IATA rule regarding passenger right to drinking water
Are airlines in the EU obligated to provide water for passengers?
"Heard me [infinitive]" vs. "heard me [present participle]" TeXShop and Mac preview crashing when opening latex/beamer built pdfs After updating to Sierra 10.12.4 last week, TeXShop crashes:   when opening an existing .tex document that has a pdf associated to it immediately after compiling a new document, i.e. as soon as a pdf is created.   Furthermore, preview crashes opening almost any pdf that has been created with TeXShop. There is virtually nothing on the internet about it, and the only solution seems to be a complete reinstall of MacOSX (so as to reinstall the supposedly broken preview), which I'd like to avoid if at all possible.  Someone else has described a similar issue, but has not received any responses ().  I would be very grateful for some help, as I can neither produce work, nor look at any at the moment. Many thanks! May $y=e^x$ be satisfied with both $x$ and $y$ be positive integers?  I think it is not possible as $e$ ,a transcendental number, when multiplied by itself would never result in rational number.  Am I right? I want to express $$\sum_{n=-\infty}^\infty \dfrac{1}{(z+n)^2+a^2}$$ in closed form. What comes to mind is the formula $$\pi\cot\pi z = \dfrac{1}{z}+\sum_{n\ne 0}\left(\dfrac{1}{z-n}+\dfrac1n\right)=\dfrac{1}{z}+\sum_{n=1}^\infty\dfrac{2z}{z^2-n^2}$$  and also $$\dfrac{\pi^2}{\sin^2\pi z}=\sum_{n=-\infty}^\infty \dfrac{1}{(z-n)^2}.$$ But neither of these gives the term $(z+n)^2+a^2$ that we want. Perhaps we can adjust somehow? How prove $p!|(a+1)$ if $p!|a^p+1$ For any real number $a \geq 1$ let $f(a)$ denote the real solution of the equation $x(1+\ln x)=a$ then the    question is to find out $$ \lim_{a \to \infty} \frac{f(a)\ln a}{a}$$.  It is clear that if we denote $h(a)$ by $h(a)=a(1+\ln a)$ then $f(a)$ is the inverse function of $h(a)$. Also $f(a)$ is increasing function in its domain. Also the limit persuades using lhospital's but I cannot see how to apply it here. Thanks. Can sweetened condensed milk be substituted for whole milk and sugar? I am making a fudge recipe that calls for 1cup whole milk and 5 cups sugar. It also uses 2 sticks of butter and 25 marshmallows. I'm wondering if I can omit the milk and cut back on the sugar by using sweetened condensed milk. Let $P$ be a probability measure on $(\Omega, \mathscr{F})$, If $a,b,\in\mathscr{F}$ and $A\subset B$, then $P(B)-P(A)=P(B\setminus A)\ge 0$.  So far I have:  $A\subset B \implies B\setminus A = B\cap A^c = \emptyset$ as $A$ and $B^c$ are disjoint. Since $A\cup (B\setminus A)=A\cup (B\cap A^c)=(A\cup B)\cap (A\cup A^c)=B\cap\Omega = B$  Then for $A,B\in \mathscr{F}\implies P(A\cup (B\setminus A))=P(A)+P(B\setminus A) = P(B)$ by countable additivity.  Rearranging, $P(B)-P(A)=P(B\setminus A) \ge 0$. One of the great 'coincidences' in physics is that the Sun happens to shine most brightly at exactly the wavelengths our eyes can see; it's an easy explanation that our eyes evolved to make the most out of what was available.  However, this spectral window is also , with Rayleigh scattering and the ozone layer protecting us from the UV and strong water vapour absorption in the IR until way into the radio range.  My question is: is this a coincidence? Were there geological factors that made it so? Or is it just lucky chance? (I also notice other planets in our neighbourhood weren't quite so lucky.) Or had atmospheric absorption been different our eyes would have tuned to whatever spectral window were brighter as a whole? The user who first created a tag wiki is treated as owner for suggested edits was declined by the user who created the tag wiki excerpt, who doesn't yet have the reputation to be a trusted user. (The site is still in beta, and the reputation necessary to be a trusted user is 4000.)        Should the user who first proposed a tag wiki, or a tag wiki excerpt be the one who can unilaterally decide about a proposed edit for a tag wiki? The user who first proposed it isn't necessarily the one who knows if the tag's purpose can be better described with different words, nor does that user necessarily know if the tag has been lately used differently from how it was first used. Since a tag wiki is different from other posts, there should be an exception to the rule "the author of a post can unilaterally decide about any edits."  