How to get memory test in GNU GRUB version 2.04, using ubuntu 20.04
How can I add the Memtest86+ options back to the Grub menu?
I am trying to route a pic32 chip to a  chip and having a bit of a hard time getting all 17 address lines and all 8 data lines connected. I am trying to tie the first 16 address pins to portB pins 0-15 and the data pins to portD 0-7.  After thinking about it for a while I realized that I am probably making my life more difficult by trying to line up rb0 with a0, rb1 with a1, etc. All I really want to be able to do is write a 16 bit value to portB and have the majority of the address loaded and ready. If I make pin assignments based on ease of routing, the logical address will be different between the mcu and the ram, but it should at least be consistent. Since nothing else needs to communicate with the RAM, I don't think it will be a problem if the mcu asks for address 0x101 and the RAM gives it address 0x110.   However, I wonder if it is a good idea. If there is some structure internal to the RAM designed to make sequential reads more efficient, or something like that, then I may want to go to the trouble of routing them 1:1. The pins arrangement on both chips fees somewhat random to me, so it would make it a lot easier on me if I could ignore the particular numbers. Is there any good reason why I should or should not do that? A student is applying to a PhD program in Computer Sciences at Harvard and MIT. He estimates that he has two out of three chances of being accepted at Harvard and two out of five chances at MIT. He further estimates the probability that he will be accepted by both has probability of one to five. What is the probability that he is accepted by MIT if he is accepted by Harvard? Is the event "accepted by MIT" independent of the event "accepted by Harvard".  I don't understand if these are odds or probabilities So light travels slower in glass (for example) than in a vacuum. What causes light to slow down? Or: How does it slow down? If light passes through the medium, is it not essentially traveling in the "vacuum" between the atoms? Need linebreaks in some columns of a wide table I am trying to create linebreaks in some of the cells of my table, since I have long sentences and the table doesn't fit on an A4 page. How to let LaTeX choose the linebreaks?  Here is my code   \begin{table}[hbt] \centering \begin{tabular}{lllllll}     \toprule     &amp;  Raumgewicht $\gamma$'$_m$ and [$\frac{kN}{m^3}$] &amp;Reibungswinkel $\phi$'$_m$[]&amp; Kohäsion c'[] &amp; M$_E$-Wert []&amp; N$_SPT$ [] &amp; k-Wert []  \\     \midrule     Auffüllungen/Deckschicht&amp; 18&amp; 27 &amp; 0 &amp; 10* &amp; 17 &amp; -\\     Rückstausedimente nicht vorbelastes&amp; 21 &amp; 28 &amp; 10 &amp; 10 &amp; 15 &amp; $5\times10^-8$ - $1\times10^-6$ \\     Rückstausedimente vorbelastet &amp; 22 &amp; 32 &amp; 10 &amp; &gt;50 &amp; 91 &amp; $5\times10^-8$ - $1\times10^-6$ \\     Moräne &amp; 22 &amp; 36 &amp; 5 &amp; &gt;50 &amp; &gt;100 &amp; $1\times10^-8$ - $5\times10^-6$\\     \bottomrule \end{tabular} \caption{Bodenkennwerte} \label{tab:Bodenkennwerte} \end{table}   My preamble is  \documentclass[12pt,a4paper]{scrartcl} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx} \usepackage{booktabs} \usepackage{stackengine} \usepackage[top=3cm, bottom=2.5cm, left=2.5cm, right=2.5cm, footskip = 1cm]{geometry} \usepackage{hyperref} How much time is too much time playing educational computer games? I recently bought an iPad primarily for my 3-year-old daughter. I put nothing on it but educational apps and children's books. No YouTube, no Internet, no (non-educational) games. I've decided to let her use it as much as she wants, for now, and see how it goes. That was a few weeks ago.  So far she's been using the iPad maybe 2 to 5 hours each day. She still enjoys other activities -- playing outside, playing with dolls and blocks, interacting with friends, being read to, etc. And I think she might be learning a thing or two from the apps. Still, several hours a day seems like a lot. How do I know if it's too much?  I've searched the web, and there's lots of info on limiting TV time and video games, but I can't find any recommendations on limiting use if it's only educational games.  Relevant: Why is the cone measurable? Problem Denote by $\lambda_n$ the Lebesgue measure on $\mathbb {R}^n$. Let $h \in \mathbb {R}_{&gt;0}$. Let $A \subset \mathbb {R}^{n-1}$ be Lebesgue-measurable with finite measure. Define the cone $C(A,h)$ as the union of all straight lines connecting a point in $A \times\{0\}$ with the point $(0, h) \in \mathbb {R}^{n-1} \times \mathbb{R}$. Prove that $\lambda_n (C(A,h))=\frac{h}{n}\cdot \lambda_{n-1}(A)$. Where I struggle  Assuming that $C(A,h)$ is (Lebesgue-)measurable, this is a simple application of Fubini. How Fubini is used is all clear to me.  