text:
Does a way to find the least amount of pizza cuts for a certain number of slices (11) exist?

I found this problem in a Logic and Reason book from 2000's which seems to be reprinted or adapted from Martin Gardner's book of recreational puzzles. In the beginning it seemed rather easy but I couldn't find a way to solve it properly and ended up just guessing.

But does a better way to solve it exist?.

The problem is as follows:

In the road coming back from the lumber store, a carpenter notices that he requires to cut a 5mm thick pine circular plate in equal parts in order to make the support stand of a satellite dish which is to be placed atop his home. Since he's running out of batteries of his only electric saw and assuming that he cannot use his truck's battery due the rain to charge his saw (Hence he's urging to cut the wood). Find the least number of cuts he can make in order to produce the $$11$$ equal slices of the same thickness (5,mm) he needs assuming that the led indicator in his saw warns him the saw can function properly for 8 cuts before the unit stops.

The choices given are:

1. 8
2. 5
3. 4
4. 7

As I mentioned it seemed easy but I tried different combinations and in the end I couldn't find the right one.

In the end what I attempted was just the obvious but this is not the answer.

No matter how many times I've attempted I ended up off by one either over the number or below the number listed in the choices.

Is there some sort of logic in puzzle?. Can someone help me with where to look for or what to do first in these kinds of situations?. Since this involves doing cuts in a flat surface it would really help me a lot to include some drawing or diagram to better understand the approach.

Note: Although it doesn't specifically indicates that overlapping the slices is allowed or not allowed (for cutting), how different would the answer be if the overlapping of slices to reduce the number of cuts is not allowed. Can it be solved this way?

Here is one answer which involves stacking to cut through multiple pieces in one cut.

First draw on the circle 11 wedges of equal size; like a pizza cut into 11 slices the same size as you would normally expect.

Our first 2 cuts are are used to cut the circle almost in half; one half will have 5/11 pieces, and the other will have 6/11 pieces. The cuts do not line up exactly through the center of the circle, hence we need 2 cuts instead of one.

Next, put the smaller piece over top the larger. There should be a single piece of the larger not covered by the smaller. Now cut the larger into 3 sections, each with two pieces. This takes 2 more cuts.

At this point, you have 5 sections which are twice the size of the end piece, and one piece which is exactly the right size (it came from the 5/11 section). Stack all 5 sections and cut them in half with your 5th cut. Now you have 11 pieces which are all the same size and shape.

• Howdy!, So in the end does it mean that it is only required 4 cuts to get the required 11 pieces? By following your directions that's what I obtained. Judging from your answer, does it mean that the way to solve these puzzles is stacking the pieces?. (Unless noted by the problem otherwise?). – Chris Steinbeck Bell Oct 29 '20 at 0:07


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# Order isomorphism explained

In the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.[1]

## Definition

(S,\leS)

and

(T,\leT)

, an order isomorphism from

(S,\leS)

to

(T,\leT)

is a bijective function

f

from

S

to

T

with the property that, for every

x

and

y

in

S

,

x\leSy

if and only if

f(x)\leTf(y)

. That is, it is a bijective order-embedding.[2]

It is also possible to define an order isomorphism to be a surjective order-embedding. The two assumptions that

f

cover all the elements of

T

and that it preserve orderings, are enough to ensure that

f

is also one-to-one, for if

f(x)=f(y)

then (by the assumption that

f

preserves the order) it would follow that

x\ley

and

y\lex

, implying by the definition of a partial order that

x=y

.

Yet another characterization of order isomorphisms is that they are exactly the monotone bijections that have a monotone inverse.[3]

An order isomorphism from a partially ordered set to itself is called an order automorphism.[4]

When an additional algebraic structure is imposed on the posets

(S,\leS)

and

(T,\leT)

, a function from

(S,\leS)

to

(T,\leT)

must satisfy additional properties to be regarded as an isomorphism. For example, given two partially ordered groups (po-groups)

(G,\leG)

and

(H,\leH)

, an isomorphism of po-groups from

(G,\leqG)

to

(H,\leH)

is an order isomorphism that is also a group isomorphism, not merely a bijection that is an order embedding.[5]

## Examples

(R,\leq)

to

(R,\geq)

(where

R

is the set of real numbers and

\le

denotes the usual numerical comparison), since −x ≥ −y if and only if xy.[6]

(0,1)

(again, ordered numerically) does not have an order isomorphism to or from the closed interval

[0,1]

: the closed interval has a least element, but the open interval does not, and order isomorphisms must preserve the existence of least elements.[7]

## Order types

If

f

is an order isomorphism, then so is its inverse function.Also, if

f

is an order isomorphism from

(S,\leS)

to

(T,\leT)

and

g

is an order isomorphism from

(T,\leT)

to

(U,\leU)

, then the function composition of

f

and

g

is itself an order isomorphism, from

(S,\leS)

to

(U,\leU)

.[8]

Two partially ordered sets are said to be order isomorphic when there exists an order isomorphism from one to the other.[9] Identity functions, function inverses, and compositions of functions correspond, respectively, to the three defining characteristics of an equivalence relation: reflexivity, symmetry, and transitivity. Therefore, order isomorphism is an equivalence relation. The class of partially ordered sets can be partitioned by it into equivalence classes, families of partially ordered sets that are all isomorphic to each other. These equivalence classes are called order types.

• Permutation pattern, a permutation that is order-isomorphic to a subsequence of another permutation

• .
• .
• .
• .

## Notes and References

1. .
2. This is the definition used by . For and it is a consequence of a different definition.
3. This is the definition used by and .
4. , p. 13.
5. This definition is equivalent to the definition set forth in .
6. See example 4 of, p. 39., for a similar example with integers in place of real numbers.
7. , example 1, p. 39.
8. .
9. .

format: plain


text:
Exponents

Exponents afford a convenient way of expressing long products of the same number. The expression ${b}^{n}$ is called a power and it stands for b Ã— b Ã— b Ã— â€¢ â€¢ â€¢ Ã— b, where there are n factors of b. b is called the base, and n is called the exponent. By definition, bÂ° = 1.

There are six rules that govern the behavior of exponents:

Rule 1:
xa â€¢ xb = xa + b

Example:
23 â€¢ 22 = 23+2 = 25 = 32.
Caution:
xa + xb â‰  x a+ b

Rule 2:
( xa )b = xab
Example:
(2 3)2= 23â€¢2 = 26 = 64

Rule 3:
(x y)a = x a â€¢ ya
Example:
(2y)3 = 23 â€¢ y3 = 8y3

Rule 4:
x y a = x a y a
Example:
${\left(\frac{x}{3}\right)}^{2}$ = $\frac{{x}^{2}}{{3}^{2}}$ = $\frac{{x}^{2}}{9}$

Rule 5:
x a x b = x a - b , if a > b
Example:
$\frac{{2}^{6}}{{2}^{3}}$ = ${2}^{6-3}$ = ${2}^{3}$ = 8
$\frac{{x}^{a}}{{x}^{b}}$ = $\frac{1}{{x}^{b-a}}$, if b>a.
Example:
$\frac{{2}^{3}}{{2}^{6}}$ = $\frac{1}{{2}^{6-3}}$ = $\frac{1}{{2}^{3}}$ = $\frac{1}{8}$

Rule 6:
x - a = 1 x a
Example:
z-3 = $\frac{1}{{z}^{3}}$ Caution, a negative exponent does not make the number negative; it merely indicates that the base should be reciprocated. For example, 3-2 â‰  - $\frac{1}{{3}^{2}}$ or - $\frac{1}{9}$.

Problems involving these six rules are common on the GRE, and they are often listed as hard problems. However, the process of solving these problems is quite mechanical: simply apply the six rules until they can no longer be applied.

Example 1:
If x â‰  0, $\frac{x{\left({x}^{5}\right)}^{2}}{{x}^{4}}$ = ?

