Nucleus validation Inside the nucleus of an atom is the Coulomb's law valid? I mean that between proton, neutron and other elementary particles, i.e., meson etc. What will be the limit or validity of charges between them. I mean can Coulomb's law can be applied here?
What is the range of the validity of Coulomb's law? What is the smallest and biggest distance in which  is valid?  Please provide a reference to a scientific journal or book. Just saying that this law is valid from this range to that range is not enough. Which experiments did result to these ranges?
Matrix given by $a_{ij} = 1/(i+j)$ is non-singular. How can I know if $2^{2^{2^{2^{2}}}}+1=?$ is prime? How to rename a group of files with what looks like a Windows file path in their names I got a bunch of files with the filename messed up. All the file names have the same beginning which appear to be windows file directories. The problem is there are 700+ files and I really don't want go through and manually rename all of them. These are examples of the file names (Note: None of these have file directories):  G:some\really\long\file\path\then\the\name1.jpg G:some\really\long\file\path\then\the\name2.png G:some\really\long\file\path\then\the\filename.txt G:some\really\long\file\path\then\the\file_name.mov ...   The important take away is that each file has G:some\really\long\file\path\then\the\ before the file name that I would like.   So I would want the above files to look like:  name1.jpg name2.png filename.txt file_name.mov   I've tried the rename command and was not successful. I am still new with Linux and really am not sure on how to go about it or really what to google. Any help would be appreciated. dpkg: error: parsing file '/var/lib/dpkg/updates/0045' near line 0: Why does polynomial factorization generalize to matrices I'm reading about linear algebra and I came across with the following theorem where I have a problem convincing myself:      Theorem 2.1 $\,$ Every linear operator on a finite-dimensional complex vector space has an eigenvalue.      Proof:       To show that $T$ (our linear operator on $V$) has an   eigenvalue, fix any nonzero vector $v \in V$. The vectors $v, Tv,  T^2v,..., T^nv$ cannot be linearly independent, because $V$ has   dimension $n$ and we have $n + 1$ vectors. Thus there exist complex   numbers $a_0,...,a_n$, not all $0$, such that      $$a_0v + a_1Tv + ··· + a_nT^nv = 0.$$ Make the $a$’s the coefficients   of a polynomial, which can be written in factored form as $$a_0 + a_1z  + ··· + a_nz^n = c(z − r_1)\cdots(z − r_m),$$ where $c$ is a non-zero complex number, each $r_j$ is complex, and the equation holds for all   complex $z$. We then have      $${\color{red}{ 0=(a_0I + a_1T + ··· + a_nT^n)v= c(T − r_1I)\cdots(T −  r_mI)v}},$$ which means that $T − r_j$ I is not injective for at least   one $j$. In other words, $T$ has an eigenvalue.$\;\blacksquare$   I'm having trouble with the factorized form of the matrix polynomial (in red). I understood that the factorization holds for a polynomial by the fundamental theorem of algebra but why does this also hold for matrices?  In other words, why is the the part I highlighted true? Does such an factorization always exist?    Could I have some help to see this? Thank you =)   P.S.  is my reference (page 3).  UPDATE:   Someone else also has asked the  before it seems. Account "last activity time" is not always updated It would appear that the account's "Last activity time" is not updated for every hit.  I've been active on SO all morning, and in the last five minutes have voted on some posts as well as posted an answer.  However,  says:     "Last activity: 2 hours ago from &lt;IP address&gt;"   Is there a certain amount of time that needs to elapse between hits before the activity time is updated again?  This issue could result in Enthusiast badges not being awarded when they should. Database does not update automatically with MySQL and Python I'm having some trouble updating a row in a MySQL database. Here is the code I'm trying to run:  import MySQLdb  conn=MySQLdb.connect(host="localhost", user="root", passwd="pass", db="dbname") cursor=conn.cursor()  cursor.execute("UPDATE compinfo SET Co_num=4 WHERE ID=100") cursor.execute("SELECT Co_num FROM compinfo WHERE ID=100") results = cursor.fetchall()  for row in results:     print row[0]  print "Number of rows updated: %d" % cursor.rowcount  cursor.close() conn.close()   The output I get when I run this program is:     4Number of rows updated: 1   It seems like it's working but if I query the database from the MySQL command line interface (CLI) I find that it was not updated at all. However, if from the CLI I enter UPDATE compinfo SET Co_num=4 WHERE ID=100; the database is updated as expected.  