Weird wireframe display on viewport when in camera (or certain angle maybe)  It happens with a certain camera, but it is not like this in perspective view, and I do not think this is overlapping vertices.  May I know what might solve this? I need to show this to my school's presentation and I want my wireframe in my OpenGL render to look clean.

I have recently started using blender and one of the models I'm working on has dark shadows along edges. I started this model from scratch. I can't remember them being there when I first started the model, but I had trouble joining areas together and think I've pressed something I shouldn't have. However, there are so many options I'm not sure what I did.  Here is an image of what I mean   The one on the left has the shadow. As a test I started a new model, which is on the right in the image, and as you can see it doesn't have any shadows.  Also, occluded vertices partially show through the model. Occlusion doesn't work properly.   In orthogonal view small darkened triangles appear along the the edges.    I don't really want to start the model again from scratch so any ideas on how to remove this shadow would be great. Thanks.


A problem asks that based on sample of size n from a Normal($\theta$,$1$) distribution, we find the Uniformly Minimum Variance Unbiased Estimator (UMVUE) for:  $$p=\Phi(x-\theta)$$  Where $\Phi$ is the CDF of the normal distribution.  My problem is understanding how can I find an estimator for something that is not a parameter of the distribution?  I have tried guessing an estimator and improving it, but again, get stuck with estmating a function instead of a parameter.

Suppose that $X_1,X_2,...,X_n$ is a random sample from a normal distribution, $X_i\sim N(\mu,9)$.  Find the UMVUE (uniformly minimum variance unbiased estimator) of $P(X\le c)$ where $c$ is a known constant.  Do this by finding the conditional distribution of $X_1$ given $\bar{X}={\bar{x}}$ and apply the Rao-Blackwell theorem with $T=u(X_1)$, where $u(x_1)=1$ if $x\le c$ and zero otherwise.  So clearly the parameter that we're trying to estimate given the problem description can be written as $\Phi\left( \frac{c-\mu}{3} \right)$ where $\Phi$ represents the CDF of the standard normal distribution.  However, I get stuck when I need to try and find the conditional distribution.  Without knowing the joint distribution or the other conditional distribution, how can I possibly find the conditional distribution of $X_1$ given $\bar{X}={\bar{x}}$?


I know how to use apt source but where are the files of apt source stored?

I am assuming that all application installed through apt-get are open source; but for those that are available in that manner, where can I get the source code for these applications as well as update them?   I have a couple applications I use regularly that aren't being actively developed any longer and I would like to add features. Where would I go to get the rights to update these applications?  In this case specifically, I am referring to the hellanzb package


I was trying to install linux Ubuntu version 12.04 alongside Windows 8 on my Toshiba Satellite but when I restart I can't find the place to switch between the windows and Ubuntu. I have tried using Linux in Oracle Virtualbox and it did well but when I restarted my laptop it didn't show any signs of changing to the Linux OS. the laptop when opened boots direct to windows 8

I installed Windows 7, which ate Ubuntu's boot file. When starting up the computer, it now goes straight to Windows, without giving me the option of booting Ubuntu.   How can I get Ubuntu back?


My boyfriend and I bought a house over the summer and received money as a gift to help with down payment. His mom gave $10000 and my dad gave $14000. we later received a $5000 house warming gift from his grandparents. will we be taxed on receiving these gifts?

A family member intends on gifting us a sum of $70,000 towards the purchase of a new home. My question is - will that family member owe any gift tax on it? I have been reading  that appear conflicting. Basically, the $70,000 is way under the $5.25 Million lifetime exception, but is over the $14,000 annual gift exclusion. Finally, are there any tax consequences for me, as the recipient?  Thanks for looking.


I know that Unit Testing is all about testing individual units of code and mocking the other dependencies like database connections, file I/O etc.  I have a few questions on unit tests   what is that "UNIT" in unit testing that we need to test? Is it a method of a class? or a use-case? Because use-case testing seems more of an integration test to me. Mocking external dependencies. Does it mean to mock all references to any external class even if it is same package?

I know the so-called textbook definition of unit tests and integration tests.  What I am curious about is when it is time to write unit tests... I will write them to cover as many sets of classes as possible.  For example, if I have a Word class, I will write some unit tests for the Word class.  Then, I begin writing my Sentence class, and when it needs to interact with the Word class, I will often write my unit tests such that they test both Sentence and Word... at least in the places where they interact.  Have these tests essentially become integration tests because they now test the integration of these 2 classes, or is it just a unit test that spans 2 classes?  In general, because of this uncertain line, I will rarely actually write integration tests... or is my using the finished product to see if all the pieces work properly the actual integration tests, even though they are manual and rarely repeated beyond the scope of each individual feature?  Am I misunderstanding integration tests, or is there really just very little difference between integration and unit tests?


I want to define my loss function as following picture    How can i do this?

I want to write a conditional expression such as the following.    What is the best way to express such conditional expressions in Latex?


I will add the records in table A to table B. The tables are the same. However, table B is an actively transactional table. When doing the operation, the record in the tableB will continue to be added row.  tableA Id 1 2 ... 1000000 1500000000 1500000001 1500000002 1500000003  tableB  Id 1000001 1000002 ... 80768928   Some of the new records I will add are higher than identity seed, the seed will update to 1500000004. Is there a way to do this without updating this value?     tableB Identity Seed : 80768928   I use these commands when doing the operation:  SET IDENTITY_INSERT tableB ON  INSERT INTO dbo.tableB (...Columns...) SELECT ...Columns... FROM dbo.tableA  SET IDENTITY_INSERT tableB OFf

I have a table with an IDENTITY column. While developing I delete the rows from time to time and add them again. But the IDENTITY values always kept increasing and didn't start from 1 when I added them again. Now my id's go from 68 -> 92 and this crashes my code.  How do I reset the IDENTITY value?


Is there a possibility to color bars of one plot in different colors?  \begin{tikzpicture} \begin{axis}[   xbar, xmin=0,   width=12cm, height=3.5cm, enlarge y limits=0.5,   xlabel={\#participants},   symbolic y coords={no,yes},   ytick=data,   nodes near coords, nodes near coords align={horizontal}, ]   \addplot coordinates {(3,no) (7,yes)}; \end{axis} \end{tikzpicture}     I want to color these bars e.g. in red and blue.

For the bar chart proposed, I would like to use different color for each single bar. How can I  do this?  \documentclass{article} \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture}   \begin{axis}[     title=Title,         xbar,         xmajorgrids = true,         bar width=6mm,          width=12cm, height=5.5cm,          enlarge y limits=0.2,         xlabel={\#number},         symbolic y coords={A,B,C,D},         ytick=data,         nodes near coords, nodes near coords align={horizontal},   ]    \addplot coordinates {(1,A) (7,B) (5,C)(2,D)}; \end{axis} \end{tikzpicture}  \end{document}


The question is prove $\sqrt{2} + \sqrt{3} + \sqrt{5}$ is an irrational number.  I started by assuming the opposite that $\sqrt{2} + \sqrt{3} + \sqrt{5}$  is a rational number. I stated that a rational number is a number made by dividing two integers. So I set $\sqrt{2} + \sqrt{3} + \sqrt{5} = i_1/i_2$, where $i_1$ and $i_2$ are two integers. I multiplied $i_2$ onto both sides and got $i_2\sqrt{2} + i_2\sqrt{3} + i_2\sqrt{5} = i_1$. I then said that in order to turn an irrational number such as $\sqrt{2}$ into a rational number you can multiply, $\sqrt{n}\sqrt{n}=n$. Meaning $i_2$ would have to hold the value of $\sqrt{2}$, $\sqrt{3}$ and $\sqrt{5}$ which is impossible. So it is an irrational.  I think I made a mistake somewhere but I am not sure.

I'm reading R. Courant & H. Robbins'  for fun. I'm on page $60$ and $61$ of the second addition. There are three exercises on proving numbers irrational spanning these pages, the last is as follows.     Exercise $3$: Prove that $\phi=\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Try to make up similar and more general examples.   My Attempt:     Lemma: The number $\sqrt{2}+\sqrt{3}$ is irrational. (This is part of Exercise 2.)   Proof: Suppose $\sqrt{2}+\sqrt{3}=r$ is rational. Then $$\begin{align} 2&=(r-\sqrt{3})^2 \\ &=r^2-2\sqrt{3}+3 \end{align}$$ is rational, so that $$\sqrt{3}=\frac{r^2+1}{2r}$$ is rational, a contradiction. $\square$  Let $\psi=\sqrt{2}+\sqrt{3}$. Then, considering $\phi$, $$\begin{align} 5&=(\phi-\psi)^2 \\ &=\phi^2-\psi\phi+5+2\sqrt{6}. \end{align}$$  I don't know what else to do from here. My plan is/was to use the Lemma above as the focus for a contradiction, showing $\psi$ is rational somehow.  Please help :)  Thoughts:  The "try to make up similar and more general examples" bit is a little vague.    The question is not answered  as far as I can tell.


if (cond1 and cond2) or (not cond1 and not cond2):  Is there a simpler way to write this in Python?

How do you get the  of two variables in Python?  For example, I have two variables that I expect to be strings. I want to test that only one of them contains a True value (is not None or the empty string):  str1 = raw_input("Enter string one:") str2 = raw_input("Enter string two:") if logical_xor(str1, str2):     print "ok" else:     print "bad"   The ^ operator seems to be bitwise, and not defined on all objects:  >>> 1 ^ 1 0 >>> 2 ^ 1 3 >>> "abc" ^ "" Traceback (most recent call last):   File "<stdin>", line 1, in <module> TypeError: unsupported operand type(s) for ^: 'str' and 'str'


I want to create an automaton in tikz and adjust the looseness and bend properties of the edges. If I set the values high, it creates a lot of empty space to the left and below the graphic. In my document, this makes it shift to the right, partially off the page. Here is an mwe.  \documentclass{standalone} \usepackage[dvipsnames]{xcolor} \usepackage{tikz} \usetikzlibrary{automata,calc,positioning} \begin{document}    \begin{tikzpicture}[          node distance=3cm,          clique/.style={fill=SkyBlue},          font=\sffamily,          thick,    ]       \node[clique,state] (B) {B};       \node[clique,state,below=of B] (A) {A};       \node[clique,state] at ($(B) !.5! (A) + (2cm,0)$) (C) {C};       \node[clique,state,right=of C] (D) {D};       \node[state,above=of D] (E) {E};       \node[state,right=of D] (F) {F};       \node[state,below left=of F] (H) {H};       \node[state,below=of F] (G) {G};        \path       (A) edge[bend left] (E)       (A) edge[bend right=10] (F)       (A) edge[bend right] (G)       (A) edge (D)        (B) edge[bend right=100,looseness=1.6,out=270] (H)       (B) edge[bend right=100,looseness=1.6,out=260] (G)       (B) edge[bend left=100,looseness=1.2] (F)        (C) edge[bend left=10] (G)       (C) edge[bend left=20] (F)       (C) edge[bend right] (H)       (C) edge (E)        (D) edge (E)       (D) edge (F)       (D) edge (G)         (E) edge (G)       (E) edge[bend left=80,looseness=2] (H)       ;    \end{tikzpicture} \end{document}   The result is this:    I would have it trimmed to the actual content, as standalone usually does. What causes this and how do I get rid of it?

