Can we mix tenses in the same paragraph?
Mixing tenses in past tense fiction
How does the telepathy supernatural ability work? What do you call the feeling you get when you're satisfied to the point of nausea? So you're craving something, say a particular chocolate or sex with one very attractive person that you desire. Take the sexual encounter one for example. You sleep with the person so many times until you are fulfilled. But it gets somewhat "nauseating" to enjoy that thing again (the sex or the chocolate) because you've overindulged earlier.   Now what is that feeling called, the feeling of being overly "satisfied" or "quenched" to the point of nausea?  I wouldn't say what I'm looking for is satisfaction or quench. Is there a more specific term?  Example sentence:     "I've been eating T-bone steak all day yesterday. I had leftovers today, but I couldn't eat them - I'm just so ____ towards (or from) steak right now." Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom Background  Suppose we have an Ordinary Least Squares model where we have $k$ coefficients in our regression model, $$\mathbf{y}=\mathbf{X}\mathbf{\beta} + \mathbf{\epsilon}$$  where $\mathbf{\beta}$ is an $(k\times1)$ vector of coefficients, $\mathbf{X}$ is the design matrix defined by  $$\mathbf{X} = \begin{pmatrix} 1 &amp; x_{11} &amp; x_{12} &amp; \dots &amp; x_{1\;(k-1)} \\ 1 &amp; x_{21} &amp; \dots  &amp;       &amp;   \vdots \\ \vdots &amp;   &amp; \ddots &amp;       &amp;   \vdots \\ 1 &amp; x_{n1} &amp; \dots  &amp; \dots &amp;   x_{n\;(k-1)}     \end{pmatrix}$$ and the errors are IID normal,  $$\mathbf{\epsilon} \sim \mathcal{N}\left(\mathbf{0},\sigma^2 \mathbf{I}\right) \;.$$  We minimize the sum-of-squared-errors by setting our estimates for $\mathbf{\beta}$ to be $$\mathbf{\hat{\beta}}= (\mathbf{X^T X})^{-1}\mathbf{X}^T \mathbf{y}\;. $$   An unbiased estimator of $\sigma^2$ is  $$s^2 = \frac{\left\Vert \mathbf{y}-\mathbf{\hat{y}}\right\Vert ^2}{n-p}$$ where $\mathbf{\hat{y}} \equiv \mathbf{X} \mathbf{\hat{\beta}}$ ().   The covariance of $\mathbf{\hat{\beta}}$ is given by $$\operatorname{Cov}\left(\mathbf{\hat{\beta}}\right) = \sigma^2 \mathbf{C}$$ where $\mathbf{C}\equiv(\mathbf{X}^T\mathbf{X})^{-1}$ () .  Question  How can I prove that for $\hat\beta_i$, $$\frac{\hat{\beta}_i - \beta_i} {s_{\hat{\beta}_i}} \sim t_{n-k}$$ where $t_{n-k}$ is a t-distribution with $(n-k)$ degrees of freedom, and the standard error of $\hat{\beta}_i$ is estimated by $s_{\hat{\beta}_i} = s\sqrt{c_{ii}}$.    My attempts  I know that for $n$ random variables sampled from $x\sim\mathcal{N}\left(\mu, \sigma^2\right)$, you can show that  $$\frac{\bar{x}-\mu}{s/\sqrt{n}} \sim t_{n-1} $$ by rewriting the LHS as $$\frac{ \left(\frac{\bar x - \mu}{\sigma/\sqrt{n}}\right)  }   {\sqrt{s^2/\sigma^2}}$$ and realizing that the numertor is a standard normal distribution, and the denominator is square root of a Chi-square distribution with df=(n-1) and divided by (n-1) ().  And therefore it follows a t-distribution with df=(n-1) ().  I was unable to extend this proof to my question...  Any ideas?  I'm aware of , but they don't explicitly prove it, they just give a rule of thumb, saying "each predictor costs you a degree of freedom". What is the best way to initialize a private, static data member in C++?  I tried this in my header file, but it gives me weird linker errors:  class foo {     private:         static int i; };  int foo::i = 0;   I'm guessing this is because I can't initialize a private member from outside the class.  So what's the best way to do this? How do I restore the default repositories? Prove by induction: $$\frac1{n+1} + \frac1{n+2} + \cdots +\frac1{3n+1} &gt; 1$$  adding $1/(3m+4)$ as the next $m+1$ value proves pretty fruitless. Can I make some simplifications in the inequality that because the $m$ step is true by the inductive hypothesis, the 1 is already less than all those values? Thailand visa exemption: any rule limiting number of entries per year? How to resize my dual-boot partitions I have a dual-boot laptop with both Windows 10 and Ubuntu 16.04.  