I use kubuntu 18.04 and the biggest number of lines you can scroll by mouse wheel is 12.  With big monitor resolutions and long folder lists (not my doing) I would like to increase the number of lines to e.g. 20 to reduce my finger scrolling.  How can I do that in a way, that it stays permanently after reboot?  I have read, that imwheel should not be used anymore with 18.04.
I find I have to scroll a lot to move the text of my page compared to Windows where I can choose the speed of the mouse wheel.   Does Ubuntu have a similar utility and if so how can I access it?
How can I parse dates and convert time zones in Perl? Can somebody help me understanding the fouries series coefficients?  I know that if we have:  $$f(t) = \sum_{n=1}^N A_n \sin(2\pi nt + Ph_n) \tag{where $Ph_n$ = phase}$$  And because of the $\sin(a+b)$ formula: $$ f(t) = \sin(2\pi nt + Ph) = \sin(2\pi nt )\cos(Ph_n) + \cos(2\pi nt )\sin(Ph_n)$$ Then:  $$\sum_{n=1}^N A_n \sin(2\pi nt + Ph) = \sum_{n=1}^N (A_n\sin(2\pi nt )\cos(Ph_n) + A_n\cos(2\pi nt )\sin(Ph_n))$$ And by definition: $$a_n = A_n\cos(Ph_n)$$ $$b_n = A_n\sin(Ph_n)$$ Then:  $$f(t) = \sum_{n=1}^N A_n \sin(2\pi nt + Ph) = \sum_{n=1}^N (a_n\sin(2\pi nt ) + b_n\cos(2\pi nt ))$$ Where does the $A_n$ in the first formula come from? Could somebody explain me where does the $\frac{a_0}{2}$ in the formula below come from? $$f(x) = \frac{a_0}{2}+\sum_{n=1}^\infty (a_n \cos(nx) + b_n \sin(nx))$$  And the most important:  How can I proof the formulas for the $a_n$ and $b_n$ coefficients?  PLEASE, I'm searchinf for these answers for DAYS. GRUB doesn't show Windows 10 Whenever I boot into my system, Linux directly boots. If I press shift, GRUB shows only Linux, not Windows. Here are results of fdisk and update-grub. I think I have installed Linux the wrong way.  $ fdisk WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk doesn't support GPT. Use GNU Parted.   Disk /dev/sda: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders, total 1953525168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000     Device Boot      Start         End      Blocks   Id  System /dev/sda1               1  1953525167   976762583+  ee  GPT Partition 1 does not start on physical sector boundary.  $ update-grub Generating grub configuration file ... Warning: Setting GRUB_TIMEOUT to a non-zero value when GRUB_HIDDEN_TIMEOUT is set is no longer supported. Found linux image: /boot/vmlinuz-3.19.0-32-generic Found initrd image: /boot/initrd.img-3.19.0-32-generic Found memtest86+ image: /boot/memtest86+.elf Found memtest86+ image: /boot/memtest86+.bin   No volume groups found done How to override Drupal.ajax.prototype.beforeSend? I need to add my own little if's and checks in 3 functions inside   misc/ajax.js (   Drupal.ajax.prototype.beforeSend,   Drupal.ajax.prototype.success,   Drupal.ajax.prototype.error )   How can I override them in my module? I can't find a manual and it's not in Examples for Developers. Sorry if it seems a dumb question, but I'm a php developer - I can work with js, but I'm not so fluent with it.   Can I simply write it in my module's js file? If 2 or 3 modules needs to modify them, how to avoid conflicts? Primary ideals of $\mathbb{Z}$ Let $R=\mathbb{Z}$ I must prove that      In $\mathbb{Z}$ the primary ideals s are precisely the ideals $(p^k)$ where $p$ is a prime number and $n\ge 1$.   $$$$ The definition of primary ideal.     Definition. An ideal $I$ of the ring $R$ is called primary if for all $a,b\in R$ $$(ab\in I\quad\text{and}\quad a\notin I)\Rightarrow b^n\in I, \text{for some positive integer $n$}.$$   Therefore I must prove that      $$(n)\;\text{is primary in}\;\mathbb{Z}\iff n=p^k, k\ge1,p\ge2,\;\text{where}\;p\;\text{is a prime}.$$   Proof ($\Leftarrow$) We suppose that $n=p^k$ for same prime $p$ and $k\ge 1$. Let $a,b\in\mathbb{Z}$ such that $ab\in(p^k)$ and $a\notin (p^k)$. Then $p^k\nmid a$, but $p^k \mid ab$ I no longer know how to proceed.  $(\Rightarrow)$ Let $(n)$ a primary ideal and we suppose for absurd that $n$ is not a power of a prime, then? how could I proceed?  Now, let $ab\in (p^k)$ with $a\notin(p^k)$, then $p^k\mid ab.$ Can I conclude that $p^k\mid b$?   How can I set up the other implication? Thanks If you have a line passing through the middle of a circle, does it create a right angle at the intersection of the line and curve? More generally, is it valid to define an angle created between a line and a curve? Is the tangent to the curve at the point of intersection a valid interpretation (I.e a semi circle has 2 right angles) I saw it in a debate thread and it got me curious now. Is it possible to spawn mobs in random places? How do I backup my Ubuntu Phone? Example of a ring with an infinite inclusion chain of ideals I'm trying to track down an example of a ring in which there exists an infinite chain of ideals under inclusion. (i.e. $I_1 \subsetneq I_2 \subsetneq I_3 \subsetneq...$) Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix I am looking for an intuitive explanation as to why/how row rank of a matrix = column rank. I've read the proof at  and I understand the proof, but I don't "get it". Can someone help me out with this ?   