Do I use the plural or singular form of a noun when saying "zero or one"?
Singular or plural verb after a series connected by "or"
How can I use Bengali script in an English document? Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$? How would one evaluate the integral $$\int_0^\infty \frac{\arctan(x) \,dx}{x(1+x^2)}$$?  I was told it had a nice closed form and could have been solved with differentiation under the integral sign; however, I tried to set $$I(\alpha) = \int_0^\infty \frac{\arctan(\alpha x) \,dx}{x(1+x^2)}$$ and got nowhere (the resulting integral was very messy). Is there a much more clever substitution that can be used to tackle the integral? Why doesn't GCC optimize a*a*a*a*a*a to (a*a*a)*(a*a*a)? If $p$ and $q = 2p + 1$ are both odd primes, show that $-4$ and $2(-1)^{(1/2)(p-1)}$ are both primitive roots modulo $q$. If $p$ and $q = 2p + 1$ are both odd primes, show that $-4$ and $2(-1)^{(1/2)(p-1)}$ are both primitive roots modulo $q$.   I cannot get heads nor tails of how to even start this let alone finish it How to implement a single instance Java application? Sometime I see many application such as msn, windows media player etc that are single instance applications (when user executes while application is running a new application instance will not created).  In C#, I use Mutex class for this but I don't know how to do this in Java. What is the most effective way for float and double comparison? What would be the most efficient way to compare two double or two float values?  Simply doing this is not correct:  bool CompareDoubles1 (double A, double B) {    return A == B; }   But something like:  bool CompareDoubles2 (double A, double B)  {    diff = A - B;    return (diff &lt; EPSILON) &amp;&amp; (-diff &lt; EPSILON); }   Seems to waste processing.  Does anyone know a smarter float comparer? Is there a fast way (without looping over all edges/faces/verts) using ops.mesh or bmesh to get the lists of indices associated with mesh islands as shown below? These islands are part of one mesh but are disjoint from each other.    I know how to select the boundaries by running the operator Select boundary Loop or calling bpy.ops.mesh.region_to_loop() but can't find any API calls to return the vert/edge/face indices associated with the individual islands. How do I change directory back to my original working directory with Python? Can't use String#trim as a callback for Array#map Why is ATP the most prevalent form of chemical energy storage and utilization in most cells? Uninformative error message when using AUCTeX For creating the graphics for my thesis (function graphs, flow charts, line art sketches) I've chosen to use the sans serif font by  \renewcommand\familydefault{\sfdefault}    However when I use mathematical symbols like $p_{s}$, they are still typeset in roman font and that looks weird:    So I wonder:   how could I force mathematical expressions also be typeset in \sfdefault if I do, are there any negative sideeffects to expect (with greek signs or other special symbols?) OR should I typeset all "mathematical" graphs (axis labels etc.) in roman font, and only make the other graphics like flow charts and sketches with sans serif font? Jackknife vs. LOOCV Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group. Prove that $(\mathbb{Z}_n , +)$, the integers  $\pmod{n}$ under addition, is a group.  To show that this is a group, I know I need to show three things (in our text, we do not need to show that addition is closed-- rather, we show these three items):  $(a)$ Associative Law  $(b)$ Existence of Identity  $(c)$ Existence of Inverse  This is what I have been working with so far:     $(a)$ Associative Law:   First, assume that $n$ is a composite number and that $a,b \in \mathbb{Z}$ s.t. $a=nx$ and $b=ny$ for some integers, $x$ and $y$. Then $a+nx+nx=n(x+y)$.     So, this is where I am stuck for the Associative Law. I'm not sure if I am headed down the correct path to show that $\mathbb{Z}_n$ is associative.      $(b)$ Existence of Identity:   Generally, when showing the existence of an identity we can use this information for addition :  $a + 0 = 0 + a =a$.    I am unsure how to insert the modular portion of the definition into the existence of this identity. I realize that for addition, we generally look at $0$ (rather than $1$ for multiplication).     $(c)$ Existence of Inverse: I need to show that for each element $a \in \mathbb{Z}_n$ that $a^{-1}=-a$. Again, I do not know how to insert the modular portion of definition into this aspect of the proof.   My question is how to incorporate this modular information into the proof that this is a group. We have not covered the integers modulo $n$, binary operations, nor groups in my intro to proofs course. I am trying to read my text to figure out how to prove this, but have a difficult time reading and interpreting math speak. How to call drupal_bootstrap from custom file in subfolder? I'm trying to call drupal_bootstrap from 'temp.php' in a subfolder called 'custom' my code as follow:  chdir('../'); define('DRUPAL_ROOT', getcwd()); require_once DRUPAL_ROOT . '/includes/bootstrap.inc'; drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL);   Once I call the temp.php I get Drupal homepage.   I also tried an explicit physical path but with no use, code as follow:  define('DRUPAL_ROOT', '/var/htdocs/drupal7'); require_once '../includes/bootstrap.inc'; drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL);   temp.php located under the following folder structure:  - var -- htdocs --- drupal7 ---- custom  ----- temp.php When starring a message from the star board, it's not reflected in the main chat window Is there a way to arrange windows within the same application in the taskbar of Windows 7?  Right now we can freely adjust each application's position in the taskbar, but within the app itself the windows can't be reordered, for example multiple windows of firefox or chrome. There are now errors when updating and I cannot install most software due to a corrupted  /etc/apt/sources.list   file. Is there a copy I can download to replace it?  The file would be for Ubuntu 12.04 (Final Beta) in the United States. Difference in sentence meaning between present continuous and simple present constructions Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$