The paradox is then that the creator of a tag wiki still needs two users to approve their suggested edit. That's what happened in .        The funny fact is that in the revisions for the tag wiki, or tag excerpt (as in the screenshot), the tag wiki/excerpt is said to be created from the Community user.        This bug is  definitely . Daily reputation cap doesn't account for reputation * loss* due to bounty awarded? There are many Q&amp;A's around this and the best explanation of daily cap model is from this answer that uses . It is an old answer but gives a good understanding.   My confusion is in applying this model to my situation yesterday.    On 31/12/2019, I awarded a bounty to , since it became eligible for bounty (2 days after posting it). Subsequently, I got more upvotes (including one accept) which exceeded the daily cap of 200. I am confused about this-loss of reputation due to bounty awarded by me preceeded subsequent gain of reputation so going by the bucket analogy, I should have my rep adjusted accordingly and those 6 up votes (at the bottom of table) should have been credited (rep should have been 177 instead of 117),  /reputation shows this   2 219845 (10)  1 219884 (2)  2 170717 (10)  2 219621 (10)  2 219845 (10) 2 219845 (10) 2 218537 (10)  2 219845 (10)  2 219892 (10)  2 219845 (10) 8 219821 (-100)  2 219845 (10)  2 219621 (10)  2 219845 (10)  2 219821 (10)  2 219845 (10)  2 219845 (10)  2 219845 (10)  2 219912 (10)  1 219912 (15)  2 219845 (10)  2 219845 (10)  2 219892 [10]  2 219845 [0]  2 219621 [0]  2 219845 [0]  2 219845 [0]  2 219845 [0]  2 219845 [0]  -- 2019-12-31 rep +117 = 27089 --   It is not the 6 votes I am bothered about, it is more about trying to correct my understanding  or have I stumbled upon an anomaly? Intel HD Graphics 620: Does my display adapter support HDMI 2.0 necessary for a 4k display? I want to connect my laptop (Inspiron 15 5000 Series) to a 4k display. When I read online about this it seems that HDMI 2.0 is a necessaity to handle the large resolutions / refresh rates involved to get full benefits of a 4k display.  Use case: I'm not going to use this to play games. Most of my use-case is editing documents, emails, spreadsheets and some engineering drawings and video (watching not editing).   The goal behind going 4k is to boost productivity by having more things open at once to read side by side.   I looked into the Dell specs and they only mention an HDMI without going into the details of what type or whether it will support HDMI 2.0 / 4K TV.     How do I tell whether my Dell Inspiron Laptop (i7 7500 U processor) supports this?  I looked under the Display Adapters and can see that I have an "Intel HD Graphics 620"  listed.   Will this suffice to tell me if this display adapter will support HDMI 2.0 / 4k display?   Or should I be checking out some other settings?  Thanks! I have, not one but two microSD cards that my phone (Samsung Galaxy Young, Gingerbread OS) seem to have broken. One is 1GB and the other is 2GB. The 1GB one won't be formatted.  When I put the 1GB one into the computer the computer prompts for a formatting. I don't care for the content so I tried to format it, but to no avail; the format fails and I have no idea what to do to make it work again.  I tried using the SDformatter software, but it can't format the card as it is write protected. I'm googling to solve it but so far no success.  My computer OS is win7 if that's of any relevance. I have a log file being written by another process which I want to watch for changes. Each time a change occurs I'd like to read the new data in to do some processing on it.  What's the best way to do this? I was hoping there'd be some sort of hook from the PyWin32 library. I've found the win32file.FindNextChangeNotification function but have no idea how to ask it to watch a specific file.  If anyone's done anything like this I'd be really grateful to hear how...  [Edit] I should have mentioned that I was after a solution that doesn't require polling.  [Edit] Curses! It seems this doesn't work over a mapped network drive. I'm guessing windows doesn't 'hear' any updates to the file the way it does on a local disk. Calculating the longest distance within polygon in QGIS I want to calculate the "diameter" of polygons in QGIS.  