I read in a physics today paper,  The electron can have nonvanishing EDM only if nature violates symmetry under time reversal (T) and under the combined operations of charge conjugation (C), which replaces particle by antiparticle (as we all know), and parity inversion (P).  I checked . So it will be nice if you can show me qualitatively and quantitatively about the above mentioned point.  Note: Simplicity in explanation is always nice. (I don't have much idea of these big words)
I am wondering if the mass density profile $\rho(\vec{r})$ has been characterized for atomic particles such as quarks and electrons. I am currently taking an intro class in quantum mechanics, and I have run this question by several professors. It is my understanding from the viewpoint of quantum physics a particle's position is given by a probability density function $\Psi(\vec{r},t)$. I also understand that when books quote the "radius" of an electron they are typically referring to some approximate range into which an electron is "likely" to fall, say, one standard deviation from the expectation value of its position or maybe $10^{-15}$ meters.  However it is my impression that, in this viewpoint, wherever the particle "is" or even whether or not the particle "had" any position to begin with (via the Bell Inequalities), it is assumed that if it were (somehow) found, it would be a point mass. This has been verified by my professors and GSIs. I am wondering if its really true.  If the particle was truly a point mass then wherever it is, it would presumably have an infinite mass density. Wouldn't that make electrons and quarks indistinguishable from very tiny black holes? Is there any practical difference between saying that subatomic particles are black holes and that they are point masses? I am aware of such problems as Hawking Radiation although at the scales of the Schwarchild radius of an electron (back of the envelope calculation yields $\tilde{}10^{-57}$ meters), would it really make any more sense to use quantum mechanics as opposed to general relativity?  If anyone knows of an upper bound on the volume over which an electron/quark/gluon/anything else is distributed I would be interested to know. A quick Google Search has yielded nothing but the "classical" electron radius, which is not what I am referring to.  Thanks in advance; look forward to the responses.
I'm working on a large c++ system that is has been in development for a few years now. As part of an effort to improve the quality of the existing code we engaged on a large long-term refactoring project.  Do you know a good tool that can help me write unit tests in C++? Maybe something similar to Junit or Nunit?  Can anyone give some good advice on the methodology of writing unit tests for modules that were written without unit testing in mind? How can one set the executable bit on files using umask? According to documentation, a umask of 000 should work, but in practice this only works on directories.  Also open to other methods of automatically setting +rwx on a particular user's created files if you have any. When a permanent magnet attracts some object, lets say a steel ball, energy is converted into for instance kinetic energy and heat when attraction happens, and they eventually collide. Does this imply that energy is drawn from the magnetic field and the magnet is depleted, making it weaker and weaker for each magnetic attraction performed?  (if the answer requires Quantum Mechanical explanations, please elaborate :)) Find when three numbers have the same remainder when divided by the same number If three numbers 112, 232, and 400 are each divided by the number D, each of their quotients will have the same remainder R. Find R where R>1  How should I approach this? How to break out of multiple loops? Given the following code (that doesn't work):  while True:     #snip: print out current state     while True:         ok = get_input("Is this ok? (y/n)")         if ok.lower() == "y": break 2 #this doesn't work :(         if ok.lower() == "n": break     #do more processing with menus and stuff   Is there a way to make this work? Or do I have do one check to break out of the input loop, then another, more limited, check in the outside loop to break out all together if the user is satisfied? So I noticed that many cards with tap-effects ship with a clause specifying that they can only be used on untapped permanents, such as  and .  