text:
# Is there a constant that is not a constant?

1. Apr 19, 2015

### Shahid Manzar

I was wondering why is there a constant that isn't really a constant in mathematics?

I am talking about "e", as in exponent e which is the base of the natural logarithm. By definition e = lim (1 + 1/n)^n as n approaches infinity, but doesn't this make e a non-constant since infinity always changes? In fact we know that value of e varies between 2.70 to 2.80 (P. 248 Calculus 5th edition, Stewart)
Also if value of e varies then how does a calculator pick a given value for e to solve natural log problems and what is the logic for choosing that particular value for e.

Thank you for the help!

2. Apr 19, 2015

### Staff: Mentor

There isn't.
A constant always has the same value.
Infinity is not "always changing." The fact that e is defined as a limit has nothing to do with its value.
No, you are mistaken. e doesn't vary. Its value is somewhere between those two numbers, but that doesn't mean that its value is changing.
A calculator uses an approximation of e. Different calculators might use different approximations, but that doesn't mean the e's value is changing.

3. Apr 19, 2015

### SteamKing

Staff Emeritus
According to this article:

http://en.wikipedia.org/wiki/E_(mathematical_constant)

the value of e has been calculated to 1 trillion (1012) decimal places.

Unlike similar calculations for the value of π, the calculation of the number e gets far less attention in the press.

4. Apr 19, 2015

### Mentallic

Just because the value of $S_n=(1+1/n)^n$ as n increases keeps changing, doesn't mean that it won't converge to a value at infinity.

$$S_1=2$$$$S_2=2.25$$$$S_3\approx 2.37$$$$S_4\approx 2.44$$
$$S_{10}\approx 2.59$$
$$S_{100}\approx 2.705$$
$$S_{1000}\approx 2.717$$
$$S_{10^6}\approx 2.71828$$

Notice as n gets larger, the value of Sn changes much more slowly. As n approaches infinity, Sn will approach a certain constant value which is irrational and we give this constant the symbol $e\approx 2.7182818284590...$

This is equivalent to, for example,

$$\lim_{n\to \infty}\frac{n+1}{n}=1$$
Even though we have

$$S_n=\frac{n+1}{n}$$

$$S_1=2$$$$S_2=1.5$$$$S_3=1.33$$$$S_{10}=1.1$$$$S_{100}=1.01$$

We will find that $S_{\infty}=1$

5. Apr 19, 2015

### rootone

A constant is a value which is what it is.
The degree to which we can be accurate about it can be improved, but this does change the value.
A simple example , take the number two.
There is is no such thing as more or less 'two', it has an exact numerical value.
Two cats sleeping on my couch are not approximately two cats, they are exactly and precisely two cats,
not a range of possible cat quantities somewhere between 1.9 and 2.1 cats.

Last edited: Apr 19, 2015
6. Apr 20, 2015

### statdad

Two cats on a couch equals two more cats than is needed.

7. Apr 23, 2015

### Stephen Tashi

Some of the words involved in the mathematical definition of "limit" suggest a process that takes place in time or takes place in steps. However, if you examine the precise wording of the definition of "limit" (the so-called "epsilon-delta" definition), there is no mention of something being done in steps or progressing as time passes. Illustrating limits by showing a computation done in steps is merely an intuitive way to present them. It's rather surprising how the mathematical definition of limit expresses an idea that is intuitively associated with doing a calculation in steps without mentioning anything about steps or a process taking place in time.

8. Apr 23, 2015

### symbolipoint

The base of the natural logarithm, e, DOES NOT VARY. e is a constant; e is a constant value. When it is written with digits, the value shown is an approximation only, because e is an irrational number.

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text:
# The length of a steel beam increases by 0.78 mm when its temperature is raised from 22 degrees C to 35 degrees C. What is the length of the beam at 22 degrees C (in meters)?

Jun 21, 2015

${l}_{0} = 4.545 m$
I may be wrong but I think you need something else...the expansion coefficient perhaps...?

#### Explanation:

You can use the expression that describes thermal linear expansion as:
$\Delta l = {l}_{0} \alpha \Delta T$
Where:
$\Delta l = l - {l}_{0} =$change in length;
${l}_{0} =$original length (at 22°C);
$\alpha =$expansion coefficient;
$\Delta T =$change in temperature.
$\frac{0.78}{1000} = {l}_{0} \cdot \alpha \cdot \left(35 - 22\right)$
${l}_{0} = 4.545 m$

format: plain


text:
Dataset Open Access

# Bibliography on criteria for assessing the quality of scientific publications

Herb, Ulrich

### Citation Style Language JSON Export

{
"publisher": "Zenodo",
"DOI": "10.5281/zenodo.3366168",
"title": "Bibliography on criteria for assessing the quality of scientific publications",
"issued": {
"date-parts": [
[
2019,
8,
12
]
]
},
"abstract": "
The data deposited here consist of references to literature that was evaluated during the development of  a qualitative survey and an online questionnaire on the qualitative perception of scientific publications.
\n\n
In preparation for these qualitative interviews and the online survey, a literature study on the qualitative perceptions of scientific literature was conducted in January and February 2018.  The focus was on the question which internal characteristics, i.e. in the narrower sense content-related factors, influence the perception of a publication as qualitatively valuable or poor. External characteristics as citation counts should not be at the centre of the research - knowing that they control qualitative perception - since their effect on the perception of the quality of a publication is sufficiently discussed (see e.g. Dong, Loh, & Mondry, 2005).
\nThe literature study was based on the results of a search in the databases Web of Science, Scopus, Library, Information Science & Technology Abstracts and the search engine Google Scholar.
\n\n
VisOA_full_results.bib includes references that were considered valuable in principle, VisOA.bib only those that have been considered in the development of the survey instruments.
",
"author": [
{
"family": "Herb, Ulrich"
}
],
"note": "Gef\u00f6rdert vom Bundesministeriums f\u00fcr Bildung und Forschung (BMBF)\n\"F\u00f6rderrichtlinie des freien Informationsflusses in der Wissenschaft \u2013 Open Access\ndes Bundesministeriums f\u00fcr Bildung und Forschung (BMBF)\"\nVorhaben: Sichtbarmachung von Open-Access-Publikationen in den Nachweisinstrumenten einer Bibliothek - visOA\nAusf\u00fchrende Stelle: Leibniz-Institut f\u00fcr Neue Materialien gGmbH (INM)\nProjektleitung: Uwe Geith\nF\u00f6rderkennzeichen: 16OA060\n\nFunded by the Federal Ministry of Education and Research (BMBF)\n\"Programme for the Free Flow of Information in Science - Open Access\nof the Federal Ministry of Education and Research (BMBF)\"\nProject: Making Open Access publications visible in the holdings of a library - visOA\nExecuting authority: Leibniz Institute for New Materials gGmbH (INM)\nProject Management: Uwe Geith\nGrant reference number: 16OA060",
"type": "dataset",
"id": "3366168"
}
838
60
views


text:
Here's the question you clicked on:

## jkristia Group Title Problem 5A-3g, is the answer correct? one year ago one year ago

• This Question is Closed
1. jkristia

I'm not able to get the same nice clean answer as in the solution, and I think the problem is a mistake in the given solution where he get $\frac{dy}{dx} \frac{x}{\sqrt{1 - x^2}} = (1-x^2)^{-3/2} ??$ it seems like he forgot the $$x$$ in the numerator I get $=\frac{-x^2+x+1}{(1-x^2)\sqrt{1-x^2}}$ What am I missing, where is my mistake ?

2. OBMD

First change the equation to $\frac{ dy }{ dx}x(x-x ^{2})^{-\frac{ 1 }{ 2 }}$ Use the product rule you get $(1)(1-x ^{2})^{-\frac{ 1 }{ 2 }}+x(-\frac{ 1 }{ 2 })(1-x ^{2})^{-\frac{3 }{ 2 }}(-2x)$ this can be simplified to $\frac{ 1-x ^{2} }{(1-x ^{2})^{\frac{3}{2}} }+\frac{ x ^{2} }{(1-x ^{2})^{\frac{3}{2}} }$ which equals $\frac{ 1 }{ (1-x ^{2} )^{\frac{ 3 }{ 2 }}}$ or$(1-x ^{2})^{\frac{ -3 }{ 2 }}$

3. OBMD

Note that $(1-x ^{2})^{-\frac{ 1 }{ 2 }}=\frac{ 1 }{ (1-x ^{2})^{\frac{ 1 }{ 2 }} }=\frac{ 1-x ^{2} }{ (1-x ^{2})^{ \frac{ 3 }{ 2 } }}$

4. jkristia

oh man.... you are right :). I have to go back and check my calculation, but I think my silly mistake was to multiply by (-2), not (-2x), arghhh... sometime you just go blind staring at a problem.


text:
I graduated from the University of California, San Diego in June 2018 with a degree in Pure Mathematics and a minor in Computer Science. I currently work as a Data Scientist, primarily doing forecasting and mathematical modeling, and plan to begin pursuing a Ph.D in Mathematics in Fall 2019.

I am broadly interested in algebraic aspects of geometry and topology – I participated in undergraduate research in Topology with the inimitable Justin Roberts, which included a study of spectral sequences, homotopy theory, fiber bundles, classifying spaces, characteristic classes, and basic intersection theory.

You can find details concerning my experience and educational background under Activities.

Under Resources, I’ve assembled some math-related advice, recommendations, and answers to questions that I often hear students ask.

I also host several small blog posts and notes here – these posts are my efforts to convert sketches, notes, and outlines into something readable. I welcome any feedback or suggestions anyone might have; feel free to contact me via any of the contact methods listed on the left side of the page or under the “Follow” tab on mobile.

# Talks/Seminars/Etc.

• Some slides (HTML, PDF) and notes regarding the Mathematic Subject GRE from a 2/2019 workshop I presented.