What is my problem? I'm running Python 2.5.2 with MySQL 5.1.30 on a Windows box. Why is the Mann–Whitney U test significant when the medians are equal? I've received a results from a Mann-Whitney rank test that I don't understand.  The median of the 2 populations is identical (6.9). The uppper and lower quantiles of each population are:   6.64 &amp; 7.2 6.60 &amp; 7.1   The p-value resulting from the test comparing these populations is 0.007. How can these populations be significantly different? Is it due to the spread about the median? A boxplot comparing the 2 shows that the second one has far more outliers than the first. Thanks for any suggestions. what is wrong with this??? please,can anyone help?  \begin{equation} \label{probabilityy} P^{t}({E_{0})=P_{0}+(1-P_{0})P_{1}+ (1-P_{0})(1-P_{1})P_{2}+.......+P_{n}\Pi_{k_{0}}^{n-1}(1-P_{k}) \end{equation} Isle vs. Island I just started real analysis.  I don't have a background in proofs or logic, simply calculus.  So I'm trying to learn more about proofs--so forgive the basic question, please.  How do you go about proving this theorem: If $a$ and $b$ are any numbers, then there is one and only one number $x$ such that $a + x=b$.  This number is given by $x=b+(-a)$.  First part of the proof I understand--it's simple.  We simply use some axioms and do the following:  $a+b-a=b$, which of course is true.  This is just true from plugging in the $b+(-a)$ for $x$.  But how about the uniqueness issue?  In my text, it says:  $$(a+x)+(-a)=b+(-a) x=b+(-a)$$  How does this prove uniqueness?  Is this equation essentially saying that the ONLY possible value of $x$ is expressed by $b+(-a)$?  How would I have known to set this up as part of the proof if I was asked to prove something is unique?  Sorry for the basic question--have to start somewhere. chkrootkit shows "tcpd" as INFECTED. Is it a false positive? Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $ How can I prove that $${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $$  I tried the following:  We use the :  $$y^{\underline k}=\underbrace{y(y-1)(y-2)\ldots(y-k+1)}_{k\text{ factors}},$$ so that $\binom{y}k=\frac{y^{\underline k}}{k!} .$   Then  $${x +y+n- 1 \choose n} = \frac{(x +y+n- 1)!}{n! ((x +y+n- 1) - n)!} =  \frac{1}{n!}. (x +y+n \color{#f00}{-1})^{\underline n} $$  And  $$ {x+n-k-1 \choose n-k}{y+k-1 \choose k}$$ $$\frac{1}{(n-k)!}.(x+n-k-1)^{\underline{n-k}}.\frac{1}{k!}.(y+k-1)^{\underline{k}}$$ $$\frac{1}{k!.(n-k)!}.(x+n-k-1)^{\underline{n-k}}.(y+k-1)^{\underline{k}}$$ $$\sum_{k=0}^n{n \choose k}(x+n-k-1)^{\underline{n-k}}.(y+k-1)^{\underline{k}}$$  According to the Binomial-coefficients:  $$ ((x+n-k-1) + (y+k-1))^{\underline{n}}$$ $$ (x+y+n\color{#f00}{- 2})^{\underline{n}}$$  What is wrong ? und How can I continue?  :/ I installed Ubuntu 12.04 a month ago and am using it till now. I failed to notice that all this time there was no sound at all while running Ubuntu, even while playing a game in Wine. The weird thing is that only the startup sound comes when I log in (Indian/African drum tone), then comes the utter silence.  I tested both Digital Output (S/PDIF) and the speakers in the sound settings but can hear nothing.  Any help? Why does DNS work the way it does? This is a  about DNS (Domain Name Service).   If my understanding of the DNS system is correct, the .com registry holds a table that maps domains (www.example.com) to DNS servers.   What is the advantage? Why not map directly to an IP address? If the only record that needs to change when I am configuring a DNS server to point to a different IP address, is located at the DNS server, why isn't the process instant? If the only reason for the delay are DNS caches, is it possible to bypass them, so I can see what is happening in real time? I really like the new sidebar. With the new top bar eliminating the &quot;Hot Questions&quot; area there, I think this is the perfect place for it. One-click access to time-wasting questions about topics I may or may not have an interest in. Seriously, it's a procrastinator's dream come true. The only suggestion I can add is to extend it. I assume the &quot;hot&quot; algorithm can spit out more than 12 questions, and since we now have a huge amount of room for it(without being restricted to a weird drop-down scrollbox), why not show more? If there's something else planned for that spot, disregard. At a minimum, the title could link to the , as ShaWizDowArd suggested in comments. I've been using SE for a couple years now, and I've never seen that page, so it would add visibility there.    