What does the symbol $\sqsubset$ mean? Is it the same as $\subset$?

I have tried looking for this symbol but I found the definition for latter only. Hence, I have this doubt if these two are same. If not, can anyone please let me know the difference? Thanks a lot.


Knuth hid a special rule for delimited arguments in exercise 20.5 of the TeXbook.     If the very last character of the   parameter text is #, so that this #   is immediately followed by {, TeX   will behave as if the { had been   inserted at the right end of both the   parameter text and the replacement   text.   This means that a macro can be defined as,  \def\a#1#{#1}   calling it as \a 10 will give a runaway argument error whereas calling it as \a{12}, will compile with no trouble.  I struggled to find a practical application for such macros even after looking at TeX by Topic, TeXbook and LaTeX source.   Here is my take on it, create some commands to typeset and do some calculations for fractions, as for example those found in basic arithmetic texbooks. You type this,  \[\FRAC ADD{3}{8}+{1}{7}\] \[\FRAC SUB{5}{8}-{1}{7}\] \[\FRAC MUL{5}{8}x{13}{1201}\]   and you get this:    Here is the code,  \documentclass{article}  \begin{document} %% macro factory \def\FRAC#1#{\csname #1\endcsname} %% add \def\ADD#1#2+#3#4{%   \frac{#1}{#2}+\frac{#3}{#4}=   \frac{\the\numexpr(#4*#1)+(#3*#2)}{\the\numexpr#2*#4} } %% subtract \def\SUB#1#2-#3#4{%ok top   \frac{#1}{#2}-\frac{#3}{#4}=   \frac{\the\numexpr(#4*#1)-(#3*#2)}{\the\numexpr(#2*#4)} } %% multiply \def\MUL#1#2x#3#4{%   \frac{#1}{#2}\times\frac{#3}{#4}=   \frac{\the\numexpr(#1*#3)}   {\the\numexpr#2*#4} } %% testing \[\FRAC ADD{3}{8}+{1}{7}\] \[\FRAC SUB{5}{8}-{1}{7}\] \[\FRAC MUL{5}{8}x{13}{1201}\] \end{document}   Are there any practical applications for such macros? Are there any special precautions one should take? Why would Knuth include this facility in the first place?


How to Line Up Author Names in IEEE Template

i have to use the IEEE Latex  for the Conference Paper. I downloaded it and the Authors do not line up correctly. The names are displayed to each other. \documentclass[conference]{IEEEtran} \IEEEoverridecommandlockouts \usepackage{cite} \usepackage{amsmath,amssymb,amsfonts} \usepackage{algorithmic} \usepackage{graphicx} \usepackage{textcomp} \usepackage{xcolor} \def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}} \begin{document}  \title{Paper Title*\\ {\footnotesize \textsuperscript{*}Note: Sub-titles are not captured in Xplore and should not be used} \thanks{Identify applicable funding agency here. If none, delete this.} }  \author{\IEEEauthorblockN{1\textsuperscript{st} Given Name Surname} \IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\ \textit{name of organization (of Aff.)}\\ City, Country \\ email address} \and \IEEEauthorblockN{2\textsuperscript{nd} Given Name Surname} \IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\ \textit{name of organization (of Aff.)}\\ City, Country \\ email address} \and \IEEEauthorblockN{3\textsuperscript{rd} Given Name Surname} \IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\ \textit{name of organization (of Aff.)}\\ City, Country \\ email address} \and \IEEEauthorblockN{4\textsuperscript{th} Given Name Surname} \IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\ \textit{name of organization (of Aff.)}\\ City, Country \\ email address} \and \IEEEauthorblockN{5\textsuperscript{th} Given Name Surname} \IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\ \textit{name of organization (of Aff.)}\\ City, Country \\ email address} \and \IEEEauthorblockN{6\textsuperscript{th} Given Name Surname} \IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\ \textit{name of organization (of Aff.)}\\ City, Country \\ email address} }  \maketitle  \begin{IEEEkeywords} component, formatting, style, styling, insert \end{IEEEkeywords}  \section{Introduction} \end{document}   Any Ideas how to fix this Problem ? (Because this simply looks stupid.)


If $c^2 = 12$, then show that $c$ is an irrational number.

Show that, if $x$ satisfies $x^2 = 3$, then $c := 2x$ satisfies $c^2 = 12$. Using this fact, show that $c$ is an irrational number.


What are the key differences between Terraria and Starbound

I'm thinking about buying Starbound, but at the moment it just looks like a Terraria with aliens and different items.  I kinda liked Terraria but I don't wanna spend money on the same game with only like 3 differences. So could one of you guys explain to me what the big differences between these two games?


What is a good book for learning mechanics at the JEE advanced level?

JEE Advanced is an entrance exam for admissions to IITs in India. I will be giving the exam next year. The exam focuses mainly on problem solving skills. So I need recommendations for a book i can use to learn mechanics. If anyone knows about video lectures that could help me,feel free to share.


Can someone explain antisymmetric versus symmetric relation of sets?

If  $$A = \{1,2,3,4\} $$ and   $$R = \{(3,3), (4,4), (1,4)\}$$      This example is antisymmetric but not symmetric.   However, the definition of Antisymmetric taken from Merriam-Webster is this:     relating to or being a relation (as “is a subset of”) that implies equality of any two quantities for which it holds in both directions (the relation R is antisymmetric if aRb and bRa implies a = b)   Please forgive my ignorance, but I'm incredibly confused by the definition. I'm obviously wrong, but it suggests to me that there is/should be a (4,1) in R. However, if there was a (4,1) in R that would make R symmetric and not antisymmetric.  I found a previous Question that asked something similar but was answered with the use of Digraphs. It made me understand how to identify antisymmetric relations, but I still don't understand the core concept.  Thank you so much for any help!


Few months ago I was watching anime on kissanime.com. In Latest update section I found interesting anime. I watched 2-3 episodes and then left site (forgot to bookmark). I thought that was airing anime, because it only had 2 or 3 episodes at that moment. After a month I tried to find it (MAL, google, browser history), but I couldn't. So lets give a try to find that dam anime :).  Story:  Nowadays. Two guys (cool looking teenagers, like a gangsters) was standing near the river. One said that life was boring. Then suddenly they had been teleported to abandoned city. They went to explore what is going on. When they ware wondering, they met women. After that they all together reach temple. In the temple game of death started. They all had to draw card with question. The answer- number. And if you guest wrong the temple are bombarded with fire arrows (arrow count is difference between correct answer and wrong answer). Finally MC (one of the guys) figured it out and escaped temple. Although his friend was shot with arrow in the leg. After then (or maybe later), someone explained all situation. That they must participate in those death games. And if they win, they can live X days more. Otherwise satellite will kill you (if you run out of time). MC was quit exited, so he suggested to participate in another game. His friend was injured, so he went with that women. The next game was in multistory building. There was about 5 levels with a lot of rooms. And outside stairs and balconies connected to each room. There were a lot of participants and all of them had to find room with red button. They they press it, they will win. Although there was walking a tough guy with MAC smg. And killing everyone.     Some information can be inaccurate. I watched this anime long   time ago and I remember it poorly.   Okay, I think that is enough story. Please help me find this anime. Thanks.


convoluted recurrence: $f(2n)=f(n)+f(n+1)+n, f(2n+1)=f(n)+f(n-1)+1$

For the recurrence relation:  $f(0)=1$  $f(1)=1$  $f(2)=2$  $f(2n)=f(n)+f(n+1)+n\ \ \ (\forall n>1)$  $f(2n+1)=f(n)+f(n-1)+1\ \ \ (\forall n\ge 1)$  (the first numbers of the sequence are: 1, 1, 2, 3, 7, 4, 13, 6, 15, 11, 22, 12, 25, 18, 28)  Given some number $S$, I would like to find $n$ such that $f(n) = S$, using an approach that runs in $O(\log n)$ time. Any ideas or tips how to solve it? I tried substitution so far but didn't get far.


Using ctrl as modifier to produce swedish letters å, ä & ö on us keyboard while typing

Pretty new to Linux (currently running Xubuntu). I want to be able to press Ctrl and the button where å, ä & ö would be on a Swedish keyboard. I have tried using both xbindkeys together with xte and using xdotool.   I have also tried creating keyboard shortcuts using the built in keyboard utility in Xubuntu, with both the aforementioned methods as well as trying to write my own .sh files to do the job. I have not had any success for hours now.  tl;dr:  I want to produce å using Ctrl+[, ä using Ctrl+' & ö using Ctrl+; whilst typing regularly into anywhere that takes text.


Can I use Schengen business visa from Germany to visit Denmark?

I am an Indian national and a Permanent Resident (Green Card) of USA. I will be traveling to Germany on Business in March, 2017 and am about to get a Schengen Visa for Business purposes. Meanwhile, I have an opportunity to visit Denmark as a personal visit in Feb.  Can I used the Schengen visa obtained from the German consulate to visit Denmark? I am a little concerned because I will be visiting Denmark (and returning to USA) before I travel to Germany.   I appreciate any help and pointers. I am confused!


I understand the PE effect quite well but I'm failing to understand one thing. Intensity is the amount of energy per second incident to a given area.   So can you can increase the intensity by either increasing the electrical energy or making the area smaller? By increasing the electrical energy, what exactly is happening?  I assume that by increasing intensity you are increasing the number of photons incident to an area of the metal thus increasing the rate of photoelectric emission. But why doesn't increasing intensity via more electrical power lead to greater energy of the electrons, if by increasing intensity you are increasing the energy of the incident waves?  I understand the results but I'm trying to understand why the intensity works the way it is thanks


Prove that for any n, $[k]_n$ is invertible in the ring $\mathbb{Z}_n$ if and only if $n$ and $k$ are relatively prime.

I have trouble proving the above statement.  Here is my approach.  First, I prove that if $n$ and $k$ are not relatively prime, it implies that $[k]_n$ is not invertible.   If $n$ and $k$ are not relatively prime, there exist $g \neq 1$ such that $nx+ky=g$ for some integers $x$ and $y$. (Bézout's identity)  Multiply the equation by, $n/g$  $(n^2x)/g+(nky)/g=n$  We can simplify this by taking the $(mod \hspace{0.1cm} n)$  $(nky)/g=0(mod \hspace{0.1cm} n)$  I don't understand how to proceed from here!. I sense that it has something to do with $k=0$ is the only solution here.  The converse proof is fairly straightforward (I assume.)  Here is my approach to prove the converse, if $k$ and $n$ are relatively prime then $[k]_n$ is invertible.  Again by the Bézout's identity (if $k$ and $n$ are relatively prime), there exist integers $x$ and $y$ which satisfy $nx+ky=1$. We can simplify this to $k\times(y+nx/k)=1$. It is clear that $(y+nx/k)$ is the inverse of $k$.


