Topologist Sine Curve
Topologist's sine curve is not path-connected
I'm granted a one-entry Schengen visa and now I can't go. Will having an unused visa in my travel passport have any consequences like future visas refusal? Do I need to do anything special? I already have the pink and red leather gloves, the armor, the crown, and the monkey's staff (and they're all enchanted). Regardless of how many health potions I use, I always die. Help! Spatial query to return multiple values I have a woodland scheme advice layer that has a polygon for each area of advice (brown layer in the picture). I also have a polygon layer of UK local authorities (red boundary layer in the picture). I would like to perform a spatial query which returns the local authority name for each woodland advice scheme. This would work fine if each woodland advice scheme was found in just one local authority boundary. However many are found across a boundary of two different authorities. For instance, one scheme sits across the boundaries of the authorities of Fife and Angus. The scheme is the yellow selected polygon in the picture and the red line is the authority boundary. How do I get the spatial join to return a value of Fife; Angus (or something similar to identify two values) instead of just Fife or Angus. I've seen many posts regarding a combinatorial proof of the following question. But for a non-combinatorial proof would the following method work? Also... is this the easiest way to arrive at a proof? It seems to be rather verbose.  Show the formula $k {n\choose k} = n {n-1 \choose k-1}$ is true for all integers $n,k$ with $0\le k \le n$.  My answer:  Observe that  $$\begin{align*} {n\choose k}&amp;= \frac {n}{k} {n-1 \choose k-1}\\ &amp;= \frac {n}{k}\left[ {n-2 \choose k-2} + {n-2 \choose k-1}\right]\\ &amp;= \frac {n}{k}\left[ \frac{(n-2)!}{(k-2)!(n-2-(k-2))!} + \frac {(n-2)!}{(k-1)!(n-2-(k-1))!}\right]\\ &amp;= \frac {n}{k}\left[ \frac{(n-2)!}{(k-2)!(n-k)!} + \frac {(n-2)!}{(k-1)!(n-k-1)!}\right]\\ &amp;= \frac{(n-1)!}{(k-1)!(n-k)!} + \frac {(n-1)!}{(k)!(n-k-1)!}\\ &amp;= \frac{(n-1)!}{(k-1)!(n-1-(k-1))!} + \frac {(n-1)!}{(k)!(n-1-k)!}\\ &amp;={n-1 \choose k-1} + {n-1 \choose k}={n \choose k}. \end{align*}$$ How to study/prepare for the Salesforce Developer Certification I am fairly new to Force.com development (less than a year). I did not learn it from the ground up. So I think it will be good to study for the developer exam to strengthen my basics and improve my overall knowledge of Force.com + it will be great to have this certification.  Now it's surprising that there is not a lot of great information on the web about how to go about obtaining this certification. Most other major certifications have dedicated study guide books available but there are few for Force.com and I don't think any of them are official.   The official page has little information. The Study guide gives a broad description of the topics in the test.   I see a lot of the esteemed members are here certified developers. I think if you guys could give us a little information, hints/tips and some advice on how to prepare for this exam, it will really be of great help. Also is DEV401 required/helpful?  Also if we could get recommendations for great resources(books, online training etc) and practice tests it will be awesome. Can sudo be reinstalled after being removed? Who is the Maker? C-3PO frequently speaks of “the Maker.” Is this a true droid religion, or is this a religious reverence by droids for their specific creators (in this case, Anakin, even though C-3PO has forgotten who he is)? Is this even a droid thing or is it just C-3PO? What else do we know about this “Maker”-worship? How do I enable error reporting in PHP? This question is about finding reasons for compile errors when using tikz.  Consider the files compiles.tex, compiles-not1.tex and compiles-not2.tex. Then it is clear that compiles-not1.tex does not compile, because the name C has not been assigned. The file compiles-not2.tex does not compile, because \draw (A) -- (A -| B ); contains a space after the name B. However, this is difficult to see from the error message.   Is it possible to tweak the error messages generated by tikz to perhaps mark tikz-code and names in some way? What I mean is that in the example, an error message ! Package pgf Error: No shape named 'B ' is known. might be more helpful, as the space in the name B\␣ (B with a trailing space) is more clearly delimited from the message.   File compiles.tex compiles without errors.  \documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture}     \node (A) {A};     \node[above right of=A] (B) {B};     \draw (A) -- (A -| B); \end{tikzpicture} \end{document}   On compilation compiles-not1.tex generates ! Package pgf Error: No shape named C is known.  \documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture}     \node (A) {A};     \node[above right of=A] (B) {B};     \draw (A) -- (A -| C); \end{tikzpicture} \end{document}   compiles-not2.tex generates ! Package pgf Error: No shape named B  is known.  \documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture}     \node (A) {A};     \node[above right of=A] (B) {B};     \draw (A) -- (A -| B ); \end{tikzpicture} \end{document} What prevents photons from getting mass from higher order Feynman diagrams Using Euler's Totient Function, how do I find all values n such that $\phi(n)=12$? How do I generalize the equation to be able to plug in any result for $\phi(n)=12$ and find any possible integer that works? Extract substring in Bash If a subring of a ring R has identity, does R also have the identity? I know it does not make sense that if a subring of a ring $R$ is commutative, then $R$ is also commutative. (For example, the set consisting of the matrices whose all entries except (1,1)-entry are zero, is a subring of ring of 2x2 real matrices.)  I also considered the case of a ring containing a subring with identity, but I had no ideas. Maybe it seems that it does not make sense, either.  Who give me some examples supporting my guess? "As a beginner, I am happy that I learned a new thing."  You will recognize this as your DoReMi-s.( at 4:52)  What is the meaning of the "AS" there and when do we use that?  In depth answers would be appreciated.  Similarly:     Do I have your word as a lawman not to shoot me down like a dog in the street?    Can you explain this sentence?   Can I understand it as a lawman wouldn't shoot down people on the street or wouldn't have his word or what? I use Firefox 35.0 on my Macbook to access Stack Exchange. Recently whenever I access a message or Community site, the "spinning circle" indicating activity starts, and never stops. This doesn't seem to happen on other non-Stack Exchange sites.  Has there been any change to the SE code which may have caused this.    The Web Developer Console shows  The connection to ws://qa.sockets.stackexchange.com/ was interrupted while the page was loading. full.en.js:1 Use of getPreventDefault() is deprecated.  Use defaultPrevented instead. jquery.min.js:3 Using JQuery and Prototype in the same page Several of my pages use both JQuery and Protoype. Since I upgraded to version 1.3 of JQuery this appears to be causing problems, because both libraries define a function named '$'.  JQuery provides a function noConflict() which relinquishes control of $ to other libraries that may be using it. So it seems like I need to go through all my pages that look like this:  &lt;head&gt;           &lt;script type="text/javascript" src="/obp/js/prototype.js"&gt;&lt;/script&gt;     &lt;script type="text/javascript" src="/obp/js/jquery.js"&gt;&lt;/script&gt; &lt;/head&gt;   and change them to look like this:  &lt;head&gt;           &lt;script type="text/javascript" src="/obp/js/prototype.js"&gt;&lt;/script&gt;     &lt;script type="text/javascript" src="/obp/js/jquery.js"&gt;&lt;/script&gt;     &lt;script type="text/javascript"&gt;         jQuery.noConflict();         var $j = jQuery;     &lt;/script&gt; &lt;/head&gt;   I should then be able to use '$' for Prototype and '$j' (or 'jQuery') for JQuery. I'm not entirely happy about duplicating these 2 lines of code in every relevant page, and expect that at some point somebody is likely to forget to add them to a new page. I'd prefer to be able to do the following    Create a file jquery-noconflict.js which "includes" jquery.js and the 2 lines of code shown above Import jquery-noconflict.js (instead of jquery.js) in all my JSP/HTML pages   However, I'm not sure if it's possible to include one JS file in another, in the manner I've described? Of course an alternate solution is simply to add the 2 lines of code above to jquery.js directly, but if I do that I'll need to remember to do it every time I upgrade JQuery. What are the pros and cons of flip lock vs. twist lock on tripods? I am in search of a tripod. While doing a bit of research myself, I came to know that there are two broad variants of leg locks, viz. flip and twist lock. In many forums, I find people expressing conflicting views preferring each one over the other. This seems to confuse me even more while not being aware of what each type of lock operates. What are the prime considerations in choosing a particular lock system? How do I install Ubuntu from an USB drive / create a live USB-stick in Windows? I tried to use the usb-creator.exe from Ubuntu 10.10 desktop i386 ISO image and it does create an USB stick that doesn't boot. When I try to boot from it I get:     Operating System not found.   I try to do this from Windows 7 x64. I'm not looking to create a live Ubuntu media, only an installation USB disk.  I repeated the process several times and I even tried to reformat the USB drive (FAT32), no success yet.  The USB stick is a 8GB one. Do Wine Viruses only work while Wine is running? I heard Linux can get viruses through Wine,and I was curious if the viruses work only while Wine is running.  In other words, could I stop a virus from doing it's thing by just quitting Wine? Application-priority based automatic bandwidth distribution in Windows? Whenever my browser wants to download data, I want it to be granted as much of the bandwidth as it wants, while other applications must do with the leftover bandwidth; and when the browser is not transferring any data, other applications could be given the bandwidth. Something like the process priority in Windows task manager. Any method/software to accomplish this automatically?