While watching a World Cup game, I noticed how the extra time given at the end of the first half is usually shorter than the extra time given at the end of the second half. That led me to wonder what was the longest extra time awarded at a football game, and after some reasearch I found this Bristol City game in 2000-2001 in a , where apparently 23 minutes of extra time were added:     "When Brentford played away at Bristol City in 2000-01, there were about 23 minutes of stoppage time in the first-half alone after a broken leg, a dislocated shoulder (Bees striker Lloyd Owusu passed out from the pain and an ambulance had to be driven up to the pitch), and serious concussion caused the delay," noted Will. "In fact, two goals were scored in that first-half injury-time, with the second being clocked in the 67th minute, I believe. The fourth official had originally held up 13 minutes' stoppage time, but one of the injuries occurred in that period to bump it up to 23. I'd be surprised if there were many games that contained more added-on time!"   Is this the longest extra time ever given during a professional football game? And if it isn't, what is the longest extra time period ever given during a professional football game?
What is the longest additional time ever used in Europe's top five leagues? Please mention the details of the match.
Volume of bounded region between sphere and a plane How do I delete Windows.old in Windows? I used to run Windows 7 32 bit, but installed the 64 bit version because of a RAM upgrade. During the installation I got this message:      The partition you selected might contain files from a previous Windows installation. If it does, these files and folders will be moved to a folder named Windows.old. You will be able to access the information in Windows.old, but you will not be able to use your previous version of Windows.   The C:\ drive now has two (2) Windows folders:   Windows (15.3 GB) Windows.old (15.7 GB)     Don't see why I need the Windows.old taking over 15GB of space on my hard drive so I tried to delete it. It didn't work.  How can I safely delete this folder? I think the following is true:  If $q$ is coprime to $a$ then $a\mid (nq-1)$ for some $n\in\mathbb Z$.  I have started to first reducing $n\in\mathbb Z$ to $n\in\{1,\ldots,a-1\}$ and then considering all the cases $q = ka + j$ for $j=1,2,3,\ldots,a-1$. I stopped at $j=3$ and found that this is kinda messy. Does anyone have an elegant proof for this (maybe using some results from number theory)?  [Note: question has been generalized from prime $q\nmid a$ to $\,q$ coprime to $a$] Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither? I'm currently considering the ideal $(2,X+1)\subset\Bbb{Z}[X]$. I'm trying to figure out if this is a prime ideal, a maximal ideal, or neither. So far I have attempted to look at the quotient ring $\Bbb{Z}[X]/(2,X+1)$. I know that if this quotient ring is a field, then our ideal is maximal, since $\Bbb{Z}[X]$ is commutative. However I'm stuck on how I should be viewing this quotient ring. Avoiding numerical cancellation question for $\sin x -\sin y$ for $x \approx y$ When trying to avoid cancellation, one tries to reformulate the equation in order to avoid subtraction between almost equal terms.   In $\sin (x) - \sin (y), x \approx y$ the suggested solution is to reformulate it to $$2\cos\left(\frac{x+y}{2}\right)\sin\left(\frac{x-y}{2}\right)$$  But I don't understand how it is any better? The subtraction between $x, y$ remains. Is it because $\lvert\,\sin(x)-\sin(y)\,\rvert\leq \lvert\,x-y\,\rvert$, so cancellation is less likely to happen between $x,y$ than the sines? How would I convert a char array to int? Delay in 4-bit ripple carry adder? In pic below I have drawn a full adder and mentioned their delays, please help me to verify my answer. "batch" tag turns into "batch-file" Scale settings for exporting to STL (for 3d printing) Do the following negations mean the same thing? I don't think you understood me. / I think you misunderstood me.    Do these senteces mean the same thing? If not, what's the difference?  Edit: I just realized that I asked something different from what I originally wanted. So I am also interested in the following comparison:     I don't think you understand me. / I think you don't understand me. Mapping Russia - Int'l dateline splitting polygon How to help a toddler overcome the fear of water on head? Why do you lose reputation for downvoting answers? I've been dealing with this problem for almost 2 hours now, with hardly any progress. I'm to prove the following inequality using induction   $$\sqrt[n+1]{n+1}&lt;\sqrt[n]{n}$$ where $n≥3$, $n∈\mathbb{N}$. How can this be done? Remove empty elements from an array in Javascript Article "communicated by" What does it mean when it says under a journal article that it has been communicated by "XYZ" where XYZ is not the author but some other scholar with a very strong reputation? What is the relationship to the actual author and/or the content? Is this some sort of seal of approval to get results out and known quickly? (I am specifically wondering in the context of mathematics and mathematical physics.) For starters I am using this GREAT answer to achieve custom post types as well as a custom way to insert those post types into other pages, you can view that answer here:   I am running into a problem however when wordpress auto saves itself, it clears whatever metadata i have put into the forms.  EXAMPLE:  I select the 3 drop downs I want from my metabox and hit update.  The page reloads and the 3 choices are still selected.  In phpMyAdmin i can look up the metadata and see the array in place as it should be.  I now wait for wordpress to auto save.  As soon as this happens i can either refresh the page (not update, just refresh) and the metadata is lost, or i can look up the metadata in phpMyAdmin and it will display nothing (ie: its gone).  I'm guessing that this has something to do with needing to tie into another hook (some sorta auto update hook) or something, but even then it doesn't make sense that it would actually delete your metadata (rather than just not auto updating it).  Last note: If you copy and paste Mikes code into functions.php, you should be able to recreate my error (in wordpress 3.1) very easy. I'd like to prove a nice property of a stochastic integral with respect to Brownian motion.   Let $(H_t)_{t\geq0}$ be a progressive and bounded process that is continuous at $0$ and $B$ a standard Brownian motion. Then  $\frac{1}{B_{\varepsilon}}\int_{0}^{\varepsilon}H_s\mathbb{d}B_s\rightarrow H_0$ as $\varepsilon\rightarrow0$ in probability.   Anyone got some hints ? I'm really puzzled and I don't know where to start.   EDIT_2.0. Applying Ito-Isometry might be a bit tricky. This Brownian Motion in the denominator kinda troubles me :/ $\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}}$ approximation By the "No Hair Theorem", three quantities "define" a black hole; Mass, Angular Momentum, and Charge. The first is easy enough to determine, look at the radius of the event horizon and you can use the Schwarzschild formula to compute the mass. Angular Momentum can be found using the cool little ergosphere Penrose "discovered". However, I don't know how to determine the charge of the black hole.   How can an electromagnetic field escape the event horizon of a Reissner-Nordström black hole? Is there any experiment we could theoretically do to a black hole to determine its charge?