Question involving triangular matrices and simple modules.

Find the simple modules of the algebra $A$, where  $A = \begin{equation*} \begin{pmatrix} K & 0\\ K & K \end{pmatrix} \end{equation*}$ and $K$ is a field $\textbf{My attempt:}$ I was thinking about something involving direct sums, I know that $A = E_{1,1}K \oplus E_{2,1}K \oplus E_{2,2}K$, but I don't know how to continue... I guess the summands are the simple modules of $A$. Could you help me?


Explicit formula for conformal map from ellipse to unit disc (interior to interior)

I was originally looking for a conformal map that maps a punctured unit disc to unit disc. The only answer I can find lead to  resource.  The final step of the answer given rely on a conformal map that maps an ellipse to a unit disc. Although we know such a map exist by Riemann Mapping Theorem, is there any way to write down the map explicitly (let's say, length of axes are given)?  The only related formula I can find is Joukowski transformation which does the other way around.


I have an old map over a part of Laos and wondering how do I georeference the map with the help of the Grid lines and other Longitude and Latitude information on the scanned map? I have searched for information on the internet and tried many times. My scanned map wont overly correctly on the base map. Any base map would be fine. As long as I can check the result.  Do I add X/East and Y/North values from the grid line crossings as marked and written in some parts of the map? How do I begin georeferencing this map? Do I have to add zeros after the two digits? For example if the Easting is 24 (its in KM right? Do I add like three/four zeros to convert it to meters?  I georeferenced the map with the option "From Map Canvas" in the georeferencer tool and I succeeded but I want to know the coordinate of a point on my old scanned map and write them as X/East and Y/North to georeference the map.   I hope I am not babbling and someone understands what I mean!  We can set the CRS to WGS84, EPSG:4326.


How to evaluate $\int _0^1\frac{\arctan \left(\frac{x^2-x}{x-2}\right)}{x}\:dx$

I want to know what are the best ways to evaluate $$\int _0^1\frac{\arctan \left(\frac{x^2-x}{x-2}\right)}{x}\:dx$$ It seems that it is equal to $\frac{G}{3}$ where $G$ is the Catalan's constant, I tried integration by parts and ended with $$-\int _0^1\frac{\ln \left(x\right)\left(2-4x+x^2\right)}{4-2x^3+2x^2-4x+x^4}\:dx$$ but this just looks complicated, I also tried to substitute the argument of the $\arctan$ and the sub $\frac{1-t}{1+t}$ but neither simplified things, can i please be given some hint on how to tackle this?. The original integral also equals $$-\frac{i}{2}\left(\int _0^1\frac{\ln \left(-2i+ix+x-x^2\right)}{x}\:dx-\int _0^1\frac{\ln \left(-2i+ix-x+x^2\right)}{x}\:dx\right)$$ But I'd prefer to avoid complex methods.


Find the exact value of the infinite sum $\sum_{n=1}^\infty \big\{\mathrm{e}-\big(1+\frac1n\big)^{n}\big\}$

How can we find the exact value of the infinite sum  $$ \displaystyle\sum_{n=1}^\infty \left\{\mathrm{e}-\Big(1+\frac1n\Big)^n\right\}? $$  This problem appears in:  , p.114.


I can no longer see the close reason I chose

In the past, we used to know the exact close reason we chose when voting to close a question.  However, in the new close dialog, it's no longer possible:        In the above, I chose "A community-specific reason --> This question does not appear to be about the software that powers the Stack Exchange network". I have no way to confirm this after the vote was cast because one can not click on top entries (first page) on the dialog to visit the subentries (subsequent pages).  Can this ability be added back please?


How do I change directory in terminal? (very beginner question)

there!  I'm new to Python (as of yesterday, when I bought a book on it called Python Crash Course (2nd ed.)).  I'm having trouble getting started with the Python terminal in that I want to run my hello_world.py program from it, but can't find the darn thing from within the terminal.  I'm running Windows 10.  I've tried putting the directory in the root (C:) directory, on my Desktop, in my OneDrive directory, and under my name in Users and still can't navigate to it in the python terminal.    When I go to the command prompt and type "python", I get the following:  C:\Users\Anne>python Python 3.7.3 (v3.7.3:ef4ec6ed12, Mar 25 2019, 21:26:53) [MSC v.1916 32 bit (Intel)] on win32 Type "help", "copyright", "credits" or "license" for more information. >>>   The book says to put the working folder "somewhere on your system", which is why I have tried so many locations.  The working folder is currently called pywk and is located at C:\Users\Anne\pywk.  Here's what I get when I try to change the directory using the cd command in the terminal:  >>> cd C:\Users\Anne\pywk   File "<stdin>", line 1     cd C:\Users\Anne\pywk        ^ SyntaxError: invalid syntax >>> cd Users\Anne\pywk   File "<stdin>", line 1 cd Users\Anne\pywk            ^     SyntaxError: invalid syntax  >>> cd Anne\pywk   File "<stdin>", line 1     cd Anne\pywk           ^ SyntaxError: invalid syntax >>> cd pywk   File "<stdin>", line 1     cd pywk           ^ SyntaxError: invalid syntax >>>     My guess is that the carat indicates where the syntax problems lie, but I don't know for sure. And I don't know what else to try or have anyone else to ask.    I'm not trying to make a program to do this (yet).  I'm just trying to get to where I can run my little programs from the terminal.  That way I can learn.    Thank you to anyone who can help me over this hump.


Are there fewer positive integers than all integers?

In our 6th grade math class we got introduced to the concept of integers. With all the talk about positive and negative, it got me wondering. Is the amount of elements in $\mathbb{Z^+}$ less than the amount of elements in $\mathbb{Z}$?  Here is how I thought of it. If we have $\mathbb{Z^+}$ and add one element to the "back" of it ($\mathbb{Z}^{\geq-1}$) there are certainly more elements in that new set, so there must be more elements in $\mathbb{Z}$ than in $\mathbb{Z}^+$ but on the other side if we try to express the amount of elements in them "numerically" (In a loose sense of the word) they both have $\infty$ elements.    So what is the right answer? Is there even one?  (Please note I am a bit of a layman when it comes to mathematics)  Edit: About the possible duplicate, I am not looking for a bijection between the two sets, I am looking for if they even have the same number of elements and why a bijection shows that they do/don't


How is the vacuum of Star Wars space different from that of the Milky Way?

Take this scene for example:                                  Anakin is wearing his regular battle outfit with a breathing helmet (whatever it's called irl) while Ahsoka is wearing a full body jumpsuit plus the breathing helmet.  This led me to question what circumstances are like in space in a galaxy far, far away. I recall common descriptions of clone and stormtrooper armour on the Internet stating how they are designed more for protection against environmental hazards rather than enemy fire, including temporary protection from exposure to space.  I also recall reading about the clone pilot outfit in an official behind-the-scenes book for RotS, for which the helmet is not completely sealed. This has the same general design as future Rebel pilot helmets (see below).       In particular, the description of the clone pilot's outfit is that it is designed to improve the pilot's odds of surviving his ship's destruction, then survive exposure to space to allow for later recovery back to capital or other support ships by extraction teams.  My impression of space irl is that it is a zero pressure, absolute zero vacuum environment. To survive space, you need a suit that keeps you pressurised, maintains your temperature, and provides oxygen to breathe. I'm not persuaded that the suits shown in the above references would survive space in our galaxy, especially the open-concept pilot helmet design.  Rebels Season Two, Episode 13 clearly presents the situation. The characters are operating in space or near-space conditions, yet they are able to safely expose parts of their skin (especially Zeb, all he wore is a breathing mask), such as the neck area below the helmets. Ezra could even survive for quite a while without his helmet.  So, what do we know about how Star Wars space is different?  Edit: This is not a duplicate. The other question asks why people do not wear environmental suits INSIDE ships. My question is asking about the differences between Star Wars and real world space. Spacesuits are mentioned to elaborate on my question as an example: Characters do not suit up much more than what they regularly wear in-atmosphere when entering space OUTSIDE of ships.  What I want to know is how Star Wars space differs from ours, regardless of how unscientific it is. I'm not really looking for an explanation of WHY Star Wars space has certain characteristics, I just want to know WHAT these characteristics are.


Will/shall - I _____ never go there. With reason

As like while teaching when such sentences come in front and we teach about using shall with I. Students come up with their books & guides to show as there is 'will' mentioned for answer this question. Please help to teach well. Thank you


How to prevent drupal select 10 articles on front page by default?

The thing is I don't know where to disable this action, even after I rebuild my frontpage with other blocks/views/panels instead the default blog list style page, drupal will still do the select from database. At /config/system/site-information can change number of articles drupal select, but cannot really turn it off.


Early 90s YA novel about a kid into special FX who meets an (animatronic, yet possibly alive) dragon

All i can remember are a few specifics, would love to rediscover the title. Haven't been able to Google up anything.   The kid (~13) made special effects models as a hobby (only one i can remember is a pair of legs which walked realistically) He got a sort of apprenticeship at a special effects production company There was a full-scale mechanical dragon model being worked on at the time, which spoke to the kid (though this might have just been one of the techs messing with him) Also renting space in the building was a sculptor / jeweler who befriended the protagonist At one point there was a break-in I think it ended with a fire, with the robot dragon moving on its own to save the main character   Sorry to be so vague :( There was an early-'90s UK TV adaptation, but i can remember even less of that than i can the novel.


Proper way to update the slug of a taxonomy using register_taxonomy?

What is the best way to update the slug of a custom taxonomy that is registered by a plugin? I want to know the minimal amount of parameters for this or if i need to go and copy paste all of the original parameters. This seems like it can be error prone if the plugin has an update. The codex says you will overwrite the original when using register_taxonomy so is there a better way to do this or a different function?


How does ubuntu ensure software security bfrom external developers

I was reading on the hack against the Transmission Bittorrent Client.   It got me thinking about how would Ubuntu protect itself against this kind of thing. Do the Ubuntu Devs review all software that they put in their repositories or do they trust that software is secure and host it anyway?


60s-70s short story: distant future, mankind has spread throughout the galaxy, and make "first contact" with other descendants of Earth

I vividly remember a scene from a short story (?) I read back in the sixties or seventies, and am trying to remember the publication and title. If it sounds familiar to you, please post.   The scene is set in the distant future after mankind has slowly spread all the way to the far side of the galaxy, the core zones being too hostile to life (energetically). In all that time, we have never encountered another star-faring race. We have been modified slowly by the course of evolution over the millenia.   As the scene opens, it appears we have finally had a first encounter with another civilization. There is a meeting set and gradually dialog is established. The twist comes when it emerges that these creatures are, in fact, also the descendants of Earth modified in different ways during their slow passage the other way around the galaxy. We have proven that we are, indeed alone.   The story ached with pathos at the loneliness of being the only intelligent species in existence. (In terms of evolutionary theory, this would likely make us a ring species.)


