The problem:  Consider the smooth quadric $Q=V(X_{0}X_{1}+X_{2}X_{3}+X_{4}^{2})\subset\mathbb{P}^{4}$ and the line $L=V(X_{0},X_{2},X_{3})$ contained in it. Prove that there exists a vector bundle $F$ on $Q$ with a section vanishing exactly at $L$.
The problem:  Consider the smooth quadric $Q=V(X_{0}X_{1}+X_{2}X_{3}+X_{4}^{2})\subset\mathbb{P}^{4}$ and the line $L=V(X_{0},X_{2},X_{4})$ contained in it. Prove that there exists a vector bundle $F$ on $Q$ with a section vanishing exactly at $L$.  The hardest thing is to get the transition matrices. Any help is appreciated.
Environments are allowed to have arguments, but reference to those arguments can only appear in the opening code of the environment, and not the closing code.  What is the reason for this, and are there preferred ways around it?  e.g.  \newenvironment{foo}[1]% {some code #1} % allowed {some code #1} % not allowed Significance of starting the Fibonacci sequence with 0, 1.... DISCLAIMER: I do not deal with in-depth mathematics on a daily basis as some of you may, so please pardon my ignorance or lack of coherence on this topic.  QUESTION: What is the significance of starting the Fibonacci sequence with $0,1$ ?  For instance, if I picked any two random integers, say 2 and 7, to start a sequence would I actually be creating some multiple or derivation of the Fibonacci sequence?  Is there a general mathematical explanation for the relationship between any sequence represented by $a[0] = x, a[1] = y, a[n] = a[n-1] + a[n-2]$ and the Fibonacci sequence?  Or, back to my example sequence, is there a general mathematical relationship between:  $2,7,9,16,25,41,66,107,173,280...$  and  $0,1,1,2,3,5,8,13,21,34...$  Perhaps the Golden Ratio explains it somehow?  Any help would be appreciated. I've tried different ways to install iTunes, but to no avail. I tried with Wine, but it didn't work. Is it possible to have iTunes on Ubuntu? My linear voltage regulator is overheating very fast I'm using a 5 V / 2 A voltage regulator () without a heatsink. I'm testing the circuit with a microcontroller (PIC18FXXXX), a few LEDs and a 1 mA piezzo buzzer. The input voltage is aprox. 24 VDC. After running for a minute, the voltage regulator starts to overheat, meaning it burns my finger if I keep it there for more than a second. Within a few minutes it starts to smell like it's burnt. Is this a normal behavior for this regulator? What could cause it to heat that much?    Other components used in this circuit:  L1:   R2:   F1: How to fix invisible form fields in Firefox while using Adwaita Dark Theme (or any other dark theme) I have this issue with some form fields in Firefox and using the adwaita-dark theme. In some webpages where the field background is white, you cannot read the text because it is also white.   This question was edited in order to clarify that this kind of wording of the question might help people who are not familiar with what a GTK+ theme. I also thing that the wording will help to get more hits through search engines. If it's still considered a duplicate, I'll accept it. How to Micro Manage Manipulator Dual boot system Windows XP Pro and Ubuntu 12.04.  I have the bios set for the correct time and Ubuntu set for US Eastern time.  Ubuntu will boot up and the time will be off by -4 hours.  If I correct the time in Ubuntu then when I boot up in Windows XP the time will be off by + 4 hours.  This is a fresh install of 12.04. I did not have this problem before reinstalling Ubuntu. Here is my situation: I know almost nothing about Perl but it is the only language available on a porting machine. I only have permissions to write in my local work area and not the Perl install location. I need to use the  Perl module from CPAN   How do I use this Parallel::ForkManager without doing a central install? Is there an environment variable that I can set so it is located?  Thanks  JD Cleaning polygon after using dissolve to repair geometry in QGIS? I'm trying to obtain the boundaries of shapefile, thus to clean the inside as a matter of speaking. While I had expected that dissolve while get me a proper polygon, unfortunately it still has some remainders. How could I get rid of them?  Does QGIS have a tool similar to Repair Geometry?  Here's the source    Result below: Installing a 16-bit Windows 95 game on 64-bit Windows 7 Home Premium Set origin to bottom center of multiple objects I have a lot of 3D objects of various sizes, shapes in blender 2.76b and I would like to set the origin to the bottom center of the objects bounds.  