So here's my question:   Doesn't that imply that, given the right situation, one can legally tap an already tapped permanent?   I'll give an example of the kinda scenarios this is relevant for: Can  activate her first ability when no untapped cards are around? Or, thinking untap-effects, could I bounce a forest with  even when there isn't a tapped creature available?  Notice that, unlike the previous batch of examples, the wording on these lacks the clause restricting their use to un/tapped permanents - does that mean that they aren't?  Any kind of clarification would be greatly appreciated here. How to measure supply currents ranging from 1μA to 10mA? I'm trying to show that for $b&gt;1$, $x&gt;0$ and $x$ irrational, that $$\sup \{b^p:p\in Q,\;0&lt;p&lt;x\} = \inf\{b^q:q\in Q,\;x&lt;q\}$$ I know this follows immediately if we define $b^x=\exp(x\log(b))$ and use the fact that the exponential function is strictly increasing and continuous over $\mathbb R$, but I'm not allowed to do that. In fact, I only have that $b^{m/n}=(b^{1/n})^m$, where $b^{1/n}$ means the positive $n^{th}$ root of $b$; $b^x$ is not yet defined for irrational $x$.  I know that the supremum and infimum both exist because if $b&gt;1$ and $p&lt;q$, then $b^p&lt;b^q$. Also, by assuming that the inf $&lt;$ sup, I got a contradiction. The part I'm stuck on is deriving a contradiction from assuming that sup $&lt;$ inf. Does anybody have any ideas?  Thank you. Hiding downvoted questions silences important discussions on Meta I just noticed a particular MSE post today on a topic I care about that was posted almost a week ago, which I entirely missed before. I'm a pretty avid MSE user, and this happens quite rarely to me.     was created by an SE employee, and is essentially the final answer to , which is the 10th most upvoted MSE post with a bit more than 900 upvotes right now. So it's kind of an important post, and on a topic I care about, but I still missed it entirely until it was linked in a comment somewhere else.  The reason I missed it is because it's heavily downvoted. This means that as it has below -8 score, it's hidden from the home page entirely, drastically reducing the visibility of the post. In particular, the negative score removes all visibility a question usually receives from being bumped due to edits, new answers and bounties.   Many of the recent heavily-downvoted Meta posts by SE have been featured manually, which grants them a lot of visibility beyond the particular meta site. This masked the problem pretty efficiently, but it is more of a workaround, and one that isn't applicable to all situations.  Voting means something different on meta sites, and not every downvoted question should be hidden from view. Closed downvoted questions can certainly still be affected by the usual rules on the home page, and that should cover the vast majority of questions that actually have a purpose being on the home page. But open questions should be displayed on the home page on meta sites even if they're heavily downvoted. Why are date-based hats awarded too early? I just got the  hat which states "post or vote on December 21".  Does SE have a time machine now? Can I register a domain name that contains a company name or trademark? I wonder is it legal to register a domain name that contains a company name. For example cococola.cc (considering that this domain name is available). Can I buy and use any domain names that contain a name of a trademark? Is it possible in Minecraft to switch over from survival to creative in single player? Let Y(1), Y(2), Y(3), Y(4), Y(5) denote the order statistics of a random sample of size 5 from a distribution having p.d.f. Help me to solve this problem please..  Let $Y_{(1)}, Y_{(2)}, Y_{(3)}, Y_{(4)}, Y_{(5)}$ denote the order statistics of a random sample of size 5 from a distribution having p.d.f. $f(y) = e^{(-y)}, 0 &lt; y &lt; \infty$, zero elsewhere. Show that $Z_1 = Y_{(2)}$ and $Z_2 = Y_{(4)} − Y_{(2)}$  are independent. Hint: First find the joint p.d.f. of $Y_{(2)}$  and  $Y_{(4)}$. Studying for CISSP these choices seemed limited:     What is the advantage of digital signatures over message authentication codes?         