Android program crashing with Null Pointer exception

I have no idea what I'm screwing up here.  Getting a null pointer exception seemingly on my array of Strings.  This is the method I'm calling in my main Activity:  public void initializeLocalDealer() {   String[] cars = new String[]{"Ford", "Chevy", "Chrysler", "Honda"};      Dealer dealer = new Dealer();     Dealer.setCars(cars); }   Here's the class object I'm trying to populate.    public class Dealer {      public String name;     public Car[] car;      public Dealer() { }      public void setCars(String[] cars) {         for(int i = 0; i < cars.length; i++) {             car[i].name = cars[i];         }     } }   What super obvious thing am I missing here?


ui:inputSelect behaves differently under aura:iteration

<aura:iteration items="{!v.getrecords.record}" var="obj">
 Items:-
 {!obj.Itemname}, {!obj.itemsize} // I get all values here             <ui:inputSelect aura:id="abc" disabled="{!!v.save}">                 <ui:inputSelectOption text="Yes" label="Yes"  />                 <ui:inputSelectOption text="No" label="No" />                 <ui:inputSelectOption text="Approved" label="Approved" value="true"/>             </ui:inputSelect>      </aura:iteration>     For this input select I am facing two issues   In controller,this line is invoked when user clicks on save button  var marketingValue = component.find("abc").get("v.value"); alert(marketingValue);    Error: [component.find(...).get is not a function] If the same input select option I put outside the aura:iteration , I get the desired value with no errors.  2.I wanted to default the input option on pageload (that is received controller) so i used the value attribute  <aura:iteration items="{!v.getrecords.record}" var="obj">
 Items:-
 {!obj.purpose}, {!obj.legalGround } // I get all values here <ui:inputSelect aura:id="abc" disabled="{!!v.save}"> <ui:inputSelectOption text="Yes" label="Yes" value="{!obj.status == 'yes'}" /> <ui:inputSelectOption text="No" label="No" value="{!obj.status == 'no'}"/> <ui:inputSelectOption text="Approved" label="Approved" value="Approved" value="{!obj.status == 'approved'}"/> </ui:inputSelect>  </aura:iteration>   On page load, I do get the defaulted value but after clicking edit even if i change the value to something different , it auto reverts back to the controller received value, after doing 2-3 times it changed but again sometimes it goes back to the inital value.


When do we assume that a rope has different tensions in different places?

Working a problem with 2 pulleys and masses in class this week the professor at one point assumed that the tension on the two sides of a pulley would be different.  Every other time we've done a similar problem, we just assumed that the tension would be the same on both sides.  And I didn't understand his explanation of why we had to do it that way this time.  My question is when can we assume the tension on both sides of a rope are the same and when do we need to assume different tensions?


I have a HP pavilion g6 1301tx laptop. It came up with 2GB of DDR3 ram, windows 7 pro (64 bit), 1 GB ATI graphic card and motherboard - hp 1670 serial number- pcela212c1bo7I. Few months back I installed Windows 10 (32 bit) . Now I want to increase ram by 2 GB , total of 4 GB so I installed a 2 GB DDR3 ram to the other slot and  checked system properties of my computer it says 2.5 GB usable out of 4 GB, now I don't understand why rest of the 1.5 GB is not usable what should i do to get 4 GB ram?


I came across a question yesterday about combinations, and I wanted to know what the correct answer was. The question states as follows:  There are 8 spaces that are alternately black and white. There is one king, one queen, two identical rooks, two identical bishops, and two identical knights. The king needs to be surrounded by the two rooks. Then, the two bishops can be put on any of the remaining spaces as long as one is on a black space and the other is on a white space. Finally, the queen and the knights can be placed anywhere in the remaining spaces in relation to the other pieces. How many possible arrangements are there considering these conditions?


What do prime ideals in $k[x,y]$ look like?

Suppose that $k$ is an algebraically closed field. Then what do the prime ideals in the polynomial ring $k[x,y]$ look like?   As far as I know, the maximal ideals of $k[x,y]$ are of the form $(x-a,y-b)$ where $a,b\in k$. What can we say about the prime ideals? Are there similar results? And what about $k[x,y,z], k[x,y,z,w]$ and so on. Would someone be kind enough to give me some hints or referrence on this topic? Thank you very much!


Using a variable declared in try using the value in catch

Long version:  I've been asked to develop a program which write files in a directory into a database. Also the files which are on deeper levels in that directory needs to be written to the database. There it should be displayed with two columns. One shows the path, the other one shows the filename + extension. I wrote a program working just fine in the test environment. However, in the live environment, I don't have all the rights and permissions to open every single directory I want. Also, due to some migrations, several directories got too long path names, and can't be opened anymore. So they told me to write those directories into the database, but instead of showing in the file_name column the file name and extension, to fill that one with "No access". However, to avoid trying to open 'bad' directories, I used a try/catch module. Now I need a variable declared in try and use it in catch. Is there anyway this is possible to do? I will post a part of the code so you can see what I have at this moment.  Short version:  I want to take a variable declared in the try module and use it in the catch module. Is there any way to do that?      public HashSet<String> getFolders(Path path, HashSet<String> folders)     {                     try         {             foreach (String folder in Directory.GetDirectories(path.getOrigineleMap()))             {                 Path p = path;                 p.setOrigineleMap(folder);                 folders.Add(folder);                 getFolders(p,folders);             }         }         catch (System.Exception e)         {             Console.WriteLine("No access to a folder");             writeToDatabase(path, folder + @"\No access");   //path is a variable of the type Path, and the String should be the entire         }                                                    //path from the directory + \No Access         return folders;     }


If I download something something from the Xbox Games Store on X360 will it have the same game saves as disc version?

If I download a game from the Xbox Games Store on Xbox 360 will it have the same game files and saves from the disc version? Specific game in mind is Sonic Unleashed.


How to I round a number in Java? Like, I have this number 3.4666666666663 and i would like to round it to the nearest floating number, which would be 3.5. I don't want to round it to 4


Where does the name "flip-flop" come from?

After I learn about the DFF (Data Flip-Flop). I understand Flip-Flop as a device that can memorize input data at the rising or falling edge of the clock sequence.  But why call it flip-flop? Why not something like edge-triggered memory circuit. It's kind of a nick name which is hard to get for a non-English speaker. And in my country, the translated version is kind of twisted.   Could anyone explain the reason of the naming in plain English? Thanks.


Having trouble setting up a nginx web server on Amazon EC2

dI logged into my EC2 console created a new instance and attached an Elastice IP to it. Then I logged into the server and installed Nginx:  $ sudo apt-get install nginx $ sudo /etc/init.d/nginx start $ Starting nginx: nginx.   When I navigate to the Elastic IP (or Public DNS) I get nothing. The default setting should be enough to show me the default Nginx welcome page right? I've hit a wall and don't know what to do next. Any suggestions would be much appreciated?  I haven't touched it but here is my default nginx.conf:  user www-data; worker_processes 4; pid /var/run/nginx.pid;  events {     worker_connections 768;     # multi_accept on; }  http {      ##     # Basic Settings     ##      sendfile on;     tcp_nopush on;     tcp_nodelay on;     keepalive_timeout 65;     types_hash_max_size 2048;     # server_tokens off;      # server_names_hash_bucket_size 64;     # server_name_in_redirect off;      include /etc/nginx/mime.types;     default_type application/octet-stream;      ##     # Logging Settings     ##      access_log /var/log/nginx/access.log;     error_log /var/log/nginx/error.log;      ##     # Gzip Settings     ##      gzip on;     gzip_disable "msie6";      # gzip_vary on;     # gzip_proxied any;     # gzip_comp_level 6;     # gzip_buffers 16 8k;     # gzip_http_version 1.1;     # gzip_types text/plain text/css application/json application/x-javascript text/xml application/xml application/xml+rss text/javascript;      ##     # nginx-naxsi config     ##     # Uncomment it if you installed nginx-naxsi     ##      #include /etc/nginx/naxsi_core.rules;      ##     # nginx-passenger config     ##     # Uncomment it if you installed nginx-passenger     ##      #passenger_root /usr;     #passenger_ruby /usr/bin/ruby;      ##     # Virtual Host Configs     ##      include /etc/nginx/conf.d/*.conf;     include /etc/nginx/sites-enabled/*; }   #mail { #   # See sample authentication script at: #   # http://wiki.nginx.org/ImapAuthenticateWithApachePhpScript #  #   # auth_http localhost/auth.php; #   # pop3_capabilities "TOP" "USER"; #   # imap_capabilities "IMAP4rev1" "UIDPLUS"; #  #   server { #       listen     localhost:110; #       protocol   pop3; #       proxy      on; #   } #  #   server { #       listen     localhost:143; #       protocol   imap; #       proxy      on; #   } #}   There is nothing in access or error logs and I've also ensured nginx is running:  ps -ax | grep nginx Warning: bad ps syntax, perhaps a bogus '-'? See http://procps.sf.net/faq.html 4305 ?        Ss     0:00 nginx: master process /usr/sbin/nginx 4306 ?        S      0:00 nginx: worker process 4307 ?        S      0:00 nginx: worker process 4308 ?        S      0:00 nginx: worker process 4309 ?        S      0:00 nginx: worker process


Proof by Induction [Number Theory by George E. Andrews 1-1 #2]

I am to use mathematical induction to prove that:     $$1^3 + 2^3 + 3^3 + \cdots + n^3 = (1 + 2 + 3 + \cdots + n)^2 $$


Does Improved Divine Smite work in an Antimagic Field?

At 11th level, a paladin gains Improved Divine Smite. This means (PHB p85):     you are so suffused with righteous might that all your melee weapon strikes carry divine power with them.   Given that the normal Divine Smite requires a spell slot to be expended, I took it to be considered as a spell and therefore unusable within an Antimagic Field (PHB, p213):     This area is divorced from the magical energy that suffuses the multiverse. Within the sphere, spells can’t be cast, summoned creatures disappear, and even magic items become mundane. [...] Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can’t protrude into it.   Improved Divine Smite, however, appears to be a quality innate to a paladin of 11th level or higher. Is it affected by an Antimagic Field?


