Why do cylinders roll easily and not square or rectangular slabs?
Why doesn't a block rotate due to friction?
I'm working on an exercise from functional analysis.  Let $E$ be a vector space and $\|\cdot\|_1$ and $\|\cdot\|_2$ be two complete norms on $E$. Now suppose that $E$ satisfies the following property:  $\bullet$ if $(x_n)$ is a sequence in $E$ and $x,y\in E$ such that $\|x_n-x\|_1\to 0$ and $\|x_n-y\|_2\to 0$, then $x=y$.  Now we want to show that the norms $\|\cdot\|_1$ and $\|\cdot\|_2$ are equivalent.  My idea is as follows: If for any $n&gt;0$, there is an element $x_n\in E$ such that $\|x_n\|_1&gt;n\|x_n\|_2$. Then consider $(\frac{x_n}{\|x_n\|_1})_{n\geq 1}$. Clearly, $(\frac{x_n}{\|x_n\|_1})_{n\geq 1}$ converges to $0$. However, I cann't get a contradicition from this. Maybe my idea is wrong.   In fact, I even don't konw how to show that a Cauchy sequence in norm $\|\cdot\|_1$ is also a Cauchy sequence in norm $\|\cdot\|_2$.   Anyone can give me some hints or a counter example? Thank you very much. Why wave theory cannot explain photoelectric effect and provides evidence for particle nature of light? How to implement a single instance Java application? Apparently you can easily obtain a client IP address in WCF 3.5 but not in WCF 3.0.  Anyone know how? I'm writing a thesis which is an aggregate of separate articles. I have the source code for the articles and I'm using \include to include them in the main document of the thesis. So in my main.tex (thesis document), I have  \include{article1} some pages in between the two articles \include{article2}   The problem that I'm getting is with the Appendix sections. In article 1, I have at the end:  \appendix \numberwithin{equation}{section} \section{Coefficients}\label{sec:Coeffic} \subsection{Good coefficients} then comes the first line of appendix   This gives in article 1 (when  compiled separately with the article class):     A. Coefficients      A.1. Good coefficients   and equation numbers in the Appendix A as (A.1), (A.2)  which is ok and what is expected.  When I put article 1 within main.tex, I use \include command. Also, I removed the document class for article 1 and put \chapter instead.  But when I compile main.tex (the thesis document), I get the appendix sections as:     .1 Coefficients      .1.1 Good coefficients   and the equation numbers in the appendix A as (.1.1), (.1.2) etc  My article 1 is treated as a chapter in the main thesis document (main.tex) and the title and section numbers, equation numbers are preceded by A in main.tex. This is what I want.  Maybe it would be ok to get the appendix in my main.tex as     A.A. Coefficients      A.A.1 Good coefficients   and the equation numbers in the Appendix as (A.A.1), (A.A.2) etc  to denote that it refers to appendix A of paper A. First A is for the first article and second A is for first appendix. How to get this? Using Python, how do I to read/write data in memory like I would with a file? Is there any term used for multiple hat tricks? If a bowler takes more than three sequential wickets (say six wickets) in one over, would this be called as two hat-tricks or does this feat, however unlikely, has a different name? $_POST vs. $_SERVER['REQUEST_METHOD'] == 'POST' Some guy called one of my Snipplr submissions "crap" because I used if ($_SERVER['REQUEST_METHOD'] == 'POST') instead of if ($_POST)  Checking the request method seems more correct to me because that's what I really want to do. Is there some operational difference between the two or is this just a code clarity issue? Alternatives to "and/or"? As a programmer, I have no problem with seeing or using "and/or" in technical documentation. For example,     I can upvote an answer that satisfies me and/or mark it as accepted.   That's perfectly good English to me. However, if I were writing a novel, or even just an essay, or — heaven forbid — a poem, "and/or" would seem extremely out of place.  My question is, what should I be using instead? (I solemnly swear I will not use that knowledge to actually write a poem.) Can HTML5 databases and localStorage be shared across subdomains? Biblatex: nested citations with the \textcites command I'd like to type a citation within the text and another citation inside the parenthesis for the year, something like this:     The work of Author 1 (year; cited by Author 2, year)   For this, I've tried different options of the \textcite command but without results. Also I saw the solution posted , which works for multiple citations within parenthesis but not for in-text citations.  Any suggestion? Redirect STDERR and STDOUT to different variables without temporary files I'm one of very few people at my company who does graphic work, and I do quite a lot of it. Headquarters doesn't quite get that graphics work requires different hardware than, for example, sales work, which is pretty much email/Excel/Powerpoint/web browser and that's it. So they give everybody the same low-end rental PCs to work on.  This was tolerable when we were all on XP.  Recently I got "upgraded" to a new computer, which happens every two years or so as leases expire. The catch: the new PC had the same Core 2 Duo processor that the previous one did, less RAM, it runs Windows 7 instead of XP, and all the Creative Suite applications have been upgraded from CS3 to CS5! I am the first in my office to get 7.  So now I am in a situation where I have the slowest machine in the office, yet I have to do the most demanding work. I got them to OK 2 more gigabytes of RAM, and I hoped that would solve the issues, but it just isn't helping that much at all. I actually have to reboot every day after lunch because the machine stops responding after wake if you leave it asleep for too long.  I am currently talking to Information Systems to see if I can get a capable machine, but it does not bode well for me. Can anyone share any performance optimizations for Win7 that I might be able to use?  Thank you very much in advance! SS What if client doesn't like any logo design concept? I'm using post thumbnails to link to a page.  Is it possible to add a class name to the post thumbnail image.  &lt;li&gt;&lt;a href="&lt;?php the_permalink(); ?&gt;" &gt;&lt;?php the_post_thumbnail(); ?&gt;&lt;/a&gt;&lt;/li&gt; Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$ Let $a$ and $b$ be positive reals. Show that $$\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$$ What is the JavaScript >>> operator and how do you use it? After much trial and tribulation, I thought I had drush all ready to roar. Much excitement. But then, no joy...  Drush is working. The sites operate fine via MAMP. Regardless, a "drush cc all" command returns:   No Drupal site found, only 'drush' cache was cleared.                                          [warning] 'all' cache was cleared.                                                                       [success]   This question has stumped drupalcon attendees and very experienced developers. Any ideas?  I am on Mac OS 10.9.3 using MAMP (free) Version 3.0.5  Here is my drush status:   Drupal version         :  7.29-dev                                 Site URI               :  http://default                           Database driver        :  mysql                                    Database hostname      :  localhost                                Database username      :  db_user                             Database name          :  db_name                        PHP executable         :  /usr/bin/php                             PHP configuration      :                                           PHP OS                 :  Darwin                                   Drush version          :  7.0-dev                                  Drush temp directory   :  /tmp                                     Drush configuration    :                                           Drush alias files      :                                           Drupal root            :  /Applications/MAMP/htdocs/mysite.dev   Site path              :  sites/default       Have tried executing drush from /Applications/MAMP/htdocs/mysite.dev; from /Applications/MAMP/htdocs/mysite.dev/sites/default; and using drush cc all --uri=http://localhost/mysite.dev  Tried running drush from sites/default. Same result. How to create a Wi-Fi Hotspot (in Access Point mode)? How to setup an Access Point (AP) mode Wi-Fi Hotspot?  Point to be noted: Wireless access points aren't the same as ad hoc networks. They differ significantly. In short, ad hoc networks aren't supported on newer devices and most Android, Windows Phone and Blackberry devices (and maybe iOS devices too), whereas AP mode Wi-Fi hotspots are. To get an idea about AP mode hotspots, ad hoc networks and their difference, refer to .