(A) x 5
(B) x 6
(C) x 7
(D) x 8
(E) x 9

First, apply the rule ( x a )b = xab to the expression $\frac{x{\left({x}^{5}\right)}^{2}}{{x}^{4}}$ :
$\frac{xÂ·{x}^{5Â·2}}{{x}^{4}}$ = $\frac{xÂ·{x}^{10}}{{x}^{4}}$

Next, apply the rule xa â€¢ xb = xa +b :

$\frac{xÂ·{x}^{10}}{{x}^{4}}$ = $\frac{{x}^{11}}{{x}^{4}}$

Finally, apply the rule $\frac{{x}^{a}}{{x}^{b}}$ = xa-b :

$\frac{{x}^{11}}{{x}^{4}}$ = x11-4 = x7

Note: Typically, there are many ways of solving these types of problems. For this example, we could have begun with Rule 5, $\frac{{x}^{a}}{{x}^{b}}$ = $\frac{1}{{x}^{b-a}}$ :
$\frac{x{\left({x}^{5}\right)}^{2}}{{x}^{4}}$ = $\frac{x{\left({x}^{5}\right)}^{2}}{{x}^{4-1}}$ = $\frac{x{\left({x}^{5}\right)}^{2}}{{x}^{3}}$

Then apply Rule 2,(xa)b = xab:

$\frac{{\left({x}^{5}\right)}^{2}}{{x}^{3}}$ = $\frac{{x}^{10}}{{x}^{3}}$

Finally, apply the other version of Rule 5, $\frac{{x}^{a}}{{x}^{b}}$ = xa - b:

$\frac{{x}^{10}}{{x}^{3}}$ = x7

Example 2:

 Column A Column B $\frac{3Â·3Â·3Â·3}{9Â·9Â·9Â·9}$ ${\left(\frac{1}{3}\right)}^{4}$
Canceling the common factor 3 in Column A yields $\frac{1Â·1Â·1Â·1}{3Â·3Â·3Â·3}$, or $\frac{1}{3}$â€¢$\frac{1}{3}$â€¢$\frac{1}{3}$â€¢$\frac{1}{3}$ . Now, by the definition of a power, $\frac{1}{3}$â€¢$\frac{1}{3}$â€¢$\frac{1}{3}$â€¢$\frac{1}{3}$ = ${\left(\frac{1}{3}\right)}^{4}$ Hence, the columns are equal and the answer is (C).

Example 3:

Column A
$\frac{{6}^{4}}{{3}^{2}}$

Column B
24â€¢32

First, factor Column A:
$\frac{{\left(2Â·3\right)}^{4}}{{3}^{2}}$

Next, apply the rule (x y)a = x a â€¢ ya :
$\frac{{2}^{4}Â·{3}^{4}}{{3}^{2}}$

Finally, apply the rule $\frac{{x}^{a}}{{x}^{b}}$ = xa - b:

24â€¢32

Hence, the columns are equal and the answer is (C).


text:
What does $\Lsh$ mean?

Source: Wikipedia (permalink), in the formula for the heat capacity ratio: $$Y=\biggl({Cp\over \Lsh Cv}\biggr)$$ The $\LaTeX$ command is \Lsh.

• I think that, thermodynamically speaking, your capital Y should be a $\gamma$ (gamma letter). – Jean Marie Apr 19 '17 at 23:09

This picture was introduced with the version of 16:08, 10 June 2016 with the comment "Replacing the typed formulae with the picture formulae". This replacement went wrong.

The previous version of 07:45, 11 April 2016 still uses the string

γ = Cp/ Cv

The link heat ratio in the text refernces a page with the picture

So the correct formula seems to be

$$\gamma=\frac{C_P}{C_V}$$

I therefore changed this in the Wikipedia article, Version of 00:00, 20 April 2017

• +1 Good use of Wikipedia history. Why not fix this on Wikipedia? – Ethan Bolker Apr 19 '17 at 23:56
• @EthanBolker: I already changed it – miracle173 Apr 20 '17 at 0:03

Typographical / transcription error? Follow the link to "Heat capacity ratio" and you see the formula $$\gamma=\frac{C_P}{C_V}.$$ That weird \Lsh symbol looks vaguely like the TeX gamma. And so does $Y$.


text: Pythagorean triples - Printable Version +- OMath! (http://math.elinkage.net) +-- Forum: Math Forums (/forumdisplay.php?fid=4) +--- Forum: Number Theory (/forumdisplay.php?fid=7) +--- Thread: Pythagorean triples (/showthread.php?tid=97) Pythagorean triples - elim - 09-22-2010 08:55 AM (1) Find all $(a,b,c) \in \mathbb{N}^+$ such that $a^2+b^2=c^2$ (2) Find all $(a,b,c) \in \mathbb{N}^+$ such that $a^2+b^2=2 c^2$ RE: Pythagorean triples - elim - 09-23-2010 07:23 PM A positive integer triple $(a,b,c)$ is called Pythagorean if $a^2+b^2=c^2$ A Pythagorean triple $(a,b,c)$ is prime if $gcd(a,b,c)=1$ (1) Let $(a,b,c)$ be a prime Pythagorean triple, then $c \equiv a-b \equiv 1 \mod {2}$ $\quad\quad$Since $\gcd(a,b)>1 \Rightarrow \gcd(a,b,c)>1$ and the sum of two odd squares is not a square $\quad\quad$Assume $2\mid b$ we then have $2 \nmid a, \; 2 \mid (c \pm a)$ and $\displaystyle{\frac{b^2}{4} = \frac{c+a}{2}\frac{c-a}{2}}$ a perfect square. Since $\quad\quad \displaystyle{\gcd(\frac{c+a}{2},\frac{c-a}{2})=\gcd(c,\frac{c-a}{2})}\le \gcd(c,c-a)=\gcd(a,c)=1$, we see that $\quad\quad \displaystyle{\frac{c-a}{2} = m^2, \; \frac{c+a}{2} = n^2, \; \gcd(m,n)=1}$ Therefore the set of prime Pythagorean triples is \$\quad\quad P_0 =\{(a,b,c) | c = m^2+n^2,\; \{a,b\} = \{n^2-m^2,2mn\}, \; m