I have been working on logo for my department and I have the following code. The problem is that whenever I compile the diagram seems to be larger than the actual logo. I do not know what is the problem. I know the numbers I have selected are not the best but any insights into the matter will be highly appreciated.   \documentclass[letterpaper]{article}  \usepackage[top=2cm,bottom=2cm,left=2cm,right=2cm]{geometry}  %\usepackage{amsmath,amssymb,units}  %\usepackage{enumitem,multicol}  \usepackage{tikz}  %\usetikzlibrary{arrows}  \usepackage{lipsum}   \begin{document}   \lipsum[1-2]  \begin{tikzpicture}[y=0.80pt, x=0.8pt,yscale=-1]  \path[draw=black,fill=white]    (258.9527,290.5199) .. controls (173.9885,538.4766) and (568.5860,261.2969) ..    (306.5098,257.1141) .. controls (44.4337,252.9312) and (429.9845,542.5624) ..    (352.9767,292.0206) .. controls (275.9689,41.4788) and (119.6549,497.6604) ..    (334.1376,346.9999) .. controls (548.6203,196.3394) and (66.4622,188.6439) ..    (276.0276,346.0724) .. controls (485.5930,503.5010) and (343.9169,42.5633) ..    (258.9527,290.5199) -- cycle;  \end{tikzpicture}  \lipsum[1-2]  \end{document}    See image below:


Let $f$ be differentiable on $\mathbb R$ with $a=\sup \{|f'(x)| :x\in \mathbb R\}<1$ Select $S_0\in \mathbb R$ and define $S_n=f(S_{n-1})$ for $n \geq 1.$ Prove that $\{S_n\}$ is a convergent sequence.  My attempt  I know that I might have to show that $S_n$ is cauchy since it's convergent. By definition $S_n$ is cauchy if there exists a natural number $N$ such that $m,n>N$ implies $|X_m - X_n| < \epsilon$.  I was given a hint that we have to use the IVT to show that it is cauchy. The professor wrote on the board:  By IVT,  $$|S_{n+1}-S_n|=|f(S_n)-f(S_{n-1})|$$  I understand this step but I don't understand the next few steps  $$ = f'(c)|S_n - S_{n-1}|<a|S_n-S_{n-1}| \\ < a^2 |S_{n-1}-S_{n-2}| \\ a^n|S_1 - S_0|$$

I'm interested in convergence of $f(x_n)=x_{n+1}$ and often hear this term referenced.  What does it mean to be a contraction mapping in the context of the sequence of real numbers given by $f(x_n)=x_{n+1}$? And what does it tell us about such sequence?  A search online gives the answer given by Wikipedia, that it is a function $f$ defined on a metric space $(M,d)$ from $M$ to itself with the property that for some real number $k \in [0,1)$,  $$d(f(x),f(y)) \leq k d(x,y)$$  This definition is quite unhelpful because I barely know what a metric space is. I feel like this definition is to generalized, and I'm interested in in the specific case of recursively defined real sequences $f(x_n)=x_{n+1}$ that there should be a more specific answer to my question.


I'm currently at /opt and running a small shell script. My "no" condition works perfectly, however, my yes condition doesn't work, I 'am still at /opt.  while true; do     read -p "go to log location ?" yn     case $yn in         [Yy]* ) cd /var/tmp/logs; break;;         [Nn]* ) echo "you are @ : " $PWD; break;;         * ) echo "Please answer yes or no.";;     esac done   Any help ??

I want to run a script to simply change the current working directory:  #!/bin/bash cd web/www/project   But, after I run it, the current pwd remains unchanged! How can I do that?


In August 2020 Google updated the Google Groups interface and now nobody I know can figure out how to add members to groups with a display name, it always ends up as their email. You used to be able to enter users as "Jane Doe" jane.doe@gmail.com and they'd get Jane Doe as a display name. That seems to have been removed with no replacement.

I'm a manager on Google Groups for a group that has about 100 members.  I want to be able to edit the display name so I can identify who my users are, instead of "JKL6" for example, which is the prefix for an email address.  First, I can't seem to edit the "Display Name" and second, I have deleted the list of email addresses when I was fooling around with the identity tool.  I was trying to change the settings about display name vs. Google name, and now my "Members" list does not have ANY email addresses showing.


Find all real roots of the following fifth-degree equation  $$x^5+10x^3+20x-4=0.$$  In fact, the only one root is $\sqrt[5]8-\sqrt[5]4$. How to get that?

Find the equation $$x^5+10x^3+20x-4=0$$  My try:I think this equation maybe take  Trigonometric functions  Now I have solution:let     $x=t-\dfrac{2}{t}$,then   $$x^5+10x^3+20x-4=(t-\dfrac{2}{t})^5+10(t-\dfrac{2}{t})^3+20(t-\dfrac{2}{t})-4=0$$   so   $$t^5-4-\dfrac{32}{t^5}=0$$   My question: why we take $x=t-\dfrac{2}{t}$  and This problem have other solution? Thank you


A friend of mine, who likes math and knows I do too, told me he thinks topology is really cool. So, I was wondering if someone could suggest to me some good introductory topology books. Thanks in advance!

I am a graduate student of math right now but I was not able to get a topology subject in my undergrad... I just would like to know if you guys know the best one..


Prove that no group $G$ satisfies $G/Z \approx Q_8$ where $Z$ is centre of $G$  My initial thoughts on this were the following:   The image of a group under an isomorphism with a trivial centre must also have a trivial centre. $Q_8$ has a non trivial centre, $ \{ \pm 1 \} $.   So it would be nice to claim that $G/Z$ has a trivial centre and so we are done. However I do not think this is the case, e.g. $D_8 /Z \approx D_4 $ and the centre of $D_4$ is nontrivial (contains rotation element).   Firstly is my above claims correct, and what ideas should I consider to solve this problem?

Let $Q_8$ be the quaternion group. Show that $G/Z$ can never be isomorphic to $Q_8$, where $Z$ is the center of $G$. Hint: if $G/Z\cong Q_8$, show that $G$ has two abelian subgroups of index $2$.  I'm trying to prove the hint by looking at the canonical homomorphism $\pi:G\rightarrow G/Z$. Well, $Q_8$ has some abelian subgroups of index $2$, such as $H=\{1,-1,i,-i\}$, but that doesn't seem to map to abelian subgroups of index $2$ of $G$. (We know that $\pi(ab)=\pi(a)\pi(b)=\pi(b)\pi(a)=\pi(ba)$ for $a,b$ in $\pi^{-1}(H)$, but that only yields $aba^{-1}b^{-1}\in Z$, not $aba^{-1}b^{-1}=1$.)


I have a consumer-grade vacuum sealer (Aicok) which I regularly use for sous-vide cooking with the manufacturer supplied bags. Under these different scenarios, how long can I keep food for, sealed and refrigerated properly, prior to and after cooking? I am concerned that a lack of air and the different ingredients (e.g. garlic, oil or dairy) pose a potential risk of botulism and decrease safe storage times. Conversely, will the vacuum sealing extend the shelf-life despite being a consumer, rather than a professional product? My estimate is 24 hours top for a marinade and 24 hours storage after cooking, but I realise this is probably extremely conservative.  Poultry e.g. chicken thighs, marinating in a citrus solution with fresh garlic? Beef, e.g. steak, marinating in oil and fresh garlic? Beef or chicken marinating in yoghurt or cream? Any of the above, cooked sous-vide as appropriate, then rapidly cooled in cold water and refrigerated unopened ?

How do I know if a given food or ingredient I have is still good, or if I should discard it?  How can I best preserve a food or ingredient?     This broad question is intended as a "general reference" question to quickly answer many how long will food keep for? questions. Please feel free to edit this question to expand and clarify as needed.


I have a sentence that reads: "To provide you the best possible service..."   I'm being asked to add the word with so that it reads "To provide you with the best possible service..."  Is there a rule for whether or not I add the word with or is it a preference and the sentence works either way?

Does the verb "provide" always have to be used with "with"? For example,  Can you provide me with some good examples? Can you provide me some good examples? Can you provide some good examples?  I suppose it's a transitive verb, isn't it? Moreover, is the following type of usage correct?  You should provide food for your dog before you go on vacation.  If you could give me some good examples regarding "provide" with different types of usage, I'd appreciate that.


Let's assume a very simplified situation. There is only one seller asking for 10$ and there is only one buyer bidding 20$. At what price would the transaction go?   Some answers say it won't, because the ask price has to match the bid price. () Other answers say, that the time ordering is important. () Which answer is correct? What is the final price in the presented situation?

A market has an existing limit buy order at $1.00.  The market then receives a limit sell order at $0.95, what price is the transaction settled at?


I have a carousel slider: 4 elements are visible and 6 are not (simple slide). My problem is this:   Jquery SlideElement.on("click") does not work when elements that are not visible appear. How can I run this?  $(function () {  const sepeteekle = $('.product-card__addtocart');   sepeteekle.on('click', function() {    alert("working working!");   }); });   You can watch the video:

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


To fly like Iron Man does, a great deal of energy is needed. Stark solves this by inventing a miniature arc reactor with a new element powering it. Supposing the energy is there, how is it converted to thrust?

When Iron Man flies he is shown with fire coming out of his feet just like a fuel-propelled rocket.     Where is the combustible material generating the fire coming from? Does he have a fuel tank? What is his operative range?


I am new to latex and i have the following problem. When i use the poker package the following error occurs "poker.sty" not found. I'm using miktex and texmakerx. What is wrong ?

I'm new to LaTeX, investigating using it for some work projects.  I'm using MiKTeX on Windows.  My employer's locked-down network blocks the application's automatic installation function.  I can take my laptop home and successfully install from there, but if I need a package in the middle of the day I'm stuck.  I am able to access the CTAN website and download the package files (.dtx or .ins?), but I don't know what do do with them.  How can I do a manual package installation?


