Conduction and propagation
How does electricity propagate in a conductor?
Possible Duplicate:          I would like to use round parentheses () instead of square brackets [] for citations in a document that I'm working on.   I figured out how to get them in the text using the round option with natbib.  I can't figure out to have the generated bibliography to show () instead of [] when it lists the references.  What do I need to change to fix the way it formats the bibliography? The link here:  shows that $\max(a,b)=\frac{a+b+|a-b|}{2}$.      Is it true that $\max(|a|,|b|)=\frac{1}{2}(|a|+|b|)$? Writing a compiler in its own language Intuitively, it would seems that a compiler for language Foo cannot itself be written in Foo. More specifically, the first compiler for language Foo cannot be written in Foo, but any subsequent compiler could be written for Foo.  But is this actually true? I have some very vague recollection of reading about a language whose first compiler was written in "itself". Is this possible, and if so how? Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$ Help, Creating a test class for an invocable method (code coverage @ 0%) I would like to declare functions in tikz for multiple uses of the same function within the code.  Sadly, it seems that the tikz "declare function" is not compatible with the french option in babel. Indeed, the following code (that I simplifed on purpose) runs fine :  \documentclass[english]{article} \usepackage{babel}                       \usepackage{tikz}  \begin{document} \begin{tikzpicture}     \tikzset{declare function={Carre(\t)=\t*\t;}}     \draw plot [domain=-1:1] (\x,{Carre(\x)}); \end{tikzpicture} \end{document}   But when I replace   \documentclass[english]{article}   with   \documentclass[english,french]{article}   compilation generates an error. This is what the log file says :     Missing character: There is no = in font nullfont!   Missing character: There is no @ in font nullfont!   Missing character: There is no @ in font nullfont!      Runaway argument?   -1:1] (\x ,{Carre(\x )}); \end {tikzpicture} \end {document}    ! Paragraph ended before \pgfmath@local@@functions was complete.                          \par    l.18       I suspect you've forgotten a `}', causing me to apply this   control sequence to too much text. How can we recover?   My plan is to forget the whole thing and hope for the best.   Before posting this, I updated all packages without success.  Any help welcome! Have we completed Diablo 3 in 9 hours? My friend and i decided to play some Diablo 3. We played for almost 9 hours straight and killed Diablo on the hard difficult. We reached level 41.  We think 9 hours is short for a game like Diablo 3.   Have we missed something? Why are we only level 41? Is there more story? Regression for an outcome (ratio or fraction) between 0 and 1 I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a &gt; 0$ and $b &gt; 0$. So, the ratio would be between $0$ and $1$.  I could use linear regression, although it doesn't naturally limit to 0..1.  I have no reason to believe the relationship is linear, but of course it is often used anyway, as a simple first model.  I could use a logistic regression, although it is normally used to predict the probability of a two-state outcome, not to predict a continuous value from the range 0..1.  Knowing nothing more, would you use linear regression, logistic regression, or hidden option c? I checked yesterday and today the new homepage in the Android app. Very surprised I saw that I would almost reach a silver tag badge, that confused be because I always take a look on possible badges I can get. However I compared the score with the website and I got a total different results. See this two screenshots: Why are SO participants so unfriendly? When will data.SE get updated data? How to align prices in columns when both 2 digit and 4 digit variations of a price exist? I am trying to display data similar to coinmarketcap with prices for coins, some above 1$ in which case they are rounded to 2 zeroes, some below 1$ in which case they have 4 digits following the decimal. I saw a bunch of posts here where people have suggested to use right alignment for numeric applications/prices  Approach 1 Decimal aligned   1. $13,700.05  2.      $0.0048   Approach 2 Right aligned   1. $13700.05  2.   $0.0048   Which of these approaches do you suggest? Thank you for your time $\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups I'm trying to solve this question of Hungerford's Algebra book:     $S_3$ is not the direct product of any family of its proper subgroups.   The same is true of $\mathbb Z_{p^n}$.   The first claim is easy: we note that every subgroup of $S_3$ is of order $2$ or $3$ by Lagrange, since its subgroups are of prime order, they are cyclic, then abelian, but $S_3$ is not abelian, contradiction because $S_3$ is not abelian while the direct product of abelian groups has to be abelian.  My problem is with the second claim, I need help. "Examine whether the given progressions converge (eventually improperly) and determine their limits where applicable.  (a) $$(a_n)_{n\in\mathbb{N}}:=\frac{n^n}{n!}$$  [...]"  I am having problems getting this homework done as I have no clue about convergency at all. Through Mathematica I know that $\lim\limits_{n\to\infty}a_n=+\infty$ however I don't know how to proove it! During my research I found out that for sufficient big $n$ the inequality $x^n\leq n!\leq n^n$ for $x\in\mathbb{R}$ and $n\in\mathbb{N}$ is true. However this doesn't help me at all. Having a look at our lecture notes I developed the following statement: every $x^n$ with $|x| \geq 1$ diverges as $x^n$ is unbounded and therefore has the improper limit $\lim\limits_{n\to\infty}x^n=+\infty$. Furthermore it seems obvious to me that I need to express the terms in a simpler way, like fractions converging to 0 etc, but I don't know how. Neither some work with the $\varepsilon$-definition of limits in combination with the triangle inequality helped me out. Any suggestions or hints?  Information: This is "Analysis for computer scientist" and therefore we haven't "officially" learned any fancy tricks like L'Hôpital's rule etc. just basic properties of $\mathbb{R}$ and some inequalities as this is an introductory lecture. Schadenfreude is the joy or pleasure derived from the misfortunes of others. What is the word for joy or pleasure derived from the happiness of others? Example of a finitely generated module with submodules that are not finitely generated A pseudometric on the space of the measurable functions is complete What is proper way to update D8 DEV? In what cases should I use a comma before "or"? Get different and common items in two arrays with LINQ