What kind of forces would follow only the second part of shell theorem?
The converse of Newton's shell theorem
It shows no question owner, not even a simple name (without link).   What happened? How long does it usually take for published articles to show up on Google Scholar? The title pretty much says it all - what's the typical delay with which Google Scholar indexes newly published articles? (Note I'm not talking about citations, but about the article showing up at all.)  Edit: the article in question went for over six months after being published (in a well-regarded Springer journal with its own Wikipedia page) without appearing on Google Scholar, until it received a citation, at which point it was added to Google Scholar almost immediately. One more motivation to write papers that get cited. :)  Edit 2: Another article in an even more mainstream journal took a little over seven weeks. The verb let means  “allow”, “permit”, “not prevent or forbid”, “pass, go or come”  and it's used with an object and the bare infinitive.         Are you going to let me drive or not?     Don't let him off the hook.     Before we let our children surf the Internet, they have to do their homework.     She lets the cats out before leaving.   He let us into the house.      The full form let us can be used similarly        Let us know as soon as possible.      Please, let us help you.   They will never let us forget.      None of the above can be contracted; however, when let us is used for making a suggestion; giving self-encouragement; expressing a consequence or plea,  it is often contracted to let's      Let's go out   Let's have a party   Let's see what happens   Let's stand together in this emergency   Let's not forget those who sacrificed their lives     Questions   I believe that let + us is the only instance where this type of contraction occurs. Is there an explanation as to why verbs such as (i) give + us, (ii) get + us or (iii) take + us were not similarly contracted? When was the apostrophe used to replace the omitted letter "u" in let us?  What is the origin of let's? So a couple of weeks ago my network manager icon stopped appearing; I still get automatically connected to my saved networks and the internet works fine, etc. If I go into System Settings and look at the Network settings I can still see all the networks, only the icon that's normal in the top bar is missing.  I have no idea what caused this, I don't remember installing anything. I think it just happened after a regular update.  I tried these commands to make sure I was properly up-to-date, (which I found on another forum post):  sudo apt-get -f install sudo apt-get update sudo apt-get upgrade   That didn't do it so I found this post:  and I followed the instructions in those answers:  sudo apt-get purge network-manager-gnome &amp;&amp; \ sudo apt-get install network-manager-gnome   And, quoted from an answer there:     Add nm-applet to the Startup Applications (which may be found by   entering "Startup Applications" in the Dash).   I restarted and then saw no Unity interface at all! So I tried those 3 commands above to update again and thankfully that fixed Unity but I still don't have my network manager.  If I try the command nm-applet in a terminal it says:  nm-applet-Message: using fallback from indicator to GtkStatusIcon   So.... I'm pretty much stumped. Any help would be appreciated. Why can't polynomials have negative exponents or division by a variable Why can't:  $$2x^{-3} - 3x$$  or  $$\frac{1}{2x}$$  be polynomials too?  Why have a definition that excludes these algebraic forms? A Hilbert space is, by definition, a complete inner product space. If $(V,|.|)$ is finite dimensional inner product space of dimension $n$ then it is (topologically) isomorphic to $\mathbb{R}^n$ which is of course complete. My instinct here is to say "and therefore, $V$ is also a Hilbert space". I'm not sure about this step however since completeness depends on the norm and the norm depends on the selected inner product (assuming the induced norm $||x|| = (x | x)^{1/2}$ is used). So, must we place some condition on the inner product or is the topological isomorphism between $\mathbb{R}^n$ enough to guarantee that V is Hilbert? How to draw simple table How should a family with young children apply for UK visas? We are sponsoring a family to visit us in UK as friends from Madagascar for two weeks. They have a 6 year old and a 16 month old.   