Why do verbs go without an "S" in these cases?
What tense should I use after the conjunction 'lest'? Must it always be an infinitive?
In what kind of rings a divisor of a product is a product of divisors? In a , if $a|bc$, then $a$ can be written as $a = a_1a_2$ so that $a_1|b$ and $a_2|c$.  Is this property of a commutative ring strictly weaker than the property of being a UFD?  If so, does it have a name, or is it equivalent to some other well-known property? How to call gdal_translate from Python code? Is it possible to use some gdal API to call gdal_translate from Python code? I do not mean simply executing the gdal_translate.exe from the file system, but rather call it somehow in code so I do not need to know the exact directory the gdal_translate executable is in? I am trying to solve a problem from Stanley's book, it says:  Fix $k,n \in \mathbb{P}$. Show that: \begin{align} \sum a_1 a_2 \cdots a_k = \binom{n+k-1}{2k-1} \end{align} where the sum ranges over all compositions $(a_1 , a_2 , \ldots , a_k)$ of $n$ into $k$ parts.  I am trying to reason like this:  we need to find the coefficient $c_n = \sum a_1 a_2 \cdots a_k$ from this generating function --  \begin{align} \sum_n c_n x^n &amp;= \sum_n \sum a_1 a_2 \cdots a_k x^n \\  &amp;= \sum_n \sum a_1 a_2 \cdots a_k x^{a_1 + a_2 + \cdots + a_k}\\ &amp;= \sum_n \sum a_1x^{a_1} a_2x^{a_2} \cdots a_kx^{a_k} \end{align}  after that, I have no clue, how do I solve this ?   moreover, what is the range in the inner sum ?    If we consider Mark Riedel's answer, and assume $n=4$, $k=2$; then the sum will be  \begin{align} \sum (z + 2z^2)^2 = z^2 + 4z^3 + 4z^4 \end{align}  On the other hand the compositions will be $(1,3), (2,2), (3,1)$, therefore the above sum will be counted as:  \begin{align} (1.3)z^{1+3} + (2.2)z^{2+2} + (3.1)z^{3+1} &amp;= 1z^1.3z^3 + 2z^2.2z^2 + 3z^3.1z^1\\  &amp;= 3z^4 + 4z^4 + 3z^4 = 10z^4 \end{align}   what's going on? what am I missing? I came across some scenarios like these:     Case 1: Obviously not true       Q: Why does the sun rise and fall every day?   A: Because the Earth .   A2: Because .     Case 2: Letting the OP do what is declared not to       Q: How can I charge my phone without a charger?   A: Try the USB ports on your computer.   A2: Go buy a charger.    Case 3: Attempt to joke (despite looking like a real answer)       Q: What's this round bird in bright red? [An image]   A: It may be a rare or mutated species of sparrow.   A2: It's a .   A3: It's an .    Should I flag A2/A3 as NAA in those cases? What laptop specs are important for intensive image editing work? How important is the following in purchasing a laptop that will be used for image editing:   processor speed amount of RAM integrated vs. dedicated graphics card HD speed (SSD; or 5400/7200/10000 rpm) I have TeX Live 2013 installed via MacTeX on my Snow Leopard laptop.  I copied the following code from page 247 of version 2.10 of pgfmanual:  \documentclass[a4paper,12pt]{report} \usepackage{tikz} \usetikzlibrary{decorations}  \begin{document}  \begin{tikzpicture} \node (a) {A}; \node (b) at (2,1) {B}; \draw (a) -- (b); \draw[decorate,decoration=brace] (a) -- (b); \draw[decorate,decoration={brace,mirror},red] (a) -- (b); \draw[decorate,decoration={brace,mirror,raise=5pt},blue] (a) -- (b); \end{tikzpicture}  \end{document}   Yet somehow I get this error:  ./Untitled2.tex:11: Package pgfkeys Error: I do not know the key '/pgf/decorati on/brace' and I am going to ignore it. Perhaps you misspelled it.  See the pgfkeys package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.11 \draw[decorate,decoration=brace]                                       (a) -- (b); ?    Is this a bug? Determine the convergence of $ \sum_{n=1}^{\infty}\left[1-\cos\left(1 \over n\right)\right] $ I dual booted ubuntu 11.04/11.10 a while ago with a USB stick and i want to uninstall it.   I would like to completely uninstall the old version and get 12.04.  I have a 64 bit laptop. Please help! How to prove the property of the Lemoine point of a triangle? From Wolfram , I know there is a Lemoine point of triangle, also called symmedian point, the sum of squared distances of this point to all the three sides is algebraically minimum.    