How do you mark a bulleted list with a common stem sentence?
Capitalization for a bullet list
It's not difficult to show that  $$(1-z^2)^{-1/2}=\sum_{n=0}^\infty \binom{2n}{n}2^{-2n}z^{2n}$$  On the other hand, we have $(1-z^2)^{-1}=\sum z^{2n}$.  Squaring the first power series and comparing terms gives us  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}2^{-2n}=1$$  that is,  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$$  My question: is there a more direct, combinatorial proof of this identity?  I've been racking my brains trying to come up with one but I'm not having much success. WI-FI Nic showing 3 different transport id {Device id} There was a problem with my network controller so i opened up cmd and started to check for interfaces. I noticed a strange thing that my Wifi network controller had 3 different Device ID (Transport id's) When i tried to disable the wifi card the different id's went away. On my other computer i tested the same thing and it only shows 1 id? Device\NPF_{4A45A363-6346-48DA-8D28-13DD9C9C1E6A} Device\NPF_{E6994972-C66C-4ABF-BE27-17BAC7C1C971} Device\NPF_{B6394772-H66C-4ABF-HRE27-17JLC0H9C971} I am using snort to check for available interfaces. Can anybody explain why i am seeing this? WLC model: intel dual band wireless-ac 8265 running default settings on the adapter however i have hyper-v open Does Auto White-Balance Really Work? How? Execute program from within a C program How should I run another program from within my C program? I need to be able to write data into STDIN of the launched program (and maybe read from it's STDOUT)  I am not sure if this is a standard C function. I need the solution that should work under Linux. How to properly hook up various maps types in Cycles? I created some texture maps in MindTex to use in Blender, but I can't figure out how to properly hook them up. The maps I have:  - Diffuse  - Normal  - Height   - Specular   - Gloss   - Self Illumination  - Reflection  - Ambient Occlusion   MindTex (left) vs. Blender (right)  As you can clearly see it's a pretty big difference.  is my material node setup in Blender. In the examples I don't actually use self illumination or reflection images, but including this in the answer would be helpful. Problem applying L'Hopitals rule. Let $R$ be a commutative ring with $1$. Suppose that all ideals $I \neq R$ are prime. Prove that $R$ is a field.   Help me some hints.  Thanks a lot. I have the task of creating a simple Excel sheet that takes an unspecified number of rows in Column A like this:  1234 123461 123151 11321   And make them into a comma-separated list in another cell that the user can easily copy and paste into another program like so:  1234,123461,123151,11321   What is the easiest way to do this? Windows losing IPv6 address after ~10 minutes When I initially connect to my home network my windows PC is assigned an IPv6 address - however after a few minutes it loses this address! I seem to have similar behaviour on multiple hosts using both wireless and wired connections.  My router is an Asus RT-AC87U.  How could it be losing the IPv6 address? How can I mintor / diagnose this issue?  Update:  Based on @grawity's suggestion below I ran wireshark on this. Sure enough I see a Router Solicitation message and a Router Advertisment message with a Router lifetime of 600 seconds. After 600 seconds my computer drops its Ipv6 address.  What is supposed to happen? Should my host send another Router Solicitation message? Or should the router periodically resend the Router Advertisment message?  Update 2:    says that Router Adverticement messages should be sent periodically. Visual Studio "Find" results in "No files were found to look in. Find stopped progress." How can I make a logo in Adobe Illustrator like the AntiParticle logo below, from ?   It is a large number circles of different, varying sizes, which form the shape of a text character. How to pipe the result of 'date' command to 'mv' command I want to rename my file to the current timestamp.I know how to get the current timestamp("date +%s") but how can I pipe it to 'mv' command? Save all render passes to EXR image? I am having an issue with EXR file export that I did not encounter in previous versions of Blender. I used to be able to render a render layer with all its passes and get all the passes included with the render layer with the EXR export; the problem I am finding now is that I am not able to "pack" the passes with the EXR file (see graphic below). I am working with "standard" EXR, as I understand that the EXR multilayer is for multiple file handling (packing all the image files into a single container), but I may be wrong.    In the screenshot, the graphic is an EXR saved from the rendered layer; you can see in the screenshot how the "extra" passes from the render layer has been ignored by the graphic and only shows the standard image, z and alpha passes. I found this issue for the first time with Blender 2.71; and maybe with Cycles; in the past I have never had an issue with EXR export.  Am I missing something? I hope EXRs still work with Blender, I wouldn't know how to composite without such invaluable aid. Sorry if this question has already been answered somewhere; I have really searched the site for information on EXR but I could not find an answer to my issue. How do I install additional drivers? I've just installed Ubuntu and I need either video, wireless, or some sort of other manufacturer (non-opensource) driver. How can I run the tool that will fetch all of these for me? I'd like graphical instructions.  Related: In another  regarding a difference between short on and short of, the  says the following:     ... But this is not always the case. A person can be short on/of money,   but lacking a specific amount, someone can only be €10 short or short   €10. This construction never uses a preposition.   but is that really true? I can see sentences like "I am short of 10 dollars" quite often. Prove that $\frac{ 5^{125}-1}{ 5^{25}-1}$ is a composite number How does conservation work in wormholes? My questions might seem naive as I haven't plunged into the mathematical descriptions, but wormholes are interesting even if I don't actually know them :)  First of all, is wormhole making two possible paths betwwen points (like the tunnel in most visualisations) or is it just making two points beside each other like in the game Portal? Of course, second case can be bent into a tunnel, but there would be nothing special about tunnel part and no preferred way to divide into "normal" and "tunnel" part of spacetime.  My main questions are these:   Is momentum conserved? Is kinetic energy conserved? How does potential energy work?   To elaborate... In the game Portal you can fall into floor and fly out of the wall or floor elsewhere with the same speed, but another direction (normal to the portal). So momentum is not conserved, but kinetic energy is. Is that how it would actually work? Where does the momentum go then?  And does it really allow you to increase your potential energy while retaining kinetic? It would seem fair to take away some kinetic energy if you are put in a region where you have more potential energy.  Either way is the change in energy non-continuous like in the game and discussion that's linked below? Or are there just more than one way to move through but the change in potential energy is smooth in any of those? That would mean more potential equilibrium points though...  Similar questions has been discussed , is it correct about how the falling guys gets a lot of energy (in form of a potential one) by draining it from the mouths? "The pair was ..." or "the pair were ..." Why can't I destroy or place blocks? Form of the Classical EM Lagrangian So I know that for an electromagnetic field in a vacuum the Lagrangian is $$\mathcal L=-\frac 1 4 F^{\mu\nu} F_{\mu\nu},$$ the standard model tells me this. What I want to know is if there is an elementary argument (based on symmetry perhaps) as to why it has this form. I have done some searching/reading on this, but have only ever found authors jumping straight to the expression and sometimes saying something to the effect that it is the "simplest possible".