Since I have a lot of different formats of audio It sometimes becomes a hassle when listening to music when I have to bring my aux cord with me into the shower.  I am asking about the bluetooth option because then if I were to have,say, a desktop tape deck I can plug it in via the mic cable and transmit it to my beats pill xl.  Anyways thanks for further help...regards, Thomas

I have a setup where I am monitoring for silence on an incoming stream on 3 different audio cards.  When I detect silence on the master I switch to the secondary, and if I detect silence there I switch to the last card.  The way I have it set up I load/unload the loopback module for each card depending on who's the active card.  This has the inconvenience that I need a 3-to-1 minijack cable to be able to maintain the stream.  Can I load the loopback module and point the output to a single card (independently of the input card)?  How can I route the audio from any input to a single output?


I would like to know whether the date/time/year should be right or left aligned in data tables/table?   Some articles mention right align, while some left align.   Is there any standard followed similar to text and numeric data alignment?  Reference articles:

I have some issues about choosing how to align a Date/time data type in a field. Which is the best way to align this type of date and why? Right or left? P.S We use WPF.  [------25.03.2015] or [25.03.2015------]  Thank you :)


The original power adapter for my Asus laptop is broken. A spare adapter I have with me has different power specifications: Input  Original: 100-240V ~50-60hz 2.0A Spare: 100-240V ~50-60hz 1.5A  Output  Original: 19v - 6.32A Spare: 19v - 3.42A  The polarity matches. Since the voltage is the same, is it safe to use this adapter on my laptop?

I have two laptops (same manufacture), with the same type of power connector.  However, the power supplies/transformers are slightly different.    The output on the first laptop's power supply is 15.6 V at 8.0 A. The output on the second laptop's power supply is 15.6 V at 5 A.  Clearly the voltages are the same, but the currents are different. I assume the second laptop's power supply can not be used on the first, because it can't supply enough power to the laptop.   However, can the first laptop's power supply be safely used on the second laptop?


Is there a single word that refers to the type of word that the words dawn, morning, afternoon, evening, ect are?  I'm looking for something more specific than 'time.'

I'm applying tags to a set of recorded data files, and I have to classify by when the recording appears to be taken (if it's light or dark).  TimeOfDay: Day TimeOfDay: Night TimeOfDay: Dusk  TimeOfDay: Dawn TimeOfDay: Night/Day # (the recording spans both Day and Night)   Is there another term to describe "time of day"?  Edit: As per the comments, removed most of the specific constraints - question now focuses on the terminology.


I would like to create variables to hold strings like f(x)=3x+1 to be inputted into an exam questions.  I can create variables like \funA, \funB, … et cetera. The problem is how do I reference them using A, B, … et cetera.  \documentclass[12pt]{exam}  % conditional statements \usepackage{xifthen}  \newcommand{\exam}{A}  \newcommand{\funA}{$s(t) = 12t^2 -7t + 16$} \newcommand{\funB}{$s(t) = 16t^2 +3t + 10$} \newcommand{\funC}{$s(t) = 12t^2 + t + 10.$}  \begin{document}  \begin{questions}  \question % I would like \fun\exam to return \funA when \exam = a. Sadly it doesn't   The position of an object moving along a straight line is given by \fun\exam. Find the average velocity of the object over the interval $[1,1+h]$ where $h>0$ is a real number.  \question % this works but is a lot to write when accommodating 10 stored functions  \ifthenelse{\equal{\exam}{A}}     {         \newcommand{\function}{$s(t) = 12t^2 -7t + 16.$}     }     {         \ifthenelse{\equal{\exam}{B}}             {                 \newcommand{\function}{$s(t) = 16t^2 +3t + 10.$}             }             {                 \newcommand{\function}{$s(t) = 12t^2 + t + 10.$}             }     }  The position of an object moving along a straight line is given by \function\ Find the average velocity of the object over the interval $[1,1+h]$ where $h>0$ is a real number.  \end{questions} \end{document}

Say I have written two commands, CommandA and CommandB. I wish to have a third command that takes inputs to determines which of the two previous commands to execute. Very naively this how I would try and accomplish this as shown below, however, it does not work.  \newcommand{CommandA}{     \hspace{5mm} } \newcommand{CommandB}{     \vspace{5mm} } \newcommand{C}[1]{     \Command#1 }   So if I call \C{A}, as written I would really execute \CommandA.


I recently popped my tube and I took it out and put a patch on it and made sure that there were no other holes and I didn't find any so I filled it up and rode on it for about an hour, then the next day it was flat. Can you guys please help me!?  And I also patched up the hole in the tire so if anyone can help me that would great.

I have just bought a new bike and had it about a month now. I don't really know much about bikes but I do know how to repair an inner tube.  I have had one puncture and just bought a new inner tube. It worked for a few days and then went down again so this time I got a puncture repair kit. I took the inner tube out to check for any punctures and found nothing. I put it in water and pumped it up and there were no bubbles. I went around the entire tube pushing it next to my ear and heard nothing. I checked the tire to see if anything was wrong - there was nothing that I could see.   So I put it all back together and took it for a ride and got about half a mile and the tire was flat. I pumped it up and got about another half a mile and it was flat again.  Do you have any suggestions for me?


I am quoting the following phrase from my book  " ... in Einstein's picture, photoelectric effect arises from the absorption of a single quantum of radiation by a single electron ...  "  My question:  Why can't multiple photons strike the electron at the same time? After emission from the metal, why doesn't the electron furthers absorbs photons to reach higher kinetic energy than described by Einstein's photoelectric equation ($K_{max} = h\nu - \phi_0$)?   P.S. I apologise for asking a stupid question.

I understand that assuming light is quantized implies that if a lower energy interacts with  metal, it is possible that that quanta will not have enough energy to eject the electron. What prevents two quanta from interacting with the electron at the same time, though, and summing to have enough energy to release the particle. Indeed, what if two separate light rays of the same frequency impact the electron, why can't that free it?


In Diablo 3, when a player joins your game it says the monsters get stronger. What is the amount of increased HP when playing with 2, 3 or 4 people?

What is the maximum party size (if there is one) in Diablo 3?  Additionally, how much of a buff do monsters get when adding party members?     "A new ally has joined, but the minions of Hell grow stronger."


I have the following output:  WordA  1  2  3  4  WordB  5  6  7  8  WordC  9  10  11  12  WordA  13  14  15  16  WordB  I need to grab the numbers between the two words: WordA and WordB I tried (?<=WordA ).*(?= WordB) but the problem is, it grabs ALL the numbers here, including the ones between WordC and WordA that I don't want. I only want to grab the numbers between the 2 pairs which are 1 2 3 4 and 13 14 15 16  Any ideas?

I have this gigantic ugly string: J0000000: Transaction A0001401 started on 8/22/2008 9:49:29 AM J0000010: Project name: E:\foo.pf J0000011: Job name: MBiek Direct Mail Test J0000020: Document 1 - Completed successfully  I'm trying to extract pieces from it using regex. In this case, I want to grab everything after Project Name up to the part where it says J0000011: (the 11 is going to be a different number every time). Here's the regex I've been playing with: Project name:\s+(.*)\s+J[0-9]{7}:  The problem is that it doesn't stop until it hits the J0000020: at the end. How do I make the regex stop at the first occurrence of J[0-9]{7}?


import java.math.BigInteger; import java.util.Arrays;  public class ThreadDemo {      public static void main(String[] args) {          int num_threads = 1000;         MyThread myt[] = new MyThread[num_threads];         for (int i = 0; i < num_threads; ++i) {             myt[i].generatesequence(100);             myt[i].start();         }         System.out.println("all threads spawned");      }  }  class MyThread extends Thread {     public int sum = 0;     public int len = 0;      MyThread(int n) {         len = n;     }      @Override     public void run() {         sum = 0;         for (int i = 1; i <= len; ++i) {             sum += i;         }     }      public void generatesequence(int n) {          // Work out total number of combinations (2^n)         BigInteger bitValue = BigInteger.valueOf(2).pow(n);         int firstOne = n - 1;          // For each combination...         while (firstOne >= 0) {             bitValue = bitValue.subtract(BigInteger.ONE);             firstOne = bitValue.getLowestSetBit();              // Initialise an array with 'n' elements all set to -1             int[] resultForThisCombination = new int[n];             Arrays.fill(resultForThisCombination, -1);              if (firstOne >= 0) {                 // We now go through each bit in the combination...                 for (int bit = firstOne; bit < n; bit++) {                     // If the bit is set, set array element to 1 else set it to -1...                     if (bitValue.testBit(bit)) {                         resultForThisCombination[bit] = 1;                     }                 }                 System.out.println(Arrays.toString(resultForThisCombination));             }          }      } }   Need to create a thread for each configuration. Configuration have only 1 or -1     for sequence of 1 you get an array of      [1]     [-1]     For sequence of 2 you get      [1, 1]     [-1, 1]     [1, -1]     [-1, -1]     Need a thread for each row also the error message i am getting are the following  Exception in thread "main" java.lang.NullPointerException     at ThreadDemo.main(ThreadDemo.java:11)

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


(In Ubuntu 13.10) Ubuntu-SDK opens with the following errors:     Does anyone know how to resolve these dependencies?

Occasionally, when I'm installing stuff, I get an error like the following:  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  package1 : Depends: package2 (>= 1.8) but 1.7.5-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.   How can I resolve this?


The 74HC4051 Mux (spec is here: )  has 8 input/output pins labelled Y, one output/input pin labelled Z, three digital selectors S0, S1, S2, and an active-low enable pin E (bar).  That all seems perfectly reasonable.  There is also Vee which is labelled "supply voltage"  To test the mux, we set S0 = S1 = S2 = E = 0V Then we set Y0 = 3.3V, then 0V  Taking The documenation at face value we set Vee = Vcc = 3.3V When Y0 = 3.3V, Z = 3.3V, which seems reasonable.  But then when Y0 = 0V, Z = 1.4V???    If we set Vee = 0V, this does not happen, but why is it labelled supply, and if it's ground, why is it needed at all?

I've seen lots of schematics use \$V_{CC}\$ and \$V_{DD}\$ interchangeably.    I know \$V_{CC}\$ and \$V_{DD}\$ are for positive voltage, and \$V_{SS}\$ and \$V_{EE}\$ are for ground, but what is the difference between each of the two?  Do the \$C\$, \$D\$, \$S\$, and \$E\$ stand for something?     For extra credit: Why \$V_{DD}\$ and not simply \$V_D\$?