The "diameter" defined as the distance between the two most distant points of the polygon.  I couldn't find a fitting solution in the field calculator. Maybe you have some ideas? Tensor product in dual-space I am a bid confused regarding the notation for tensor products when going into dual-space  If $\left| \Psi \rangle \right. = \left| A \rangle \right. \left| B \rangle \right.$ is $ \left. \langle \Psi \right| = \left. \langle A \right| \left. \langle B \right|$ or $\left. \langle B  \right| \left. \langle A \right|$?  My guess is the last choice, since operators should act on   $\left| 0 \rangle \right. = \left( \begin{matrix}   1 \\   0  \end{matrix} \right) $  $\left| 1 \rangle \right. = \left( \begin{matrix}   0 \\   1  \end{matrix} \right) $  so  $\left| 01 \rangle \right. = \left| 0 \rangle \right. \left| 1 \rangle \right. = \left( \begin{matrix}   0 \\   1 \\   0 \\   0  \end{matrix} \right) $  But then, for me, it should be  $\left( \begin{matrix}   0 &amp; 1 &amp; 0 &amp; 0  \end{matrix} \right) = \left \langle 10 \right|$ But this is not correct if i calculate the tensor product, since   $\left \langle 1 \right| \left \langle 0 \right| = \left( \begin{matrix}   0 &amp; 0 &amp; 1 &amp; 0  \end{matrix} \right)$  For instance, shoulden't it be  $\left| 01 \rangle \right. \left \langle 10 \right| = \left( \begin{matrix}   0 &amp; 0 &amp; 0 &amp; 0\\   0 &amp; 1 &amp; 0 &amp; 0\\   0 &amp; 0 &amp; 0 &amp; 0\\   0 &amp; 0 &amp; 0 &amp; 0\\  \end{matrix} \right) $ ?  I hope I have made my confusion clear Approximate order statistics for normal random variables A game called  is making rounds on social media. I am trying to determine the maximum score attainable for this game.  Let's assume WLOG that only 2s are returned (if 4s are possible the max score is doubled).  First, I'll relax some of the rules to create a game, $\mathcal{G}$, that can achieve a score at least as high as the original, 2048 game.  A run $R$  of $\mathcal{G}_n$ consists of a sequence of moves $m_1,\ldots,m_k$ which manipulate a multiset, $\mathcal{S}$ of maximum size n.  Each $m_i$ is either:   a put $p$, which inserts a 2 into $\mathcal{S}$, or a merge, $\alpha_i$, which replaces two $2^i$ elements from $\mathcal{S}$ with a single $2^{i+1}$ elt.   I allow sequential moves of the same type because 2048 allows multiple merges or no-merge turns.  The score of a position is the sum of $\mathcal{S}$.  What is the maximum score possible on a game of order n?  Note: The final position must have only unique values, else a merge and put would be possible in increase score.  I claim it is $\sum_{i=1}^{n} 2^i$, but couldn't come up with any good induction arguments.  It's pretty easy to prove that an element $2^k$ is producible in a game $\mathcal{G}_k$, but proving an upper bound for production got a bit hairy, and also doesn't cover the full space. Can non-magical persons see the Hogwarts Express during its journey to and from Hogwarts? First order differential equations with 2 varriables Does anybody know how to solve the following differntial equation?  $$w^2\cdot r+\frac{dw}{dt}\cdot r+\frac{dr}{dt}\cdot w=3g$$  where w and r are a function of time so $w(t)$ and $r(t)$. $g$ is a constant  EDIT: This equation came from a thought problem of mine which I will now explain since I still do not know how to approach the problem.  Basically I want to design a spiral track in which a vehicle will accelerate. However the total acceleration needs to be constant.   The vehicle will have 2 acceleration components, a radial component ($a_r$) and a change in speed component ($a_s$). Since we want constant acceleration: $a_r + a_s = constant$  From circular motion we know that $a_r = \omega ^2 r$ where $r$ is the radius, and $\omega$    Further we know that $v=\omega*r$, therefore: $a_s=\frac{d}{dt}(\omega r)$  For constant acceleration $a_{total} = a_r + a_s = \omega ^2 r + \frac{d}{dt}(\omega r) =constant$  Further usefull information: Length of the track covered at a certain time $l=v*t=\omega r t$  With all this the radius will be a function of time, $r(t)$ and the angular velocity will be a function of time, $\omega (t)$  Boundary conditions: $r(0)  = 0$ $\omega (0) = 0$  Now I would like to find a possible set of solutions to create a track by implementing end boundary conditions that i choose e.g. $v(t_{end})=100 [m/s]$ and $l(t_{end})=5000 [m]$  Here is a diagram for clarity: