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# Toronto Math Forum

## MAT334-2018F => MAT334--Tests => Final Exam => Topic started by: Victor Ivrii on December 18, 2018, 06:14:31 AM

Title: FE-P3
Post by: Victor Ivrii on December 18, 2018, 06:14:31 AM
Find all singular points, classify them, and find residues at these points of
$$f(z)= \tan (z) + z\cot^2(z);$$
infinity included.
Title: Re: FE-P3
Post by: hz12 on December 18, 2018, 11:13:44 AM
f(z) = $\frac{\mathrm{sin}\mathrm{}(z)}{\mathrm{cos}\mathrm{}(z)}+z\frac{\mathrm{cos}\mathrm{}\wedge 2(z)}{\mathrm{sin}\mathrm{}\wedge 2(z)}$
=$\frac{{{\mathrm{sin}}^{\mathrm{3}}\left(z\right) +\ }{\mathrm{zcos}}^{\mathrm{3}}\left(z\right)\ \ \ \ =g}{{\mathrm{cos} \left(z\right)\ }{sin}^2\left(z\right)\ \ \ \ =h}$

Cos(z)sin$\mathrm{\wedge}$2(z) = 0

cos(z) = 0 or sin$\mathrm{\wedge}$2(z) = 0

so z =k$\pi$ or $z=\frac{\pi }{2}+k\pi$

1, when z = k$\pi$

g = ${sin}^3(z)+z{cos}^3\left(z\right)\neq 0$                            h= ${\mathrm{cos} \left(z\right)\ }{sin}^2\left(z\right)=0$
$h^=-{sin}^3\left(z\right)+2{cos}^2\left(z\right){\mathrm{sin} \left(z\right)\ }=0$                    ${\ h}^{''}\neq 0$

So pole of order = 2

2, when z =$\frac{\pi }{2}+k\pi$

g = ${sin}^3(z)+z{cos}^3\left(z\right)\neq 0$                            h= ${\mathrm{cos} \left(z\right)\ }{sin}^2\left(z\right)=0$
$h^=-{sin}^3\left(z\right)+2{cos}^2\left(z\right){\mathrm{sin} \left(z\right)\ }\ \neq 0$

So pole of order = 1
Title: Re: FE-P3
Post by: Ziqi Zhang on December 18, 2018, 11:17:50 AM
I think when z=0, it should have pole of order 1. Because at z=0, the numerator is not 0 when taking derivative once and denominator is not 0 when taking derivative twice.
Title: Re: FE-P3
Post by: Ziqi Zhang on December 18, 2018, 11:28:38 AM
Residue at z=0: 0+cos2(0)=1

Residue at z=kπ, but k≠0: 0-2(kπ)cos(kπ)sin(kπ)+cos2(kπ)=(-1)n

Residue at z=0.5π+kπ: -1+0=-1
Title: Re: FE-P3
Post by: Zixuan Miao on December 18, 2018, 11:37:21 AM
for infinity case, it is a non-isolated singularity
Title: Re: FE-P3
Post by: Siying Li on December 18, 2018, 12:45:02 PM
I think the residue at 0 should be 0..
Here's my answer: (in calculation I ignore k for convenience)

${\rm f}\left({\rm z}\right){\rm =}{\tan \left({\rm z}\right)\ }{\rm +z}{{\cot }^{{\rm 2}} \left(z\right)=\frac{{\sin \left(z\right)\ }}{{\cos \left(z\right)\ }}+\frac{z{{\cos }^2 \left(z\right)\ }}{{{\sin }^2 \left(z\right)\ }}\ }=\frac{{{\sin }^3 (z)\ }+z{{\cos }^3 (z)\ }}{{\cos \left(z\right)\ }{{\sin }^2 \left(z\right)\ }}$
If ${\cos \left(z\right)\ }=0$, then ${\rm z=}\frac{\pi}{2} + k\pi$

For numerator, ${{\sin }^3 (\frac{\pi}{2})\ }+\frac{\pi}{2}{{\cos }^3 \left(\frac{\pi}{2}\right)\ne 0\ }$, the numerator has zero order of zeros

For denominator, ${\cos \left(\frac{\pi}{2}\right)\ }{{\sin }^2 \left(\frac{\pi}{2}\right)=0\ ,-{{\sin }^3 \left(\frac{\pi}{2}\right)\ }+\frac{\pi}{2}{{\cos }^2 \left(\frac{\pi}{2}\right)\ }{\sin \left(\frac{\pi}{2}\right)\ }\ne 0\ }$, the denominator has zeros of order 1

Then ${\rm f}\left({\rm z}\right)$ has simple pole ${\rm z=}\frac{\pi}{2}+k\pi$

If ${{\sin }^{{\rm 2}} \left(z\right)\ }=0$, then ${\rm z=0}$ or ${\rm z=}k\pi$

When ${\rm z=0}$,

For numerator, ${{\sin }^3 (0)\ }+0{{\cos }^3 \left(0\right)=0\ },3{{\sin }^2 \left(0\right)+{{\cos }^3 \left(0\right)\ }+3{{\cos }^2 (0)\ }{\rm sin}?(0)\ }\ \ne 0\$, the numerator has zero order of 1

For denominator, ${\cos \left(0\right)\ }{{\sin }^2 \left(0\right)=0\ ,-{{\sin }^3 \left(0\right)\ }+2{{\cos }^2 \left(0\right)\ }{\sin \left(0\right)\ }=0\ },\ -3{{\sin }^2 \left(0\right){\cos \left(0\right)\ }-4{\cos \left(0\right)\ }{{\sin }^{{\rm 2}} \left(0\right)\ }+2cos^3\left(0\right)\ne 0\ }$, the denominator has zeros of order 2

Then ${\rm f}\left({\rm z}\right)$ has simple pole ${\rm z=0}$

When ${\rm z=}k\pi$,

For numerator, ${{\sin }^3 (\pi )\ }+0{{\cos }^3 \left(\pi \right)\ne 0\ }$ the numerator has zero order of 0

For denominator, ${\cos \left(\pi \right)\ }{{\sin }^2 \left(\pi \right)=0\ ,-{{\sin }^3 \left(\pi \right)\ }+2{{\cos }^2 \left(\pi \right)\ }{\sin \left(\pi \right)\ }=0\ },\ -3{{\sin }^2 \left(\pi \right){\cos \left(\pi \right)\ }-4{\cos \left(\pi \right)\ }{{\sin }^{{\rm 2}} \left(\pi \right)\ }+2cos^3\left(\pi \right)\ne 0\ }$, the denominator has zeros of order 2

Then ${\rm f}\left({\rm z}\right)$ has pole ${\rm z=}k\pi$ with order 2

${\rm Res}\left({\rm f}\left({\rm z}\right),\frac{\pi}{2}+k\pi\right)=\frac{{{\sin }^3 (\frac{\pi }{{\rm 2}})\ }+\frac{\pi}{2}{{\cos }^3 (\frac{\pi}{2})\ }}{-{{\sin }^3 \left(\frac{\pi }{{\rm 2}}\right)\ }+2{{\cos }^2 \left(\frac{\pi }{{\rm 2}}\right)\ }{\sin \left(\frac{\pi }{{\rm 2}}\right)\ }}=\frac{1}{-1}=-1$
${\rm Res}\left({\rm f}\left({\rm z}\right),k\pi\right)=\frac{3{{\sin }^2 \left(\pi\right)+{{\cos }^3 \left(\pi\right)\ }+3{{\cos }^2 (\pi)\ }{\rm sin}(\pi)\ }}{1!}=\frac{-1}{1}=-1$
Since ${\rm f}\left({\rm z}\right)=\frac{{{\sin }^3 (z)\ }+z{{\cos }^3 (z)\ }}{{\cos \left(z\right)\ }{{\sin }^2 \left(z\right)\ }}=\frac{{\left(\int^{\infty }_0{{\left(-1\right)}^n\frac{z^{2n+1}}{\left(2n+1\right)!}}\right)}^3+\int^{\infty }_0{{\left(-1\right)}^n\frac{z^{2n+1}}{\left(2n\right)!}}}{\int^{\infty }_0{{\left(-1\right)}^n\frac{z^{2n}}{\left(2n\right)!}}\ {\left(\int^{\infty }_0{{\left(-1\right)}^n\frac{z^{2n+1}}{\left(2n+1\right)!}}\right)}^2}$ has no term of ${\left({\rm z-0}\right)}^{{\rm -}{\rm 1}}$, then
${\rm Res}\left({\rm f}\left({\rm z}\right),0\right)=0$
Title: Re: FE-P3
Post by: Yifei Wang on December 18, 2018, 12:55:26 PM
let $w = \frac{1}{z}$ then $Z = \frac{1}{w}$
${Z\to\infty}$ ${w\to0}$