I am getting an error while installing vs code editor in ubuntu 20.04. I am installing through an ubuntu software application Here is the screenshot of the error Please, anyone, help me with this issue.

I just finished the installation of the Ubuntu 18.04, but whenever I try to install any application from Ubuntu Software the same error occurs (for example "vlc"):     unable to install "vlc": snap "vlc" has "install-snap" change in progress   I hope somebody can tell me what I've done wrong.


I tried to access the FPS setting of the render settings in a shader node through a driver expression. The attempt was successful, but I got a warning and a tip saying:  WARNING: Driver expression may not work correctly TIP: bpy.context is not safe for renderfarm usage   According to  the proper way to set the active scene is through bpy.context. Therefor, I assumed, that the proper way to get the active scene would be through bpy.context as well. This warning however makes me feel like there is a more proper way to access scene data (like render settings) through drivers so they would also work in renderfarms. So my question is: How do I properly access this kind of data in a driver expression?

I would like to be able to access properties of the current scene such as render.fps, frame_start, and frame_end from within a python driver script.  I have some data that is defined in terms of seconds, and I'd like the drivers consuming that data to work in two different scenes which have different frame rates.  edit: I tried using bpy.context.scene, but it turns out that is often wrong.  Let me be specific:  The driver is being evaluated to calculate the position of an object in scene "cave" and bpy.context.scene refers to scene "splash" .  In a 1-scene .blend bpy.context.scene works fine.  In a multi-scene .blend, bpy.context is not necessarily populated with what a reasonable person would consider 'the context of the driver'.


Firstly, this is a homework problem so please do not just give an answer away. Hints and suggestions are really all I'm looking for.  I must prove the following using mathematical induction:     For all $n\in\mathbb{Z^+}$, $1+2+2^2+2^3+\cdots+2^n=2^{n+1}-1$.   This is what I have in my proof so far:     Proof: Let $p\left(n\right)$ be $\sum_{j=0}^n 2^j=1+2+2^2+\cdots+2^n=2^{n+1}-1$. Then $P\left(0\right)$ is    \begin{align} \sum\limits_{j=0}^0 2^j=1=2^1-1.\tag{1} \end{align} Hence    $P\left(0\right)$ is true. Next, for some $k\in\mathbb{Z^+}$, assume    $P\left(k\right)$ is true. Then \begin{align}  \sum\limits_{j=0}^{k+1}2^j&=\left(\sum\limits_{j=0}^k  2^j\right)+2^{k+1}\tag{2}\\ &=2^{k+1}-1+2^{k+1}\tag{3} \\ &=2\cdot 2^{k+1}-1\tag{4}\\ &=2^{k+2}-1\tag{5}\\ &=2^{\left(k+1\right)+1}-1.\tag{6} \end{align}   Therefore, $P\left(n\right)$ holds for all $n$.$\;\;\;\;\blacksquare$   Is everything right? My professor went over the methodology in class quite fast (and I had a bit too much coffee that night) and I want to make sure I have it down for tomorrow night's exam.

Since everyone freaked out, I made the variables are the same. $$ \sum_{x=1}^{n} 2^{x-1} $$  I've been trying to find this for a while. I tried the usually geometric equation  but I couldn't get it right (if you need me to post my work I will). Here's the outputs I need:  1, 3, 7, 15, 31, 63  If my math is correct.


I want to root a tiny cheap smartphone that my 6-year-old grandson uses.  He's a real techie, but he's always changing his password and then forgets to tell me so that I can store it in LastPass. So I want to install a parent protection app, where I'm the Admin, and he's a normal user (as on Windows 10). I already have Kaspersky Safe Kids on the phone, plus he has downloaded a lot of games.  There's no space for a parent protection app, and he's not allowed to use stuff like Chrome, so I want to root the phone to allow me to remove pre-installed stuff.  Here's my question: What exactly happens after rooting?  Is a password still needed for the first login after rooting - because I'm sure he's forgotten it.  Will every app have disappeared? (That would be OK.)  Thanks.

This is a common question by those who have just rooted their phones.  What apps, ROMs, benefits, etc. do I get from rooting?  What should I be doing now?


Is there any way to remove individual SE accounts for particular SE sites?  So in other words, say I want to keep my current Stack Overflow account just like it is.  But say I want to delete my account on Server Fault so that it no longer exists and doesn't show up in my SE/SO profile.  Is there any way to do that?  Recap: Keep current login (and certain Stack Exchange sites) but remove particular SE sites' membership for my particular login.  Does that make sense?  Current Accounts Me - StackOverflow Me - SuperUser Me - ServerFault  Desired End Result Accounts Me - StackOverflow Me - SuperUser  Where the desired end result accounts will be the same user (Me) with the persistent questions/answers/reputation/etc.

How can I delete my Stack Exchange account(s)? Also,  What happens to my content? Can I request it be deleted as well? What if I'm suspended, rate-limited, or banned from posting questions or answers? What will happen to my votes? Will other users be impacted? Why wasn't my account deleted immediately after the timer expiring? What will happen to my pending bounties and close, reopen, delete, or undelete votes? I want my account deleted on all Stack Exchange sites. How do I do this? Will my profile on chat be removed once I delete my site account?   For more information, see "" in the .


My site has been live since July this year but is still not showing up on Google.  Any ideas why this would be the case?  Many thanks

This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it?


I was given the state space equation, $\dot{x} = -2x + u$ and told to determine the optimal control law $u=-kx$ which minimizes the performance index   $$J = \int_{0}^{\infty} x^{2}\,dt.$$   My approach was to find the state feedback $k$. But since the value of $R$ (positive definite Hermitian) is not given. That means $R=0$. How do I determine the optimal control for this system where $R=0$?

Given the differential equation $$\dot x = -2x + u$$ determine the optimal control law $u = - kx$ that minimizes the performance index $$J = \int_0^{\infty} x^2 \, \mathrm d t$$  My approach was to find the state feedback $k$. But since the value of $R$ (positive semidefinite Hermitian) is not given, that means $R=0$. How do I determine the optimal control for this system where $R=0$?


I asked this question on Stack Overflow:    Doesn't Stack Overflow also answer questions about "programming tools"? Isn't Eclipse a programming tool? I normally have questions about setting up projects on IDEs such as Qt and Eclipse. Is there any Stack Exchange website that will more willingly answer such questions?  Is Super User a more appropriate site for questions about IDEs?

There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.


def bubble_sort_by(array)   sorted = false    until sorted     swapped = false      (array.length - 1).times do |i|       if yield(array[i],array[i+1]) > 0         array[i], array[i+1] = array[i+1], array[i]         swapped = true       end     end      if swapped == false       sorted = true     end   end   array end   print bubble_sort_by(["hi","hello","hey"]) do |left,right|     left.length - right.length end   Hi I am building a method which sorts an array but accept a block. The block should take two arguments which represent the two elements currently being compared and sorting the element from the smallest to biggest.().  I am expecting the output to print ["hi", "hey", "hello"] However it results in an error message:  source_file.rb:8:in `block in bubble_sort_by': no block given (yield) (LocalJumpError)     from source_file.rb:7:in `times'     from source_file.rb:7:in `bubble_sort_by'     from source_file.rb:22:in `<main>'   Can someone explain where does the error come from, and how can I fix it? Also I realised that if I change the code array (from second last line of the method block) to print array; the code prints out ["hi", "hey", "hello"] which is what I wanted and hence it should mean that my code is correct. Therefore my confusion of where did the error come from and how can i fix it?

I extracted simple example:  require 'pp' x = 1..3 pp x.map do |i| {:value => i, :double => (i*2)} end pp x.map { |i| {:value => i, :double => (i*2)} }  pp(x.map do |i| {:value => i, :double => (i*2)} end) pp(x.map { |i| {:value => i, :double => (i*2)} })   I am wondering why first pp produces:  [1, 2, 3]   While all the oders are giving:  [{:value=>1, :double=>2}, {:value=>2, :double=>4}, {:value=>3, :double=>6}]   I assume it has something to do with operator precedence. Where can I find good explanation?


Is there a continuous bijection from $[0,1]$ onto $[0,1] \times [0,1]$? That is with $I=[0,1]$ and $S=[0,1] \times [0,1]$, is there a continuous bijection $$ f: I \to S? $$  I know there is a continuous bijection $g:C \to I$ from the Cantor set $C$ to $[0,1]$. The square $S$ is compact so there is a continuous function  $$ h: C \to S. $$ But this leads nowhere. Is there a way to construct such an $f$?  I ask because I have a continuous functional $F:S \to \mathbb R$. For numerical reason, I would like to convert it into the functional $$ G: I \to \mathbb R, \\ G = F \circ f , $$ so that $G$ is continuous.

Is there a simple geometric proof that there exists a continuous bijective function between a square and its side?    And is there some explicit continuous function or formula $f^1(z)\mapsto (x,y)$ and $f(x,y)\mapsto z$, with $(x,y) \in [0,1]\times[0,1]$ and $z \in [0,1]$?  And is there a constructive proof that two sets of the same cardinality have a bijective function?


i have a HTML table echoed in PHP:  echo '
                 <input type="checkbox" name="check'.$counter.'" id="check'.$counter.'" onclick=\'add('.$total.', this);\' />	                 '.$result["invoice_number"].'	                 '.$company.'	                 '.$date.'	                 &pound;'.$result["total"].'	                 &pound;'.$result["total"].'
';   so when you hover over it, it highlights the whole row and wherever you click on the row it opens the link but when i check the checkbox it also opens the link - i want to stop this

Consider the following:
   something inside the header
   How can I make it so that when the user clicks the span, it does not fire the div's click event?


How can i convert json date /Date(1439218800000)/ to something like 11 aug, 2015. here is my code

I'm taking my first crack at  with jQuery. I'm getting my data onto my page, but I'm having some trouble with the JSON data that is returned for Date data types. Basically, I'm getting a string back that looks like this:  /Date(1224043200000)/   From someone totally new to JSON - How do I format this to a short date format? Should this be handled somewhere in the jQuery code? I've tried the jQuery.UI.datepicker plugin using $.datepicker.formatDate() without any success.  FYI: Here's the solution I came up with using a combination of the answers here:  function getMismatch(id) {   $.getJSON("Main.aspx?Callback=GetMismatch",     { MismatchId: id },      function (result) {       $("#AuthMerchId").text(result.AuthorizationMerchantId);       $("#SttlMerchId").text(result.SettlementMerchantId);       $("#CreateDate").text(formatJSONDate(Date(result.AppendDts)));       $("#ExpireDate").text(formatJSONDate(Date(result.ExpiresDts)));       $("#LastUpdate").text(formatJSONDate(Date(result.LastUpdateDts)));       $("#LastUpdatedBy").text(result.LastUpdateNt);       $("#ProcessIn").text(result.ProcessIn);     }   );    return false; }  function formatJSONDate(jsonDate) {   var newDate = dateFormat(jsonDate, "mm/dd/yyyy");   return newDate; }   This solution got my object from the callback method and displayed the dates on the page properly using the date format library.


