I set up an account at BlueHost and my unfinished site is now live at columbiablooms.org.  My understanding is that when I make modifications, such as enhancements, that changes are made not only to the file structure, but also the database meaning that from this point forward I need to make all my changes and content additions to this live site. Also, I want to be very careful to backup both the file structure and the database before I make changes in case I mess things up.  At this point my Acquia Dev Desktop is not very useful since there appears to be no way to merge what I've done on my local machine with what's live out there on the web.
The migration is from the local environment to the production environment. The production environment has run some time and created a lot of articles.   In order to add new things to my site, I added a custom theme and installed CCK, Views and other modules in my local test environment. Now that the local test environment is finished, how do I migrate it to the production environment, without destroying the content of its database?
I'm taking Calculus II next semester so I don't have all the tools from it to back me up but something came up in a discussion this evening that asked me to prove that the following sequence converges. As I'm new to formal math I'm hoping someone can verify my proof, especially step $6$. I must prove that $$\lim_{n\to\infty}P_n=b$$ where $$P_{n+1} = P_n + \frac{b-P_n}{2}$$ $$P_0 = a$$ and $a,b \in \mathbb{R}$ such that $a&gt;b$ My proof goes as follows:   We must prove that $$\lim_{n\to\infty}P_n=b$$  That is, $\forall\epsilon&gt;0$ there exists a $\delta$ such that there exists an $n$ satisfying $$n&gt;\delta \iff b-P_n&lt;\epsilon$$  First, let us prove that $P_n$ is bounded by $b$ by contradiction. Let us choose an $i$ such that $P_i &lt; b$ and $P_{i+1}&gt;b$. Then we have $P_{i+1} = P_i + \Delta P$ where $\Delta P &gt; b-P_i$. but this is impossible because by the definition of the recurrence $\Delta P = \frac{b-P_i}{2} &lt; b-P_i$. Therefore, $P_i$ is bounded from above by $b$.  Additionally, it is trivial to show that $P_{i+1} &gt; P_i$.  With this in mind, choose an arbitrary $\epsilon$. We need to show that there exists an $n$ such that $P_n &gt; b-\epsilon$. Assume the contrary, that $P_n$ is bounded by $\epsilon$.  Using a similar argument to what which was used before, assume $P_n$ is bounded by $\epsilon$ and then there exists a $P_i$ such that $P_{i+1}\not &gt; P_i$. But this results in a contradiction with (4)  Therefore, $P_n$ is not bounded by $\epsilon$ and we have proved what we want to prove. I couldn't add defer tag in plugin javascripts. Google developer pagespeed test suggests me to add defer tag in contact form 7 javascripts.   This is how contact form 7 includes javascript in header.  add_action( 'wp_enqueue_scripts', 'wpcf7_enqueue_scripts' );  function wpcf7_enqueue_scripts() {     // jquery.form.js originally bundled with WordPress is out of date and deprecated     // so we need to deregister it and re-register the latest one     wp_deregister_script( 'jquery-form' );     wp_register_script( 'jquery-form', wpcf7_plugin_url( 'jquery.form.js' ),         array( 'jquery' ), '2.52', true );      $in_footer = true;     if ( 'header' === WPCF7_LOAD_JS )         $in_footer = false;      wp_enqueue_script( 'contact-form-7', wpcf7_plugin_url( 'scripts.js' ),         array( 'jquery', 'jquery-form' ), WPCF7_VERSION, $in_footer );      do_action( 'wpcf7_enqueue_scripts' ); }   Now how to add defer="defer" tag in the above code? Though tangentially related to another post on MathOverflow (), the questions below are mainly out of curiosity. They may be very-well known ones with very well-known answers, but...    Suppose $\Sigma$ is a sigma-algebra over a set, $X$. For any given topology, $\tau$, on $X$ denote by $\mathfrak{B}_X(\tau)$ the Borel algebra over $X$ generated by $\tau$.     Question 1. Does there exist a topology, $\tau$, on $X$ such that $\Sigma = \mathfrak{B}_X(\tau)$?   If the answer to the previous question is affirmative, it makes sense to ask for the following too:     Question 2. Denote by ${\frak{T}}_X(\Sigma)$ the family of all topologies $\tau$ on $X$ such that $\Sigma = \mathfrak{B}_X(\tau)$ and let $\tau_X(\Sigma) := \bigcap_{\tau \in {\frak{T}}_X(\Sigma)} \tau$. Is $\Sigma = \mathfrak{B}_X({\frak{T}}_X(\Sigma))$?   Updates. Q2 was answered in the negative by Mike (). Are Mersenne prime exponents always odd? I have been researching  so I can write a program that finds them. A Mersenne prime looks like $2^n-1$. When calculating them, I have noticed that the $n$ value always appears to be odd. Is there confirmation or proof of this being true? Difference between declaring variables before or in loop? A real nxn matrix always has a real eigenvalue when n is odd what do it mean by "A real nxn matrix always has a real eigenvalue when n is odd?" Shouldnt it be that regardless of odd or even there will always have a real root?  hope to hear from you guys soon:) Expected log value of noncentral exponential distribution Let $a_1,a_2,a_3,\ldots$ be reals. Prove that if $\sum_{n=1}^{\infty} a_n^{2}$ converges, then so does $\sum_{n=1}^{\infty} \frac {a_n}{n}$.   For this I have shown the case for when $ a_n^{2} \le\frac {|a_n|}{n}$ $\Rightarrow$ $ |a_n|\le\frac {1}{n}$ $\Rightarrow$ $\frac {|a_n|}{n} \le \frac{1}{n^{2}}$ and we know that $\sum_{n=1}^{\infty} \frac {1}{n^{2}}$ converges and hence $\sum_{n=1}^{\infty}\frac {a_n}{n}$ converges by the comparison test. Now considering $ a_n^{2} \ge\frac {|a_n|}{n}$ $\Rightarrow$ $\frac {|a_n|}{n} \le a_n^{2}$ $\rightarrow$ combining the two cases for any n we have: $\frac {|a_n|}{n}\le\frac{1}{n^{2}}+a_n^{2}$ Hence using the comparion test again we know that $\sum_{n=1}^{\infty} a_n^{2}$ converges and $\sum_{n=1}^{\infty} \frac {1}{n^{2}}$ converges hence the sum converges so we can conclude that $\sum_{n=1}^{\infty} \frac {a_n}{n}$ is absoluetly convergent $\Rightarrow$ convergent.  Not to sure if this is correct, any help would be much appreciated, many thanks. Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$ How can I prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$?   This is an exercise in my textbook associated with orthogonal projections and Gram-Schmidt process, but I am unsure how they are relevant. Prove $[A,B^n] = nB^{n-1}[A,B]$ I am trying to show that $[A,B^n] = nB^{n-1}[A,B]$ where A and B are two Hermitian operators that commute with their commutator. However, I am running into a little problem and would like a hint of how to proceed.  If A and B commute then $[A,B] = ABA^{-1}B^{-1} = e$ where e is the identity element of the group.  $$\therefore AB=BA$$  $$n=1; [A,B^1] = (1)B^0[A,B] = e$$ This statement is certainly true. however moving on to $n = 2$ I find...  $$[A,B^2] = AB^2A^{-1}B^{-2} = ABBA^{-1}B^{-1}B^{-1} = BBAA^{-1}B^{-1}B^{-1}$$  Where in the last step I have used the fact that A and B commute to rearange the terms. However, it is plain to see that this last term simply reduces to the identity as well and for the n = 2 case we have:  $$[A,B^2] = e \ne 2B[A,B] = 2Be = 2B$$  Clearly I have assumed something I shouldn't have. The fact that there is a multiplicative factor of n implies I should be adding things, but I thought if I kept it as general as possible, the answer should just fall out naturally. I don't want an answer please, only guidance. Let consider the power series $$ \sum_{k=1}^\infty a_kx^k. $$ We know that it converges when  $$\lim_{n\to \infty }\sqrt[n]{|a_n|}|x|&lt; 1\quad\text{or}\quad |x|&lt; \frac{1}{\lim_{n\to \infty }\sqrt[n]{|a_n|}}$$  But D'Alembert test tells us that it converges if $$|x|&lt; \frac{1}{\lim_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|},$$ so since the radius of convergence is unique, we should have that $$\lim_{n\to \infty }\sqrt[n]{|a_n|}=\lim_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|.$$  I tried to prove it, but this result looks strange to me. So if it doesn't work always, how can we have those to limit as radius of convergence? I guess the equality of those two limit should be true most of the time.  So under what conditions is it true? A better class to update property files? Though java.util.properties allows reading and writing properties file, the writing does not preserve the formatting. Not surprising, because it is not tied to the property file.  Is there a PropertyFile class out there -- or some such -- that preserves comments and blank lines and updates property values in place? com.mysql.jdbc.exceptions.jdbc4.CommunicationsException: Communications link failure How can I find non-ASCII characters in MySQL? I'm working with a MySQL database that has some data imported from . The data contains non- characters (em dashes, etc.) as well as hidden carriage returns or line feeds. Is there a way to find these records using MySQL? Why is printf better than echo? I'm having some issues SSH'ing to a server when logged into a particular VM.  From my local PC, I can log in to the server just fine using the command ssh -i .ssh/[my private key] username@domain.  If I then SSH into another unrelated server which also has the same private key and run the above command it will also log in just fine in to the server.  