$f(z) = f(\frac{1}{w}) = \frac{sin{\frac{1}{w}}}{cos\frac{1}{w}}+\frac{1}{w}\frac{cos^2{\frac{1}{w}}}{sin^2{\frac{1}{w}}}$

at ${w\to0}$, we have a non-isolated singularity
Title: FE-P3 official
Post by: Victor Ivrii on December 20, 2018, 05:04:59 AM
$\newcommand{\Res}{\operatorname{Res}}$
(a) Singular points are of $g(z)=\tan(z)$ and $h(z)=z\cot ^2(z)$, that is $z_n= (n+\frac{1}{2})\pi$ and $w_n = \pi n$.

(b) $z_n$ are simple poles and $\Res (f,z_n)= \Res (\tan(z), z_n)= \frac{\sin(z)}{(\cos (z))'}\bigr|_{z=z_n} =-1$.

$w_0$ is a simple pole
$$\Res (f,w_0)= \Res (z\cot^2(z), w_0)= \Res (z\cot (z) \times \cot(z), 0)= \Res (\cot(z),0)= 1$$
because $\lim _{z\to 0} z\cot(z)=1$.

$w_n$ with $n\ne 0$ are double poles and
\begin{align*}
\Res (f,w_n)=&\Res (z\cot^2 (z), w_n)= \Res ((\pi n +w)\cot^2 (w) , 0) =\\
&\pi n\Res (\cot^2 (w) , 0) +\Res (w\cot^2(w),0) =1
\end{align*}
because $\Res (\cot^2 (w) , 0)=0$ (since $\cot^2(w)$ is an even function) and $\Res (w\cot^2(w),0) =1$ we already calculated.

$\infty$ is a not isolated singularity and therefore residue here is not defined.


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## 1 May 2018

### Torus

In geometry, in popular language, the torus is an object whose shape is a donut. More precisely, the torus is a surface of revolution generated by revolving a circle of radius $r$ in three-dimensional space about an axis coplanar at a distance $R$ from its center.

The shape of the torus depends on the sign of the expression $R-r$:
• $R=0$: The torus is a sphere, because the rotation axis is one of the diameters of the circle;
• $R<r$: The torus is said to be a "spindle torus" and takes the form of a pumpkin;
• $R=r$: The torus is said to be a "horn torus", with no "hole";
• $R>r$: The torus is said to be "open" and resembles to a donut.

$\left(x^2+y^2+z^2+0.57^2-0.52^2\right)^2=0.57^2\left(x^2+y^2\right)$

format: plain


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# Tack has a 30% tax rate. What amount should Tack report as adjusted beginning retained earnings in...

Tack, Inc. reported a retained earnings balance of $150,000 at December 31, 2005. In June 2006, Tack discovered that merchandise costing$40,000 had not been included in inventory in its 2005 financial statements. Tack has a 30% tax rate. What amount should Tack report as adjusted beginning retained earnings in its statement of retained earnings at December 31, 2006?

1. $190,000 2.$178,000
3. $150,000 4.$122,000


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# How can I calculate a number of lines needed to fit the text?

I want to make a command that works like

\CalcNumber{<the text>}{<width>}{<cs>}

And stores the number of lines (i. e. height in \baselineskip rounded up) needed for <the text> in <cs> if it was typeset in a box of a width <width>.

For example \CalcNumber{A}{\columwith}{\AHeight}\AHeight should yield 1, while something like \CalcNumber{M M M}{1em}{\MMMHeight}\MMMHeight should give smth like 3.

How can I do that?

P. S. A LuaLaTeX solution is also welcomed.

• Have a look at get height on a block of latex output. Nov 23, 2017 at 17:45
• \newbox\calcbox \setbox\calcbox\vbox{\hsize#2\relax#1\par} \edef#3{\the\dimexpr(\dp\calcbox+\ht\calcbox)/(\baselineskip)\relax} Sorry, haven't tested and probably doesn't work, because of limitations of \dimexpr and may be because of problems with the syntax (I don't know much about boxes), but something like that would work. Nov 23, 2017 at 17:48
• Count Lines Nov 23, 2017 at 17:54
• tex.stackexchange.com/q/242003/21930 Nov 23, 2017 at 17:56
• IMO the question is not well-defined. If you can have large display math in it, what does it even mean to talk of the number of lines? Does all the math count as “one line”? And do you want the number of lines, or the height? And if your actual use-case is “I need to calculate the height to put it inside a minipage of that height” why not ask that as the question (because there are other solutions to that, that do not involve this complicated workaround of calculating the height or the number of lines)? Dec 19, 2017 at 3:19

You can use adjustbox to box the content in a minipage of the given width and store its total height, then calculate the factor of the baselineskip using eTeX (and finally discard the content).

This is similar to other answers which using boxing, but a more out-of-the-box solution (no pun intended).

\documentclass{article}

\newlength\mycalclength

\newcommand\CalcNumber[3]{%
\edef#3{\the\numexpr\dimexpr \mycalclength/\baselineskip\relax\relax}%
}

\begin{document}

\CalcNumber{A}{\columnwidth}{\AHeight}\AHeight

\CalcNumber{M M M M M M M}{1em}{\MMMHeight}\MMMHeight

\end{document}

If you rearrange the order of the arguments and have the content last, you can use the feature of \adjustbox to read the last argument as box, not as argument, allowing for verbatim and other special content. Note that the assignment is then global as it happens in a group.

\documentclass{article}

\newlength\mycalclength

\newcommand\CalcNumber[2]{%
}

\begin{document}

\CalcNumber{\columnwidth}{\AHeight}{A}\AHeight

\CalcNumber{1em}{\MMMHeight}{M M M M M M M}\MMMHeight

\end{document}

There are two ways that you can do this: one is with \prevgraf, and the other by calculating the lines manually.

If you do it with \prevgraf, that gives you the amount of lines in the previous paragraph. This will only work if your input is meant to be only one paragraph. What we do is we use \setbox0 to put the text into a vbox which we don't print. In the vbox, we set the hsize to your width, the second argument, and then print the first argument as a paragraph. We manually end the paragraph with \par, and the use \xdef to save the current value of \prevgraf into the cs you passed as the third argument.

\def\CalcNumber#1#2#3{%
\setbox0\vbox{\hsize=#2 \noindent#1\par\xdef#3{\the\prevgraf}}}

If your input is more than one paragraph, then you can use the same setup as follows:

\makeatletter
\long\def\CalcNumber#1#2#3{%
\setbox0\vbox{\hsize=#2 \noindent#1}}
\@tempcnta=\dimexpr(\ht0+\dp0)/\baselineskip
\xdef#3{\the\@tempcnta}}
\makeatother

In a similar fashion to our other approach, we typeset our text in a box. We need to define our \CalcNumber as \long, so it can accept text of more than one paragraph. Then, we add the height and depth of the box, and divide by \baselineskip, saving it in a LaTeX temporary count register (this will round the number for us). We then store this in our give control sequence, as above.

