By the Gerlach-Stern experiment, the silver atom has a net magnetic moment. But silver as a metal is not magnetic. Or more precisely, it does not show any permanent magnetic moment.   What is the reason behind? How about a cluster of silver atoms?
Cu has an unpaired electron in 4s, but it is diamagnetic. I thought that it has to be paramagnetic. What am I missing?
Does the cross-entropy cost make sense in the context of regression? Does the cross-entropy cost make sense in the context of regression (as opposed to classification)? If so, could you give a toy example through TensorFlow? If not, why not?   I was reading about cross-entropy in  by Michael Nielsen and it seems like something that could naturally be used for regression as well as classification, but I don't understand how you'd apply it efficiently in TensorFlow since the loss functions take logits (which I don't really understand either) and they're listed under classification How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$? I would like to find the apothem of a regular pentagon. It follows from   $$\cos \dfrac{2\pi }{5}=\dfrac{-1+\sqrt{5}}{4}.$$  But how can this be proved (geometrically or trigonometrically)? To show for following sequence $\lim_{n \to \infty} a_n = 0$ where $a_n$ = $1.3.5 ... (2n-1)\over 2.4.6...(2n)$ PostgreSQL Shapefile import failed I am very new to PostGIS/PostgreSQL. In fact, I downloaded it because of the answers I got to this question:   I installed both PostgreSQL and PostGIS. But I am not able to import a shapefile to the database? It gives an error, "Shapefile import failed". What am I doing wrong? The keyboard I am trying to create has a lot of Unicode and looks like this:   Being unsuccessful with the following tutorial:    (There are a few errors in the tutorial, and it uses imprecise language such as "Cutting" things instead of "Deleting" them, and it is formatted strangely)   I was wondering if anybody would be so kind to provide a better tutorial with step by step instructions? Unable to Telnet into port 25 on CentOS PostFix Server Inverse function of $x^x$ How can I find the inverse function of $f(x) = x^x$? I cannot seem to find the inverse of this function, or any function in which there is both an $x$ in the exponent as well as the base. I have tried using logs, differentiating, etc, etc, but to no avail. What's the best way to communicate between view controllers? I have a lot of Excel sheets for all sorts of things - but none has ever acted up like this one here:    This used to be a totally normal Excel 2007 sheet which I was able to resize, maximize etc. - but not anymore. The MDI child window is fixed, both in position and size. I cannot move it around, more can I maximize it to use the full size of the screen anymore. I cannot double-click on it's title bar to maximize it either :-(  What happened? What can I do to "undo" whatever I did to it.  Any ideas? I tried to share / undo sharing, I tried to protect / unprotect the sheet - nothing seems to work... Cookie blocked/not saved in IFRAME in Internet Explorer I have two websites, let's say they're example.com and anotherexample.net. On anotherexample.net/page.html, I have an IFRAME SRC="http://example.com/someform.asp". That IFRAME displays a form for the user to fill out and submit to http://example.com/process.asp. When I open the form ("someform.asp") in its own browser window, all works well. However, when I load someform.asp as an IFRAME in IE 6 or IE 7, the cookies for example.com are not saved. In Firefox this problem doesn't appear.  For testing purposes, I've created a similar setup on  .  example.com uses cookie-based sessions (and there's nothing I can do about that), so without cookies, process.asp won't execute. How do I force IE to save those cookies?  Results of sniffing the HTTP traffic: on GET /someform.asp response, there's a valid per-session Set-Cookie header (e.g. Set-Cookie: ASPKSJIUIUGF=JKHJUHVGFYTTYFY), but on POST /process.asp request, there is no Cookie header at all.  