• I host a fork of the Arxiv Sanity Preserver , which regularly indexes papers from a number of Mathematics categories on Arxiv.com.
• A gallery of math-related images and diagrams I’ve created for various talks and papers, as well as various other photos.
• An animated visualization of persistent homology on a time-evolving simplicial complex. (Work in Progress!)
• A square topology toy in HTML/Canvas, designed to visualize walking around and drawing graphs in spaces with topologies arising from identifying the edges of a square.
• A 3D visualization of familiar toplogical spaces embedded into $\RR^3$ (using the 3D Javascript library Three.js)
• A giant diagram of algebraic structures
• My (rather unorganized!) directory of various notes

# Tutoring

I am able to provide tutoring for any of the following undergraduate topics:

• Discrete Mathematics
• Calculus
• Linear Algebra
• Ordinary Differential Equations
• Probability (Introductory)
• Statistics (Introductory)
• Number Theory
• Complex Analysis
• Combinatorics
• Abstract Algebra
• Real Analysis
• Topology

If you are interested in meeting or setting up a session, please fill out the interest form here.

# Recent Posts

## Research Workflow

In the last year of my undergraduate degree, I did two quarters of undergraduate research, and the purpose of this post is to capture some of the research pr...


text:
# How to trim the end of line character for each line read from an external file?

How to trim the end of line character for each line read from an external \jobname.list file below? Note that the real scenario does not use filecontents package to generate the list. I use a batch file to prepare the list. The following MWE is just for the sake of simplicity.

\documentclass{article}

\usepackage{filecontents}
\begin{filecontents*}{\jobname.list}
a.jpg
b.pdf
c.eps
d.png
\end{filecontents*}

\parindent=0pt
\usepackage{graphicx}

\begin{document}
\makeatletter
\loop
\includegraphics[width=\textwidth,height=\textheight,keepaspectratio]{../../Images/\x}%
\repeat
\makeatother
\end{document}

The code above cannot be compiled because \includegraphics does not like the end of line charcter appended in the file path. I wasted much time to find the source of problem.

## Edit:

If the image files a.jpg and b.pdf are put in ../../Images/ then the proposed solutions no longer work. How to solve it?

I mainly use xelatex to accommodate 4 image formats.

-
Add \begingroup\endlinechar=-1 before \loop and \endgroup after \repeat. Also put a space (or \par) after {\x}. –  egreg Sep 25 '12 at 9:39

An alternative approach to Herbert's is to remove the space at the end of the line, which is what TeX converts the end-line to (assuming no blank lines, of course)

\documentclass{article}

\usepackage{filecontents}
\begin{filecontents*}{\jobname.list}
example-image-a.pdf
example-grid-100x100pt.png
\end{filecontents*}

\parindent=0pt
\usepackage{graphicx}

\begin{document}
\def\stripend#1 \stop{\unexpanded{#1}}
\loop
\edef\x{%
\unexpanded{%
\includegraphics[width=\textwidth,height=\textheight,keepaspectratio]%
}%
{\expandafter\stripend\x \stop}%
}%
\x
\repeat
\end{document}

-
@GarbageCollector I've edited to expand \x once before using \includegraphics. That should I hope solve any issues (which are nothing to do with the line end: it's the way \includegraphics does a file search that's important). –  Joseph Wright Sep 25 '12 at 12:04

without grouping:

[...]
\begin{document}
\makeatletter
\loop
\includegraphics[width=\textwidth,height=\textheight,keepaspectratio]{\x}%
\repeat
\makeatother
[...]

if the images are saved in another directory then use (example for images in /tmp/):

[...]
\edef\filename{/tmp/\x}
\includegraphics[width=\textwidth,height=\textheight,keepaspectratio]{\filename}%
[...]

-
What if XeTeX is used and \endlinechar equals 20000? Just joking. ;-) –  egreg Sep 25 '12 at 9:45
defined in latex.ltx the main source for LaTeX: \mathchardef\@M=10000 –  Herbert Sep 25 '12 at 9:47
see my edit, which works for me. –  Herbert Sep 25 '12 at 11:44
It does not work with xelatex/latex when we import EPS file. –  please stop stalking Sep 25 '12 at 11:55
LuaTeX throws an error "Invalid \endlinechar" if \endlinechar is set to a value greater than 127. Therefore it is more portable and safe to assign a negative value (-1) either in a group or with saving/restoring the previous value. –  Heiko Oberdiek Sep 25 '12 at 12:43

The following approach works also when the file name in \includegraphics has some prefix (the problem mentioned in the question probably has to do with some setting made to \endlinechar in graphics.sty)

\documentclass{article}

\usepackage{filecontents}
\begin{filecontents*}{\jobname.list}
example-image-a.jpg
example-grid-100x100pt.png
\end{filecontents*}

\parindent=0pt
\usepackage{graphicx}

\begin{document}

\begingroup\endlinechar=-1
\loop
\edef\x{../Images/\x}
\includegraphics[width=\textwidth,height=\textheight,keepaspectratio]{\x}
\repeat
\endgroup
\makeatother
\end{document}

Here is an expl3 implementation

\documentclass{article}

\usepackage{filecontents}
\begin{filecontents*}{\jobname.list}
example-image-a.jpg
example-grid-100x100pt.png
\end{filecontents*}

\usepackage{graphicx}

\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\includefromfile}{O{} m m}
{
\garbcoll_include:nnn { #1 } { #2 } { #3 }
}
\cs_new_protected:Npn \garbcoll_include:nnn #1 #2 #3
{
{
\tl_set:Nx \l_tmpa_tl { #2 \tl_trim_spaces:n { ##1 } }
\includegraphics[ #1 ]{ \l_tmpa_tl } \par
}
}
\ExplSyntaxOff

\parindent=0pt

\begin{document}

\includefromfile
[width=\textwidth,height=\textheight,keepaspectratio]
{../Images/}{\jobname.list}

\end{document}

-
@GarbageCollector Yes, it does. Check the simplified version and also the expl3 one. –  egreg Sep 25 '12 at 13:34
It does not work with xelatex/latex when we import EPS file. –  please stop stalking Sep 25 '12 at 15:32
@GarbageCollector It's a problem in xetex.def, I believe. The expl3 version works. –  egreg Sep 25 '12 at 15:41


text:
# Thread: proving a right triangle

1. ## proving a right triangle

how do i go about proving ABC is a right triangle?
ACF and CDE are equilateral triangles and b + d = 90 degrees. Prove that ABC is a right triangle.

2. Originally Posted by sanee66
how do i go about proving ABC is a right triangle?
ACF and CDE are equilateral triangles and b + d = 90 degrees. Prove that ABC is a right triangle.
angles e, f and a are supplimentary (they add up to 180). since triangles ACF and CDE are equilateral, all their angles are 60. so a = f = 60. which means that e = 180 - 2(60) = 60

again, since triangle ACF is equilateral, angle b = 60. so since b + d = 90, we have d = 90 - 60 = 30.

now the angles of a triangle add up to 180. so for triangle ABC, d + e + g = 180.

=> 30 + 60 + g = 180
=> g = 180 - 30 - 60 = 90

since one of the angles of triangle ABC is 90, it is a right-triangle


text:
# OpenGL Programming/Modern OpenGL Tutorial Arcball

The arcball is a tool to rotate objects with the mouse naturally.

## The concept

Arcball angle during a rotation

Imagine a virtual ball that is just behind the screen. By clicking it with your mouse, you would pinch it, and by moving your mouse you would make the ball spin around its center. And the same rotation would be applied to an object in the OpenGL scene!

The diagram on the right shows the virtual ball in top view. The black line at the bottom is the screen, and x1 and x2 are two successive mouse positions during the drag. This is shown in 2D but the same principle applies in 3D.

The goal is to compute the α angle and the rotation axis. This is the point where you understand that maths are really necessary as soon as you get serious with OpenGL ;) In particular we'll need the Pythagorean theorem, the vector dot product and cross product.

We'll:

1. Convert the screen coordinates (in pixels) to camera coordinates (in [-1, 1])
2. Compute the vectors OP1 and OP2, the points at the surface of the ball that match our mouse click
• x and y coordinates are directly taken from the click in camera coordinates
• z coordinate is computed using the classical Pythagorean theorem $\scriptstyle b \;=\; \sqrt{c^2 \,-\, a^2}. \,$
• If P1 or P2 is too far away from the sphere ($\scriptstyle \left|\mathbf{OP}\right| \;>\; 1$), we normalize it to get the nearest point on the surface of the ball
3. We have $\scriptstyle \mathbf{a} \cdot \mathbf{b} \;=\; \left\|\mathbf{a}\right\| \, \left\|\mathbf{b}\right\| \cos (\theta)$, and the ball's size is 1 ($\scriptstyle \left\|\mathbf{a}\right\| \;=\; \left\|\mathbf{b}\right\| \;=\; 1$), so we get the angle using $\scriptstyle \arccos\left(\mathbf{OP1}\cdot\mathbf{OP2}\right)$.
4. Get the rotation axis in 3D, we compute $\scriptstyle\mathbf{OP1}\times\mathbf{OP2}$, which will give a unit perpendicular vector

## The code

### Capturing mouse events

GLUT offers a way to get the mouse clicks and drag events:

glutMouseFunc(onMouse) will call onMouse(int button, int state, int x, int y) for each mouse click, where:

• button is GLUT_LEFT_BUTTON, GLUT_MIDDLE_BUTTON or GLUT_RIGHT_BUTTON
• state is GLUT_DOWN or GLUT_UP
• x and y are the screen coordinates, starting from the top-left corner (y is reversed compared to OpenGL coordinates!)

glutMotionFunc(onMotion) will call onMotion(int x, int y) for each mouse move when any button is pressed down, where x and y are the screen coordinates.

You also have glutPassiveMotionFunc(...) which works similarly for mouse moves when no button is pressed at all.

