Does English have written words for each letter in the alphabet?
Is there a formal spelling for the English letter names?
How to get my actual data from ContentNote API in Salesforce using SOQL? Does mass distribution/center of mass affect free fall? An everyday is example would be cars. If you were to drop a car, not taking air resistance into account, would a front-heavy car tumble forward as it fell? And a car with a perfect 50/50 front/rear weight distribution fall straight? Does mass distribution/center of mass affect free fall? Or would they both fall straight down without tumbling? Can you explain why please? class variable vs instance variable --Python How do I have a camera follow my object in Unity? I have an object that automatically moves by itself and I want the main camera to automatically follow it.(Like in games such as geometry dash and jetpack joyride)  This is the code for the automatic moving object in case it is needed:  using UnityEngine; using System.Collections; public class automove : MonoBehaviour { public static int movespeed = 5; public Vector3 userDirection = Vector3.right;    public void Update() {     transform.Translate(userDirection * movespeed * Time.deltaTime);  } }   So does anyone know any good scripts I could add to the main camera to follow this object that automatically moves? Thanks in advance! Multiplying two dimensional data by a constant The second part of an exercise asks that I show:     There does not exist a surjective bounded linear map from $\ell^2(\mathbf{N})$ to $\ell^1(\mathbf{N})$.     The first part was to show that these two spaces are separable in their respective $L^p$ norms.    I've really hit a wall on this one.  I know, in fact, that there does exist a surjective bounded linear map from $\ell^1(\mathbf{N})$ to $\ell^2(\mathbf{N})$.  So my intuition says that if there were also one going the other way, then the two spaces would have to be isomorphic, which is false .  But I don't know of any such theorem that I could apply to "the category of Banach spaces".    My only other idea is to argue by contradiction using the open mapping theorem, but nothing is coming to me...  My guess is that separability is also going to be important, given the first part of the exercise.  -Thanks. Show $\lim_{n \to \infty} n^{-1} E \left( \frac{1}{X}1_{[X>n^{-1}]} \right) =0$ Suppose $X$ is a non-negative random variable satisfying  \begin{align*} P[0 \le X &lt; \infty ]=1. \end{align*} Show   a)  \begin{align*} \lim_{n \to \infty} n E \left( \frac{1}{X}1_{[X&gt;n]} \right) =0 \end{align*} b)  \begin{align*} \lim_{n \to \infty} n^{-1} E \left( \frac{1}{X}1_{[X&gt;n^{-1}]} \right) =0 \end{align*}  What I did  I showed part a) already here is the proof:  \begin{align*} n E \left( \frac{1}{X}1_{[X&gt;n]} \right) \le n E \left( \frac{1}{n}1_{[X&gt;n]} \right)=n\cdot\frac{1}{n}P[X&gt;n]=P[X&gt;n] \end{align*} So $\lim_{n \to \infty} n E \left( \frac{1}{X}1_{[X&gt;n]} \right) \le \lim_{n \to \infty} P[X&gt;n]=0$.  What about part b)? The same techniques no longer works.  I was thinking that  \begin{align*} \lim_{n \to \infty} n E \left( \frac{1}{X}1_{[X&gt;n]} \right) \le \lim_{n \to \infty} n E \left( \frac{1}{X} \right) \le 0 \end{align*} but I am not sure that $E \left( \frac{1}{X} \right) &lt; \infty$ Error when using apt-get update How to use fakeslant as slanted but not italic font with fontspec? Using fontspec with Luatex it is possible to create a fake slant and use that as italic should no italics be around:  \setmainfont[ AutoFakeSlant=0.15 ]             {FontName}   However, also if an italic version exist this faked slant will be used both for \itshape and \slshape. How can I keep using the shipped italic font defined by the ItalicFont= parameter to \setmainfont but use fake slant for \slshape? Hello,    This question is about the Command Line Developer Tools that are usually installed with xcode-select --install and updated via a software update from the Mac App Store (at least until macOS 10.13). I use the developer toolchain on a daily basis and it has always worked and updated without issues.    Today I've updated my mac from High Sierra 10.13.6 to Mojave 10.14.1, and I've lost the ability to update the Developer Tools.    After the update I've executed a terminal command that relies on the developer tools being installed. It was a command to update , although I don't think that the specifics matter, as I believe that any task that tried to access the developer tools would have triggered the same error message.    