text:
# Fancyhdr Latex

%%%%% %% %% gametex. pandoc seems to be trying to parse the header-includes content as if it were variables, and : is used to separate variables and values. The fancyhdr package is a page layout customizing package that replaces the fancyheadings package. CTAN: Package fancyhdr. Im writing my thesis using the book class. Es definiert Befehle für den Seitenstil fancy. Paper size, orientation. Hier die Originaldokumentation als dvi-bzw. 8 Abstract This package provides a exible and easy interface to page dimensions. LaTeX 插图指南·中文版, (version 2. Quick Start Try typesetting sample-handout. Really busy with school and behind, but I am trying to make an effort to update a bit now!. An online LaTeX editor that's easy to use. 13 For even more color capability use xcolor. The fancyhdr package lets us add things in the left (L), right (R) and centre (C) of the header or footer and also lets us specify a different arrangement depending on whether its on an odd (O) or even (E) page. Section Headings in LaTeX. Join GitHub today. GitHub Gist: instantly share code, notes, and snippets. The fancyhdr package is a page layout customizing package that replaces the fancyheadings package. Whether you are just getting started with LaTeX and wondering what the fuss is about, here to share the clever trick you've discovered, or need urgent help with your bibliography, welcome to the LaTeX subreddit! \section{New to \LATEX ?} Here is a thread with useful links \section{Resources} Extensions to view LaTeX on reddit: Chrome: TeX All. Input (for 8:5 11 paper): \topmargin=0in \headheight=0in. Folien für einen Vortrag mit und ohne eigebettete Beispiele (die Seite habe ich natürlich auch mit fancyhdr gestaltet). There are, however, a great number of alternative styles available, some of which being very fancy or playful. als pdf-Datei. It has the same behavior of the previous code, but you will get empty header Massive Empire. For starters, page numbers will appear on all pages which have a page style of plain , headings or myheadings (ie: anything other than empty ). [LaTeX] Double Ligne de séparation (footer fancyhdr) × Après avoir cliqué sur "Répondre" vous serez invité à vous connecter pour que votre message soit publié. fancyhdr is a massive package with a crazy number of tweaks and modifications available for your document’s header and footer styles. \author \author{names} The \author command declares the author(s), where names is a list of authors separated by \and commands. minidocument creates miniature documents inside other LaTeX documents minifp Fixed-point real computations to 8 decimals. LaTeX Page Styles The \documentstyle command determines the size and position of the page's head and foot. 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PDF - Download latex for free This modified text is an extract of the original Stack Overflow Documentation created by following contributors and released under CC BY-SA 3. sty 4 Seitenaufbau Kopfzeile EL EC ER OL OC OR Der Text Der Text Der Text Fußzeile EL EC ER OL OC OR \fancyhf{}% Alle Felder loeschen % Seitenzahl bei geraden/linken Seiten nach links/aussen. I want my thesis to be onesided (left and right margins of same size), but I would also like to use the fancyhdr package to give me chapter names in the pagehead of even pages and section names in the pagehead of odd pages. % Piet van Oostrum, % Dept of Computer and Information Sciences, University of Utrecht, % Padualaan 14, P. In this post, I will briefly show how to define an alternative page style in general and illustrate two possible applications including complete code examples:. 14 An excellent. nLaTeX, ntextbackslash, n% Note: % is a special character reserved for comments (after a %, the rest of a line is ignored by the compiler). of Computer Sciencey Utrecht University January 31, 2019 Abstract. net) wrote: Hi Toby, An old bug, right. You can also experiment with the headings by changing the fancyhdr line to this. % Fancy headers and footers for LaTeX. To change the size of a font use a new font size parameter. ~\cite{latex}. If use-latex-citations is used adjacent citation references (separated only by a single space or a newline) are combined to a single citation group, i. Note that all formulas are enclosed by \\$ and occur in \textit{math mode}. I am using the muthesis template to write my. Common length macros are: \baselineskip The normal vertical distance between lines in a paragraph. Quick Start Try typesetting sample-handout. LaTeX Letter Format You can use LaTeX to typeset letters, both personal and business. The solution here is not a number,because it will depend on the value of b. This is a short introduction, showing the most important features of the package. If you know "fancyhdr" and are looking for something particular, refer to the fancyhdr-documentation. The fancyhdr package Two Examples Practice 17 In TeXnicCenter, open the third example ﬁle (. Name of chapter” but then on odd pages gives the section name and number. fancyhdr is a package that. latex thesis fancyhdr Hi, I used the command for displaying only chapters in the header, but the header line stops before the right margin. tex) posted on Sakai. Orange Box Ceo 6,844,188 views. It provided several di‡erent classes for a number of journals and conference pro-ceedings. Therefore TeXstudio has numerous features like syntax-highlighting, integrated viewer, reference checking and various assistants. 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LATEX THESIS FANCYHDR - You can also use someting negative if you like the space to be below 1 inch. nl % License, as described in lppl. % % % \section{A driver for this document} \label{sec:docstrip} % % The next series of code contains the documentation driver file for % \LaTeX, i. without changing the way LATEX works you may consider using fancyhdr, by Piet van Oostrum, sectsty, by Rowland McDonnell, and tocloft, by Peter Wilson, which you can make pretty things with. Sign in Sign up. An easy-to-install open source TeX distribution for MacOSX. Package Fancyhdr Warning: \headheight is too small (12. If you don't know if you have fancyhdr already, then you should download this file and put it in the same folder as your solutions file. LATEX page formatting W. LATEX THESIS FANCYHDR - Below is the code for one side. tex) posted on Sakai. \end{document} change textwidth Usepackage geometry also allows an esay way to change the textwidth as the next exmaple would show us: set. The fancyhdr package is a page layout customizing package that replaces the fancyheadings package. 14 An excellent. If you're feeling adventurous, go to "Editor" and change the font family to "Consolas" :) TeXstudio (and its parent TeXmaker) operate on the principle that you don't need any fancy project files getting in the way. Mit dem Paket fancyhdr können Sie Kopf- und Fußzeile frei gestalten. If you know how to redefine pages styles with fancyhdr and now you want to learn how to use titleps, this little guide will help you. nLaTeX, ntextbackslash, n% Note: % is a special character reserved for comments (after a %, the rest of a line is ignored by the compiler). I'm using the package fancyhdr to format my footers and headers, with my name in the header and a n of m pages format for the footer. Here’s a basic example for Chinese:. LaTeX LaTeX Notes for Professionals Notes for Professionals GoalKicker. 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A simple example demonstrating how to put texts at different locations of the headers/footers using fancyhdr. Piet van Oostrum Dept. Marking mechanism. scrreprt ist plain, bei der Klasse book bzw. The title of the section should be surrounded by braces and placed immediately after the relevant command. Time for action – customizing headers with the fancyhdr package The default shape of the page headings is slanted. Creating headers and footers in Latex can be done by using the package “fancyhdr”. Version: 3. Reply lolo says October 19, 2012 at 5:13 pm. Text Math Macro Category Requirements Comments 000A5 ¥ U \yen mathord amsfonts YEN SIGN 000AE ® r \circledR mathord amsfonts REGISTERED SIGN 000F0 ð g \eth mathalpha amssymb arevmath eth 00302 x̂ (bx) \hat mathaccent # \widehat (amssymb), circumﬂex accent. Section headings of various sizes are produced (in the article document style) using the commands \section,\subsection and \subsubsection commands. com/get/Programming/File-Editors/Texmaker. tex' with desired file name. r latex sweave. It is essentially gwTeX plus XeTeX, with a simple GUI installer and a few extra applications. 