How can I allow my mouse cursor to pass from larger monitor to smaller based on relative positioning?
Cursor hitting "border" between differently sized monitors
Is there a general formula for image size vs. print size? Unable to boot into Windows after installing Ubuntu, how to fix? I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this? Finishing a proof: $f$ is injective if and only if it has a left inverse I've already done a lot of searching (in particular: ) to try to prove this statement:      $f: A \to B$ is injective if and only if it has a left inverse. [I'm going to also assume $A$ and $B$ are nonempty.]   My attempt so far:     $\Leftarrow$ Suppose $f$ has a left inverse and $f(a_1) = f(a_2)$ for    $a_1, a_2 \in A$. Then there is a function $g: B \to A$ such that   $g\left(f(a_1)\right) = a_1$ and $g\left(f(a_2)\right) = a_2$. Since   $g$ is well-defined, it follows that $g\left(f(a_1)\right) =  g\left(f(a_2)\right)$, and hence $a_1 = a_2$.         $\Rightarrow$Now   suppose $f$ is injective. Then $f(a_1) = f(a_2) \implies a_1 = a_2$.   Furthermore, since $A$ is nonempty, there is an element $x \in A$.   Define $g: B \to A$ by  \begin{equation*} g(b) = \begin{cases}  f^{-1}(b), &amp; b \in \text{Im}(f) \\ x, &amp; b \in A \setminus  \text{Im}(f)\text{.} \end{cases} \end{equation*} This mapping is   well-defined, since if $f$ is injective, $f^{-1}(b)$ is unique.   My main question: does this imply that if $f: A \to B$ is injective that any mapping $g: \text{Im}(f) \to A$ is bijective? Otherwise, I don't understand why we can even use $f^{-1}$ on an element. [Please read the link above for more details - in proof 1.] I need to update a vector layer's data when the visibility is turned back on.  My update does not occur when the visibility is off.  To what signal do I need to connect to catch the visibility change? Is a capacitor in an open circuit charged? Say I have a circuit consisting of a battery, a wire, an open switch, and a capacitor. The circuit is open since the switch is open.  My book says that the capacitor will only be charged when the switch is closed, but I don't see why this is true. I would expect the capacitor to be charged a little - not as much as if the circuit is closed, but still charged none the less.  To further illustrate my point consider this: If the circuit is open, the current must be zero. Consequently the field must be zero. For the field to be zero, the capacitor's field must cancel out the battery's field. Therefore the capacitor must be charged.  Generalizing this concept, shouldn't capacitors be charged (to a lesser degree) in open circuits?  EDIT: In other words, if the field is zero, the capacitor must be charged to cancel out the field of the battery. I've completed 20 suggested edits reviews today. Then, I came across a  and I approved it.   Then, I had a doubt that whether the review count has incremented or not, oh! it's not incrementing. System works fine.  But, take a look at review page,     The edit was already reviewed by one reviewer and then I reviewed it. As I'm the Owner of the post it's enough to approve the edit. But, the review history doesn't show the detail that I had approved it. It's misleading that only one vote of a reviewer who is neither the community user nor the OP nor the moderator, is enough.  So, what should we do in this type of situation?  Is it correct to make OP to review the suggested edit after completing daily limit?  Should we need to display/hide the OP has approved the edit in the review history? Use mathematical induction to prove that 6(n+2) + 7(2n+1) is divisible by 43 for n >= 1.  So start with n = 1:  6(1+2) + 7(2(1)+1) = 63 + 73 = 559 -> 559/43 = 13. So n=1 is divisible  Let P(k): 6(k+2)+7(2k+1) , where k>=1  Show that P(k+1): 6((k+1)+2) + 7(2(k+1)+1) is true  = 6(k+1+2) + 7(2k+2+1)  = 6(k+3) + 7(2k+3)  I'm unsure where to go from here, I've tried several directions after this but have got nowhere. I don't know how to get the 43 or 559 out the front.  Any help would be great How do I run an executable using Lua? Let Y(1), Y(2), Y(3), Y(4), Y(5) denote the order statistics of a random sample of size 5 from a distribution having p.d.f. Help me to solve this problem please..  Let $Y_{(1)}, Y_{(2)}, Y_{(3)}, Y_{(4)}, Y_{(5)}$ denote the order statistics of a random sample of size 5 from a distribution having p.d.f. $f(y) = e^{(-y)}, 0 &lt; y &lt; \infty$, zero elsewhere. Show that $Z_1 = Y_{(2)}$ and $Z_2 = Y_{(4)} − Y_{(2)}$  are independent. Hint: First find the joint p.d.f. of $Y_{(2)}$  and  $Y_{(4)}$. Did the date of Frodo's rescue out of the fire of Mordor have any particular meaning in The Lord of the Rings? Is there any gold standard for modeling irregularly spaced time series? If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree? Any help would be appreciated.  If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree? Correlation coefficient between a (non-dichotomous) nominal variable and a numeric (interval) or an ordinal variable I've already read all the pages in this site trying to find the answer to my problem but no one seems to be the right one form me...  First I explain you the kind of data I'm working with...  