The error was:   xcrun: error: invalid active developer path (/Library/Developer/CommandLineTools), missing xcrun at: /Library/Developer/CommandLineTools/usr/bin/xcrun       The phrasing was new (maybe), but I thought that it was caused by the usual need to re-install the Developer Tools after some macOS updates.    Later I tried to dig a bit deeper into the failure, and found out that:  $ ls -l /Library/Developer/CommandLineTools/usr/total 0drwxr-xr-x  3 root  admin  96  4 Nov 19:32 share$ which xcrun/usr/bin/xcrun$ xcode-select -p/Library/Developer/CommandLineTools    Still, as I normally do, I entered the command to install and update the Developer Tools in the terminal:  xcode-select --install    This started the usual procedure: modal window to confirm, then request to accept the license agreement, followed by a progress bar. Except that it failed very quickly with an unexpected error:     Can&rsquo;t install the software because it is not currently available from the Software Update server.     I've tried several times, to no avail. It gets always stuck.    Sometimes, however, the failure causes the System Preferences to report a pending update:      If I open that preference panel it starts searching for updates, and it always finds nothing except the first time that it happened. The first time, it found this:          It literally suggested me to install the updates for macOS 10.11 and 10.13. I have no idea why.  I closed the preference without installing, and as I said it hasn't shown them again. There is also no update available in new Mac App Store.   Is this a known issue? Is there any way to resolve the problem?     Update  Of course I can download the Dev Tools for macOS 10.14 installer from .  Before installing them manually, though, I'm wondering if there is anything that's broken with the system. What do LRESULT, WPARAM and LPARAM mean? Should I activate the additional driver: Processor microcode firmware for Intel CPUs for intel-microcode I have recently noticed that there is an additional driver called Unknown: Unknown here which was not there before:    I have already read , and understand why it is there, but my question is, should I activate it? Will this make a difference? Or should I just leave it as it is as it sounds rather useful?    OS Information:  Description:    Ubuntu 15.04 Release:    15.04 Trying to find a story about an unborn telepathic baby who can save a spaceship from doom I was trying to prove following inequality:  $$|\sin n\theta| \leq n\sin \theta \ \text{for all n=1,2,3... and } \  0&lt;\theta&lt;π $$  I succeeded in proving this via induction but I didn't get "feel" over the proof. Are there other proof for this inequality? $\DeclareMathOperator{\tr}{tr}$Let's consider a $n \times n$ matrix and the sequence of traces $\tr(A)=\tr(A^{2})= \ldots = \tr(A^{n})=0$. How to prove that $A$ is a nilpotent matrix (a matrix so that $A^{k} \times u = 0$ for all $u \in V$ and for some $k$)?  Maybe it would be reasonable to consider $A$'s Jordan form (we assume that the action occurs over an algebraically closed field, such as $\mathbb{C}$). For example, suppose that we have found it and $A'$ consists of $m$ blocks of sizes $r_{1}, \ldots r_{m}$ ($r_{1}+r_{2}+\ldots+r_{m}=m, r_{i} \in \mathbb{Z}_{+}$) with $\alpha_{1}, \ldots \alpha_{m}$ as corresponding eigenvalues to each of the blocks. Then, according to the problem will get the system  $$\begin{align} r_{1}\alpha_{1}+&amp;\ldots+r_{m}\alpha_{m}=0 \\ r_{1}{\alpha_{1}}^{2}+&amp;\ldots+r_{m} {\alpha_{m}} ^{2}=0\\ &amp;\ ~\,\vdots \\ r_{1}{\alpha_{1}}^{n}+&amp;\ldots +r_{m}{\alpha_{m}}^{n}=0  \end{align}$$  But the system's analysis over $\mathbb{C}$ seems to be too much complicated.  Actually, the problem must have more or less simple solution.  Any piece of advice would be much appreciated. Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$ I need hint proving this $$\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$$ Is it possible to add entries to the bibliography based on keyword using Biblatex/Biber and within the document code? I would like to print a bibliography which includes all entries with a certain keyword (and possibly some additional entries).  I know that I can filter by keyword when I print the bibliography using  \printbibliography[keyword=&lt;keyword&gt;]   but this will only print entries which I have cited. I could, of course, use  \nocite{*}   to add all entries to the bibliography and then print just those I want.  However, this will make my .bbl file huge as my database is enormous.  Another possibility is to use Biber or another tool to prepare a document-specific .bib file containing only those entries with the keyword. However, this would need to be recreated if additional entries with the keyword are added to my main database files.  