However, why is $C(A,h)$ measurable? It seems one could roughly argue as follows: As $A$ and $[0,h]$  are measurable so is $A \times [0,h]$. As $A \times [0,h]$ is measurable it is the union of a null set and a Borel set. $C(A,h)$ is the image of $A \times [0,h]$ under a certain diffeomorphism (c.f. ). Diffeomorphisms map null sets to null sets, and Borel sets to Borel sets. Hence, $C(A,h)$ is (as a finite union of measurable sets) measurable.  Unfortunately, I am not allowed to use the above properties of diffeomorphisms. What are other ways to prove the claim? Please only give a hint to set me thinking. Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$ Apparently $1+2+3+4+\ldots+n = \dfrac{n\times(n+1)}2$.  How? What's the proof? Or maybe it is self apparent just looking at the above?   PS: This problem is known as "The sum of the first $n$ positive integers". Let $f\colon(0,\infty)\to\mathbb R$ be differentiable on $(0,\infty)$ and suppose that $\lim\limits_{x\to\infty} f'(x)=L$.         a. Show that for any $h&gt;0$, $\lim\limits_{x\to\infty} \frac{f(x+h)-f(x)}h=L$.      b. Show that $\lim\limits_{x\to\infty} \frac{f(x)} {x} =L$.   this is a differentiation question.  i don't know how to solve this question  Because it is Korean, it is difficult to deal with this cite. So for me, it is not easy to write.  thank you Restrict the access to suggested edit reviews on deleted posts on an answer deleted as rude/abusive is visible, even without logging in (and for users with less than 10k reputation). These users can't see the answer , via the , or a direct link to the .    This is a potential avenue for spammers, just like the suggested edit spam used to be, but is ; according to the :     In addition, in order to reduce the incentive for spammers to make spam edits that get rejected, suggested edit spam is hidden from logged-out users, so they can't show their clients public-facing pages with spam (so they won't get paid).   For this to work, the spammer would need two accounts, one to post the spam and a second one to suggest an edit. Even if the spam post is quickly nuked, the review link will be active forever. One could argue that logged-in users without 10k reputation shouldn't be able to see the suggested edits either; I'm partial to that. How come Dropbox gets an icon in Finder sidebar? Why can rm remove read-only files? If I create a file and then change its permissions to 444 (read-only), how come rm can remove it?  If I do this:  echo test &gt; test.txt chmod 444 test.txt rm test.txt   ...rm will ask if I want to remove the write-protected file test.txt. I would have expected that rm can not remove such a file and that I would have to do a chmod +w test.txt first. If I do rm -f test.txt then rm will remove the file without even asking, even though it's read-only.   Can anyone clarify? I'm using Ubuntu 12.04/bash. What is scientific mind? I would like to do two things   Increase the size of inmargin area (i.e., customize inner sidebar so that more contents could fit there) Reduce the empty space between the title of block environment and the slide edge (from the example below, the title of block has too much of wasted space to its left which could be used to create more readable sentences)     MWE  \documentclass[xcolor={x11names}]{beamer}  \usecolortheme{structure} \useinnertheme{rectangles} \useinnertheme{inmargin}  \usecolortheme{crane}  \usefonttheme{structurebold}   \usepackage{fontspec}  \usepackage{calc}  \usepackage[inline]{enumitem} % Description list defaults      % To change font     \newcommand{\descriptionfont}{\fontencoding{T1} \fontfamily{bch} \selectfont}      % Label indentation     \newcommand{\descLabOffset}{\widthof{\hspace{2.6mm}}}      % Left of description aligned with the left margin     \newcommand{\descLeftLabMarInd}{0mm - \descLabOffset}      % Left of description aligned with \parindent     \newcommand{\descLeftLabParInd}{\parindent - \descLabOffset}      % Set the list options     \setlist[description, 1]{font=\descriptionfont, leftmargin=*, labelsep=3mm, labelindent=\descLeftLabMarInd, align=left}  \begin{document}   \begin{frame}{Induction Motors}      \begin{block}{Why is induction motor very common?}          Induction motors are very practical for the following reasons          \begin{description}             \item[Rigid] Rigid             \item[Cheap] Cheap             \item[Low Maintenance] Low Maintenance             \item[Self-Starting] Self-starting             \item[No Excitation Needed] No Excitation Needed         \end{description}      \end{block}  \end{frame}  \end{document} The company I work for makes hardware that communicates to the computer though a serial port. Third party companies write software that communicates with our hardware.   