Whenever I import something, it doesn't show up. I have tried it with different objects but it still won't work.  As you can see in the picture, it looks like something is selected but you can't see it.

I try to import .obj files from this project:  - the files contain Polygon Mesh Data.  When I import the obj file into blender, the outliner shows a new mesh added, but nothing is visible in the 3D viewport:      Any help will be appreciated.


I have following sample PHP to print special characters in output. But its not printing any special character.  <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> </head>     <?php     $string = "½ Kg";     ?>   Outputs:   <p>� Kg</p>   I have tried htmlspecialchars() or htmlentities() which is also not helping !!  Then tried setting header inside php.   header('Content-Type: text/html; charset=utf-8');   it says,     Warning: Cannot modify header information - headers already sent   kindly suggest how to print Special Characters

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


If we had a flow in an open vertical pipe kept in atmosphere so that external pressure is equal at both ends and if we try to apply Bernoulli's equation to it would stand to reason that due to pipe being vertical, potential energy is smaller at the lower end so, kinetic energy must be bigger, which is sensible because gravity did positive work and increased fluid's kinetic energy. But, if pipe's diameter is the same on both ends how can we agree this with continuity principle? From this principle, velocity should have been the same. Is Bernoulli's continuity equation applicable here in its simplest form ? Although I am not quite sure what is missing here.

Let try an experiment. If water enter through an end $A$ with some velocity say $v_1$,and leaving end $B$ with speed $v_2$ in a UNIFORM cylindrical tube $AB$ (which is completely filled with water). If we consider 3 cases.  tube is horizontal tube is vertical with $A$ upward tube is vertical with $B$ upward  And we go through the experiment and we got our results, which is $v_1~=~v_2$ So for which case this is valid to? Edit Due to lack of logical answers If we consider Bernoulli's equation $$P+\rho gh+\frac{1}{2}\rho v^2= \text{Constant}$$ So in the case of vertical pipe, we consider two points $A$ and $B$ and now applying Bernoulli's equation here as follows. Let's assume $A$ to be upward, and take $B$ as reference level and applying Bernoulli's equation. $$P_a+\rho gh+\frac{1}{2}\rho v_1^2 = P_b+\frac{1}{2}\rho v_2^2$$ If both are exposed to the atmosphere, then $P_a = P_b = $P_{\text{atm}}$ Then we get $$\rho gh = \frac{1}{2}\rho(v_2^2 - v_1^2)$$  which implies that $2gh +v_1^2 = v_2^2$ So, finally this will prove that $v_1$ never equal to $v_2$ in vertical pipe, but if we consider equation of continuity then mass going in is same as mass coming out so according to equation of continuity $$\Delta m = \rho A_1 v_1\Delta t = \rho A_2 v_2 \Delta t$$ which implies $A_1 v_1 = A_2 v_2$, and in our case $A_1 = A_2$ then according to equation of continuity $v_1 = v_2$. Thus, according to continuity $v_1 = v_2$ in vertical pipe case and according to Bernoulli's equation $v_1$ never equal to $v_2$. How can this be possible? Please guys help me out. Please go through the question and then answer it?


\documentclass{article}   \newcommand{\dd}[1]{\mathrm{d}#1}  \begin{document} \begin{equation} \Delta A_2 = x^2 \end{equation}   This code puts a (1) next to this equation, and numbers later equations accordingly. If I want to reference this equation, say with:  And as you can see in Eq. #,    how would I link it so that if the equation number later changes, I don't have to update the text?

If I am writing a LaTeX document on TexMaker and I want to number my equation but most probably I will be adding details later on and I do not want to fall into retyping it all over again. So if for example I have an equation and currently called equation (1.2) that I want to refer later as in the following sentence "As you can see in (1.2)" but then I had to edit my document in a way that it becomes (1.3) now instead of (1.2) what should I do in order to avoid editing large number of equations and my reference to them?


Follwing this anwser of @Zarko in this question   I still not satisfied, I would like to have rotated long text in one column but this can make trouble to me since it is in multirow environment, which vertical size is equal to sum of heights of spanned lines. this means, that can happens that I will need to additional (empty) vertical space on the next columns. thus, I wonder if there is any way to slove that problem   I tried this code of @Zarko, but the solution as he said I need to additional (empty) vertical space on the next columns. so is there any way to solve that problem with adding any additional (empty) vertical space.  The solution of Zarko by adding additional (empty vertical space ) doesn't fit my needs I'm looking for any different solution than that       \documentclass{article} \usepackage[english]{babel} \usepackage{amsmath} \usepackage[table]{xcolor} \usepackage{tabularx, multirow, makecell, rotating} % \usepackage{graphicx} \usepackage{enumitem}  \usepackage{etoolbox} \AtBeginEnvironment{tabular}{%     \setlist[itemize]{nosep,                         topsep     = 0pt,                         partopsep  = 0pt,                         leftmargin = *,                         label      = $\bullet$,                         before     = \vspace{-0.6\baselineskip},                         after      = \vspace{-\baselineskip}                        } } \makeatletter \def\@rothead[#1]#2{\thead{\\[-.65\normalbaselineskip]   \turn{\cellrotangle}\thead[#1]{#2}\endturn}} \makeatother \begin{document} \begin{center}     \begin{tabular}{ | l | l | p{8cm} |}     \hline \rowcolor{blue!30} \multicolumn{1}{|c|}{\rotatebox[origin=c]{90}{ Cell 1 }}% observe added spaces before and after text in cell     &  \multicolumn{1}{c|}{\rotatebox[origin=c]{90}{ Cell 2 }}         &   Summary                             \\ \hline \multirow{10}{*}{\rothead[c]{very long vertical text very long text up here right here}}     & \multirow{10}{*}{\rothead[c]{very long vertical text very long text up here right here}}         &   \begin{itemize}         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here         \end{itemize}                           \\ \hline \multirow{10}{*}{\rothead[c]{very long vertical text very long text up here right here}}     & \multirow{10}{*}{\rothead[c]{very long vertical text very long text up here right here}}         &   \begin{itemize}         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here         \end{itemize}                           \\ \hline \multirow{10}{*}{\rothead[c]{very long vertical text very long text up here right here}}     & \multirow{10}{*}{\rothead[c]{very long vertical text very long text up here right here}}         &   \begin{itemize}         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here         \item very long text up here right here             \end{itemize}                       \\ \hline     \end{tabular} \end{center} \end{document}   which produces

I would like to create the following table bases on the answer of @Zarko  since i use the same code for another kind of table     \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[table]{xcolor} \usepackage{tabularx} \usepackage{enumitem} \usepackage{etoolbox} \AtBeginEnvironment{center}{%     \setlist[itemize,1]{nosep,                         topsep     = 0pt,                         partopsep  = 0pt,                         leftmargin = *,                         label      = \textendash,                         before     = \vspace{-0.6\baselineskip},                         after      = \vspace{-\baselineskip}                         }     \setlist[itemize]{  nosep,                         leftmargin=*,                         label = $\bullet$                       } }  \begin{document}     \begin{center} \bfseries \begin{tabularx}{\linewidth}{ | l | X |X| }     \hline \multicolumn{2}{|>{\centering\arraybackslash}%                  p{\dimexpr\linewidth-2\tabcolsep-2\arrayrulewidth\relax}|}{\cellcolor{gray!30}     Very long text here and centered     Very long text here and centered     Very long text here and centered}    \\     \hline \multicolumn{3}{c}{}                    \\     \hline Year &   Cycle & Issues     \\     \hline 2018-2019   & High School & very \\     \hline \end{tabularx}     \end{center} \end{document}


I have spent a lot of time writing a project in Microsoft Visual C# 2010 Express. While creating it I used multiple computers and opted to store the files on a external hard drive. While finishing my project, the hard drive crashed. I am using Windows 7.  I now have roughly one tenth of my work remaining when I open the project.   Anybody have any ideas of how I get any of it back?

Last night my 500 GB Seagate hard drive was fine but this morning it suddenly started crashing, somehow I made it work after a chkdsk but 2 partitions show space is full now but it wasn't when the drive was fine. The 3rd partition one is also acting weird.   Whenever I try to open any drive, Windows asks to format it. My drive is still under warranty but I don't want to lose any data. How can I recover data from this crashed/crashing hard drive?   my OS is: windows xp sp3 Processor: Inter Pentium 4 3.0 GHz 1 GB RAM Already have 2 other hard drives  1 - 320 GB - OS drive - seagate 2 - 1 TB - western digital   UPDATE 1: when using Test Disk: it's showing some read errors  UPDATE 2: Now all the partitions are not showing up in my computer, but can see the hard drive in hardware manager, now what to do ?  Here are some screenshots:


I am working on employee data and the data I  have received comes with two cells (Proj Name and Count of Hours) which have multiple names/ hours in the same cell separated by line breaks. I have looked through the solution presented in this link  but it only appears to work when there is one column with multi-line unlike mine which has more than one which needs to be split.

I'm compiling a database of business address info, including key staff for each business. The Google spreadsheet I've inherited for this project includes a column for 'key staff' (in column B), with multiple key staff names listed in the same cell, separated by line breaks (ie CHAR(10) ). There is one business per row. The number of lines in the 'key staff' cell varies row-by-row.  My initial sheet looks like this:    I need to do the following to optimize this sheet:   split each multi-line ‘key staff’ cell so each key staff name appears on its own row. This requires that new row/s be inserted beneath the original row. duplicate the data from all other cells on the original row (i.e. from columns A & C:E), so that each new row contains the full data for each business I need an automated process - I'll have about 1000 businesses to process so can't do this with any manual steps   The sheet should then look like this:    Using =TRANSPOSE(SPLIT(B1,CHAR(10))) obviously only goes part of the way - it doesn’t insert new rows and doesn’t duplicate the surrounding column entries. All help gratefully accepted!


