1 while loop, to find factorial of a number n! *. 4 = 24 procedure to reach the completion of this program is 720 ( x! 6 x 5 x 4 x 3 x 4 x 3 x 2 3... A factorial notation for non-negative integers and fractions is a bit complicated 4 is 24 1! Bang '' or 5 shriek '' is factorial: factorial can be using... Is sequence of a number as they wish and get the solution, we to... The following factorial algorithm with while loop formula: by convention, 0 Java. Number using recursion by an exclamation mark: 8 x 7 x 6 x 5 x 6 x x... In C: factorial can be calculated using following recursive formula first, note that the factorial of as... Means that you multiply 8 by every number below it starting from to! Test the program for a different number, change the value of num to divide the factorial of number. - of, relating to, or being a factor or a non-recursive program the completion of this program page... Factorial examples for numbers 5 and 7, change the value of any integer through! 1 5 an empty product formula to calculate the factorial is normally in... About factorial with the simulations and practice questions to find factorial of number... Will write three Java programs to find factorial of number using for and loop.: Now in this problem to get the solution, we have to divide the factorial of 7 equal! By all previous number factorial of 7 720 to 7×6×5×4×3×2×1 = 5040 also called n... '' and is calculated by multiplying all the integers starting from 1 to n. for n > 0,!! Factorial: factorial of a number is calculated by following formula: by convention 0. Previous number by multiplying it with all the numbers below it 6 is 720 1... Of factorials, many complicated things are made simpler to reach the completion of this.. Following factorial algorithm with while loop: by convention, 0 shriek.. The program for a different number, change the value of num result is the product of all the starting... * 4 * 3 * 2 * 1 while loop a bit complicated number change... Formula factorial definition formula factorial definition formula factorial definition formula factorial definition formula definition... And Permutations ( mathematics ) in this example, factorial of a positive number is...: 8! =n * ( n-1 ) *.... 2 * 1=5040 seem very,. Numbers by 7 and the final result is the product of integer numbers from 1 till the number. Always found for a different number, change the value of num to. Link brightness_4 code # python 3 program to find # factorial of a number * 2 * 3 *.. Of given number 720 ( 1 x 2 x 1 = 720....
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Let $a, b, c, d, e$ be distinct positive integers such that $a^4 + b^4 = c^4 + d^4 = e^5$. Show that $ac + bd$ is a composite number.
There is a prime number $p$ such that $16p+1$ is the cube of a positive integer. Find $p$.
Let $N$ be the least positive integer that is both $22$ percent less than one integer and $16$ percent greater than another integer. Find the remainder when $N$ is divided by $1000$.
Show that, if $a,b$ are positive integers satisfying $4(ab-1)\mid (4a^2-1)$, then $a=b$
Show that $2x^2 - 5y^2 = 7$ has no integer solution.
Let positive integer $d$ is a divisor of $2n^2$, where $n$ is also a positive integer. Prove $(n^2 + d)$ cannot be a perfect square.
Prove there exist infinite number of positive integer $a$ such that for any positive integer $n$, $n^4 + a$ is not a prime number.
What is the smallest positive integer than can be expressed as the sum of nine consecutive integers, the sum of ten consecutive integers, and the sum of eleven consecutive integers?
Find all positive integer $n$ such that $(3^{2n+1} -2^{2n+1}- 6^n)$ is a composite number.
Find $n$ different positive integers such that any two of them are relatively prime, but the sum of any $k$ ($k < n$) of them is a composite number.
Let $B$ be the set of all binary integers that can be written using exactly $5$ zeros and $8$ ones where leading zeros are allowed. If all possible subtractions are performed in which one element of $B$ is subtracted from another, find the number of times the answer $1$ is obtained.
Let $S$ be the increasing sequence of positive integers whose binary representation has exactly $8$ ones. Find the $1000^{th}$ number in $S$ (in base $10$).
Find the number of positive integers $m$ for which there exist nonnegative integers $x_0$, $x_1$ , $\dots$ , $x_{2011}$ such that $m^{x_0} = \sum_{k = 1}^{2011} m^{x_k}.$
Joe uses 9 different digits out of 0 to 9 to create a 2-digit number, a 3-digit number, and a 4-digit number. He \ffinds the sum of these three numbers is 2014. Do you know which digit is not used?
Let $N$ be the greatest integer multiple of $36$ all of whose digits are even and no two of whose digits are the same. Find the remainder when $N$ is divided by $1000$.
Let $K$ be the product of all factors $(b-a)$ (not necessarily distinct) where $a$ and $b$ are integers satisfying $1\le a < b \le 20$. Find the greatest positive integer $n$ such that $2^n$ divides $K$.
True or false: Let $\tau({n})$ denotes the number of positive divisors that $n$ has. Then $$\tau({1}) + \tau({2}) +\tau({3}) +\cdots + \tau({2015})$$ is an odd number.
Is it possible to equally divide the set {$1, 2, 3, \cdots, 972$} into 12 non-intersect subsets so that each subset has exactly 81 elements, and the sums of those subsets are all equal?
Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker \\underline{1}\underline{A}\underline{2}$. What is the missing digit A of this 3-digit number? What is the minimum number of digits to the right of the decimal point needed to express the fraction$\frac{123456789}{2^{26}\cdot 5^4}$as a decimal? Back in 1930, Tillie had to memorize her multiplication facts from$0 \times 0$to$12 \times 12$. The multiplication table she was given had rows and columns labeled with the factors, and the products formed the body of the table. To the nearest hundredth, what fraction of the numbers in the body of the table are odd? For every composite positive integer$n$, define$r(n)$to be the sum of the factors in the prime factorization of$n$. For example,$r(50) = 12$because the prime factorization of$50$is$2 \times 5^{2}$, and$2 + 5 + 5 = 12$. What is the range of the function$r$,$\{r(n): n \text{ is a composite positive integer}\}$? For how many positive integers$n$is$\frac{n}{30-n}$also a positive integer? Let$S$be the set of positive integers$n$for which$\tfrac{1}{n}$has the repeating decimal representation$0.\overline{ab} = 0.ababab\cdots,$with$a$and$b$different digits. What is the sum of the elements of$S$? A group of$12$pirates agree to divide a treasure chest of gold coins among themselves as follows. The$k^\text{th}$pirate to take a share takes$\frac{k}{12}$of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which this arrangement will allow each pirate to receive a positive whole number of coins. How many coins does the$12^{\text{th}}\$ pirate receive?
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Journal topic
Ocean Sci., 15, 1531–1543, 2019
https://doi.org/10.5194/os-15-1531-2019
Ocean Sci., 15, 1531–1543, 2019
https://doi.org/10.5194/os-15-1531-2019
Research article 22 Nov 2019
Research article | 22 Nov 2019
# The life cycle of submesoscale eddies generated by topographic interactions
The life cycle of submesoscale eddies generated by topographic interactions
Mathieu Morvan1, Pierre L'Hégaret1, Xavier Carton1, Jonathan Gula1, Clément Vic1, Charly de Marez1, Mikhail Sokolovskiy2,3, and Konstantin Koshel4 Mathieu Morvan et al.
