In the spirit of , if I've remapped the Caps Lock key itself to be the Win key, can I somehow map some key or combination to the "Caps Lock" functionality? In case I ever wanted to actually lock caps again? I think Scroll Lock or Ctrl + Esc would be great.  I'd like to be able to do this via the registry (see link above), as opposed to installing something. I understand that there are     , but I don't see one suggesting a registry or app-free solution.
One of my laptop's keys has fallen off. Is there any way I can remap another key to serve as that key?  I'll 'sacrifice' the other key because I never use it.
No more WIFI. oem-wifi-intel-iwlwifi doesn't build on the new 4.4 kernel How can i show that two $R$-modules of finite rank are isomorphic if and only if they have the same rank, i.e., $R^n \cong R^m$ iff $n=m$. I want to supply constant voltage to my LED's but the supply varies from 3.7V to 4.2V (Li-ion battery). I cannot use 3.3V voltage regulator as it will need at least 4.3V voltage at the input but my battery can supply only 4.2V max. so is there any other way I can supply regulated 3.3V to my LED.   RGB LED = 3.3V, 60mA Battery = 3.7V - 4.2V, 3000mA Number of LEDs = 24 The LED's are connected in parallel Why commutator subgroup is normal to G? If $G$ is a group and $G'$ is generated by $\{xyx^{-1}y^{-1}|x,y\in G\}$, then $G'\trianglelefteq G$ and  $G/G'$ is Abelian.  At first, I thought this is easy because I thought $g[x,y]g^{-1}=[gxg^{-1},gyg^{-1}]$. But it was a mistake. I could not prove that it is also subgroup of G and $G/G'$ is abelian. I need help. Evaluate the following limit of finite sum A uncharged capacitor $C$ is connected to a battery with potential $V$. It becomes fully charged and has a charge $Q=CV$ stored on it.   Now the polarity of the battery is reversed. The capacitor will have the charge $Q$ still but with polarity reversed too.  My question is: What is the work done by the the battery?  According to me, during 1st charging it will do a work of $QV$. The energy of the capacitor is also not changing, then what is the work done to change its polarity? Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups Let $U(n)$ to be the set of all positive integers less then $n$ and relatively prime to $n$. Then $U(n)$ is a group under multiplication modulo $n$.  A. Find integer $n$ such that $U(n)$ contains subgroup isomorphic to $Z_5\oplus Z_5$.  B. Show that there is an $U(n)$ containing a subgroup isomorphic to $Z_3 \oplus  Z_3$, but not isomorphic to $Z_4 \oplus  Z_4$. Is accessing a variable in C# an atomic operation? I've been raised to believe that if multiple threads can access a variable, then all reads from and writes to that variable must be protected by synchronization code, such as a "lock" statement, because the processor might switch to another thread halfway through a write.  However, I was looking through System.Web.Security.Membership using Reflector and found code like this:  public static class Membership {     private static bool s_Initialized = false;     private static object s_lock = new object();     private static MembershipProvider s_Provider;      public static MembershipProvider Provider     {         get         {             Initialize();             return s_Provider;         }     }      private static void Initialize()     {         if (s_Initialized)             return;          lock(s_lock)         {             if (s_Initialized)                 return;              // Perform initialization...             s_Initialized = true;         }     } }   Why is the s_Initialized field read outside of the lock? Couldn't another thread be trying to write to it at the same time? Are reads and writes of variables atomic? Can a druid in Ape wildshape use weapons? I came across following problem     Evaluate $$\int\frac{1}{1+x^6} \,dx$$   When I asked my teacher for hint he said first evaluate     $$\int\frac{1}{1+x^4} \,dx$$   I've tried to factorize $1+x^6$ as  $$1+x^6=(x^2 + 1)(x^4 - x^2 + 1)$$ and then writing  $$I=\int\frac{1}{1+x^6} \,dx=\int\frac{1}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx=\int\frac{1+x^2-x^2}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx$$ $$I=\int\frac{1}{x^4 - x^2 + 1} \,dx-\int\frac{x^2}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx$$  However $$x^4-x^2+1=\left(x^2-\frac12\right)^2+\frac{3}{4}$$ But I can't see how it helps  I've also tried to reverse engineer the   And I need to have terms similar to $$\frac{x^2-1}{x^4-x^2+1} \quad , \quad \frac{1}{1+x^2} \quad , \quad \frac{1}{(x+c)^2+1}\quad , \quad \frac{1}{(x+c)^2+1}$$ in integrand, How can I transform my cute looking integrand into these huge terms?  