Mutating a variable in a closure
Global and local variables in R
What is color temperature and how does it affect my photography? Example of modules that are projective but not free; torsion-free but not free Sum of binomial coefficients with index divisible by 4 I am trying to obtain a closed form expression for  $\sum {n \choose 4k}$  I am trying to use the binomial expansion of $(1 + i)^n$ and $(1 - i)^n$. $$(1 + i)^n + (1 - i)^n = 2\left(\sum {n \choose 4k} -\sum {n \choose 4k + 2}\right)$$ Stuck at this now. I can't come up with a way to simplify the second term on RHS. Any help would be appreciated. Title does not appear when LaTeX code is compiled Change pivot or local origin of an object How can I change the local origin of an object, without changing the object location in the world space.  This is the object located at position (0,0,0) in the world space    This is the same object located at position (0,1,0) in the world space, but with its local origin offset so that the object is in the same place    Is there a way to do this in a single step? I told my follower (Serana) to wait. But this is different. I told her to go somewhere and wait so it will activate the enemies. Well it did and I killed them. But Serana seems to be not following me anymore. I can't tell her to follow me. And she is constantly in a squatting position. The only thing I can do is tell her to wait somewhere else to move her. And I can't part ways because I'm doing a main quest and she has to be there. Can anybody give me a tip on what to do? Geodesics equations via variational principle I would like to recover the (timelike) geodesics equations via the variational principle of the following action:  $$ \mathcal{S}[x] = -m \int d\tau = -m \int \sqrt{-g_{\mu\nu}\,dx^{\mu}\,dx^{\nu}} $$  Using an arbitrary auxiliary parameter $\lambda$, then one is able to rewrite the action and obtains: $$ d\tau = \sqrt{-g_{\mu\nu}\, \tfrac{dx^{\mu}}{d\lambda}\tfrac{dx^{\mu}}{d\lambda}} d\lambda $$ $$ -m \int d\tau = -m \int (d\tau / d\lambda) d\lambda =  -m\int\sqrt{-g_{\mu\nu}\, \tfrac{dx^{\mu}}{d\lambda}\tfrac{dx^{\mu}}{d\lambda}} d\lambda $$  Now we can vary the paths $x^{\mu}(\tau) \rightarrow x^{\mu}(\tau) + \delta x^{\mu}(\tau)$.  I need the following equation to be true, so i get the geodesics equations, but I don't know how one can say the following: $$ \int d\tau \,\delta g_{\mu\nu}\frac{dx^{\mu}}{d\tau} \frac{dx^{\nu}}{d\tau} = \int d\tau\, g_{\mu\nu, \rho} \frac{dx^{\mu}}{d\tau} \frac{dx^{\nu}}{d\tau} \delta x^{\rho} $$ I know there is a simpler action, which leads to the same equation of motion, but there one has to do the same manipulation, which I sadly don't understand.  Thanks for helping me! Why did Itachi say that he needs to get someone's MS to get EMS while Sasuke only had a normal Sharingan? After installing Ubuntu Studio 12.04, I have found that it uses a low latency kernel.   I searched for an explanation and how to change back it to a real-time or generic one. However, it looks like this part of Linux hasn't been covered to explain the details.   Q: Why choose a low latency kernel over a generic or real-time one?  PS: I have already read the answers from  question and  post. The Next tag badge block overlaps the badge score block. There are 'n' candies and 't' boxes. Find the number of ways to place the candies in the boxes for each of the conditions (given in the problem). There are 'n' candies and 't' boxes. Find the number of ways to place the candies in the boxes for each of the conditions (all the candies must be spread out) : (a) candies and boxes are different; (b) candies of the same diiferent boxes should not be empty cartons: (c) candies equally new, boxes are different; Edit :(d) candies are different, the boxes are the same, there should be no empty boxes; (e) candies of different boxes alike.(Edit : candies are different, boxes are equal) Specify the display type that matches the placement, if possible. My Answers : (a) Each layout is encoded with a word of $n$ letters from the alphabet of 't' letters $\implies$ possible $n^t$ variants. (b) Write, $n$ candies in the form of balls ina line, we need to put $(t-1)$ partition in $(n-1)$ place, but we can't put two partitions on one place, so we get : $^{t-1}C_{n-1}$. (c) First we need to choose a candy in a box (in the first box $n$ ways, in the second box $(n-1)$, $\cdots$ in the $t-th$ : $(n-t+1)$ ways $\implies$ total $n!/(n-t)!