Here's an MWE to play with, annotated to indicate the way I'd like it to work ;), and the disadvantages of the way it (almost) works.  The issue of excluding explicitly cited entries is less of an issue for me. The thing I'd really like to work around is adding the entire database contents to the .bbl.  \RequirePackage{filecontents} \begin{filecontents}{\jobname.bib} @book{new-stuff,     author          =   {Watt, Brian},     title           =   {Happy Times with Penguins},     publisher       =   {Harvard University Press},     address         =   {Cambridge, MA},     year            =   1995,     pagination      =   {section},     keywords        =   {happy}} @book{den-coll,   author                =   {Till, Jr., Dennis E.},     booktitle           =   {Penguin Land and Further North: Human Influence},     title               =   {Penguin Land and Further North: Human Influence},     publisher           =   {Oxford University Press},     year                =   2008,     address             =   {Oxford and New York},     keywords            =   {penguin, human}} @book{old-stuff,   author                =   {Harvey, Jr., Dennis E.},     booktitle           =   {Penguin Land and Further North: Human Influence},     title               =   {Penguin Land and Further North: Human Influence},     publisher           =   {Someone \&amp; Daughters},     year                =   1567,     address             =   {Oxford},     bookpagination      =   {paragraph},     keywords            =   {penguin}} \end{filecontents} \documentclass{article} \usepackage[defernumbers=true]{biblatex} \bibliography{\jobname} \begin{document}  \cite{old-stuff}  % what I would like to work % \nocite[keyword=happy] % \printbibliography  % what does work - except that \cite{old-stuff} is ignored and, more importantly, den-coll is added to the .bbl \nocite{*} \printbibliography[keyword=happy]  \end{document} How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the structure of this ring. I'm making exercises to prepare for my ring theory exam:     How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the   structure of the this ring.   I find it always difficult if the ideal is generated by two elements.   I thought about someting like this. $X=2$ and $X^2=3$. Therefore $4=3$ therefore $1=0$. As $2=1$ then $X=0$. And then everyting seems to become $0$.   I'm not sure if I'm allowed to see it this way, but this is the first thing that comes to my mind. It would be nice to be able to put emphasis on specific bits of a fragment or of a quote (bold can help for a quote but I find that it makes things less readable sometimes). What do you think? Update: On , you can highlight particular lines by prefixing each line with @@. See also: Trying to install Ubuntu on Dell XPS 15 (9570) I have been trying to install Ubuntu on my new laptop:     Dell XPS 15 (9570)   Windows 10 Home 64bit English   8th Generation Intel(R) Core(TM) i7-8750H Processor (9M Cache, up to 4.1 GHz, 6 cores)   16GB, 2x8GB, DDR4, 2666MHz   256GB M.2 2280 PCIe Solid State Drive   NVIDIA(R) GeForce(R) GTX 1050Ti with 4GB GDDR5     I began by trying to install Ubuntu 18.04 LTS using an 8GB USB drive. The first issue I ran into was getting frozen on the bootup screen on the fourth dot. After a couple tries, I plugged in my monitor (through HDMI) and it stopped getting stuck all of a sudden.    Next, I tried to go through the installation and when I clicked on restart now, my computer froze and I had to shut it down manually and start it back up again. At this point I got to the login screen and logged in but after entering my password it got stuck on a purple screen with my mouse pointer (which was frozen). I was able to get into a shell at this point (with ctrl+alt+f4) and attempted to run sudo apt-get install nvidia-390 but this froze when it reached building initial module for 4.15.0-22-generic and upon reboot I had to run sudo dpkg --remove -a.    I was unable to work around this so I attempted to install Ubuntu 16.04 which I could only do by adding acpi=off to the boot configuration (which by the way, I had a lot of trouble getting to since GRUB usually flashed in and then immediately disappeared and only occasionally would it stick around long enough for me to use). But when I try to boot up now, I never reach the screen with the five dots and instead immediately get stuck on a purple screen (with no mouse pointer).  I reinstalled Ubuntu 18.04 and am back to being stuck on the log-in screen.  What should I do?