Currently, the Windows side has too much disk space, and I want to resize things so that the Ubuntu side has more.  Firstly, I went into the Windows disk management and shrunk the Windows partition by 20GB. I then wanted to expand the Ubuntu partition, but it seemed like this option was greyed out.  Can I expand the Linux partition from Windows or do I need to be in Ubuntu or do I need to create a boot disk and do it that way?  Or do I need third party software?  Any help gratefully received. How can I repeat the header but not the caption with longtable? I am trying to set up a longtable where the header is repeated on every new page but the caption only appears once at the top of the page.  The table is defined as follows:  \begin{longtable}{|l|l|l|} \caption{the table caption} \label{tab:11swpkg}\\ \hline \rowcolor{gray} HeaderCol1 &amp; HeaderCol2 &amp; HeaderCol3\endhead     \hline\hline Item11 &amp; Item12 &amp; Item13 \\ \hline Item21 &amp; Item22 &amp; Item23 \\ \hline Item31 &amp; Item32 &amp; Item33 \\ \hline \end{longtable}   This nearly works because the header is indeed repeated after a page break but so is the caption. How can I get rid of the caption after a page break? What's the difference between TRUNCATE and DELETE in SQL What's the difference between TRUNCATE and DELETE in SQL?  If your answer is platform specific, please indicate that. How do I create an .exe for a Java program? The Wifi is working fine but no internet connection in Windows 8 I would like to draw an arrow like this using TikZ:    This is taken from . I didn't succeed in reproducing the arrow; is somewhat beyond my (extremely limited) TikZ abilities. I don't need all the workflow stuff. I simply want to draw such an arrow at a certain place in my text, e.g. -->  \documentclass{article} \usepackage{&lt;???&gt;} \usepackage{tikz} \usetikzlibrary{&lt;???&gt;} \begin{document} Donec vehicula augue eu neque. Pellentesque habitant morbi \tikz &lt;???code for the arrow???&gt; ; tristique senectus et netus \end{document}   PS: Some explanations in your solution would be much appreciated, otherwise it will be difficult to customize it. Cards changing mana color What cards across all sets allow the utilization of mana, either colorless or otherwise, as colored mana of another color?  One early example with an unlimited  1:1 ratio:     Sunglasses of Urza   Continuous Artifact: White mana in your mana pool can also be used as red mana.   What other cards have similar abilities? Refer to an item in `dirs` I use pushd to work with multiple directories in bash and zsh. I've aliased dirs to dirs -v so that I get an ordered list when I want to see what's on the directory stack:  chb$ dirs 0  /Volumes/banister/grosste_daever_gh/2013-03-27/reader 1  /tmp/20130618202713/Library/Internet Plug-Ins 2  ~/code/foo/view/static/css 3  ~/Downloads   Is there a way (either in bash or zsh) that I can refer to one of the directories listed on the command line using an alias for its position on the stack? For example, instead of typing:  chb$ cp ~/code/foo/view/static/css/baz.css ~/code/bar/view/static/css/   I'd type:  chb$ cp &lt;2&gt;baz.css ~/code/bar/view/static/css/   ...or something like that, maybe using a dollar sign and a variable name instead of &lt;n&gt;. How to make a water vortex I'm very new to Blender and I'm trying to make a water vortex like this.(may be not the easyest first project for a newbie)     I watched several tutorial on liquids particle etc but I'm not sure what is the best aproach. What I tried  until now:   I made a particle system with a vortex force field. It looks good, but I'm not able to add the right material.      I played around with the fluid physics, the water looks good but if I add a vortex force field it does nothing.   I would be very grateful if somebody could point me in the right direction because I'm definitely stocked. Calculating the total number of surjective functions It is quite easy to calculate the total number of functions from a set $X$ with $m$ elements to a set $Y$ with $n$ elements ($n^{m}$), and also the total number of injective functions ($n^{\underline{m}}$, denoting the falling factorial). But I am thinking about how to calculate the total number of surjective functions $f\colon X \twoheadrightarrow Y $.  