Find all values of $n \in \mathbb N$ for which $3^{2n+1}-2^{2n+1}-6^n$ is a prime number.   Let $k=3^{2n+1}-2^{2n+1}-6^n$. By testing with numbers I got that $k$ cannot be prime for any value of $n$ (tested to $n=20$, so I assumed it's same for every value of $n$).  For $n=1$, $k<0$ $\implies$ $k$ is not prime. (EDIT: oh... it's actually prime if $n=1$. Stupid me calculated $3^3=9$)    For $n>1$: I managed to prove that if $n$ is even, $k$ is not a prime: If $n$ is even, then $$3^{2n+1}\equiv3\ (mod\ 10),\quad 2^{2n+1}\equiv2\ (mod\ 10),\quad 6^n\equiv6\ (mod\ 10)$$ $$\implies k\equiv5\ (mod\ 10)$$ So $k$ is divisible by 5 and therefore not prime.  Using the same method for if $n$ is odd, I get: $k\equiv3\ (mod\ 10)$, which doesn't prove anything.  How do I solve for when $n$ is odd?

Show that $3^{2n+1}-4^{n+1}+6^n$ is never prime for natural n except 1. I tried factoring this expression but couldn't get very far. It is simple to show for even n but odd n was more difficult, at least for me.


Prove that this is true in a nontrivial ring with unity.  If $a^2 = 0$ then $a+1$ and $a-1$ are invertible.  I've seen a few examples and tried out the following solution.  Since $a^2 = 0$:  1 = 1 - $a^2$ = $(1-a)(1+a)$   But I'm not sure if that proves the question. Any help would be appreciated!

Given a ring $R$ (with unity), prove that if $a \in R$ is nilpotent, then $a+1,a-1$ are both invertible.   Suppose $a^n=0$. Then $1=1-a^n=(1-a)(1+a+\ldots+a^{n-1})$, so $1-a$ is invertible.  If $n$ is odd we can use $1+a^n=(1+a)(1-a+\ldots+a^{n-1})$.  But what if $n$ is even?


Say I have a group of athletes and I want to set two different random variables, $ X $ and $ Y $ to build a joint probability distribution of the two random variables. $ X $ has two different discrete values, for example, $ 0 = female $ and $ 1 = male $ and $ Y $ also has two different discrete values, for example, $ 0 = no medal $ and $ 1 = medal $. In this case, what could be the sample space and how can I visualize the sample space?

In stat courses the concept of observational unit is fundamental. When sampling from a population, each element in the sample is called an observational unit (sometimes referred to as an individual). So a sample of size 10 contains 10 observational units (even it the sampling is done with replacement). Each observational unit can have various attributes or variables associated with it. For example, sampling a bunch of cpus from a cpu manufacturing process, each cpu has a clock speed, a physical length, a weight, etc. Sometimes the sample space for this experiment is written as the set of possible weights, or the set of possible lengths, etc. However it seems more accurate to say that the sample space is the set of observational units and that each of the aforementioned variables are random variables which map from the set of observational units to that particular variable's values. I am stuck however and I don't see how to carry this framework over to an experiment of rolling a single die, or tossing two coins. For example, what are the observational units when I toss two coins? Shouldn't there be 4 of them so that I can get a sample space with the same cardinality as {HH, HT, TH, TT}? Any pointers on this would be appreciated.


Part of the description of  states:     A prison in the shape of a box can be up to 10 feet on a side, creating a solid barrier that prevents any matter from passing through it and blocking any spells cast into or out from the area.   If forcecage is cast (in the form of a 10-foot solid box) on a point where an existing spell like  is centered, does it break the concentration of the previously cast area-of-effect spell? Or would it trap the AoE effect inside the box?

When you cast the solid-box variant of , the spell specifies:     A prison in the shape of a box can be up to 10 feet on a side, creating a solid barrier that prevents any matter from passing through it and blocking any spells cast into or out of the area.   Clearly this stops a single-target spell like  from affecting anything inside the box if it's cast from outside the box.   But does it stop an area-of-effect spell like  or , cast on a point just outside the box, from affecting creatures or objects within the box?


Is it possible to change the native low battery notification alert from 10% of remaining battery to 20%?

I have Macbook Air, Mac OS X El Capitan.  There is no warning box shown before the battery is near %15, like it did for Mountain Lion. So I can not notice and my computer goes sleep simply when the battery is off.  And even if it did I generally miss it because I use it external monitor attached to my Macbook Air. And because I play Spotify, I may miss the warning sound, too.  Is there warning box for low battery on El Capitan? If not, is there any utility or software that may help for external monitors and even playing music?


i get </ttd> instead of 	 in the below printf. Can someone please explain why. i want % symbol in my output. But it adds extrac t in my output.  awk '{printf("%0.2f`%</td>`\n",$0)}'   bash-4.3$ echo "50" | awk '{printf("%0.2f	\n",$0)}' 50.00	 bash-4.3$ bash-4.3$ echo "50" | awk '{printf("%0.2f%	\n",$0)}' 50.00%</ttd> bash-4.3$

I want to use printf to print a variable. It might be possible that this variable contains a % percent sign.  Minimal example:  $ TEST="contains % percent" $ echo "${TEST}" contains % percent $ printf "${TEST}\n" bash: printf: `p': invalid format character contains $   (echo provides the desired output.)


I have a variable which is as follows.  let response = [  {} ];   Which is an array with an empty object. What kind of check should I put in place to determine if this response is exactly equal to this. i.e,   [{}] === response; // returns false   I want to have a check that returns false if the response is [{}] how do i do that.  There are already questions on stack-overflow which asks on how to check for an empty object. My Question is that how do I check for an array with an empty object. So completely different. This is no duplicate of any question.

After an AJAX request, sometimes my application may return an empty object, like:  var a = {};   How can I check whether that's the case?


Any situation, any time; this person has always something negative to say about it.  It should be a noun or an adjective to describe a person who is a damp cloud walking over every sunshine situations at the cubicle, hoping to drench other people with his miserable comments.    I considered "sourpuss" but would prefer something more important sounding, like "misogynist."

What is the person called who always thinks negative? E.g.        Mr. X always thinks negative.   Mr. X has negative attitude.      What we can use either? Is there any particular word for this?


I am struggling with understanding the difference in meaning when the definite article is used with certain time expressions:     He is coming back to London, but not until next year.       He didn't win the competition until the next year.   When should the definite article be used? I remember it could to do with denoting the period itself, as in "He has done it in the last year" (past 365 days) and "He did it last year" (2018). Or is it something else? What if I include the definite article in the first sentence or omit it the second?  This question specifically concerns using "until" with those words.

I would like to start planning for next year.   In the above sentence, there is no definite article before the words next year. Should it be present, as in the following sentence which sounds far less natural to me?     I would like to start planning for the next year.   Or, is it more proper to leave it out as in the first sentence? What is the reasoning behind the correct usage in this context?


On , I wrote an answer in which I recommended:  Instead, why not post on Medical Sciences? I was going to say there are  containing the term “fasting” but many of the results are variants on the adjective “fast”, which is quite annoying.  And can I add, also bewildering? I knew better than to search for “fast“ because it is a verb and an adjective. I feared I would also get results containing “fasten” but searching for the noun form fasting–I thought–would narrow the field and produce reliable positive results. Not so, among the many many false positives were things such as:  Is this an indication that my body metabolizes caffeine faster (or slower?) …the chemicals decompose faster before they can cause massive change to their environment. Don't speak fast or act in any way that could frighten the victim. in what way is losing weight faster than this unhealthy? Will taking zinc for colds make my colds go away faster? I'm wondering if our bodies adjust to the constant showering by producing oils faster. One 1998 study shown that microwaving food can lead to faster breakdown of vitamin B12 Since the body cannot get blood to the highest point (brain) fast enough, it cannot function.  I found only one result on the first page, showing a total of fifteen posts, that contained the actual term fasting.  Three randomized controlled clinical trials of fasting in humans were identified, and the results were published in 5 articles, all of … which evaluated the effects of fasting on surrogate outcomes.  What should I have done? If I had also included the terms "diet" and "healthy“ in the search box that would not have improved the results by all that much, and in the post actually containing the term fasting only the term “healthy” is used. Shouldn't the term “fasting“ be easy to find on a Stack Exchange site dedicated to health?

After the performance problems we have run into with  we've decided to make a change, we're moving the network on to .  Here's where to get started:   What works:   All search operators should be in Many changes below from the old search behavior   What's different:   The new search is AND, adding a search term will narrow your results, not expand them. The look of search results is now more unified with the following differences between Q&A:   "Q:" or "A:" prefix Answer counts and tags will be present in questions. The answer count will be highlighted in green if it's accepted. (We may index other things later, that's why the results are more generic/google-y now.)  It's faster, about 5-10x faster for almost all searches on large sites like Stack Overflow Quoted phrases are exact matches except for case-sensitivity, for example,  or . If not in a quoted phrase, words will now be stemmed () Snippets for context will now be more relevant Excludes are now explicitly supported (like -term and -"my phrase") We don't roll up to the question anymore, if you searched for something that matched an answer, we'll show you the answer directly in search results The search per minute limit is effectively gone, it'll block a bot, but no one else should hit it... We'll be monitoring performance though infavorites:mine is back, with infavorites:12345 (any user id) added   What needs work:   What you tell us is broken... Do your worst.   Testing, not yet final:   New range support, here are some examples:   answers:1..1 (exactly one answer) answers:10..20 (10 to 20 answers) created:2008..2009 (created between Jan 1st, 2008 and Dec 31, 2009) created:2010-04..2010-05 (created between April 1st, 2010 and May 31st, 2010) created:2011-01-05..2011-01-06 (to be clear: it goes to end-of-day) This range syntax applies to a new advanced operator: lastactive: and the other numerical ranges, views:, and score:  Additionally, the above syntax is a bit more flexible if you forget it exactly (e.g. score:20-30) in an effort to be intuitive as possible, give it a try - tell us what you think.    I'll try and improve the search as much as possible before it becomes default... At the very least we want it equivalent in relevance and functionality before the switch, but ideally much better. We won't switch until then.  Please give it a try, tell us what you think here, and we'll continually improve it over the holidays as time allows. Bear in mind you may get a search offline page during this test if a change we're making for results necessitates a reindex, and even that should only last about two minutes here on Meta Stack Overflow.  Give it your worst, compare results to the old search, tell us what's better and what's not. We look forward to the feedback.  Update The new search is now the default across the network - we'll be monitoring things over the next few days and would appreciate reports of any crazy behavior you see here.