A caveat here is that this will use whatever the baselineskip is when you call the macro. You'd need to account for variations in font sizes, depending on what you plan on using this for.

FWIW, ConTeXt provides a macro \determinenofline{...} that determines the number of lines of the content (when typeset in a \vbox). The result is stored in the counter: \noflines.

This counts the number of typeset lines (not the height in the multiple of \lineheight (or what is called \baselineskip in LaTeX). Here is one example from supp-box.mkiv to show that:

\starttext

\determinenoflines{test\\test}
\the\noflines

\determinenoflines{\bfd test\\test}
\the\noflines

\determinenoflines{\definedfont[Sans at 40pt]test\\test}
\the\noflines
\stoptext

All three of these tests give 2.

To count the number of lines for a content of a specific width, you can simply set \hsize for the content. For example:

\starttext
\vbox{\hsize=3cm \input ward\relax}

\determinenoflines{\hsize=3cm \input ward\relax}
\the\noflines
\stoptext

which gives (the first \vbox is just to verify the result).

This is an attempt based on the lineno package.

\documentclass{article}
\usepackage[running]{lineno}
\usepackage{lipsum}
\newcounter{mylines}
\newsavebox{\marmot}
\newcommand{\CalcNumber}[3]{
\savebox{\marmot}{\begin{minipage}{#2}\linenumbers*
\begin{internallinenumbers}
#1 \par
\end{internallinenumbers}
\end{minipage}}
\let#3=\themylines}
\begin{document}

\CalcNumber{\lipsum[1]}{8cm}{\myx}

\myx

\CalcNumber{A}{8cm}{\myy}

\myy

\end{document}

This uses \vsplit to count the lines. The only surprise was from intemise which adds a blank line (and some negative \vspace) at the start.

One can return the number of lines by adding \theNLcount to the end of the macro. In this case, I wanted to show the number using \marginpar and it was using \marginparwidth as the default width.

Since you want to split off only one line at a time, it is better so request as little as possible, hence the 0pt.

\documentclass{article}
\usepackage{amsmath}
\usepackage{blindtext}

\newcounter{NLcount}

\newcommand{\numberoflines}[2][\linewidth]% #1=width (optional), #2=text
{\bgroup
\hsize=#1\relax
\clubpenalty=0
\widowpenalty=0
\displaywidowpenalty=0
\predisplaypenalty=0
\postdisplaypenalty=0
\interlinepenalty=0
\setbox0=\vbox{#2}%
\setcounter{NLcount}{0}%
\loop\ifdim\ht0>0pt
\stepcounter{NLcount}%
\setbox1=\vsplit0 to 0pt
\repeat
\egroup}% \theNLcount

\begin{document}

\numberoflines{above $x=a$ more text $$y=b$$ below}

\hrule\leavevmode\marginpar{\theNLcount{} lines}
above $x=a$ more text $$y=b$$ below
\hrule

\numberoflines{above\newline \rule{1in}{1in}\newline below}

\hrule\leavevmode\marginpar{\theNLcount{} lines}
above\newline \rule{1in}{1in}\newline below
\hrule

\numberoflines{\begin{itemize}
\item One
\item Two
\end{itemize}}

\hrule\leavevmode\marginpar{\theNLcount{} lines}
\begin{itemize}
\item One
\item Two
\end{itemize}
\hrule

\numberoflines{\blindtext}

\hrule\leavevmode\marginpar{\theNLcount{} lines}
\blindtext
\hrule

\numberoflines{\tiny\blindtext}

\hrule\leavevmode\marginpar{\theNLcount{} lines}
{\tiny\blindtext}
\hrule

\newpage
\numberoflines[2in]{\blindtext}
\hrule\noindent\marginpar{\theNLcount{} lines}
\parbox{2in}{\strut\blindtext}
\hrule

\end{document}

A LaTeX solution, maybe a bit more complicated than necessary, but it is working:

\documentclass[12pt]{article}

\makeatletter

\def\RoundLines#1\relax{%
\@tempdimb=#1\relax
\@tempcnta=0
\loop%
\ifdim\@tempdimb>0\p@%
\global\@tempdimb\dimexpr\@tempdimb-\baselineskip\relax
\repeat
\xdef\result{\@tempcnta}%
}

\newbox\calcbox
\def\CalcNumber#1#2#3{%
\edef\@argii{#2}%
\expandafter\@tempdima\@argii\relax
\setbox\calcbox\vbox{\hsize\@tempdima\relax\noindent#1\par}%
\@tempdima=\dimexpr(\dp\calcbox+\ht\calcbox)\relax
\RoundLines\@tempdima\relax
\expandafter\xdef\csname#3\endcsname{\the\result}%
% \copy\calcbox%% for testing
}
\makeatother

\begin{document}
\CalcNumber{A}{20mm}{AHeight}
has {\AHeight} lines

\CalcNumber{M M M}{1mm}{MMMHeight}
has {\MMMHeight} lines
\end{document}


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What would draw a student of the humanities to (La)TeX systems?

I've been given permission to put up a poster in the campus writing center. The primary users of this writing center are from the humanities—those students who need to write rather long papers on a regular basis.

Given that it is strictly non-technical writing, what features of (La)TeX systems would draw such a user, and how should I advertise these strengths on a small poster or pamphlet?

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I'd go with a poster full of ducks. :) – Paulo Cereda Sep 10 '13 at 18:37
@PauloCereda And maybe a lemonade stand… I wonder if Alan Munn has anything to say; as I recall, he's in such a field. – Sean Allred Sep 10 '13 at 18:38
None. They will corner you in a dark alley after they receive the corrections from their supervisors as annotated pdfs. – percusse Sep 10 '13 at 19:17
Automated bibliography stuff: I often have articles with over 100 footnotes. My dissertation had about 1200+, I think. For critical editing, packages like (e)ledmac/(e)ledpar surpass (affordable) commercial options. And the same reasons separation of form and content, and writing structured documents still applies. (And writing a dissertation is the best time to learn something completely new like *TeX because one has at least a year or two to come to grips with a completely new type of workflow.) – jon Sep 10 '13 at 19:22
A two step process: First, teach them about distributed version control and how to use it, then teach them about LaTeX. Clearly nothing could possibly go wrong and this isn't overly complicated at all.</sarcasm> – Sam Whited Sep 10 '13 at 20:18

not sure how to present these in a poster, but here are some features of latex that should be especially attracive to users in the humanities:

• plain text input, not dependent on software upgrades or versions, and input is not corrupted (or lost) if a run doesn't complete successfully; plain text also means that it's very easy to rearrange paragraphs with minimal side effects
• automatic tables of contents, and reliable indexing facilities
• ability to use multi-layered footnotes, as required for critical editions, provided by the eledmac package
• many multilingual capabilities, including language-specific hyphenation (on a paragraph level) and ability to intermix different scripts (latin, cyrillic, greek, arabic, kanji, ...)
• powerful tools designed for linguistics; a large population of linguists who use latex in their work (including Geoffrey Pullum, one of the authors of the Phonetic Symbol Guide), and a forum devoted specifically to that discipline
• document classes such as memoir that are more in keeping with humanities work and "fine publishing" than the "usual" technical-oriented styles

some of these capabilities won't be appreciated even for long papers, but as soon as one is ready to tackle a dissertation or a book, there's really nothing new to learn if familiarity with the system has been nurtured through practice with shorter projects.