If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $$\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$$  Without using calculus. There are a few ways I've tried solving this:  $1)$ We could try using the Cauchy-Schwarz inequality: $$\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge \frac{(x+y+z)^2}{(x-1)^2+(y-1)^2+(z-1)^2}$$  But it's apparent that nothing's useful here.  $2)$ We could use AM-GM as well: $$\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 3\sqrt[3]{\frac{x^2y^2z^2}{(x-1)^2(y-1)^2(z-1)^2}}=\frac{3}{\sqrt[3]{(x-1)^2(y-1)^2(z-1)^2}}$$  So we only have to prove that: $$\sqrt[3]{(x-1)^2(y-1)^2(z-1)^2}\le 3$$  We could raise both sides to the power of 3: $$(x-1)^2(y-1)^2(z-1)^2\le 27$$  But this inequality doesn't hold.   $3)$ We could try cleaning the denominators by multiplying both sides by $(x-1)^2(y-1)^2(z-1)^2$. After a bunch of expanding and simplifying we get that: $$x^2y^2+y^2z^2+x^2z^2-6(xy+yz+xz)+2(x+y+z)+9\ge 0$$  I can't tell so easily whether the inequality is true or not. You could help me out on this one. Just don't forget that $x,y,z\in\mathbb R\setminus\{1\}$ and so we can't just simply use AM-GM, unless we're using it for squares that have to be non-negative.


Do GUIs represent a type of separate shell?

When I install some Linux distros with a GUI, they come with the shells sh and Bash. The CLI let you operate the system through sh and Bash, but what about the GUI? Does the GUI let you operate the system through sh and Bash or it has it's own shell to intermediate between you and the kernel?


Ability to alter my favorite sites in the Android app

So I finally got my invitation (yay! It's awesome! Thanks!) and I'd like this first feature request to be typed from here.   I propose the ability to change the "favorite" sites, and also include meta sites in there.   Right now, I presume it's reading the list of sites ordered by reputation.  I propose the following:    If I am a moderator on any site, those sites and their metas should come first. After that, ordered by reputation.  The above is only the default order, and can be altered freely by the user.


Every time I try to install a package, I get this error

E: Problem parsing dependency 53 of libmat io-doc:all=1.5.17-3 E: Error occured while processing libmat io-doc (NewVersion2) E: Problem with MergeList /var/lib/apt/lists/us.archive.ubuntu.com_ubuntu_dists_focal_universe_binary-amd64_Packages E: The package lists or status file could not be parsed or opened  Also note that I cancelled e2fsck before this and that I cannot get into login screen, I get stuck on fsck: /dev/sda5 clean:xxx/xxx files, then the screen goes to blank then fsck thing over and over again, and I'm currently in root recovery mode trying to download a package [just thought this might be of help.]


Bothe of these phrases seem to express and depict the same meaning.   As I can remember, John was kind-hearted and tolerant; let alone, he was a man of God.  As I can remember, John was Kind-hearted and tolerant; not to mention, he was a man of God.    How to use and differentiate between them?  Dictionary: not to mention: In addition to or as well as what's been discussed; used for adding a comment that emphasizes the main idea of what you have already said.  Let alone: used for saying that something is even less likely to happen than another unlikely thing; used to emphasize that something is more impossible than another thing:


What is the value of lim$_{n\to \infty} a_n$ if $\lim_{n \to \infty}\left|a_n+ 3\left(\frac{n-2}{n}\right)^n \right|^{\frac{1}{n}}=\frac{3}{5}$?

Let $\{a_n\}$ be a sequence of real numbers such that $$\lim_{n \to \infty}\left|a_n+ 3\left(\frac{n-2}{n}\right)^n \right|^{\frac{1}{n}}=\frac{3}{5}.$$  What is the value of $\lim_{n\to \infty} a_n$?


Which side of wave-particle duality to choose in a given situation

How does one know whether, in treating a certain problem, one should consider particles as waves or as point-like objects? Are there certain guidelines regarding this?


How to get smooth movement in a low resolution game?

I am using monogame to make a simple platformer with a fairly low resolution.  Right now I am struggling to get smooth movement like in the mario games. In those games despite having the low resolution mario can still slowly accelerate from standing still and the movement looks smooth. How did they achieve this?  My current solution performs all of the game's physics and movement in floats and when it comes to drawing the x and y coordinate of the player it is rounded to an int. This results in very jagged looking movement.  Is there any way to improve this so that the movement is smooth and still has acceleration? I was thinking about scaling up all of my assets by 4 and working at a higher resolution but then the player would be able to walk between pixels (as 1 pixel in the assets would be represented by 4 pixels on the screen).  Any help would be much appreciate.  Here is an awful video of my character's movement:


I want to make a GUI for a program written in python.It is said that Gnome tool kit is helpful for this task.But,I want to know how to install it?and the way I should use it? I am using Ubuntu 12.04 64-bit and using unity environment.Python version is 3.2


How to deal with values between methods and constructors

Its rough right now, but I'm stuck because I can't find a way to access either digits (an array of integers (it has to be a private array, per the assignment rules)) or size. Is there a way to access constructor variables in methods within the same class?  I'm not sure what to try, as I'm still in the very basic stages (only a lesson or two in Java) and I don't know how to continue.  public class Zillion {     private int[] digits;     String strdigits;     public Zillion(int size) {         int[] digits = new int[size]; } public String toString() {     for(int x=0; x<digits.length; x++) {         strdigits += digits[x];         System.out.println(strdigits);     }     return(strdigits); }  public static void main(String[] args) {     Zillion z = new Zillion(2);        System.out.println(z);  //  00  2 points   }   }  Below are my errors; System.out.println(z) is supposed to output 00, but it seems the code gets trapped by a NullPointerException when I try to access digits.length in line 10.  Exception in thread "main" java.lang.NullPointerException     at lab4_carl6188.Zillion.toString(Zillion.java:10)     at java.base/java.lang.String.valueOf(String.java:3042)     at java.base/java.io.PrintStream.println(PrintStream.java:897)     at lab4_carl6188.Zillion.main(Zillion.java:19)


Can you catch a native exception in C# code?

In C# code can you catch a native exception thrown from deep in some unmanaged library? If so do you need to do anything differently to catch it or does a standard try...catch get it?


What is the difference betwen focal, focal-security, focal-updates? ubuntu@ubuntu:/etc/apt$ cat sources.list deb cdrom:[Ubuntu 20.04.1 LTS _Focal Fossa_ - Release amd64 (20200731)]/ focal main restricted   deb http://archive.ubuntu.com/ubuntu/ focal main restricted universe multiverse   deb http://security.ubuntu.com/ubuntu/ focal-security main restricted universe multiverse   deb http://archive.ubuntu.com/ubuntu/ focal-updates main restricted universe multiverse


! Extra alignment tab has been changed to \cr.  \endtemplate - cline

\documentclass{cta-author}  \newtheorem{theorem}{Theorem}{} \newtheorem{corollary}{Corollary}{} \newtheorem{remark}{Remark}{} \usepackage{blindtext} \usepackage{enumitem} \usepackage{array} \usepackage{mathrsfs} \usepackage{amsfonts} \usepackage{bm} \usepackage{tabularx} \usepackage{multirow} \usepackage{amsmath} \usepackage{graphicx} \usepackage{float} \usepackage{makecell} \usepackage{adjustbox} \usepackage{textcmds} \usepackage{lineno} \usepackage{rotating}  \begin{document}   \begin{table*}[t] \renewcommand{\arraystretch}{1} \caption{C at PCC} \label{Table1} \centering \begin{tabular}{c|c|c|c|c|c|c|c|c}  \hline \hline  Standards &\multicolumn{2}{c}{IEEE 2014}& \multicolumn{2}{|c}{IEEE 2018}& \multicolumn{2}{|c}{IEC 27} &\multicolumn{2}{|c}{EN61-2}\\ \cline{2-4}  \end{tabular} \end{table*}    \end{document}   I use this code to generate table but is showing an error as given below. While I give \hline instead of \cline{-} it is working properly. But I need to use that \cline.


Find a function that matches the following conditions.  (a) $f(x)$ is continuous for all real numbers  (b) $f(0)$ = 3  (c) For all real numbers $x$, $f(x) = f(x/2)$  This is from a past paper, and the answer has been given as the following steps:   $f(a) = ... = f(a/2n)$ $f(a)$ = lim as n approaches infintiy $f(a)$ = lim as n approaches infinity of $f(a/2n)$ $f$(lim as n approaches infinity of $\frac{a}{2n}$ therefore $f$ is continuous $f(0) = 3$   My question arises due to poor printing of my answer book. In step 1 is $f(a/2n)$ the correct step or should it be $(f(\frac{a}{2^n})$? If so could you please explain why? Because for both possibilities I can't seem to figure out why that's a step in proving the continuity. I'm sorry for the very elementary question. Thank you!


I'm trying to add the mmbt3904lt1g model to LTspice. - I've copied its data from the MMBT3904LT1.LIB.txt in the standard.bjt library. - I've added an NPN to my schematic then I've changed its value to mmbt3904lt1g  - through the Edit->spice directive I've pasted the path to this library I thought it was all to use this device but no simulation is achieved.. I get only: Can't find definition of model "MMBT3904LT1g"  where I'm doing wrong ?


New Beamer Version: Transparent Title Page Boxes

Consider the following file:  \documentclass{beamer}  \setbeamercolor{title}{bg=red} \setbeamercolor{author}{bg=yellow} \setbeamercolor{date}{bg=} \setbeamercolor{institute}{fg=red,bg=green}  \title{TitelTitelTitel} \author{meiermueller} \institute{Institute} \date{lalala}  \begin{document}  \usebackgroundtemplate{\color{blue}\rule{20cm}{15cm}}    \begin{frame}    \titlepage  \end{frame} \end{document}   On one of my computers (using MiKTeX 2.9 and beamer 2015/01/05 3.36), the result is the following:    Note how, in particular, the date box has a transparent background  On my other computer, I installed a new MiKTeX version (2.9.6800), including beamer 2018/09/02 v3.52, and get this:    Here, the date field has a white background, and I cannot seem to get it to be transparent.   Apparently, the difference has some relation to the beamer version, or maybe some other change in the new MiKTeX version.  But what ist the reason, and how do I get transparent backgrounds?


How to limit the number of active logins per user?

How can I limit the number of active logins per user?  I've seen this on various servers before, and I was wondering how I could set this up myself.  Perhaps in those cases, this was accomplished by limiting the number of active SSH logins per user?  And I guess that would be the way to go.  How would I set this up?


