Why is : $ \mathrm{dim}_{ \mathbb{C} } V(d,n) = \binom{d+n-1}{n-1} $?
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
How do Rpy2, pyrserve and PypeR compare? $g^k$ is a primitive element modulo $m$ iff $\gcd (k,\varphi(m))=1$ Seriously, I had not noticed e.g. Jeff's edit  had he not also retagged my question. If $X, Y$ are jointly standard normal with correlation $r$, and $a, b$ are constants, what is $p(Y < b | X < a)$? The application here is interpreting the correlation coefficient $r$ in terms of $X$'s ability to predict $Y$ for extreme values of $X$. For example, if $r = .8$, then what is $p(Y &lt; 0 | X &lt; -2)$? How to mount an ISO file? I'm running into trouble trying to mount a large iso:  dev@dev-OptiPlex-745:~$ sudo mount -o loop /home/dev/Hämtningar/matlab2011a_64.iso /cdrom mount: warning: /cdrom seems to be mounted read-only. dev@dev-OptiPlex-745:~$    Can you tell me how I should do it? iOS 9 Screen Recording in El Capitan I used to record iOS devices through QuickTime, however now it's only recording audio (not sure is this linked to OS X 10.11 or iOS 9).  How can I fix this (without third party sofrware)? Truly destroying a PHP Session? math behind complex numbers C||RLC I have a mathematical problem with the following formula. The goal is to transform this equation to have a seperated real and imaginary part. I have already done this with several other equasions, but for this particualar one I don't know where to start.  I dont expect you to do the complete work of transforming for me, it would already be very nice if you could give me a hind on how you would start.  Thank you in advance!  C||RLC      This is my current progress:    My question is:  How can I get rid of the imaginary part jωC2*R?  When the denominator is completely real I can just split up the formula and have an imaginary and a real part. I'm playing Minecraft on Xbox 360 and I can't find the . I have tried every trick I can think of, including the xray glitch, and recreating the world in Creative mode to dig out the entire stronghold and the surrounding areas. I have found nothing and I am totally lost on where it could be.  The seed is 1833758535681455132 Intersect (analysis) of polygons generating empty output Why is the empty set considered an interval? Balancing long table inside multicol in LaTeX I would like to put some longer tabular data inside the multicols environment while maintaining its balancing abilities. I have tried supertabular with the trick to redefine \newpage as columnbreak. This isn't good though, because the columns aren't properly balanced. Finally I ended up using \halign:  \documentclass[11pt, a4paper]{article} \usepackage[margin=3cm]{geometry} \usepackage{supertabular} \usepackage{multicol}  \def\shortlipsum{\par Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque.\par}  \newcounter{entryno} \setcounter{entryno}{1} \def\tabline{Test &amp; \the\value{entryno} &amp; Description\addtocounter{entryno}{1}\\} \def\tablines{\tabline\tabline\tabline\tabline\tabline} \def\mybreak{\hrule width \columnwidth height 0pt \columnbreak}  \begin{document} \begin{multicols}{2} \shortlipsum \medskip  % % This doesn't balance the columns. Whole table ends up in the left column (it fits) % \begingroup\let\newpage\mybreak % \noindent\begin{supertabular*}{\columnwidth}{@{\indent}l l l} % \tablines\tablines\tablines\tablines\tablines\tablines % \end{supertabular*} % \endgroup  \begingroup\let\\\cr \noindent\halign{\indent#\quad&amp;#\quad&amp;#\hfil\cr \tablines\tablines\tablines\tablines\tablines\tablines} \endgroup  \medskip \shortlipsum \end{multicols} \shortlipsum \end{document}     I was wondering if I'm the only one using \halign to achieve this result. On the other hand supertabular leaves me with an undesired almost empty right column. How would you approach this problem? What is the easiest way to duplicate an activerecord record? I want to make a copy of an ActiveRecord object, changing a single field in the process (in addition to the id).  What is the simplest way to accomplish this? I realize I could create a new record, and then iterate over each of the fields copying the data field-by-field - but I figured there must be an easier way to do this. Perhaps something like this:  new_record = Record.copy(:id) Use 'import module' or 'from module import'? How do I fix a puncture? I got a flat/puncture on my bike tube, how can I fix it myself without going to the nearest bike shop? What kind of equipment would I need? Does a Readied spell immediately use a spell slot? Need help in the longtable with the figure I was reading through some of the questions and answers here on the Rings of Power and I just wondered why the ring effects, affected different races in a slightly different way.  I know other questions ask and answer some of these things, but I just wondered why the Rings of Power caused greed in Dwarves for ever more amounts of treasure.  It's true that Dwarves loved mining and loved wealth and were built of sturdier stuff than men, but why did the Rings of Power not control Dwarves in the way the other Rings of Power controlled men and why did it produce greed and not invisibility? What are best practices for choosing and pairing fonts? I've always found font selection to be a little bit of a mystery. What factors should be considered when choosing a font? How does one successfully incorporate two fonts into a design?  I realize that some factors will include things like:   Legibility Scalability Appropriateness/Mood/Emotion   However, how does one objectively judge legibility or appropriateness? Are there objective principles that can be applied for font selection? If possible, please list resources or examples in your answers. Studies focused on the effectiveness of different fonts would also be extremely useful. Moderator flag notifications should reach mobile I spend a great deal of time surfing SE sites from my phone during commutes and other down times. The global inbox is quite effective at reaching me even for chat pings. Quite frankly the mobile site is very well done!  However as a community moderator, there is a whole class of information not getting through. There are no notifications for moderator flags! I can switch to the full site and see these but that is inconvenient for browsing, so I only end up checking for flags periodically.  Ideally the moderator tools should all be available in mobile templates, but as a stand-by it's reasonable to switch to the full view to handle flags, but flags would get addressed in a much more timely manner if I knew about them. As it stands I often come and go from the site without even knowing there are outstanding flags.  A simple flag counter added to the header next to the notification counter and linked to the tools page (which automatically opens the full version anyway right now) would fix this.