How do I work out the correct PWM frequency for my application (motor)?
Is there an ideal PWM frequency for DC brush motors?
COUNT(*) vs. COUNT(1) vs. COUNT(pk): which is better? I would like to know if anyone can help me with installing Ubuntu on VirtualBox Setting Blend Width on Mosaic Dataset using ArcMap I have some simple python code that searches files for a string e.g. path=c:\path, where the c:\path part may vary. The current code is:  def find_path(i_file):     lines = open(i_file).readlines()     for line in lines:         if line.startswith("Path="):             return # what to do here in order to get line content after "Path=" ?   What is a simple way to get the text after Path=? Travelling on Business visa to UK for tourism purposes I already have a 6 month valid UK business visa received prior to April 24 2015. I was supposed to travel to the UK in April, but my trip was cancelled on medical grounds.  I am now planning to visit the UK in July for tourism. Would it be fine for me to do so? Will I be allowed to enter the UK? Should I carry the original invite letter and medical certificate to prove why I didn't go the first time? How does damage dealt increase as you level up I've recently taken over as GM in my group.  We are all new to RPGs except for our original GM, so they decided to run an adventure path so it would be easier to change GMs if they had to stop playing.  Along this path, we had one CR 4 encounter that took us an hour, almost killed our bloodrager and knocked our brawler unconscious. When we leveled up, our GM told us to increase the damage we did by "one level," so my 1d6 became 2d6 and my friend's 2d6 became 4d6.  I saw no problem with this as a player, but I was looking over the adventure path and later encounters that also have a CR of 4 could be ended in one turn by our bloodrager. This would make encounters really boring, and my goal is to avoid boredom.  My question is: As you level up, how does the damage you do increase? Does it go up like my GM said so that at level 3 my rapier does 3d6 and the bloodrager's earth breaker does 6d6, or does it go up by some other method?  I have read the PHB and I don't think that what the GM was saying is correct, but being a first-time player I wasn't sure if had just missed something, so I figured I should ask elsewhere. Escape velocity from a rotating black hole Why is gradient the direction of steepest ascent? $$f(x_1,x_2,...x_n):\mathbb{R}^n \rightarrow \mathbb{R}$$ The definition of the gradient is  $$ \frac{\partial f}{\partial x_1}\hat{e}_1 +\  ... +\frac{\partial f}{\partial x_n}\hat{e}_n$$  which is a vector.  Reading this definition makes me consider that each component of the gradient corresponds to the rate of change with respect to my objective function if I go along with the direction $\hat{e}_i$.  But I can't see why this vector (defined by the definition of the gradient) has anything to do with the steepest descent.  Why do I get maximal value again if I move along with the direction of gradient? Display current layout (language code/country flag) in keyboard indicator Just upgraded from 10.04 to 10.10, and the keyboard indicator applet no longer displays the two-letter country code for the active layout.  This is terrible. Is this the default behaviour? Anyone using two layouts can't tell which language they're in.  I can't seem to find the setting for this, it used to be in the preferences for keyboard layout.  Update 1: In case this wasn't obvious - I have two keyboard layouts - English and Hebrew. I just upgraded form 10.04, where the country code (USA/IL) was displayed, overlaid on the flag.  Now all I get is a vague keyboard icon, and can't find the settings for this.  Update 2: this seems to be a , and is now back in Maverick When I type uname -a, it gives the following output.  Linux mars 2.6.9-67.0.15.ELsmp #1 SMP Tue Apr 22 13:50:33 EDT 2008 i686 i686 i386 GNU/Linux   How can I know from this that the given OS is 32 or 64 bit?  This is useful when writing configure scripts, for example: what architecture am I building for? There are many red and black spots in my photos,what are those? Show that $f(z)=0$. Suppose that $f:\mathbb{C}\rightarrow\mathbb{C}$ is analytic on the open unit disc and continuous on the closed unit disc. Assume that $f(z)=0$ on an arc of the circle $\{z\in\mathbb{C}:|z|=1\}$. Show that $f(z)=0$. For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent? Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X Here X is a Hausdorff Space.  I know that singleton sets, {x}, are closed in a Hausdorff space. Although Im not sure if thats how to use the Hausdorff property.   Should I investigate $h=F(x)-x$?  Can anyone give a hint Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$ I started to study inequalities - I try to solve a lot of inequlites and read interesting .solutions . I have a good pdf, you can view from  . The inequality which I tried to solve and I didn't manage to find a solution can be found in that pdf but I will write here to be more explicitly.  Exercise 1.3.4(a) Let $a,b,c$ be positive real numbers. Prove that $$\displaystyle \frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4.$$ (b) For real numbers $a,b,c \gt0$ and $n \leq3$ prove that: $$\displaystyle \frac{a}{b}+\frac{b}{c}+\frac{c}{a}+n\left(\frac{3\sqrt[3]{abc}}{a+b+c} \right)\geq 3+n.$$ Solving multiple congruences by CRT = Chinese Remainder Theorem Real definition of "countable set" Sum of infinite series $\sum_{i=1}^{\infty} \frac 1 {i(i+1)(i+2)...(i+n)}$ Lets define the following series $$S_n =\sum_{i=1}^{\infty} \frac 1 {i(i+1)(i+2)...(i+n)}.$$ I know that $S_0$ does not converge so let's suppose $n \in N$ and define $S_n$ for some $n$. We have $S_1=1$ , $S_2=\frac1 4$ , $S_3=\frac 1 {18}$ , $S_4=\frac 1{96}$ , $S_5=\frac 1{600}$ etc.. the numerator in all results is 1the pattern in denominator is $[1,4,1,96,600...]$ and   that is equal to $n*n!$ Finally I want to prove the general equality: $\sum_{i=1}^{\infty} \frac 1 {i(i+1)(i+2)...(i+n)}=\frac 1 {n*n!}$ change citation style ( [1-4] to [1]-[4], and [5, 8-9] to [5], [8]-[9] ) with natbib? I have spent a whole day trying to solve the following problem. Please help if you know how to do this.  I am using natbib (\usepackage[sort&amp;compress,square,comma]{natbib}), and my current citation style looks like [1-4], [5, 8-9].  What is the easiest way to change the citation style to [1]-[4] and [5],[8]-[9]? Why do people not upvote, or accept answers that worked for them? I am regular Stack Exchange user, especially at Stack Overflow.  One of the things I really dislike about new and sometimes veteran users is that:   Either they do not accept an answer that works for them, Or they accept the answer but do not vote it up   I mean they can really both accept the answer and vote it up but somehow they wouldn't =(.  How many of you feel the same way?