Incompatibility between tikz-cd and language

Sorry for the bad English. I'm trying to use the tikz-cd package to make commutative diagrams. My code  \documentclass{article} \usepackage[brazil]{babel} \usepackage{tikz-cd} \begin{document} \begin{tikzcd} A \ar[r, "x"] & B \end{tikzcd} \end{document}    The problem occurs when putting a name under the arrow, the syntax "x" is incompatible with the brazil option of the babel package. When exchanging brazil for english it works normally. I already tried using  \usepackage[main=brazil, english]{babel}, \usepackage[brazil, english]{babel} e  \usepackage[brazil, main=english]{babel}   But it did not work. I also tried to use  \usepackage[english, brazil]{babel} \usepackage{polyglossia} \setmainlanguage{brazil} \setotherlanguages{english}   And finally  \selectlanguage{english}   However, it only works if I remove the option brazil


We have inline comment editing, inline editing of questions on Area 51, and inline re-tagging.  Can we please have inline Question and Answer editing on the Stack Exchange sites?  This has been implemented using a GreaseMonkey Script.  Try it out yourself.  It's old, so I'm not sure if it will still work:


I need to use method like:  DoSomething<(T)>();   But i don't know which Type i have, only object of class Type. How can i call this method if I have only:  Type typeOfGeneric;


When to use "throws RuntimeException" Java

I am doing a code review and I have came across this method definition:  public void something() throws RuntimeException   Is there a rational reason to write 'throws RuntimeException' in Java?


Me and wife were planned to travel to France to attend a wedding.  She is from the EU region and i am not, i apply for schengen visa as an EU spouse which recently is required of her to sign a letter saying that she will be travelling with me.  Now, something has come up and she will not be able to travel with me.  Will i be allowed to travel alone ?  regards r


What's the easiest way to find the version of Windows on a PC?

The title says it all: what's the easiest way to find what version of Windows is installed on a PC? I often find myself trying to help people with various issues on their computers, and the first question I ask is "what Windows do you have?". Most of them don't know how to answer, so I'd like to find out what's the easiest way to find out. Thank you!


How to put special characters into the text of an input

Im just now getting into python, and my assignment is to write a Celsius to Farenheit (and vice versa) converter. I get bonus points for having the degree symbol incorporated.  I want to have degree_symbol show up in the text of the initial input question  degree_symbol = chr(176) temperature = input("Is your temperature in", degree_symbol, "F or", degree_symbol, "C?\n")  if temperature == "C":     temp_c = float(input("What is your temperature in C?\n"))     print("That is", ((temp_c * (9/5)) + 32), degree_symbol, "F!")   else:     temp_f = float(input("What is your temperature in F?\n"))     print("That is", ((temp_f - 32) * (5/9)), degree_symbol, "C!")     this is the error that shows up      3.4.3 (v3.4.3:9b73f1c3e601, Feb 24 2015, 22:43:06) [MSC v.1600 32 bit (Intel)] Python Type "help", "copyright", "credits" or "license" for more information. [evaluate -------_As01.py] Traceback (most recent call last):   File "C:/Users/-----------/----------_As01.py", line 10, in <module>     temperature = input("Is your temperature in", degree_symbol, "F or", degree_symbol, "C?\n") builtins.TypeError: input expected at most 1 arguments, got 5


Calculate the remainder of $11^{2020} / 7$

I tried to get a pattern by doing  $11^1 / 7 = 1 , r=4$  $11^2/7 = 17, r=2$  $11^3 / 7 = 190, r=1$  but the numbers keep getting larger and larger and I think this is not the way to go about this problem. Can someone please explain the correct way on how to deal with these problems?


I need to show that $\{(x,y,z)\in\mathbb{R}^{3}:x^2+y^2+z^2 = 1\}$ is connected. Intuitively I understand that it is path connected and, therefore, connected. However, I don't understand how I would define such a path mathematically. For example, if I wish to show that every point on the unit sphere connected to the north pole and, therefore, to every other point, how would I show this?


How do I access a superclass method in java if it has already been overridden by a subclass?

Assuming I have the abstract Shape class, within I have the method getArea(). As a subclass of the Shape class, I have the Rectangle class, which overrides the getArea() method. As a subclass of the Rectangle class, I have the Square class, but in the Square class, I want to reference the getArea() as implemented in the Shape class. How can I do this without copying the code over?


What does "Enable Improved Caching of Org Schema" actually do?

This  sounds like a welcome change, but it's not terribly specific. What does this Critical Update actually entail? Will we still be able to sniff hidden object types using Id.getSObjectType()? Will this somehow make it impossible to leak versioned API fields (e.g. LastViewedDate to a < 28.0 class)? This sounds like a great new feature if it eliminates bugs, but the wording seems a bit vague.


Prove that if a prime $p$ divides $a^2 + b^2$ then it must divide both a and b.

I proved this by taking cases for different remainders and using modular arithmetic,  when the prime is $3$.However this method won't give a general proof for all primes.I was eager to get a proof for all primes $p$, but i couldn't get one.I have seen in Pythagorean triples that if both $a$ and $b$ are not divisible by $p$, $c=a^2 + b^2$ is also not, but how do i prove it?  Proving by contradiction may help...maybe induction. Also we can try proving for all numbers. of the form $6n+1$ and $6n-1$ so that it becomes evident for all primes.  The question changed and now is about  proving that for all primes equivalent to $3 \bmod 4.$


Following is the code to generate a table with input fields and buttons.

         <input type="text" class="text1">	         <input type="text" class="text2">	         <input type="text" class="text3">	         <button type="button" class="append_up">Up</button>	         <button type="button" class="append_down">Down</button>

         <input type="text" class="text1">	         <input type="text" class="text2">	         <input type="text" class="text3">	         <button type="button" class="append_up">Up</button>	         <button type="button" class="append_down">Down</button>

         <input type="text" class="text1">	         <input type="text" class="text2">	         <input type="text" class="text3">	         <button type="button" class="append_up">Up</button>	         <button type="button" class="append_down">Down</button>

   I want to be able to append a similar row anywhere in the table using JavaScript. If I click the Up button I want a similar row to be appended just above that row, and if clicked down, just below that row. And finally I want to be able to get all the data from the table in the order as created by clicking the buttons. Please help.  After receiving few answers this is what i did.  $(document).ready(function(){           var html = '
<input type="text" class="text1">	<input type="text" class="text2">	<input type="text" class="text3">	<button type="button" class="append_up">Up</button>	<button type="button" class="append_down">Down</button>
';            $('.append_up').click(function(e) {               e.preventDefault();               $(this).closest('tr').before(html);           });            $('.append_down').click(function(e) {               e.preventDefault();               $(this).closest('tr').after(html);           });        });    I was able to append rows but clicking on the button from the new row does nothing.


Find a vector parallel to the line of intersection of the two given planes.

The given planes are $2x - y + z = 1$ and  $3x + y + z = 2$.  Adding the two equations I choose the two points of intersection of the planes to be $P= (3, -1, -6)$ and $X = (5, -2, -11)$. Then, the equation of the line is $(5, -2, -11)= (3, -1, -6) + tA$. So the vector $tA = (2, -1, -5)$. Any vector parallel to $tA$ must be parallel to the line. Let $t = -1$. Then $A = (-2, 1, 5)$ is parallel to $tA$.  I am not sure if my solution is correct. I just noticed that the problem that comes right after this one asks to find a parametric representation for the line of intersection of the planes of the given equations above. It suggests that they might have solved the problem in a different manner. I looked up the answer to that question and it's $X = (1, 0, -1) + t(-2, 1, 5)$. My vector A and theirs don't match. So I might have made a mistake.   Please, elaborate. Thanks.   edit: Turns out vectors do match!


This 12-year-old question was just resurrected by a brand-new user:  The Community system user has a habit of providing attention to un-answered questions by pushing them to the top of the feeds (this is a good thing!); however, the question in...question, can never have an answer selected as correct because the original poster is long gone: their account has been deactivated or deleted (no profile). Users, particularly new ones, don't tend to notice the age of a question before answering, or that other answers are adequate and just need to provide an upvote instead of a whole new, potentially not useful, answer. This behavior inevitably could cause an infinite loop of "No selected answer, Community pushes it to the top of the feed, uninformed user adds an answer, [time passes], No selected answer, Community pushes it to the top of the feed, ...continue ad infinitum" Should there be a system in place to review unanswerable questions like this and potentially delete them? Either add a queue for real users to review them or add logic to Community to purge them after say, 12 months?


An error in printed book is my fault: what do I do?

I designed a kids' activity book for my client. She handwrote all the text correctly and I typed a sentence out incorrectly. She approved the proof before print but that was the 6th draft so I guess both of us were too tired by that stage to spot this error.  If it was her provided text, I wouldn't see it as entirely my fault. But I typed it myself from her correct notes so it is. Should I give a discount? A full refund? She's printing labels to put over the incorrect text. Should I at least pay for that?


Manual occlusion culling with glDrawElements

How should I go about doing occlusion culling with glDrawElements? I am dealing with voxel-like terrain. I want to avoid drawing the faces that are facing another block. I just don't know how to incorporate this with glDrawElements. Should I even use glDrawElements?


E: Sub-process /usr/bin/dpkg returned an error code (2) -- whats the problem with this?

error when installing any packages.. pls help.. thanks in advance..  been trying to solve this for days now.. still can't solve it.. Already tried       $ sudo apt-get update     $ sudo apt-get upgrade     $ sudo apt-get autoremove     $ sudo apt-get clean   etc..  Preconfiguring packages ... Selecting previously unselected package libglade2-0:amd64. dpkg: unrecoverable fatal error, aborting:  reading files list for package 'linux-headers-3.8.0-19': Input/output error E: Sub-process /usr/bin/dpkg returned an error code (2)


Extending the User model with custom fields in Django

What's the best way to extend the User model (bundled with Django's authentication app) with custom fields? I would also possibly like to use the email as the username (for authentication purposes).  I've already seen a   to do it, but can't decide on which one is the best.


How can I open the containing folders of items in Nautilus search results?

After searching for a file in Nautilus, how can I open its parent folder?


Prove that interchanging the $ij$-entries of $n \times n$ matrix will not change the result(eigenvalues).

I want to prove that interchanging the entries of an $n \times n$ matrix will not change the result.But I don't know how. Please help!


is it ok to put the side nav menu on application for the iOS? Because I can't find it on iOS guideline design.


How to convert an std::string to C-style string

I am programming in C++.  As basic as this question is I cannot seem to find an answer for it anywhere. So here is the problem:  I want to create a C-style string however I want to put an integer variable i into the string. So naturally, I used a stream:  stringstream foo; foo                 << "blah blah blah blah... i = "                  << i                 << " blah blah... ";   However, I need to somehow get a C-style string to pass to a function (turns out foo.str() returns an std::string). So this is technically a three part question --   1) How do I convert std::string to a C-style string?  2) Is there a way to get a C-style string from a stringstream?  3) Is there a way to use a C-style string directly (without using stringstreams) to construct a string with an integer variable in it?