I cannot select the bottom edge and snap to cursor etc as each shapes edges are in different X/Y positions.  Is there a script or tool that will allow me to set the origin to the lowest edge z position? What is the scope of variables in JavaScript? jQuery - Is it okay to use $('#ElementId') everytime? I have a website running in English and Japanese and the default language is Japanese.  What are the advantages of one over the other solution:   Solution 1. When accessing example.com, you will see only Japanese. When accessing example.com/en, you will see only English. Solution 2. When you access example.com, it will redirect you to example.com/ja, where you will see only Japanese. English site is still example.com/en. Correct ssh config file settings to tunnel to a 3rd machine I'm trying to tunnel to a server via a bridge server. So far, I've been able to get it working from the command shell properly using the following command:  ssh -A -t bridge_userid@bridgemachine.com ssh -A remote_userid@remoteserver.com   But I've been trying to wrap this into my ~/.ssh/config file and I have troubles. I've tried:  Host axp   User          remote_userid   HostName      remoteserver.com   IdentityFile  ~/.ssh/id_rsa.eric   ProxyCommand ssh -A -t bridge_userid@bridge_userid.com ssh -A remote_userid@%h   But when I do, I get the following error message from remoteserver.com and I'm not sure what is causing it:     ksh: SSH-2.0-OpenSSH_6.8^M:  not found   I know that when I log into remoteserver.com , my shell is /usr/bin/ksh.  I've tried to add path arguments to the ssh commands in the config file, but it made no difference.  Any ideas what it can be? Passing arguments forward to another javascript function Can a character in the middle of a move action alter his movement based on a change in his surroundings? For example:      A player (speed 6) moves two squares towards a human bandit (pg. 162 MM) becoming adjacent to him, then proceeds to move around him to the right, provoking an opportunity attack. The bandit hits with his basic melee attack (+4 vs. AC; 1d8+1 damage, and the human bandit shifts 1 square), shifting one square to the left immediately.    This free shift makes it so that the PC would no longer flank the bandit at the END of his move. Can the player adjust his remaining three squares of movement so that he can once again flank the now-shifted bandit, or does he have to stick with his earlier movement designation?  This question boils down to: Is movement counted as you go, or do you say, "I am moving to here, it is within my range, and on the way to my destination 'blah' happens?" I am travelling to Calgary from Delhi. I have an Air India flight from Delhi to Dubai then British Airways flight from Dubai to London and Air Canada flight from London to Calgary. My query is "Do I require a transit visa." Plz help as I am travelling in four days change color of pgfplot bar plot I want to plot two bar plots next to each other. This works without a problem. However both use the first color defined in a pre or selfdefined colorseries. I tried to modify the color manually in the plot, but the color and fill definitions have no effect:  \documentclass[border=5mm]{standalone} \usepackage{pgfplots, pgfplotstable}  \begin{document}  \pgfplotstableread[header=false, col sep=comma]{  1, first item 5, second item }\datatable  \begin{tikzpicture}   \begin{axis}[             ,xbar     ,bar width=2ex, y=3ex     ,enlarge y limits={abs=0.75}     ,ytick={data} % (\empty,data,{coordinate list})     ,yticklabels from table={\datatable}{1}   ]   \addplot table [     ,red!20!black,fill=red!80!white,     y expr=-\coordindex, % Use negative coordinate index as y coordinate     x index=0 % Use first column as x coordinate   ] {\datatable};   \end{axis} \end{tikzpicture}  \end{document}   The plot is still in the default blue. Is the wave-particle duality a real duality? I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' that everything is made up out of particles, whether those are photons, electrons, or maybe even strings. That light for example, also shows wave-like properties, why does that even matter? Don't we know that everything is made up of particles? In other words, wasn't Young wrong and Newton right, instead of them both being right?