I want to generate a narrow pulse of very small duration. How can I implement it using PWL function. Or is there any other method for this.
I have designed a circuit where I want to give a pulse of very short duration using a switch. How can I implement it in spice.
What is the origin of Dol Goldur, and why did Sauron start there? Who built the fortress of Dol Goldur, and when was it built? And was it always a place for evil, or Sauron just occupied it?  Despite the fact that Mordor is much better fortified; artificially by the old fortifications,  and geographically, as it is surrounded by the mountains. Also considering the presence of mount doom that seem to enhance Sauron's power, Sauron chose to start his campaign from Dol Goldur, despite Mordor being ready for quite some time.  Why did he choose this enigmatic fortress, and not go straight for Mordor or even go earlier? I am trying to rotate a dual monitor which is attached to the VGA output of my laptop. My system is Ubuntu 15.10.  However, here is the outcome I get when I use xrandr:  xrandr --output VGA-1-0 --rotate right xrandr: output VGA-1-0 cannot use rotation "right" reflection "none"   I have seen other posts on this subject, which all recommend editing xorg.conf. I have tried that, too. Here's my current xorg.conf file:  Section "ServerLayout" Identifier "layout" Screen 0 "nvidia" Inactive "intel" EndSection  Section "Device" Identifier "intel" Driver "modesetting" BusID "PCI:0@0:2:0" Option "AccelMethod" "None" Option "RandRRotation" "True" EndSection  Section "Screen" Identifier "intel" Device "intel" EndSection  Section "Device" Identifier "nvidia" Driver "nvidia" BusID "PCI:1@0:0:0" Option "ConstrainCursor" "off" Option "RandRRotation" "True" EndSection  Section "Screen" Identifier "nvidia" Device "nvidia" Option "AllowEmptyInitialConfiguration" "on" Option "IgnoreDisplayDevices" "CRT" Option "RandRRotation" "True" EndSection   Still, I keep getting the same error when trying to use xrandr to rotate that screen.   Is there another way of doing so? Proof that the relation $5 \mid (a + 4b)$ is symmetric and transitive Take the relation $R$ to be defined on the set of integers:  $$aRb \iff 5 \mid (a + 4b)$$  As part of a larger proof, I have to show that $R$ is both symmetric and transitive. I'm lost.  I see the first steps, but I can't find how to progress further. Here's what I have at this point:    Proof of Symmetry  We have to prove that if $5 \mid (a + 4b)$, then $5 \mid (b + 4a)$. Clearly, this is true if $a = b$, but apart from that, it's unclear in my mind.  Proof of Transitivity  We have to prove that if $5 \mid (a + 4x)$ and $5 \mid (x + 4b)$, then $5 \mid (a + 4b)$.    I've fiddled around with sample values, but I still don't see it. I'm pretty lost here. Thoughts? Is there any way to view which applications are accessing the Internet on Mac OS X? I think I remember a command line utility that did this, but I can't remember what it's called and a few Google searches turn up nothing. I don't mean people with low self esteem.  But there are people who feel happy at being able to make other people laugh at their own expense. I remember someone telling me there is a word for them, I can't find it.  Let me explain:  I sometimes, while sitting with a group of people, might just tell them a personal embarrassing story, which might be completely fabricated, to make other people laugh. And when they laugh, I feel happiness.  I'm also self deprecating, but not in a way that I hate myself, rather,  just my work (I'm a screenwriter) and knowing I can do better. I do not self deprecate myself in public (I don't praise myself either).   Edit: Now that its mentioned, I think the word I'm talking about was used to describe a person's sense of humor. Or it could be a word used to describe a psychological trait/disorder.  Edit: I just looked up humor styles on Wikipedia. And after reading it, I guess the word that closely matches what I'm looking for is 'Affiliated Humor' but in a 'Self Defeating' style. What is a decoupling capacitor and how do I know if I need one? What is a decoupling capacitor (or smoothing capacitor as referred to in the link below)?  How do I know if I need one and if so, what size and where it needs to go?    mentions many chips needing one between VCC and GND; how do I know if a specific chip is one?   Would an  4-bit parallel access shift register used with an Arduino need one? (To use my current project as an example) Why or why not?  I feel like I'm starting to understand the basics of resistors and some places they're used, what values should be used in said places, etc, and I'd like to understand capacitors at the basic level as well. What exactly is weakly informative prior? Is there a precise definition of weakly informative prior?  