2 % Fancy headers and footers for LaTeX. Using fancyhdr. online LaTeX editor with autocompletion, highlighting and 400 math symbols. I'm using the package fancyhdr to format my footers and headers, with my name in the header and a n of m pages format for the footer. The geometry package Hideo Umeki [email protected] to jump to the place where they are in the paper (at least for the DVI and PDF versions): include \usepackage{hyperref}. Open an example of the fancyhdr package in Overleaf Decorative lines on header and footer. where "Section Name" and "Chapter Name" are left-aligned in the header of the page, and would be dynamically replaced by the actual values of the current section and chapter names, respectively. For most purposes, the best package for decorating your documents with informative headers and footers is fancyheadings. Package: texlive-base Version: 2017. The fancyhdr package does not come with MiKTeX, but assuming that you installed MiKTeX using our recommendations, it should prompt you to install it the first time you try to use it. An online LaTeX editor that's easy to use. What is the LaTeX command for it? Hi Tom, I tried alot but in vain, actually i want For other chapter pages: I have been looking for simple instructions how to modify the headers and footers. a guest Feb 23rd, 2012 54 Never Not a member of Pastebin yet? Sign Up, it. LATEX THESIS FANCYHDR - Thank you so much it did solve the problem! To configure the page layout, we enter instructions into the square brackets of this command. I plan to use the fancyhdr package in the preamble section of the document, but I get the. I'm using the package fancyhdr to format my footers and headers, with my name in the header and a n of m pages format for the footer. You may also find this post helpful. However, this is a pilot program with limited scholarships available and residents served by the six libraries. Hence a safe head height will be around 110pt. Get the LaTeX chapter name and section name on the document header. Piet van Oostrum Dept. They all provide the same features, you just use them differently. Email: [email protected] You write text and mathematics in your document without having to know a programming language or exit to an equation editor. sty) packages for ALTLinux, CentOS, Fedora, openSUSE. Hola Estoy escribiendo un documento en tipo 'report', y quiero incluir en la parte superior de todas las páginas una línea horizontal, que vaya de Utilizamos cookies propias y de terceros para mejorar la experiencia de navegación, y ofrecer contenidos y publicidad de interés. Im writing my thesis using the book class. Orange Box Ceo 6,844,188 views. Not all LaTeX compilers were created equal, and Pdf is likely the format you'll want. For starters, page numbers will appear on all pages which have a page style of plain , headings or myheadings (ie: anything other than empty ). Version: 3. Macros don't consume any of TeX's length registers, which is part of the motivation that the fancyhdr author gives for this implementation. There is a problem you may come across using package fancyhdr: Package Fancyhdr Warning: \headheight is too small (12. The oﬃcial documentation is Packages in the ‘graphics’ bundle. tex) posted on Sakai. First of all, you need to tell Latex to use the package: \usepackage. When you are using fancyhdr in your document, there are two decorative lines on both the header and the footer, the latter has 0pt thickness and hence is not visible. 0pt): Make it at least 14. LATEX THESIS FANCYHDR - February at 6: Don't load multiple packages which are designed to format the same document elements in different ways e. It's easy to change that:. [LaTeX] Double Ligne de séparation (footer fancyhdr) × Après avoir cliqué sur "Répondre" vous serez invité à vous connecter pour que votre message soit publié. Headers and footers in standard LaTeX are somewhat clumsy. With the two \markright{Table of Contents} I can change the section name in the fancyhdr to Table of Contents on page 1 and on page 3 of my table of contents. 重新定义了 \chaptermark 与 \sectionmark，这两个重定义一定要记住放在 \pagestyle{fancy}之后，因为在 fancyhdr 宏包中对这两个命令重新进行了定义，在 \pagestyle{fancy} 之后重定义它们就可将 fancyhdr 中的相应命令覆盖掉。. It has the same behavior of the previous code, but you will get empty header Massive Empire. latex fancyhdr：代わりにleftmarkとrightmarkを使用できますか？ 8 は、私は、ヘッダーのレイアウトをカスタマイズするには、このコードを使用しています：. Try changing the margins by altering the second line to \usepackage[margin=1in]{geometry}. Common length macros are: \baselineskip The normal vertical distance between lines in a paragraph. To change this, you can use \setlength{\headheight}{110pt} or. sty version 3. Some examples of using $$\LaTeX$$ in R Markdown documents. There's a couple of things you need to do to use them: the first is to add a line saying. It supports most characters for latin languages, but that's it. How can I alter the position of page numbers so that they become visible?. latex thesis fancyhdr Professional Help with Writing Great Academic Papers Our academic writing service is an expert. Package Fancyhdr Warning: \headheight is too small (12. Whether you are just getting started with LaTeX and wondering what the fuss is about, here to share the clever trick you've discovered, or need urgent help with your bibliography, welcome to the LaTeX subreddit! \section{New to \LATEX ?} Here is a thread with useful links \section{Resources} Extensions to view LaTeX on reddit: Chrome: TeX All. The LaTeX fancyhdr package. ISO-8859-1 (a. Creating headers and footers in Latex can be done by using the package “fancyhdr”. Fancyhdr ist ein eingeführtes, eigenständiges Paket zur einfacheren Manipulation von Kopf-und Fußzeile. >>Date: Tue, 7 Nov 2000 11:37:40 +0100 >>From: Jan Goebel <[EMAIL PROTECTED]> >>To: [EMAIL PROTECTED] >>Subject: Re: fancyhdr - different headers and footers >>Mail. However, it cannot help all the times. Beschreibung []. Evaluate, simplify, solve, and plot functions without the need to master a complex syntax. 0pt): Make it at least 103. For starters, page numbers will appear on all pages which have a page style of plain , headings or myheadings (ie: anything other than empty ). We'll continue working on the same project as last time and the first thing we will. If you're feeling adventurous, go to "Editor" and change the font family to "Consolas" :) TeXstudio (and its parent TeXmaker) operate on the principle that you don't need any fancy project files getting in the way. For example, if you want to put the current page number in the context of the page numbers in the whole document (page 1 of 10 or 1/10), the following. 本站是提供个人知识管理的网络存储空间，所有内容均由用户发布，不代表本站观点。如发现有害或侵权内容，请 点击这里 或 拨打24小时举报电话：4000070609 与我们联系。. I have headers on all other pages, but it seems like the \maketitle command disables the header on the first page (the titlepage). fancyhdr – Extensive control of page headers and footers in LaTeX2ε. The fancyhdr package provides an easy and flexible way to customize the page style. One of the easiest and most flexible options is to use the fancyhdr package. Alternative head- and footlines in LaTeX The standard LaTeX document classes define a small set of 'page styles' which (in effect) specify head- and footlines for your document. Möchte man jedoch sein eigenes Titel-Layout erstellen, so bietet LaTex allein dabei keine große Unterstützung. [fancyhdr] Bug de numérotation par Gearbox » Dimanche 05 Avril 2009, 23:05 4 Réponses 721 Vus Dernier message par Gearbox Lundi 06 Avril 2009, 19:27 Code fancyhdr par parfos » Lundi 08 Août 2011, 05:20 7 Réponses 2837 Vus Dernier message par Sya23 Mercredi 22 Août 2012, 16:14 fancyhdr et geometry. However, this is a pilot program with limited scholarships available and residents served by the six libraries. Can fancyhdr: Page headers/footers/numbering (fancyhdr). 0 This website is not affiliated with Stack Overflow. If use-latex-citations is used adjacent citation references (separated only by a single space or a newline) are combined to a single citation group, i. Or if you don’t want the whole package (it’s huge), grab whatever you need for latex-cjk-chinese, latex-cjk-japanese or latex-cjk-korean (and whatever relevant font packages). % Piet van Oostrum, % Dept of Computer and Information Sciences, University of Utrecht, % Padualaan 14, P. This feature is not available right now. The Tufte-LaTeX document classes use the fancyhdr package to set up the running heads and feet. LyX combines the power and flexibility of TeX/LaTeX with the ease of use of a graphical interface. Here's an example of how we might customise our headers and footers:. The LaTeX fancyhdr package. I plan to use the fancyhdr package in the preamble section of the document, but I get the. It has the same behavior of the previous code, but you will get empty header Massive Empire. On page two, however, the section name in fancyhdr is just CONTENTS (yes, in uppercase). O que se faz,…. However, this is a pilot program with limited scholarships available and residents served by the six libraries. The fancyhdr package is a page layout customizing package that replaces the fancyheadings package. Piet van Oostrum Dept. Bei diesem Prozess muss man sich um alle Textsatz Einstellungen selbst bemühen. % % This manual is typeset according to the conventions of the % \LaTeX{} \textsc{docstrip} utility which enables the automatic % extraction of the \LaTeX{} macro source files~\cite{GOOSSENS94}. I'm using the package fancyhdr to format my footers and headers, with my name in the header and a n of m pages format for the footer. Not all LaTeX compilers were created equal, and Pdf is likely the format you'll want. 사용하기 쉬운 온라인 LaTex 편집기. Sign in Sign up. sty et je ne sais pas où les placer dans Miktex quand j'essaie de compiler, TexnicCenter me répond qu'il n'arrive pas à trouver fancyhdr. 