How to set visibillity Property of same .exe by diffrent Process

Im trying to make my programm behave like others (e.g. Steam) do. If the program is minimized and you start the .exe of it again, it shouldnt start a second instance, but maximise the first one. I already archived that with a little use of the winapi (User32.dll) like this:  if (AlreadyRunning(ref secondProcess)) {     if(secondProcess != null)     {          //forces a minimize         ShowWindow(secondProcess.MainWindowHandle, 11);          //shows the window         ShowWindow(secondProcess.MainWindowHandle, 1);      }     //Stops the second instance     Process.GetCurrentProcess().Kill();  }   The problem I now have is, that my programm often runs with Visibillity = Visibility.Hidden on the MainWindow. When this is the case and the function^ gets called, nothing happens. I have no idea how to change the property from the outside.


How can one link / merge / combine / associate two accounts / users? (Anonymous / unregistered / cookie, or Google / Facebook / registered)

I accidentally posted a question without being logged in. Is there a way to associate that question with my account?   For more information, visit "" in the .   a.k.a. How can you link a registered account to a cookie-based account? a.k.a. How do I merge an unregistered account with a registered account a.k.a. Merging users a.k.a. How do I associate anonymous questions I’ve asked with my registered account? a.k.a. Is there a way to claim an unregistered user? (in case anyone searches with those terms)


Creating Two Views and Passing a Value Between Them

I'm new to Xcode and am trying to make a simple application where I enter a value hit a button and the value is passed to the next view and displayed. I am having trouble finding content on the internet on how to do this.  I created a Single View Application and another view controller, then connected them with a modal but cannot figure out how to pass values between the two.  Any pointers or good references would be awesome.


I upgraded my system to the latest Ubuntu. However, it seems that it's shipped with java 11. I removed it because I need  Java 8. However, it seems that Java 8 won't install on my system and I was googling and I stumbled by this:  How can I install Jre and jdk 8 on my system?


MariaDB is Forgetting Previous Auto Increment IDs

I'm using  5.5.39, and it seems like it is forgetting the max id of the auto-incremented primary key if I delete all rows from the table and then too much time passes before another row gets inserted. Here's the schema according to :  CREATE TABLE `submissionqueue` (     `SubmissionID` BIGINT(20) NOT NULL AUTO_INCREMENT,     `JSON` TEXT NULL,     PRIMARY KEY (`SubmissionID`), ) COLLATE='latin1_swedish_ci' ENGINE=InnoDB AUTO_INCREMENT=354;   The original AUTO_INCREMENT was probably 1, HeidiSQL is probably just indicating what the code would be to create the table right now.  I'm using this table as a queue to hold submissions until approval, where the id column is auto incremented.  Later, the queue is processed leaving this table empty. When a new submission occurs, if the table is functioning correctly, a new row is inserted into this table and it receives a new auto increment ID that is higher than the IDs of all previously inserted rows (even though most "previous rows" were deleted long ago).  Over time, more than 600,000 rows have been processed from this queue. So you'd expect the auto increment id to be in the 600,000s.  However, for some time now, the auto increment IDs keep becoming reset. And when I go to process this queue, the auto increment IDs have started over at 1.  It seems like, when I empty that table, and too much time passes before another row is added to it, MariaDB is forgetting the max auto increment ID that was previously in that table and instead the IDs start over at 1.  This is a problem because during processing, any rows deleted are first moved to another table with the exact same schema. Because the auto increment IDs have started over, the program errors out because the ids are no longer unique in respect to all previously processed rows.  For years this program worked flawlessly, but at some point the database started forgetting the correct auto id, starting over at 1 instead.  This table, I'm experiencing this with, has never been dropped. The only thing I do, is remove all the rows that are in the table each time the queue is processed. After this, if I immediately go insert a row, it will received the proper Auto Increment ID (respecting all the previous ids that use to be in the table). Again, however, if too much time passes before an insert occurs, the increment starts over instead of respecting previously existing row's auto IDs.  I'm just using plain old delete statements like:  delete from tableName where id < 600000


Galois group is determined by action on roots of polynomial

This is a very simple question but I can't give a good answer to it. If we have a field $K$ and a Galois extension $L/K$ where $L=K(\alpha_1,\ldots,\alpha_n)$ and $\alpha_1,\ldots,\alpha_n$ are the roots of some separable polynomial in $K[x]$, then any automorphism of $L/K$ is uniquely determined by its action on the $\alpha_i$. I suppose it is 'clear' because any element of $L$ is formed by combining elements of $K$ and the $\alpha_i$ with field operations but this is not really rigorous enough for me. I'm sure there's a better explanation but I can't see it.  (Explanation in suggested problem didn't explain the specific point I did not understand, but I understand now.)


Ubuntu installed but doesn't boot: error parsing PCC subspaces from PCCT

I got a new PC and I'm installing Ubuntu again as a dual boot alongside Win10, but this time Ubuntu won't even boot, instead I get some errors.   I think that there is something wrong with GRUB give that when I turn on my PC Windows boots automatically; the GRUB menu never appears.  Here's what i get when I try to force boot into Ubuntu from BIOS    System information: Dell latitude, Legacy BIOS, secure boot OFF.


Let $f$ be an analytic function on $\bar{𝐷} = \{z \in \mathbb{C}: |z| \le 1\}$. Assume that $|𝑓(𝑧)| ≤ 1$ for each $z\in \bar{D}$. Then, which of the following is NOT a possible value of $(e^{f})''(0)$??  $(A) 2$  $(B) 6$  $(C) \frac{7}{9}e^{\frac{1}{9}}$  $(D) √2 + 𝑖√2$  So I take a look at Cauchy Integral Formula and then $$(e^{f})''(0)=\frac{1}{\pi}\int_{|z|=1}\frac{e^{f(z)}}{z^3}$$  Taking modulus on both sides we have $$|(e^{f})''(0)| \le \frac{e}{\pi}2\pi=2e$$  Hence (b) cannot be the choice.   Is this alright!!  Thanks for the help!


bibliography entry all on one page (formatting)

I am using a .bib file and am trying to program my .cls file to print the bibliography so that every entry is on complete and not broken up on different pages. Can anyone help?


I had the brilliant idea of switching from windows to Ubuntu 20.04, however i soon realized that Adobe does not support Linux. I downloaded Vmware but it had an issue with Kernel. Not knowing how to deal with it i downloaded Virtualbox instead, however, I had the same issue. How would I go about solving the issue? probelem message: Kernel driver not installed (rc=-1908) The VirtualBox Linux kernel driver is either not loaded or not set up correctly. Please try setting it up again by executing '/sbin/vboxconfig' as root. If your system has EFI Secure Boot enabled you may also need to sign the kernel modules (vboxdrv, vboxnetflt, vboxnetadp, vboxpci) before you can load them. Please see your Linux system's documentation for more information. where: suplibOsInit what: 3 VERR_VM_DRIVER_NOT_INSTALLED (-1908) - The support driver is not installed. On linux, open returned ENOENT


What is the equation that determines evaporation rate for water?

So I'm guessing it has to do with temperature of surface water, temperature of surrounding, surface area, humidity,... I always wondered if there was an equation to describe evaporation, never learned one in high school.


"I would have liked to come" and "I would like to have come" - difference?

Please read the following:   I would like to come with you.  I would have liked to come with you. I would like to have come with you.   Another example:   I would prefer to drink coffee. I would have preferred to drink coffee. I would prefer to have drunk coffee.   I perfectly understand the first sentence in both the groups. What I would like to know is the difference between second and third sentences. Could you please explain that?


Before and after data: Which test for average comparison of Likert scale data?

I have one group of respondents which answer on a scale of 1-5 once before and once after an experiment. I want to see if the experiment made a difference to their responses.  I was told not to use a t-test because of the Likert scale (ordinal data does not seem to fit a t-test) and because my data are not nearly normally distributed (answers to the questions lean heavily to the 1 of the scale (which is not a mistake in the design)).  I am not sure if the Wilcoxon signed-rank test works, because it seems to be designed for differences in groups (as in "Do men respond differently from women?").  Any suggestions on what could actually be used here?  (The answer  refers to a "special paired t-test", but does not explain which one)


Ctrl+Alt+F1 is not working anymore after installing VMware View Agent

I have successfully installed GUI/Python/VMware View Agent on one Ubuntu VM. But the second day after I powered it on, Ctrl+Alt+F1 was not working any more.  Is there any possibility to back to Command line?     Update: Finally I figured out Ctrl+Alt+F1 is not functional because I installed VMware View Agent. But so far I don't have any solution.


Should we really be suggesting that people put the answer in the question?

I saw  that the user had self-answered by editing the question. I pointed out that they should really answer the question. I know they wouldn't be able to straight away, but I assumed they'd tried and got the "you need to wait a bit" prompt. However, what I didn't realise was that the message says:  Oops! Your answer couldn't be submitted because: Users with less than 100 reputation can't answer their own question for 8 hours after asking. You may self-answer in 7 hours. Until then please use comments, or edit your question instead  (my bold). Should we really be suggesting that people put the answer in the question even as a temporary measure? What's the next step for this? Is there any agreement that this phrase should be removed? If there is how do I turn it into a feature request without asking a new question? Should I just ask a new question which is a feature request?


Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality

Let the set S be infinite, and the set T countably infinite. S and T are both subsets of R. Show that S and S U T have the same cardinality.  I know we can discuss whether S is countable or uncountable, but is it true that, for example like this, countable set's cardinality basically does not count in the union of itself and an uncountable set?


Error when I try to use set() function in a class

I have a class that contains 4 Calendar variables:  public class Ponto {     Calendar entrada;     Calendar saidaAlmoco;     Calendar entradaTarde;     Calendar saida;      public Ponto(Calendar entrada, Calendar saidaAlmoco, Calendar entradaTarde, Calendar saida) {         this.entrada = entrada;         this.saidaAlmoco = saidaAlmoco;         this.entradaTarde = entradaTarde;         this.saida = saida;     }      public void setEntrada(Calendar entrada) {         this.entrada = entrada;     }      public void setSaidaAlmoco(Calendar saidaAlmoco) {         this.saidaAlmoco = saidaAlmoco;     }      public void setEntradaTarde(Calendar entradaTarde) {         this.entradaTarde = entradaTarde;     }      public void setSaida(Calendar saida) {         this.saida = saida;     } }   Then when I try to send the values via set() function i it gives the error:  Attempt to invoke virtual method 'void pt.eu.metaloapp.Ponto.setEntrada(java.util.Calendar)' on a null object reference;  This is the code:  Calendat picagem = Calendar.getInstance(); String hora = sdf.format(picagem.getTime()) + "h";  switch (verificarPonto()) {       case 1:          txtHoraEntrada.setText(hora);          ponto.setEntrada(picagem);          break;       case 2:          txtHoraSaidaAlmoco.setText(hora);          ponto.setSaidaAlmoco(picagem);          break;       case 3:          txtHoraEntradaTarde.setText(hora);          ponto.setEntradaTarde(picagem);          break;       case 4:          txtHoraSaida.setText(hora);          ponto.setSaida(picagem);          break;        }   Is there any problem with sending Calendar values to a class or something?