How is it different from a subjective prior with broad support? Kinematics with non constant acceleration A particle experiences an acceleration described by  $$ a=kx^{-2} $$ where x is the displacement from the origin and k is an arbitrary constant.  To what value does the velocity v of the particle converge to as x approaches infinity if the particle starts at some point x0?  If I approach this problem with energy, then $$ W = \int F \mathrm{d}x $$ $$  = \int_{x_0}^\infty mkx^{-2} \mathrm{d}x $$ $$  = mk(-\infty^{-1}+{x_0}^{-1}) $$ $$ W = K = mk{x_0}^{-1} $$ $$ \frac{1}{2}mv^2 = mk{x_0}^{-1} $$ $$ v = \sqrt{2k{x_0}^{-1}} $$  How would I solve this problem with pure kinematics? (there appears to be some sort of cyclical dependency where acceleration affects velocity, velocity affects displacement, and displacement affects acceleration)  Likewise, two particles experience accelerations described by $$ a_1=k_1x^{-2} $$ $$and $$ $$ a_2=-k_2x^{-2} $$ where x is the distance between the two particles  What two velocities do the particles reach as x approaches infinity if the two particles are initially separated by some x0? Is there an unsubdivide function in Blender? If $A$ is a ring and $S=\{1,f,f^2,f^3,...\}$ a multiplicative set of $A$, prove that $\mathrm{Spec}(A_f)=\mathfrak{V}((f))^c$.   Notation: $A_f=S^{-1}A$ and $\mathfrak{V}((f))=\{P \in \mathrm{Spec}(A): P \supset (f)\}$  My attempt:   On one hand, if $P \in \mathrm{Spec}(A)$ and $P \cap S$ is empty then we identify $\mathrm{Spec}(A_f)=\mathrm{Spec}(S^{-1}A)=\{P \in \mathrm{Spec}(A): P\cap S= \emptyset\}$.  On the other hand, $\mathfrak{V}((f))^c=\{P \in \mathrm{Spec}(A): P \nsupseteq (f)\}$.   So the exercise is equivalent to prove: $$\{P \in \mathrm{Spec}(A): P\cap S =\emptyset\}=\{P \in \mathrm{Spec}(A): P \nsupseteq (f)\},$$ but I can't continue so I'd appreciate if somebody could help me.   Thanks in advance. Redirect console output to textbox in separate program I'm developing an Windows Forms application that requires me to call a separate program to perform a task.  The program is a console application and I need to redirect standard output from the console to a TextBox in my program.    I have no problem executing the program from my application, but I don't know how to redirect the output to my application.  I need to capture output while the program is running using events.    The console program isn't meant to stop running until my application stops and the text changes constantly at random intervals.  What I'm attempting to do is simply hook output from the console to trigger an event handler which can then be used to update the TextBox.  I am using C# to code the program and using the .NET framework for development.  The original application is not a .NET program.  EDIT: Here's example code of what I'm trying to do.  In my final app, I'll replace Console.WriteLine with code to update the TextBox.  I tried to set a breakpoint in my event handler, and it isn't even reached.      void Method()     {         var p = new Process();         var path = @"C:\ConsoleApp.exe";          p.StartInfo.FileName = path;         p.StartInfo.UseShellExecute = false;         p.OutputDataReceived += p_OutputDataReceived;          p.Start();     }      static void p_OutputDataReceived(object sender, DataReceivedEventArgs e)     {         Console.WriteLine("&gt;&gt;&gt; {0}", e.Data);     } I get different lightning render with the same scene camera setup.  Cycles render (both experimental and supported feature set) gets weaker lightning and needs more energy.  How can I get the same lightning and reflection setup with EEVEE and Cycles? Duplicity Backup Browse I have made a duplicity backup with Ubuntu 14.04 in another laptop of my home directory.  I copied all duplicity back files to my current laptop to "/home/user/Ubuntu-backup"  How do i browse the content of that backup see if it is worth restoring? I want to restore how do i restore from those files. Multiple file upload in php Currently questions are added in a rapid pace to SO, so that new questions disappear very quickly from the homepage. It I want to see questions from my areas of interest I can do either:   Go to the tagged/my tags page, but then I will see the questions only according to the votes Supply a list of tags "x or y or z", but it seems the list is limited to 15 or 20 tags.   What I suggest is to have categories as grouping of tags - the .net category , java category , web development category , etc. It can also help new users to locate questions from their area of expertise they can answer. We can decide that a category can contain between 5 and 20  tags in order no to have too narrow or too broad categories (numbers were given just for the sake of argument) What is the difference between the three sentences below?   