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I'll comment on this answer, since it's pretty much exactly the one that I would give. What's notable about this answer is its lack of appeal to the beauty of TeX. This argument is, IMO, a red herring, and even more so in the humanities where most documents (other than critical editions) are just plain paragraphs plus footnotes. And the real value definitely comes in longer documents such as a thesis or book. So for undergraduates in the humanities the appeal is limited. (And most linguists would consider themselves cognitive or social scientists, and not in the humanities.) – Alan Munn Sep 10 '13 at 21:41
@AlanMunn :-) I know precious little about linguistics, so I'll trust you on that point. I agree that trying to convince people simply on typographical terms has been less than effective; when it comes right down to it, most people just don't care; there has to be a practical advantage. (I would be very interested if there is a study that shows the grading advantage in particular.) – Sean Allred Sep 10 '13 at 21:53
@SeanAllred To think that there would be a grading advantage is to take a very cynical and in my experience unlikely view of professors' grading practices. However, I do know that in certain areas of the humanities, citation practices are fetishized, so having good bibliography tools (as TeX does) would definitely be a plus. – Alan Munn Sep 10 '13 at 21:59
@AlanMunn -- when i worked on a master's degree, b.c. (before computers), i was actually told by one of my professors that a paper of mine got kicked up a grade because it was typed on real bond paper with an executive typewriter using a carbon ribbon. i don't know who was more cynical -- that professor or i. (i didn't mind the grade inflation though.) but a fair statement about linguists being social scientists; that's what my degree is in, although there was a heavy concentration in ancient germanic languages that was more to the humanities side. – barbara beeton Sep 10 '13 at 22:06
Philosophy is a humanities subject and lots of logicians use LaTeX. Some non-logicians, too. Not just philosophers of mathematics etc. However, I think the appeal to undergraduates is minimal. Postgraduates, yes. (There stuff like bibliographical management, control of layout and version control will convince a minority.) But usually it seems to take off in departments where some dedicated person teaches others or where there is a critical mass of logicians or whatever. Otherwise, you're the lone weirdo who insists on doing it differently. – cfr Jan 22 '14 at 4:40

In the centre of your poster, have a side-by-side comparison of a page of text typeset by Microsoft Word and a page of text typeset by LaTeX, in the style of various examples I've seen on this website that show off the beauty of its output. Emphasise that for typical essay-writing, the learning curve is incredibly short, and the difference in quality of output is both great and beneficial (because graders are unconsciously driven to give beautiful work higher grades).

Pick a nice font like Garamond with old-style figures. Use someone's actual essay rather than lipsum filler text.

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While someone like me would think this is fantastic and be drawn to it, I actually don't think most humanities majors would care at all. It sounds counter intuative since they probably deal with text all day, but most English majors and the like probably have never considered the design and formatting of what they do; they're concerned with the content. It's a sad truth (in my experience). – Sam Whited Sep 10 '13 at 20:16
@SamWhited It's good they're concerned with the content: one of the best aspects of LaTeX is that you're able to change formatting from the ground up with only minimal modifications to the input file. – egreg Sep 10 '13 at 20:43
@egreg Absolutely, and focusing on that sounds like a great idea (but that's not what he said). Focusing on typesetting minutia though probably won't hook too many humanities folks. My earlier comment did say formatting' though; wrong word, they probably do care about that. – Sam Whited Sep 10 '13 at 20:59
I agree that it's not something many humanities students would think to care about, in the sense of having it as a concern they're aware about when selecting a system to work with, but if you confront them with it, showing two A4 pages, one of which clearly looks more beautiful, you can make it become a consideration. Humanities students do care about their work looking professional, like the academic papers and books they spend all day reading. – dbmag9 Sep 10 '13 at 21:13

Why not reminding readers on the annoying character of word processors?

• LaTeX does not try to outsmart you, neither changing the order of letters, nor the layout, without your explicit command!
• You can have an enumeration directly after a numbered headline and LaTeX will never take an item of the enumeration for another headline!
• Hyphenation will work! There won't be a single paragraph without hyphenation, except you forbid it.
• There is microtypography and hence no rivers, almost.
• Even if you stick with science for all your life, LaTeX will be there. And since your texts are written in ASCII, you can become old and grey and still giggle about the nonsense you wrote when you were a student.
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I would say that hyphenation is something to be avoided, and TeX will do a good job of avoiding it! (And, of course, uses it well when necessary.) – Sean Allred Sep 10 '13 at 20:49
"Latex does not try to outsmart you". Sure, \begin{figure}[h]` => "No no no, you don't mean 'here'. Let's put it elsewhere.". – stefan Sep 11 '13 at 8:52
@stefan Well, but LaTeX places figures reasonably, while placing pictures in a Word file, closing and reopening it may have very strange consequences. But I agree, "h" as an option is misleading, if you read "here", instead of "here?". – Keks Dose Sep 11 '13 at 9:36


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## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$25$
The domain of the variable requires that $x>0$ and $x-21>0$ This means that $x>21$. Recall: $\log_a (MN) = \log_a M+\log_a N$ Thus, the given equation is equivalent to: $\log(x(x-21))= 2\\ \log(x^2-21x)=2$ Recall further that: $y = \log_a b \text{ is equivalent to } b=a^y$. Therefore, $x^2-21x = 10^2$ $x^2-21x = 100$ $x^2-21x-100=0$ By Factoring: $(x+4)(x-25)=0$ Using the Zero-Product Property: $x+4=0 \hspace{5pt} \hspace{15pt} \text{or} \hspace{15pt} x-25 =0\\ x=-4 \text{ or } x=25$ Since $x>21$, then $x$ cannoe be $-4$ Hence, $x= \boxed{25}$


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# Is the impulse 0 in a perfectly inelastic collision?

I have this problem:

An object $$A$$ of mass $$48\: \text{kg}$$ hits with a velocity of $$7.0 \:\text{ms}^{-1}$$ another object $$B$$ which is not moving. After the collision the two objects move together at the same velocity of $$1.4\: \text{ms}^{-1}$$. What's the mass of $$B$$? What's the impulse applied on $$B$$ during the collision?

So this is my doubt: the mass of $$B$$ is $$192 \:\text{kg}$$, since the impulse equals the change of momentum, is the impulse equal to $$0$$ since the change of momentum doesn't change in an inelastic collision? Is it possible not to have an impulse during a collision?

• Focusing just on object B, doesn't its momentum change? – Not_Einstein May 14 '20 at 13:39
• Think of momentum as the quantity needed to completely stop a moving object. In this framework impulse = momentum for an inelastic contact when measured from a reference point co-moving with the center of mass. – John Alexiou May 15 '20 at 16:05

The momenta of individual objects in a collision do change (no matter whether it's elastic or inelastic). However, the total momentum is conserved (does not change), again, irrespective of the fact that the collision is elastic or inelastic. Thus there is a non zero, and in fact equal and opposite impulse on both the objects. Due to this equal and opposite impulse (caused by the normal force between them), the net impulse on the system of those two objects becomes zero and thus the net momentum of the system is conserved.

The initial momentum of $$A$$ is $$p_a = 48 \times 7 = 336\,\text{kgms}^{-1}$$, and the initial momentum of $$B$$ is zero since it is not moving.

Since momentum is always conserved, the total initial momentum, $$336\,\text{kgms}^{-1}$$, must equal the total final momentum, $$1.4m_a + 1.4m_b$$.

I.e

$$336 = 1.4m_a + 1.4m_b$$

So

$$m_b = \frac{336 - 1.4 \times 48}{1.4} = 192\,\text{kg}$$

as you found.

