On generalised character counting number of solutions of $x^n = 1$
Problem 4.6, I. Martin Isaacs' Character Theory
Can you flank with a reach weapon? The Variant: Flanking rules in the DMG (page 251) require adjacency, but is the intent that the Enemy has combatants on opposite sides and thus someone with Reach (and using the reach) could still flank even if not directly adjacent?  Looking for both RAW as well as Intent of the flanking rule. Argument list too long error for rm, cp, mv commands Prove that $\sum_{n=2}^\infty (\ln n)^{- \ln n}$ converges As the title suggests, I'd like to prove that the sum $$ \sum_{n=2}^\infty (\ln n)^{- \ln n} $$ is finite.  The root and ratio test both fail here, but  suggests that there is a comparison that can be used to show convergence.  The only thought I have is that it may help to write the terms as $e^{-\ln(n)\ln(\ln(n))}$, but this has not led me to any particular insight.  Any ideas are appreciated. Time taken for collision We have three particles at the vertices of equilateral triangle of side $d$. At $t=0$ they start moving in such away that at all instant of time each of them has a speed $v$ towards adjacent one. We have to find the time after which they will collide. I know that you can solve this by calculating from reference frame of any one particle, but I want a way to solve this by calculating the total distance traveled first in ground frame and then dividing by speed. How does Java's PreparedStatement work? Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$ Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$? Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$?   If I can show that $y^3+z^3-1$ is irreducible, I believe I can use Eisenstein's criterion. But I don't see how to show even this.  The other approach on my mind is to show that $k[x,y,z]/(x^3+y^3+z^3-1)$ is an integral domain, but this doesn't seem particularly promising either. Recovering the data from a failed WD My Book NAS drive My Western Digital 500GB NAS drive (which is my main backup device) has recently broken. Windows can no longer use it as a network drive (using Map Network Drive), and the web-based control panel is INCREDIBLY sluggish, taking as much as 5 minutes to load a single page.  However, when it does load, it reports the Drive Status as OK, and has the correct disk usage values, which leads me to think the actual drive is OK, and it's the networking components that have failed.  I have checked the wires and router, and so it their isn't another point in the network causing the problem.  Is there any way to get the data back? It's a backup, so I still have about 80% of the data spread out across 3 computers (the only major loss being my music library, and I have the discs for a fair proportion of that).  However, it'd be much more convenient if I can get the data from the drive itself, as it is organised properly on the drive. What is the advantage of using sudo apt-get autoremove over a cleaner app? Apex:OutputText to Currency Format from String Wrapper is there a way to pass a string to the &lt;apex:outputText&gt; so that it can be formatted as a currency or percent value?  Here's what I have inside a column of my visual force table:  &lt;apex:outputText value="{0, number, currecny}"&gt; &lt;apex:param value="{!row.values[1]}" /&gt; &lt;/apex:outputText   this gives me an error at runtime (when the visual force page loads), which I think may be some kind of type mismatch, where &lt;apex:outputText&gt; is expecting a Decimal or number but I am passing a string.  This is the error at runtime:     The value attribute on  is not in a valid format. It must be a positive number, and of type Number, Date, Time, or Choice.   Thanks Prove $\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$ with the epsilon-delta definition of limit. It is well known that   $$\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$$  I know several proofs of this: the geometric proof shows that $\cos(\theta)\leq\frac {\sin(\theta)}{\theta}\leq1$ and using the Squeeze Theorem I conclude that $\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$, other proof uses the Maclaurin series of $\sin(x)$. My question is: is there a demonstration of this limit using the epsilon-delta definition of limit? Appending the same string to a list of strings in Python Are there Ubuntu security notices feeds for specific releases How many possible electromagnetic wavelengths are possible? Disclaimer: Please keep in mind that I am a young highschool student with no background in physics, this research was done in the course of an hour, and my reasoning could very well be wrong.  After a short conversation about color, I did some thinking, and read  The answer claims that there are $\infty^{\infty}$ colors   My first problem is the definition of colors, I'm going to simplify this (although it's not the same thing) as electromagnetic frequencies. This is what I mean when I refer to color in the rest of this question  The problem with $\infty^{\infty}$ colors is that the plank length exists. This causes two problems to arise with $\infty^{\infty}$. If $l_p$ is assumed to exist (as it is), this means the smallest distance in the universe is $l_p$. So, all wavelengths of light can be divided into a set, of the wavelengths produced by objects at $0^{\circ}$ Kelvin to $\infty^{\circ}$ Kelvin. According to this logic, there are simply $\infty$ colors.  Things are complicated further, when you introduce the Plank Temperature ($P_t$). $P_t$ is the theoretical limit temperature of the universe (at least for the purposes of light and color) Because an object hotter than $P_t$ will produce light with wavelengths shorter than $l_p$. This would introduce an upper limit on colors too.  Wouldn't this mean that the total number of possible colors is equal to however many plank lengths difference there is between an electromagnetic wave produced by a 0 degree object and a $l_p$ object? And therefor far less than $\infty$? Does this reasoning make sense at all? Find the eigenvector associated with the smallest eigenvalue, not smallest in magnitude Calling future method from batch class? Numbering a set of horizontally distributed equations I guess the proof of the identity $$ \sum_{n = 0}^{\infty} \frac{1}{n!} \equiv \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x $$ explains the connection between such different calculations. How is it done? Suppose $A$ is a $n \times n$ constant matrix. How can I prove $\det(e^A) = e^{\displaystyle \sum_{\lambda_i\in\sigma(A)} \lambda_i}$,  where $\sigma(A)$ is the multiset of eigenvalues of $A$?  The following matlab code shows this is true in $n = 3$ case:  A = rand(3) detA = exp(sum(eig(A))) detmA = det(expm(A)) LaTeX to plain text for e.g. generation of statistics I would like to convert a large LaTeX project (i.e. spanning multiple files) into plain text. The purpose is generation of statistics, so representing mathematics is not an issue. In fact, all mathematics is ideally ignored.  I have found  but could not get it to run. It seems unfinished, but is exactly what I am looking for otherwise.