Since in exams I will neither have access to WA nor time to reverse engineer the solution moreover it does not seem intuitive,is there any way to solve this problem with some nice tricks or maybe substitutions? Coupon Collector Problem with Batched Selections I am trying to solve a variation on the .  In this scenario, someone is selecting coupons at random with replacement from n different possible coupons. However, the person is not selecting coupons one at a time, but instead, in batches.  Here's an example problem formulation: There are 100 distinct coupons. A person makes selections in 10-coupon batches at random (each coupon with replacement). What is the expected number of batches necessary to have selected 80 unique coupons?  I have been able to determine the expected number of selections necessary to have selected k unique coupons when selecting one at a time (much like Henry's ), but I'm a bit stumped as to how to go about solving it with this particular wrinkle.  Any tips/guidance would be greatly appreciated. I have a table and I am always getting the data by ordering a column. In my case, I  order by datenum. However, the selection is so slow because of the ordering.  Is it possible to order the table after datenum. This column is defined as unique. If  defined as an index, would the selection will be faster? An inequality for a sum of sine functions I want to show for $x\in\mathbb{R}$, the following inequality holds. $$ \left|\sin x\right|+\left|\sin (x+1)\right|+\left|\sin (x+2)\right|&gt;8/5. $$ This trigonometric inequality has been verified by Mathematica using the Plot commend. However, using the sum formula for the sine function seems doesn't work, and I cannot give a rigorous proof of it. Any suggestion, idea, or comment is welcome, thanks! Show only hidden files (dot files) in ls alias Why do I get "warning longer object length is not a multiple of shorter object length"? How do Stack Overflow questions appear in Google search results in seconds? Why is Android File Transfer necessary? Apparently newer versions of Android require the use of Android File Transfer. I have an older machine that doesn't require this, and just mounts as a USB mass storage device. I can't see a technical reason why Android File Transfer is now required when it used not to be.  What changed in order to make this necessary? Why is it necessary? OneDrive isn't uploading all my photos from my phone I've got an Office 365 (Microsoft 365) Family license. I've set up OneDrive on my Samsung Galaxy S10 phone. I've verified that it is set up by following the . I've got it set up to upload photos using either Wi-Fi or mobile. And I see photos I've taken with my phone, uploaded to OneDrive from as recently as a few days ago. So, it works. But not all the time or for all my photos. I've scrolled through my photos on my phone's Gallery app. I see some photos from as recently as 4 days ago to several months ago, are not uploaded to OneDrive. Why is that? I have a battery pack of NiMH batteries. It is ten cells with 1.2V, 4000mAh each, put together in series. So rated voltage is 12V. After charging, i.e. when the charging device says that it is finished, I measure 14.3V.   When I now discharge, at what voltage should I consider my battery as "empty"? Is this the lowest voltage that I can discharge it to without damaging it? Which voltage is that? Time travel film: character with male and female reproductive organs is taken back in time by a barman who turns out to be themselves I have had a friend give me a rough description of a film and I'm curious to find out what it actually is. I don't know very much. I understand this will be difficult, especially since every time my friend explains the tale it's different so this description is likely to contain some inaccuracies.  The film's plot begins with a recounting given by the main character, who had both male and female reproductive organs but had one set removed (not sure which, think male ones were removed). The main character is narrating this tale to the barman in a bar. The barman then takes the main character back in time, where they make love to themselves and produce a child.  The child, once born, is abandoned by the mother in the past - but the barman takes the child to the orphanage and leaves them there, ensuring their survival. Eventually it is revealed that the child was the main character themselves, and so was the barman.  In other words every major character introduced up to that point was the same person who had severely messed with their own timeline.