$ methods, and then we distribute the remaining $(n-t)$ candies into $t$ boxes, this is encoded with owrds from the alphabets (for each candy $t$ variants) $\implies$ $t^{n-t}$. The Answer is : $\frac {n!}{(n-t)!}*t^(n-t)$ Are my answers (a), (b) &amp; (c) are correct? For (d) &amp; (e) I don't know how to proceed? Please help me. Is it posible to change the locale of my device? Photoelectric Effect - Dependence of current on frequency We all know that the amount of current flowing b/w the plates is independent of the frequency. If I were to ask why doesn't it depend then you'd probably say that it depends on the number of electrons rather than the frequency or you might show me a current vs frequency graph.  But here is my theoretical argument. Electric current is defined as the amount of charge flowing through a point/space/wire per unit time. Let I be current due to photo electrons ejected by photons of some frequency. Now if I would increase the frequency, the kinetic energy of the ejected electron would increases, therefore it will move faster and therefore contribute more current (charge will through the same point many times per unit time) . Thereby, giving a net current greater than I.  What is wrong with my argument?  After thinking a lot, I came up with a possible reason. However fast the electrons may move, but when they hit the metal plate, they would lose their velocity and start moving in drift velocity. Now there is a problem with this argument. If this were to be true then I should expect to see a big chunk of extra electrons getting stuck at the anode.  If my reasoning was correct, then why can't I see a big charge buildup at the anode. Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$ How to move the center of scaling Hello. I'm a beginner.  In the model shown, when I select all of the top vertices and then scale them to the center, the center of scaling is not the center of the 3d-model.   How do I move the center of scaling? How do I move the manipulator widget where I want it after selecting? what is a thyristor As part of my 2330 lv3 am required to know about thyristors. I just want to confirm my understanding is correct. A thyristor is basically similar to a transistor, only it stays switched on when it's trigged for as long as there isn't a break in the circuit it's switching. Am I correct? I have a question about my choice of name for publication.  I recently got married and legally changed my name to my husband's surname (for example's sake: from Hunter to Jones). So, despite legally being Ms Jones now, I would quite like to use the hyphenated name Hunter-Jones in the professional context and in publications. This is so that people realise that it is still me and so that I can somewhat keep my maiden name.  Is this possible or do I have to use my legal name professionally and when publishing? Thank you for any help How to get rights of admin after I disabled all admin accounts in my computer I accidentally disabled my admin account.  After I login to another account I found I can not get admin rights, because all admin accounts on my computer are disabled.  I clicked on 'run as administrator' but only see a smart card choice (all the admin accounts are disabled so no choice provided)    I don't want to re-install my OS, help!    Details:  I have account A on my computer.    I got a new computer so I want to give the old one to my mother.    Creating a new user account B for her and disable account A.    Logout and restart.    Successfully login B, now I found I could not get admin rights because no account choice is provided.    More informations about my machine:  OS is Windows 10 and my admin account is a Microsoft Account.  I have an arch-linux installed on my computer and dual-boot it using GRUB, so maybe I can not use safe mode. Should I put a comma before the last item in a list? Should I put a comma before the last item in a list?     I would like crackers, cheese and some soda.   I would like crackers, cheese, and some soda. I'm not sure if this is possible architecturally, but when judging whether to set a bounty and how much it should be, it would be nice to see the impact based on our previous questions. If you're not visiting the site throughout the day, there is no way to tell how effective that bounty might be--particularly for increasing traffic. There is a similar question with adding and removing tags that increase the visibility in the right places, and the effect on views that may have.