Imagine a wedding invitation which ends with the following sentence:     To round off the weekend celebrations, please join us for lunch.   Would it be more, less, or equally correct to say:     To round off the weekend's celebrations, please join us for lunch.
In the following is it better to use a possessive noun with an apostrophe or an attributive noun without an apostrophe?     The following list details the assumptions that have been made in   conjunction with the Dell Company’s staff.   Or      The following list details the assumptions that have been made in   conjunction with the Dell Company staff.   Assume Company is the name of a company, such as Dell.
Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$ How to prove the following product? $$\frac{\sin(x)}{x}= \left(1+\frac{x}{\pi}\right) \left(1-\frac{x}{\pi}\right) \left(1+\frac{x}{2\pi}\right) \left(1-\frac{x}{2\pi}\right) \left(1+\frac{x}{3\pi}\right) \left(1-\frac{x}{3\pi}\right)\cdots$$ How to modify an array's values by a foreach loop? How do I calculate the power consumed by a lightbulb? Confusing article status for journals of American Mathematical Society: "reviewing" AND "being handled by an editor" The web page of my article in the AMS editorial system for some three months says &quot;Article status: Reviewing&quot; and in the next line &quot;Your paper is being handled by an editor&quot;. I find this confusing as the &quot;reviewing&quot; status appears to suggest that the article is with the referee(s) rather than with the editor but this in turn seems to contradict the line &quot;Your paper is being handled by an editor&quot;.  Could someone with enough experience with AMS journals please explain how should one interpret the combination of &quot;Article status: Reviewing&quot; and the line &quot;Your paper is being handled by an editor&quot; at the article page? More broadly, which are the possible article statuses in the AMS editorial system?  Many thanks in advance. I have to find an easy ring which this ring is isomorphic with.  I can prove that $5 = (2+i)(2-i) \in (2+i)$ but this doesn't help me further.  My book says the answer is $\mathbb {Z_5} $ How does one attack a two-time pad (i.e. one time pad with key reuse)? I use time manager for a polygon layers with dates and it works. I would like to see the cummulative addition of my polygons. So I have 4 periods I want the poylgons from 1900-1950 to be added to the new ones in 1950-2000 etc in the next time step. How can I perform that or does another open source tool exist for that? A number of times I have encountered in text-books and articles that neutrinos might contribute only a small fraction to dark matter. The reason has to do with the fact that if all of the dark matter consisted of neutrinos, then small-scale structures in the Universe could not have formed yet, because, as they say, neutrinos "wash out" small fluctuations. However, none of these texts provided a reference to any specific sources explaining in detail what is meant by "washing out". After all, neutrinos are notorious in their weak interaction with baryonic matter, so if there is a small-scale fluctuation of baryons, then how background neutrinos can prevent it from growing further if they practically do not interact with baryons? I guess the question boils down to calculating cross-sections of interactions at specific temperatures. I would appreciate comments and references to sources addressing this particular issue. Set Theory: Tree Property Why does the tree property hold for regular cardinals but not singular cardinals? (I.e. There exists a tree of height $\kappa$ with countable levels and no cofinal branch for $\kappa$ a singular cardinal) This is something that has long bothered me, and I have asked a few physicists and chemists and never gotten a very satisfying answer. Why are particles charged? And I'm not asking (and this is the answer you often get) why some molecule might be negatively charged because the answer to that is simply is that there was one more negatively charged particle than positively charged particle. That doesn't answer my question, however, of why there are charged particles at all?  So, on a fundamental level, what makes one particle charged and another one neutral.  For instance, protons and neutrons have almost exactly the same mass, which I'm assuming that means they have very similar internal compositions, yet one is positively charged and the other neutral. What is going on that makes these particles different?  On a similar note, and I'd really like to know this, how is it that a proton and an electron have exactly equal and opposite charge, yet an electron is about 1000 times less massive than a proton?  I have particular trouble with this question because if the answer were something along the lines of "particle X which composes protons all have partial positive charges of n amount..." I would just ask why particle X has any charge and we'd be in the same predicament.  