Let's say that I have an array vector with several names of city, one for each of 300 users. I also have another array vector with scores response to a survey of each user or a continuous value for each user.  I would like to know if exist a correlation coefficient that compute the correlation between these two variables so, between a nominal and a numeric/continuous or ordinal variables.  I've searched on the Internet and in some pages they suggest to use the contingency coefficient or Cramer's V or Lambda coefficient or Eta . For each of this measure the just say that they could be applied for such data in which we have a nominal variable and interval or numerical variable. The thing is that searching and searching, trying to understand every one of them, sometime is written or watching the examples that they are reasonable to use them if you have dichotomous nominal variable, except for Cramer's V, other time is not written any requirement for the type of data. A lot of other pages say that is right to apply regression instead, that is right, but I would just simply like to know if there is a coefficient like pearson/spearman for this kind of data.  I also think that is no so properly to use Spearman Correlation coeff since the cities are not sortable.  I have also built the function of Cramer'sV and Eta by myself (I'm working with Matlab) but for Eta they don't talk about any p-value to see if the coefficient is statistically significant...  In the matlabWorks site there is also a nice toolbox that says to compute eta^2 but the kind of input it needs is not understandable.  Is here someone that have done a test like mine? If you need more detail to understand the kind of data I'm using just ask me and I'll try to explain you better. Uneven movement on camera following a path. I render a short movie. I set the camera to the circle curve to make it fly in circle. The problem is after render, the camera is a little shaky. Can anyone help me? Thanks first. An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root? Problem: Is there an irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root for $p$ prime? If there is, what is the minimal degree possible?   I can only prove that $x^2-c$ is impossible, by quadratic reciprocity and Chinese remainder theorem. Even the case of $a x^2 - c$ is unknown to me.  Meanwhile, if $f$ is not required  to be irreducible, but only have no root in $\mathbb{Z}$, then $(x^2-a)(x^2-b)(x^2-ab)$ is a solution for non-sqaure $a,b,ab$, since if both $a,b$ are not squares in $\mathbb{Z}/p\mathbb{Z}$, then $ab$ is a square. Yet I still don't know if this is of minimal degree.  Also, it is natural to pose generalizations   When $p$ is not necessarily prime (equivalently for all prime powers). When $p$ is odd prime. When $p$ represents sufficiently large primes (equivalently all but a finite number left). How to find image coordinates of the rendered vertex? I have a simple mesh of a cube.  I would like to know what are the coordinates of each vertex in the rendered image (i.e. for each 3d vertex I'd like to know it's pixel coordinates).  Is there a way to do this?  Clarification:  I'm experimenting with a pose estimation algorithm (i.e. finding out the 3d pose of the object) from a (set of) 2d image(s).  Instead of taking an image of a real object with a real camera I synthetically render the image of a cube using blender.  In this way I know the pose of the object and the intrinsics of the camera, so I can easily validate the results of the pose estimation algorithm. Pose estimation algorithms usually require to provide them with world points on the object and the corresponding image points.  So what I'm looking for is a way to produce a dump of correspondences of the 3d point &lt;--> image point as a byproduct of the rendering procedure. Thanks, Alex I recently installed Ubuntu 17.10, and when I tried to set my keyboard layout to change with alt+shift, I hit a . There is  which works, but then it creates an unwanted behaviour on Firefox (perhaps other programs as well).   After setting alt+shift through gnome-tweak-tool as the combination to change language, whenever this combination is pressed within Firefox, it triggers a toggle that Firefox uses to show/hide the Menu Bar (with File/Edit/View etc.), and 'focus' is taken away from wherever the cursor was.   It's very frustrating, because one has to go and click again at the cursor.  The only solution I found was to permanently enable Menu Bar in Firefox because then alt doesn't do anything and I can use it to change languages. But I don't want to have Menu Bar on top always.  I hope you can understand what I'm trying to explain.  Any thoughts? Is there a good tool/program that allows me to clone a system drive to another, smaller hard drive?  I've bought a new 64GB SSD drive and would like to move my current Windows 7 Professional 64-bit installation to that new drive. My current drive is a 200GB SATA drive with one partition only. Of course there's enough free space to shrink my current partition to less than 64GB. How can I convert audio from MP4 or FLV video files to mp3? Is there an application that allows me to extract the audio from a MP4 or FLV video file and store it as an MP3 file for use in a portable media player? Solving linear congruences by hand: modular fractions and inverses