I added a virtualserver to my apache config file so I can use SSL on my site like this:  &lt;VirtualHost *:443&gt;  DocumentRoot "/var/www/html/site"  ServerName mysite.net  SSLEngine on  SSLCertificateFile /etc/webmin/letsencrypt-cert.pem  SSLCertificateKeyFile /etc/webmin/letsencrypt-key.pem  SSLCertificateChainFile /etc/webmin/letsencrypt-ca.pem &lt;/VirtualHost&gt;   but as I restart Apache I get this error:  Invalid command 'SSLEngine', perhaps misspelled or defined by a module not included in the server configuration  I consulted similar topics on this site and I installed mod_ssl but no use. The topics are like 8 years old now so maybe something has changed. What am I missing?  Thank you.
When I restart httpd, I get the following error.  What am I missing?  [root@localhost ~]# service httpd restart Stopping httpd:                                            [  OK  ] Starting httpd: Syntax error on line 22 of /etc/httpd/conf.d/sites.conf: Invalid command 'SSLEngine', perhaps misspelled or defined by a module not included in the server configuration   I have installed mod_ssl using yum install mod_ssl openssh  Package 1:mod_ssl-2.2.15-15.el6.centos.x86_64 already installed and latest version Package openssh-5.3p1-70.el6_2.2.x86_64 already installed and latest version   My sites.conf looks like this  &lt;VirtualHost *:80&gt; #    ServerName shop.itmanx.com     ServerAdmin webmaster@itmanx.com      DocumentRoot /var/www/html/magento     &lt;Directory /var/www/html&gt;         Options -Indexes         AllowOverride All     &lt;/Directory&gt;      ErrorLog logs/shop-error.log     CustomLog logs/shop-access.log &lt;/VirtualHost&gt;  &lt;VirtualHost *:443&gt;     ServerName secure.itmanx.com     ServerAdmin webmaster@itmanx.com      SSLEngine on     SSLCertificateFile /etc/httpd/ssl/secure.itmanx.com/server.crt     SSLCertificateKeyFile /etc/httpd/ssl/secure.itmanx.com/server.key     SSLCertificateChainFile /etc/httpd/ssl/secure.itmanx.com/chain.crt      DocumentRoot /var/www/html/magento     &lt;Directory /var/www/html&gt;         Options -Indexes         AllowOverride All     &lt;/Directory&gt;      ErrorLog logs/shop-ssl-error.log     CustomLog logs/shop-ssl-access.log     &lt;/VirtualHost&gt;
Do the electric and magnetic components of an electromagnetic wave really generate each other? Frequently when EM waves are taught, it is said that the change in electric field causes a change in the magnetic field, which then causes a change in the electric field, and so on and so forth.   But from my understanding of basic electromagnetics, it is not necessarily a changing electric field that creates a change in magnetic field, but instead an accelerating charge. and it is this charge that creates both the electric and magnetic field. Again, from my understanding, a changing magnetic field is not generated by a changing electric field, but instead just happens to always be present perpendicular to a changing electric field due to the laws of electromagnetism.   Am I wrong? Or is the "mutual generation" concept between the electric and magnetic components of an EM wave an actual thing? How to remove the lines which appear on file B from another file A? How can I pad a value with leading zeros? How to group distinct values from a list using odata rest api What is the difference between the memory usage report in System Monitor and the one by free? I am using System Monitor 2.28.0.  When I look in the Resources tab, I see a nice graph with for memory and swap.  Memory is about 60% 2.3 GiB of 3.8.  When I type the command free, I got :               total       used       free     shared    buffers     cached Mem:       3994908    3962396      32512          0     100852    1477032 -/+ buffers/cache:    2384512    1610396 Swap:      8000328      28468    7971860   cat /proc/meminfo | grep MemFree give  MemFree:           34536 kB   The situation has remained the save for several minute.  