I have a hardtail mountain bike and recently I broke the 4 year old chain that I had on it. I’m looking for a new one and I’m wondering how many links I need for a 3x9(27 speed) bike.
My chain broke and in a moment of silliness (I was cold wet and slightly annoyed)  I threw the broken one away before thinking about measuring the new one.  Is there a guide to getting the chain length/tension correct ?  It's an 8 speed road bike (Shimano Sora back, double ring front)
I am stuck on the following problem that says:       a) Find a weak formulation for the partial differential equation $${\partial u\over\partial t\ }+ c{\partial u \over \partial x\ }=0$$    b) Show that $u=f(x-ct)$ is a generalized solution of $${\partial u\over\partial t\ }+ c{\partial u \over \partial x\ }=0$$ for any distribution $f$    My Attempt:   I know that in order to find a weak form of a pde, we need to multiply it by a test function, then integrate it. Also, to find a generalized solution, we need to find a weak solution and just multiply it by the Heaviside function.  Let's take any test function $\phi $, then we have (integrating by parts second part of the integral) $$\int_{\Omega } ( {\partial u\over\partial t\ }+ c{\partial u \over \partial x\ })*\phi(x) dx= \int_{\Omega } {\partial u\over \partial t}\phi(x) dx - c\int_{\Omega } u(x,t)\phi'(x)dx$$ where $\phi $ vanishes at boundaries. So, is it the final form or can we proceed further? And how am I supposed to find a generalized solution?  Can someone help me out? Thanks in advance for your time. An example of a sequence of Riemann integrable functions $(f_n)$ that converges pointwise to a function $f$ that is not Riemann integrable. What are badges? How do users get badges? How can users get tag badges? Can badges be lost/revoked/taken away after they are awarded? If so, how and when? How can I suggest a new badge?   For more information, see &quot;&quot; and the  in the . What is the derivative of this? I have a function of the following form:  $J = \|W^TW-I\|_F^2$   Where, $W$ is a matrix and $F$ is the Frobenius Norm.  How can I find the derivative of $\frac{\partial J}{\partial W}$ ? Are any of these verb phrases grammatical?        allows the user of modeling and resolving     allows the user to model and resolve      Which version of the following sentence is correct/better?        In particular, it allows to acquire a signal using a sample rate significantly lower than the one dictated by the Nyquist criterion.   In particular, it allows acquiring a signal using a sample rate   significantly lower than the one dictated by the Nyquist criterion.      I searched Google Scholar for "" and "", and it seems people use both more or less with the same frequency. Childrens fantasy, blind monk leading boy who can control the elements What does why would I do it mean in this context? I've often heard people saying this. And even I say it when someone accuses me of doing something that I didn't do.  I'd say:  Why would I do that?  But what's the grammar behind it?  Is it future from the past tense or something or what? It's obviously not a conditional construction 😒  Context from SE01 EP02 Austin &amp; Ally  Austin: what does the jacket have to do with the music video?  Trish: It's a line in Ally's song, "my jacket's in the lost and found."  Ally: "my jacket"? It says "I like it." The line is "I like it when you hang around."  Dez: "hang around"? I thought it said "kangaroo." ♪ I like it when you kangaroo. ♪.  Ally: Why would I write "I like it when you kangaroo"? I found this confusing when I use the neural network toolbox in Matlab. It divided the raw data set into three parts:   training set validation set test set   I notice in many training or learning algorithm, the data is often divided into 2 parts, the training set and the test set.  My questions are:   what is the difference between validation set and test set?  Is the validation set really specific to neural network? Or it is optional. To go further, is there a difference between validation and testing in context of machine learning? Why is the main page showing only the user login form? "error: XDG_RUNTIME_DIR not set in the environment." when attempting to run nautilus as root I am attempting to run nautilus as root but when I run "sudo nautilus" from the terminal, I get the following error:     error: XDG_RUNTIME_DIR not set in the environment.      (nautilus:9341): Gtk-WARNING **: cannot open display:   The issue does not occur when I attempt to run nautilus as non-root. I am using ubuntu 14.04. Does anyone know how I can fix this? What's the deal with a leading underscore in PHP class methods? While looking over various PHP libraries I've noticed that a lot of people choose to prefix some class methods with a single underscore, such as  public function _foo()   ...instead of...  public function foo()   I realize that ultimately this comes down to personal preference, but I was wondering if anyone had some insight into where this habit comes from.  My thought is that it's probably being carried over from PHP 4, before class methods could be marked as protected or private, as a way of implying "do not call this method from outside the class".  However, it also occurred to me that maybe it originates somewhere (a language) I'm not familiar with or that there may be good reasoning behind it that I would benefit from knowing.  Any thoughts, insights and/or opinions would be appreciated. Let $G$ be a group and $H$ a subgroup with $[G:H]=n$. Is it true that $x^n\in H$ for all $x\in G$?   