Running sudo apt update, I got this error:  W: Failed to fetch http://dl.google.com/linux/earth/deb/dists/stable/Release  Unable to find expected entry 'main/binary-i386/Packages' in Release file (Wrong sources.list entry or malformed file)   How do I fix this? I am running Ubuntu 14.04 64-bit.  Update: I followed , but the error returned today. The file /etc/apt/sources.list.d/google-earth.list is back to the way it was, and I just noticed it has these two lines:  ### THIS FILE IS AUTOMATICALLY CONFIGURED ### # You may comment out this entry, but any other modifications may be lost.   So it seems the file was overwritten, meaning the current answer is not a permanent fix, and neither is the duplicate.  Update 2: I've decided to uninstall Google Earth and delete its .list file. I never use it anyway. If anyone is having the same issue, let me know and I'll help you out.  Update 3: muru mentioned in the comments that there is a cron file, /etc/cron.daily/google-earth. I read through it and found it appends this to the .list file:  deb http://dl.google.com/linux/earth/deb/ stable main   So maybe editing this part of the cron job, or disabling it outright, would solve the problem.


Insert an Arabic script within an English

Actually this question asked many times before such as , ,  and the article written in . However, I'm using the online editor and when I tried the solutions mentioned I still get an errors and no resulted file after compilation. It appears like the used packages is not recognized.   The last choice I tried is to use this in the preamble:  \usepackage{arabxetex}  \newfontfamily\arabicfont[Script=Arabic, Scale=1.5]{Scheherazade}   and this for the Arabic text:  \textarab{نص عربي}   After compilation I got this error:    I tried the two compilers inside the yellow square but it didn't work    I opened a test project that has only this package and this was the result: as     It's worth to mention that I can't use the offline editor   Any thoughts about how to solve it?  Thanks


Are there gaps present between lines in a continous line spectrum?

It might seem counter-intuitive for gaps to be formed in a "continuous spectrum", but according to Planck energy carried by a photon is quantised and can have only discrete values so therefore accordingly the wavenumber should also be quantised and have only discrete values. Does that mean that when we use an ultra-powerful hypothetical microscope we should be able to see gaps between discrete lines in a continuous spectrum (hypothetical because how would you see gaps between light using light? wouldn't Heisenberg be disappointed? especially when then the gap is very minute? or maybe we might be using sensitive detectors to see if there are gaps between photons or something I didn't consider)


rank of complex conjugate transpose matrix property proof

I have a question about complex conjugate matrix.  Prove that for any rectangular matrix $A$,  rank $A$=rank $A^*$ where $A^*$ is complex conjugate transpose of A.


Mr. Weasley puts a charm on the car to make it bigger on the inside.      Mr. Weasley has used this charm on his flying car, which we see in Harry Potter and the Chamber of Secrets, to make the inside of the car larger than the outside.     However, we learn that electricity doesn't work around magic.      Magic was known to interfere with the functionality of Muggle technologies powered by electricity.     How can anyone drive the car if electricity won't work?


Request for apps for Mathematical Drawing

I have been for long looking for some software apps which can help me draw various mathematical and geometrical figures and drawings.Can someone please tell me something about these which will run on Windows or Android ?


Why is Blender not saving my render after I already set the output location?

Why is Blender not saving my render after I already set the output location This seems to be themost common problem I see in all the forums Ive read so far, yet after doing it, its still not saving anything? I do Render>Render image and see the render in blender but its not in the folder I specified


Sorry for the stupid question, but is the following sentence correct: "The main strength of the paper is the results"? I am always confused by the form of the verb in such sentences, so should the verb "to be" here correspond to the "strength" or to the "results"?


What is this manga where a girl is told that she's never been seen only as a friend?

This picture is really cute so I want to know what manga this is so please help me thank you for your consideration.


What is the math behind ^^+ being replaced by k?

In my readings I've come across that the TeX preprocessor replaces ^^+ with k.  The explanation given is the following:      For instance, the sequence ^^+ is replaced by k because the ASCII   codes of k and + differ by 64. Since this replacement takes place   before tokens are formed, writing \vs^^+ip 5cm has the same effect as   \vskip 5cm.   I'm not a mathematician but I've looked at the ASCII table, and while I can see the ASCII codes of k with ASCII code of 107 and + with ASCII code of 43 differ by 64.    Yet I don't see what the mathematical relationship that he is describing is.  What is going on here?


What could someone do if they had a check made out to me?

Suppose I receive a check.  Maybe it's for employment, or a class-action settlement, or maybe even just a graduation present from a relative.  Doesn't matter.  Point is, it grants me some amount of money.  Now, let's say that I somehow lose the check in a public place.  The details of that doesn't matter either, except that the check is still intact and is easily found.  Assume the following:   I live in the United States, specifically New York state. The check is made out to me, and my name (which is very uncommon) is spelled correctly.  It also specifies a valid monetary amount. I still have my wallet, debit card, bank account credentials, and other important financial info. The check itself is perfectly legitimate, as is my reason for receiving it. The person who found my check does not know who I am. I haven't endorsed, signed, or otherwise written anything on the check. The person who found my check is in the United States, but not necessarily in New York (maybe I had to go to New Jersey for the day).   Given the above, if someone else acquired a check made out to me, could they use it for nefarious purposes (i.e. to bleed me dry)?


In LaTeX the symbol for material implication is produced by $\to$, but for  ?


Should I put indefinite article in the sentence She became (a) soloist of/with the American Ballet Theatre?


How to the set permission of content types for a specific user role?

How to set the permission of content types for a specific user role?


How can I generate the smallest enclosing sphere from a mesh?

I have a polygon which is defined by a set of vertices and I need the smallest sphere encompassing the mesh.  The spheres are defined by a position vector (x,y,z) and a radius.  Is there an algorithm that given a solid collision mesh with no holes generates the smallest sphere that encompasses a solid collision mesh with no holes in all cases    This is not a duplicate of  question because the question is only about a sphere encompassing a polygon soup a. I'm asking if there is an algorithm that given any solid collision mesh with no holes generates the smallest sphere that encompasses a solid collision mesh in all cases.


Trouble with terminal updating getting an error

Could not get lock /var/lib/apt/lists/lock.  It is held by process 1453 (packagekitd).  can any one tell what this and how to fix plz and thank you.


What is the use of Hidden layers in Neural Networks? How do we know the role of each hidden layer?


How to modify the header of a HttpUrlConnection

Im trying to improve the Java Html Document a little but i'm running into problems with the HttpUrlConntion. One thing is that some servers block a request if the user agent is a Java VM. Another problem is that the HttpUrlConnection does not set the Referrer or Location header field. Since several sites use these fields to verify that the content was accessed from their own site, I'm blocked here as well. As far as I can see the only resolution is to replace the URL handler of the HTTP protocol. Or is there any way to modify the default HTTP Handler?


There are quite some houses and clothes for sale, but I do not have any money. What is the fastest way to get money in GTA San Andreas?


How do I create a Windows 7 USB installer with preinstalled software?

I was wondering if it was possible to make a bootlable image of a Windows 7 Pro OEM Installation CD that I have and put it on an USB stick for faster/easier installation. I am asking because we have a couple of PC´s where I´d have to install the OS using the same key (MAK).  Also is it possible to kind of populate that image with software that would have to be installed anyways on all machines (like Chrome, Outlook, etc)?  It would be really helpful to just install a Windows 7 image with customized software already installed. I would just make an image of an OS and use that, but the hardware of the machines differ.


Is there a way I can give players enchanted items and armor in MCPE with commands?

I am making a minigame and want to be able to give players enchanted items by the click of a button. I know how to use /give but can you also enchant it? I have tried this: /give @p diamond_sword 1 0 {ench:[{id:17,lvl:2},{id:19,lvl:2}]}  If it does not work I can just have them click buttons while holding the items.


I used to just add some blocks inside the water and once removing them again the water would drain away. But since 1.2 (or at least since i last played) this does not work anymore, the water just reappears behind the block.  I currently just want to make a shaft downwards without water in it.


Python subprocess: how to use pipes thrice?

I'd like to use subprocess on the following line:  convert ../loxie-orig.png bmp:- | mkbitmap -f 2 -s 2 -t 0.48 | potrace -t 5 --progress -s -o ../DSC00232.svg   I found thank to other posts  but in the example we use only twice pipe.  So, I try for two of the three commands and it works  p1 = subprocess.Popen(['convert', fileIn, 'bmp:-'], stdout=subprocess.PIPE) # p2 = subprocess.Popen(['mkbitmap', '-f', '2', '-s', '2', '-t', '0.48'], stdout=subprocess.PIPE) p3 = subprocess.Popen(['potrace', '-t' , '5', '-s' , '-o', fileOut], stdin=p1.stdout,stdout=subprocess.PIPE) p1.stdout.close()  # Allow p1 to receive a SIGPIPE if p3 exits. output = p3.communicate()[0]   Can you help me for the third command?  Thank you very much.