We can now calculate the impulse of $$A$$ and $$B$$.

$$\text{Imp}_a = \Delta p = 1.4\times48 - 336 = -268.8\,\text{kgms}^{-1}$$ $$\text{Imp}_b = \Delta p = 1.4\times192 - 0 = 268.8\,\text{kgms}^{-1}$$

As you can see $$\text{Imp}_b = -\text{Imp}_a$$.

This can be explained by Newton's Third Law: the force exerted on $$B$$ by $$A$$ is equal and opposite to the force exerted on $$A$$ by $$B$$ during the collision. And since they collide for the same time the impuse, $$\int Fdt$$, has the same magnitude for both objects, but different directions (signs).

Getting to your specific questions...

Is the impulse equal to $$0$$ since the change of momentum doesn't change in an inelastic collision?

Remember their is only a particular object's impulse, just like you can't have a force without an object. Although the total momentum of the system does not change, since it is conserved, clearly the momentum of the individual objects changes. This means an impulse has been delivered to both of them.

Is it possible not to have an impulse during a collision?

If you define a collision as objects changing speeds, then momentum must have changed so impulses must have been delivered in every collision.

Impulse is applied over time by the normal force when two bodies are in contact. Since there is only one particle after the collision, it is hard to say there is an impulse theoretically because there would not be another body in the system for an equal and opposite force. If you think about it in a realistic context, if there is no normal force pushing the particles away from each other that would stop them combining(like how you cant punch though every wall), then yes there is no impulse. However, there is likely to be some resisitive force pushing them away from each other since things generally don't want to be combined, so you may measure an impulse in real life.


text:
## GMAT Killer: 490 to 770 in 3 months

Find out how Beat The GMAT members tackled GMAT test prep with positive results. Get tips on GMAT test prep materials, online courses, study tips, and more.
##### This topic has expert replies
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### GMAT Killer: 490 to 770 in 3 months

by joshcollins » Fri Aug 30, 2013 9:43 am
Hi everyone,

When I used to lurk on this site before becoming a member, I liked reading about how people had done well on the GMAT and I'm happy to say that I can add my story to that list of GMAT killers!

The Basics:

Timeframe:
3 months (late May to late August)

Books/Programs Used:
OG 13th edition Book
Manhattan GMAT SC Book
Kaplan Premier Book
Empowergmat Course
2 CATs and questions from mba.com
CATs from ManhattanGMAT
Free Videos and articles on Youtube, GMATPrepNow, etc.
Beat The GMAT Forum

Studying:
Usually 2-3 hours on weekdays, but I always took one day off/week
Usually 4-5 hours on Saturdays and Sundays. Usually 1 CAT on the weekend with review (weekend usually included going back to redo old questions, even questions I got right before)

CAT Scores:
GMATPrep1: 490
MGMAT1: 540
MGMAT2: 550
MGMAT3: 630
MGMAT4: 680
MGMAT5: 680
GMATPrep2: 730
Test Day: 770 (Q50, V45)

Total Money Spent: $351 +$250 for the GMAT (no way to avoid that!)

1) The books were pretty good, but there's a lot of advice that conflicts from book to book, so it takes a little while to figure out what's true and what's not. The OG 13th edition is a MUST HAVE.
2) Find an expert to work with. Use a course or a tutor, but spending the money is worth it. I'm looking at some potentially big scholarship money because I killed the GMAT. That's worth the extra few hundred bucks I spent. For me, Empowergmat made all the difference. On Test Day, I felt like Neo in The Matrix. I was ready for everything. The EMPOWER guys know their stuff.
3) There's a lot of bad advice out there about pacing, representative questions, etc. (and the problem is a lot of it's free). Be suspicious. If you practice something for a full month and it doesn't work, then it's not going to help you hit your goal. Be prepared to learn some new things.
4) Stay calm and write everything down. GMAT questions are actually pretty straight forward if you just stay organized. Don't EVER do anything in your head (thanks for that one, Rich!)
5) The Quant section is NOT a math test and the Verbal section is NOT a vocabulary test, so don't treat them like they are.
6) Learn which questions to avoid. I dumped 4 questions (2 in the Quant and 2 in the Verbal) because I was told to dump them. I can't argue with the advice or the results.
7) Take the 2 breaks, no matter how good you feel. Have a snack, a drink and run to the bathroom.

Now, I'm reading through the Veritas MBA Essential Guides and getting really excited by my prospects.

If I can do it, then anyone can do it. I was really unsure of everything when I started, but I learned the right way to look at this whole process and it made all the difference. To everyone who's helped me on this journey, I say thanks!

Josh

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by red217 » Fri Aug 30, 2013 4:06 pm
Hi there!!!

Congratssss!!! this is great score!!!..i started off wid the same score and i got so demotivated.

I would like you to give me more feedback about the empower course.
i ve been looking into options but they all seem promising

thanks

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by Troika » Fri Aug 30, 2013 5:33 pm
Congrats Josh! This is a huge achievement; earning a 770 is no mean feat! Thank you for sharing your experience with us.

### GMAT/MBA Expert

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by [email protected] » Sat Aug 31, 2013 3:35 pm
Hi Josh,

Congratulations on your success; you worked hard and clearly earned that killer score. Regardless of how much the EMPOWERgmat program contributed to your success, I think that if you bring the same attitude and level of commitment to the other parts of your application, then everything will turn out well (and you'll have plenty of options when it comes to choosing which school to attend).

Congrats again. Another GMAT assassin has been MADE!
Rich
Contact Rich at [email protected]

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by fourteenstix » Tue Sep 03, 2013 6:16 pm
joshcollins wrote:
CAT Scores:
GMATPrep1: 490
MGMAT1: 540
MGMAT2: 550
MGMAT3: 630
MGMAT4: 680
MGMAT5: 680
GMATPrep2: 730
Test Day: 770 (Q50, V45)
Josh,

First, congrats! Tremendous score!

Second, can you provide dates for the CATs above and the date of your exam? I'm curious how much progress you made over the last 4-6 weeks along the way.

Thanks!

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by ani781 » Tue Sep 03, 2013 6:40 pm
Hi Josh, many congrats ! I have a request. Can you pls tell me which course did you find to be helpful in the empower GMAT... I would also like to know how did you stress on internalizing the concepts maintaining work study balance. All the best with your apps.

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by ani781 » Tue Sep 03, 2013 6:42 pm
Hi Josh, many congrats ! I have a request. Can you pls tell me which course did you find to be helpful in the empower GMAT... I would also like to know how did you stress on internalizing the concepts maintaining work study balance. All the best with your apps.

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by ganeshrkamath » Tue Sep 03, 2013 7:54 pm
Wow! Respect.

That's an incredible mountain you've climbed. I hope you get into the school of your choice.

Congratulations.
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494

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by paromaroy » Tue Sep 03, 2013 9:07 pm
Many congratulations on the superb achievement
I am also on my way to re-write the GMAT after an epic downfall last July

Keep at it and I hope you get into your B-school of choice

All the best

Cheers!!

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by johnperregaux » Wed Sep 04, 2013 6:13 am
This is insane. Unreal. Unbelievable. Wow. Under average to super elite GMAT ninja pro in 3 months.

Let me ask you, why did you pass on the Manhattan guides? Did you already have a super strong Quant background? Take advanced math classes in the past??

Do you think it was a lack of knowledge the first CAT you took or was it more you needed to get properly acclimated to the GMAT trickery??

I started at a 550 one month ago and now am sitting at 660, hoping to break the 730 level.

You have given me some super-fine inspiration sir.

+1

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by salochi » Wed Sep 04, 2013 7:32 am
HI Josh u have done an amazing job. I got 450 in my first CAT and then I quit studying Gmat. Your debrief give me new courage and I have started studying fm Manhattans series. How did u prepared ur quant Can u pls explain a little more in detail and do write about ur verbal experiances too.