I'm sure there is a satisfactory answer to my question, I just can't find it and don't know what resources are reliable or detailed enough to be satisfactory. Logical XOR operator in C++? What are Java command line options to set to allow JVM to be remotely debugged? Reading list in topological QFT I want to trace a border in a box or minipage like this model. A border customizable in left angle on top and right angle in bottom. Somebody can help me? Thanks a lot JPierre Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk For any $z, a$ in the open unit disk, we define$$d(z,a)=\left \vert \frac{z-a}{1-\overline{a}z} \right \vert$$  Show that $d$ is a metric on the open unit disk.     It is easy to show $d(z,a)=d(a,z)$ and $d(z,a)=0$ $\rm iff$ $z=a$. However, I am having trouble showing that it satisfies triangle inequality. Any help would be appreciated! How much time is too much time playing educational computer games? I recently bought an iPad primarily for my 3-year-old daughter. I put nothing on it but educational apps and children's books. No YouTube, no Internet, no (non-educational) games. I've decided to let her use it as much as she wants, for now, and see how it goes. That was a few weeks ago.  So far she's been using the iPad maybe 2 to 5 hours each day. She still enjoys other activities -- playing outside, playing with dolls and blocks, interacting with friends, being read to, etc. And I think she might be learning a thing or two from the apps. Still, several hours a day seems like a lot. How do I know if it's too much?  I've searched the web, and there's lots of info on limiting TV time and video games, but I can't find any recommendations on limiting use if it's only educational games.  Relevant: I used the following code to list my java code, but the it looks like there's too much space between words. What can I do?  % source code listing \usepackage{listings} \usepackage{color} \usepackage{xcolor}  \usepackage{caption}  % citation style \usepackage{apacite} \DeclareCaptionFont{white}{\color{white}} \DeclareCaptionFormat{listing}{\colorbox{gray}{\parbox{\textwidth}{#1#2#3}}}  \begin{document} \begin{lstlisting}[label=some-code,caption=bind to service call] bindService(new Intent(this, Recognizer.class), recConnection, Context.BIND_AUTO_CREATE); \end{lstlisting} \end{document}   The snapshot of what I got. The code not completely shown, and space too wide, in function bindService. In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False? I am studying entailment in classical first-order logic.  The Truth Table we have been presented with for the statement $(p \Rightarrow q)\;$ (a.k.a. '$p$ implies $q$') is: $$\begin{array}{|c|c|c|} \hline p&amp;q&amp;p\Rightarrow q\\ \hline T&amp;T&amp;T\\ T&amp;F&amp;F\\ F&amp;T&amp;T\\ F&amp;F&amp;T\\\hline \end{array}$$  I 'get' lines 1, 2, and 3, but I do not understand line 4.      Why is the statement $(p \Rightarrow q)$ True if both p and q are False?  We have also been told that $(p \Rightarrow q)$ is logically equivalent to $(~p || q)$ (that is $\lnot p \lor q$).  Stemming from my lack of understanding of line 4 of the Truth Table, I do not understand why this equivalence is accurate.       Administrative note. You may experience being directed here even though your question was actually about line 3 of the truth table instead. In that case, see the companion question  And even if your original worry was about line 4, it might be useful to skim the other question anyway; many of the answers to either question attempt to explain both lines. Why won't the location of the light affect the direction of the shadows? So I'm new to blender, and I've been working on a project with a tutorial. (some of you might know this)   I was going through quite smoothly until I noticed that no matter where I place my light, the rendered version appears the same. (directly above the objects) I tried different types of lighting, different brightnesses, (light is currently at around 4.000 brightness) nothing works. But if I delete the light, it becomes dark and grainy. (I checked on the side bar, there are no other light sources or objects..)  Even if I put the light source under my objects, the rendered version appears the same.  Am I doing something wrong? Why can't I change the direction of the light?        Uh.. Since I'm not allowed to post more than 2 links, I'll just post extra info here (also replying to @bertmoog)  I tried changing the light types, but they all do nothing (except for Sun, of course, and Hemi, which is interpreted as Sun for some reason) The brightness is set on 4.200, color set to white, shadows enabled, etc. But it still won't do anything. As you can see, nothing appears in the preview.    EDIT: I found that by rotating the sun to point where I want it to, it works almost like normal point lighting (sorta). This pretty much solves my problem, but still, why won't the other lighting modes work? Custom setting Setting type not visible