Update: They added a link! Just noticed this, I'm pretty sure it wasn't there yesterday. When you click it, it loads 12 more. At the moment, the link disappears once clicked, so you can see a total of 24 here now. Not a link to the full list, but better: Step to step how to install Cinelerra I have some problems installing cinelerra on my Ubuntu.  How do I install it? To make your opinion known on MSE you need both up and downvotes. Given at the moment you need 125 rep to downvote on this site, the voting patterns will be skewed positive because not everyone is active on the site.   This is to be expected for regular Stack Exchange sites as you are expected to be involved in the community before you are deemed knowledgeable enough to be part of the community voice. However, MSE is different because you are voting for the entirety of the Stack Exchange network and you shouldn't need to be active on MSE itself to have a voice on changes to the entire network.  This is especially important for questions like  because it will effect every network to do with coding at all. This was brought up in .  I would suggest reducing the rep required to downvote on MSE down to 100 (or 101) rep. This is the amount you get for the site association bonus. This is given once you achieve 200 rep on any network site and shows that you are active in at least one community. I think this would be the perfect use of the association bonus in showing that you are a member of the Stack Exchange community. apt-get install with '-' (minus / hyphen) removes packages I was looking for some package (nautilus-terminal), and accidentally did this:  $ sudo apt-get install nautilus- Reading package lists... Done                                                                                                                                                                                                  Building dependency tree                                                                                                                                                                                                       Reading state information... Done                                                                                                                                                                                              The following packages were automatically installed and are no longer required:                                                                                                                                                  apturl apturl-common libgail-3-0 linux-headers-4.4.0-57 linux-headers-4.4.0-57-generic linux-image-4.4.0-57-generic linux-image-extra-4.4.0-57-generic                                                                       Use 'sudo apt autoremove' to remove them.                                                                                                                                                                                      The following packages will be REMOVED:                                                                                                                                                                                          gnome-session-flashback nautilus nautilus-sendto nautilus-share ubuntu-desktop                                                                                                                                               0 upgraded, 0 newly installed, 5 to remove and 69 not upgraded.                                                                                                                                                                After this operation, 2 031 kB disk space will be freed.                                                                                                                                                                       Do you want to continue? [Y/n] ^[[^C                                                                                                                                                                                             That's quite dangerous because remove is much harder to mistype than a simple dash from a failed autocompletion.     Is that an equivalent of apt-get remove? I couldn't find any documentation for that. Edit: except for overlooking the man page... How do I find values not given in (interpolate in) statistical tables? Often people use programs to obtain p-values, but sometimes - for whatever reason - it may be necessary to obtain a critical value from a set of tables.   Given a statistical table with a limited number of significance levels, and a limited number of degrees of freedom, how do I obtain approximate critical values at other significance levels or degrees of freedom (such as with $t$, chi-square, or $F$ tables)?  That is, how do I find the values "in between" the values in a table?