returning value in a nested function
Return a value when using jQuery.each()?
Legendre symbol, second supplementary law $$\left(\frac{2}{p}\right) = (-1)^{(p^2-1)/8}$$ how did they get the exponent. May be from Gauss lemma, but how.  Suppose we have a = 2 and p = 11. Then n = 3 (6,8,10), but not  $$15 = (11^2-1)/8$$  n is a way to compute Legendre symbols from Gauss lemma: $$\left(\frac{a}{p}\right) = (-1)^n$$ 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? Running 64 bit programs on a 32 bit system Can Resharper be set to warn if IDisposable not handled correctly? Is there a setting in Resharper 4 (or even Visual Studio itself...) that forces a warning if I forget to wrap code in a using block, or ommit the proper Dispose call in a finally block? Post to facebook fan page as a user Is there a term for the moment when a lot of users visit/log onto your website at the same time? Is there a term for the moment when a lot of users visit/log onto your website at the same time? Is $x^x=y$ solvable for $x$? Given that   $x^x = y$; and  given some value for $y$   is there a way to expressly solve that equation for $x$? Let $N = \{N(t) \}_{t\geq 0 }$ be a Poisson process. I already know that $N(t)- \lambda t$ is a martingale where $\mathbb{E} [ N(t) ] = \lambda t$.   I want to prove that $$ \frac{N(t)}{t} \rightarrow \lambda, \quad t \rightarrow \infty \quad \text{ a.s.}. $$  To prove this I received a hint that I should use the martingale law of large numbers which states that:  Theorem: (Martingale LLN)  Let $S= (S_n = \sum_{k=1}^n X_k)_{n=1,2,\ldots}$ be a martingale with respect to the filtration $(\mathcal{F}_n)_{n=1,2,\ldots}$. Then $\sum_{k=1}^n X_k/k$ converges almost surely on the set $\left\{ \sum_{k=1}^\infty k^{-2} \mathbb{E}\left[ X_k^2 \mid \mathcal{F}_{k-1} \right] &lt; \infty \right\}$. Hence $S_n/n \rightarrow 0$ a.s. on the same set.  Now to use this theorem I think I need to use Doob-Meyer to decompose $N(t)$ as the sum of a martingale and an increasing process. Which would be the martingale $M(t) = N(t) - \lambda t$ and increasing process $A(t) = \lambda t$. But how is $M(t)$ the sum of a martingale? And I do not know how this exactly relates to the thing I have to prove. Thanks for any help. How can I fix the non-stitched seam that is present after applying mirror modifier? Would the One Ring even work for anyone but Sauron? The temptation of the One Ring, we quickly learn, is always tied up with power: each character's fantasies of possessing it seem to be about what they would do with great power. Even Sam, as I recall, imagines the power to create great huge sweeping gardens. Boromir wants the power to save Gondor, etc.  But does the One Ring actually convey power to anyone but Sauron? It actually seems to diminish its bearers: Bilbo feels "thin" and "stretched", Sméagol becomes the wretched Gollum, Frodo is never quite the same even after it is destroyed. None of them seem more "powerful," even in the abstract way that magic-users in Tolkien operate. No mention is made, that I can recall, of a Ringbearer having greater stature or authority, or of people naturally following them or obeying their commands, while they possess the Ring.  The accepted answer to  implies that a being as powerful as Gandalf could dominate the Ring and break Sauron's hold over it, but even then Tolkien says that "It would have been the master in the end", and his descriptions of a Ringbearing Gandalf sound pretty much like Gandalf is using his own powers, not terribly augmented by the Ring:     [Gandalf] would have remained 'righteous', but self-righteous. He would have continued to rule and order things for 'good', and the benefit of his subjects according to his wisdom (which was and would have remained great).   Now that sounds out of character for a being as humble as Gandalf, but it doesn't actually sound like something he would have been unable to do before. It's a twisted motive, but not really an enhanced power.  Pretty much everyone in Middle-earth agrees that the One Ring will corrupt you, but they all seem to agree that it DOES convey great power even so. Why? Do we ever see any actual, "positive" effects from possessing the One Ring? Determining the Actual Server Create Date I am interested in determining the ages of all 70+ my servers. I would like to create a growth graph showing when servers and databases were added to the environment either/both monthly or annually. I executed the following query using the SSMS multi-query feature with only partial success.  