Do the kids need their own visas, and are they the standard visitor visa or a special child visa?   Also, when I try and apply on the website I can only apply for one person so how do I apply for all the individuals in the family?   I have looked on the Immigration website and can't find the answers I need. I'm trying to solve    So far I've done the first part, evaluating the summation ;  where a is just n. I'm not sure where to go from here or what it even means deduce the second summation. I understand that the summation of simply $$\sum\limits_{k=0}^n\cos(kx)$$ is derived from looking at the real part of  $$\sum_{k=0}^n{\rm e}^{ikx} $$I'm guessing they want me to see how the second summation in the question is defined by 'playing around' with the original? Problems in Creating InfoWindow on each individual circle with mouseover using Google Map API Order of items in a context menu How to run scripts on start up? How can I run scripts automatically when Ubuntu starts up so I don't have to run them manually after startup? I am running the latest version of Linux Mint with Cinnamon. I'm trying to map Caps Lock to Ctrl, but I cannot figure out how to do it. All web searches I've done have led me to older versions of Linux Mint (there is no keyboard layout option in my settings). How can I do this? $\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$ Possible Duplicate:        $b$, $x$, $y$, $z$, $\ldots$ are integers greater than 1. How can we prove that  $$ \gcd (b ^ x - 1, b ^ y - 1, b ^ z - 1 ,\dots)= b ^ {\gcd (x, y, z, \dots)} - 1\ ? $$ TikZ: remove margin, padding, border around nodes containing images Show that, if $a$ and $h$ are positive numbers, $h &lt; a^2$, then $$\sqrt{a^2 + h}-a &lt; \frac{h}{2a} &lt; a - \sqrt{a^2 - h}$$  I've been working on this problem for about 2 hours now, but I've made no progress. I'm not looking for an answer, but I just need some help to get me started since we didn't practice inequalities this complex in highschool. Thanks.   All I can tell is that we're supposed to take the square root of an expression at some point since one inequality ( h &lt; a^2 ) becomes two.   Edit : Thank you guys for the replies, but I'd appreciate only hints in the future (like Robert Israel) so that I can learn. Regardless, I found a different way to do it, so it's cool :) Can I use my laptop as a second monitor? Is it possible to make my laptop's screen act as a second monitor for my desktop computer? Does anyone have an intuitive explanation of why this is the case? Why can't an electric field line suddenly break? My book has the following question in it as an exercise:  An electrostatic field line is a continuous curve i.e. a field line cannot have sudden breaks. Why not?  I cannot seem to be able to reason for or against this statement.  Can somebody please tell me why they can't suddenly break and if that were to happen then what will be its outcome? My current prompt is colorized and edited as so -  #!/bin/bash  # GIT Prompt help if tput setaf 1 &amp;&gt; /dev/null; then     tput sgr0; # reset colors     bold=$(tput bold);     reset=$(tput sgr0);     txtund=$(tput sgr 0 1);     black=$(tput setaf 0);     blue=$(tput setaf 33);     cyan=$(tput setaf 37);     green=$(tput setaf 64);     orange=$(tput setaf 166);     purple=$(tput setaf 125);     red=$(tput setaf 124);     violet=$(tput setaf 61);     white=$(tput setaf 15);     yellow=$(tput setaf 136); else     bold='';     reset="\e[0m";     black="\e[1;30m";     blue="\e[1;34m";     cyan="\e[1;36m";     green="\e[1;32m";     orange="\e[1;33m";     purple="\e[1;35m";     red="\e[1;31m";     violet="\e[1;35m";     white="\e[1;37m";     yellow="\e[1;33m"; fi; ORIG=$PS1 HOST=$HOSTNAME PS1="\[${txtund}${green}\]${HOST}\[\[${reset}\]"; PS1+="\$(prompt_git \"\[${white}\] on \[${violet}\]\")"; PS1+="\[${reset}\]"; PS1+="\[ at - ${orange}\W\]"; PS1+="\[${reset}\]"; PS1+="\[ - \u \]"; PS1+="\n\$ ";   I know that the line  PS1+="[ - \u ]"; will show me my current user. However, I want that section to be red if it is root. All other users should be the default color of gray. Is there a way to change the color in that section based off of current user or should I just declare a variable and use an IF statement to insert that section or a modified section with red as a color?  My expected output is gray named user for all normal users. Root should be red. This is BASH.