关键是琢磨一下下面的例子, 在看看相应的说明, 一般就可以得到你想要的结果了. Like so: \pagestyle{fancy} \fancyhf{} % clear all header and f. The fancyhdr package provides an easy way to place text on the top and/or bottom of every page. Es definiert Befehle für den Seitenstil fancy. You can find comprehensive information on this package in The LaTeX Companion. We will use \LaTeX, which is based on \TeX\ and has many higher-level commands (macros) for formatting, making tables, etc. I still have one. I am trying to customise the position of the page number to make them all appear at the bottom centre in Lyx. Often, the authors make use of the default chapter style. Hola, Estoy usando el paquete fancyhdr para hacer los encabezados de un documento tipo libro. % Piet van Oostrum, % Dept of Computer and Information Sciences, University of Utrecht, % Padualaan 14, P. I was driven by the fact that this was a very complicated technical document,. sty: texmf\tex\latex\fancyhdr: fancyhdr. 3 What is fancyhdr The fancyhdr macro package allows you to customize in LATEX your page headers and footers in an easy way. The standard set is very limited, but LaTeX is capable of much more. 8 Abstract This package provides a exible and easy interface to page dimensions. We just made a new paragraph. CTEXwiki关于fancyhdr的说明可以在这里找到。. So I have used solution with tikz and fancyhdr packages in book class, and tried to move chapter heading to the left on left hand side pages by using ifthen package, but as I am not very skilled user, all I got was a bunch of mistakes. Há uma outra forma de usar o fancyhdr para construir cabeçalhos e rodapés. Hier die Originaldokumentation als dvi-bzw. UTF-8: a Unicode multi-byte encoding. This is exactly the line where my TexHeader is placed. There are a number of ways to change the document header and footer styles in LaTeX. LaTeX FAQ: "How do I use font colors in LaTeX?". GitHub Gist: instantly share code, notes, and snippets. sty version 3. However, this is a pilot program with limited scholarships available and residents served by the six libraries. This looks really ugly. sty, which is not in any LaTeX distribution, but which is required to create the. A simple example demonstrating how to put texts at different locations of the headers/footers using fancyhdr. You never know what you will meet when you use Latex, luckily, we can search Google or Yahoo to find the answer. You write text and mathematics in your document without having to know a programming language or exit to an equation editor. Há uma outra forma de usar o fancyhdr para construir cabeçalhos e rodapés. Using fancyhdr. latex thesis fancyhdr Hi, I used the command for displaying only chapters in the header, but the header line stops before the right margin. J'ai commencé à créer de mon côté mes 1ères fiches, ou plutôt essayé, parce que là ça fait maintenant peut-être 4 heures que j'écume le net à comprendre comment utiliser le package fancyhdr, et faire apparaitre cette image en en-tête, sans jamais réussir T_T. I am trying to define a base class for some reports to share the same page layout. En online LaTeX editor, der er let at bruge. The page style determines what goes in them. Re: Fancyhdr and \chapter{} page numbering Post by frabjous » Sat May 29, 2010 6:59 pm I don't understand why you'd be getting the empty page style on chapter pages, and I don't understand why redefining the plain page style using the methods described in the fancyhdr package documentation wouldn't work. It compiles if you quote the lines in question (don't forget, then, to escape the leading backslash). O que se faz,…. 0pt): Make it at least 103. Orange Box Ceo 6,844,188 views. Name of chapter” but then on odd pages gives the section name and number. It provided several di‡erent classes for a number of journals and conference pro-ceedings. Note : This program is the "authentic" Texmaker editor and there is strictly no relationship between this original program developed since 2003 and another latex editor, not compatible with Texmaker, which pretends to be based on Texmaker to trick users. This is what you need to include: \documentclass{article} \usepackage{fancyhdr} \pagestyle. The solution here is not a number,because it will depend on the value of b. We just made a new paragraph. Often, the authors make use of the default chapter style. A LaTeX class for fulfilling the documentation duties according to the German minimum wage law MiLoG milsymb LaTeX package for TikZ based drawing of military symbols as per NATO APP-6(C) minibox A simple type of box for LaTeX. How can I customize headers and footers in LaTeX? It's easy to customize your page headers and footers using a set of macros available in the sipb locker. An online LaTeX editor that's easy to use. sty ainsi que lastpage. The default header with fancyhdr for a book (two-sided by default) displays the chapter at the inner side (left odd, right even) and the section title at the outer side (left even, right odd). Here's a brief summary on how to get it sorted. LATEX THESIS FANCYHDR - Sign up using Facebook. Ensure that you latex thesis fancyhdr have the permission of the photo's owner before editing photos which are not your own!. % Piet van Oostrum, % Dept of Computer and Information Sciences, University of Utrecht, % Padualaan 14, P. Name of chapter” but then on odd pages gives the section name and number. Marking mechanism. Can fancyhdr: Page headers/footers/numbering (fancyhdr). June at 9: Latex Thesis Headers how to show only chapter name in all pages two sided Ask Question. It's simpler to locate a specific word or element in a short file. Folien für einen Vortrag mit und ohne eigebettete Beispiele (die Seite habe ich natürlich auch mit fancyhdr gestaltet). txt in the base LaTeX distribution. Instead, I have now set up the main matter geometry in the preamble and used \newgeometry and \restoregeometry for the front mater. I'm not sure this will work, because I don't have LaTeX installed on my current machine But you could try setting a \markleft command after your \chapter* command like so: \chapter*{Chapter title goes here} \markleft{Chapter title goes here} % content should be added to the \leftmark Hope this helps. fancyhdr - Extensive control of page headers and footers in LaTeX2ε The package provides extensive facilities, both for constructing headers and footers, and for controlling their use (for example, at times when LaTeX would automatically change the heading style in use). 02 Toby Speight ([email protected] Contribute to AlongWY/Latex-Template development by creating an account on GitHub. An online LaTeX editor that's easy to use. A simple example demonstrating how to put texts at different locations of the headers/footers using fancyhdr. So I have used solution with tikz and fancyhdr packages in book class, and tried to move chapter heading to the left on left hand side pages by using ifthen package, but as I am not very skilled user, all I got was a bunch of mistakes. This is a short introduction, showing the most important features of the package. screenshot for Frank's student. The fancyhdr package provides an easy way to place text on the top and/or bottom of every page. TeXstudio is an integrated writing environment for creating LaTeX documents. Contribute to AlongWY/Latex-Template development by creating an account on GitHub. Many books, theses and reports are written in LaTeX using the report or book document classes. Puisqu'une illustration vaut mieux qu'un long blabla :. fancyhdr - Extensive control of page headers and footers in LaTeX2ε The package provides extensive facilities, both for constructing headers and footers, and for controlling their use (for example, at times when LaTeX would automatically change the heading style in use). \end{document} change textwidth Usepackage geometry also allows an esay way to change the textwidth as the next exmaple would show us: set. 사용하기 쉬운 온라인 LaTex 편집기. It handles footers and headers efficiently, but also works with placement of floats. We will use \LaTeX, which is based on \TeX\ and has many higher-level commands (macros) for formatting, making tables, etc. We can use the LaTeX package fancyhdr to customize how the page numbers are displayed. Open an example of the fancyhdr package in Overleaf Decorative lines on header and footer. I am trying to define a base class for some reports to share the same page layout. Re: Probleme fancyhdr et titres de chapitre par fp » Samedi 15 Mai 2010, 18:01 Ça me semble être un comportement normal : fancyhdr essaie de loger quelque chose de très long donc il est obligé de le faire sur deux lignes et, ce faisant, il empiète sur la page. If you know "fancyhdr" and are looking for something particular, refer to the fancyhdr-documentation. The different font sizes are listed below. replace "Sphinx format for Latex and HTML" with correct name. % Piet van Oostrum, % Dept of Computer and Information Sciences, University of Utrecht, % Padualaan 14, P. Section Headings in LaTeX. ThearticleappearedinProc. MLA Template. It compiles if you quote the lines in question (don't forget, then, to escape the leading backslash). Puisqu'une illustration vaut mieux qu'un long blabla :. You can de ne: three-part headers and footers decorative lines in headers and footers headers and footers wider than the width of the text 4. This is a type of a literal equation, which is very common in algaebra. 在latex中用自定义页眉页脚, 一般都要使用宏包fancy. Paper size, orientation. Creating headers and footers in Latex can be done by using the package "fancyhdr". If you know how to redefine pages styles with fancyhdr and now you want to learn how to use titleps, this little guide will help you. (from the fancyhdr README).