SELECT [name], create_date FROM sys.databases   It's partial success because the master and model databases return with a date of 'April 8, 2003' when I know that I created some of these servers during the past couple years.  I refresh databases from one server to another several times a week, which appears to be causing issues with the database create date.   Is there a simple method to determine the actual create date for both servers and databases? Why is the Converse to Lagrange's Theorem False? How does the color of a car influence its inner temperature change over time when parked outside in windless, hot and sunny regions?  I know what's the common idea about that: black cars are supposed to build up high temperatures faster because black objects absorb radiations instead of reflecting them off. Is it true? And then, what happens during the steady state? Some claim the black car will stay hotter, some others claim it will be the same whatever the color. Do all cars have the same temperature inside in the long run, or are some of them hotter?  I've Googled it but the best I could find was . It claims to be based upon ~20 articles. But there's not even a mention of absorption or emission spectrums. A priori, a black car could absorb all visible radiations and emit it as infrared while reflecting all of the Sun's infrared. And it's still only qualitative. I've found nothing on Physics stackexchange, the closest being . The website I'm working is allegedly going to have a massive hit rate soon after launch. The client is talking about the possibility  of around 2500 hits per second over a day or so.   Ignoring the fact that this hit rate is probably wild client optimism and apart from getting the largest servers possible, what is the best way that Drupal should be configured to support a large hit rate.  I've read Scaling the , ,  and many other pages, but what I'm looking for is real experience of doing this, what works, what doesn't, and what to expect. Is there an Amazon.com API to retrieve product reviews? I've seen this message several times whenever someone has a problem installing, upgrading or removing some piece of software, but I wonder, what does it mean, and more importantly, is possible to solve it?  (Reading database ... 81657 files and directories currently installed.)  Removing mongodb-10gen ...  arg: remove  invoke-rc.d: unknown initscript, /etc/init.d/mongodb not found.  dpkg: error processing mongodb-10gen (--remove):   subprocess installed pre-removal script returned error exit status 100  invoke-rc.d: unknown initscript, /etc/init.d/mongodb not found.  dpkg: error while cleaning up:   subprocess installed post-installation script returned error exit status 100  Errors were encountered while processing:   mongodb-10gen  E: Sub-process /usr/bin/dpkg returned an error code (1)   (the above is just an example, not my actual problem) Lightning tags in beta I came across some lightning tags that are still in beta, ex: lightning:input (Beta) lightning:tabset (Beta) etc  Not sure for how long they were in beta, is it advisable to use them for building UI and deploy to production? I wanted to try out different desktop environments so I installed XFCE, KDE, GNOME, etc on top of Unity in Ubuntu 12.04  After a while I decided that I didn't like those other DEs and would stick to Unity. So I changed my default DE to Unity by configuring gdm.  sudo dpkg-reconfigure gdm   Now I am able to choose my DE at login time and all of DEs are working properly.   But the strange thing is that my boot up screen says 'lubuntu', my login screen is KDE, and my desktop is Unity.   How and why is this happening? Why didn't my gdm configuration have any effect? Does login and boot up screen need to be configured separately from the DE?  There are other similar questions here but they are not the same as this one. I do not want to remove the other enviroments I'm quite happy with having a list of DEs to select from. I want to know how to set proper defaults. Find the last two digits of $3^{45}$ I was wondering if there is a simpler way to find the last to digits of a power such as $3^{45}$. I reduced it modulo 100 to get the answer, which is 43. But I was curious if there was a simpler, or more eloquent way to get this result.  Here's my method:  Using the fact that $3^4=81\equiv -19 \pmod{100}$ and $19^5=2,476,099\equiv -1 \pmod{100}$  $$ 3^{45}\equiv 3(3^4)^{11}\equiv 3(-19)^{11}\equiv 3(-19)(19^5)^2\equiv 3(-19)(-1)^2 \equiv -57 \equiv 43 \pmod {100} $$  I just felt like this was sort of a messy way to find out that the last two digits are 43. Do you ever center AND standardize variables in multiple regression? It seems as if standardization would automatically center variables...is this true?