If the title of the magazine is plural, eg "Reflections", "Homes and Gardens" - should I write:   "Reflections" explore the issue ... or: "Reflections" explores the issue...  Is a singular or plural form correct?
1) "The book 'The Three Musketeers' is a wonderful example of..." Here we have a proper noun, a title that happens to end in a plural, and I have no sense that the verb should be plural. "Musketeers"/is seems proper/natural/correct, and 'are' not at all.   However, such certainty begins to wane in other examples: 2) "'The Heidi Chronicles' is a wonderful example of..." doesn't completely shake my confidence, but it moves the needle, at least a little bit. But, practically speaking, I wouldn't have a second thought about correcting a student who used 'are' instead of 'is'.  Here's the one that really bothers me: 3a) " 'The Basement Tapes' are a wonderful example of..." I don't think this sounds any less proper/natural/correct than 3b) " 'The Basement Tapes' is..." In fact, 3a seems less awkward than 3b.  Why?
cardinality of the set of $ \varphi: \mathbb N \to \mathbb N$ such that $\varphi$ is an increasing sequence I know that the set of functions $ f:\mathbb N \to \mathbb N$ is uncountable, but what if we consider only $f$ such that $f$ is increasing? I want to know if this set is countable D: and also the case of bijective and increasing (clearly if the firstone holds then this too). I think that it could be possible that it's countable Proof of upper-tail inequality for standard normal distribution $X \sim \mathcal{N}(0,1)$, then to show that for $x &gt; 0$, $$ \mathbb{P}(X&gt;x) \leq \frac{\exp(-x^2/2)}{x \sqrt{2 \pi}} \&gt;. $$ What new capabilities do user-defined literals add to C++? introduces  which will allow the introduction of new literal syntax based on existing literals (int, hex, string, float) so that any type will be able to have a literal presentation.  Examples:  // imaginary numbers std::complex&lt;long double&gt; operator "" _i(long double d) // cooked form {      return std::complex&lt;long double&gt;(0, d);  } auto val = 3.14_i; // val = complex&lt;long double&gt;(0, 3.14)  // binary values int operator "" _B(const char*); // raw form int answer = 101010_B; // answer = 42  // std::string std::string operator "" _s(const char* str, size_t /*length*/)  {      return std::string(str);  }  auto hi = "hello"_s + " world"; // + works, "hello"_s is a string not a pointer  // units assert(1_kg == 2.2_lb); // give or take 0.00462262 pounds   At first glance this looks very cool but I'm wondering how applicable it really is, when I tried to think of having the suffixes _AD and _BC create dates I found that it's problematic due to operator order. 1974/01/06_AD would first evaluate 1974/01 (as plain ints) and only later the 06_AD (to say nothing of August and September having to be written without the 0 for octal reasons). This can be worked around by having the syntax be 1974-1/6_AD so that the operator evaluation order works but it's clunky.   So what my question boils down to is this, do you feel this feature will justify itself? What other literals would you like to define that will make your C++ code more readable?    Updated syntax to fit the final draft on June 2011 How can I find tv shows/films similar to one I like? As a general case, how can I find movies or TV shows similar to an existing movie or TV show that I like? I need some help with the exercise I was assigned in math class. We were given a 3x3 square made of unit squares, and we wanted to paint all the squares. We had 3 sets of paint, red, blue, and green. Each paint was distinct from each other, but two unit squares with the same color were the same. Additionally, there's only enough paint of each color to color 3 unit squares, and all the paint has to be used. The goal of the exercise was to find the total amount of distinct possible ways such that no two unit squares that share an edge (that is to say they are next to each other vertically or horizontally, having same color across a diagonal is fine). I've started by trying to take a look at each possible arrangement of the bottom 3 unit squares, but I can't seem to find a pattern between it. Is there a better way than continuing by brute force? Any ideas on how I should proceed from here? Where is a good place to learn classical optics for high school competitions? I need to learn basic optics for a high school academic competition. Does anyone know any good places, preferably free and online, to learn the basics of optics, like lenses, angles of incidence, etc.? I can't seem to find an MIT OpenCourseWare course addressing the issue. Prove that if $V$ and $W$ are three-dimensional subspaces of $\Bbb R^{5}$, then $V$ and $W$ must have a non-zero vector in common.  So far I got $V = \{v_{1}, v_{2}, v_{3}\}$ and $W = \{ w_{1}, w_{2}, w_{3}\}$ because they are 3-dimensional subspaces. Then $V \cup W = \{v_{1}, v_{2}, v_{3}, w_{1}, w_{2}, w_{3}\}$  My prof said that now I need to prove that they are linearly independent so this is a contradiction and the statement is wrong because we are in $\Bbb R^{5}$ and we have 6 elements on it.  I don't know how to express them as a linearly independent proof, so I hope anyone can give me a good explanation on it. "The thing is, is that..." I have a map a at the link below:    I added one of my GeoServer WMS layers to the map, now I try to add the attributes window pop up on click. I found to examples on the OpenLayers 3 homepage, but I cannot put together a working code...      