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Factorize $2x-6{x}^{2}$
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Question 4f6f6

Dec 5, 2017

$\text{1.65 g}$

Explanation:

The first thing that you can calculate here is the number of moles of calcium chloride dissolved to make your solution.

As you know, the molarity of the solution tells you the number of moles of solute present in every $\text{1 L} = {10}^{3}$ $\text{mL}$ of the solution.

In your case, a $\text{0.550-M}$ solution will contain $0.550$ moles of calcium chloride, the solute, in every ${10}^{3}$ $\text{mL}$. This means that your sample will contain

27.0 color(red)(cancel(color(black)("mL solution"))) * "0.500 moles CaCl"_2/(10^3color(red)(cancel(color(black)("mL solution")))) = "0.01485 moles CaCl"_2#

To convert the number of moles to grams, you need to use the molar mass of the solute.

$0.01485 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles CaCl"_2))) * "110.98 g"/(1color(red)(cancel(color(black)("mole CaCl"_2)))) = color(darkgreen)(ul(color(black)("1.65 g}}}}$

The answer is rounded to three sig figs.


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# How do you write 100 in scientific notation?

$1 \times {10}^{2}$
To write $100$ in scientific notation, move the decimal to the left to places so that the coefficient is $1$. Multiply by ${10}^{2}$. The exponent positive two means the decimal was moved to the left two places.


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Ground state and nodal solutions for a class of double phase problems
Papageorgiou, Nikolaos (Author), Rǎdulescu, Vicenţiu (Author), Repovš, Dušan (Author)

Abstract
We consider a double phase problem driven by the sum of the ▫$p$▫-Laplace operator and a weighted ▫$q$▫-Laplacian ▫\$(q
Language: English double phase operator, weight function, superlinear reaction, Nehari manifold, ground state solution, nodal solution Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2020 Str. 1-15 Vol. 71, Iss. 1, art. 15 517.956.2 0044-2275 10.1007/s00033-019-1239-3 18868057 249 208 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Zeitschrift für angewandte Mathematik und Physik Z. angew. Math. Phys. Birkhaeuser Verlag 0044-2275 26662656

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text:
# Blog: Machine Learning Equations by Saurabh Verma

## Blog: Hunt For The Unique, Stable, Sparse And Fast Feature Learning On Graphs (NIPS 2017).

• Tutorials

How can we convert a graph into a Feature Vector?

Graph is a fundamental but complicated structure to work with from machine learning point of view. Think about it, a machine learning model usually require inputs in some form of mathematical objects like vectors, matrices, real number sequences and then produces the desired outputs. So, the question is how we can convert a graph into a mathematical object that is suitable for performing machine learning tasks such as classification or regression on graphs.

For past one year, I have been working on developing machine learning models for graph(s) in order to solve two specific problems:

1) Graph Classification: Given a collection of graphs $\{G_i\}_{i=1}^{M}$ and associated graph labels $\{y_i\}_{i=1}^{M}$ where $y_i\in \mathbf{R^{c}}$ ($c$ is the number of classes), we need to come up with a learning model or function $F:G \rightarrow Y$ that can classify or predict the label associated with a graph.

2) Node Classification: Given a graph $G=(V,E,W)$, where $V$ is vertex set, $E$ is edge set & $W$ is adjacency matrix and labels $\{y_i\}_{i=1}^{M}$ where $y_i\in \mathbf{R^{c}}$ associated with each node, our task is to classify or predict the labels on each node. That is, come up a learning function $F:V\rightarrow Y$.

## Blog: Stability of Learning Algorithms Part 3.

• Tutorials

Extending to Ranking Algorithms

## Blog: Stability of Learning Algorithms Part 2.

• Tutorials

Extending to Randomized Algorithms

Let $R$ be a set of random parameters.

Let’s assume that our algorithm $A_{(S,R)}$ has uniform stability $(\beta,\rho)$, if it satisfies,

## Blog: Stability of Learning Algorithms Part 1.

• Tutorials

This is walk-through on how to derive generalization bounds based on the stability of algorithms. Understanding the proof helps to extend or modify the results according to your needs. For instance, I had a loss function which was unbounded, and since to apply generalization results your loss function must be bounded, I was stuck. So, this my effort to state the proof as clear as possible along with the assumptions needed.

## Blog: Dirichlet Distributions.

• Tutorials

Dirichlet Distribution is a distribution over distributions. More specifically, it is a distribution over pmfs (probability mass functions). You can imagine, as if there is a bag of $L$ dices, and each dice has a corresponding pmf (related to six possible outcomes). Now picking a dice is like sampling a particular pmf from a distribution. The probability of picking a dice, which results in a pmf, comes from the Dirichlet distribution $Dir(\boldsymbol\alpha)$.

Let $\mathbf{q}=[q_1,q_2,...,q_k]$ be a pmf (or a point in simplex $\in$ $\mathbf{R}^{k}$), where $\sum\limits_{j=1}^{k}q_j=1$ and $\mathbf{q} \sim Dir(\boldsymbol\alpha)$. Here $\boldsymbol\alpha$ is dirichlet parameter $\boldsymbol\alpha=[\alpha_1,\alpha_2,...,\alpha_k]$ and $\alpha_0=\sum\limits_{j=1}^{k}\alpha_j$. Then, the probability density of $\mathbf{q}$ is given by:

Graphical Model:

Suppose $\{x_i\}$ is a set of samples drawn from $i^{th}$ pmf where $i\in[1,L]$. For eg. $\{x_i\}$ could be a sequence of outputs of a dice $\{1,2,1,3,4,3,6,..\}$. Let $\mathbf{q}_1,\mathbf{q}_2,...,\mathbf{q}_L$ are $L$ pmfs. Then:

Let $n_{ij}$ be the number of outcomes in $\{x_i\}$ sequence of samples that is equal to $j^{th}$ event where $j\in[1,k]$, and let $n_i = \sum\limits_{j=1}^{k} n_{ij}$.

Therefore,

## Blog: Bayesian Sets.

• Tutorials

Bayesian Sets Graphical Model:

Bayesian sets are simple graphical models used to expand a set. For instance, suppose you are given a set of few words (or items) $S=\{cat, dog, lion, ...\}$ which we refer as “seeds” and we wish to expand this set to include all similar words from the given text corpus. Then, we can employ Bayesian sets which rank each item based on its importance of belonging to seed set.

Let $D$ be a data set of items, and $\mathbf{x} \in D$ be an item from this set. Assume the user provides a query set $D_c$ which is a small subset of $D$, bayesian sets rank each item by $score(\mathbf{x})$. This probability ratio can be interpreted as the ratio of the joint probability of observing $x$ and $D_c$ to the probability of independently observing $x$ and $D_c$.

Assume that the parameterized model is $p(\mathbf{x} \vert \theta)$ where $\theta$ are the parameters as shown in figure above. Here, we assume that $\mathbf{x}$ is represented by a binary feature vector and $\theta_j$ is the weight associated with feature $j$. Then,

For each $\mathbf{x}_i$ (Note: $\mathbf{x}$ vector $j^{th}$ component is $x_{.j}$ and bold letters are vectors):

The conjugate prior for the parameters of a Bernoulli distribution is the Beta distribution:

## Blog: Why Regularized Auto-Encoders learn Sparse Representation?

• PaperList

This paper has some great insights to offer in design of autoencoders. As title suggests, it addresses “whether regularized helps in learning sparse representation of the data theoretically?”

Here is the setup: we have an input $\mathbf{x} \in \mathbf{R}^{d}$ which is mapped to latent space $\mathbf{h=s(Wx+b)}$ via autoencoder where $\mathbf{s}$ is encoder activation function, $\mathbf{W} \in \mathbf{R}^{m\times n}$ is the weight matrix, and $\mathbf{b} \in \mathbf{R^m}$ is the encoder bias and $\mathbf{h} \in \mathbf{R^m}$ is hidden representation or outputs of hidden units.

