Regression for looping (circular?) variable
How to include time factor in a mixed model (investigating the interaction between two factors and time)?
I need your help with this: Let $f$, $p$, and $g$ be a polynomials in $F[x]$, assume that $f$, $g$, and $p$ are nononzero.  If $\gcd(f,p)=1$ and $fg$ is divisible by $p$ with no remainder, I need to prove that $g$ is  divisible by $p$ with no remainder  Thanks. Why does this test program result in a java.lang.IllegalMonitorStateException?  public class test {     static Integer foo = new Integer(1);     public static void main(String[] args) {         synchronized(foo) {             foo++;             foo.notifyAll();         }         System.err.println("Success");     } }   Result:  Exception in thread "main" java.lang.IllegalMonitorStateException         at java.lang.Object.notifyAll(Native Method)         at test.main(test.java:6) How do you pass a function as a parameter in C? Why is "improve this question / answer" shown to anonymous users instead of "edit"? If I browse a site as an anonymous user, instead of "edit" I see: "improve this question / answer".        I don't get it, are anonymous users considered to be kinda dumb and don't understand "edit"?  Why to reword this action? How to use grep on column? I want to apply grep on particular column in column command.  myfile.txt  3,ST,ST01,3,3,856 3,ST,ST02,4,9,0234 6,N1,N101,2,3,ST 6,N1,N102,1,60,Comcast 6,N1,N103,1,2,92   My Command:  column -s, -t &lt; myfile.txt | grep -w "ST"   Here I want to only grep the pattern ST in 2nd column. How to do this ?  Expected Result:  3       ST            ST01              3            3            856 3       ST            ST02              4            9            0234 Count the items from a IEnumerable without iterating? private IEnumerable&lt;string&gt; Tables {     get     {         yield return "Foo";         yield return "Bar";     } }   Let's say I want iterate on those and write something like processing #n of #m.   Is there a way I can find out the value of m without iterating before my main iteration?  I hope I made myself clear. Can hard drives fully utilize SATA III? My motherboard currently supports both SATA II and III (3 Gb/s and 6Gb/s respectively), but after reading some online, it seems as though connecting a HDD to the 6 Gb/s is pretty much pointless. If this is the case I'm going to leave my two SATA III ports open for something that can actually use it (which at this point I'm not really sure what can).  This is part of an article I read:     In terms of everything else, we saw basically no difference from the same single drive being plugged into a SATA 6Gb/s or SATA 3Gb/s port. All of this is obviously due to the hard drive not being able to actually take advantage of the 6Gb/s bus.   from . Flames with no gravity? I was watching  today, and noticed this: in some moment the space station changed orbit and the people inside experienced zero-gravity. At that moment, a candlestick passed floating in the air, with the candles burning ().   But in our environment the flames go upward because the hot air is less dense, and that effect should disappear when no gravity is present, am I right? How would a candle flame look then? Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$ Let $\Omega$ be an open set in $\Bbb{R}^n$ and $f:\Omega\to \Bbb{R}^m $ be of class $\Bbb{C}^2.$ Let $a,b$ be in $\Omega$ such that $[a,b]\subset \Omega.$ Prove that  \begin{align}\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2.\end{align} where $$f'(a)(b-a)=\big&lt;\nabla f(x),(b-a)\big&gt;=\sum^{n}_{k=1}\frac{\partial f_i}{\partial x_k}(a)(b_k-a_k).$$  I  think the idea of Mean Value Theorem for $C'$ functions in $\Bbb{R}^n$ () will help me in showing it but I don't know how to! Please, can anyone show me a proof or reference? Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})} = \mathbb{Z}[\phi]$, where $\phi={1+\sqrt{5}\over 2}$ is the golden ratio?  I know that $5 \equiv 1 \mod 4$, so that then $\mathbb{Z}[\sqrt{5}]$ is not closed as far as integers go. But I'm a little confused cause  $\mathcal{O}_{\mathbb{Q}(\sqrt{-3})} = \mathbb{Z}\left[-\frac{1}{2} + \frac{\sqrt{-3}}{2}\right]$? So how do I know when to use $\frac{1}{2}$ rather than $-\frac{1}{2}$? Which one applies for $\mathcal{O}_{\mathbb{Q}(\sqrt{5})}$? In some scenes in Avengers: Age of Ultron Iron man, War Machine, and Captain America try to lift Thor’s hammer but they end up failing. At some point Vision lifts it easily. How can Vision lift it? Show that $E(X)=\int_{0}^{\infty}P(X\ge x)\,dx$ for non-negative random variable $X$ Show that for a non-negative random variable $X$,   $$\mathbb E(X)=\int_0^\infty \mathbb P(X\ge x) \, dx.$$   I started with  $$\mathbb E(X)=\int_0^\infty x \, dF(x)=\int_0^\infty \int_0^x dt\,dF(x).$$ This is my try. Next badge select dialog broken The "Select your next badge" dialog box is not displaying correctly. It looks like this:    Freehand circles, as requested:    It seems to be an issue with box-sizing, because when it's content-box, it looks fine. I think the width and height rules for .popup-badges .all-badge-progress .badge-progress should be increased a little, for example:  .popup-badges .all-badge-progress .badge-progress {   width: 214px;   height: 96px; }   Tested on the latest Chrome and Firefox on Linux Mint. Show that all horses are of the same color. Im trying to understand the solution about this, and all the other solutions are.. a bit weird for me and dont answer all my questions!  Reference :   Im using the answer there as reference, but my understanding is a bit different!     Find the error in the following proof that all horses are the same   color. CLAIM: In any set of h horses, all horses are the same color.      