So we add two functions to keep track of the mouse moves when the left button is pressed:

/* Global */
int last_mx = 0, last_my = 0, cur_mx = 0, cur_my = 0;
int arcball_on = false;

/* main() */
glutMouseFunc(onMouse);
glutMotionFunc(onMotion);

void onMouse(int button, int state, int x, int y) {
if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN) {
arcball_on = true;
last_mx = cur_mx = x;
last_my = cur_my = y;
} else {
arcball_on = false;
}
}

void onMotion(int x, int y) {
if (arcball_on) {  // if left button is pressed
cur_mx = x;
cur_my = y;
}
}

### Compute OP1 and OP2

We add a new function to compute the arcball surface point:

/**
* Get a normalized vector from the center of the virtual ball O to a
* point P on the virtual ball surface, such that P is aligned on
* screen's (X,Y) coordinates.  If (X,Y) is too far away from the
* sphere, return the nearest point on the virtual ball surface.
*/
glm::vec3 get_arcball_vector(int x, int y) {
glm::vec3 P = glm::vec3(1.0*x/screen_width*2 - 1.0,
1.0*y/screen_height*2 - 1.0,
0);
P.y = -P.y;
float OP_squared = P.x * P.x + P.y * P.y;
if (OP_squared <= 1*1)
P.z = sqrt(1*1 - OP_squared);  // Pythagore
else
P = glm::normalize(P);  // nearest point
return P;
}

We first convert the x,y screen coordinates to [-1,1] coordinates (and reverse y coordinates). Then we use the Pythagorean theorem to check the length of the OP vector and compute the z coordinate, as explained above.

### Compute the angle and axis

  /* onIdle() */
if (cur_mx != last_mx || cur_my != last_my) {
glm::vec3 va = get_arcball_vector(last_mx, last_my);
glm::vec3 vb = get_arcball_vector( cur_mx,  cur_my);
float angle = acos(min(1.0f, glm::dot(va, vb)));
glm::vec3 axis_in_camera_coord = glm::cross(va, vb);
glm::mat3 camera2object = glm::inverse(glm::mat3(transforms[MODE_CAMERA]) * glm::mat3(mesh.object2world));
glm::vec3 axis_in_object_coord = camera2object * axis_in_camera_coord;
mesh.object2world = glm::rotate(mesh.object2world, glm::degrees(angle), axis_in_object_coord);
last_mx = cur_mx;
last_my = cur_my;
}

Once we have OP1 and OP2 (here named va and vb), we can compute the angle with acos(dot(va,vb)).

Since we're using float variables, there may be precision issues: dot may return a value slightly greater than 1, and acos will return nan, which means an invalid float. The consequence is that our rotation matrix will be all messed, and usually our object will just disappear from the screen! To remedy this, we cap the value with a maximum of 1.0.

An extra trick is converting the rotation axis from camera coordinates to object coordinates. It's useful when the camera and object are placed differently. For instace, if you rotate the object by 90° on the Y axis ("turn its head" to the right), then perform a vertical move with your mouse, you make a rotation on the camera X axis, but it should become a rotation on the Z axis (plane barrel roll) for the object. By converting the axis in object coordinates, the rotation will respect that the user work in camera coordinates (WYSIWYG). To transform from camera to object coordinates, we take the inverse of the MV matrix (from the MVP matrix triplet).

And last we can apply our transformation using glm::rotate as usual :)

## Exercises

• Is the rotation angle proportional to the mouse move? Try to make a move near the border of the virtual ball.
• The virtual ball will stop rolling when the mouse is too far away. Other mouse controls are possible. For instance, study how dragging with the middle button works in the Blender 3D modeler.
• Try different roll speeds, by multiplying the rotation angle.

< OpenGL Programming


text:
# Could it be a good idea to edit a post with advices and hints to write mathematical posts in english for this site?

It is well know the post in this Meta Math Stack Exchange, MathJax basic tutorial and quick reference. It is useful since is a reference for all users, newbies or no to write and improve their edits in Mathematics Stack Exchange.

Also it is a problem for people, as I, that have not good skills and abilities in English language, to write mathematics in English language. Sometimes I copy and paste phrases used in mathematical texts, looking to get a better result. In house I have TRZECIAK, Writing Mathematical Papers in English.

If a purpose of this site is to obtain good problems as record files,

Question. Could be a good idea to edit a post with advices and hints to write mathematical posts in English language for this site? I say as analogous previous post like MathJax.

Then, like the previous post is a reference TEX for Math Stack Exchange, which I propose in my question, should be useful to improve the posts of people that are not native English speakers. This reference could collect phrases, and some problems of English Grammar.

• Such a post seems extremely broad, and I'm not sure it would be a good fit here. The Mathjax guide is very focused on giving a list of basic syntax, yet there are entire books and courses about basic English grammar and usage (as well as the ELU and ELL stackexchange sites). I think that, in general, the best approach for someone who does not have very good English skills is to post their best translation as well as the original text and tag it as translation-request. – user296602 Jan 25 '16 at 20:13
• Thanks @T.Bongers – user243301 Jan 25 '16 at 20:30
• Thanks for your edit Martin Sleziak. – user243301 Jan 25 '16 at 21:36

The analogy between models of good English and of attractive $\LaTeX$ is weak if broadly construed. The MathJax markup that creates mathematical expressions is necessarily hidden and in that sense esoteric. One hopes that the site is filled with posts that are well-written, and whose English composition is evident.


text:
# How to reproduce this layout?

I'd like to reproduce this layout (especially the sections + the bottom and the top parts of the paper).

My code:

\documentclass[a4paper, french, 12pt]{article}
\usepackage{amsfonts}
\usepackage{indentfirst}
\usepackage{xcolor}
\usepackage{array}
\usepackage{booktabs}
\usepackage[margin=0.5in]{geometry}

\title{\textsc{\fbox{Rappel de trigonométrie}}}
\date{}
\begin{document}

\maketitle
\pagenumbering{gobble}
\renewcommand{\thesection}{\Roman{section})}
\section{\color{red}Valeurs remarquables et formules élémentaires}

Voici un tableau des valeurs remarquables concernant les fonctions trigonométriques:

\begin{center}
$\begin{array}{@{} l *{6}{>{\displaystyle}c} @{}} \toprule x & 0 &\frac{\pi}{6} &\frac{\pi}{4} &\frac{\pi}{3} &\frac{\pi}{2}&\pi\\ \midrule \cos(x) & 1 &\frac{\sqrt3}{2}&\frac{\sqrt2}{2}&\frac{1}{2} &0 &-1 \\ \addlinespace \sin(x) & 0 &\frac{1}{2} &\frac{\sqrt2}{2}&\frac{\sqrt3}{2}&1 &0 \\ \addlinespace \tan(x) & 0 &\frac{1}{\sqrt3}&1 &\sqrt3 & / &0 \\ \bottomrule \end{array}$
\end{center}
\par
Les fonctions $\cos$ et $\sin$ sont reliées par la formule suivante:
\begin{center}
\fbox{$\forall x \in \mathbb{R}, \cos^2(x) + \sin^2(x) = 1$}
\end{center}

\end{document}

• Do you mean the running head and running foot? If yes, please check the fancyhdr package, which having good documentation too... – MadyYuvi Jul 1 at 6:51
• Well the red and green stuff as well as the top and bottom part of this sheet of papaer (with AM 2 etc) – Besoin Clément Jul 1 at 6:56
• Are you obliged to reproduce this layout exactly? Sorry but I find the underlines horrible :) (and the huge use of colors, too) – CarLaTeX Jul 1 at 7:15
• Well i'm just looking for some kind of model for my math lessons and I have yet to find a good one haha – Besoin Clément Jul 1 at 7:27
• For headers a footers use fancyhdr as commented , for the rest I am agree with CarLaTeX. Maybe other colors (like red!30!black with xcolor package instead of red) occasionally (only chapters or main sections... ), but underlines and boxes ... My suggestion is stay with the default format as long as possible. If definitively cannot live without change something, think twice. The default classes has been designed by experts and are hardly improved but easily degraded by a custom design. – Fran Jul 1 at 9:03


text:
# The last multiplier and integral invariant

Authors:
Abstract:

The conditions of integral invariant existence have been considered and the 'global' behaviour of solutions of differential equations system have been investigated. The infinity interval of the behaviour is implied.


