In the workbook that I'm working with, there is a strange structure of sentence for me and I would like to check with you if it's not wrong or mistake such as typo. The sentence is:      Only after buying the cottage did we discover that it was infested with mice"   The location of the auxiliary verb "did" in this  is not clear to me. Normally, when it comes before the pronoun then the sentence is turned into an .   We can use also the auxiliary verb as an emphasizer but in such cases it should come after the verb (e.g. Only after buying the cottage we did discovered that it was infested with mice"). In addition, I do not understand the omission of the past form (ed) from the word "discover".
Occasionally I see constructs like this in English sentences:        Not only is this true in this case, but ...      What puzzles me is the "is this" part of it. The sentence is not a question, yet it seems to have a question-like order. Isn't this correct/preferred:        Not only this is true in this case, but ...      Are there other cases where non-question sentences contain question-like parts (so to speak)?
Every $R$-module is a quotient of a free module I'm reading through my notes, and I have a theorem as the title says. As proof I have only a picture.    where $v:m\mapsto(0,...,0,1,0,...,0)$ and 1 is at $m$-th position. I know, that $\oplus_M R$ is a free module generated by set  $M$, but is this all? I do not see how the statement is proved. Are there any tools for Windows 7 that will allow me to enable/disable monitors from the command-line?  For example, my GTX 480 has three outputs (2x DVI and 1x HDMI) but only two displays can be active at any given time.  I'd like for a command-line to allow me to disable one of the DVI monitors and enable the HDMI monitor, etc.  (I've found NirCmd which is an amazing utility but it doesn't seem to support this...)  EDIT: UltraMon seems capable of doing this but I really hoping for a more light-weight command-line solution... First of Tablet info :   Model number : Micromax P275  Android version : 4.0.4  Baseband version : v3.0  Kernal version : 3.0.8+ linda@SKYWORTHSERVER3 #52  Fri Sep 21 14:00:53 CST 2012  Build number : P275_HW.V0.1_V3.0_20120921  I dont know anything about android  now the issue is that the screen keeps randomly jerking and there are random touches that happen which will open apps and close apps randomly. this happens after few minutes since  Tablet turn on. When these things happen i cannot do anything. even if i try to power down by pressing the power key the dialog box disappears because of this random behavior.  i observer this behavior mainly when i travel in bus. so i'm thinking that the vibrations are affecting the accelerometer and thus causing the random movements. When i'm in a stationary place i rarely see this issue, but it has occured.  now i disabled  1)Auto rotate  2)Disabled all options in Developer options except Force hardware rendering.  the system update will happen and i cant turn it off(atleast i dont know).  my main useage in the Tablet are 1) pdf reading 2)videos 3)small c programmin(using CCtools).  please help me with this issue. its is very very frustrating. last thing,i brought this device 28 days ago. also i would like links on reinstalling android. How do I survive in the Nether? How do I bind the tmux prefix to a Super? I find even Ctrl+b to be very emacs like but I understand the point. I'm wondering if I could bind it to a single keypress of a key I don't other wise use? namely Super_L (also known as the left windows key. for why I say Super_L start xev in a terminal and press that key) During self-study, I ran across the question of how many ways six numbers can be chosen from the numbers 1 - 49 without replacement, stipulating that no two of the numbers be consecutive.  I can obtain a simple lower bound by saying that, in the worst-case scenario, when you choose a particular number, there are now three numbers that cannot be chosen next.  For example, if I first pick 17, then I can't choose 16, 17, or 18 for the remaining choices.  This gives me the lower bound  $$\frac{49*46*43*40*37*34}{6!} = 6,773,770 \frac{8}{9}$$  This is about 48% of ${}_{49}C_6 =  13,983,816$.  The real answer must be bigger (and an integer).  I haven't found a way to calculate it, though.  The original problem asked to show that the probability of having non-consecutive integers when you choose six is greater than 50%, so if the problem is complicated to count exactly, better approximations that show the answer is above 50% would also be appreciated.   Of course, I can use a computer to do the counting, but I'm interested in learning what methods I'm missing. Evaluate $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$$  All i could do was to see that $$\frac{1}{3}=\frac{1}{2.1+1},\frac{1}{5}=\frac{1}{2.2+1},\frac{1}{7}=\frac{1}{2.3+1},\dots$$  SO, we should be able to write   $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots=1+\sum_{n=1}^{\infty}\frac{1}{2n+1}.\frac{1}{4^n}$$  This is what i could simplify the given question to...   But, this is doing me no good.. I could not go any further..  I would be thankful if some one can help me to clear this.  I would request users who are trying to help me to just give necessary hints but not post it as answer.  Thank You. Textcase, Listings, and Tilde Consider the following MWE:  \documentclass{scrreprt}  \usepackage{textcase}  \RequirePackage{listings} \usepackage[american]{babel}  \begin{document}     \MakeTextLowercase{A~B} \end{document}   LaTeX fails with the error  ! Undefined control sequence. &lt;to be read again&gt; az                      b l.9     \MakeTextLowercase{A~B}  ?    The error seems to lie in the combination of MakeTextLowercase, the listings package and the tilde. Whenever I remove any of these three components, everything works fine. Does anyone have a clue where the problem is? Changing data type in ArcGIS attribute table? How do I get the difference between two Dates in JavaScript? I'm creating an application which lets you define events with a time frame.  