How to prove such a property? Quad tree vs Grid based collision detection Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$ Enable USB debugging (under settings/applications/development) programmatically from within an app How can I view the contents of tar.gz file without extracting from the command-line? How to connect to device via SSH over direct ethernet connection I have a device that I need to connect to over SSH. The device is connected to my workstation via a direct ethernet connection. I'm attempting to assign the connected device an IP address somehow that I can SSH to, however all of the guides I'm finding have the user configure the IP from whatever device they're working with (namely Raspberry Pi's and so on). This is not something I can do with this device as I've no physical interface to work with.  I've been recommended to setup a DHCP server on my workstation so it would take care of this for me, however I've no idea how to configure it and none of the guides I have followed have been helpful. With that approach, I seem to have been able to bind an IP to the interface the device is connected on, however SSHing to that IP just brings me back to my own machine.  So my main question is: How do I assign an IP address to a device directly connected to my computer via ethernet cable without having any kind of access to the device (no interface, keyboard, monitor, etc). If the answer is to set up a DHCP server on my machine, how do I properly configure this and get an IP I can SSH to?  For reference, I am using Ubuntu 16.04 with OpenSSH installed. The device is also running some flavor of Linux and has SSH software installed, but again there's no way to interact with it except through SSH. I also do not have access to my router, so plugging the device in there and letting the router do the work is not an option. Why isn't smoke flowing with the shape of the domain? I created this Smoke domain.    Then When I added smoke, it didn't stay within the domain, it went through the hole. What counter balances gravity here? Lets consider a stone tied to one end of a massless and unstretchable string... Now if i'll start rotating, it will form a conical pendulum &amp; then the equilibrium is achived when the pendulum attains horizontal circular motion.... Now to maintain that state we give a constant force to string.... Here, which force counterbalances gravity? Is it the torque due to applied force cancels out the torque due to gravity?  The angle θ changes from 0 to 90° Another word for a troll not on the internet The definition of an internet troll:     In Internet slang, a troll (/ˈtroʊl/, /ˈtrɒl/) is a person who sows   discord on the Internet by starting arguments or upsetting people,   by posting inflammatory,[2] extraneous, or off-topic messages in an   online community (such as a forum, chat room, or blog), either   accidentally[3][4] or with the deliberate intent of provoking readers   into an emotional response[5] or of otherwise disrupting normal   on-topic discussion.[6]      This sense of the word troll and its associated verb trolling are   associated with Internet discourse, but have been used more widely.   Media attention in recent years has equated trolling with online   harassment. For example, mass media has used troll to describe "a   person who defaces Internet tribute sites with the aim of causing   grief to families."[7][8]     What is the equivalent for a person who does this type of thing in real life (non-cyber) troll? How to use manual partitioning during installation? I'd like to see the full How-To on how to use manual partitioning during Ubuntu installation. The existing guides (at least those I found here) cover only automatic part and leave untouched the manual part (or extremely short and contain no pictures).  I'd like to cover such situations:     If your disk contains other systems: How to cite sources written in a different language than English? Assume one wants to cite a paper written in a different language than the article citing said paper (e.g., ones own article is written in English, but the source is French).   How to properly handle citation in such a case?  Do I cite the original (French) title or a translated title? If I use a translated title, people might have a hard time to find the source; if the original (French) title is cited, people might have a hard time understanding it. How do I Parameterize a null string with DBNull.Value clearly and quickly