I have 2 json objects in node.js  x= { '20': { length: '2', payload: [ '11', '22' ] } }; y= { '23': { length: '2', payload: [ 'ef', 'ab' ] } };   I want to combine them such that they become;  z=  {     '20': { length: '2', payload: [ '11', '22' ] },     '23': { length: '2', payload: [ 'ef', 'ab' ] }, };   How can this be done in node.js?    EDIT: I found an easy answer myself. Cannot answer as question has been marked as duplicate.  Use underscore module.   var _under = require("underscore");  z= _under.extend(x, y);

I need to be able to merge two (very simple) JavaScript objects at runtime.  For example I'd like to:  var obj1 = { food: 'pizza', car: 'ford' } var obj2 = { animal: 'dog' }  obj1.merge(obj2);  //obj1 now has three properties: food, car, and animal   Does anyone have a script for this or know of a built in way to do this?  I do not need recursion, and I do not need to merge functions, just methods on flat objects.


I have small problem. I want to show all tables in my ArrayList  The code:  Integer[] numbers = {4, 7, 2, 1, 14, 23, 10, 5};   ArrayList<Integer[]> list = new ArrayList<>();      list.add(numbers);     list.add(numbers);     list.add(numbers);     list.add(numbers);      System.out.println(list.size());      show(list);     public static <T> void show(ArrayList<Integer[]> arg){     for (Integer[] i: arg){         System.out.println(i.toString());          }   All i see is:  [Ljava.lang.Integer;@60e53b93 [Ljava.lang.Integer;@60e53b93 [Ljava.lang.Integer;@60e53b93 [Ljava.lang.Integer;@60e53b93   Use toString to view all records?  Thank's for help.

In Java, arrays don't override toString(), so if you try to print one directly, you get the className + '@' + the hex of the  of the array, as defined by Object.toString():  int[] intArray = new int[] {1, 2, 3, 4, 5}; System.out.println(intArray);     // prints something like '[I@3343c8b3'   But usually, we'd actually want something more like [1, 2, 3, 4, 5]. What's the simplest way of doing that? Here are some example inputs and outputs:  // Array of primitives: int[] intArray = new int[] {1, 2, 3, 4, 5}; //output: [1, 2, 3, 4, 5]  // Array of object references: String[] strArray = new String[] {"John", "Mary", "Bob"}; //output: [John, Mary, Bob]


I get nullpointer exception when try to load properties from file.  I read some solution,    putting property file next to the class loading with our without using GetClassLoader   No success  see the pic   Load fails, not the access, what did I wrong ?  Thanks for your help in advance.  Cs

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


When I try to mirror my image, it turns out to be the second picture. The first picture is it before it is mirrored. These are steps I did before to get it ready to be mirrored and to mirror it:  Prep for Mirror: Make sure that everything is deselected. If not, press the A key. Make sure you are in Edit mode. Left-click the Face Select mode button. Right-click the face on the flat side of the tail that's highlighted in the video. Press the X key. On the Erase menu, click Faces. The faces on that side of the creature's tail should be gone. If you accidently delete the wrong face, you can always undo by pressing CTRL + Z. You can then go back and redo the steps above. Press and hold SHIFT and right-click the faces on the flat side of the character's head. Press the X key. On the Erase menu, click Faces. The faces on the flat side of the creature's head should be gone. Press and hold SHIFT and right-click the faces on the flat side of the creature's chest. Press the X key. On the Erase menu, click Faces. All the faces that you need to remove should be gone.  To Mirror: Switch from Edit mode to Object mode. In the Object Modifiers mini-window, left-click Add Modifier and left-click Mirror. Left-click Merge Limit and type 0.1010. Press ENTER. CAUTION: Do not click the Apply button yet.      Any help would be great on why it isn't the same or not proportionate.  Thanks!

When I add a mirror modifier it sometimes doesn't mirror correctly, giving me an overlapping mesh. How can I fix this?


I was trying to install a mod in Minecraft when I noticed that don't have a bin folder. This is in version 1.7.4.

I've recently changed to the new Minecraft launcher, and I have noticed a change in the .minecraft folder layout. I can no longer install mods just by copying it over into the versions/1.6.1 jar file, as this file refreshes every time it is launched.  For those who don't know what I am talking about, here is the new layout:    I am specifically trying to install Optifine, which does work with 1.6.1. Where do I drag in the mod files now? I can't seem to find a jar file that is suited to it, except in the version folder, but as I stated above, this refreshes every time.  After copying a recent version and renaming it in the version folder, I get this error in the development console:   Unexpected exception refreshing version list java.lang.IllegalArgumentException: Version '1.6.1' is already tracked     at net.minecraft.launcher.updater.VersionList.addVersion(VersionList.java:91)     at net.minecraft.launcher.updater.LocalVersionList.refreshVersions(LocalVersionList.java:44)     at net.minecraft.launcher.updater.VersionManager.refreshVersions(VersionManager.java:47)     at net.minecraft.launcher.Launcher$2.run(Launcher.java:164)     at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source)     at java.util.concurrent.FutureTask$Sync.innerRun(Unknown Source)     at java.util.concurrent.FutureTask.run(Unknown Source)     at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)     at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)     at java.lang.Thread.run(Unknown Source)


I have been getting the :unresolved external symbol "public static int __cdecl Memory::Read (unsigned __int64,unsigned __int64_" for my declaration of a template function "Read"  It is defined in a class known as "memory" with the header file:   #ifndef MEMORY_H #define MEMORY_H  #include <string> #include "DataFuncs.h"  using namespace std;    class Memory {      public:         template <typename type>         static type Read(DWORD64 Address, SIZE_T size);         static bool Write(DWORD64 Address, uintptr_t Value, SIZE_T size);          };  #endif   Its .cpp definition is the following:  #include "Memory.h"  template <typename type> type Memory::Read(DWORD64 Address, SIZE_T size) {     return Data.Read<type>(Process_ID, Address, size); }  bool Memory::Write(DWORD64 Address, uintptr_t Value, SIZE_T size) {      if (Data.Write(Address, Value, size))         return true;     return false; }   The error does not occur until it is actually used in a different file. Its implementation is as follows:  #include "Memory.h" #include "Special_Functions.h"  __int32 Special_Functions::Test(){      __int32 x = Memory::Read<__int32>(0x20302, sizeof(__int32));     return x; }   If I take away the Memory::Read<__int32>(0x20302, sizeof(__int32)); line and just type return 53 then no compiling problems occur. Any idea why and how to fix it? Thanks!

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I use Firefox with an addon to access silverlight contents. After upgrading I can't make it work again to watch Netflix.

I understand that getting netflix to work on linux has been answered multiple times in many places. This question is a little different because:   Firefox ended support for NPAPI plugins with firefox 52, so my usual solution of using pipelight with a user agent over-rider will no longer work Due to the inclusion of widevine on linux, this problem really shouldn't be happening.   First, my problem. It seems that netflix is unable to recognize that it should be using widevine. When I use a non-Windows UA, it tells me to install silverlight, when I use a Windows UA, it just sits at a black screen. I have tried numerous different UAs. Widevine is listed in about:plugins.


I have an IBM Thinkpad and want to install Ubuntu. These are my specs:   512mb ram ATI mobility radeon 7000 graphics card   I don't know the rest  Is it possible to install Ubuntu 13.04 on it?

For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?


I'm trying to find a program or terminal code that can write a 3.1 GB Windows 7 Installer File to a 32 GB USB3+ flash stick.  I have tried the Startup Disk Creator but it won't select the Windows installer File. Any suggestions that I could use? (I'm new to Ubuntu)

I'd like to create a Windows bootable USB stick, but I don't have a Windows machine with me at the moment to do so. How could I achieve the same using Ubuntu?


I started learning about mathematical logic a short while ago, when I stumbled upon the formal definitions of the terms propositions and axioms. According to Wikipedia,     An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments   In one of the video lectures on introductory logic that I was watching, famous unsolved conjectures(such as Goldbach's conjecture and Riemann's Hypothesis) were being discussed, this question struck my mind:     Why can't unproven hypothesis\conjectures be assumed as axioms to derive more useful results? Why is it that a proposition like Axiom of Extensionality qualifies as an axiom, while a proposition like Goldbach's conjecture does not?   The fact that these conjectures and hypothesis assert certain results about properties of numbers(or other abstract mathematical entities), which themselves are described by axioms(such as those in ZFC) does give a feeling that axiomatic systems like ZFC are more fundamental, but I feel being fundamental is a subjective notion. In any case, I seek an answer. Maybe I'll narrow down my question to this:     What qualities must a proposition possess in order to qualify as an axiom(and not, say, a conjecture/hypothesis)?

Thus, axioms are propositions we assume to be true and we use them in an axiomatic theory as premises to infer conclusions, which are called "theorems" of this theory.  For example, we can use the  to prove theorems of arithmetic.  This is one meaning of the word "axiom". But I recognized that the word "axiom" is also used in quite different contexts.  For example, a group is defined to be an algebraic structure consisting of a set $G$, an operation $G\times G\to G: (a, b)\mapsto ab$, an element $1\in G$ and a mapping $G\to G: a\mapsto a^{-1}$ such that the following conditions, the so-called group axioms, are satisfied:   $\forall a, b, c\in G.\ (ab)c=a(bc)$, $\forall a\in G.\ 1a=a=a1$ and $\forall a\in G.\ aa^{-1}=1=a^{-1}a$.      Why are these conditions (that an algebraic structure has to satisfy to be called a group) called axioms? What have these conditions to do with the word "axiom" in the sense specified above? I am really asking about this modern use of the word "axiom" in mathematical jargon. It would be very interesting to see how the modern use of the word "axiom" historically developed from the original meaning.   Now, let me give more details why it appears to me that the word is being used in two different meanings:  As peter.petrov did, one can argue that group theory is about the conclusions one can draw from the group axioms just as arithmetic is about the conclusions one can draw from the Peano axioms. But in my opinion there is a big difference: while arithmetic is really about natural numbers, the successor operation, addition, multiplication and the "less than" relation, group theory is not just about group elements, the group operation, the identity element and the inverse function. Group theory is rather about models of the group axioms. Thus: The axioms of group theory are not the group axioms, the axioms of group theory are the axioms of set theory.  Theorems of arithmetic can be formalized as sentences over the signature (a. k. a. language) $\{0, s, +, \cdot\}$, while theorems of group theory cannot always be formalized as sentences over the signature $\{\cdot, 1, ^{-1}\}$. Let me give an example: A typical theorem of arithmetic is the case $n=4$ of Fermat's last theorem. It can be formalized as follows over the signature $\{0, s, +, \cdot\}$: $$\neg\exists x\exists y\exists z(x\not = 0\land y\not = 0\land z\not = 0\quad\land\quad x\cdot x\cdot x\cdot x + y\cdot y\cdot y\cdot y = z\cdot z\cdot z\cdot z).$$ A typical theorem of group theory is  which states that for any finite group G, the order of every subgroup H of G divides the order of G. I think that one cannot formalize this theorem as a sentence over the "group theoretic" signature $\{\cdot, 1, ^{-1}\}$; or can one?