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by joshcollins » Wed Sep 04, 2013 1:21 pm
Everyone,

Thanks for all the kind words; it's a bit overwhelming. I'll try my best to answer all of your questions.

Red217 - I used the entire Empowergmat course. A friend of mine had mentioned it to me as a great investment (he got 750 on his GMAT, he's a friend of mine, but he's not someone I'd consider really smart, so the course obviously helped him). I took 3 months to prep, which is another thing I was told to do. Part of the practice was just to accept what I was taught and go with it. Part of it was memorizing formulas and grammar. I did practice a lot but when I was taking the GMAT, all that training kicked in and everything felt easy. My pacing was good (dumping a few questions helped - but I learned how to do from the course too).

Troika, Ganeshrkamath, Paromaroy - Thanks for the thanks! If I can do, you can do it too.

Rich - This might seem like a joke, but on certain questions it was like I could hear your voice in my head. EVERYTHING ON THE PAD EVERY TIME!!!

Fourteenstix - Here are my approximate test dates for each of the CATs and the real GMAT. I had some off weekends when I couldn't find the necessary block of time to take a CAT, so I did smaller practice blocks, reviewing old CATs, timing exercises, etc.

5/14: 490
5/19: 540
5/26: 550
6/2: 630
6/16: 680
7/7: 680
Big lag here; work got crazy and I had a couple of weddings to go to in there
8/12: 730
8/26: 770
8/12: 730

Ani781 - From a training standpoint, I think every Module mattered and I never got the sense that there was filler. The early Quant Tactics and Data Sufficiency Modules were SUPER helpful. The CR Box made doing those questions really easy. The Triage Module turned hard questions into more of a game. All the Tactical Modules helped me to change my perspective on what I thought about the GMAT.

Johnperregaux - I did use the ManhattanGMAT SC book, so I didn't pass on the set entirely. And no, I don't have a super strong Quant background, but I didn't think that the books meshed with the other things I was learning. Most of the math on the GMAT was stuff I learned in 9th grade or earlier, so I did some review and refamiliarized myself with it all.

On my first CAT, my big problems were pacing and not knowing how to handle DS questions. Many of the things that I learned in the Empower course were about how to view the questions and my own work, the fastest way to answer questions, etc. You can absolutely pick up another 70 points but you might need to learn some new things.

Salochi - For the verbal, I practiced the tactics that I was taught (taking notes and understanding what the wrong answers look like definitely helped). I didn't worry about understanding every word in a CR or RC passage (sometimes I just shot past big words, science words, names, etc.), but I did focus on the words that I DID know. For SC, I had to learn a bunch of grammar rules, but grammar is mostly a "matching game" (Max taught me that one), so I treated SCs like little mysteries - where are the clues, what has to match up, what's wrong with this sentence, etc.

I hope I answered everyone's questions. Thanks again for the kind words. If you have any other questions, then fire away and I'll do my best to answer them.

Josh

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by ses4db » Thu Sep 05, 2013 6:20 am
Josh,

You said you dumped 2 Quant and 2 Verbal questions. How did you choose which ones to dump? What were your reasons? Were there certain question types you knew you would automatically skip?

I'm 11 days from my scheduled GMAT! I'm feeling both confident and nervous: I've been consistently scoring well on the CAT's, but you never know what you'll get on test day. I'm just trying to spend these last few days sharpening things up.

Really appreciate it! Thanks for the inspiration!

Sammy Stalcup

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by joshcollins » Sat Sep 07, 2013 1:17 pm
Sammy,

It's easy to say that I "chose" to dump those questions but the truth is that I was "advised" to dump them and I just followed instructions. It's something I learned in the Empowergmat Course. I think that the number and type of questions to dump varies a little from person to person (and how well that person's doing in the section), but after studying for a few months I knew what to look for and how to do it.

Go crush the GMAT!

Josh

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by Busytrying » Sun Sep 08, 2013 3:30 pm
Amazing achievement - thank you for sharing and many congratulations!


text:
## Friday, 26 June 2015

### Pipeline for the Word Level Alignment using Kaldi in English using Trained Acoustic Models

Hi,

This week marks the beginning of the Mid Term Evaluations of GSoC and this post  describes the pipeline employed that will be deployed to decode the video files.

The picture below depicts the basic steps involved in the task:

Audio Extraction from the Video Files:

For this module, I've used ffmpeg, which is a cross-platform solution to process video and audio stream.  This step produces 2 channel wavefiles which have a sampling rate of 44.1khz.

I've downsampled the files to 8000 Hz and mono channel using sox, which is a command line utility in ubuntu to process audio files.

The down sampled wave files are then split into smaller chunks based on silence regions as mentioned in my first post

As I plan to decode the files using Kaldi, I've written the scripts in such a way that the smaller chunks are saved in the format compatible with Kaldi recipe that I've built for English( as explained in my post 2).

**********************************
Code :

ffmpeg -i video_file audio_file
sox wave_file -c 1 -r 8000 wave_downsampled
sox wave_downsampled wave_downsampled 1 0.1 1% 1 0.7 1% : newfile : restart

***********************************

Decoding Using Kaldi Trained Models:

The files necessary for the process of decoding are the graphs which are present in the exp folder.

Once this is done, adjust the paths in the Kaldi recipe to point to the test files and run the decoding step. The predictions are stored in the exp folder.

The utils folder has the script int2sym.pl which is required to generate the symbols corresponding to the phones/words.

Brief Sequence of Steps:

(1) Prepares data.
(2) Prepares the Language Model.
(3) Extracts MFCC( Mel Cepstral Coefficients) features as mentioned in the previous post.
(4) Decodes the data using acoustic model trained on 100 hrs of clean Librispeech data.

The code is updated here. Feel free to have a look and suggest changes.

## Sunday, 21 June 2015

### Building Acoustic Models using Kaldi Voxforge recipe to obtain word level transcripts for long video files

Hi all,

This is the second post in the series and deals with building acoustic models for speech recognition using Kaldi recipes.

In this post, I'm going to cover the procedure for three languages, German, French and Spanish using the data from VoxForge.

BRIEF WORKFLOW:

Toolkit

Kaldi is an opensource toolkit for speech recognition written in C++ and licensed under the Apache License v2.0. I've included the installation instructions in the readme file in the git repo.

Step 1 :
Set the DATA_ROOT variable in the shell script path.sh to point to the location on drive where you intend to store the data.
I've stored it in /home/$USER/database/voxforge. Step 2: Execute getdata.sh. This step a) Downloads the language specific speech data from the voxforge portal and saves it in a folder tgz. b) Extracts the files into a folder called extracted. Ex: I've them in /home/$USER/database/voxforge/$LANGUAGE/tgz and /home/$USER/database/voxforge/$LANGUAGE/extracted Details of the data files: French - 55 hours , 1600 speakers Spanish - 53 hours, 1712 speakers German - 50 hours, 1600 speakers Mapping anonymous speakers to unique IDs We'd like to be able to perform various speaker-dependent transforms and therefore avoiding anonymous speakers is an important step in building the models. Also, the "anonymous" speech is recorded under different environment/channel conditions, by speakers that may be both males and females and have different accents. I've given each speaker unique identity following Voxforge recipe. Train/test set splitting and normalizing the metadata The next step is to split the data into train and test sets and to produce the relevant transcription and speaker-dependent information. I've used 20 speakers for test. Building the language model I decided to use SRILM toolkit to estimate the test-time language model. SRILM is not installed by default under$KALDI_ROOT/tools by Kaldi installation scripts, but needs to be installed manually. The installation  assumes you have GNU autotools, C++ and Fortran compilers, as well as Boost C++ libraries installed.
Preparing the dictionary
The script, used for this task is called local/voxforge_prepare_dict.sh. It downloads the CMU's pronunciation dictionary first, and prepares a list of the words that are found in the train set, but not in cmudict. Pronunciations for these words are automatically generated using Sequitur G2P, which is installed under tools/g2p. The installation assumes you have NumPy, SWIG and C++ compiler on your system. Because the training of Sequitur models takes a lot of time this script is downloading and using a pre-built model trained on cmudict instead.
Feature Extraction:
I've used MFCCs( Mel Frequency Cepstral Coefficients) as features to train the acoustic models.  Mel-frequency cepstrum (MFC) is a representation of the short-term power spectrum of a sound, based on a linear cosine transform of a log power spectrum on a nonlinear mel scale of frequency. The

 MFCC Extraction Procedure

They are derived from a type of cepstral representation of the audio clip (a nonlinear "spectrum-of-a-spectrum"). The difference between the cepstrum and the mel-frequency cepstrum is that in the MFC, the frequency bands are equally spaced on the mel scale, which approximates the human auditory system's response more closely than the linearly-spaced frequency bands used in the normal cepstrum. This frequency warping can allow for better representation of sound.