I started a lot of process with a script and the script is waiting for the free memory to get lower.  According to what I am seeing in the Process tab (or with top), the number in System Monitor seem a lot closed to the total of the memory of the process that the one reported by free.   Thanks Book about classical mechanics I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical consideration related to these to formalism (like tangent bundle, cotangent bundle, 1-form, 2-form, etc.).  I have , but I would like to go into more details about the [symplectic] geometrical and mathematical foundations of classical mechanics.  Additional note: A chapter about relativistic Hamiltonian dynamics would be a good thing. Why do clocks measure arc-length? Apologies in advance for the long question.  My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to $x^\mu(\lambda_b)$, then his clock will measure that an amount of time $t_{ba}$ given by the curve's arc length; $$   t_{ba} = \int_{\lambda_a}^{\lambda_b}d\lambda \sqrt{-g_{\mu\nu}(x(\lambda))\dot x^\mu(\lambda)\dot x^\nu(\lambda)} $$ will have elapsed where $g_{\mu\nu}$ is a metric on spacetime with signature $(-,+,+,+)$.    Why is this so?     Here is how I would attempt to justify this fact in special relativity with $g_{\mu\nu} = \eta_{\mu\nu}$.  Consider an inertial observer $O$ in $\mathbb R^{3,1}$, and suppose that this observer sees a clock, which I'll call observer $O'$ moving around on a curve $x^\mu(\lambda)$.  If $O'$ were also an inertial observer, then given any event with coordinates $x^\mu$ as measured by $O$, observer $O'$ would measure the coordinates of the event to be $x'^\mu = \Lambda^\mu_{\phantom\mu\nu} x^\nu + x_0^\mu$ for some Lorentz transformation $\Lambda$.  If $O'$ is not inertial, then this is no longer true, and there is some more complicated family of transformations, say $T_\lambda$ between events as seen by both observers.  I would argue, however, that if we were to partition the interval $[\lambda_a, \lambda_b]$ into a large number $N$ of intervals $I_1=[\lambda_a, \lambda_i], \dots, I_N=[\lambda_{N-1}, \lambda_b]$ with $\lambda_n = \lambda_a+n\epsilon_N$ and $\epsilon_N=(\lambda_b-\lambda_a)/N$, then on each interval $I_n$, $O'$ is approximately an inertial observer in the sense that $$   T_{\lambda_n} = P_n + \mathcal O(\epsilon_N), \qquad (\star) $$ for some Poincare transformation $P_n$.  Then we would note that since $O'$ is stationary in his own reference frame, he measures his worldline to have the property $\dot x'^\mu(\lambda) = (\dot t(\lambda), \mathbf 0)$ so that $$   I_{ba}=\int_{\lambda_a}^{\lambda_b}d\lambda \,\sqrt{-\eta_{\mu\nu}\dot x'^\mu\dot x'^\mu} = \int_{\lambda_a}^{\lambda_b} d\lambda \, \sqrt{\dot t^2} = t(\lambda_b) - t(\lambda_a) = t_{ba} $$ On the other hand the integral on the left can be written as a Riemann sum using the partition above, and we can invoke ($\star$) above to get \begin{align}   I_{ba}  &amp;= \lim_{N\to\infty}\left[\sum_{n=1}^N \epsilon_N\sqrt{-\eta_{\mu\nu}\dot x'^\mu(\lambda_n)\dot x'^\nu(\lambda_n)}\right] \notag\\ &amp;= \lim_{N\to\infty}\left[\sum_{n=1}^N \epsilon_N\sqrt{-\eta_{\mu\nu}\dot x^\mu(\lambda_n)\dot x^\nu(\lambda_n)} + \mathcal{O}(\epsilon_N^2)\right] \notag\\ &amp;= \int_{\lambda_a}^{\lambda_b}d\lambda \,\sqrt{-\eta_{\mu\nu}\dot x^\mu\dot x^\mu} \end{align} Combining these two computations gives the desired result.  How do others feel about this argument?  I'm not completely comfortable with it because of the assumption $(\star)$ I made on $T_\lambda$.  