A word for feeling simultaneously happy & sad
Words for "a bit sad" and "a bit happy"?
all the LaTeX-tutorials tell me how LaTeX is an extention simplifying the building of TeX documents. Understandably, no one uses plain TeX anymore, right?  But I seem to learn better when I grasp the link between TeX and LaTeX. Does someone have a link to example files in plain TeX? I'd like to know which commands, macros etc. are LaTeX-specific. How is Faulhaber's formula derived? I have been wanting to understand how to find the sum of this series.   $$1^p + 2^p + 3^p +{\dots} + n^p$$  I am familiar with Gauss' diagonalised adding trick for the sum of the first $n$ natural numbers.  I can prove the formulas for  $$\begin{align}   \sum_{1}^{n} k^2 &amp;= \frac{n(n+1)(2n+1)}{6}\\  \sum_{1}^{n} k^3 &amp;= \frac{n^2(n+1)^2}{4}\\ \sum_{1}^{n} k^4 &amp;= \frac{n(n+1)(2n+1)(3n^2+3n-1)}{30} \\ \end{align}$$  With mathematical induction. But, beyond that even proofs with mathematical induction are difficult.  I'm interested in learning the theory and the proof behind Faulhaber's formula. What is the knowledge required to understand this proof ? Do gravitational lenses work on gravitational waves? Do gravitational lenses work on gravitational waves? Could we get an Einstein cross of gravity? Rollback Committed transaction in SQL Server Is it possible to rollback a committed transaction?  I have deleted all the data in a table. The delete statement is inside Begin Transaction and I have committed the transaction with a commit transaction command. Now is it possible to rollback and get the data back? Getting javax.crypto.IllegalBlockSizeException: Input length must be multiple of 16 when decrypting with padded cipher? Say I have two independent random variables $X \sim N(u_1, \sigma_1)$ and $Y \sim N(u_2, \sigma_2)$. I want to get the conditional distribution of X given whether X is bigger than Y or not.  $P(X|X&lt;Y)$ = ... and  $P(X|X&gt;Y)$ = ...  I am thinking solving this in this way:  \begin{align} P(X|X&lt;Y) &amp;= \frac{P(Y&gt;X|X)P(X)}{P(Y&gt;X)} \\ &amp;= \frac{(1-\Phi(\frac{x-\mu_2}{\sigma_2}))N(\mu_1,\sigma_1)}{\Phi(\frac{\mu_2-\mu_1}{\sqrt{\sigma_2^2+\sigma_1^2}})}\\ P(X|X&gt;Y) &amp;= \frac{P(Y&lt;X|X)P(X)}{P(Y&lt;X)} \\ &amp;= \frac{\Phi(\frac{x-\mu_2}{\sigma_2})N(\mu_1,\sigma_1)}{1-\Phi(\frac{\mu_2-\mu_1}{\sqrt{\sigma_2^2+\sigma_1^2}})} \end{align}  My questions are:   (1) Whether above solution is correct  (2) How to get the mean and sd for $P(X|X&lt;Y)$ and $P(X|X&gt;Y)$ if they are still normal? Is there a rule in British English about how to pronounce "either"? Why are polymorphic values not inferred in Haskell? Simple Math Problem A bat and ball cost \$1.10.  The bat costs a dollar more then the ball.  How much does the ball cost?  If this is not the correct place to ask a question like this please tell me and I will remove it :)     The ball costs \$0.05, not \$0.10 In the sentence: "I didn't know she had a son,"   Can I say "I didn't know she has a son" instead, because he is a teenager now?  Or are both correct? Everything I've seen points to no (and I would love that to be true since applying for a visa online costs money) but I'm worried about getting refused due to the length of time I wish to stay, which is 6 months.  I went to university in the UK on a Tier 4 visa, but have never just been a tourist which is what I would like to do now. Since graduating, I have started working but am underwhelmed and would love to travel again. My original plan was Australia but now I would like to see the rest of the UK as well beforehand.  If I arrived with the following, would I be refused entry simply for not applying online?: an approved Australian work &amp; holiday visa, a mini itinerary, bank statements for the last 6 months. When solving this issue (  ), I did a function so that the plugin would auto-hide from all users except one (me:).  The flaw is that it only auto-hides when active.  At first, it was a mu-plugin, but I had to enable/disable it manually. It really doesn't need to run all the time, as it may slow the site (?) or even contain some sensitive manipulation of the site's language (another question mark).  But mainly the motivation is that I don't want the client activating/deactivating/deleting this plugin (is for my own use), and don't want it cluttering her own plugins list.  So, decided to split the functions in two plugins:   One is a Must-Use used to hide the regular one.  