How do I get Xubuntu to stop asking to upgrade to 15.04
How do I suppress the "New release '12.10' available" message?
Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$ Let $m,n$ be two integers such that, $m\ge n$. Compute the number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$   There are $n^m$ functions (total).  we subtract from $n^m$ the number of non-surjective functions.  There are $\binom{n}{1}(n-1)^m$ functions missing one element.  There are $\binom{n}{2}(n-2)^m$ functions missing two elements, but how many times did we count this in the previous count ?  Then we have to add this again by inclusion-exclusion but why is the difference always 1? What is the daily reputation cap and how can I hit it? I've found some questions and those two badges "Epic" and "Legendary" regarding the "daily reputation cap". What is it and how can I hit it? Compiling with either XeLaTeX or LuaLaTeX, \emph{} no longer displays text as expected, i.e. in italics. \textit{} works fine. Here is a MWE demonstrating the issue.  \documentclass{article}  \usepackage{fontspec}  \begin{document}      \emph{lorem ipsum}      \textit{lorem ipsum}  \end{document}   Here is the output I get :   I have TeXLive 2016 (MacTeX) installed. I updated it an hour ago with sudo tlmgr update --self --all.  I guess there is something wrong but what ? I'd be happy to have some help. Thank you. I found the problem described in the attached picture on the internet. In the comment sections there were two opposing solutions. So it made me wonder which of those would be the actual solution.  So basically the question would be the following. Assume we would have two identical beakers, filled with the same amount of the same liquid, lets say water. In the left beaker a ping pong ball would be attached to the bottom of the beaker with a string and above the right beaker a steel ball of the same size (volume) as the ping pong ball would be hung by a string, submerging the steel ball in the water as shown in the picture. If both beakers would be put on to a scale, what side would tip?  According to the internet either of the following answers was believed to be the solution.   The left side would tip down, because the ping pong ball and the cord add mass to the left side, since they are actually connected to the system. The right side would tip down, because of buoyancy of the water on the steel ball pushing the steel ball up and the scale down.   Now what would the solution be according to physics? Top Down RPG Movement w/ Correction? Where are all islands and discoverable locations? After taking off in Simpleplanes and flying around over the ocean for a while, I've found a lots of tiny islands all over the place, and a few really big ones that unlock new spawn locations once found.  Large islands appear to also have many discoverable 'locations' around them as well, like airports, carriers, or landmarks.  These locations automatically become available as start points once discovered.  Where can I find all of these major islands, and once there, where should I look to unlock all of the locations? Possible to create new Application Handler? Blender's application handlers are listed , but is it possible to create a new one?  For example, I'd like an application handler which is a callback for every time I add a strip to the Video Sequence Editor. Magic leaves "smudges" and a sorceress becomes a book I could use some help identifying a book I read some time in the last year or so. The book goes between two different stories:  1) A student of magic finds a book in a cave that turns out to be a person transformed into a book. The book talks to the student and they share thoughts. At some point, the student runs away, chase ensues, and at the very end of the book, he manages to travel to another plane.  2) A girl in a religious society where magic is forbidden. She is the daughter of painters. She discovers she can see magic. Falls in love with some random painter, risks performing magic to not be pregnant, does it again so she can, and is arrested and sent to some prison thing.  The common element between the stories is that magic use leaves behind a smudge of some kind that can be visible.  