• 1LOPS, Univ. Brest-CNRS-IFREMER-IRD, IUEM, Plouzané, France
• 2Institute of Water Problems of the RAS, Ul Gubkina 3, Moscow, 199333, Russia
• 3Shirshov Institute of Oceanology of RAS, 36 Nahimovskiy pr., Moscow, 117997, Russia
• 4V.I.Il'ichev Pacific Oceanological Institute, 43 Baltiyskaya Street, Vladivostok, 690041, Russia
Correspondence: Mathieu Morvan (mmorvan3@univ-brest.fr)
Abstract
Persian Gulf Water and Red Sea Water are salty and dense waters flowing at intermediate depths in the Gulf of Oman and the Gulf of Aden, respectively. Their spreading pathways are influence by mesoscale eddies that dominate the surface flow in both semi-enclosed basins. In situ measurements combined with altimetry indicate that Persian Gulf Water is stirred in the form of filaments and submesoscale structures by mesoscale eddies. In this paper, we study the formation and the life cycle of intense submesoscale vortices and their potential impact on the spreading of Persian Gulf Water and Red Sea Water. We use a primitive-equation three-dimensional hydrostatic model at a submesoscale-resolving resolution to study the evolution of submesoscale vortices. Our configuration idealistically mimics the dynamics in the Gulf of Oman and the Gulf of Aden: a zonal row of mesoscale vortices interacting with north and south topographic slopes. Intense submesoscale vortices are generated in the simulations along the continental slopes due to two different mechanisms. First, intense vorticity filaments are generated over the continental slope due to frictional interactions of the background flow with the sloping topography. These filaments are shed into the ocean interior and undergo horizontal shear instability that leads to the formation of submesoscale coherent vortices. The second mechanism is inviscid and features baroclinic instabilities arising at depth due to the weak stratification. Submesoscale vortices subsequently drift away, merge and form larger vortices. They can also pair with opposite-signed vortices and travel across the domain. They eventually dissipate their energy via several mechanisms, in particular fusion into the larger eddies or erosion on the topography. Since no submesoscale flow clearly associated with the fragments of Persian Gulf Water was observed in situ, we modeled Persian Gulf Water as Lagrangian particles. Particle patches are advected and sheared by vortices and are entrained into filaments. Their size first grows as the square root of time: a signature of the merging processes. Then, it increases linearly with time, corresponding to their ballistic advection by submesoscale eddies. On the contrary, without intense submesoscale eddies, particles are mainly advected by mesoscale eddies; this implies a weaker dispersion of particles than in the previous case. This shows the potentially important role of submesoscale eddies in spreading Persian Gulf Water and Red Sea Water.
1 Introduction
Mesoscale eddies [𝒪(10−100) km] are ubiquitous in the world's oceans. The mesoscale eddy field dominates the energy content of oceanic currents at sub-inertial frequencies and is crucial to large-scale budgets of heat and geochemical tracers. Although their generation mechanisms are clearly identified and quantified, largely stemming from large-scale current instabilities, how they dissipate their energy remains unclear . The interaction of these mesoscale vortices can lead to the formation of smaller-scale features (Carton2001). Submesoscale eddies [𝒪(1−10) km] can be generated as the result of frontal instabilities (Capet et al.2008a, b, c) feeding off the energy of the mesoscale currents. Recently, numerical models highlighted one possible mechanism for mesoscale energy dissipation, which is the interaction of mesoscale eddies with the underlying seafloor topography . This specific interaction also leads to the formation of submesoscale eddies. In this regime, the influence of stratification is still important, but the Coriolis force is less prevalent in the horizontal momentum budgets (viz. the Rossby number of the flow is not always small; ). Submesoscale eddies have been sampled for decades, yet their life cycle (from generation to dissipation) is poorly understood .
The Arabian Sea is home to an energetic mesoscale eddy field . In particular, they can interact with the salty and dense waters of the outflows from the Persian Gulf and from the Red Sea . These salty and dense waters flow out of these seas into the Gulf of Oman and into the Gulf of Aden and settle at 250–300 and 600–1000 m depths, respectively . These two gulfs also receive Rossby and Kelvin waves, and vortices, propagating westwards from the Arabian Sea . Mesoscale vortices divert the outflow paths away from the coast, advect them along curved trajectories around the eddy rims, elongate these outflows as salty filaments and finally can break these filaments into small eddies . The chaotic dispersion of a tracer by a mesoscale vortex row in a realistic numerical simulation of the Japan Sea has previously been studied by . However, the details of the spreading mechanism, involving submesoscale eddies, have not been explored.
In this paper, we focus on the life cycle of the submesoscale eddies generated by mesoscale eddy–topography interactions, combining observational data from dedicated campaigns and idealized numerical simulations. studied the case of a mesoscale dipole along a continental shelf, reminiscent of the situation described in . But satellite observations during the spring intermonsoon and the summer monsoon reveal the presence of vortex rows with alternate polarities in the Gulf of Aden and in the Gulf of Oman. A vortex row is more efficient than a single dipole to form small eddies, but it is also more prone to destroying them by shearing and stretching effects. These mechanisms will be studied here. We further quantify how these submesoscale eddies are instrumental in the spreading of passive particles, then the implications regarding the dispersion of dense waters such as Persian Gulf Water (PGW) and Red Sea Water (RSW). We compare and analyze a set of three numerical experiments with different bottom boundary conditions (with or without bottom drag and bottom boundary layer) and with different topographies (with or without cape).
The data and numerical model used in this study are presented in Sect. 2. Observations of submesoscale eddies and fragments formed from the Persian Gulf Water outflow in the Gulf of Oman in spring 2014 are presented in Sect. 3.1. Then, generation and life cycle of the submesoscale eddies due to the interaction of a vortex row with continental slopes is analyzed using idealized numerical simulations in Sect. 3.2, 3.3 and 3.4.
2 Material and methods
## 2.1 The Phys-Indien 2011 campaign
The Phys-Indien experiment was carried out in spring 2011 to study the Persian Gulf Water outflow current in the Gulf of Oman and to monitor the eddies there and south of the Arabian Peninsula. The Beautemps-Beaupré research vessel deployed a CTD/ADCP (conductivity–temperature–depth probe/acoustic Doppler current profiler) at different locations to record vertical profiles of pressure, salinity, temperature and currents; it also towed a Seasoar, a platform carrying two CTDs, undulating between 0 and 350 m depths behind the ship. The measurement accuracies after processing and validation on other (independent) sensors were 10−3C, $\mathrm{5}×{\mathrm{10}}^{-\mathrm{3}}$ psu. The horizontal velocity was obtained with a 38 kHz ship-mounted ADCP; this device measures currents from the surface to about 1000 m depth; the depth range depends on the matter in suspension in seawater, which can reflect the acoustic signal. The long time average data are used, giving one profile every 10 min. The accuracy of the horizontal components of velocity is $\mathrm{5}×{\mathrm{10}}^{-\mathrm{3}}$ m s−1. The characteristics of the Persian Gulf Water are highlighted via the vertical sections of temperature, salinity and density.
## 2.2 Numerical setup
To investigate the origin and the dynamics of submesoscale vortices, we set up idealized simulations of a row of four surface-intensified mesoscale vortices with alternate polarities, in a zonally periodic channel, by using the Coastal and Regional Ocean COmmunity (CROCO) model at submesoscale-resolving resolution on an f plane.
The CROCO model is a primitive-equation model solving the hydrostatic Boussinesq–Navier–Stokes equations with Coriolis acceleration due to the Earth rotation. On the horizontal, the momentum and tracers equations are solved by using the fifth-order upstream-biased advection scheme. On the vertical, the momentum and tracers equations are solved by using the splines vertical advection scheme. The extent of the channel is $\left[\mathrm{600}\phantom{\rule{0.125em}{0ex}}\mathrm{km};\mathrm{200}\phantom{\rule{0.125em}{0ex}}\mathrm{km};\mathrm{2000}\phantom{\rule{0.125em}{0ex}}\mathrm{km}\right]$ in the x, y and z directions, respectively. The horizontal grid spacing is 1 km. On the vertical, 100 submesoscale-resolving σ levels stretched at the bottom are used (the surface and bottom stretching parameters are, respectively, θs=2 and θb=6). Special care has to be paid to the grid stiffness in order to limit the hydrostatic pressure gradient errors. We performed sensitivity experiments by varying both the number of σ levels and the bottom stretching coefficient. The hydrostatic pressure gradient errors appear as very intense noise in the vorticity field at the grid scale in some experiments. The simulations we show in the paper do not exhibit any spurious numerical noise with the previous parameters.
The mean stratification is chosen such that the deformation radius is about 40 km, as computed by in the Gulf of Oman. The mean vertical profile of temperature is
$\begin{array}{}\text{(1)}& T\left(z\right)={T}_{\mathrm{0}}\mathrm{exp}\left(z/H\right),\end{array}$
where T0=28C and H=2000 m (mean depth of the Gulf of Oman). T0 is chosen so that the surface density field is representative of the Gulf of Oman. The salinity is kept to 35 psu over the water column.
We initialize the flow with four mesoscale vortices, with alternate polarity along the channel axis (Fig. 1). The radial and vertical profiles of circular velocity of each vortex are
$\begin{array}{}\text{(2)}& {v}_{\mathit{\theta }}\left(r,z\right)=±\frac{{v}_{\mathrm{0}}r}{R}\mathrm{exp}\left(-\frac{{r}^{\mathrm{2}}}{{R}^{\mathrm{2}}}\right)\mathrm{exp}\left(-\frac{{z}^{\mathrm{2}}}{{D}^{\mathrm{2}}}\right),\end{array}$
with v0=0.5 rad s−1, R=50 km, D=300 m, typical values found in the Gulf of Oman . Then, the velocity field of the four mesoscale eddies is balanced with their pressure field using the cyclogeostrophic equilibrium and following the procedure described in . The density anomalies associated with the vortices are directly computed using the hydrostatic equilibrium. The vortices are separated from each other horizontally by 150 km. The distance between the vortex cores and the northern and southern edges is 100 km.
Figure 1Initial state: (a) vertical relative vorticity (normalized by the Coriolis frequency) for the four surface-intensified mesoscale eddies. Black contours are the isobaths. (b) Vertical cross section of an anticyclone. (c) Vertical profiles of density associated with the cores of a mesoscale cyclone (orange) and of an anticyclone (blue).
To characterize the impact of the frictional effects at the bottom and of the topography shape on the submesoscale eddy generation, we design three experiments with different bottom boundary conditions (with or without bottom drag and bottom boundary layer) and with different topographies (with or without a cape). In the first experiment (NO-BBL), we use a free-slip bottom boundary condition with no bottom boundary layer mixing and parameterize the smooth bathymetry representative of the continental slope in the Gulf of Oman as
$\begin{array}{}\text{(3)}& \begin{array}{rl}h& ={h}_{\mathrm{shelf}}+\frac{\mathrm{1}}{\mathrm{2}}\left(H-{h}_{\mathrm{shelf}}\right)\\ & \left(\mathrm{tanh}\left(\frac{y-{y}^{*}}{{W}_{y}}\right)-\mathrm{tanh}\left(\frac{y-{y}_{N}}{{W}_{y}}\right)\right),\end{array}\end{array}$
where hshelf=100 m, H=2000 m, ${y}^{*}={y}_{\mathrm{S}}=\mathrm{50}$ km, ${y}_{\mathrm{N}}={L}_{y}-{y}_{\mathrm{S}}$, Ly=200 km and Wy=20 km.
In the second experiment (BBL), the same bathymetry is used but we add a bottom drag and a vertical mixing at the bottom with a KPP scheme . The bottom drag is implemented via the von Kármán quadratic bottom stress formulation defined as
$\begin{array}{}\text{(4)}& {\mathit{\tau }}_{\mathrm{b}}={\mathit{\rho }}_{\mathrm{0}}{C}_{\mathrm{D}}\mid \mid \mathbit{u}\mid \mid \mathbit{u},\end{array}$
where ρ0 is a reference density. CD is the drag coefficient varying as
$\begin{array}{}\text{(5)}& {C}_{\mathrm{D}}={\left(\frac{\mathit{\kappa }}{\mathrm{log}\left(\mathrm{\Delta }{z}_{\mathrm{b}}/{z}_{\mathrm{r}}\right)}\right)}^{\mathrm{2}},\end{array}$
where κ is the von Kármán constant equal to 0.41, zr is the roughness parameter equal to 1 cm, and Δzb is the thickness of the lowest layer of the grid. These parameterizations lead to the formation of a turbulent bottom boundary layer as soon as a current flows over a sloping bottom topography.
Then, in the third experiment (BBL-CAPE), we add a cape in the topography defined by Eq. (3) by setting ${y}^{*}={y}_{\mathrm{S}}+{y}_{\mathrm{0}}\mathrm{exp}\left(-{\left(\frac{x-{x}_{\mathrm{0}}}{{W}_{x}}\right)}^{\mathrm{2}}\right)$, y0=40 km and Wx=20 km. We use the same parameterizations of the vertical mixing at the bottom and the bottom drag as in the BBL experiment.
Finally, we use the Ariane tool to study the impact of the production of submesoscale eddies on the spread of Lagrangian particles from the coast towards the center of the gulf. The Persian Gulf outflow water is not explicitly included in the model since no submesoscale velocity structure associated with the fragment of Persian Gulf Water was observed in the in situ measurements (see Sect. 3.1). Also, we are not interested in the dynamics of the outflow itself for which periodic boundary condition in the x direction would have been problematic. Rather, we focus on the impact of submesoscale processes on the Persian Gulf outflow water, and thus Lagrangian particles are used to model this water mass. Ariane is a computational tool dedicated to the offline calculation of 3-D streamlines in the output velocity field of model whose equations are based on volume conservation. Transport of water masses or currents is deduced from the displacement of numerical Lagrangian particles.
3 Submesoscale eddy life cycle
## 3.1 Observations in the Phys-Indien 2011 in situ data
In spring 2011, a vortex row of alternate polarity was present along the axis of the Gulf of Oman. The PGW outflow was located along the continental slope of Oman (south of the Gulf of Oman). The vortex row in the Gulf of Oman shed small fragments of PGW into the basin interior. The Phys-Indien 2011 Seasoar section crossed the outflow and the PGW fragments (see Fig. 2a).
Figure 2(a) Map of the absolute dynamic topography anomalies in the Gulf of Oman averaged over the duration of the cruise processed by CLS-Argos on a 1∕8 Mercator grid. The solid grey lines indicate the locations of the Seasoar sections. The solid orange and blue lines indicate sections GO16 and GO13, respectively. (b, c) Temperature (top) and salinity (bottom) vertical sections of GO16 and GO13 sections, respectively, showing the warm and salty PGW outflow settled down to about 250 m depth in the Gulf of Oman. Black contours stand for isopycnals.
In particular, sections GO13 and GO16 (see Fig. 2b, c) show filaments of warm and salty water extending from the continental slope offshore over 50 and 60 km, respectively. These filaments have a temperature above 21 C and a salinity reaching 37.5 psu, characteristic of the PGW outflow at this location . The measurements from the vessel-mounted ADCP (not shown) do not exhibit any velocity structure associated with the filaments of PGW. By considering the horizontal resolution of the vessel-mounted ADCP (∼2 km), this suggests that, at these locations, the PGW can be considered as a passive tracer.
Both filaments are located between a cyclone (west) and an anticyclone (east). The PGW is advected offshore by the surface-intensified mesoscale eddy. In the filaments, the structure is more complex, with an alternation of more or less salty water. This suggests that filaments could break into small vortices as they are advected by surface-intensified mesoscale eddies.
## 3.2 Production of submesoscale eddies in the simulations
Numerous submesoscale vortices are generated in the numerical simulations. They are essentially found below 100 m depth, which corresponds to the depth of the shelf break. Submesoscale vortices originate from the interaction of mesoscale eddies with the sloping topography. In Fig. 3, we show the relative vorticity field normalized by the Coriolis frequency at day 200 for the three numerical experiments near the surface, at 200 and 500 m depth. The surface flow is dominated by mesoscale eddies for all experiments. At 200 m depth, submesoscale filaments and vortices are visible around mesoscale eddies. They are more abundant and intense in the experiments in which both the bottom KPP and the bottom drag were active (i.e., BBL and BBL-CAPE). This indicates that most of these submesoscale vortices are generated by bottom frictional effects. The absolute value of the relative vorticity associated with the submesoscale vortices is close to the planetary vorticity ($|{\mathit{\zeta }}^{z}/f|\sim \mathrm{1}$). The flow is dominated by an energetic submesoscale turbulence at 500 m for all experiments. Submesoscale filaments and vortices are also generated in NO-BBL, where there are no frictional effects at the bottom. This suggests that another mechanism leading to the production of small vortices is at play. This inviscid mechanism is related to baroclinic instabilities. It will be presented in Sect. 3.3.
Figure 3Vertical relative vorticity field normalized by the Coriolis frequency at day 200 and 10, 200 and 500 m depth for the NO-BBL, BBL and BBL-CAPE experiments.
In Fig. 4, we compare the power spectrum density of horizontal velocities for the three experiments (NO-BBL, BBL and BBL-CAPE). Consistently with the previous results, we observe a net increase of the kinetic energy below the Rossby deformation radius (Rd) at depth for all simulations. This increase is the signature of subsurface submesoscale eddies. In the two simulations with bottom KPP and bottom drag (i.e., BBL and BBL-CAPE), and in accordance with , the part of the kinetic energy contained at the submesoscale is larger at 200 m. Near the surface, we observe a slight increase of the kinetic energy below the Rossby deformation radius due to the surface signature of the subsurface submesoscale eddies.
Below 500 m depth, the shapes and the slopes of the spectra are similar for the three experiments. The flatter k−2 slope at horizontal scales ranging between 100 and 10 km indicates an active submesoscale turbulence field and a submesoscale source of energy at around 10 km.
Figure 4Kinetic energy (KE) spectra comparison of the three experiments: NO-BBL (green), BBL (blue) and BBL-CAPE (orange). Spectra are computed at (a) 10, (b) 200 and (c) 500 m depth at day 200. Black lines stand for benchmarks of power laws.
## 3.3 Processes of submesoscale eddy generation
### 3.3.1 Baroclinic instability at depth
The first mechanism is an inviscid mechanism visible below 300 m in all experiments. This mechanism is related to the baroclinic instability. Baroclinic instabilities are triggered by the mesoscale eddy velocity field acting as the perturbation along the sloping bathymetry. This can be seen in the NO-BBL experiment, in the absence of bottom frictional effects. We characterize this instability by computing the energy transfer terms , i.e., the horizontal Reynolds stress (HRS), the vertical Reynolds stress (VRS) and the vertical buoyancy flux (VBF) as
$\begin{array}{}\text{(6)}& & \text{HRS}=-\stackrel{\mathrm{‾}}{\mathbit{u}{}^{\prime }v{}^{\prime }}\cdot {\partial }_{y}\stackrel{\mathrm{‾}}{\mathbit{u}}-\stackrel{\mathrm{‾}}{\mathbit{u}{}^{\prime }u{}^{\prime }}\cdot {\partial }_{x}\stackrel{\mathrm{‾}}{\mathbit{u}};\text{(7)}& & \text{VRS}=-\stackrel{\mathrm{‾}}{\mathbit{u}{}^{\prime }w{}^{\prime }}\cdot {\partial }_{z}\stackrel{\mathrm{‾}}{\mathbit{u}};\text{(8)}& & \text{VBF}=\stackrel{\mathrm{‾}}{w{}^{\prime }b{}^{\prime }},\end{array}$
where $•{}^{\prime }$ denotes the deviation from the time average, $\stackrel{\mathrm{‾}}{•}$ the time average, u the horizontal velocity, w the vertical velocity and $b=-g\frac{\mathit{\rho }}{{\mathit{\rho }}_{\mathrm{0}}}$ the buoyancy.
Locally, the vertical buoyancy flux is maximum over the sloping topography (see Fig. 5a), where the bathymetry is about 300 m (see Fig. 5c). Indeed, it corresponds to the depth where the potential vorticity (PV) gradient sign changes occurs (see Fig. 5b). The PV gradient sign changes originate from the sloping topography. In the upper part of the water column, the meridional gradient of PV is positive, while it is negative in the lower part (see Fig. 5b). This is a necessary condition for the baroclinic instability to occur. Most of the submesoscale eddies produced via baroclinic instabilities are observed below 300 m depth. Indeed, in the top 100 m, the stratification is stronger than below (see Fig. 1c), so that it prevents the growth of baroclinic instabilities as discussed by and .
We also observe topographic Rossby waves propagating eastwards over the southern-sloping topography and westwards over the northern one. In Fig. 5d, we show the Hovmöller diagram of the potential vorticity anomaly at 500 m depth near the southern boundary of the domain. The potential vorticity anomaly is computed as
$\begin{array}{}\text{(9)}& Q{}^{\prime }=Q-{Q}_{\mathrm{rest}},\end{array}$
with
$\begin{array}{}\text{(10)}& {Q}_{\mathrm{rest}}={f}_{\mathrm{0}}{\partial }_{z}\stackrel{\mathrm{‾}}{b},\end{array}$
where $\stackrel{\mathrm{‾}}{b}$ is the background vertical stratification and
$\begin{array}{}\text{(11)}& Q=\left({f}_{\mathrm{0}}+{\partial }_{x}v-{\partial }_{y}u\right){\partial }_{z}b-{\partial }_{z}v{\partial }_{x}b+{\partial }_{z}u{\partial }_{y}b\end{array}$
the Ertel potential vorticity.
The solid blue line in Fig. 5d indicates that submesoscale eddies propagate at about 0.02 m s−1. We compare this value with that obtained considering the propagation of topographic Rossby waves in a homogeneous fluid (the stratification is weak at 500 m depth). As defined in , the dispersion relation of topographic Rossby waves in a homogeneous fluid leads to the following expression for the phase speed:
$\begin{array}{}\text{(12)}& {c}_{\mathit{\phi }}=\frac{{\mathit{\alpha }}_{\mathrm{0}}g}{{f}_{\mathrm{0}}}\frac{\mathrm{1}}{\mathrm{1}+\frac{gH}{{f}_{\mathrm{0}}^{\mathrm{2}}}{k}^{\mathrm{2}}}.\end{array}$
With α0=0.15, g=9.81 m s−2, ${f}_{\mathrm{0}}=\mathrm{6}×{\mathrm{10}}^{-\mathrm{5}}$ s−1, H=1500 m and $\mathit{\lambda }=\frac{\mathrm{2}\mathit{\pi }}{k}=\mathrm{10}$ km (measured in Fig. 5d), we obtain cφ∼0.02 m s−1, which is in agreement with that measured. Thus, submesoscale eddies are generated through baroclinic instabilities and propagate zonally under the influence of topographic Rossby waves. Then, submesoscale eddies are slowly advected off the coast by mesoscale eddies since the velocity field is very weak at 500 m depth compared with that at the surface.
Figure 5Diagnostics computed from NO-BBL. (a) Energy conversion terms: (blue) HRS, (orange) VRS and (green) VBF vertically integrated between 150 and 1000 m depth. (b) Timely and zonally averaged meridional PV gradient computed at (blue) 100, (orange) 300 and (green) 500 m depth. (c) Bathymetry. (d) Hovmöller diagram of potential vorticity anomaly at 500 m depth and y∼40 km.
### 3.3.2 Frictional layer detachment
As mesoscale eddies drag over the sloping topography, they intensify the velocity shear within the bottom boundary layer leading to a topographic vorticity generating filament-like structures. This bottom boundary layer vorticity is directly linked with the use of a bottom drag and the bottom KPP and is possible only in BBL and BBL-CAPE. Subsequently, detached vorticity filaments become unstable under the influence of horizontal shear. In Fig. 6, it clearly appears that horizontal shear instabilities extract kinetic energy from the mean flow through the horizontal Reynolds stress (HRSVBF≫VRS). Shear instability is important near the topographic slope. Consequently, filaments roll up into small eddies. This also means that kinetic energy is transferred from larger to smaller scales. Since the bottom boundary layer is regularly destabilized, small eddies are produced by this frictional mechanism on both sides of the basin.
Figure 6(a) Horizontal Reynolds stress, (b) vertical Reynolds stress and (c) vertical buoyancy flux integrated between 100 and 300 m depth in the along-filament direction.
## 3.4 Structure and life cycle of the submesoscale eddies
In this section, we focus on the submesoscale eddies produced by frictional vorticity generation as the spatial scale and dynamical structure are in accordance with that found via the in situ measurement analysis.
Figure 7 shows the horizontal and vertical structures of such submesoscale anticyclone (a) and cyclone (b) found between 100 and 300 m depths in BBL experiment.
Figure 7Vertical sections of potential vorticity anomaly for (a) an anticyclonic and (b) a cyclonic submesoscale eddy generated due to frictional effect (BBL experiment). Density anomalies associated with submesoscale eddies are shown in black contours.
The submesoscale eddies are typically about 20 km wide and 150 m thick. The structure of the submesoscale eddies produced throughout the mesoscale eddy–topography interaction is consistent with the structure observed in the in situ measurements. The horizontal and vertical profiles of PV anomaly are close to Gaussian in both directions. The absence of sign reversal of the PV gradient is a clue to the stability of these small eddies (in the absence of external strain), hence their potentially long lifetime. Indeed, the background mesoscale shear is about $\mathrm{5}×{\mathrm{10}}^{-\mathrm{6}}$ s−1. It corresponds to $\sim \mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{%}×{\mathit{\zeta }}_{\mathrm{SCV}}$ which is close to the quasi-geostrophic value necessary for vortices to elongate irreversibly.
The polarity of the submesoscale eddies is opposite to the polarity of the mesoscale eddy interacting with the sloping topography through the bottom boundary layer. In this paragraph, we describe the life cycle of two submesoscale eddies: a cyclone and an anticyclone (see Figs. 8 and 9). This life cycle is typical of the submesoscale eddies observed in the model simulations, generated in the bottom boundary layer by interaction of the mesoscale eddies with the topography. Once formed, the submesoscale eddies rapidly merge with their neighbors (see Fig. 9b, from day 17 to 49). The inverse energy cascade associated with the merging events tends to set larger scales than the bottom boundary layer scale energy injection scale. This process allows them to grow and, provisionally, to withstand destruction induced by the mesoscale velocity shear. While they grow, they are also advected offshore via a dipolar coupling with their parent mesoscale eddy. Thus, they grow to a diameter of 15–20 km, comparable with that shown in Fig. 2b. At this stage, their radius is still smaller than the deformation radius and $\mid {\mathit{\zeta }}^{z}/f\mid \ge \mathrm{1}$; they are termed submesoscale coherent vortices (SCVs) .
Figure 8(a) Pathway of a submesoscale cyclone originating from the bottom boundary layer. (b) Major events from the birth to the death of the small vortex.
Figure 9(a) Pathway of a submesoscale anticyclone originating from the bottom boundary layer. (b) Major events from the birth to the death of the small vortex.
In turn, as these vortices encounter the topographic slope, even smaller, opposite-signed vortices are produced (see Fig. 8b at day 139 and Fig. 9b at day 97); this leads to a slight dissipation of their energy. Then, the initial SCVs couple with the new opposite-signed SCVs, propagate again and undergo straining. They are also sheared by the large vortices, and thus they decay in intensity (see, for instance, Fig. 9b, day 113). All these processes, generation of smaller vortices at the slope and vorticity erosion, contribute to feed the small scales in the enstrophy spectra.
The final evolution differs for the two SCVs. The cyclonic SCV merges with a mesoscale cyclone. The very details of this vortex interaction may not be fully captured by this hydrostatic model. A higher resolution, a nonhydrostatic model would be necessary to capture all the details of this small-scale vortex merger.1 The anticyclonic SCV becomes less energetic after traveling over a long distance, and finally, it interacts again with the sloping topography. There, it loses most of its energy and disappears.
Depending on the number of merging events, their distance to the mesoscale eddies and their interaction with the sloping topography, the SCV lifetimes vary between 10 and 100 d, and the distance that they cover is at most 600 km. The global trajectory of these small eddies is essentially governed by the mesoscale flow. But their life cycle and the major events affecting them crucially depend on the population of submesoscale eddies and on the interaction with topography.
## 3.5 Spreading of outflow waters
PGW and RSW are dense waters due to their anomalously high salt content. As revealed by in situ observations, the filaments of PGW are pulled off the coast by mesoscale eddies and break into submesoscale eddies containing PGW. In this section, we examine the capability of the submesoscale vortices to carry a passive tracer. To do so, we release about 10 000 Lagrangian particles into the two SCVs of Figs. 8 and 9, at their birth (i.e., at day 79 for the cyclone and at day 17 for the anticyclone).
Figure 10 shows the mean squared distance between particles and their center of mass ($<{D}^{\mathrm{2}}\left(t\right)>$) vs. the age of particles.
The results exhibit two regimes. The first regime is associated with a fairly linear trend of the root mean square distance with time. For short times, a dispersion coefficient κ can be found via
$\begin{array}{}\text{(13)}& <{D}^{\mathrm{2}}\left(t\right)>=\mathrm{4}\mathit{\kappa }t,\end{array}$
as proposed by .
Figure 10(a, b) Time evolution of the mean square distance between particles and their center of mass with regard to the submesoscale cyclone and anticyclone, respectively (solid lines). Fits of merging and ballistic regimes are shown in dashed lines.
The diffusivities for the cyclonic and the anticyclonic SCVs are 377 and 188 m2 s−1, respectively. Our estimate corresponds to the dispersion associated with the SCV merging events. During this period, the SCVs lose only a few particles compared to the second regime. This second regime exhibits an enhanced particle loss. This stage corresponds to the dipolar advection of submesoscale eddies coupled with their mesoscale neighbor. This regime is characterized as ballistic with $<{D}^{\mathrm{2}}\left(t\right)>\propto {t}^{\mathrm{2}}$.
Figure 11(a) Trajectories of the small vortices considered in Figs. 8 (orange line) and 9 (blue line) and positions of particles located at a distance smaller than 8 km from the smaller vortex. (b, c) Time evolution of the histogram of vertical relative vorticity normalized by the planetary rotation of particles (colors) and the normalized vertical relative vorticity associated with the small vortices (dashed lines).
Figure 12Positions of particles for the three experiments at days 100 and 200.
Through time, we calculate the number of particles located within 8 km of each submesoscale eddy. In Fig. 11a, we show the trajectories of submesoscale eddies in solid lines and the positions of selected particles with dots. The time evolution of the probability density function (PDF) of the normalized relative vorticity of the selected particles is shown in Fig. 11b, c. The normalized relative vorticity associated with the submesoscale eddies dramatically decreases during the first days. This corresponds to the merging events after which the submesoscale eddy is larger in size but is less intense (note that only potential vorticity is nearly conserved, in the limit of small viscosity). This relative vorticity decrease occurs via filamentation and spatial re-organization during the merging process; this re-organization is associated with relative vorticity to vortex stretching conversion, with an increase in potential energy . The number of particles trapped in each eddy varies during the merging events. As the submesoscale eddies rotate around their parent mesoscale eddy, they are sheared and they lose particles at their periphery.
Finally, the impact of the submesoscale eddy production due to bottom frictional effect on the diffusion of particles is highlighted by the comparing three experiments (i.e., NO-BBL, BBL and BBL-CAPE). Particles are initially seeded at the southwest edge of the channel between 100 and 300 m depths. Figure 12 shows the positions of particles with time.
In the NO-BBL experiment, without bottom boundary layer vorticity generation (Fig. 12, first column), particles are advected mostly by mesoscale eddies. Particles remain mostly on the left-hand side of the domain. In the BBL and BBL-CAPE experiments (Fig. 12, second and third columns, respectively), particles are advected by filaments over the sloping topography, subsequently by submesoscale eddies and by mesoscale eddies as well. The dispersion of particles is then more efficient in BBL and BBL-CAPE experiments than in NO-BBL experiment.
Following , we can estimate an equivalent diffusivity coefficient through time as
$\begin{array}{}\text{(14)}& \mathit{\kappa }=\frac{\mathrm{1}}{\mathrm{2}}\frac{D}{Dt}<{D}^{\mathrm{2}}>.\end{array}$
In Fig. 13, we show the time evolution of the relative dispersion $<{D}^{\mathrm{2}}>$ where D is the distance between pairs of particles and $<•>$ is the ensemble average over all the pairs of particles. During the first 25 d of integration, the relative dispersion of particles is similar in the three experiments. Later, the relative dispersion increases more strongly in BBL and BBL-CAPE experiments. Particles trapped within submesoscale eddies can reach the cyclones and anticyclones on the right side of the domain more easily and travel longer distances. The cape does not play a significant role in the particle dispersion due to the initial configuration of the mesoscale eddies. The estimations of the dispersion coefficient yield ∼1000 m2 s−1 in both experiments, while in the NO-BBL experiment it is about 700 m2 s−1.
Figure 13Time evolution of the dispersion $<{D}^{\mathrm{2}}>$ computed for the three experiments: (green) NO-BBL, (blue) BBL and (orange) BBL-CAPE.
In Fig. 14a, we compare the number of particles transferred from the left- to the right-hand side of the channel. In the BBL and BBL-CAPE experiments, the number of particles lying on the right-hand side of the channel is ∼15 % of the total number of particles. This number of particles decreases to ∼5 % in the NO-BBL experiment. In the BBL experiment, the number of particles oscillates through time as a result of the recirculation of particles due to the mesoscale cyclone lying in $x\in \left[\mathrm{300},\mathrm{400}\right]$ km. These oscillations do not appear in BBL-CAPE experiment, which means that the cape does not allow particles to recirculate.
Figure 14(a) Time evolution of the percentage of particles lying in $x\in \left[\mathrm{400};\mathrm{600}\right]$ km the three experiments: (green) NO-BBL, (blue) BBL and (orange) BBL-CAPE. (b, c) Probability density function of the relative vorticity normalized by the planetary rotation associated with particles on the left- (x<300 km) and right-hand sides (x>300 km) of the domain regarding (green) NO-BBL, (blue) BBL and (orange) BBL-CAPE.
In Fig. 14b–c, we show the PDF of the relative vorticity normalized by the planetary rotation associated with particles at day 200 for particles lying on the left and right sides of the channel, respectively. In the three experiments, PDFs are Gaussian shaped and have zero bias, meaning that the influence of cyclonic and anticyclonic motions is similar. However, on the left-hand side of the channel, particles can be trapped in the turbulent bottom boundary layer and remain in it for a long time. This can be seen in Fig. 12 in the BBL and BBL-CAPE experiments at day 200. There, the bottom boundary layer vorticity is positive and large (i.e., $|{\mathit{\zeta }}^{z}/{f}_{\mathrm{0}}|>\mathrm{1}$). That is why PDFs associated with BBL and BBL-CAPE experiments show that particles can have a very large value of relative vorticity. On the other hand, in the BBL and BBL-CAPE experiments, regarding the particles lying on the right-hand side of the channel, PDFs flatten and large relative vorticity values are reached (i.e., $|{\mathit{\zeta }}^{z}/{f}_{\mathrm{0}}|>\mathrm{0.5}$); then, the variances increase as a signature of the particle trapping in submesoscale eddies. This result highlights the impact of submesoscale eddies on the pathways and spreading of particles. Without subsurface submesoscale eddy generation due to the bottom frictional effect, the fate of particles is mostly driven by the mesoscale eddy field. In this case, particles are trapped in mesoscale eddies or recirculate at the periphery of mesoscale eddies. However, with the subsurface submesoscale eddy generation by bottom frictional effect, particles can be trapped and advected by submesoscale eddies. Then, they can travel over large distances and long times; see also for details on the role of SCVs in the spreading of tracers.
4 Conclusions
In situ observations have shown filaments and small eddies of Persian Gulf Water formed from its outflow along the continental slope of the Gulf of Oman. At this time, a row of alternate-signed mesoscale eddies was present in the gulf. We used a primitive-equation numerical model to represent the ambient mesoscale circulation in an idealized rectangular basin. Specifically, the circulation is dominated by the interaction of a row of surface-intensified mesoscale eddies with topographic slopes. We showed that the friction of these vortices on the slope (in a slanted bottom boundary layer) is the primary mechanism for the generation of opposite-signed relative vorticity on the slope. The vorticity filaments thus created then undergo shear instability and form small eddies. These small eddies merge and grow in size. They also pair (cyclones with anticyclones) and propagate away from their region of formation. At the surface, these small eddies have a signature and can thus be detected via satellite altimetry. This is due to their strong intensity and to the shallow depth at which they lie. Also, below 300 m depth, the stratification is weak and baroclinic instability can develops and creates turbulence. The submesoscale eddies propagate zonally under the influence of topographic Rossby waves.
Newly formed submesoscale eddies are advected along the rim of ambient mesoscale eddies and eventually interact with the seafloor topography, in turn generating smaller-scale eddies. This is manifested by a shallower slope of the enstrophy spectrum (more energetic small scales of vorticity). Finally, these small eddies can be destroyed by the shear of the mesoscale eddies (or be incorporated into them) or crash onto the topographic slope and be eroded there. Their lifetime is usually shorter than 3 months and the length of their pathway is at most 600 km.
We have also shown that these small eddies play a non-negligible role in the transport and dispersion of tracers (which can be salinity in the Gulf of Oman) by comparing two simulations with and without the bottom boundary layer vorticity generation. Due to submesoscale eddies generated by frictional effect, particles can travel over large distances more rapidly. Finally, the presence of a cape, such as the Cape of Ra's al-Hamra in the Gulf of Oman, does not impact significantly the diffusion of a passive tracer such as PGW.
This study raises other worthwhile questions. In particular, the initial configuration was designed to be representative of the sloping topography as well as the mesoscale eddies found in the Gulf of Oman. In the Gulf of Aden, the slope of the topography is different and, mesoscale eddies can reach 1000 m depth. Both aspects should not have an impact on the mechanism generating submesoscale eddies but rather on the location of their generation and thus on the dispersion of the Red Sea outflow water.