MODEL BUILDING:

I've built the models using triphone context. The following improvements have been tried:
Improvement using MinimumPhone Error rate training.
Improvement using Maximum Likelihood Training.
Improvement using SGMMs.
Improvements using Hyperparameter tuning of DNNs.

I'll explain each of these  in detail in my next post.

The next step is decoding the test files using the models built. In my previous post I've mentioned the procedure to pre process the test files to decode them using the models built using Kaldi.
The code for both the posts is updated. Please feel free to have a look and suggest changes.  Both the posts contain readme files and run.sh to help navigate through the code.

*******************************************************************************************

Progress so far:

Model Building:
Built Acoustic Models for  the following languages:
English
Spanish
German
French

*********************************************************************************************
Whats's next:

Model Building:
Danish
Swedish
Norwegian

Model Deployment:
English

Wrapper:
Python wrapper to cover the decoding process.

Documentation

**********************************************************************************************

What will be in the next post:

a) Improving the transcripts using different techniques
I'll be explaining the variants of the training procedures and the ways to fine tune them to improve the accuracy.  Basically the following:
Monophone vs triphone training.
Improvement using MinimumPhone Error rate training.
Improvement using Maximum Likelihood Training.
Improvement using SGMMs.
Improvements using Hyperparameter tuning of DNNs.

b) Model building :
How to build models when Voxforge data is not available.

## Friday, 5 June 2015

### An Introduction to Speech Processing and Forced Alignment of Speech and Text

This is the initial one in a series of posts explaining the techniques used and procedures followed to achieve forced alignment of speech and text as a part of Google Summer of Code 2015.

Lets think about it. What is this forced alignment and why is it important. From the title it seems very intuitive right?, we have speech and we have text....whats so big about aligning both of them ?

Here are the questions:

Why even bother about different techniques to achieve this?
Whats even so special about speech processing as a whole?
Speech is just a signal right? Apply DSP techniques and get over it.

What's in Speech Processing ?

Speech processing is the study of speech singals and the processing methods of these signals. The specific and interesting properties of speech, the natural variations, quasi stationarity, aperiodicity, uff.....can be a bit boggling once we start knowing a bit more about speech and definitely intimidating after a point in time.

" Lets write rules and capture the variations" ......someone thought.

Fair enough...but how many? Each and every phoneme( basic unit in speech....much like atoms in physical world), has its own specific properties and whats more cool... the rules for individual phonemes modify effortlessly when they combine with other phonemes. Consontant clusters are a headache. Coarticulation is a curse in disguise if not taken care of. Whats more....rules are dependent upon language . Too many things to consider. Lol !! And there are  shameless exceptions.

"Machine Learning" .........A light bulb blew in the engineer's mind. Lets make machines learn. Its difficult to design a machine that can defeat human in chess but really easy and straight forward to design a machine which can understand and interpret humans was the idea. How cute !!!!!. Fast forward ten years and the exact opposite happened. We have chess as the basic game on our PC and the natural language processing is still a distant dream !!!!

So, the way out....at least now, seems to be to take the best of the two worlds...apply machine learning and cover the exceptions using the rules (sort of ). This is what I'll be doing. Push the baseline, see the results, cover the exceptions, push version 1...see exceptions......and some wer version 5 is gonna give us near 100% accuracy.

Forced Alignment:
Forced alignment is the process of taking the text transcription of an audio speech segment and determining where in time particular words occur in the speech segment.

Large recordings like radio broadcasts or audio books are an interesting additional resource for speech research but often have nothing but an orthographic transcription available in terms of annotation. The alignment between text and speech is an important first step for further processing. Conventionally, this is done by using automatic speech recognition (ASR) on the speech corpus and then aligning recognition result and transcription.
The most common approach to this text-to-speech alignment is to make use of a standard commercial speech recognizer to produce a time-aligned transcription of the recording which is then aligned with the original text transcript on a graphemic level.  The idea was introduced by Robert-Ribes ( the system was called FRANK).

Approach:

Now that we know what alignment is, it's almost effortless to apply a speech recognizer on the audio file and get the transcriptions. Or is it? The process is straight forward for smaller audio files. Having said that It goes without the need for saying that processing a huge audio file is a computationally intensive process.

An intelligent and logical approach to solve the same problem would be to break the huge audio file into smaller chunks.

Cool. But where to chunk the audio?? Obviously we don't want to chunk at the middle of speech. So...cut it at the silence. May be? Here is the basic formulation of the audio chunking module that I'm gonna use:

Silence Detection:
Speech signals usually contain many areas of silence or noise. In case the speech is free from noise, a threshold based on signal energy usually suffices the detection of silence regions.  I've described the process of obtaining signal energy in detail in one of mys.

In the current scenario though, I'm expecting the presence of environment noise(traffic, birds, etc) along with the speech. Therefore, I'm trying out another feature in addition to the signal energy. I'm typically looking for a feature which emphasizes the brighter sounds (per se). As of now something that's closer to the desired function is the spectral centroid. Roughly saying, divides the entire spectrum into two parts,  a high frequency region and a low frequency one.

Feature Calculation:

An excerpt from a post of one of my joint blogs:

Speech Segments Detection:

Here's the basic algo to get the speech segments:
1) Compute the histogram of the feature sequence’s values.
2) Apply a smoothing filter on the histogram.
3) Detect the histogram’s local maxima.
4) Let M1 and M2 be the positions of the first and second
local maxima respectively.
The threshold value is computed using T = (W·M1 + M2)/(W+1).

Speech Recognition:

As of now I'm using the speech recogntion module given by Kaldi recipe using the acoustic model of Librispeech data. I'll be explaining the fundamentals of recognition in the next post.


text:
# Trigonometrysystem of equations

#### jacks

##### Well-known member
How can i solve system of equations , if $$x,y,z\in \left[0,\frac{\pi}{2}\right)$$

$$\begin{cases}\tan x+\sin y+\sin z = 3x\\ \sin x+\tan y+\sin z = 3y\\ \sin x+\sin y+\tan z = 3z\end{cases}$$

#### soroban

##### Well-known member
Hello, jacks!

How can i solve system of equations , if $$x,y,z \in \left[0,\tfrac{\pi}{2}\right)$$

$$\begin{array}{ccc}\tan x+\sin y+\sin z &=& 3x\\ \sin x+\tan y+\sin z &=& 3y\\ \sin x+\sin y+\tan z &=& 3z\end{array}$$

I don't think you can.
. . The equations are transcendental.