For analysis, paper assumes that decoder is linear i.e. $\mathbf{W^{T}h}$ decodes back the encoded hidden representation and loss is squared loss function. Therefore, for learning $\mathbf{W,b}$ parameters of autoencoder; objective function is:

Now we are interested in sparsity of $\mathbf{h}$, hidden representation.

Besides above, paper makes two more assumptions.

Assumption 1: Data is drawn from a distribution $\mathbf{x} \sim X$ for which $\mathbb{E_x}[\mathbf{x}]=0$ and $\mathbb{E_x}[\mathbf{xx^T]=I}$, where $\mathbf{I}$ is identity matrix.

Basically, it assumes that data is whitened which is reasonable for some cases. There is one more assumption from analysis point of view which is needed for the derivation of theorems, we will see that later.

Finally, for a give data sample $\mathbf{x}$, each hidden unit $h_j$ gets activated if pre-activation unit $a_j$ is greater than $\delta$ threshold:

## Blog: Learning Convolutional Networks for Graphs

• PaperList

For past couple of months, I have been wondering about how convolutional networks can be applied to graphs. As we know, convolutional networks have became the state of the art in image classification and also in natural language processing. It is easy to see how convolutional networks exploits the locality and translation invariance properties in an image. People have now also realized on how to exploit those properties in NLP using convolutional networks efficiently. It is time to look at other, more general, domains such as graphs where notion of locality or receptive field needs to be defined. At this point, we can start thinking about graph neighborhood concepts as it is going to play a major role in connecting with receptive fields of convolutional networks.

## Reading List: ICML Papers 2016

• PaperList

To make a habit of reading more papers, I have decided to write comments, may be some quick or sometime detail, on the papers which I find interesting and related to my research area. Hopefully, this will come handy in solving my own research problems.

Starting with ICML 2016 Papers:

• Revisiting Semi-Supervised Learning with Graph Embeddings ICML 2016
• Why Regularized Auto-Encoders learn Sparse Representation? ICML 2016
• On the Consistency of Feature Selection With Lasso for Non-linear Targets. ICML 2016
• Additive Approximations in High Dimensional Nonparametric Regression via the SALSA. ICML 2016
• The Variational Nystrom method for large-scale spectral problems. ICML 2016
• A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation. ICML 2016 (Possibly a new way to measure difference in probability distribution other than most common – KL divergence )
• Low-Rank Matrix Approximation with Stability. ICML 2016
• Unsupervised Deep Embedding for Clustering Analysis. ICML 2016
• Online Low-Rank Subspace Clustering by Explicit Basis Modeling. ICML 2016
• Community Recovery in Graphs with Locality. ICML 2016
• Analysis of Deep Neural Networks with Extended Data Jacobian Matrix. ICML 2016
• Stochastic Variance Reduced Optimization for Nonconvex Sparse Learning. ICML 2016
• Compressive Spectral Clustering ICML. 2016
• Variance-Reduced and Projection-Free Stochastic Optimization. ICML 2016
• Learning Convolutional Neural Networks for Graphs. ICML 2016
• Discrete Deep Feature Extraction: A Theory and New Architectures. ICML 2016


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# One-step Binomial model's Radon-Nikodym derivative

In the one-step binomial model...

Question 1: What exactly is a '$$\frac{d \mathbb Q}{d \mathbb P}$$'?

I think it's $$\frac{d \mathbb Q}{d \mathbb P} = \frac{q_u}{p_u}1_u + \frac{q_d}{p_d}1_d$$, so it's some asset with payoffs $$\frac{q_u}{p_u}$$ and $$\frac{q_d}{p_d}$$, expected value of 1 and replicating portfolio $$(x,y)$$ of

$$x=\frac{1}{1+R}\frac{u(\frac{q_d}{p_d})-d(\frac{q_u}{p_u})}{u-d}$$ $$y=\frac{1}{S_0}\frac{\frac{q_u}{p_u}-\frac{q_d}{p_d}}{u-d}$$

This seems to be some replicating portfolio that is expected to payoff 1 at $$t=1$$.

Well, $$(x,y)=(\frac{1}{1+R},0)$$ seems to give the same payoff but with -100% lower risk

Question 2: What exactly is a/an '$$X\frac{d \mathbb Q}{d \mathbb P}$$'?

We could say that the price of X uses not

$$E[X] = X_up_u+X_dp_d$$

but rather

$$E^{\mathbb Q}[X] = E[X\frac{d \mathbb Q}{d \mathbb P}] = X_u\frac{q_u}{p_u}p_u + \frac{q_d}{p_d}p_d$$

I guess it's some asset that pays $$X_u\frac{q_u}{p_u}$$ or $$X_d\frac{q_d}{p_d}$$ then replicating portfolio is...then idk. Not sure we need one since we're using real world probabilities anyhoo

In economics, the Radon-Nikodym density $$\frac{d \mathbb Q}{d \mathbb P}$$ of the risk-neutral measure $$\mathbb Q$$ with respect to the physical measure $$\mathbb P$$ is the price of Arrow-Debreu securities. It is a price, not a claim.
In the binomial setting, there are two AD securities, $$1_u$$ and $$1_d$$. The former entitles the holder to 1 unit of numeraire if, and only if, state $$u$$ realizes. The no-arbitrage price of $$1_u$$ is $$\frac{q_u}{p_u}1_u$$ (say $$R = 1$$). Similarly for $$1_d$$.
In general, the price of the AD portfolio $$1_{\Omega'}$$---which pays off 1 unit of numeraire if, and only if, state $$\omega \in \Omega'$$ realizes---is $$E^{\mathbb P}[ 1_{\Omega'} \frac{d \mathbb Q}{d \mathbb P}] = \mathbb Q (\Omega').$$ So $$E^{\mathbb P}[\frac{d \mathbb Q}{d \mathbb P}] = 1$$ is then the price of a bond/risk-free security (discount accordingly if $$r \neq 1$$).
Extending from $$1_{\Omega'}$$ to a general $$X$$ gives the usual risk-neutral pricing formula $$E^{\mathbb Q}[X]$$, as you have written out.
• Thanks for answering 1st question. Wait so what exactly is a '$1_{\Omega'} \frac{d \mathbb Q}{d \mathbb P}$' ? That's my 2nd question. I'll edit post to be more clear – BCLC Jul 25 '20 at 8:17


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## Hardness of combinatorial optimization after adding one constraint

I'm interested generally in discrete optimization problems formulated as 0-1 integer programs; essentially, anything of the form $$\Phi = \max_{\mathbf{x} \in \left\{0,1\right\} ^N} f(\mathbf{x})$$

My question is this: suppose the original problem is solvable in polynomial time. Now, add a constraint that $x_i = 0$ or $x_i = 1$:

$$\Phi_{x_i;j} = \max_{\mathbf{x} \in \left\{0,1\right\} ^N, x_i=j} f(\mathbf{x})$$

Can you give me an example problem (preferably a moderately well-known combinatorial optimization problem) where $\Phi_{x_i;j}$ can no longer be found in polynomial time? Alternatively, is there an argument to be made that no such example exists?

Edit: clearly there are cases where a variable can switch between hard and easy problems, so examples will exist. I'm looking for a case that isn't "contrived" in this sense--preferably a well-known combinatorial problem that becomes harder when you condition on a partial solution. Is there some characteristic of functions/problems that describes whether they get harder or easier to solve as you condition on more variable assignments?

-

Okay, here's a less contrived example. While minimal edge coverings can be found in polynomial time, finding a minimal hyperedge covering in general (equivalently, set covering) is NP-hard. On the other hand, finding such a covering when one of the hyperedges spans all vertices on the graph is easy: you just use that edge.