I find it hard to wrap my head around the idea of how the column space and the row space is related at a fundamental level. Suppose there is a message that is encrypted with AES-128-CBC.  The message is as follows, new lines are used to delimit the 16 byte boundary for each block:  Wire funds from: Alice to Bob in   the amount of $ 1   Because this message is encrypted using CBC mode,  any modification of the first block of cipher text would propagate throughout the message.   However, the amount of the fund transfer falls in the last block.  I am under the assumption that an attacker can use the property of  to alter the last block and produce a valid amount that is greater than \$1 in far fewer than $2^{128}$ operations.   Is this a correct assumption?  Is there a name for this attack or do you know of a real world example?    My instinct is that if you just need one byte of the 16 byte block to be of a specific value then it would only require $2^8$ operations because the other 120 bits of the plain text could be any value. For example lets say we wanted the last block of cipher text to decrypt to 9\0 (where \0 denotes a single null byte, and the message would be interpreted as \$9), then it would take only $2^{16}$ operations to find this cipher text block.  Is there something I am missing? What is tail recursion? Let $n \in ℕ$. Show that the ring $ℤ/nℤ$ is a field if and only if $n$   is prime.   Let $n$ prime. I need to show that if $\bar{a} \neq 0$ then $∃\bar b: \bar{a} \cdot \bar{b} = \bar{1}$. Any hints for this ?  Suppose $ℤ/nℤ$ is a field. Therefore: for every $\bar{a} \neq 0$ $∃\bar b: \bar{a}\cdot \bar{b}=1$. How can I show that $n$ must be prime ? What is the "canary thread" and why is it starving? How does a uniform prior lead to the same estimates from maximum likelihood and mode of posterior? I am studying different point estimate methods and read that when using MAP vs ML estimates, when we use a "uniform prior", the estimates are identical. Can somebody explain what a "uniform" prior is and give some (simple) examples of when the MAP and ML estimators would be the same? Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)? I've had no luck with this one. None of the convergence tests pop into mind.  I tried looking at it in this form $\sum \sin n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}$ and apply Dirichlets test. I know that $\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n} \to 0$ but not sure if it's decreasing.  Regarding absolute convergence, I tried:  $$|\sin n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}|\geq \sin^2 n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}=$$  $$=\frac{1}{2}\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}-\frac{1}{2}\cos 2n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}$$  But again I'm stuck with $\cos 2n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}$. Assuming it converges then I've shown that $\sum \sin n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}$ doesn't converge absolutely. C# How do I click a button by hitting Enter whilst textbox has focus? I'm working with a WinForm app in C#, after I type something in a textbox I want to hit the Enter key but the textbox still has focus (flashing cursor is still in textbox), how can I achieve this? When using divs when is it best to use a class vs id?   Is it best to use class, on say font variant or elements within the html? Then use id for the structure/containers?   This is something I've always been a little uncertain on, any help would  be great. What would I prefer - an over-fitted model or a less accurate model? Let's say we have two models trained. And let's say we are looking for good accuracy.  The first has an accuracy of 100% on training set and 84% on test set. Clearly over-fitted. The second has an accuracy of 83% on training set and 83% on test set.   On the one hand, model #1 is over-fitted but on the other hand it still yields better performance on an unseen test set than the good general model in #2.   Which model would you choose to use in production? The First or the Second and why? Install macOS Sierra on VirtualBox? I’m trying to install macOS Sierra on VirtualBox, but can’t seem to make it work. For reference, here are the steps I took.   Downloaded the Install macOS Sierra app from the App Store. Used the inbuilt media creation executable, CreateInstallMedia on a disk image. Created a new VM with the default settings for an OS X El Capitan, plus 128 VRAM. Since VirtualBox refused to accept the DMG, I tried splicing out the InstallESD. VirtualBox now accepted it, but wouldn’t boot. I tried to boot through rEFInd, but still no luck. I tried to patch it both ways (base system and ESD) with iesd. No luck. When booting to GParted LiveCD, it flat-out refused to discover any of the installer CDs.   How can I patch the installer to work with VirtualBox? I don’t want to use pre-patched versions of either the installer or an existing installation, as though to avoid piracy.