PROOF: By induction on h.      Basis: For h = 1. In any set containing just one horse, all horses   clearly are the same color. Induction step: For k > I assume that the   claim is true for h = k and prove that it is true for h = k + 1. Take   any set H of k + 1 horses. We show that all the horses in this set are   the same color. Remove one horse from this set to obtain the set H1   with just k horses. By the induction hypothesis, all the horses in H,   are the same color. Now replace the removed horse and remove a   different one to obtain the set H2 . By the same argument, all the   horses in H2 are the same color. Therefore all the horses in H must be   the same color, and the proof is complete.   Here's what i have come up with :  Suppose a set of 1 horse. $H_a = { horse_{1} }$  Obviously, all the horses in set $H_a$ are the same, since theres just 1 horse.  So using that as the Basis of the induction we can proceed and try to prove its true for $N$ horses.  -- I dont fully understand the part below   As an example : set $H_0$ :   $H_0 = { horse_{1}, horse_{2}, horse_{3}... horse_{n} }$  In my understanding, its because, I can make a subset  formed by 1 horse :  $K_1  = {horse_{1}}$ $K_2  = {horse_{2}}$ ...  I don't get it. I clearly know that this proof is a lie.  And for me, its because you cant claim theres a relation on a set with size $&gt;= 2$ , since :  $H_1 = { horse_{1}, horse_{2}}$  Theres nothing that says $horse_{1}$ equals $horse_{2}$. The basis was for one horse. But that alone is not a proof.  So what should I do ? Becoming Thieves Guild Guildmaster, am I bugged? I've completed the Thieves Guild main questline () and chosen my special power (Shadowcloak of Nocturnal). It says completed in my quest log.  I also completed the  in each city you can give Thieves guild influence to (Markarth, Whiterun, Windhelm, and Solitude) and done their special jobs from Delvin. They show completed in my quest log. I've even done at least one of each kind of job from Vex and Delvin (but not in each city).  I got  in the Ragged Flagon and have done the quest for Tonilia (delivering the Moon Sugar to a caravan) and Vekel (getting the 4 books). I've also upgrade one of my pieces of Thief Armor.  I talk to  to become guild master and I get no dialogue options but he just says he's busy and we'll talk another time. There is a guild chest in front of his desk but it's locked and I don't have the key.  What am I missing? Is there some bug I've encountered? Since I updated Windows to 8.1 my Grub menu disappeared. I ran Ubuntu using Live USB, I used Boot-Repair but something went wrong. If I click on Reccomended repair I get this error:     GPT detected. Please create a BIOS-Boot partition (>1MB, unformatted filesystem, bios_grub flag). This can be performed via tools such as Gparted. Then try again. Alternatively, you can retry after activating the [Separate /boot/efi partition:] option.   So I tried to set my sda9 (I think that it's the Ubuntu system partition, since it's ext4) with the bios_grub flag and then to run Boot-Repair again. It didn't work.  I don't know what to do. My Grub was working fine (using UEFI) before I updated Windows.  I removed the bios_grub flag. Then I used fsck and it didn't find any error. So I tried again with Boot-Repair but it always gives me the "GPT detected" error. My boot is on UEFI mode, Secure Boot is "off".  When I boot my PC with SecureBoot OFF, I can reach the GRUB menu. But it's empty (the only voice is "System Setup").  I mounted my Ubuntu system disk:  sudo mount /dev/sda9 /mnt   and the other things:  sudo mount --bind /dev /mnt/dev sudo mount --bind /proc /mnt/proc sudo mount --bind /sys /mnt/sys   I logged on the system with chroot:  sudo chroot /mnt   I re-installed grub:  grub-install /dev/sda update-grub2   But it still doesn't work. Is a quotient group a subgroup? Is a quotient group a subgroup?   I am trying to solve the question below, and if the answer to above is "yes," then my proof will follow below.   I am trying to prove that a cyclic group G, has a cyclic quotient group G/N.  Where N is a normal subgroup.  A SUBGROUP OF A CYCLIC GROUP IS CYCLIC.  By   So if   (1) G is cyclic   (2) G/N is a subgroup   (3) G/N is a cyclic subgroup   (4) The Quotient group G/N is cyclic   I am unsure about my reasoning in step (2), Is this a valid assumption? I googled it but I couldn't find the answer... maybe I didn't seek it in the proper way. My question is if &quot;to&quot; must be repeated in sentences such as the following ones:   In the past, women used to do the housework and to take care of children.  The aim of this meeting is to control their progress and to discuss the new working plan.    If I had to bet, I would omit the second to... But I am not sure about it. Moving a doorbell transformer Can a doorbell transformer that is on the outside of a wall be place inside the wall behind the drywall. I’m concerned about it getting too hot. Mine is in the kitchen by the ceiling lights Benefit of date in URL segments I was curious about the date in URL segments, is there any SEO point of benefit? For example the following URLs:  http://techcrunch.com/2013/06/18/netflix-will-launch-in-the-netherlands-later-this-year-as-its-international-expansion-slows/ http://tips-for-new-bloggers.blogspot.in/2007/02/adding-favicon-icon-to-blogger-url.html  https://community.jivesoftware.com/blogs/jivespace/2013/05/15/eol-of-the-html5-ipad-web-app   In all the above URLs there is date segment. The information of those blogs can be fetched via blog stub like "netflix-will-launch-in-the-netherlands-later-this-year-as-its-international-expansion-slows" so why to use that date part?