The other will be activated/deactivated upon necessity and is the one from the above linked issue.   But now I run into another question: how to hide one plugin from the Must-Use listing? If $f$ is continuous from $ [0,1]$ to itself and $f(0)=0$, $f(1)=1$ and $f(f(x))=x$ then show that $f(x)=x$ for every $ x $ in the domain of function.  I'd like to prove this statement, my idea goes like below:  Suppose that the converse of the statement holds. then without loss of generality, assume that there exists some $c$ in $[0,1]$ such that $d=f(c)&gt;c$. By symmetry, $f(d)=f(f(c))&lt;f(c)=d$. And $f$ is bijective because $f$ has an inverse function in this domain. So $f$ should be strictly increasing function. But on $[c,d]$, $f$ is decreasing. This is a contradiction.  So it should be that $f(x)=x$ on $[0,1]$.  Is this argument right? And I'd like to know another argument which prove this statement. Thank you for your answer in advance :) I'm working under 12.04 and suppose I have a Firefox windows active (or in foreground) with English as input language and I need to type a document in other language using some text editor.   With the text editor in foreground (or active) and the input language set to a non-English one, when I bring Firefox in foreground (or making it active) the input language remains set to the non-English and the language flag does not switch to English (as it would be expected, since I do not alter the language during the whole Firefox session).  Because of this, I have to make extra moves and change the input language manually every time I switch from the text editor to Firefox and back to text editor. This was not happening with 10.04, and each application windows had the corresponding input language set to its default or previous session every time I was bringing it to the foreground!   How will I make 12.04 to behave the same way? I'm trying to include a tabu inside a new definition of an environment but it fails if the postamble (enddef) of the new environment includes tabu's contents, so cells. With tabular or tabular* works. The error is:   ! Missing number, treated as zero. \tabu@0.H5   The MWE:  \documentclass{article} \usepackage{tabu} \newenvironment{testt} {\begin{tabu} to \textwidth{cccc}  11 &amp; 12 &amp; 13 &amp; 14 \\  21 &amp; 22 &amp; 23 &amp; 24 \\} {  41 &amp; 42 &amp; 43 &amp; 44 \end{tabu} }  \begin{document}  \begin{testt}  31 &amp; 32 &amp; 33 &amp; 34 \\ \end{testt} \end{document}   How to solve this? Suddenly Okular will not open any more I have made my laptop double boot a few months again, with Ubuntu 18.04.1 . I have been working with okular to open pdf files (for the commenting option) but suddenly okular doesn't work anymore. When trying to open okular I get the following error:     Unable to find the Okular component: Cannot load library /snap/okular/39/usr/lib/x86_64-linux-gnu/qt5/plugins/okularpart.so: (libKF5JSApi.so.5: cannot open shared object file: No such file or directory)   I don't understand how to solve this problem. Okular was working fine until today and I didn't change anything to my ubuntu system in the mean time. Perhaps the problem comes from the fact that I have been working on windows the last few days and also used the windows ubuntu app.   How can I make okular work again? How prove this $\lim_{n\to \infty}\sin{n^m}$ divergent. show that $$\lim_{n\to \infty}\sin{(n^m)}$$  divergent,where $m\in N^{+}$  I have kown $$\lim_{n\to\infty}\sin{n^2}$$  to be divergent and dense in $[-1,1]$. This is very  famous problem,the problem is first is post $AMM$( The American Mathematical Monthly,1970-1975) problem,and after some years  $AMM$ post $\sin{(n^{14})}$ in $[-1,1]$ was dense? and this is open problem.so I Guess  $$\sin{(n^m)}$$ is dense in $[-1,1]$. How to get Lookup ID from Search API with REST I'm trying to get the ID of a lookup field when using search api. My query looks something like this:  /_api/Search/query?querytext='ListId:12345678-1234-1234-1234-123456789012'&amp;selectproperties='Title,Company'   Where Company is the lookup field, in a specific list.  The result looks like this:  &lt;d:element m:type="SP.KeyValue"&gt;   &lt;d:Key&gt;Company&lt;/d:Key&gt;   &lt;d:Value&gt;Some company&lt;/d:Value&gt;   &lt;d:ValueType&gt;Edm.String&lt;/d:ValueType&gt; &lt;/d:element&gt;   I have created a managed property which looks like this: How do I get rid of the noise on my Hayes Stroker Trail brakes How to play DVDs in Ubuntu 16.04?