Any assistance is appreciated. Can a concentration spell be cast without actually concentrating on it for an "instant" effect? Capital letters in "Theorem", "Conjecture" etc This is my first post and as you can probably guess I am a mathematician so I have no clue about grammar. I am writing a mathematical document at the moment and I would appreciate some advice on my usage of capital letters. Can somebody please confirm if the following are correct?  1) "We know by T​heorem 4.6.1 that..."   2) "the following c​onjecture, due to..."  3) In order to prove the "Mckay-Stevens $k$-covering C​onjecture, once needs to show that..."  I'm particularly confused about 3).  Many thanks for any help How to add a script to Startup Applications from the command line? How are Pokestops chosen? After playing the game for a little while, I've noticed that Pokestops are chosen seemingly at random locations on the map. A few of them are even in inaccessible places; an abandoned church building, inside of an airforce base, etc. How are these locations chosen as Pokestops? Why do first order languages have at most countably many symbols? Every proof that I read seems to assume that $|L|\leq\aleph_0$. But then how do you model things like field over $\mathbb{R}$ without running out of variable symbols?  More importantly, how can I prove that $|L|\leq\aleph_0$? (This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent pushes a cart of mass, say, $m$, accelerating it from rest to $v_2$, relative to the plane (so relative to the ground, its velocity goes from $v_1$ to $v_1+v_2$). From your perspective, the work done is then $$W = \Delta E = \dfrac{1}{2}mv_2^2$$ but from the perspective of the ground, the work done is $$W = \Delta E = \dfrac{1}{2}m(v_1+v_2)^2 - \dfrac{1}{2}mv_1^2 = \dfrac{1}{2}mv_2^2 + mv_1v_2.$$ Why are these quantities unequal?  I've seen some similar problems, like a body colliding with a wall in different reference frames, but I don't have the physics experience to tell if that question is analogous to this one. So, my apologies if this is a duplicate. :) Design problem - Implement an approval process on case, which sends email to approver showing some additional info, which should not be visible to case owner/agent (who clicked on "Submit for approval" button).  Possible solution - All that additional info will not be stored on Case (otherwise agent will also be able to see it). I am creating a child object to case, where all that additional info be stored. We can make sure agent does not have access to that child object (lets call it ChildObj).   In the email template used, we can include info about that child object. From what i understand, standard email templates dont allow cross object reference. We probably need to use visualforce email templates.  Questions -  1) Can anyone see/point out any issues with that design? 2) I am very new to salesforce. Can anyone give me any example of how i will access child record's field? I mean there won't be any lookup or anything to child object, right? How do i access a field on the child object? Any clue would be helpful I simply know that a single free quark does not exist. What is the reason that we can not get a free quark?  If we can't get a free quark then what is single-top-quark? Correct user names when tracking /etc/ in git repository and committing as root “Fire” a weapon before firearms existed? Did the verb “fire a weapon” exist before the actual introduction of firearms on battlefields?  More specifically, does it make sense for a creative work to have archers (or whatever ranged weaponry) be told to “fire!”, when the world they live in has not yet seen firearms?  It seems some kind of an anachronism to me, since before firearms, “fire” would never propel any projectile...  I've seen several movies do it; I can't remember them all, but for instance I verified it in The Lord of the Rings trilogy (left), Kingdom of Heaven (top right), and more recently Frozen (bottom right):    The first two do it several times (with Kingdom of Heaven also using it on ballistae, and The Return of the King even having Aragorn ask Legolas to ), whereas firearms never appear on the battlefields they feature (Kingdom of Heaven is set in the 12th century; as for The Lord of the Rings, apart from one occurrence of a witchcraft-ish bomb, it's archery and medieval siege engines all the way).  Frozen may be debatable, happening probably somewhere in the 18th or 19th century, but since we only see swords, spears and the like, it made me flinch to hear crossbowmen use “fire!”