I imagine that in GR a similar argument could be made by invoking local flatness of the metric. Spontaneous electroweak symmetry breaking (i.e. $SU(2)\times U(1)\to U(1)_{em}$ ) is at scale about 100 Gev. So, for , gauge bosons $Z$ &amp; $W$ have masses about 100 GeV. But before this spontaneous symmetry breaking ( i.e. Energy > 100 GeV) the symmetry $SU(2)\times U(1)$ is not broken, and therefore gauge bosons are massless.  The same thing happens when we go around energy about $10^{16}$ GeV, where we have the Grand Unification between electroweak and strong interactions, in some bigger group ($SU(5)$, $SO(10)$ or others). So theoretically we should find gauge bosons $X$ and $Y$ with masses about $10^{16}$ GeV after GUT symmetry breaks into the Standard Model gauge group $SU(3)\times SU(2)\times U(1)$, and we should find massless X and Y bosons at bigger energies (where GUT isn't broken).  So this is what happened in the early universe: when temperature decreased, spontaneous symmetry breaking happened and firstly $X$ &amp; $Y$ gauge bosons obtained mass and finally $Z$ &amp; $W$ bosons obtained mass.   Now, I ask: have I understood this correctly? In other words, if we make experiments at energy above the electroweak scale (100 GeV) we are where $SU(2)\times U(1)$ isn't broken and then we should (experimentally) find $SU(2)$ and $U(1)$ massless gauge bosons, i.e. $W^1$, $W^2$, $W^3$ and $B$ with zero mass? But this is strange, because if I remember well in LHC we have just make experiments at energy about 1 TeV, but we haven't discovered any massless gauge bosons. Comma before "and" in compound sentences? I read this sentence on an educational website:     Now times have changed and you are ready for situations involving forces in two dimensions.   Shouldn't there be a comma before and, since the subject of the sentence has changed (things vs. you)?      Now times have changed, and you are ready for situations involving forces in two dimensions.   What is the exact comma rule for joining two clauses with and? How can I gear my follower post 2.0? I'm a little confused as to how I'm supposed to gear up my follower since the installation of smart loot in Loot 2.0. My follower still has most pre loot 2.0 items because I have yet to find comparables that are rolling with the right affixes.   To be clear, I play a DH and so I used the Templar as my tank. I very rarely find items that roll with Strength because smart loot sees my DH and rolls Dex for me instead. With the use of the Enchantress I thought it would get better because I could replace Dex with Strength...but that's not true. It seems as though the Enchantress will only roll Dex for me too.   With the auction house down for good, no outlet for trading, and the installation of smart loot, it seems that gearing a follower has become almost impossible unless I want to jump on another character that uses strength and get items that way. I want to find items that I can use while I'm playing. How do I gear my follower post Loot 2.0? Do I have any options other than character jumping? Programmatically determining amount of parameters a function requires - Python Hash join between master/detail tables produces too-low cardinality estimate How to solve ~(P → Q) : P & ~Q by natural deduction? I'm trying to solve the following by natural deduction:  ~(P → Q) : P &amp; ~Q  It's a trivial problem if identities are used, as can be seen by the following:   {1}      1.   ~(P → Q)                    Prem. {1}      2.   ~(~P ∨ Q)                   1 Mat. Impl. {1}      3.   ~~P & ~Q                    2 De Morgan's {1}      4.   P & ~Q                      3 DNE   Starting from step 2 of the previous proof, it's also fairly straightforward to reach a conclusion using natural deduction; i.e. starting from ~(~P ∨ Q), which is an identity of ~(P → Q):  ~(~P ∨ Q) :  P &amp; ~Q   {1}      1.   ~(~P ∨ Q)                   Prem. {2}      2.   ~P                          Assum. {2}      3.   ~P ∨ Q                      2 ∨I {1,2}    4.   ~(~P ∨ Q) & (~P ∨ Q)        1,3 &I {1}      5.   P                           2,4 RAA {6}      6.   Q                           Assum. {6}      7.   ~P ∨ Q                      6 ∨I {1,6}    8.   ~(~P ∨ Q) & (~P ∨ Q)        1,7 &I {1}      9.   ~Q                          6,8 RAA {1}      10.  P & ~Q                      5,9 &I   I also found that it's fairly easy to conclude ~Q:   {1}      1.   ~(P → Q)                    Prem. {2}      2.   Q                           Assum. {3}      3.   P                           Assum. {2,3}    4.   P & Q                       2,3 &I {2,3}    5.   Q                           4 &E {2}      6.   P → Q                       3,5 CP {1,2}    7.   ~(P → Q) & (P → Q)          1,6 &I {1}      8.   ~Q                          2,7 RAA ... {1,2}    12.  P & ~Q   In spite of how easy it looks, I can't figure out how to do it. I believe it can be done in 12 steps. Thanks! How to remove the top horizontal bar in fancyhdr? When using fancyhdr, how do you remove the top horizontal rule?  I do not want a header at all, just a footer.  This is what I do now:  \documentclass{article} \usepackage{fancyhdr} \pagestyle{fancy}  \lfoot{text} \cfoot{text 2} \rfoot{text 3}  \begin{document} Foo Bar \end{document} Why does an object with a glossy shader render in black? When I apply a glossy shader to the material of my text, the text becomes just black. Why?    I have lamp and everything, but the problem persists. The text is red before I add the glossy shader.  I'm using Cycles render.   Thanks! I'm using IEEEtran to format an article, and I wanted to include an image. I included the graphicx and hyperref packages, and used the following code, like normal, to include an image.  \begin{figure}[!t] \centering \includegraphics[width=3in]{fetch} \caption{Pipeline: Fetch Instruction} \label{fig:fetch} \end{figure}   What appears, however, is this:    Fetch.png is a file in the directory, and if I remove it, pdflatex errors instead of producing an output. I'm using MiKTeX 2.9 on Windows 7. Any ideas? Is this correct for Rudin exercise 3.7? Prove the series is convergent This is Baby Rudin exercise 7 of Chapter 3. Prove that the convergence of $\sum{a_n}$ implies the convergence of $\sum{\sqrt {a_k} \over k}$ if $a_n \ge 0$.  Proof:  I will attempt to show that the cauchy criterion is met so $${\sum_{k=n}^m {\sqrt {a_k} \over k}} \le \epsilon $$ for all $n,m \le N_1$. Im disregarding the absolute value since its all positive terms.   Since $\sum{a_n}$ converges, we know that the $\lim \limits_{n \to \infty} a_n =0$ So there exists some $N_2$ such that for all $n \ge N_2$, $$   a_n \lt \ {{(m-n)}^2k^2(\epsilon)^2} $$ I am again disregarding the absolute values because its always positive Let N=max{$N_1,N_2$} then for all $n,m \ge N$ $$\sum_{k=n}^m {\sqrt {a_k} \over k} \le \sum_{k=n}^m {\sqrt {{(m-n)}^2k^2(\epsilon)^2} \over k} \le \sum_{k=n}^m{(m-n)(\epsilon)} = \epsilon $$  Maybe this is just crazy, should I just use Cauchy-Schwarz inequality and forget about this or could I possibly make this method work? Activity has leaked window com.android.internal.policy.impl.PhoneWindow$DecorView@44f72ff0 that was originally added here If someone could help me with the proposed change of variables, it would be greatly appreciated. Consider Euler's equation:  $$z^2w'' + \alpha zw' + \beta w = 0$$  where $w$ is a function of $z$ and $\alpha, \beta$ are constants. How would the change of variables $t =\ln(z)$ transform this equation? Getting different answers when integrating using different techniques