There are times when I need to diagnose our hardware. However, a third party software app connects to the serial port when Windows starts up, blocking any other connection. I don't know the name of this application/service and it's not always the same one.  Is there any way to either:   Find the name/pid of the app/service that is currently using a given serial port or Steal the serial port connection from another app.   vb.net preferably, but I'll take a language agnostic answer as well. How to use Parameterized MessageFormat with non-Value attributes of JSF components Any Set with Associativity, Left Identity, Left Inverse is a Group Proof of "continuity from above" and "continuity from below" from the axioms of probability One of the consequences of the axioms of probability ($\sigma$ field and probability axiom) is the "infinite subset" and "infinite union" property, I can't figure out how it follows from them.  if $A_1 \subseteq A_2 \subseteq \cdots$ then   $$P\left(\bigcup_{i=1}^{\infty}A_i \right) = \lim_{k \to \infty} P(A_k)  $$  If $A_1 \supseteq A_2 \supseteq \cdots$ then   $$P\left(\bigcap_{i=1}^{\infty}A_i \right) = \lim_{k \to \infty} P(A_k)  $$ Does it give higher quality to shoot in low-res mode in-camera, or to downsize high-res photos later? Suppose you want to store your photos at some lower resolution, let's say about ~1 MB large.  You own a camera able to make photos at 5 MPix and more.  And, you want to have the maximum quality at the smaller size.  Would it be better to make a photo at highest resolution and then resize it with PC software (with a good filter of course), or to directly set the camera to make photos at 2 MPix only? Why is the inclusion of the tensor product of the duals into the dual of the tensor product not an isomorphism? Let $V$ and $W$ be vector spaces (say over the reals). There is a linear injection $V^* \otimes W^* \to (V \otimes W)^*$ which sends $\sum_i f_i \otimes g_i \in V^* \otimes W^*$ to the unique functional in $(V \otimes W)^*$ sending $v \otimes w \mapsto \sum_i f_i(v) \cdot g_i(w)$ for all $(v,w) \in V \times W$. In the finite dimensional case it is easy to see this is an isomorphism by comparing dimensions on both sides. I'm aware that this is not an isomorphism in the infinite-dimensional case (see Relation with the dual space in the  on tensor products) but I must admit that I'm not sure why. Cardinal arithmetic does not seem help here and, even if it did, I would be much happier to see an explicit example of a functional in $(V \otimes W)^*$ outside the range of this map. I'm having trouble cooking one up myself.  Added: Let me elaborate on my comment about cardinal arithmetic. Suppose that $X$ and $Y$ are infinite dimensional vector spaces over a field $k$. I'm confident that $\dim (X \otimes Y) = \dim X \cdot \dim Y$ holds. It is clear that $|X^*| = |k|^{\dim X}$ since we may identify a functional on $X$ with a function from a basis for $X$ to $k$. Also I think I've convinced myself that if $\dim X \geq |k|$ then in fact $|X| = \dim X$ ie. the cardinality and dimension of a vector space agree when the dimension is larger than the cardinality of the ground field. Consequently, assuming say that $|k| \leq \dim X \leq \dim Y$ it seems we have $$ \dim(X \otimes Y)^* = |k|^{ \dim X \cdot \dim Y} = |k|^{ \dim Y} = \dim Y^* = \dim X^* \cdot \dim Y^* = \dim (X^* \otimes Y^*)$$  which implies that in fact $(X \otimes Y)^*$ and $X^* \otimes Y^*$ are isomorphic but, rather frustratingly, the obvious map does not do the job. Did I make a mistake here? If not, is it generally true (ie without making assumptions about $|k|$) that there exists some isomorphism $(X \otimes Y)^* \to X^* \otimes Y^*$? Rsync filter: copying one pattern only I am trying to create a directory that will house all and only my PDFs compiled from LaTeX. I like keeping each project in a separate folder, all housed in a big folder called LaTeX. So I tried running:  rsync -avn *.pdf ~/LaTeX/ ~/Output/   which should find all the pdfs in ~/LaTeX/ and transfer them to the output folder. This doesn't work. It tells me it's found no matches for "*.pdf". If I leave out this filter, the command lists all the files in all the project folders under LaTeX. So it's a problem with the *.pdf filter. I tried replacing ~/ with the full path to my home directory, but that didn't have an effect.  I'm, using zsh. I tried doing the same thing in bash and even with the filter that listed every single file in every subdirectory... What's going on here?  Why isn't rsync understanding my pdf only filter?    OK. So update: No I'm trying  rsync -avn --include="*/" --include="*.pdf" LaTeX/ Output/   And this gives me the whole file list. I guess because everything matches the first pattern...