Why is $R^2$ so difficult to calculate for mixed models (both for the model as a whole and the fixed effects)?
Why are effect size estimates (such as $R^2$) difficult in mixed-effects models?
If $A = \tan6^{\circ} \tan42^{\circ},~~B = \cot 66^{\circ} \cot78^{\circ}$ find the relation between $A$ and $B$ My trigonometric problem is:     If $A = \tan6^{\circ} \tan42^{\circ}$ B = cot$66^{\circ} \cot78^{\circ}$ find the relation between $A$ and $B$.    Working :   $$B = \cot 66^{\circ} \cot78^{\circ} = 1- \frac{\tan24^{\circ}+\tan18^{\circ}}{\tan42^{\circ}}$$  $$A= \tan6^{\circ} \tan42^{\circ} = 1- \frac{\tan6^{\circ} +\tan42^{\circ}}{\tan48^{\circ}}$$  but it seems  this is the wrong way of doing this...please suggest. Thanks! I have an ec2 instance on AWS which already installed a few Wordpress-es in it.  I want to set things up to let more people handle their own projects, with me also being able to go into the server using terminal if I still want to.  I have been following tutorials such as  and a few others.  I figured all of them just teach users how to sftp into their own home folder, also the steps keep saying addUser but some users already existed and removing them might cause some issue.  How can I give existing users the permission to use SFTP for Wordpress projects?  Let's say all my Wordpress projects are already under /var/www/ which has already been set up with www-data:www-data.  Really new with setting things like this.  Thanks in advance for any help. Show that $x_{n+1}-\dfrac{x_n}{2}$ converges to zero implies that $(x_n)_n$ also converges to zero. Let $(x_n)_n$ be a sequence of real numbers such that $$\lim\limits_{n\rightarrow \infty}\left( x_{n+1} - \dfrac{x_n}{2}\right)=0.$$ Show that $(x_n)_n$ must also converge to zero.     $\textbf{My Attempt:}$   My original idea was to use the triangle inequality and the fact that $$\lim\limits_{n\rightarrow \infty}\left( x_{n+1} - \dfrac{x_n}{2}\right)=0$$   to show that the sequence $(x_n)_n$ is Cauchy and hence converges to some real number $a$, which would give me $$\lim\limits_{n\rightarrow \infty}x_n=a=\lim\limits_{n\rightarrow \infty}x_{n+1}\implies a-\dfrac a 2= \lim\limits_{n\rightarrow \infty}\left( x_{n+1} - \dfrac{x_n}{2}\right)=0\implies a=0.$$ However, I'm having trouble showing that $(x_n)_n$ is Cauchy.   Any suggestions/hints would be greatly appreciated. Thanks! I have two areas of my house which are cantilevered. One is a bay area which extends about 2'. The other is the bottom of a fireplace box (gas fireplace). I have placed two layers of R-13 (I think) insulation in this area, but inside the house it's like a heat sink where all of the heat is sucked out ... very cold to the touch in the winter time. Obviously there must be a better way to insulate this area.  My question is, what is the best way to insulate a cantilevered area so as to allow the inside area of the house to not be so cold in the winter time? Answering your own question? Accept it. Dim screen past the minimum on Ubuntu My laptop's screen is far too bright at night, even if I set it to minimum brightness. I know that it is capable of being dimmer, because Windows will dim it further if I leave it idle. However, I can't figure out how to dim it lower to minimum on Ubuntu. Is there a way?  I've looked at  question, but it's talking about Windows. Punctuation in an indirect quotation I don't have any knowledge in hardware and would like to know which RAM should I buy for my laptop.  How do I discover what RAM I need &amp; how much my machine can take?  I have a Razer Blade 15 (RZ09-02705F76) 2018 but don't know if there is a specific type or format of RAM that suits it and don't know where to find this information. What does “the lowest common denominator” mean in the context other than math? In the  (May 31) article under the title, “Stephen Hawking angers Trump supporters with baffling array of long words,” Andy Borowitz wrote;     “Speaking to a television interviewer in London, the theoretical   physicist, Hawking called Trump “a demagogue who seems to appeal to   the lowest common denominator. --- “For a so-called genius, this was an   epic fail,” Trump’s campaign manager, Corey Lewandowski, said. “If   Professor Hawking wants to do some damage, maybe he should try talking   in English next time.”        Later in the day, Hawking attempted to clarify his remark about the presumptive Republican Presidential nominee, telling a reporter, “Trump bad man. Real bad man.”   From the context of Professor Hawking’s remark, I take “the lowest common denominator” as referring to the  “social segment of low educated, unsophisticated people,” but I’m not sure.   I thought  "common denominator" is a simple mathematic term. What does it mean in the context of the above quote?  Mr. Trump’s campaign manager says Professor Hawking should try to talk in English. Is this a farfetched way of using “common denominator” from math to politics?   Did Professor Hawking misuse "the common denominator"? Or does Mr. Trump's campaign manager not understand the meaning of "common denominator", which some call an "everyday-use" English phrase?  P.S.  I found the following definition of 'common denominator' in Oxford Advanced Learners English Dictionary;   2) an idea, attitude or experience that is shared by all the members of group - see also Lowest common denominator.  Readers English Japanese Dictionary at hand, published by Kenkyu-sha, a foreign language, especially English language dictionary specialist publisher in Japan, and rated as the most reliable English Japanese dictionary totally dropped the reference to this paticular meaning.  