Remarks. The answer is positive whenever $H$ is normal, e.g., for $n=2$. In general, by using the normal core of $H$, one can find an $m\ge 1$ such that $x^m\in H$ for all $x\in G$. What's so special about standard deviation? What safety precautions should I take when taking photos in the snow? I’m going to Queenstown, NZ in a couple of weeks and want to take my (very new, very precious) Canon 7D with me. I’ve done a little bit of research on how to protect my baby from cold climate (e.g. ) and found that the biggest problem is probably going to be condensation. Some suggestions have been to place the camera in a plastic bag or letting the camera gradually adjust to the new temperature or placing silica gel in the camera bag to absorb moisture. I am leaning toward the latter at the moment because it sounds like it’s the easiest, so I was just wondering if anyone has had any experience in this matter and could share their wisdom.  As an alternative I could take my Canon 350D, as I really wouldn’t care if that got damaged in the snow. However I’m a film student and tend to take just as many videos as photos – hence why I really want to take the 7D. But I would seriously regret it if it got damaged… dilemma!   So as I actually haven’t used a question mark in the body of text, I will specify that the question is: What safety precautions should I take when taking photos in the snow?  Cheers. The equivalence between Cauchy integral and Riemann integral for bounded functions Definitions  Suppose $P\colon a=x_0&lt;x_1&lt;\dotsb&lt;x_n=b$ is a partition of $[a,b]$. Let $\Delta x_k=x_k-x_{k-1}$ and $\lVert P\rVert$ denotes $\max_{0&lt;k\le n}\Delta x_k$.  The Cauchy integral of a function $f$ on closed interval $[a,b]$ equals to $I$ if and only if for each $\epsilon&gt;0$, there's some $\delta&gt;0$, for each partition $P$ of $[a,b]$ such that $\lVert P\rVert&lt;\delta$, we have $\left\lvert\sum_{k=1}^nf(x_k)\Delta x_k-I\right\rvert&lt;\epsilon$.  Problem  If $f$ is bounded on $[a,b]$ whose Cauchy integral equals to $I$, then $f$ is Riemann-integrable and $\int_a^bf=I$.  Background  It's an exercise from our calculus(analysis) problemset book, and there's a hint: consider the partitions whose $x_k-x_{k-1}$ is a constant for different $k$'s, and try to estimate the Riemann sum for each of these partitions through the Cauchy integral.  I have no idea about such estimation. After drawing some pictures, I discouraged. I googled on the Internet and found an . I realized that it's a quite different approach and with some advanced techniques (such as the analysis of a positive measure set -- discontinuities). I hope there will be some simpler approachers, just as the hint says. I need a more detailed hint, or a solution. Can anybody help me? Thanks! Omitting fields in Bibliography How best to determine if an argument is not sent to the JavaScript function I have now seen 2 methods for determining if an argument has been passed to a JavaScript function. I'm wondering if one method is better than the other or if one is just bad to use?   function Test(argument1, argument2) {       if (Test.arguments.length == 1) argument2 = 'blah';        alert(argument2);  }   Test('test');   Or   function Test(argument1, argument2) {       argument2 = argument2 || 'blah';        alert(argument2);  }   Test('test');   As far as I can tell, they both result in the same thing, but I've only used the first one before in production.  Another Option as mentioned by :  function Test(argument1, argument2) {     if(argument2 === null) {         argument2 = 'blah';     }      alert(argument2); }   As per Juan's comment, it would be better to change Tom's suggestion to:  function Test(argument1, argument2) {     if(argument2 === undefined) {         argument2 = 'blah';     }      alert(argument2); } I came to think about some situations where it would be almost impossible to miss a melee spell attack (target is grappling you or vice versa, target is holding you or is close to you, your character already has it's hand on the target, etc.). How do you manage those situations?    Do you give an advantage to the caster? Does the spell automatically succeed? Or you just don't ask yourself the question and just play along with the base rules? How to know the partition where grub is installed I am Dual Booting Maverick with Natty. I want to know which partition has Grub installed.   I want to make sure that grub is installed in the maverick partition not in natty, so that when I remove the natty partition, I don't have booting problem in the absence of grub.  On maverick there is no menu.list file in /boot/grub but natty has one.  Here is the output of fdisk -l  gaurav@gaurav-desktop:~/Desktop$ sudo fdisk -l  Disk /dev/sda: 320.1 GB, 320072933376 bytes 255 heads, 63 sectors/track, 38913 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x9cdb9cdb     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *           1        7295    58592773+  83  Linux /dev/sda2            7295       25475   146033664   83  Linux Partition 2 does not end on cylinder boundary. /dev/sda3           25476       32194    53970367+  83  Linux /dev/sda4           32195       35483    26414081    5  Extended /dev/sda5           32195       32444     1999872   82  Linux swap / Solaris /dev/sda6           32444       35483    24413184   83  Linux gaurav@gaurav-desktop:~/Desktop$ Plotting a 3d surface in tikz, with a limit to the infinity