I want to automatically fill in the end date when the user selects or changes the start date.  I can't quite figure out, however, how to get the difference between the two times, and then how to create a new end Date using that difference. Tikz /.style with two parameters How do I pass two parameters to a tikz style?  I would like to do something like this:  \begin{tikzpicture}[     transformer/.style={draw, cylinder, gray!80, rotate=90, minimum height=#1, minimum width=#2},   And then, I want to use this style in a node:  \node [transformer{2.3cm}{1cm}] () at (0,0.6) {}; In the Breusch-Godfrey test we use a model  $$ e_t = \varepsilon_t + \beta_1 \varepsilon_{t-1} + \dots+ \beta_p \varepsilon_{t-p}. $$  If we reject the null hypotesis of no serial auotocorrelation of the error, it means that the residuals follow an auto-regressive model of order ($p$).  If I want to avoid this problem, I must add a certain number of lags of the response variable $y$ as regressors in the original model. However, in some cases this method is not useful.   Are there other options to consider? Missing links to responses to comments on nomination posts In the responses tab in my profile, responses to comments on nomination posts include a working link in the page source, but because there's no title the links are empty and useless.    When listed in the inbox such posts do have a title, though in this case the link is to the post and not directly to the comment. (Actually, the links in responses end up being redirected and also go to the post and not to the comment, but they try to go to the comment.)  In Supercollider:    In Global Profile: Vehicles required/allowed in weigh stations on US interstates How to read from two input files using while loop I wanted to know if there is any way of reading from two input files in a nested while loop one line at a time. For example, lets say I have two files FileA and FileB.   FileA:  [jaypal:~/Temp] cat filea this is File A line1 this is File A line2 this is File A line3   FileB:  [jaypal:~/Temp] cat fileb this is File B line1 this is File B line2 this is File B line3   Current Sample Script:  [jaypal:~/Temp] cat read.sh  #!/bin/bash while read lineA     do echo $lineA      while read lineB         do echo $lineB          done &lt; fileb done &lt; filea   Execution:  [jaypal:~/Temp] ./read.sh  this is File A line1 this is File B line1 this is File B line2 this is File B line3 this is File A line2 this is File B line1 this is File B line2 this is File B line3 this is File A line3 this is File B line1 this is File B line2 this is File B line3   Problem and desired output:  This loops over FileB completely for each line in FileA. I tried using continue, break, exit but none of them are meant for achieving the output I am looking for. I would like the script to read just one line from File A and then one line from FileB and exit the loop and continue with second line of File A and second line of File B. Something similar to the following script -  [jaypal:~/Temp] cat read1.sh  #!/bin/bash count=1 while read lineA     do echo $lineA          lineB=`sed -n "$count"p fileb`         echo $lineB         count=`expr $count + 1` done &lt; filea  [jaypal:~/Temp] ./read1.sh  this is File A line1 this is File B line1 this is File A line2 this is File B line2 this is File A line3 this is File B line3   Is this possible to achieve with while loop? How to create vector graphics In Photoshop? I know people prefer using CorelDraw or Adobe Illustrator, but I want to know if there is a technique I can follow to use Adobe Photoshop to make vector Images. Is $C[0,1]$ a Banach space for the $L^1$ norm? Is $C[0,1]$ a Banach space with respect to the norm $\|f\| = \int\limits_0^1|f(t)| \, dt$?   People keep telling me it is, but lets consider: $f_n(x) = x^n$. This function defines a Cauchy sequence, yet the limit clearly isn't a continuous function! Creating a link using an 18 character ID I have an 18 character SFDC ID. I was under the impression that I should be able to create a link to that record using the following pattern: https://&lt;org server&gt;.salesforce.com/&lt;id&gt;  For example: https://na12.salesforce.com/00TU000000Nf5NP  That link works fine for me. However, when I try to link to the same object using the 18 character, case insensitive ID (ex. https://na12.salesforce.com/00tu000000nf5npmaz), I get the following error:     Insufficient Privileges      You do not have the level of access necessary to perform the operation   you requested. Please contact the owner of the record or your   administrator if access is necessary.   What exactly is the problem? If all I have is the 18 character ID, how can I create a link back to the correct SalesForce record? Can I bake in a convection microwave? I have microwave oven, but I can't bake cakes and cookies in it. So I need an electric oven, but people are suggesting I buy a convection microwave to do both baking and normal microwaving. Will that work? Or do I really need to get an electric oven to bake? Extreme cursor delay with Acer Aspire E15 on Ubuntu 16.04 Occasionally my laptop will enter a state where the cursor starts lagging so bad that it's unusable.  Oddly during this state, everything other than the cursor is still completely responsive.  I.e. anything that only involves the keyboard (opening a terminal, typing, etc) is unaffected.  Once it enters this state, on successive reboots and shutdowns it re-enters this state within seconds.  However, if I shutdown and leave it alone for a few minutes, it does not immediately re-enter this state.  Based on search results for "acer aspire ubuntu freeze" I have tried setting the intel_idle_max_cstate field in grub to 0, 1, and 2, but this did not seem to help.  To be clear - I am not experiencing any crashes, the system is completely responsive except for the cursor is delayed to the point where it would take several seconds to go from one edge of the screen to the other.