It was a learning. I told to myself that I should have made more homework on English-to-English dictonaries beforehand. I have searched, but not found anything on this. I am looking for a functionality in bash, using a terminal.  Way back when, I had a user on a debian system, and a friend set me up with a convenient history search feature (I believe I used tcsh then), where I would type the beginning of a previous command, hit up-arrow, and it would do a search, based on the partial string.  E.g. if my history is:  ./script.pl ./script.pl arg1 cat output cat output | grep yada   And I type ., and press up-arrow, it would show me: ./script.pl arg1. Press it again and it would show ./script.pl, etc.  Very much like it would perform a grep on .bash_history. Is there a way to get this functionality? None of the physics sensors in my game work, I'm trying to create an AI man that chases after a player, but for whatever reason, he just won't sense the player, I've tried copying and pasting the property name just to be sure, but that's not it. I am an Indian citizen. I am flying from Toronto to New Delhi. I have two transits: one at Lisbon airport and the second one at Madrid airport.  While the Consulate of Portugal has assured me that I do not need an airport transit visa during my 2 hours stay in Lisbon airport, I did not get a definitive answer from the consulate of Spain in Toronto.   At Madrid airport, I need to make a transfer from Terminal 2 to Terminal 1.   Does anyone here know whether I need to pass through immigration while making this transition in Madrid and if so, do I need a Schengen visa for that? Split List into Sublists with LINQ Is there any way I can separate a List&lt;SomeObject&gt; into several separate lists of SomeObject, using the item index as the delimiter of each split?  Let me exemplify:  I have a List&lt;SomeObject&gt; and I need a List&lt;List&lt;SomeObject&gt;&gt; or List&lt;SomeObject&gt;[], so that each of these resulting lists will contain a group of 3 items of the original list (sequentially).  eg.:   Original List: [a, g, e, w, p, s, q, f, x, y, i, m, c] Resulting lists: [a, g, e], [w, p, s], [q, f, x], [y, i, m], [c]   I'd also need the resulting lists size to be a parameter of this function. Is it possible to run Snow Leopard on a LATE 2011 MacBook Pro? Is there any way to get the number of pending chat request on omni channel? I have a requirement to get the number of pending chat request in the omni channel.  I have set the presence configuration capacity to 5 so that an agent can have only 5 chat requests. if a case is solved agent will get one of the pending chat request. But right now i can't see the number of pending request.     Lets say i have 10 pending request in the queue, but i don't have any numbers to see how many are pending in the queue.   Is there any way that can show the pending chat requests in the queue? Self-Studying Measure Theory and Integration As the title says, I'm interested in reading about measure theory and integration theory on my own time, and was hoping for book recommendations, prerequisites, and things like that.  As for my background, I've taken introductory analysis, where we covered the "typical" subjects up until some theorems about differentiable functions.  I'm taking intermediate real analysis now; we talked about metric spaces in general for a while, but lately we've focused solely on $\mathbb{R}^n$. Now we're working towards a proof of the implicit function theorem in $\mathbb{R}^n$.  I haven't learned any of the theory behind Riemann integration, unfortunately. Is it important to be familiar with this first? Problem  Let $n \geq 3$ be an odd number and let $G=\{1,...,2n\}$ be a group of order $2n$. Let $\phi:G \to S_{2n}$ be the morphism defined by $\phi(g_i)(g_j)=g_ig_j$ and let $H=\phi^{-1}(A_{2n})$. Show that $H$ is a proper normal subgroup of $G$.  So basically the result of this problem is that every group of order $2n$, with $n$ odd, is not simple.   The morphism $\phi$ can be seen as the action of $G$ on itself by left multiplication. Since $A_{2n} \lhd S_{2n}$, then $H=\phi^{-1}(A_{2n}) \lhd G$. I am stuck at showing that $H \neq \{1\},G$. All I could think of is that $G$ has an element $g$ of order $2$, then $\phi(g)$ is of order $1$ or $2$, but it is easy to see that $\phi(g)=1$ if and only if $g=1$, so $ord(\phi(g))=2$. I don't know which are the elements of order two in $S_{2n}$. I would appreciate some help to solve the problem, thanks in advance. Prove that for all $n&gt;2$ there exists at least one prime $p$ such that $\sqrt{n}&lt;p&lt;n$ using elementary methods.  My try: If not, $\sum_{p&lt;\sqrt{n}} (\lfloor n/p \rfloor-\lfloor \sqrt{n}/p \rfloor) \geq n-\sqrt{n}$  then...? Value of Vandermonde type determinant Let $x_1,...,x_n $ are distinct real numbers.  Is it a formula for the Vandermonde type determinant $V(x_1, \cdots,x_n)$  whose last column is $x_1^k,\ \cdots,\ x_n^k$, where $k \geq n$, instead of $x_1^{n-1},\ \cdots,\ x_n^{n-1}$?  Thanks Why can I modify a read-only file? Short Question:  Why can we manipulate a read-only file in Vim using : + w + q + ! even without being an administrator?  Long Question:  I have a text file (myFile.txt) which is read-only for everyone:  navid@navid-ThinkPad-T530:~/ubuntuTest$ ls -l myFile.txt  -r--r--r-- 1 navid navid 26 Aug 22 21:21 myFile.txt   I can open it with Vim without having admin privileges:  navid@navid-ThinkPad-T530:~/ubuntuTest$ vi myFile.txt    I modify it and press: Esc + : + w + q + Enter and I see this error message:  E45: 'readonly' option is set (add ! to override)   So far, everything makes sense.  But when I press: Esc + : + w + q + ! + Enter, Vim saves the changes.  I'm using Ubuntu 16.04 and VIM 7.4.