Digital Signature provides integrity verification while message authentication code does not   Digital Signature provides confidentiality while message authentication code does not   Digital Signatures provide authenticity while message authentication code does not   Digital Signatures works faster than message authentication codes      Using the following chart as a reference, I'm leaning towards #2, but none of the choices really fit properly…  Cryptographic primitive | Hash |    MAC    | Digital Security Goal           |      |           | signature ------------------------+------+-----------+------------- Integrity               |  Yes |    Yes    |   Yes Authentication          |  No  |    Yes    |   Yes Non-repudiation         |  No  |    No     |   Yes ------------------------+------+-----------+------------- Kind of keys            | none | symmetric | asymmetric                         |      |    keys   |    keys   Hopefully an expert here can clarify. $|a_{n+1}-a_n| \leq \frac{1}{2} |a_{n}-a_{n-1}|$. I'm trying to show that $(a_n)$ is convergent by showing that $(a_n)$ is Cauchy.  let $|a_2 - a_1 |  =x$.   $|a_3-a_2| \leq \frac{1}{2}x$  $|a_4-a_3| \leq \frac{1}{2}|a_3-a_2|\leq \frac{1}{4}x$  In general, for every $n$:  $|a_{n+1}-a_n| \le \frac {1}{2^{n-1}}x$  Let $\epsilon &gt;0$  for every $m,n &gt; 0 $, say $m&gt;n$ the following holds:  $$|a_m-a_n| = |a_m-a_{m-1} + a_{m-1} - a_{m-2} \dots a_{n+1}- a_n| \le$$  $$|a_m-a_{m-1}| + |a_{m-1} - a_{m-2}| + \dots |a_{n+1}-a_n| \leq \frac{x}{2^{m-2}} + \frac{x}{2^{m-3}} + \dots + \frac{x }{2^{n-1}}$$.  I can say that for big enough $n,m$, $|a_m-a_n|&lt;\epsilon$ and therefore, this sequence is Cauchy? It sounds not good enough to me yet I don't know what else to do here. I have a question regarding classification in general. Let $f$ be a classifier, which outputs a set of probabilities given some data D. Normally, one would say: well, if $P(c|D) &gt; 0.5$, we will assign a class 1, otherwise 0 (let this be a binary classification).   My question is, what if I find out, that if I classify the class as 1 also when the probabilities are larger than, for instance 0.2, and the classifier performs better. Is it legitimate to then use this new threshold when doing classification?  I would interpret the necessity for lower classification bound in the context of the data emitting a smaller signal; yet still significant for the classification problem.  I realize this is one way to do it. However, if this is not correct thinking of reducing the threshold, what would be some data transformations, which emphasize individual features in a similar manner, so that the threshold can remain at 0.5? What is the integral of 1/x? What is the integral of $\frac{1}{x}$? Do you get $\ln(x)$ or $\ln|x|$? In general, does integrating $f'(x)/f(x)$ give $\ln(f(x))$ or $\ln|f(x)|$? Also, what is the derivative of $|f(x)|$? Is it $f'(x)$ or $|f'(x)|$? A regular expression to exclude a word/string Firstly, this is a homework problem so please do not just give an answer away. Hints and suggestions are really all I'm looking for.  I must prove the following using mathematical induction:     For all $n\in\mathbb{Z^+}$, $1+2+2^2+2^3+\cdots+2^n=2^{n+1}-1$.   This is what I have in my proof so far:     Proof: Let $p\left(n\right)$ be $\sum_{j=0}^n 2^j=1+2+2^2+\cdots+2^n=2^{n+1}-1$. Then $P\left(0\right)$ is    \begin{align} \sum\limits_{j=0}^0 2^j=1=2^1-1.\tag{1} \end{align} Hence    $P\left(0\right)$ is true. Next, for some $k\in\mathbb{Z^+}$, assume    $P\left(k\right)$ is true. Then \begin{align}  \sum\limits_{j=0}^{k+1}2^j&amp;=\left(\sum\limits_{j=0}^k  2^j\right)+2^{k+1}\tag{2}\\ &amp;=2^{k+1}-1+2^{k+1}\tag{3} \\ &amp;=2\cdot 2^{k+1}-1\tag{4}\\ &amp;=2^{k+2}-1\tag{5}\\ &amp;=2^{\left(k+1\right)+1}-1.\tag{6} \end{align}   Therefore, $P\left(n\right)$ holds for all $n$.$\;\;\;\;\blacksquare$   Is everything right? My professor went over the methodology in class quite fast (and I had a bit too much coffee that night) and I want to make sure I have it down for tomorrow night's exam. How can I make my browser lie about my operating system? I'm using Chromium (Version 30.0.1599.114 Ubuntu 12.10) under Linux. I'm trying to access  that claims that it doesn't work under Linux. Of course, this is most likely crazy since the web is platform-independent (unless they're using some kind of evil plug-in).  I've used a user agent switcher to supply a Windows user agent, but to no avail. Upon viewing the source, it appears that the site is using Javascript to determine the operating system. I'm looking for a way to get my browser to report in Javascript that it is Windows or MacOS.  Do you know how to do it?