However, by inspection, $$(x,y,z) \,=\,(0,0,0)$$ is a solution.


text:
# Inserting overline

I am interested in placing an overline above a number for XRD peak labeling. I managed to get something reminiscent of what I want using the unicode U+0305 character, however the overline is offset from the number, as shown in the attached image (supposed to over the final "1").

Is there a clever way to do this so that it's not offset? I would like to incorporate this into a procedure, but may end up doing it manually by drawing lines, if need be.

Thanks!
Using code like \Z24\[01\X0¯23

Displayhelptopic "Elaborate Annotations".

The help topic about this feature seems too simpe in Igor 7. You can get a detailed description in Igor 6.37 using displayhelptopic "Elaborate Text Info Variables Example" instead.
I did some experimentation with "combining overline" and the results were... not great. Here is my attempt:
TextBox/N=overline "12"+U+0305+"3"
The result depends on the font. On my Macintosh, using Helvetica, the overline is in the correct place horizontally, but it seems designed for lower case combining letters.
If I change to Arial on Macintosh, I get something that looks a lot like the original picture; the overline is high enough, but misplaced horizontally.
This gets really close using only Igor's annotation escape codes:
\Z161\[02\[1\y+45\L0600\Y03
In this, the \Z16 just makes the font bigger. Then there's a "1", then a code to save the current position into variable 0, then a "2", then a code to raise the drawing position to a place over the characters in the line, then a code to draw a 1-point line from the position saved in variable 0 to the current X position, a code to restore the drawing Y position, then a "3". Result is attached- it looks like with Helvetica font on a Macintosh the X position for the 3 isn't quite right...

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

I've attached a procedure I wrote for an XRD customer a while ago that adds an "Add Crystal Annotation..." item to the Graph menu.

Perhaps that'll help.

--Jim Prouty
Software Engineer, WaveMetrics, Inc.

JimProuty wrote:
I've attached a procedure I wrote for an XRD customer a while ago that adds an "Add Crystal Annotation..." item to the Graph menu.

Perhaps that'll help.

--Jim Prouty
Software Engineer, WaveMetrics, Inc.

Hi Jim,

This is great and exactly what I need. Thanks for sharing.

It seems that the new

\$WMTEX$

option to use Tex in Igor could be useful here.

The \overline{} Tex command puts an horizontal bar above the character:

TextBox/C/N=text0/F=0/A=MC "\\$WMTEX$ \\overline{3} \\$/WMTEX$"

Yes, this is WAY easier than the Igor version!  Unfortunately, the implementation of LaTeX in Igor seems very limited.  For example, \dot{x} does not work, even though it does work in the online editor at https://latex.codecogs.com/eqneditor/editor.php, which is what I thought Igor uses.

In recent work, we've had to use awkward (and not very pretty) kluges with dots in graphics mode.  Writing a procedure code as above also does not seem attractive.

Any comments as to why \dot{x} does not work in $WMTEX$ ?

While this does not answer your question, you know that you can just use unicode characters for this right? As the manual states, Igor uses only a subset of commands, which are most useful and otherwise would be tedious to realize. You can also write an email to the support with commands you need to create your annotations and the staff may consider adding it.

Thanks.  I am not too familiar with using special unicode characters.  Do you know how this would work?  (One would want to add the dot -- and occasionally a double-dot -- to a chosen letter, not just 'x'.)

And, yes, I know that Igor only implements a subset of LaTeX.  I just thought it was a larger set than it seems to be.  But adding various things over or under a letter (dots, tildes, bars, etc.) are just the kind of thing that I often need and for which Igor has been very klugey.  It seems to me a fairly basic / standard category that should be better supported.

I can only guess that any additional command needs to be specifically implemented by the Igor team, and they rather want to avoid recreating all this stuff which can be achieved differently in a simple way.

As for unicode support, this is easy: Just copy the character from a unicode table or website or use the character map from within Igor (Character => Character Map). If you happen to know the code for the character you want, you can also enter codes directly by choosing Character => Enter Character and then write the character code in hex. For example, for a dot over the small x the code is 0x1E8B. Copying the character from a document or website is usually easiest. For example, you can have a small file with all characters you usually use listed, so you can quickly copy them in. Here is a list of characters with a dot above:

https://unicode-table.com/en/search/?q=dot+above

Naturally, the font you use needs to support the character. You can, of course, always switch to a different font in-between just for these special characters.

Thanks, chozo!  I can't get this to work -- I have to say that WM's manual on how to use UTF-8 characters is confusing at best.  I don't see how to get your code as a label on a graph.  For example, I did put in (in the Label axis dialog)

 \{U+02D9}W

but this gives an overdot that is to the left of the W, not on top as I want.

When I try \{0x1E8B} I just get the string '7819' (in smaller font, amusingly), so again not what is hoped for....

Regarding your speculations about why there are so few LaTeX commands implemented, I suppose that is a reasonable explanation. But I would have naively thought there is a way to leverage all that coding to the LaTeX program itself, so that all that would be needed is to make sure the proper package is included.  Having to program each character seems a painful way to go.

Maybe WM folks can comment on all this?

You can use a Unicode combining character to get a W with a dot above using this command:

Label bottom "W\\{U+0307}"

U+02D9 is Unicode "dot above", but that's not what you actually want.

Igor doesn't use the LaTeX package itself. All supported LaTeX commands use our own drawing code (some of which might have been adapted from the original LaTeX drawing code).

Thanks, aclight.  That will work for now (it's not beautiful for Wdot but is better for Fdot).

I guess this will count as a plea for \dot{x}, \ddot{x}, and \vec{x}.  I notice you have \overline{x} and \tilde{x}, so these would be natural "cousins" of those symbols.  Using slightly bigger dots (more like "small filled circles") and placing them slightly higher than the unicode would look much nicer.

PS  Accommodating italics (math mode) characters is also important.  At least for me, this issue is arising in describing the rate of change of a variable.  It looks like the unicode does not work with italics.  (Or, I couldn't get it to work...)

An alternative option on macOS could be to use LaTeXiT, create a PDF or PNG image for the label text, import the image to the experiment, and add the image as the label.

The best option would be when Igor Pro would have a flag or preference setting to indicate that a LaTeX string should be run through a local LaTeX compiler to create the text.


text:
# Asking questions on puzzle creation

What are the rules for questions on puzzle-creation?

Should we ask them on Puzzling SE or on the meta?
What are their scope? (I'm afraid a question like "How do I write a good quiz?" will be too broad)

Are questions asking for good books/websites on puzzle-writing on-scope?

• Your example does seem too generalised, however very specific questions like 'how do I check this sudoku for the unique character of the answer' would be perfectly acceptable. By any chance, is 'LookingForAName' the same person as 'NeedAName'? I couldn't help but notice... Sep 29 '15 at 11:10

What are the rules for questions on puzzle-creation?

They are perfectly on-topic on the main site. The site is for puzzles and puzzle related questions. Your question falls under puzzle related questions and therefore is on-topic on the the main site. In fact, we have a tag named whose excerpt reads A question about the creation and development of puzzles. Currently, it has 71 questions.

Should we ask them on Puzzling SE or on the meta?

Definitely on puzzling.se. The meta is for discussion about the the main site. If your question is about puzzles in general ask them on the main site. However, if your question is about puzzles on puzzling.se, you should probably be asking them on meta.

What are their scope?

I think, as long as they are puzzle related and not too broad or too subjective they should be fine. While How do I write a good riddle? will be too broad, you can narrow it down by specifying what you are looking for. Example:1,2,3

Are questions asking for good books/websites on puzzle-writing on-scope?

I'm not sure about this one. Personally, I think what are good sites for puzzles should be too broad. But, if you narrow them down (for example by mentioning what type of puzzles you are looking for), it should be on-topic. Again, this is personal opinion. I do not know about the community's stance on this.