I have been married with her for three years. I was married with her for three years. I married her for three years. How to include jQuery and JavaScript files correctly? I'm doing it right now with the following code:   function uw_load_scripts() {     // De-register the built in jQuery     wp_deregister_script('jquery');     // Register the CDN version     wp_register_script('jquery', 'http://ajax.googleapis.com/ajax/libs/jquery/1.7.1/jquery.min.js', array(), null, false);      // Load it in your theme     wp_enqueue_script( 'jquery' ); } add_action( 'wp_enqueue_scripts', 'uw_load_scripts' );   This works, but should I do this for everyone, like this, or for everyone but admin (so that backend uses the WordPress version?):  if (function_exists('load_my_scripts')) {   function load_my_scripts() {       if (!is_admin()) {       wp_deregister_script( 'jquery' );       wp_register_script('jquery', 'http://ajax.googleapis.com/ajax/libs/jquery/1.7.1/jquery.min.js', array(), null, false);      wp_enqueue_script('jquery');        }   }   }   add_action('init', 'load_my_scripts');   This version doesn't work at all actually, I get the WordPress jQuery-version and not the Google one.  Therefore, should I deregister the jQuery that is included in WordPress at all?    Also, how do I add my own scripts (slider scripts, modernizr and my own custom.js) the correct way? I guess I should do this via functions.php as well and not in the header like I'm doing it now, but I'm unsure of how I would do that. How to get rid of notch at pgfplots axes intersection? Neg Binomial and the Jeffreys' Prior I'm trying to obtain the Jeffreys' prior for a negative binomial distribution. I can't see where I go wrong, so if someone could help point that out that would be appreciated.  Okay, so the situation is this: I am to compare the prior distributions obtained using a binomial and a negative binomial, where (in both cases) there are $n$ trials and $m$ successes. I get the right answer for the binomial case, but not for the negative binomial.   Let's call the Jeffreys' prior $\pi_J(\theta)$. Then,  $$ \pi_J(\theta)\propto [I(\theta)]^{1/2}. $$  Under the regularity conditions (fulfilled as we are dealing with the exponential family),  $$ I(\theta)=-E\left(\frac{\partial^2 \log L(\theta|x)}{\partial \theta^2}\right) $$ where for the negative binomial $n$ is $x$ in the above expression (the total number of successes $m$ is fixed, $n$ is not). The distribution --I think-- is  $$ p(m|\theta)\propto\theta^m(1-\theta)^{n-m} $$ since $\theta$ is defined as the probability of success and $m$ is the number of successes. This is also the likelihood, since $m$ is a scalar and not a vector. Hence,  $$ L(\theta|n)\propto\theta^m(1-\theta)^{n-m}\\ \log L(\theta|n)=m\log\theta +(n-m)\log (1-\theta)\\ \frac{\partial\log L(\theta|n)}{\partial \theta}=\frac{m}{\theta}-\frac{n-m}{1-\theta}\\ \frac{\partial^2\log L(\theta|n)}{\partial \theta^2}=-\frac{m}{\theta^2}-\frac{n-m}{(1-\theta)^2} $$ so the Fisher information is  $$ I(\theta)=-E\left(\frac{\partial^2\log L(\theta|n)}{\partial \theta^2}\right)=\frac{m}{\theta^2}+\frac{E(n)-m}{(1-\theta)^2}=\frac{m}{\theta^2}+\frac{\frac{m\theta}{1-\theta}-m}{(1-\theta)^2}\\ =\frac{m(1-\theta)^2+\frac{m\theta^3}{(1-\theta)}-m\theta^2}{\theta^2(1-\theta)^2}=\frac{m(1-2\theta)+\frac{m\theta^3}{(1-\theta)}}{\theta^2(1-\theta)^2}\\ =\frac{m(1-2\theta)(1-\theta)+m\theta^3}{\theta^2(1-\theta)^3}=\frac{m(1-3\theta+2\theta^2+\theta^3)}{\theta^2(1-\theta)^3}\\ \propto\frac{1-3\theta+2\theta^2+\theta^3}{\theta^2(1-\theta)^3} $$  This, however, does not give me the correct answer. The correct answer is  $$ \pi_J(\theta)\propto \frac{1}{\theta(1-\theta)^{1/2}} $$ which means that the Information I get should be   $$ I(\theta)=\frac{1}{\theta^2(1-\theta)} $$ since the prior should be proportional to the square root of the information.   Can anyone find any mistakes? I wouldn't be surprised if I screwed something up with the set up of the distribution (successes vs failures with their respective probabilities, etc).   I used the expected value from  and I know the correct answer from . How to write below bullet I have to write something under the symbol \bullet in Latex. Is it possible? I'm using the class beamer. Here it is an example of a frame:  \begin{frame} \begin{itemize} \item&lt;1-&gt; Products Market\mbox{}\\ \footnotesize{where $p_{i,t}=u_{i,t}$, with $u_{i,t}\sim u[0,2]$} \vspace{0.5cm} \item&lt;2-&gt; Credit Market \mbox{} \vspace{0.2cm} \\ \footnotesize{where \hspace{0.1cm} $\bullet_{bank} \xrightarrow{loan} \bullet$} \vspace{0.5cm} \item&lt;3-&gt; Interbank Market\mbox{} \vspace{0.08cm} \\ \footnotesize{where \hspace{0.1cm} $\bullet \xrightarrow{loan} \bullet$} \end{itemize} \end{frame}   In particular I want to write "bank" under the bullet, while now it is only in subscript.  Thanks