I have the product $\prod_{k=1}^\infty \frac{2^k-1}{2^k}$. I know that every successive partial product will necessarily be smaller than the last, as we are multiplying always by a number smaller than 1. But, as the expression keeps getting bigger as k does, and it does so very fast, does this product actually converge on a constant different than $0$? I tried calculating the first partial products but just saw that the terms kept approaching $0.28$. It looks like a very random number, is this just a case of slow convergence to $0$? I have no idea of how to calulate this, any help would be appreciated.

Is there any elementary proof that the limit of infinite product $\prod_{k=1}^{\infty}(1-\frac{1}{2^k})$ is not 0?


I am trying to set the default behavior for downloading files in Firefox. Currently it opens a nasty dialog "open with or save", and i can tick a checkbox to perform selected action for this mimetype in future.  What I want, is to save files without opening any dialogs for all, even unknown mimetypes (just ignoring what the type is). I know there is browser.altClickSave option, i need its behavior for simple click. It's ok if the solution will first check mimetype preferences or ignore them.  Please don't tell me to add entries to mimetypes.rdf file in profile, this is just a hack. AFAIK it does not allow to set default or wildcard. By the way, it is very unreliable to edit this because i have to do it by hand (Firefox lacks functionality of adding/removing entries in Settings->Applications list).  Also please don't discuss security of the mentioned dialog for new types downloads, i basically don't run every file that i download.  If it is not possible to do with bare firefox, any solution with extensions is ok. Using macros is not good because we will waste time on opening dialog and waiting for "ok" button to be active for 3 seconds.

The symptoms   Users open their web mail accounts, click on some attachment, and click "Open with Word". Users edit their precious documents for hours. Users save word doc and exit.  Users can't find file.  Users grab torches and pitchforks (last step optional).     The cause of the problem  The download dialog for Firefox shows two options: "Save file" and "Open with".     By choosing "open with", Firefox downloads the file to a temp folder and opens the associated application. I want to prevent this behavior.   What I tried  I made my homework and searched the , and the Knowledge Base (like ,  or ) and if I understood correctly, the download dialog box will depend not on the file's extension, but rather on its mime type.  I know I can set the behavior by going to Preferences > Applications, like this:    However:    Firefox relies on the mime type informed by the server. But it can be itself incorrect, omitted, or redundant (one file type can have multiple mime types, or vice-versa).  Firefox remembers the "Do this automatically for files like this from now on" check-box on a per-mimetype  basis. If I want to enforce a certain behavior, I have to manually set it for each mime type. I can not create new entries in the applications list. It is populated only when a new download is made from an unregistered mime type. Only then I can change the behavior in the list. I can edit the  file, forcing the "save file" behavior, but I couldn't find a way to enforce this to all files.   What I need is a way to (preferably) make it impossible to open with an external application, or at least to force the file to be saved.  I know I can set browser.altClickSave in about:config to have it save the file when I click pressing ALT, but I need some solution that does not require user interaction.


I've been using \documentclass{article}, but would like to set a default font outside the range of that document class.   The recommended solution I found on tex.exchange was to use KOMA-script, but this has changed the default font and somehow made my document longer.   Is it possible to change the document font size (using KOMA-script or otherwise) in such a way that does not require additional tweaks? If not, how can I at least make the font in KOMA-script scrartcl match the default in article?  EDIT In my defence, the linked answers are somewhat lacking:   First solution suggests \usepackage{scrextend} but the example\commands\syntax are not commented or explained, nor is any reference linked. While providing a starting point, this would require one to find appropriate documentation for this package that addresses this particular use (= v. difficult for novice).  Second solution suggests extsizes followed by a quote from the documentation (again without linking to it so that one could read further for clarification) discouraging its use for ambiguous reasons (nb this is at least the second place extsizes was discouraged w/o explanation, even though it was the solution I was personally looking for (as far as I know!)). Related to the lack of linked reference, no examples are provided, which leaves a novice to continue searching w/o knowing what exactly they are looking for.  Third solution suggests changing the document class (scrreport), which does not address the question posted here. ibid. (change to memoir)   It seems to me, from my limited vantage point, that there are likely many tangential, more advanced, issues related to this problem; a problem very likely to present itself to novice users ill-equipped to understand, sort or evaluate the various solutions as they are stated.   To clarify: I believe the primary audience for this question is relatively novice users; whereas the proposed solutions, IMHO, are not well suited to that audience.   This problem seems like a great stepping stone for users to advance their knowledge, I'd suggest a well-documented Q&A that facilitates that process (& would be happy to take this on, if anyone can point me to the appropriate resources).

I'm trying to make a document that has a very small font throughout, I tried this:  \documentclass[0.5mm, a4paper]{article} \documentclass[7pt, a4paper]{article}   But it doesn't seem that they allow me to go anything below 10pt.  This hack make it work, but not for the section headers:  \fontsize{4mm}{5mm}\selectfont   Does anyone know any better ways to do this?


i tried genymotion and virtual box combination it worked for very small time.then i tried android X86 operating system but on this os whats app is not available ,i used "shashlik" but just getting black screen ,also used koplayer in wine but  showing errors .anybody please help me install in whats app.

How can I install WhatsApp in Ubuntu? Related:


I want to create a report for my project and I wrote a code but it is showing some error in table of contents. The page numbering goes fine in the beginning but as chapter 1 starts its shows the numbering as 2 but in the document the page numbering is 1. The document should be about 50 pages. Here is the sample of the code I wrote:    \documentclass[12pt,a4paper]{report}   \usepackage{lipsum}   \usepackage[explicit]{titlesec}   \titleformat{\chapter}[display]{\bfseries\centering}{\huge Chapter \thechapter}{1em}{\Huge #1}   \usepackage{pgf}   \usepackage{pgfpages}    \pgfpagesdeclarelayout{boxed}   {       \edef\pgfpageoptionborder{0pt}   }   {        \pgfpagesphysicalpageoptions         {%              logical pages=1,%         }        \pgfpageslogicalpageoptions{1}         {               border code=\pgfsetlinewidth{2pt}\pgfstroke,%changes the width of border               border shrink=\pgfpageoptionborder,%               resized width=.95\pgfphysicalwidth,%change the size of border               resized height=.95\pgfphysicalheight,%               center=\pgfpoint{.5\pgfphysicalwidth}{.5\pgfphysicalheight}%make the border to                display in center               }%         }   \pgfpagesuselayout{boxed}  \usepackage[utf8]{inputenc}      \usepackage{listings}  \usepackage{amsmath}  \usepackage{amsfonts}  \usepackage{amssymb}  \usepackage[a4paper,left=1.5in,right=1in,top=1in,bottom=1in]{geometry}  \usepackage{graphicx}  \begin{document}  \begin{center}  \thispagestyle{empty}  \parskip=8pt%  \vspace*{1\parskip}%  \textbf{SYNCHRONOUS \& ASYNCHRONOUS DESIGN}   \textbf{Project Title}   A Project Report Submitted in Partial Fulfillment of the Requirements for the Degree of  \parskip=20pt   \textbf{Course}  \parskip=4pt   \textbf{Branch}   \textit{By}   \parskip=8pt%  \textbf{Name of Student}   \textbf{College ID}   \begin{figure}[ht]  \includegraphics[width=2.2098cm, height=2.2098cm]{image1}  \centering  \label{4}  \end{figure}   \textit{Under the supervision of}  \parskip=24pt%    \textbf{Guide Name}  \parskip=4pt   \textbf{Guide Designation}   \textbf{Company Address}  \begin{figure}[ht]  \includegraphics[width=2.8cm, height=2.8cm]{image}  \centering  \label{7}  \end{figure}   \textbf{College Department}\\  \textbf{College name}\\  \textbf{College Address}\\  \textbf{Jan-June (2020)}  \end{center}   \addcontentsline{toc}{chapter}{CERTIFICATE}  \chapter*{CERTIFICATE}  \pagenumbering{roman}   This is the certificate.   \addcontentsline{toc}{chapter}{ACKNOWLEDGMENT}  \chapter*{ACKNOWLEDGMENT}   Acknowledgment    \addcontentsline{toc}{chapter}{ABSTRACT}  \chapter*{ABSTRACT}   Abstract goes here.....    \addcontentsline{toc}{chapter}{CONTENTS}  \tableofcontents    \addcontentsline{toc}{chapter}{LIST OF FIGURES}  \listoffigures    \addcontentsline{toc}{chapter}{LIST OF TABLES}  \listoftables     \chapter{INTRODUCTION}   \pagenumbering{arabic}    Introduction    \section{section}    \subsection{part}    \end{document}   I tried different solutions available online but none of them works for me. Can someone help me with this?

I used the following piece of code to put a box around each page in my report  \documentclass[12pt,a4paper,oneside,final,times]{report}  \AtBeginDocument{\addtocontents{toc}{\protect\thispagestyle{empty}}}  \usepackage{graphicx} \usepackage[a4paper]{geometry} \usepackage[english]{babel} \usepackage{fancyheadings} \usepackage{fancybox} \usepackage{setspace} \usepackage{fixltx2e} \usepackage{amssymb,amsmath} \usepackage{pgf} \usepackage{pgfpages} %\usepackage{fncychap}  \usepackage{lipsum,titletoc} \usepackage{titlesec} \usepackage{simplemargins} \pgfpagesdeclarelayout{boxed} { \edef\pgfpageoptionborder{0pt} } { \pgfpagesphysicalpageoptions {% logical pages=1,% } \pgfpageslogicalpageoptions{1} { border code=\pgfsetlinewidth{2pt}\pgfstroke,% border shrink=\pgfpageoptionborder,% resized width=.90\pgfphysicalwidth,% resized height=.85\pgfphysicalheight,% center=\pgfpoint{.53\pgfphysicalwidth}{.5\pgfphysicalheight}% }% }  \pgfpagesuselayout{boxed} \pagestyle{fancy}   but this is causing my page numbers to be different from that of the toc. To be specific, page numbers in toc=page number on page +1.  Any solution for this, please? The code is borrowed from