The way I thought of doing this is as follows: firstly, since all $n$ elements of the codomain $Y$ need to be mapped to, you choose any $n$ elements from the $m$ elements of the set $X$ to be mapped one-to-one with the $n$ elements of $Y$. This results in $n!$ possible pairings. But the number of ways of choosing $n$ elements from $m$ elements is $\frac{m!}{(m-n)!\,n!}$, so the total number of ways of matching $n$ elements in $X$ to be one-to-one with the $n$ elements of $Y$ is $\frac{m!}{(m-n)!\,n!} \times n! = \frac{m!}{(m-n)!}$.  Now we have 'covered' the codomain $Y$ with $n$ elements from $X$, the remaining unpaired $m-n$ elements from $X$ can be mapped to any of the elements of $Y$, so there are $n^{m-n}$ ways of doing this. Therefore I think that the total number of surjective functions should be $\frac{m!}{(m-n)!} \, n^{m-n}$.  Is this anything like correct or have I made a major mistake here? My question is similar to  except it's about VMware Workstation Player instead of VirtualBox.  How do I disable mouse integration? I want the VM to "capture" my mouse. One option is to pass my mouse directly to the VM, but that's more difficult if I need to exit the VM (I want to just use Ctrl+Alt).  I'm using "VMware Workstation 15 Player (Non-commercial use only)" I heard the following comment of Mr. Marco Rubio about Mr. Donald Trump on CBS’s “Face the Nation” in a clip in February 29th AP Radio News:  “There is never gonna be a time where the Republican Party rallies around and says you have to get out or anyone has to get out for purposes of rallying around Donald Trump. Donald Trump is not Republican Conservative. Donald Trump is trying to pull off the biggest scam in American political history.”  I thought I misheard “There is never gonna be a time where –“ for “There is never gonna be a time when –“ at first, because I was in understanding that time should be trailed by “when” as a relative noun or adverb. An English Japanese dictionary at hand (Readers English Japanese Dictionary published by Kenkyusha) provides “where” singly as a relative to refer the ‘place.’ However, my lookup of the following two sources endorsed that I heard it right:  Here is what is never going to happen in this race. There's never going to be a time where the Republican Party rallies around and says you have to get out or anyone has to get out for purposes of rallying around Donald..  “Here is what is never going to happen,” Rubio continued. “There's never going to be a time where the Republican Party rallies around and says you have to get out or anyone has to ...   Is it common, at least not uncommon to use “where” after “time” as a relative? How to rig a shirt with buttons so that the buttons follow the mesh of the shirt I didn't address this in a while because I was busy with something else, but now it has cycled back into my schedule.  Right now I have a shirt modeled and bones set in place. It's already technically rigged, but the only issue is the buttons.   I'm not entirely sure how to go about connecting them to the shirt's deformations. I tried to combine them and the shirt into one object, but because of the shirt's modifiers, (Solidify and subsurf, which I don't want to apply yet), the buttons become extremely deformed. I've tried to match the weight painting intensity where a button is at in correspondence with the shirt, but that doesn't seem to work, maybe it has to do with the specifics of where the button is?   Is there a way to make the buttons follow the shirt's deformations without deforming the mesh vertices of the button? I know that if I probably apply the modifiers on the shirt and combine it with the buttons, it would be okay, but I'm not okay with doing that just yet with the shirt.    I rigged the shirt by deleting all vertex groups, assigning empty groups to the mesh from the armature, and then assigned automatic groups in the weight paint menu.  Is there a way to do this?