Is there any chance to have a working sample somewhere? Why does the atmosphere rotate along with the earth? I was reading somewhere about a really cheap way of travelling: using balloons to get ourselves away from the surface of the earth. The idea held that because the earth rotates, we should be able to land in a different place after some time. As we all know, this doesn't happen.  Someone said that the reason why this doesn't happen is because the atmosphere (air, clouds etc.) also revolves around the earth (with the same angular velocity as the earth's rotation). Since we are also part of the atmosphere, our position doesn't change relatively.  Well, I'm not convinced with that answer. Why does the atmosphere rotate along with earth?  Gravitational force is towards the centre of the earth, but I don't see how it's making the atmosphere rotate. Libraries module. Where to extract? Where should I be extracting the  module, sites/all/modules or sites/all/libraries? I want to show that $$\log N&lt;\sum_{n=1}^{N}\frac{1}{n}&lt;1+\log N.$$ But I don't know how to show this. I am currently writing an essay on artificial moral agents, and I need to explain the difference between ethics and morals. However, I am finding it really hard to find a good book or research paper which contains a citable definition.   Could someone point me in the right direction? Question I use pgfplots with the ultra thick option ans without explicitly giving the domain for the y-axis. It seems that in this case, some part of my graph is &quot;eaten&quot; by the margin: see the picture below to understand what I mean. Is there a way to avoid this? Code \documentclass{article} \usepackage{pgfplots} \begin{document}  \begin{tikzpicture}  \pgfplotsset{every axis/.append style={                     axis x line=middle,    % put the x axis in the middle                     axis y line=middle,    % put the y axis in the middle                     axis line style={-&gt;},  % arrows on the axis                     xlabel={$x$},          % default put x on x-axis                     ylabel={$y$},          % default put y on y-axis                     grid = major                     }}  \begin{axis}[xmin=-5,xmax=5] \addplot[orange,smooth, ultra thick] {sin(deg(x))} ;                  \end{axis} \end{tikzpicture}  \end{document} How to read a csv file and use the values as x and y points in blender? How can i use the value in column 'lon' and 'lat' as the position of my uv_sphere? For example,read the values from line 4, (116.4559081, 39.9139083), and make these 2 numbers as my uv_sphere x and y position in blender? and gives different colors for different mode, for example i have 4 modes in the csv , i want to make the uv sphere that represents the bus mode to be red, and subway to be green , rail to be blue and tram to be yellow., and use the row ['from'] and ['to'] to connect the nodes with a cylinder with x scale 0.5 , y scale 0.5 and the z scale with the value in ['length'] value. Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$ I was hoping to find a more "mathematical" proof, instead of proving logically $\displaystyle \sum_{k = 0}^n {n \choose k}^2= {2n \choose n}$.  I already know the logical Proof:  $${n \choose k}^2 = {n \choose k}{ n \choose n-k}$$  Hence summation can be expressed as:  $$\binom{n}{0}\binom{n}{n} + \binom{n}{1}\binom{n}{n-1} + \cdots + \binom{n}{n}\binom{n}{0}$$  One can think of it as choosing $n$ people from a group of $2n$  (imagine dividing a group of $2n$ into $2$ groups of $n$ people each. I can get $k$ people from group $1$ and another $n-k$ people from group $2$. We do this from $k = 0$ to $n$. How to install Estru3D - Structural Analysis Software? I had problems installing Estru3D. It requires Gambas3 to be installed as a prerequisite. But it doesn't work with the newest Gambas3 installed in Ubuntu 16.04. This is a  about File Permissions on a Linux web server.   I have a Linux web server running Apache2 that hosts several websites. Each website has its own folder in /var/www/.  /var/www/contoso.com/ /var/www/contoso.net/ /var/www/fabrikam.com/   The base directory /var/www/ is owned by root:root. Apache is running as www-data:www-data. The Fabrikam website is maintained by two developers, Alice and Bob. Both Contoso websites are maintained by one developer, Eve. All websites allow users to upload images. If a website is compromised, the impact should be as limited as possible.  I want to know the best way to set up permissions so that Apache can serve the content, the website is secure from attacks, and the developers can still make changes. One of the websites is structured like this:  /var/www/fabrikam.com     /cache     /modules     /styles     /uploads     /index.php   How should the permissions be set on these directories and files? I read somewhere that you should never use 777 permissions on a website, but I don't understand what problems that could cause. During busy periods, the website automatically caches some pages and stores the results in the cache folder. All of the content submitted by website visitors is saved to the uploads folder. Best practices for catching and re-throwing .NET exceptions How to change the name of document elements like "Figure", "Contents", "Bibliography", "Appendix", etc.? I'd like to modify the names used to typeset some of my document elements. For example, the caption of figure floats should change from "Figure" to "Fig.", and my \tableofcontents sectioning heading shouldn't read "Contents", but "Table of Contents". How can I do that?  \documentclass{article} % \usepackage[english]{babel} \begin{document} \tableofcontents \section{foo} \begin{figure}[h] \centering \rule{1cm}{1cm}% placeholder for graphic \caption{A figure} \end{figure} \end{document}