A bundle map $E\to \bigwedge^2 T^*M \otimes E$ corresponds to a global section of the bundle $\bigwedge^2 T^*M\otimes \text{Hom}(E,E)$
An unclear sentence in the book "Griffiths, Harris-Principles of algebraic geometry"
Yesterday I was copying a single, 8 GB file to a USB with a slow, 7 MB/s write speed, while my RAM is 3 GB. While copying the system froze, to the point where I couldn't even move the cursor.  I managed to log into the text console, and ran iotop, it showed that a process named kswapd0 was taking 99.99% of IO.  Are there workarounds so copying a large file doesn't make my system unusable? Is the prefix "pre-" meaningless in the terms "pre-heated" and "pre-board"? This question poses a paradox of meaning. The general question is whether, if two sentences (x and y) can be used in the same situation, with the same literal meaning, and x and y only differ in that x has morphological affixes that y doesn't, aren't the surplus affixes "meaningless" by the alternation test?   Take this example:  I put the chicken inside a preheated oven.    Wouldn't it make more sense to say:  I put the chicken inside a heated oven.      There is only two states an oven can possibly be in—heated or unheated.      Another example: Does first-class board the plane, or pre-board the plane?  What does that mean—to get on before you get on? The abstract environment changes the \linewidth for the whole document In the article class, it seems that using the abstract environment has an effect to the rest of the document. More precisely, it seems that it redefines the \linewidth, which equals \textwidth without abstract, is smaller with the abstract. My feeling is that \linewidth is redefined for the abstract environment, but the value is not reseted at the end of the abstract.  Here is a minimal example:  \documentclass{article} \begin{document} \abstract{This is an abstract. This is an abstract.}\bigskip  This is text. This is text. This is text. This is text. This is text. This is text.\\  \rule{\textwidth}{3em} \rule{\linewidth}{3em} \end{document}   The output is not the same if you comment the \abstract line or not.  Do you have the same problem as I do when you compile (if not, I will upload some PDF files to show)? Is this a (known) bug in LaTeX2e? How can we circumvent the problem?  Note: I compile with the pdflatex command, and I use pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian). Best WPF open source projects When posting an HTTPS url like https://stackoverflow.com/..., it does not onebox in chat. For example: Insert missing dates within table I have a table with a column for ID, Date and Frequency of occurrence for that particular date and ID.  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-20      1 4     2014-05-18      6   I'm looking to insert the dates for each ID that aren't currently there (assuming that the date ranges from 2014-05-18 to 2014-05-20) and add a value of 0 in Frequency for those.  For example, you can see that  ID 1 has an observation for all three dates;  ID 2 is missing 2014-05-18 and 2014-05-19;   ID 3 is missing 2014-05-19;   ID 4 is missing 2014-05-19 and 2014-05-20.  Therefore, the output should look like this  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-18      0 2     2014-05-19      0 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-19      0 3     2014-05-20      1 4     2014-05-18      6 4     2014-05-19      0 4     2014-05-20      0   I've attempted the following from . However, that will only add dates with 0 Frequency that aren't present throughout the entire table instead of on an ID level.   DECLARE @s DATE = '20140518', @e DATE = '20140520';  SELECT c.date, Frequency = COALESCE(a.Frequency,0) FROM dbo.Calendar AS c LEFT OUTER JOIN dbo.table AS a ON c.date = s.[date] WHERE c.d &gt;= @s AND c.d &lt; DATEADD(DAY, 1, @e); Using "that" and "this" interchangeably My wireless has suddenly became disabled by hardware switch, BIOS, rfkill, fn+f8 do nothing How do we remove an ex-girlfriend from a car loan? I have a following problem: when I plug-in my USB flash drive, it isn't shown in Windows Explorer or recognized by system at all. In device properties, it is shown as:     USB MEMORY BAR     There's no partitions on the drive, so I can't format it:    DISKPART:     Virtual Disk Service error:   There is no media in the device.   HP USB format tool:     There is no media in the specified device.   Any help will be greatly appreciated! Thank You! Need intuition about independence of events Suppose that we have the situation as depicted in the figure: a random experiment which has 4 outcomes $x_1, ..., x_4$ and two events $A$ and $B$. Also assume that $P(x_i)=0.25$.  Now, since $P(A \cap B) = P(A)P(B) = 0.25$, by definition the events $A$ and $B$ are independent. This does not make sense to me. Why are they independent? Is there an intuitive explanation?  Another thing is, suppose that there is a 5th outcome, $x_5$, outside of $A \cup B$, in that case the events $A$ and $B$ are no longer independent since  $P(A \cap B) \ne P(A)P(B)$. This result also does not make sense to me. Link Google Form responses To Already Existing Google Spreadsheet Tab I have a Google Form. I had all of my Google Form responses linked to a specific tab in my Google Spreadsheet. Somehow my form responses were unlinked from my tab. When I go to re-link my form responses to my already existing tab it only gives me the option to create a new tab in my spreadsheet.   How do I simply re-link my Google Form responses to my already existing tab in my Google Spreadsheet? Interpreting the Kretschmann scalar Using \left( & \right) around amsmath's align delimiter ("&") I want to align equations (using the align environment from the amsmath package) inside matching \left( and \right) commands. For example:  \documentclass[a4paper,12pt]{article}  \usepackage{amsmath}  \begin{document}  \begin{align}     a \left( b &amp;= c \right)\\     d \left( e &amp;= f \right) \end{align}  \end{document}   But that code gives this error:     Extra }, or forgotten \right.   The error disappears when I remove the delimiters. Is there a workaround for this? Export iMessages in human readable form for archival I have a long (several months' worth) iMessage conversation with a contact.  He lost these messages when he re-installed his OS, but I still have the archive.  There is some important information there that we'd like to keep.  Is there a simple way to export this conversation for archival in a human readable form, and also keep any images?  I can select parts of the conversation, copy it to the clipboard and paste it into a rich text document, but this discards all images.  I'm looking for a way that keeps the images.  Note: I use iMessage on OS X only, not iOS.  (Ideally I'd also like to export all non-image file attachments, but I'm not expecting that this will be possible.) How to add a PPA on a server? I ran into something a couple of weeks ago that I'd never seen before: A filesystem (ext3 I believe) installed to a storage device without a partition. In essence /dev/sdb was the entire filesystem. I know many filesystems can be extended into empty space, so doing this allows extending without dealing with LVM or some other kind of volume manager, but are there any other advantages for setting up storage this way?  The specific case I saw was as the ephemeral data volume for a number crunching server, the boot and root volumes were traditional partitions on a different storage device entirely. - How can I remove malicious spyware, malware, adware, viruses, trojans or rootkits from my PC? What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits. What is Uplay? Can I play Ubisoft games without it? Heroes of Might and Magic VI seems to have installed a program called "Uplay", which it uses to launch (in addition to Steam, mind!)  What exactly is Uplay supposed to be? I notice that when I stop playing, it captchalogs the highlights of my past session (achievements earned, etc.) - which is kinda cool, but also kinda creepy and big-brotherish. Given that I value my privacy, is there anyway to play Uplay games without using Uplay?  Is this just Ubisoft's infamous "always-on" DRM? "Geometric" or "Geometrical"? I have read the excellent answers to  - my question is specifically about usage.   Is there a best practice for deciding between the variants geometric and geometrical in writing? A  shows that geometrical was more popular until about 1965, when they switched. What grammatical rules, if any, would be relevant here?