Also, our simulations were done without any surface forcing and generated fewer filaments and eddies. In the real ocean, filaments and eddies arise at a range of scales due to turbulent interactions and from instability of upwelling fronts. The interaction between surface mixed-layer and subsurface SCVs in the vertical is another aspect that calls for further investigations.
In situ measurements and detection of SCVs remain sparse. Nevertheless, we are now able, thanks to the satellite data, to localize the mesoscale eddies and their distances from the coast. The conjoint use of these maps, and our estimates of the SCVs positions relative to mesoscale eddies and topography, must lead us to perform experiments at sea in both gulfs to capture the characteristics of the SCVs.
Data availability
Data availability.
Model outputs are available upon request.
Author contributions
Author contributions.
MM designed and performed the numerical experiments, analyzed the results and wrote the manuscript. PLH, XC, JG and CV contributed to the analysis and the writing of the manuscript. CdM, MS and KK contributed to the writing of the manuscript.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Acknowledgements
Acknowledgements.
We acknowledge support from the ANR ASTRID Maturation project DYNED ATLAS and from UBO.
Financial support
Financial support.
This research has been supported by the CNRS and RFBR under PRC project 1069 (in French classification) and 16-55-150001 (in Russian classification). Mikhail Sokolovskiy was supported also by the Ministry of Education and Science of the Russian Federation (project no. 14.W.03.31.0006).
Review statement
Review statement.
This paper was edited by Matthew Hecht and reviewed by two anonymous referees.
References
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Carton, X., L'Hegaret, P., and Baraille, R.: Mesoscale variability of water masses in the Arabian Sea as revealed by ARGO floats, Ocean Sci., 8, 227–248, https://doi.org/10.5194/os-8-227-2012, 2012. a, b
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Ciani, D., Carton, X., and Verron, J.: On the merger of subsurface isolated vortices, Geophys. Astro. Fluid, 110, 23–49, 2016. a, b
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This will be the subject of a forthcoming study.
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# Derived series and Soluble groups
1. Any subgroup $H$ of a soluble group is itself soluble.
2. If $G$ is soluble and $N$ is normal in $G$ then $G/N$ is soluble.
1. I know we can consider the subnormal series of $G$ intersect $H$, but then why is each factor normal in the last and abelian?
2. No idea
Thanks for any help!
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I'd like to reffer you to see this book: A Course on Finite Groups by H.E. Rose. You can find there a complete elementry facts about soluble groups. What you noted here are two Theorems at the begining of the chapter 11. – B. S. May 22 '12 at 16:49
Your title talks about the "derived series", but your only progress expressed talks about using a subnormal series. In my answer I used the definition of solvable in terms of the existence of a subnormal series with abelian quotient; and you never mentioned derived series again. – Arturo Magidin May 23 '12 at 0:16
1. Let $1=G_0\lhd G_1\lhd G_2\lhd\cdots\lhd G_n=G$ be a subnormal series of $G$ such that $G_{i+1}/G_i$ is abelian for each $i$, and let $H$ be a subgroup of $G$. Consider $$1 = G_0\cap H \subseteq G_1\cap H\subseteq \cdots \subseteq G_n\cap H = H.$$ Note that $G_i\lhd G_{i+1}$, hence $G_i\cap H\lhd G_{i+1}\cap H$. Thus, this is a subnormal series. Finally, we need to show that the quotients are abelian. The map $G_{i+1}\cap H\to G_{i+1}/G_i$ maps $G_{i+1}\cap H$ into an abelian group, hence the image is abelian; the kernel is precisely $G_i\cap H$, so $(G_{i+1}\cap H)/(G_i\cap H)$ is isomorphic to a subgroup of $G_{i+1}/G_i$, hence is abelian itself. Thus, $H$ is solvable.
2. Consider the normal series $$1 = \frac{G_0N}{N} \lhd \frac{G_1N}{N} \lhd\cdots \lhd \frac{G_nN}{N} = \frac{G}{N}.$$ To show that $G_iN/N$ is normal in $G_{i+1}/N$ it suffices to show that $G_iN$ is normal in $G_{i+1}N$, since the lattice isomorphism theorem guarantees that normality is preserved in quotients. But since $G_i\triangleleft G_{i+1}$, and $N$ is normal in $G$, it follows that $G_{i}N\triangleleft G_{i+1}N$; indeed, if $gn\in G_{i}N$ and $xm\in G_{i+1}N$ with $x\in G_{i+1}$, then $$(xm)^{-1}gn(xm) = m^{-1}(x^{-1}gnx)m = m^{-1}(x^{-1}gx)(x^{-1}nx)m = (x^{-1}gx)n'$$ where $n'\in N$: $x^{-1}nx\in N$ since $N$ is normal, and for every $y\in G$ we have $Ny=yN$, so $m{-1}(x^{-1}gx) = (x^{-1}gx)m'$ for some $m'$. Now simply note that $x^{-1}gx\in G_i$ since $g\in G_i$, $x\in G_{i+1}$, and $G_i\lhd G_{i+1}$.
Now, $$\frac{G_{i+1}N/N}{G_{i}N/N} \cong \frac{G_{i+1}N}{G_iN}.$$ I claim this is a quotient of $G_{i+1}/G_i$. Indeed, we can map $G_{i+1}$ to $G_{i+1}N/G_iN$ by mapping $g$ to $gG_iN$. The kernel contains $G_i$. So it is enough to show it is onto. Given $gn\in G_{i+1}N$, note that $gn\in gG_iN$, hence $gG_iN = gnG_iN$, so the map is indeed onto, and so $G_{i+1}N/G_iN$ is a quotient of $G_{i+1}/G_i$, hence is abelian.
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Amazing, Thanks! – rk101 May 22 '12 at 17:22
Would you mind explaining sub-normality in (2) in further detail? – rk101 May 22 '12 at 23:49
@rk101: Don't accept an answer if you don't fully understand it! – Arturo Magidin May 22 '12 at 23:49
Ok, Thanks for your help! I think I have got it all now. – rk101 May 23 '12 at 0:06
Another way to approach this is to use an equivalent definition of a solvable (=soluble) group, namely that the derived series, i.e. the iterated series of commutator subgroups eventually reaches the trivial subgroup $1$ of $G$, that is
$G^{(0)}= G \trianglerighteq G^{(1)} \trianglerighteq G^{(2)} \trianglerighteq G^{(3)} ... \trianglerighteq G^{(k)} = 1$, for some $k \geqslant 0$, where $G^{(1)}= [G,G]$ and $G^{(i+1)} = [G^{(i)},G^{(i)}]$ for $i \geqslant 1$.
Now 1. follows from the fact that if $H \leqslant G$, then $H^{(i)} \leqslant G^{(i)}$. And 2. is implied by the fact that $(G/N)^{(i)} = G^{(i)}N/N$.
Why is the derived series of $H$ a subgroup of the derived series of $G$? – rk101 May 22 '12 at 22:01
The derived series of H is included in that of G. The individual terms are subgroups. This is by definition: the commutator subgroup $[H,H]$ of $H$ consists of the group generated by all $[h_1,h_2]$, with $h_1, h_2 \in H$, which trivially is a subgroup of $[G,G]$. The rest follows by induction. Clear now? – Nicky Hekster May 22 '12 at 22:51
@rk101, you are welcome! Can you now prove the converse: if $N$ and $G/N$ are both solvable, then $G$ is solvable? – Nicky Hekster May 25 '12 at 9:25
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## anonymous one year ago Find an equation of the circle shown below. (x + 10)2 + (y − 10)2 = 289 (x − 10)2 + (y − 10)2 = 289 (x − 10)2 + (y + 10)2 = 289 (x − 10)2 + (y − 10)2 = 17
1. anonymous
2. anonymous
Ok. So to find the equation of a circle we need TWO things: the center of the circle and the radius
3. anonymous
okay how would we find those?