So, given an arbitrary hypergraph, attach a new hyperedge to every vertex and look for a minimal cover. This can be done quickly. But constrain yourself to not using that edge, and you're back to the original NP-hard problem.

-
For a graph $G$ on $n$ vertices, consider binary words of length $2n+1$. This will represent an assignment of colors 1-4 on the $n$ vertices, with the last bit telling us what the restriction on neighboring colors is. Namely, if the last digit is $i$, then $f$ spits out a 0 (calls it an improper coloring) if some pair of adjacent vertices have colors that are $i$ apart. When it is proper, $f$ spits out the reciprocal of the number of colors used.
 Thanks. Any $f$ with this sort of switching behavior of course will work--so clearly there are examples. I'm looking for a less contrived example. For example, if bipartite matching became hard when fixing $u_i$ to be matched to $v_j$, that would be ideal (I know that's not the case for bipartite matching--it's just an example). Also, are there conditions that can be placed on $f$ that cause this condition to hold or not hold? – Andrew Dec 24 2009 at 1:18


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FPS Weapon

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This could be a general subject, but im searching for a precise answer in relation with DirectX. I'm currently working on a game engine and now im on the first person wepon part. You know the arm with a gun who always follow you everywhere ? So, that was hard to make it follow correctly the camera, but i finally did it. Now that this work, my problem is that the weapon get trough things. I thought that wasn't a problem since with collision the gun should never get trough walls, but to have a good size at the screen the weapon has to be big, and so the collision box could be strange. So, is there a way to say to directx to always draw the gun over the rest (but not over gui of course), or another solution ? thanks !

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It is quite easy actually.

1. Draw the scene like you used to do.
2. Turn of the zbuffer in the DirectX device by setting the zbufferenabled value to false. This makes sure that the weapon doesn't use the zbuffer so it is always rendered "on top". Don't forget to enable the zbuffer again after this step.
3. Render the overlay.

Hope this works for you!

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I tought about that. The problem is that the gun is a mesh, composed of subsets wich render sepraratly. So by desactivating z buffering i screw all. Polygons going oevr each other and all the rest you can imagine.

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i haven't used direct x before, but its available in opengl, so you'll have to look for the equivalent function. what you need to do is clear the z buffer.

basic steps
Draw entire scene excluding gun and hud.
clear z buffer
draw gun
draw hud

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I think my explanation was not enough clear. The problem with z-buffering is in the gun itself. Because, for example, the back part of the canon draw over the handle, ect..

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and you are sure you have enabled z buffer reads/writes?

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If you are using matrices and vectors the correct way, it should be easy to calculate the final world-space position of the gun. At that point, you can perform collision detection on it.

Since you are coding an FPS application, I assume that you are using a quaternion-based camera. Basically, this allows you to move in the direction that you are pointing.

Camera-Relevant Code:

// Update player positionplayerPosition.yaw	+= playerPosition.yawVel;playerPosition.pitch	+= playerPosition.pitchVel;// Normalize and addD3DXVECTOR3 cameraVel;D3DXVec3TransformNormal( &cameraVel, &playerPosition.vel, &matOrientation );playerPosition.pos += cameraVel;// Use quaternions to rotate the camera and avoid gimble lockD3DXQUATERNION quat;D3DXQuaternionRotationYawPitchRoll( &quat, playerPosition.yaw, playerPosition.pitch, playerPosition.roll );D3DXMatrixAffineTransformation( &matOrientation, 1.25f, NULL, &quat, &playerPosition.pos );D3DXMatrixInverse( &matView, NULL, &matOrientation );

The following code will offset the player's position to obtain the gun's position:

/* BUILD THE GUN MATRIX */D3DXVECTOR3 meshModify = D3DXVECTOR3( 3.0f, -1.5f, 10.5f );			// Offset from camera positionD3DXVec3TransformNormal( &meshModify, &meshModify, &matOrientation );	// NormalizeD3DXVECTOR3 meshPosition = playerPosition.pos + meshModify;			// Add to player's position// Build translation matrixD3DXMatrixTranslation( &matMeshWorld, meshPosition.x, meshPosition.y, meshPosition.z );// Build rotation matrixD3DXMATRIX rotation;D3DXMatrixRotationYawPitchRoll( &rotation, playerPosition.yaw, playerPosition.pitch, playerPosition.roll );// Combine rotation and transformationmatMeshWorld = rotation * matMeshWorld;

You now have the final world-space position in meshPosition, and the final world-space matrix in matMeshWorld.

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Draw the scene
CLEAR the z-buffer but don't turn ZBUFFER off! and dont turn zwite-enabe off!
To draw the weapon succesfully, translate it farer (not so close) from the camera! (sorry, my english is...)
near clip-plane here:|
|
WEAPON MESH WEAPON MESH WEAPON MESH
|
|
THIS SECTION <-- before the NearCplane. will to be drawn.

So, translate it, into the current position.
(It's able, that you have to set som things in the MatrixPerspFOV before the Weapon drawing.)

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I've been told before by a few graphics guys that they don't want to do the clear zbuffer then draw gun because it stalls the pipeline. Is this true? and if so does it incur a significant performance penalty? Also that it apparently doesn't work when using some types of shadowing.

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Why don't you look at how Quake 3 does it (Quake 3 was open sourced after all). It may not use DX but who cares? The concepts are still there. If you still insist on seeing DX code then check out DXQuake3. :)

-SirKnight

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# What is the mass of "sodium bicarbonate", NaHCO_3, in "amu"?

Jun 5, 2017

For $N a H C {O}_{3}$, well take...........................
{1xx23+1xx1+1xx12+3xx16}*"u"=??

#### Explanation:

And I make this $84 \cdot u \ldots \ldots \ldots \ldots . .$

From where did I get the individual atomic masses?


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# Fairy Tale Story?

So the Vegas Golden Knights, about the stupidest unnecessarily long name in all of pro sports, may make the Stanley Cup finals in just their first year. The media is going crazy over this. Vegas is eating it all up. Fairy tale story, right?

Not even close.

First off, this idea that Vegas cares about this team is completely based on the fact they are winning. This is not unusual at all, but Vegas is not a solid sports town. It is highly transient, never had a history of supporting any team (UNLV had its day, but that is as close as it gets), and is in the middle of the desert…..why hockey? Need proof? Well, when they did their inaugural season ticket drive 3 years ago (the NHL’s way of dipping their toe in the water to gauge interest), Vegas had a goal of selling 10,000 spots. They did……after lowering their price to hold a seat to $150 and thrwoing in swag like shirts and jerseys………in over a month. In contrast, Seattle ran their ticket drive a few months ago. They sold 10,000 seats in 12 minutes….for$500 a pop….no swag.

Secondly, this new Vegas team is being branded as a bunch of cast-offs and no-names that other teams abandoned, much like all other expansion drafts in the past. This is simply not the case. The rules for this particular expansion draft was very favorable to the new team. Without getting into specifics, teams only could have protected 14-16 players (depending on if they were goalies, defenders, etc). This let Vegas pick many quality players; some at the end of contracts, some veterans that did not fit in a team’s long-term plans, and ex-good players that may have had one bad season. I mean why else is Vegas’s goalie a former Stanley Cup winner for the Penguins? As a result of this, NHL teams are furious at these expansion rules and will surely change them when Seattle gets their team.

Finally, think about all of the other franchises that have struggled over years and years. Their fans care just as much, if not more, than these fake Vegas fans. They have built up more sports collateral and deserve a team with success far more than this beginner’s luck Vegas thing. I mean ask any St Louis Blues fan what they think, or a Canucks fan if they feel this is fair. Or even better, ask yourself as a long suffering fan of team X if this was happening against your franchise?

Vegas is not a real city at all. A small, made-up little town in the middle of the desert run by a bunch of broken-noses and other seedy folks, does not deserve any franchise at all, much less a winning one after one season. This is not a fairy tale, as the media lazily likes to proclaim it is, it is some serious bullpoo.