But, when I SSH into a particular OpenStack VM (again has the same private key) on the unrelated server and then SSH in to the server from there I start getting prompted for a passphrase. But a passphrase hasn't been set for the key so inevitably I get a "Permission denied (publickey)." error.  To double check, I removed the private key from the VM and scp'd the private key from my PC into it again and tried the same command I still get prompted for a passphrase.  In other words:   PC - SSH - Server1 = Works fine  PC - SSH - Server2 - SSH - Server1 =     Works fine  PC - SSH - Server2 - SSH - Virtual Machine - SSH - Server 1 =         Asks for a passphrase   What could be the reason behind this? It's definitely the right private key I'm using and it has the appropriate permissions.  Edit - Output of ssh -v -i .ssh/[my private key] username@domain as requested  OpenSSH_7.4p1, OpenSSL 1.0.2k-fips  26 Jan 2017 debug1: Reading configuration data /etc/ssh/ssh_config debug1: /etc/ssh/ssh_config line 58: Applying options for * debug1: Connecting to xxx.xxx.xxx.xxx [xxx.xxx.xxx.xxx] port 22. debug1: Connection established. debug1: key_load_public: No such file or directory debug1: identity file /.ssh/[my private key].ppk type -1 debug1: key_load_public: No such file or directory debug1: identity file /.ssh/[my private key].ppk-cert type -1 debug1: Enabling compatibility mode for protocol 2.0 debug1: Local version string SSH-2.0-OpenSSH_7.4 debug1: Remote protocol version 2.0, remote software version OpenSSH_7.2p2 Ubuntu-4ubuntu2.4 debug1: match: OpenSSH_7.2p2 Ubuntu-4ubuntu2.4 pat OpenSSH* compat 0x04000000 debug1: Authenticating to xxx.xxx.xxx.xxx:22 as '[my username]' debug1: SSH2_MSG_KEXINIT sent debug1: SSH2_MSG_KEXINIT received debug1: kex: algorithm: curve25519-sha256@libssh.org debug1: kex: host key algorithm: ecdsa-sha2-nistp256 debug1: kex: server-&gt;client cipher: chacha20-poly1305@openssh.com MAC: &lt;implicit&gt; compression: none debug1: kex: client-&gt;server cipher: chacha20-poly1305@openssh.com MAC: &lt;implicit&gt; compression: none debug1: kex: curve25519-sha256@libssh.org need=64 dh_need=64 debug1: kex: curve25519-sha256@libssh.org need=64 dh_need=64 debug1: expecting SSH2_MSG_KEX_ECDH_REPLY debug1: Server host key: ecdsa-sha2-nistp256 SHA256:ZiugTjR5fM0E3evOwHoePFKspDQChA0Ab6L0q88KP/g debug1: Host 'xxx.xxx.xxx.xxx' is known and matches the ECDSA host key. debug1: Found key in /home/centos/.ssh/known_hosts:2 debug1: rekey after 134217728 blocks debug1: SSH2_MSG_NEWKEYS sent debug1: expecting SSH2_MSG_NEWKEYS debug1: SSH2_MSG_NEWKEYS received debug1: rekey after 134217728 blocks debug1: SSH2_MSG_EXT_INFO received debug1: kex_input_ext_info: server-sig-algs=&lt;rsa-sha2-256,rsa-sha2-512&gt; debug1: SSH2_MSG_SERVICE_ACCEPT received debug1: Authentications that can continue: publickey debug1: Next authentication method: publickey debug1: Trying private key: /.ssh/[my private key].ppk Enter passphrase for key '/.ssh/[my private key].ppk': Enter passphrase for key '/.ssh/[my private key].ppk': Enter passphrase for key '/.ssh/[my private key].ppk': debug1: No more authentication methods to try. Permission denied (publickey). $\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime Do I have to enter the UK on my UK passport? I'm a British National (Overseas), which basically means that while I don't have the right of abode in the UK, I am permitted to visit the UK without a visa. However, my passport has expired, and while it's being renewed, the schedule is a bit tight.  At the same time, I'm an US Citizen, and since I'm only planning to visit the UK, I don't need a visa if I enter on my US passport.  I'm not familiar with UK immigration law, and given that this probably isn't too common a situation, the UK Border Agency website doesn't have an answer that I can can find, nor do they seem to have a contact form that fits my situation, so here's hoping someone knows—given that I'm a British National (Overseas), am I required to enter the UK on my UK passport, or can I just use my (valid) US passport? Is there a program to mount all of my drives automatically? Configure up-arrow to browse through commands with same initial characters rather than all previous commands On the bash command-line, ↑ gives me the previous command. On the command-lines in ipython or matlab, when I type a few characters, ↑ gives me the previously entered command starting with those characters. How can I enable exactly this behaviour in bash? I am aware of more advanced ways of searching through the command-line history, but sometimes a simple way is more convenient.