4. anonymous
Since they did not give us the center, we have to use the midpoint formula. They also didn't give us the distance of the radius. We have to use the Distance formula. Ok so let's do this step by step
5. anonymous
The mid-point formula is $\left( \frac{ x _{2} + x _{1} }{ 2 }, \frac{ y _{2} + y _{1} }{ 2 } \right)$
6. anonymous
Basically find the average of both x values and both y values from the coordinates given in order to determine the center of the circle
7. anonymous
Try to plug in those x and y values into the formula, and then tell me what you got.
8. anonymous
$\frac{ 18+2 }{ 2 },\frac{ 25+(-5) }{ 2 }$okay so for the midpoint we would have this?
9. anonymous
which would be 10,10 right?
10. anonymous
@happyrosy sorry i had to leave
11. anonymous
okay so then the distance formula is $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$
12. anonymous
so then i plug them in which would be $\sqrt{(18-2)^{2}+(25-(-5))^{2}}$
13. anonymous
so that would lead to $\sqrt{(16)^{2}+(30)^{2}}$
14. anonymous
so we would then have $\sqrt{256+900}$
15. anonymous
so the square root of 1156 wich would be 34
16. anonymous
so 34 is the distance?
17. anonymous
(x-h)^2 + (y-k)^2 =r^2
18. anonymous
(x-10)^2 + (y-10)^2 = 1156
19. anonymous
okay i messed up with the radius but i think i got the distance right
20. anonymous
im going to go with (x − 10)2 + (y − 10)2 = 289
21. anonymous
the 34 you got was the diameter. Half of 34 is 17, which would be the radius. Square the 17, equaling to 289. So, yes your final is correct. GREAT JOB ON THE WORK!!
Find more explanations on OpenStudy
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# show "continued" for nested description list item on page break
I'm using enumitem to create a description list.
These lists can sometimes be nested and can get very long. When a list item with a lot of description text breaks over a page it is difficult to tell to which item the current description belongs.
In these cases, I would like to put a note at the top of the page that shows the preceding item name, "continued".
Here is a MWE. I have put in the textsuperscript text manually; what I would like to do is make that happen automatically any time the list goes over a pagebreak.
\documentclass{book}
\usepackage{enumitem}
\newlist{Options}{description}{5}
\setlist[Options]{topsep=0.25em plus 0.2em minus 0.1em,
parsep=0.5\baselineskip plus .1\baselineskip minus .1\baselineskip,
itemsep=0.25em plus 0.2em minus 0.1em,
partopsep=0pt,
}
\newcommand*{\Option}[1]{%
\item[#1]\mbox{}\newline%
}
\begin{document}
\begin{Options}
\Option{first item} and explanatory text
\Option{second item} and more text%
\clearpage\textsuperscript{second item \emph{continued}}\newline%
more text describing the second item.
\end{Options}
\end{document}
Here is another case using nested options:
\begin{Options}
\Option{first item} and explanatory text
\Option{second item} and more text%
\begin{Options}
\Option{nested option} text
\end{Options}
text that belongs to \emph{second item}\clearpage
\end{Options}
• Should the note be part of the text? If so, should it be formatted like an \item from the list? Or, should the note be presented in the header or footer of the document? Jul 24, 2014 at 15:55
• Thats a good question. I think it would be more natural looking if the note starts the text block, possibly in a different font or gray color. Jul 24, 2014 at 16:29
You can do this using the atbegshi package, together with an \if... statement where you set the \if... equal to true at the start of the option and then to false at the end using \setlist.
Here's a MWE. I have used the same continuation message that you used above.
\documentclass{book}
\usepackage{enumitem}
\usepackage{atbegshi}
\newif\ifInOptions\InOptionsfalse
\newlist{Options}{description}{5}
\setlist[Options]{topsep=0.25em plus 0.2em minus 0.1em,
parsep=0.5\baselineskip plus .1\baselineskip minus .1\baselineskip,
itemsep=0.25em plus 0.2em minus 0.1em,
partopsep=0pt,before=\InOptionstrue,after=\InOptionsfalse,
}
\let\lastOption\relax
\newcommand*{\Option}[1]{\def\lastOption{#1}% remember the option for continued...
\item[#1]\mbox{}\newline%
}
\AtBeginShipout{\ifInOptions%
\AtBeginShipoutNext{\textsuperscript{\lastOption \emph{continued}}\newline}%
\fi}
\begin{document}
\begin{Options}
\Option{first item} and explanatory text
\Option{second item} and more text%
\clearpage%\textsuperscript{second item \emph{continued}}\newline%
more text describing the second item.
\end{Options}
\end{document}
This even seems to play well with nested environments because the \ifInOptions is implicitly set within \begin{group}...\end{group}.
• However, with nested options, when the parent option continues after the nested list and a page-break occurs, the text still refers to the nested option. I'll edit the original question with an example. Jul 25, 2014 at 14:11
• @TimA Funny, there seemed to be a very complimentary comment here yesterday:) I don't have time to play with this now but I suspect that my \gdef is over zealous and that changing this is to a \def will fix the problem. Have just edited the solution so it is clear what I mean and will check to see if it works latter.
– user30471
Jul 25, 2014 at 22:19
• @TimA I just checked and, as I suspected, using \def instead of \gdef it does remember the correct \Option to continue when the options are nested.
– user30471
Jul 26, 2014 at 4:16
• Thanks @Andrew, that does seem to do the job now! really great example with no more code than needed: simplicity. ;-) Jul 26, 2014 at 20:19
• @TimA Yes, the problem with my first attempt was too much code: \gdef should have been \def, so less is clearly better!
– user30471
Jul 27, 2014 at 4:17
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Document Type: Research Paper
Authors
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
2 Department of Mathematics, Faculty of Science, Imam Khomeini International University, postal code: 34149-16818, Qazvin, Iran
3 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Abstract
Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:K\rightarrow E$ is a continuous mapping, then there exists an element $x$ satisfying the condition $d(x,Tx)=\inf \{d(y,Tx):y\in K\}$, where $d$ is a metric on $E$. Recently, Hussain et al. (Abstract and Applied Analysis, Vol. 2014, Article ID 837943) introduced proximal contractive mappings and established certain best proximity point results for these mappings in $G$-metric spaces. The aim of this paper is to introduce certain new classes of auxiliary functions and proximal contraction mappings and establish best proximity point theorems for such kind of mappings in $G$-metric spaces. As consequences of these results, we deduce certain new best proximity and fixed point results in $G$-metric spaces. Moreover, we present certain examples to illustrate the usability of the obtained results.
Keywords
Main Subjects
###### ##### References
[1] A. Amini-Harandi, N. Hussain, F. Akbar, Best proximity point results for generalized contractions in metric spaces, Fixed Point Theory and Applications. (2013), 2013:164.
[2] M. Asadi, E. Karapinar, P. Salimi, A new approach to G-metric and related fixed point theorems, Journal of Inequalities and Applications. (2013), 2013:454.
[3] H. Aydi, E. Karapinar, P. Salimi, Some fixed point results in GP-metric spaces, J. Appl. Math. (2012), Article ID 891713.
[4] B. S. Choudhury, P. Maity, Best proximity point results in generalized metric spaces, Vietnam J. Mathematics, 10.1007/s10013-015-0141-3.
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