In the following sentence , should locally owned have a hyphen?  A fun, causal way to sample the sights, stories and flavors of a cross-section of locally owned restaurants.
Which of these are acceptable? Is one preferable over the other?   "Chemically-deposited tourmaline is never periwinkle." "Chemically deposited tourmaline is never periwinkle."   Also, is the title to the this question asking what I'm trying to ask?  (I realize that there are other questions about hyphenation in similar contexts; I'm asking specifically about -ly adverbs.)
Word or phrase for mere coincidence that brings happiness How do I change NEI to cheat mode? Suppose I have a document with multiple include or input statements  \input{fileA} \input{fileB}   etc.   Is there an easy way to generate a single .tex file where \input{fileA} is replaced by the actual content of fileA etc. without copying it manually? I'm getting a PC with Windows and I want to dual boot using Ubuntu as my primary OS.  I want to create a Home partition to store all my files and hopefully be able to access them on Windows 7 without having to manually mount the partition or anything.  I want to know what kind of partition should I create and if I can share my Home partition to simplify matters.  Thanks Is there a difference between single and double quotes in Java? Expected time to roll all 1 through 6 on a die It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth would be moving relative to the clock on the spaceship, and since time always dilates and never goes faster regardless of the direction of relative motion,  the clocks on earth should register less time than the clock on the spaceship.  Is this true? Whenever there is a fast-moving object such as a rocket do all clocks on earth really become slow?  If the rocket with the clock landed after moving at relativistic speed, would its clock and the earth's clock again show the same time since during its travel both appeared slow to each other?  Or is all this just an illusion, ie. the clocks just appear to be slow to each other but in actually run at normal speed, and neither is behind when the rocket actually lands? Hey I want to connect the bottom loop with the top loop so that it forms a solid.  I have tried selecting multiple vertices and pressing F but that just creates a large face which I do not want. I have tried using grid fill bu that doesn't work either. The solution that seems to work is by selecting four vertices and pressing F and then selecting the next 4 and pressing F and on and on. That just takes too long. Should I mention my Canadian visa refusal in my UK visa application? Range of $(a_{1}-a_{2})^2+(a_{2}-a_{3})^2+(a_{3}-a_{4})^2+(a_{4}-a_{1})^2$ is If $a_{1},a_{2},a_{3},a_{4}\in \mathbb{R}$ and $a_{1}+a_{2}+a_{3}+a_{4}=0$ and $a^2_{1}+a^2_{2}+a^2_{3}+a^2_{4}=1.$ Then Range of $$E =(a_{1}-a_{2})^2+(a_{2}-a_{3})^2+(a_{3}-a_{4})^2+(a_{4}-a_{1})^2$$ is  Try: From $$(a_{1}-a_{2})^2+(a_{2}-a_{3})^2+(a_{3}-a_{4})^2+(a_{4}-a_{1})^2$$ $$=2(a^2_{1}+a^2_{2}+a^2_{3}+a^2_{4})+2(a_{1}a_{2}+a_{2}a_{3}+a_{3}a_{4}+a_{4}a_{1})$$ $$=2-2(a_{1}+a_{3})(a_{2}+a_{4})=2+2(a_{1}+a_{3})^2\geq 2$$ and equality hold when $\displaystyle a_{1}=-a_{3}$ and $a_{2}=-a_{4}$ Could some help me how to find its upper bound, Thanks If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$ If $A^2 = I$ where $A$ is an $n\times n$ matrix, then why is $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$.   I am not sure why this seems to be true. Dependency injection and Libraries/Frameworks Automatic line breaking of long lines of text? Here, it is just a example. I have a line:  aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa   Now, I want to let LaTeX automatically wrap the line according to the width of the text block/margins. How to detect if a function is called as constructor? Given a function:  function x(arg) { return 30; }   You can call it two ways:  result = x(4); result = new x(4);   The first returns 30, the second returns an object.  How can you detect which way the function was called inside the function itself?  Whatever your solution is, it must work with the following invocation as well:  var Z = new x();  Z.lolol = x;  Z.lolol();   All the solutions currently think the Z.lolol() is calling it as a constructor. Consider this reverse biased diode :     I read that no or very small current flows in reverse biased diode as depletion layers get widened and huge resistance is offered so no electrons can cross it. But, why the electrons or holes need to cross the depletion layer? In the diagram above, the positive charges (holes) are moving towards left and the current due to electrons is also in left, so won't the circuit be completed? Prove that the additive groups of $\Bbb Z$ and $\Bbb Q$ are not isomorphic.    It is hard to create a map that will show homomorphism. Root of unity for $n+1$ Let $n \ge 1$ and $u_{1},u_{2},...,u_{n}$ are all root of unity for $n+1$ and there are different from $1$.(a) Find polynomial $f \in \mathbb R[x]$ of degree $n$ for which: $f(u_{k})=0$ for $k=1,2,...,n$.(b) Calculate real coefficient and imaginary part for $(2-u_{1})(2-u_{2})\cdot...\cdot(2-u_{n}).$    I have a knowledge about root of unity but I completely don't know how to do it because I think that I need some extra trick to do it but my ideas finished. I know that $\varepsilon_n^{(k)} = \cos\left(\tfrac{2k\pi}{n}\right) + i\sin\left(\tfrac{2k\pi}{n}\right) = e^\frac{2\pi i k}{n}$ and for $n&gt;1$ $\sum _{{k=0}}^{{n-1}}e^{{\frac  {2\pi ik}{n}}}=0$ but I think it is too little knowledge to solve this task.Can you help me? is it possible to skip immediately preceding time points? So that, if, for example, you are using model order 2, that is, two time points, but not the two immediately previous time points, but rather, say for example, skipping 2 points, and then using those two points.  So, e.g., it would be y=x(t-3) + x(t-4). Book series about aliens who put "caps" on people to control them I'm aware there are been several similar questions, and some great answers with hints on how to prove this, for example  and .  But I've never really seen a detailed proof of the absolute convergence of the Riemann zeta function in the half-plane $\Re(s)&gt; 1$.  I hope there's interest on a detailed proof of this for reference. Here is my attempt. Please, fill in any detail that might be missing, or point out any mistake!  On $\Re(s)=\sigma&gt; 1$, we have  $$\sum_{n=1}^{\infty}\bigg|\frac{1}{n^s}\bigg|=\sum_{n=1}^{\infty}\frac{1}{n^\sigma}$$  and  $$\frac{1}{n^\sigma}\leq\frac{1}{n^{1+\epsilon}}$$  for any $\epsilon &gt;0$, so by the direct comparison test, if   $$\sum_{n=1}^{\infty}\frac{1}{n^{1+\epsilon}}$$  converges absolutely, then so do $\sum_{n=1}^{\infty}|1/n^s|$ and $\zeta(s)$.  By the integral test, the convergence of $\sum_{n=1}^{\infty}1/n^{1+\epsilon}$ is equivalente to the finitude of the integral  $$\int_1^\infty \frac{1}{n^{1+\epsilon}}=\bigg[-\frac{1}{\epsilon x^\epsilon}\bigg]=\frac{1}{\epsilon}$$  which holds for any $\epsilon &lt; \infty$.  Any correction or improvement is welcomed! Thanks in advance.