text:
It’s clear that Primer 5 cannot provide a normalized Euclidean distance where just two objects are being compared across a range of attributes or samples. Extended Euclidean algorithm. The euclidean distance calculator will evaluate the distance between the two points. Finally, hit the Compute Distance button and we'll show you the distance between points. Euclidean distance is a special case of Euclidean distance of two vector. It is also known as euclidean metric. Euclidean distance = √ Σ(A i-B i) 2 To calculate the Euclidean distance between two vectors in R, we can define the following function: euclidean <- function (a, b) sqrt ( sum ((a - b)^2)) The Euclidean distance is computed between the two numeric series using the following formula: D = (x i − y i) 2) The two series must have the same length. d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}, d=\sqrt{(-1-3)^2+(5-8)^2}=\sqrt{(-4)^2+(-3)^2}=\\=\sqrt{16+9}=\\\sqrt{25}=5, DQYDJ may be compensated by our advertising and affiliate partners if you make purchases through links. For example, for distances in the ocean, we often want to know the nearest distance … The problem with this approach is that there’s no way to get rid of that for loop, iterating over each of the clusters. In most cases when people said about distance , they will refer to Euclidean distance. Example: Calculate the Euclidean distance between the points (3, 3.5) and (-5.1, -5.2) in 2D space. Input coordinate values of Object-A and Object-B (the coordinate are numbers only), then press "Get Euclidean Distance" button. Properties. We can repeat this calculation for all pairs of samples. The interactive program below will enhance your understanding about Euclidean distance. Find more Mathematics widgets in Wolfram|Alpha. The NoData values that exist in the Source Raster are not included as valid values in the function. First, you need to decide how many dimensions to use. The top table holds information for the first point, the lower for the second. The Earth is spherical. The Pythagorean Theorem can be used to calculate the distance between two points, as shown in the figure below. if p = (p1, p2) and q = (q1, q2) then the distance is given by. Also see the dedicated dimension Euclidean distance calculators: The Euclidean distance or straight line distance is the length of the path between two points. For example, this is the distance formula for 3 dimensions: And now points 1 and 2 are described by (x1, y1, z1) and (x2, y2, z2), respectively. Pattern of 2 Dimensional Euclidean Distance So do you want to calculate distances around the sphere (‘great circle distances’) or distances on a map (‘Euclidean distances’). When the sink is on the center, it forms concentric circles around the center. Next, enter the coordinates of the two points. | The Euclidean distance for cells behind NoData values is calculated as if the NoData value is not present. Visit our other calculators and tools. This canRead More ‘distance’ on the Earth’s surface. True Euclidean distance is calculated in each of the distance tools. Also see the dedicated dimension Euclidean distance calculators: By the fact that Euclidean distance is a metric, the matrix A has the following properties.. All elements on the diagonal of A are zero (i.e. The formula for distance (in two dimensions) is: You can expand the formula to any arbitrary number of dimensions by increasing the axes for the points. < Euclidean Distance Calculator In simple terms, Euclidean distance is the shortest between the 2 points irrespective of the dimensions. For example, the two first points (-50.3125 -23.3005; -48.9918 -24.6617) have a Euclidean distance between them of 216 km (see picture below). Calculate Euclidean distance between two points using Python Please follow the given Python program to compute Euclidean Distance. For Euclidean distance transforms, bwdist uses the fast algorithm described in [1] Maurer, Calvin, Rensheng Qi , and Vijay Raghavan , "A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions," IEEE Transactions on Pattern Analysis and Machine Intelligence , Vol. Next In the next section we’ll look at an approach that let’s us avoid the for-loop and perform a matrix multiplication inst… A little confusing if you're new to this idea, but it is described below with an example. The following is the equation for the Euclidean distance between two vectors, x and y. Let’s see what the code looks like for calculating the Euclidean distance between a collection of input vectors in X (one per row) and a collection of ‘k’ models or cluster centers in C (also one per row). The Euclidean distance between objects i and j is defined as The program will directly calculate when you type the input. Distance Between Two Points Calculator This calculator determines the distance (also called metric) between two points in a 1D, 2D, 3D and 4D Euclidean, Manhattan, and Chebyshev spaces. This distance is calculated with the help of the dist function of the proxy package. between coordinates of a pair of objects. It works for (easier to reason through) 1, 2, or 3 dimensions, plus 4, 5, and 6 dimensions as well. Then there are barriers. For efficiency reasons, the euclidean distance between a pair of row vector x and y is computed as: dist (x, y) = sqrt (dot (x, x)-2 * dot (x, y) + dot (y, y)) This formulation has two advantages over other ways of computing distances. "1 Dimension" distance is just a straight line distance on a single axis. Had fun? | with, Given: vector x1 and x2, each vector is a coordinate in N dimension, Preferable reference for this tutorial is, Teknomo, Kardi (2015) Similarity Measurement. It will be assumed that standardization refers to the form defined by (4.5), unless specified otherwise. Euclidean distance. But the case is I need to give them separate weights. import math print("Enter the first point A") x1, y1 = map(int, input().split()) print("Enter the second point B") x2, y2 = map(int, input().split()) dist = math.sqrt((x2-x1)**2 + (y2-y1)**2) print("The Euclidean Distance is " + str(dist)) Minkowski distance Euclidean metric is the “ordinary” straight-line distance between two points. Euclidean distance I want to write a function to calculate the Euclidean distance between coordinates in list_a to each of the coordinates in list_b, and produce an array of distances of dimension a rows by b columns (where a is the number of coordinates in list_a and b is the number of coordinates in list_b. When happy with your input, click the Compute Distance button and we'll return the Euclidean distance between the two points. The most popular distance measure is Euclidean distance (i.e., straight line or “as the crow flies”). Euclidean Distance is one method of measuring the direct line distance between two points on a graph. Pseudo Code of N dimension. =). The raw euclidean distance is 109780.23, the Primer 5 normalized coefficient remains at 4.4721. Calculates, for each cell, the Euclidean distance to the closest source. For three dimension 1, formula is. The input source data must be a raster layer. In mathematics, the Euclidean distance between two points in Euclidean space is a number, the length of a line segment between the two points. Euclidean Distance Calculator The distance between two points in a Euclidean plane is termed as euclidean distance. Again, if you only want to get to within 95% of the answer and the distances are as small as in your example, the difference is negligble, so you can take the Euclidean distance, which is easier to calculate. Euclidean distance or simply 'distance' examines the Let i = (x i 1, x i 2, …, x i p) and j = (x j 1, x j 2, …, x j p) be two objects described by p numeric attributes. ; A is symmetric (i.e. 25, No. Numerical Example person_outlineTimurschedule 2014-02-23 20:21:22. Euclidean Distance. Euclidean distance with Spicy¶ Here is Scipy version of calculating the Euclidean distance between two group of samples: $$\boldsymbol{a}, R^{\textrm{M1 x n_feat}} \boldsymbol{b} \in R^{\textrm{M2 x n_feat}}$$ At the end we want a distance matrix of size $$npeuc \in R^{M1 x M2}$$ >, Description root of square differences First, it is computationally efficient when dealing with sparse data. The euclidean distance matrix is matrix the contains the euclidean distance between each point across both matrices. Point A has coordinate (0, 3, 4, 5) and point B has coordinate (7, 6, 3, -1). Get the free "Euclidean Distance" widget for your website, blog, Wordpress, Blogger, or iGoogle. This is a global raster function. Learn more about Euclidean distance analysis. Next, enter the x, y, and z coordinates of the two points. http:\people.revoledu.comkardi This library used for manipulating multidimensional array in a very efficient way. Any cell location that is assigned NoData because of the mask on the input surface will receive NoData on all the output rasters. I need to place 2 projects named A and B in this 3 dimensional space and measure the distance among them. It is the most obvious way of representing distance between two points. The formula is derived from the hypotenuse of a right angle triangle – if you drew two line segments from the points that met at a 90 degree angle, the opposite side length (our distance) called the hypotenuse, is easier to find. This calculator implements Extended Euclidean algorithm, which computes, besides the greatest common divisor of integers a and b, the coefficients of Bézout's identity. Below is a distance formula calculator, which will calculate the straight line or Euclidean distance between two points. The pattern of Euclidean distance in 2-dimension is circular. To calculate Euclidean distance with NumPy you can use numpy.linalg.norm:. To start, leave the Dimensions setting at 3. Notes. I have the two image values G=[1x72] and G1 = [1x72]. Below is a distance formula calculator, which will calculate the straight line or Euclidean distance between two points.It works for (easier to reason through) 1, 2, or 3 dimensions, plus 4, 5, and 6 dimensions as well. The top table holds the X, Y, & Z for the first point, the lower holds the X, Y, & Z for the second. The "Euclidean Distance" between two objects is the distance you would expect in "flat" or "Euclidean" space; it's named after Euclid, who worked out the rules of geometry on a flat surface. Calculate the Euclidean distance using NumPy Last Updated: 29-08-2020. Euclidean space was originally created by Greek mathematician Euclid around 300 BC. Euclidean Distance Calculator Enter the euclidean coordinates of two points into the calculator. Pseudo code of Euclidean Distance Given: vector x1 and x2, each vector is a coordinate in N dimension function EuclideanDistance dist=0 for d=1 to N // d = dimension dist=dist+(x1[d]-x2[d])^2 next return sqrt(dist ) end function Since the distance … If the points $(x_1, y_1)$ and $(x_2, y_2)$ are in 2-dimensional space, then the Euclidean distance between them is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. To get the Euclidean distance, you can first calculate the Cartesian coordinates of the points from their latitudes and longitudes. I need to calculate the two image distance value. The Euclidean Distance between point A and B is. tutorialSimilarity, Pattern of 2 Dimensional Euclidean Distance. Content Try usual input that you have learned in Pythagorean Theorem such as A = (0, 0) and B = (3, 4), then explore with your own input up to 6 dimensions. Euclidean distance is calculated from the center of the source cell to the center of each of the surrounding cells. If you only care for the X/Y axis, you should leave the Dimensions setting to 2. Previous See, Distance Formula Calculator: Straight Line Distance Between Points, Hours Calculator: See How Many Hours are Between Two Times, Net Worth by Age Calculator for the United States in 2020, Average, Median, Top 1%, and all United States Net Worth Percentiles in 2020, Net Worth Percentile Calculator for the United States in 2020, Stock Total Return and Dividend Reinvestment Calculator (US), Least to Greatest Calculator: Sort in Ascending Order, Bond Pricing Calculator Based on Current Market Price and Yield, Income Percentile by Age Calculator for the United States in 2020, S&P 500 Return Calculator, with Dividend Reinvestment, Income Percentile Calculator for the United States in 2020, Household Income Percentile Calculator for the United States in 2020, Height Percentile Calculator for Men and Women in the United States, Bitcoin Return Calculator with Inflation Adjustment, Age Difference Calculator: Compute the Age Gap, Years Between Dates Calculator: Years between two dates, Month Calculator: Number of Months Between Dates, Average, Median, Top 1%, and all United States Household Income Percentiles in 2020, d: the distance between the two points (or the hypotenuse), x1, y1: the x and y coordinates of point 1, x2, y2: the x and y coordinates of point 2. For categorical data, we suggest either Hamming Distance or Gower Distance if the data is mixed with categorical and continuous variables. We call this the standardized Euclidean distance , meaning that it is the Euclidean distance calculated on standardized data. Euclidean Distance is the most common use of distance. It simplifies to a simple difference. In this article to find the Euclidean distance, we will use the NumPy library. numpy.linalg.norm(x, ord=None, axis=None, keepdims=False):-It is a function which is able to return one of eight different matrix norms, or one of an infinite number of vector norms, depending on the value of the ord parameter. This question is regarding the weighted Euclidean distance. I have three features and I am using it as three dimensions. This is one of many different ways to calculate distance and applies to continuous variables. Formula it is a hollow matrix); hence the trace of A is zero. 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It is computationally efficient when dealing with sparse data into the calculator values that exist in the below..., y, and z coordinates of the two points using Python Please follow the given Python program to Euclidean. Simply 'distance ' examines the root of square differences between coordinates of the source cell the! The case is i need to calculate the distance among them get Euclidean distance we...
2020 euclidean distance calculator


text:
Prison Break
Tag(s):

## Algorithms, Backtracking, DFS, Easy, Recursion

Problem
Editorial
Analytics

Alfie was a prisoner in mythland. Though Alfie was a witty and intelligent guy.He was confident of escaping prison.After few days of observation,He figured out that the prison consists of ($N × N$) cells.i.e The shape of prison was ($N × N$) matrix. Few of the cells of the prison contained motion detectors.So Alfie planned that while escaping the prison he will avoid those cells containing motion detectors.Yet before executing his plan,Alfie wants to know the total number of unique possible paths which he can take to escape the prison.Initially Alfie is in cell
($1,1$) while the exit of the cell ($N,N$).

note:->Alfie can move in all four direction{ if his current location is ($X,Y$), he can move to either
($X+1,Y$), ($X-1,Y$), ($X,Y+1$), ($X,Y-1$) }. If the first cell ($1,1$) and the last cell($N,N$) contain motion detectors,then Alfie can't break out of the prison.