Edit3: some AJAX+serverside scripting is apparently capable to sidestep the problem, but that looks very much like a bug, plus it opens a whole new set of . I don't want my applications to use a combination of bug+security hole just because it's easy.  Edit: the P3P policy was the root cause, full explanation below. onChange event doesn't trigger Count number of increasing functions, nondecreasing functions $f: \{1, 2, 3, \ldots, n\} \to \{1, 2, 3, \ldots, m\}$, with $m \geq n$. I stumbled upon a question given like:  Let $m$ and $n$ be two integers such that $m \geq n \geq 1$.   Count the number of functions $$f: \{1, 2, · · · , n\} \to \{1, 2, · · · , m\}$$ of the following two types:  (a) strictly increasing; i.e., whenever $x &lt; y, f(x) &lt; f(y)$, and  (b) non-decreasing; i.e., whenever $x &lt; y, f(x) \leq f(y)$.  I tried in the following way.  For (a). We can say $f(n)&gt;f(n-1)$ AND $f(n)&gt;f(n-2) \ldots f(n)&gt;f(1)$ (total $n-1$ elements)  Similarly for $f(n-1)&gt;f(n-2), f(n-1)&gt;f(n-3) \ldots f(n-1)&gt;f(1)$ (total $n-2$ elements)...  and $f(2)&gt;1$  Like this $$(n-1) + (n-2) + \ldots + (1) = \frac{n(n-1)}{2}$$  Is this correct?  For (b). Since there's equality, it will be $$n + (n-1) + ... (1) = \frac{n(n+1)}{2}$$  Is my approach correct? Any help is appreciated. Thanks in advance. Ubuntu 12.04 on Amilo LA1703 after istalling graphics doesn't start? Is the $\sum\sin(n)/n$ convergent or divergent? Possible Duplicate:          So, in my calculus class (one I'm teaching, not taking), the sum $\sum_{n=1}^\infty \frac{\sin(n)}{n}$ has come up a few times.  Unfortunately, as someone not exactly an expert in the convergence of sums, it seems to resist the few techniques I know.  Certain none of the usual first year calculus tricks (integral test, alternating series test, ratio test, etc.) work, and the only more tricky technique, partial summation, I can think of doesn't seem to work either (one would need that $\sum_{n=1}^N\sin(n)$ is bounded, which I believe is false).  It seems like it should converge, since it switches sign quite often, but on the other hand, the harmonic series can mess with your intuition, so I don't have much trust in that.  So, I ask to you:     Does this series converge? Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$ I want to calculate the sum:$$\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}=$$  $$\sum_{n=1}^\infty\frac{n}{(n+1)!}=$$ $$\sum_{n=1}^\infty\frac{n+1-1}{(n+1)!}=$$ $$\sum_{n=1}^\infty\frac{n+1}{(n+1)!}-\sum_{n=1}^\infty\frac{1}{(n+1)!}=$$ $$\sum_{n=1}^\infty\frac{1}{n!}-\sum_{n=1}^\infty\frac{1}{(n+1)!}.$$  I know that $$\sum_{n=0}^\infty\frac{1}{n!}=e$$  so $$\sum_{n=1}^\infty\frac{1}{n!}=\sum_{n=0}^\infty\frac{1}{n!}-1=e-1$$  But, what can I do for $$\sum_{n=1}^\infty\frac{1}{(n+1)!}$$ ?  Am I allowed to start a sum for $n=-1$ ? How can I bring to a something similar to $$\sum_{n=0}^\infty\frac{1}{n!}$$? What's the best way to check if a String represents an integer in Java? I normally use the following idiom to check if a String can be converted to an integer.  public boolean isInteger( String input ) {     try {         Integer.parseInt( input );         return true;     }     catch( Exception e ) {         return false;     } }   Is it just me, or does this seem a bit hackish?  What's a better way?    See my answer (with benchmarks, based on the  by ) to see why I've reversed my position and accepted  to this problem.  I think this original code will be used by most people because it's quicker to implement, and more maintainable, but it's orders of magnitude slower when non-integer data is provided. Browse for Servers does not display local instance Key Presses in Python No such file or directory? But the file exists! I've downloaded a game (Shank) but the bin file doesn't run. The error that is shown when I try to launch the executable is:  bash: ./shank-linux-120720110-1-bin: No such file or directory I have an array of Foo objects. How do I remove the second element of the array?  I need something similar to RemoveAt() but for a regular array.