.  I've also noticed other movies avoiding this, using “loose!” instead, such as Troy (left) and Gladiator (right):    This makes me think it would be the right thing to say instead... although I'm still wondering why not use “shoot”, which seems simpler to me. Bound on the difference of two determinants Let $A$ and $B$ be two real, $n\times n$ matrices. Using Hadamard's inequality, it is not hard to show that $$ \left|\det A - \det B \right| \leq \|A-B\|_{2} \frac{\|A\|_{2}^n -\|B\|_{2}^n}{\|A\|_2 -\|B\|_2}. $$ Where $\|A\|_2=\sqrt{\sum_{i,j}a_{ij}^2}$.  From this, I can derive a sup bound, for example  $$ \left|\det A - \det B \right| \leq n^{n+1} \|A-B\|_{\infty} \max (\|A\|_{\infty}^{n-1},\|B\|_{\infty}^{n-1}). $$ Where $\|A\|_\infty=\sup_{i,j}|a_{ij}|$.   The constant $n^{n+1}$ is not the best bound possible : any reference (or proof) for a better (or the best) one? I show below that one can obtain $n^2(n-1)^{n-1}$, but that isn't much better. I just tried  $10^5$ random matrices on Maple and obtained a maximal constant (much) smaller  than one : this is not a proof, but it looks like there is room for improvement nevertheless.    Just for completeness (and in case someone sees a factor I missed), to get the first bound, writing $A=[A_1,\ldots,A_n]$ in terms of its column vectors, an expansion shows \begin{eqnarray*} \det A &amp;=&amp; \det (A_1 -B_1,A_2,\ldots,A_n) + \det (B_1,A_2,\ldots,A_n) \\   &amp;=&amp; \sum_{j=1}^n \det (B_1,\ldots, B_{j-1}, A_j -B_j,A_{j+1},\ldots,A_n) \\ &amp;&amp; + \det B,  \end{eqnarray*} Thus by Hadamard's inequality, \begin{eqnarray*} \det A -\det B &amp;\leq&amp;  \sum_{j=1}^n \prod_{i=1}^{j-1} \|B_i\|_{2}\prod_{i=j+1}^{n} \|A_i\|_{2} \|A_j-B_j\|_{2} \\ &amp;\leq&amp;  \|A-B\|_{2} \sum_{j=1}^n \|B\|^{j-1}_{2}\|A\|^{n-j}_{2} \\  &amp;=&amp; \|A-B\|_{2} \frac{\|A\|_{2}^n -\|B\|_{2}^n}{\|A\|_2 -\|B\|_2}. \end{eqnarray*}  The second bound is just that $x^n -y^n\leq n \max(|x|^{n-1},|y|^{n-1}) |x-y|$ and $\|A\|_2 \leq n\|A\|_\infty$.    Another approach is calculus, namely, to write that $\det B - \det A = f(1)-f(0)$, with $f(t)=\det(A + t(B-A))$.   By the mean value theorem $f(1)-f(0)\leq \max |f^\prime (t)|$.   We can compute that $$f^\prime(t) =  {\rm trace}\left({\rm Cofm}(A +t(B-A))(B-A)\right)$$  (if I did not mess up, using the formula for the differential of a determinant, where Cofm means the matrix of Cofactors).   Then, it should deliver something better, if there is a nice way to bound it. The simplest thing is to use Cauchy-Schwarz, namely $$ \left|{\rm trace}\left({\rm Cofm}(A +t(B-A))(B-A)\right)\right|\leq \|B-A\|_{2} \|{\rm Cofm}(A +t(B-A))\|_{2} $$ and then, by lack of a better idea,  $$ \|{\rm Cofm}(A +t(B-A))\|_{2}\leq n \max_{ij} |{\rm Cof}_{i,j}(A +t(B-A))|, $$ and brutally, $|{\rm Cof}_{i,j}(A +t(B-A))|\leq ((n-1) \max(\|A\|_\infty,\|B\|_\infty))^{n-1}$ gives a slightly better constant, namely $$ n^2(n-1)^{n-1} &lt;n^{n+1} $$ but that still seems a very rough way to bound a determinant, as it is never sharp, since to attain this bound all coefficients should be equal, and therefore the cofactor would be zero. They are of the same order in $n$, and I suspect this order is wrong. What is the best way to animate the camera path? I'm modeling a car driving along a road(speeds up, slows down, and stops at traffic lights to wait till the lights turn green, etc.) What is the best way to animate the camera path for the following scenario?   The camera starts moving from point A, and it takes 500 frames to get to point B. During this 500 frames, the camera first gradually speeds up, then moves at a constant speed, and finally slows down to a complete stop at point B. The next 50 frames, the camera will stay at point B. From frame 551, it takes another 500 frames to get to point C from point B. The camera experiences the same motion as described in #1 (speeds up, constant speed, slows down, then stop.) Again, the camera will stay at point C for another 50 frames.  Point C to D is a curve path ( added using Shift + A -> add path). I want the camera to move along the path from frame 1101 to frame 1200. The camera should have the same motion as before(speeds up, constant speed, slows down, then stop.)   What is the best way to animate the camera path in this case? Is there any Python scripts available and can be applied to case like this? Thank you all in advance for your replies.