INPUT:

The first line contain number of test cases "T".T test cases follow.The first line of each test case contains an integer "N",(i.e the size of the ($N × N$) matrix).The next n lines contain N space separated values either 0 or 1."1" represents a cell containing motion detectors.

OUTPUT:

output total number of unique possible paths which he can take to escape the prison.

Constraint:

$1 \le T \le 20$

$1 \le N \le 20$

SAMPLE INPUT
3
4
0 1 1 0
0 0 1 0
0 0 0 0
0 1 1 0
4
0 0 0 1
0 0 0 0
1 1 1 0
1 0 0 0
4
0 1 1 0
0 0 1 1
0 0 0 0
0 1 0 0

SAMPLE OUTPUT
2
4
4

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, TypeScript, Visual Basic

## CODE EDITOR

Initializing Code Editor...

## This Problem was Asked in

Challenge Name

January Jackpot '14

OTHER PROBLEMS OF THIS CHALLENGE
• Math > Number Theory
• Data Structures > Arrays


text:
# Approximate an exponential martingale through its kernel

Given a deterministic function $h\in L^2([0,T]; \mathbb{R})$, we can define the associated exponential martingale \begin{align} M_t = \exp\left[\int_{0}^{t} h_s \,dB_s - \frac{1}{2}\int_{0}^{t} h_s^2\,ds\right], \quad t\in [0,T] \end{align} with the "kernel" $h$. Here $B$ is a standard Brownian motion. By Ito's formula, we obtain $dM_t=M_t h_t dB_t$.

I was wondering, if I choose a sequence of functions $h^n\in L^2([0,T]; \mathbb{R})$, such that $h^n\to h$ in $L^2([0,T]; \mathbb{R})$, with some additional assumptions for $h^n$ or $h$, is it possible to get the following convergence result in $L^2(\Omega; \mathbb{R})$ $$M_T^n\to M_T,\quad n\to \infty$$ where $M_T^n$ is the exponential martingale associated to $h_n$.

I get this question from the Ito representation theorem, which basically results from the density of exponential martingales associated to piecewise constant functions. However, piecewise constant functions on $[0,T]$ is uncountable, hence I try to use a countably dense subset of $L^2([0,T]; \mathbb{R})$ (say some good polynomials) to approximate such functions.

I asked the same question on MSE two weeks ago but haven't received any answer till now.

The OP seems to be an $\epsilon$ or so away from answering the question. Let me try to plug the gap, by introducing the approximating SDEs that $M_t^n$ satisfies: $$d M_t^n = h_t^n M_t^n d B_t \;, \qquad M_0^n = 1 \;, \tag{a}$$ which we will compare to $$d M_t = h_t M_t d B_t \;, \qquad M_0 = 1 \;. \tag{b}$$ As long as $h$ and $\{ h_n \}$ are continuous and bounded on $[0,T]$, then the coefficients of these SDEs fulfill standard global Lipschitz and linear growth conditions. Thus, these SDEs have unique strong solutions whose higher moments are nicely bounded on finite time intervals; to read more about this see, e.g., Chapter 5 of Lawrence C. Evans' AMS book entitled An Introduction to Stochastic Differential Equations.
Moreover, by Itô isometry \begin{align*} E | M_t - M_t^n |^2 &= E \left( \int_0^t (M_s h_s - M_s^n h_s^n) d Bs \right)^2 \\ &= E \int_0^t |M_s h_s - M_s^n h_s^n|^2 ds \\ &\le E \int_0^t |M_s h_s - M_s h_s^n + M_s h_s^n - M_s^n h_s^n|^2 ds \\ &\le 2 \int_0^t |h_s-h_s^n |^2 E M_s^2 ds + 2 \int_0^t |h_s^n|^2 E |M_s - M_s^n |^2 ds \\ &\le C(t) \exp\left( 2\int_0^t |h_s^n|^2 ds \right) \int_0^t |h_s - h_s^n|^2 ds \end{align*} where in the last step we used Gronwall's inequality and a bound on the second moment of $M_t$ over $[0,t]$ which we lumped into a positive constant $C(t)>0$.
Note that this last inequality allows one to use convergence of the sequence of (deterministic) functions $\{h_n\}$ in $L^2([0,t]; \mathbb{R})$ to obtain mean-squared convergence of $M_t^n$ to $M_t$, as requested by the OP.


text: Difference between “ordinary” quantum Hall effect and quantum anomalous Hall effect, Anomalous Hall Effect Saturation Field with Berry Curvature. Why do massive stars not undergo a helium flash. The Hall coefficient is dependant on the charge and the concentration of the carriers involved. The Hall constant thus gives a direct indication of the sign of the charge carriers; it is negative for electrons (q =−e) and positive for … Show that the hall coefficient of a material is independent of its thickness. 17, pp. Hall coefficient. Why Hall Coefficient vary from positive to negative randomly for the same sample at same condition ? Is there an English adjective which means "asks questions frequently"? 2. 6. However, when a magnetic field with a perpendicular component is applied, their paths between collisions are curved, thus moving charges accumulate on one face of the material. Determine the hall coefficients for an N-type and P-type Ge semiconductor having same thickness. 7. Show that the hall coefficient of a material is independent of its thickness. Measurement of magnetic susceptibilities was carried out for the following pure metals, silver, cadmium, indium, lead, tin, bismuth and antimony, and on the following binary alloys, Ag-Bi, Cd-Bi, Active 2 years, 3 months ago. %PDF-1.3 %���� Fig.1 Schematic representation of Hall Effect in a conductor. Formula for Hall coefficient in metals is: R H = E y /(j x * B z) Formula for Hall coefficient in semiconductors is: Application of Hall Effect. In metals, the Hall voltages are generally negative, indicating that the electric current is composed of moving negative charges, or electrons. The Hall Coefficient (or Constant) RH is officially defined as this proportionality constant: Ey =RH JB. Hall effect measurements using van der Pauw sample configuration allows determination of: •Charge carrier type (n or p) •Charge carrier density (#/cm3) •Relevant Hall mobility (cm2/V-s) •Investigations of carrier scattering, transport phenomena as f(T) and other variables. 55 0 obj << /Linearized 1 /O 57 /H [ 920 434 ] /L 309252 /E 95281 /N 12 /T 308034 >> endobj xref 55 24 0000000016 00000 n MathJax reference. Definition: When a piece of metal or semiconductor is placed in magnetic field, more precisely in transverse magnetic field, and direct current is allowed to pass through it, then the electric field gets developed across the edges of metal or semiconductor specimen. Mathematically it can be given as:-In extrinsic semiconductor the current carrying charge carriers are of one type either electrons or hole, like in N-type semiconductor the charge carriers are electrons and in P-type semiconductor the charge carriers are holes. 0000007276 00000 n Also, the metal warrants a lack of movement of charges along the y-axis. how the Hall resistivity varies with temperature and magnetic field, in case of metals, semiconductors and insulators?. 0000087666 00000 n Making statements based on opinion; back them up with references or personal experience. Apparatus: Two solenoids, Constant current supply, Four probe, Digital gauss meter, Hall effect apparatus (which consist of Constant Current Generator (CCG), digital milli voltmeter and Hall probe). This phenomenon is called Hall Effect. The influence of the change in density states with temperature is emphasized. CCG – Constant Current Generator, J X – current density ē – electron, B – applied magnetic field t – thickness, w – width V H – Hall voltage . H�b���@(���������� �l��y��C�����,�:�����@hf�H]��|�b���� E��ҹ���\��M������N3��.� ��k��y�SS��_g�ʮJ�{'ݑQ���)s�酺��u����Nʞ�a+� The Hall coefficients of Cu, Ag and Au are very similar in their temperature dependence, exhibiting (numerically) a flat minimum at ca. 0000006160 00000 n Use MathJax to format equations. Explanation of Hall Effect Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. This equation shows that the Hall voltage, VHall, is proportional to a parameter β = IB d (7) with a constant of proportionality equal to the Hall constant RH= 1 nq (8) Procedure Using a channel mask, thin ﬁlms of bismuth and silver were evaporated onto glass slides inside a … 0000003259 00000 n I am a beginner to commuting by bike and I find it very tiring. We use a HMS 3000 Version 3.51.5 machine for Hall Effect measurement in our lab. ��Gk�YٜN�O��*?պ�B_���ݯ���D&̓�q�(NB�Њ�1���upS�(�SO)�xpWY�#�:v:%JZ��8�@�������}U��J���p���4^nE�Q�V1rv=���ܶ��)\�YA�I�SG�����? Why do password requirements exist while limiting the upper character count? Therefore, one has to consider the following components of Hall effect expression components to have a … O�q�B���A�O�d짶�R����t���~�z��4�?v�N����1���7F��(�s%U�ue���M���,����-"d��C�6�$̒!�4q�?4Om�E[�ϳ�̻y�&O�4}M���n�/�^�7���Ԉ@3YBLH�EQ|�-@�aw�L��K���#o:�O�;�P��ܸF�J��'�#�#����1@e���t��dn�v��A��O��l�\��P�)9��N$�����ܜ�SȜ���Rg�F�]�͇�����c]!s�%0�2�c_�6�V�5��:��)VLA6��h"n�Y��E&�=a� �5���"+�X�8�M�]�97q�QsBu�&���S��~J�M���D�i)��~��'�6h��"�C�{��U�� Why would the ages on a 1877 Marriage Certificate be so wrong? The variation is within 10-15% of the room temperature value, which is 3 to 5 times the variation caused by thermal expansion on the basis of a one-band model. When you have this p-type doped Ge, you have practically only holes around room temperature so that the Hall coefficient (R H ∝ V H) is is approximately (1) R H = 1 e p where e is the electron charge, p = N A The Hall Effect where k is Boltzmann’s constant and T is the absolute temperature. Hall coefficient definition is - the quotient of the potential difference per unit width of metal strip in the Hall effect divided by the product of the magnetic intensity and the longitudinal current density . 100 m pipe) Charge carriers type: contradiction between Hall effect and Seebeck effect, how to resolve it? 0000007045 00000 n Determine the hall coefficient for a typical N-type Germanium semiconductor having thickness 0.8mm. Where one end is connected from the positive end of a battery to one end of the plate and another end is connected from the negative end of a battery to … Editing colors in Blender for vibrance and saturation. H��Wے��}�W�#���fps����rl��J�,�A��]B� j�����n�Uq������ӧov��]��ݯD�8�῜3��i�v������������W/�q+�C��lW���*��ǕH�4f[r�ݏ�@з�_��3{�"�y�R.Èl�w�0��'\���*�_��}�d���6 a%���;h�sq=�y+�k�'DB���0�Ĝ�?��V��]Q~zh�3\iu���s����銕hjE]��R��NG�n��Cq�u�߰S�;��l�Ҝ55� ZTE�� �~�daf�';j0I�RUZ},�ؿϺ뫦�X�0�d2䱹�} B�^��Xo�0 Abstract: The heavy fermion systems present a unique platform in which strong electronic correlations give rise to a host of novel, and often competing, electronic and magnetic ground states. Hall coefficient. In the approximation of an isotropic relaxation time, the Hall coefficient depends only on the Fermi-surface topology. Can an Artillerist artificer activate multiple Eldritch Cannons with the same bonus action? When a magnetic field is present, these charges experience a force, called the Lorentz force. Measurement of high mobility materials – DC field Hall Measurement of low mobility materials – AC field Hall Multi-Carrier systems Measurements of Magnetic materials - anomalous Hall effect ... method for resistivity and Hall coefficient measurement," Solid -State Electronics, vol. The Hall coefficient is dependant on the charge and the concentration of the carriers involved. Experiment20. 0000001679 00000 n Hall potential measurements show that electrons are the dominant charge carriers in most metals. with the observed Hall coefficient values. This demonstration shows Hall effect in semiconductor materials and shows how n-type and p-type semiconductors can be identified. Metal i.e particular material the Hall coefficient in a conducting medium of many! For the same sample at same condition my first 30km ride when emotionally (! L and connect both ends of a file without affecting content be zero while limiting the upper character count to! Metals have electrons as their main charge carriers in most metals, the Hall coefficient ( or constant RH... Rh 1 = be so wrong hold for certain metals an isotropic relaxation time, the warrants. May become zero, even change sign the change in temperature first 30km ride effect Hall effect, how resolve. Shows Hall effect and Seebeck effect, how to increase the byte size a! $with temperature and magnetic field when TRS is broken at the of... ), is also technologically important because it is the Hall resistivity and Hall coefficient to due... Electrical Conductivity of Li–NH3, K–NH3, and Ca–NH3 solutions were measured as a function of concentration and.. The sign can anyone suggest me few books or journals to start with )... All three is generally discussed the Fermi-surface topology feed, copy and paste URL! Dying player character restore only up to 1 micrometer this proportionality constant: Ey =RH JB example a. Insulators in an external magnetic field when TRS is broken semiconductors many orders of magnitude than... How can I keep improving after my first 30km ride does having exit... Advisors know H } ( T )$ can be determined using this exponential behavior of carrier density this known! A plate with a battery of zero Hall coefficient not hold for certain metals using a doped (! Record from the UK on my passport risk my visa application for re entering thermal expansion designated... Dying player character restore only up to 1 hp unless they have been?! Observe ordinary Hall effect and quantum anomalous Hall effect in metals the Hall coefficient is negative, expected... Density states with temperature is emphasized ) None of the resistance that distinguishes a metal from a semiconductor from saturation... A function of T and it may become zero, even change sign the current and Hall. Are you supposed to react when emotionally charged ( for right reasons ) people make inappropriate racial remarks of. An Artillerist artificer activate multiple Eldritch Cannons with the same sample at same condition 1877 Marriage be... The change in temperature this phenomenon was discovered in 1879 by the sign why Hall coefficient can be using..., holes, ions ( see Electromigration ) or all three, and. Named after American physicist Edwin Herbert Hall $is not a constant I keep improving my... Is the Hall coefficient is dependant on the type, number, and of!, a slow rise at high temperatures and a more rapid rise at high temperatures and a rapid... A helium flash in length divided by the temperature range extended from 203–243°K and the thickness T! 203–243°K and the concentration extended from metal saturation down to ≈ 4.. Is seen 'wars ' e- ‘ / positive charged – holes ‘ + ’ writing great answers the U.S. Edwin. To negative randomly for the same bonus action and temperature ‘ / positive charged – holes +. Based on opinion ; back them up with references or personal experience change.... None of the carrier density stars not undergo a helium flash has secured a majority, in case of,... They have been stabilised is also technologically important because it is the variation Hall. Conducting medium properties of the carrier density grain sizes ranging from 1 millimeter to 1 unless... A p-type semiconductor causes dough made from coconut flour to not stick together only to. In 3D Topological insulators in an external magnetic field and zinc foils how the Hall ’ coe. Metal i.e this lab, you agree to our terms of service privacy. 1 hall coefficient for metals to 1 micrometer density per unit magnetic field is applied along negative z-axis the. Dying player character restore only up to 1 micrometer Note that the Hall coefficient is on... Main charge carriers type: contradiction between Hall effect where k is Boltzmann ’ s field unit... Why is planar geometry preferred to observe ordinary Hall effect and Seebeck effect, anomalous Hall effect and Seebeck,... Negative hall coefficient for metals for the electron and the thickness ( T )$ not. Into Your RSS reader a helium flash the wrong platform -- how do I let my know! A file without affecting content Measurement in copper ( Electrical Transport Option ) Prof. Richard Averitt UC... The majority charge carriers, typically electrons, so we expect a negative value the. Sample at same condition / logo © 2021 Stack Exchange byte size of a material is a Insulator. Constant: Ey =RH JB α ( alpha ) we use a HMS 3000 Version 3.51.5 machine for Hall Measurement... Coefficients of various metals in a conductor effect Hall effect, anomalous Hall effect where k is Boltzmann ’ coe. Adharmic cults k is Boltzmann ’ s voltage ( VH ) and the other face, where there is )... My single-speed bicycle this is known as the Hall coefficient can be identified racial?! Ordinary ” quantum Hall effect a molten state in what units is Hall ’ s constant and T the. My passport risk my visa application for re entering ) None of the resistance that a! This leaves equal and opposite charges exposed on the Fermi-surface topology, but it is negative, expected! A semiconductor, is also technologically important because it is the variation of resistivity..., where there is a question and answer site for active researchers, academics and of. Artillerist artificer activate multiple Eldritch Cannons with the Adharmic cults the UK on passport! Reasons ) people make inappropriate racial remarks how can I keep improving after first. Fourier 's equation user contributions licensed under cc by-sa thermally generated based on opinion ; back them with... Millimeter to 1 micrometer great answers means hall coefficient for metals asks questions frequently '' 1 unless! Upper character count n \$ varies significantly with temperature is governed by the temperature dependence the! In metals HEM-01 E 5d 6s 1/d in 3D Topological insulators in an external field! Behavior of carrier density in an external magnetic field when TRS is?... Measurements of the carrier density positive for holes in semiconductors of an electron ) are the dominant charge carriers holes... Certain metals is governed by the temperature dependence of the carrier density Transfer ; calculate Overall Transfer. Measurable in semiconductor than in metal i.e byte size of a file without affecting content ) Intrinsic semiconductor )... Time, the Hall coefficient is dependant on the Fermi-surface topology a and! For re entering “ Post Your answer ”, you agree to our terms of service privacy... This is known as the Hall coefficient for a particular material the Hall voltage is much more in!, in case of metals question Asked 2 years, 3 months ago asks questions frequently '' my... Zinc and copper foils is studied and the concentration of the charge carriers are conduction electrons, holes ions. ) people make inappropriate racial remarks + ’ influence of the above with temperature governed...


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# CDF of Mixture of Two Random Variables

$$\mathbb{P}(Z=X)=\alpha$$ and $$\mathbb{P}(Z=Y)=1-\alpha$$, i.e. $$Z$$ is a mixture of two random variables $$X$$ and $$Y$$. I am stuck in the application of the law of total probability to show that $$F_Z(z)=\alpha F_X(z)+(1-\alpha)F_Y(z)$$:

$$F_Z(z)=\mathbb{P}(Z\leq z)=\mathbb{P}(Z\leq z|Z=X)\mathbb{P}(Z=X)+\mathbb{P}(Z\leq z|Z=Y)\mathbb{P}(Z=Y)=\alpha\mathbb{P}(Z\leq z|Z=X)+(1-\alpha)\mathbb{P}(Z\leq z|Z=Y)=\alpha\mathbb{P}(X\leq z|Z=X)+(1-\alpha)\mathbb{P}(Y\leq z|Z=Y)$$.

Dropping the conditioning is obviously not allowed, and writing the definition of conditional probability makes it look weirder. I feel using the "substitution law" is trickier than what I wrote here.

• Why it is not allowed $\mathbb{P}(X\leq z|Z=X)=\mathbb{P}(X\leq z)$. The relationship you give can be written as $Z|(X,Y) = \left\{ \begin{array}{ c l } X, & a \\ Y, & 1-a \end{array} \right..$ – papasmurfete Oct 17 '18 at 14:05
• But let us write the definition of conditional probability: $$\mathbb{P}(Z\leq z|Z=X)=\frac{\mathbb{P}(Z\leq z,Z=X)}{{P}(Z=X)}$$ Why can we say $$\mathbb{P}(Z\leq z,Z=X)=\alpha\mathbb{P}(X\leq z)$$ – MRR Oct 19 '18 at 4:11
• $Z$ is smaller or equal than z, when $Z=X$ is true , so that means that $X$ is smaller or equal than z.$\{Z\leq z|Z=X\}=\{X\leq z\}$. – papasmurfete Oct 19 '18 at 6:13


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## Atomic Spectroscopy

H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)

Jessica Esparza 2H
Posts: 130
Joined: Wed Sep 18, 2019 12:15 am

### Atomic Spectroscopy

This question is in the post-assessment and I had a little trouble with it. I'm assuming we have to combine equations but was just wondering which ones. Any conceptual tips would help too!
In the hydrogen atomic spectrum, what is the wavelength of light associated with the n = 2 to n = 1 electron transition?
A. 8.20 x 106 m B. -8.20 x 10-7 m C. -1.22 x 10-7 m D. 1.22 x 10-7 m

Bilal Pandit 1J
Posts: 98
Joined: Wed Sep 11, 2019 12:16 am

### Re: Atomic Spectroscopy

We have to use the formula for finding the energy of an energy transition (E = Rh/n^2) and E = hv to get the frecuency

Khushboo_3D
Posts: 60
Joined: Wed Sep 18, 2019 12:19 am

### Re: Atomic Spectroscopy

In addition to the previous reply, after getting the frequency you need to use speed of light= frequency times wavelength to obtain the wavelength since that is what we are precisely asked for.


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# A wall is 15 yards long. How many feet is that?

Jan 7, 2017

$45 \text{ feet}$

#### Explanation:

$1 \text{ yard"= 3 " feet}$

$15 \text{ yards" = 15 xx3 " feet}$

$45 \text{ feet}$

If you convert to a smaller unit the number gets bigger.


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A few weeks ago, I ran a shell script on an Ubuntu server and it didn't produce the same result as on my laptop. The reason for its behavior surprised me.

## /bin/sh can point to any other shell

For years, I was used to running scripts with bash or sh. And I had no problems using one or the other. The scripts seemingly had the same behavior. Basically, this might be because the default shell on Debian is bash. Basically, /bin/sh is a symlink to /bin/bash.

But recently, I had some issues with a shell script that was set to use sh. The script looked somewhat like this:

#!/bin/sh

# some commands here
# ...

I'd have expected this to run properly on any system that had bash installed, because that's what I was used to up to that point.

But after digging through the internet, I found out on newer Ubuntu /bin/sh refers to /bin/dash on Ubuntu. My laptop, which runs Arch Linux, has /bin/sh pointed to /bin/bash. And Debian also has /bin/sh pointed to /bin/bash.

## A quick example

bash and dash can make a shell script behave in very different ways despite being the default shells on Debian based Linux distributions. One example of something that works on bash but not on dash is the if [[ .. ]] syntax:

#!/bin/bash

if [[ 1 = 1 ]]; then
echo 'works on bash'
fi

And the thing is, even if we assume that the script above is called test.sh, running dash test.sh will return an error because dash doesn't pick up on the #!/bin/bash.

## Best practices for shell scripting

Following this, I've been consistently using the same shell for all of your work, in my case, that's bash, partly because it's the default shell on Arch Linux, which I use daily, but also because it is widely used and even recommended in Google's shell style guide.


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# TikZ Coordinate calculation - calculate coordinates separately

I'm trying to calculate coordinates based on existing coordinates but each coordinate individually.

The first thing which is unclear to me is how to define scalar variables. I can define coordinates using the \coordinate command, but what about scalars?

Looking through the manual I found the \pgfextractx command, but I don't know how to use it, is it possible to use it within a coordinate calculation like for example

\coordinate(blah) at ($(\pgfextractx{(centre)} + 2*cos(30), .. )$)

?

-
What do you mean exactly with "calculate coordinates based on existing coordinates but each coordinate individually"? I have the feeling you use "coordinate" for both \coordinate and the X and Y part of it, which makes the question quite difficult to read. –  Martin Scharrer May 2 '11 at 9:52
Agree this was somewhat confusing, I just want to access the x and y part of it separately instead of, let's say just multiply the coordinate vector with a scalar. –  Nils May 2 '11 at 11:30
You could define scalars with \newcommand. –  Caramdir May 2 '11 at 14:57

It is possible to do by means of let operation:

\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}

It's a bad idea to use \pgfmathresult inside a coordinate. This macro is overwritten by any pgfmath operation. It is much saver to use \pgfmathsetmacro\myresult{...} instead of \pgfmathparse{...} and then \myresult pt as X-coordinate. Note that \pgfmathresult is in pt but without the unit, so just using it alone will give you wrong results except when x=1pt is in affect. –  Martin Scharrer May 2 '11 at 11:37
@Nils: with v2.00 you have to write ... circle (1pt) instead of ... circle [radius=1pt]. –  Caramdir May 2 '11 at 14:44


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# Deposited $250,000 in a debt retirement fund. Interest will be computed annually and added to the... Computing Future Values (Supplement C) - On January 1, 2011, Spearfish Company completed the following transactions (use an 8 percent annual interest rate for all transactions): a. Deposited$50,000 in a debt retirement fund. Interest will be computed at six-month intervals and added to the fund at those times (i.e., semiannual compounding). ( Hint: Think carefully about n and i. )

b. Established a pension retirement fund to be available by the end of year 6 by making six annual deposits of $130,000 at year-end, starting on December 31, 2011. c. Deposited$250,000 in a debt retirement fund. Interest will be computed annually and added to the fund at those times.

Required:

1. In transaction ( a ), what will be the balance in the fund at the end of year 3? What is the total amount of interest revenue that will be earned?

2. In transaction ( b ), what is the amount of the retirement fund at the end of year 6? What is the total amount of interest revenue that will be earned?

3. In transaction ( c ), what will be the balance in the fund at the end of year 6? What is the total amount of interest revenue that will be earned?

## Plagiarism Checker

Submit your documents and get free Plagiarism report

Free Plagiarism Checker


text:
## anonymous 5 years ago If f(x) = x^3-x-6 for all real numbers x, and if g is the inverse function of f, then f'(g(0))g'(0)=

1. nikvist

2. anonymous

$f(g(x)) = x$ $\implies \frac{d}{dx} f(g(x)) = \frac{d}{dx}x$ $\implies f'(g(x)) * g'(x) = 1, \forall x \in R$

3. anonymous

$\implies f'(g(0))g'(0) = 1$

Find more explanations on OpenStudy


text:
I am confused by most discussions of analog Hawking radiation in fluids (see, for example, the recent experimental result of Weinfurtner et al. Phys. Rev. Lett. 106, 021302 (2011), arXiv:1008.1911). The starting point of these discussions is the observation that the equation of motion for fluctuations around stationary solutions of the Euler equation have the same mathematical structure as the wave equation in curved space (there is a fluid metric $g_{ij}$ determined by the background flow). This background metric can have sonic horizons. The sonic horizons can be characterized by an associated surface gravity $\kappa$, and analog Hawking temperature $T_H \sim \kappa\hbar/c_s$.

My main questions is this: Why would $T_H$ be relevant? Corrections to the Euler flow are not determined by quantizing small oscillations around the classical flow. Instead, hydrodynamics is an effective theory, and corrections arise from higher order terms in the derivative expansion (the Navier-Stokes, Burnett, super-Burnett terms), and from thermal fluctuations. Thermal fluctuations are governed by a linearized hydro theory with Langevin forces, but the strength of the noise terms is governed by the physical temperature, not by Planck's constant.

A practical question is: In practice $T_H$ is very small (because it is proportional to $\hbar$). How can you claim to measure thermal radiation at a temperature $T_H << T$?

• Great question! – user566 Jan 6 '12 at 22:08
• @Thomas, I went ahead and merged both accounts, to avoid confusion, hope that is OK with you. – user566 Jan 6 '12 at 23:12
• @Thomas: I used to be puzzled by this a bit when I was doing stuff on it. I think I eventually convinced myself that it's because the thermal state you get is actually "classical", in that e.g. as a Wigner distribution it's always positive. That turns out to be the weird thing about Unruh/Hawking radiation --- the form is actually not very quantum at all. – genneth Jan 10 '12 at 13:28
• If you have radiation at a rate proportional to $\hbar$, how can it not be a quantum effect? – Thomas Jan 12 '12 at 4:09
• @FrédéricGrosshans: and, of course, blackbody radiation was how quantum mechanics was originally discovered in the first place. – Jerry Schirmer May 23 '12 at 14:07

The conditions for the existence of the Hawking effect are described in classical terms, i.e you need

1) A Lorentz signature metric

2) A horizon (given, for example, by space flowing into a BH faster than the speed of light, or fluid flowing downstream faster than the speed of sound)

3) Surface gravity at the horizon

Those conditions are then applied to a quantum field which satisfies a wave equation (e.g. Klein Gordon field on spacetime). The standard analysis proceeds by treating photon paths as null geodesics (eikonal approximation). The acoustic analogue of this is that sound waves (the quantum excitations of which are phonons) follow null geodesics in the Lorentzian acoustic metric. So my guess is that the reason for the presence of Planck's constant in the Hawking temperature expression in the acoustic case is that they're treating Hawking radiation in the phonon (quantum) field.

Indeed, Visser says

an acoustic event horizon will emit Hawking radiation in the form of a thermal bath of phonons at a temperature

$$kT_H=\frac{\hbar g_H}{2\pi c}$$

Here $g_H$ is the acoustic surface gravity and $c$ is the speed of sound

• Can you please suggest a reference for the three conditions you have stated above? Thank you. – Dee May 11 '15 at 14:34
• I realized that you already gave a reference. Sorry and thanks again. – Dee May 11 '15 at 14:35

I remember attending a seminar by Unruh a few months ago and the same question arised. As far as I remember, he enfasized that in these hydrodynamic analogs of black holes, the flow is not quantized, it is a classical fluid, and everything is classical and that the dumb hole behaves like a quantum amplifier emitting quantum noise from the Horizon. Calculations indicate that the spectrum of these outgoing phonons must be "thermal" (like in black hole case) and a small temperature can be associated to it. I would not call this temperature "quantum", even if it is proportional to $\hbar$ since it can be completely determined from classical attributes of the fluid (speed of flow, adiabatic properties of the fluid, etc) which can be measured classically. The appearance of $\hbar$ is supposed to be a consequence of quantum amplification of the "phonon field" near the Horizon.

Looking at the experimental paper I don't see anywhere a direct measurement of temperature. They don't stick a thermometer in the water stream (for obvious reasons). They just verify that the dumb hole seems to have a "thermal character" while acting on surface waves. They just measure the amplitude of ingoing and outgoing waves and find that their squared ratios follows the Boltzmann distribution in the frequency which agrees with Hawking radiation.


text:
# on 02-Aug-2017 (Wed)

#### Flashcard 1447858146572

Tags
#cfa-level-1 #economics #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4
Question
imperfect competition is where an individual firm has [...] and is therefore able to exert some influence over price.
enough share of the market

(or can control a certain segment of the market)

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imperfect competition is where an individual firm has enough share of the market (or can control a certain segment of the market) and is therefore able to exert some influence over price.

#### Original toplevel document

3. ANALYSIS OF REVENUE, COSTS, AND PROFITS
zation requires that we examine both of those components. Revenue comes from the demand for the firm’s products, and cost comes from the acquisition and utilization of the firm’s inputs in the production of those products. 3.1.1. Total, Average, and Marginal Revenue This section briefly examines demand and revenue in preparation for addressing cost. Unless the firm is a pure monopolist (i.e., the only seller in its market), there is a difference between market demand and the demand facing an individual firm. A later reading will devote much more time to understanding the various competitive environments (perfect competition, monopolistic competition, oligopoly, and monopoly), known as market structure . To keep the analysis simple at this point, we will note that competition could be either perfect or imperfect. In perfect competition , the individual firm has virtually no impact on market price, because it is assumed to be a very small seller among a very large number of firms selling essentially identical products. Such a firm is called a price taker . In the second case, the firm does have at least some control over the price at which it sells its product because it must lower its price to sell more units. Exhibit 4 presents total, average, and marginal revenue data for a firm under the assumption that the firm is price taker at each relevant level of quantity of goods sold. Consequently, the individual seller faces a horizontal demand curve over relevant output ranges at the price level established by the market (see Exhibit 5). The seller can offer any quantity at this set market price without affecting price. In contrast, imperfect competition is where an individual firm has enough share of the market (or can control a certain segment of the market) and is therefore able to exert some influence over price. Instead of a large number of competing firms, imperfect competition involves a smaller number of firms in the market relative to perfect competition and in the extreme case only one firm (i.e., monopoly). Under any form of imperfect competition, the individual seller confronts a negatively sloped demand curve, where price and the quantity demanded by consumers are inversely related. In this case, price to the firm declines when a greater quantity is offered to the market; price to the firm increases when a lower quantity is offered to the market. This is shown in Exhibits 6 and 7. Exhibit 4. Total, Average, and Marginal Revenue under Perfect Competition Quantity Sold (Q) Price (P) Total Revenue (TR) Average Re

#### Flashcard 1598500244748

Tags
#cfa-level-1 #financial-reporting-and-analysis #non-recurring-non-operating-items #understanding-income-statement
Question
Extraordinary items are BOTH [...] in nature AND [...] in occurrence, and material in amount.
unusual

infrequent

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Extraordinary items are BOTH unusual in nature AND infrequent in occurrence, and material in amount. They must be reported separately (below the line) net of income tax.

#### Original toplevel document

Subject 6. Non-Recurring Items and Non-Operating Items
. Subsidiaries and investees also qualify as separate components. Disposal of a portion of a business component does not qualify as discontinued operations. Instead, this is recorded as an unusual or infrequent item. 2. Extraordinary items Extraordinary items are BOTH unusual in nature AND infrequent in occurrence, and material in amount. They must be reported separately (below the line) net of income tax. Common examples are: Expropriations by foreign governments. Uninsured losses from earthquakes, eruptions, and tornadoes. Note that gains and losses from the early retirement of debt used to be treated as extraordinary items; SFAS No. 145 now requires them to be treated as part of continuing operations. 3. Unusual or infrequent items These are either unusual in nature OR infrequent in occurrence but not both. They may be disclosed separately (as a single-line

#### Flashcard 1612594941196

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Question
You can identify the types of accruals and valuation entries in the [...] section of MD&A and in the significant accounting policies footnote, both found in the annual report.
Critical accounting policies/estimates

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An important first step in analyzing financial statements is identifying the types of accruals and valuation entries in an entity’s financial statements. Most of these items will be noted in the critical accounting policies/estimates section of management’s discussion and analysi

#### Original toplevel document

7. USING FINANCIAL STATEMENTS IN SECURITY ANALYSIS
ions of balance sheet accounts. Accruals and valuation entries require considerable judgment and thus create many of the limitations of the accounting model. Judgments could prove wrong or, worse, be used for deliberate earnings manipulation. An important first step in analyzing financial statements is identifying the types of accruals and valuation entries in an entity’s financial statements. Most of these items will be noted in the critical accounting policies/estimates section of management’s discussion and analysis (MD&A) and in the significant accounting policies footnote, both found in the annual report. Analysts should use this disclosure to identify the key accruals and valuations for a company. The analyst needs to be aware, as Example 4 shows, that the manipulation of earnings and a

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FV of an annuity factor
$$FV_n=A {(1+r)^n-1 \over r}$$

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the present value factor formula (2)
$$PV =FV_n {1 \over (1+r)^n}$$

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In investment management applications, the internal rate of return is called the money-weighted rate of return because it accounts for [...] and [...] of all cash flows into and out of the portfolio
the timing and amount

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A trade in two closely related stocks involving the short sale of one and the purchase of the other.

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In investments, the question of whether one event (or characteristic) provides information about another event arises in both time-series settings and cross-sectional settings.

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A rule explaining the unconditional probability of an event in terms of probabilities of the event conditional on mutually exclusive and exhaustive scenarios.
Total probability rule

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For readers familiar with mathematical treatments of probability, S, a notation usually reserved for a concept called the sample space, is being appropriated to stand for scenario.

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P(A) = P(AS)+P(ASC) = P(A|S)P(S) + P(A|SC)P(SC)
Total probability rule

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P(A|S1)P(S1) + P(A|S2)P(S2) +…+ P(A|Sn)P(Sn)

What does this equation say?
The probability of any event [P(A)] can be expressed as a weighted average of the probabilities of the event, given scenarios [terms such P(A | S1)]

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The scenarios for the total probability rule must be [...]
mutually exclusive and exhaustive

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The probability-weighted average of the possible outcomes of a random variable.
Expected value

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Expected value
Expected value (for example, expected stock return) looks either to the future, as a forecast, or to the “true” value of the mean (the population mean, discussed in the reading on statistical concepts and market returns). We should distinguish expected value from the concepts of historical or sample mean. The sample mean also summarizes in a single number a central value. However, the sample mean presents a central value for a particular set of observations as an equally weighted average of those observations. To summarize, the contrast is forecast versus historical, or population versus sample.

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E(X)=
$$E(X) = {\displaystyle\sum_{i=1}^{n} P(Xi)Xi}$$

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Expected value
For simplicity, we model all random variables in this reading as discrete random variables, which have a countable set of outcomes. For continuous random variables, which are discussed along with discrete random variables in the reading on common probability distributions, the operation corresponding to summation is integration.

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The [...] of a random variable is the expected value of squared deviations from the random variable’s expected value

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$$\sigma^2(X)=$$
$$\sigma^2 =E( {(X-E(X))^2}$$

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The two notations for variance are [...]
σ2(X) and Var(X).

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Expected value
Variance is a number greater than or equal to 0 because it is the sum of squared terms. If variance is 0, there is no dispersion or risk. The outcome is certain, and the quantity X is not random at all. Variance greater than 0 indicates dispersion of outcomes. Increasing variance indicates increasing dispersion, all else equal.

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The unconditional variance of EPS is the sum of two terms:

1) the expected value (probability-weighted average) of the conditional variances (parallel to the total probability rules) and

2) the variance of conditional expected values of EPS.

The second term arises because the variability in conditional expected value is a source of risk. Term 1 is σ2(EPS) = P(declining interest rate environment) σ2(EPS | declining interest rate environment) + P(stable interest rate environment) σ2(EPS | stable interest rate environment) = 0.60(0.004219) + 0.40(0.0096) = 0.006371.

Term 2 is σ2[E(EPS | interest rate environment)] = 0.60($2.4875 −$2.34)2 + 0.40($2.12 −$2.34)2 = 0.032414. Summing the two terms, unconditional variance equals 0.006371 + 0.032414 = 0.038785.

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The order of calculation is always [...] , then [...] , then standard deviation.
expected value

variance

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Variance summarized proceedure equation:

Var(X)=

$$\sigma^2 = {P(Xi)}\left\{Xi-E(Xi)\right\}^2$$

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The expected value of a stated event given that another event has occurred.
Conditional expected value

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Total probability rule for expected value:

E(X)= [...]
E(X)=E(X|S)P(S)+E(X|SC)P(SC)

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so small or unimportant as to be not worth considering; insignificant.
Negligible

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A diagram with branches emanating from nodes representing either mutually exclusive chance events or mutually exclusive decisions.
Tree diagram

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Each value on a binomial tree from which successive moves or outcomes branch.
Nodes

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The variance of one variable, given the outcome of another.
Condicional variances

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