Compiler issues: NullPointerException in the line "mass[i].mainN = scan.nextInt();". To my mind, I've inizialized all variables "mainN" and the array "mass". What can be the reason of the exception?  import java.util.Scanner;  public class Robotics{  public static void main(String[] args) {      Scanner scan = new Scanner(System.in);     int N = scan.nextInt();     Robo[] mass = new Robo[N];     for(int i = 0; i < mass.length; i++) {         mass[i].mainN = scan.nextInt();         mass[i].auxiliary = scan.nextInt();     }     scan.close(); }  class Robo{     int mainN;     int auxiliary; }


Let $A,B\subseteq\mathbb{R}$ two non-empty sets such that $a<b$ for all $a\in A$ and $b\in B$.   Which of the following properties hold:  (1) $\sup A<\infty$  (2) $\sup B<\infty$  (3) $\sup A<\inf B$  (4) $\sup A=\inf B$ iff there exist sequences $(a_n)_{\mathbb{N}}$ in $A$ and $(b_n)_{\mathbb{N}}$ in $B$ such that $\lim\limits_{n\to\infty}x_n=\lim\limits_{n\to\infty}y_n$  (5) $\sup A<\inf B$ iff there exist sequences $(a_n)_{\mathbb{N}}$ in $A$ and $(b_n)_{\mathbb{N}}$ in $B$ such that $\lim\limits_{n\to\infty}x_n<\lim\limits_{n\to\infty}y_n$  My ideas:  (2) is false:  Consider $B=\{x+y: x,y\in \mathbb{R}_{>0}\}$ and $A=\{0\}.$ Then $A$ and $B$ satisfy $a<b$ for all $a\in A$ and $b\in B$, but $\sup B$ does not exist in $\mathbb{R}$.  (3) My attempt: Fix $b\in B$, by assumption it is $a<b$ for all $a\in A$. Thus, $b$ is an upper bound for $A$, therefore $\sup A<b$. Or follows $\sup A\le b$ (I'm not sure at this point)? Since $\sup A$ is a lower bound for $B$, $\sup A<\inf B$...or is $\sup A=\inf B$ as well possible?  (1) is correct: $\sup A\le \inf B$ and $\inf B$ exists in $\mathbb{R}$. (Suppose $\inf B$ doesn't exist in $\mathbb{R}$. $\inf B=-\infty$ only can happen if $B$ is not bounded below which is a contradiction to $B$ is bounded below by a non-empty set $A$.)   (4) Suppose $\sup A=\sup B$. Take $(a_n)_{\mathbb{N}}$ in $A$ converging to $\sup A$ and $(b_n)_{\mathbb{N}}$ in $B$ converging to $\sup B$, for the existence see here  . Then: $\lim\limits_{n\to\infty}x_n=\lim\limits_{n\to\infty}y_n$. However, I don't know about the other direction.  (5) I don't know..  Is everything what I have tried correct? How does it work for (3) and the remaining directions in (4) and (5)? Thank you


a = open("file", "r"); a.readline() output without \n

I am about to write a python script, that is able to read a txt file, but with readline() there is always the \n output. How can i remove this from the variable ?   a = open("file", "r") b = a.readline() a.close()


Induction proof: $n! > 2^n$ for all $n \geq 4$

Prove: $n! > 2^n$ for all $n \geq 4$  I already proved the base case: $24 > 16$.   Then I assume this holds for $n=k$, and start proving it for $n=k+1$:  $(k+1)k! > 2^{k+1}$  $(k+1)k! > 2^{k}(2^1)$  After this I'm not sure how to proceed. Any help is appreciated, thanks in advance.


If I become an imperial legion member can I still join the stormcloaks?


I am trying to understand reflection. I am trying to use reflection to get the properties from objects. I first was using  var propertiesForManuallyCreated = typeof(T).GetProperties();   but then realized it wasn't getting the base properties. I tried  var propertiesForManuallyCreatedBase = typeof(T).BaseType.GetProperties();   but that didn't get me the base properties. How can I get the base properties? Below is an image of what I am talking about when I say base.


Event on a button click when the button is generated after the load of the page

in my code, I duplicate a piece of html code with jquery for some reasons. In this piece of code, I have a button. The initial button, when it's clicked, displays something in the page. But the problem is that my new button, generated in jquery, doesn't run the event. It does nothing.   My button (in a table) :  <button></button>   The way it's duplicated :      var table = document.getElementById("table_cultures");      var row = document.getElementById('clonedRow');     var clone = row.cloneNode(true);      table.appendChild(clone);   The "onclick" function :  $(".afficher_itk").click(function(){     //do something });


How do photons travel? Do they have a specific shape?

Generally photons are EM waves (2-axis i.e, 2 dimensions); from that we can imagine a photon basically travels in a cyclic wave pattern. If we go into higher dimensions, will they trace a spiral path to travel? Do they have a specific shape? I don't have an idea what photons are actually comprised of.


Serial voting should not be reversed when all of the posts belong to a single question

Our community took () a poll on our meta. The question has 14 answers, 12 of which are all posted by the same user. By the looks of it, some votes were reversed due to the serial voting detection mechanism.  It seems to me that "real" serial voting would occur across many questions. If one user posts 12 answers to the same question, it is perfectly reasonable to vote on all of them. It might even be reasonable to downvote ten of them and only upvote two.  Can we amend the logic for detecting serial voting to look wide instead of deep? In other words, can we modify it to detect patterns across many questions instead of triggering from a bunch of votes on a small handful of questions? Is there a reason why we wouldn't want to do this?


Suppose I have a piece of steel that is made up of one row of 100 atoms. Now, suppose I try to slide it across a surface by pushing it forward, the atom I come into contact with (the last atom in the row) can only move forward if the atom in front of it moves forward, and so on. So,  is motion like a train, in which between carriages(atoms being our carriages) there are links that can stretch and vibrate; I know that on an atomic level atoms have vibrational and stretch energy.   I guess what I am asking is, when objects move, is there a constant shortening and lengthening of the object until it comes to rest.  Sorry if my question is incredibly stupid and overlooking something very basic.


In my home, we're not very fond of capsaicin, and I put too much crushed red pepper (, bloomed) into a vegetable soup[1]. What can I do to remedy the soup? (Obviously, I can cook another pot of soup and combine them, but I'd rather not. Any other remedies?)    [1] The soup was made roughly thus: I bloomed the crushed red pepper in a heavy-handed application of  and added onion and garlic to saute a little and then to sweat; then I added vegetables and water and seasonings, heated it, and let it simmer.


An $i \in [n]$ is called a fixed point of a permutation $\sigma \in S_n$ if $\sigma(i) = i$. Let $D(n)$ be the number of permutations $\sigma \in S_n$ without any fixed point.  Prove that  i) $D(n) = n \cdot D(n-1) + (-1)^n$ for $n \geq 2$ ii) $D(n) = (n-1)(D(n-1) + D(n-2))$ for $n \geq 3$   First I tried to write down all fixed point-less permutations (in one-line notation): $n \leq 1 \rightarrow$: none $n = 2$: (2 1) $n = 3$: (2 3 1) (3 1 2) $n = 4$ (2 1 4 3) (2 3 4 1) (2 4 1 3) (3 1 4 2) (3 4 1 2) (3 4 2 1) (4 1 2 3) (4 3 1 2) (4 3 2 1) Unfortunately I didn't find any way of constructing these permutations by using the ones from $(n-1)$. Could you please help me a little bit? Thank you in advance!


Please excuse the selfishness of the following question:     Let $G$ be a group and $H \le G$ such that $|G:H|=2$. Show that $H$ is normal.   Proof:  Because $|G:H|=2$, $G = H \cup aH$ for some $a \in G \setminus H$.   Let $x\in G$. Then $x \in H$ or $x \in aH$.  Suppose $x \in H$. Then $xhx^{-1} \in H$ because $H$ is a group.  Suppose $x \in aH$. Then $ahH(ah)^{-1} = ahHh^{-1}a^{-1} = a(hHh^{-1})a^{-1}$ ***1  ***1: Can I say now that $x \in H$, based on the that $hHh^{-1} \in H$ and that $aa^{-1} = e$ ?  Thank you for the time you spent reading my doubts.


Preserve bash history in multiple terminal windows

I consistently have more than one terminal open. Anywhere from two to ten, doing various bits and bobs. Now let's say I restart and open up another set of terminals. Some remember certain things, some forget.  I want a history that:   Remembers everything from every terminal Is instantly accessible from every terminal (eg if I ls in one, switch to another already-running terminal and then press up, ls shows up) Doesn't forget command if there are spaces at the front of the command.   Anything I can do to make bash work more like that?


I have the following command:  \newcommand*{\code}{\lstinline[basicstyle=\relscale{0.9}\ttfamily\color{inline code},keywordstyle=\color{inline code},stringstyle=\color{inline code},keepspaces=true]}   I am using this extensively throughout my book, and sometimes the inline code is fairly long (such as a fully-qualified class name). This is causing hbox overflow problems, which is understandable because TeX is unable to hyphenate the code.  One approach that works is to break long code up, so instead of this:  \code{AReallyLongClassName}   I can do this:  \code{A}\-\code{Really}\-\code{Long}\-\code{Class}\-\code{Name}   Whilst this works, it would be really laborious going through all my \code usages and converting them. Also, it makes the source harder to read.  I've been reading through a few existing questions on this matter and found some advice to do this:  \usepackage[htt]{hyphenat} % enable line breaks   However, that seems to only be supported with texttt, which I'm not using (and am not familiar enough with it to know whether I should be using it, but what I've read suggests not).  I've also tried this:  \hyphenation{A-Really-Long-Class-Name}   But that also seems to be ignored by lstinline.  Here is a MWE:  % !TEX program = xelatex  \documentclass[fontsize=11pt,pagesize=auto,hidelinks,cleardoublepage=empty,parskip]{book}  \usepackage{listings} \usepackage{xcolor} \usepackage{relsize}  \usepackage[paperheight=10in,paperwidth=6in,margin=2cm,heightrounded,bindingoffset=5mm,showframe=false]{geometry}  \sloppy  \newcommand*{\code}{\lstinline[basicstyle=\relscale{0.9}\ttfamily\color{red},keywordstyle=\color{red},stringstyle=\color{red},keepspaces=true]}  \begin{document}  Here is a paragraph with some inline code. \code{ReallyLongName.First.Second.Third.Fourth.Fifth}.  Here is a paragraph with some inline code. \code{Really}\-\code{Long}\-\code{Name}\-\code{.First}\-\code{.Second}\-\code{.Third}\-\code{.Fourth}\-\code{.Fifth}. \end{document}   Output:   Is there a better solution here?


What's the meaning of this present perfect sentence?

The sentences are:   Mary has worked as a teacher for over 25 years. It has rained heavily for 2 hours.   Does it mean "Mary" is still working as a teacher or she is no longer working now? Does it mean it is still raining or it stopped?  Since it cannot mean both, so how to suggest either one of the meanings?


How does one delete a VF page from production?  There is no delete button there.  Is it possible to delete it from a sandbox and somehow migrate the deletion to production?


two equivalent truth tables, two seemingly inequivalent statements

While I'm relatively new to Boolean algebra, I feel like I understand the rules reasonably well. I was legitimately surprised to find that what I call A NAND B, i.e. $\lnot(A\land B)$, has an identical truth table to what I call (NOT A) OR (NOT B), i.e. $\lnot A \lor \lnot B$. That table is here: A | B | out 0 | 0 | 1 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0  I believe that if two different logical statements share the same truth table, then they are equivalent, but my algebraic manipulations of the two statements don't lead me to find that they're equivalent. My questions, then:  Is it correct that if the truth tables of two (or more) statements are identical, then we know those statements are logically identical? How does one show that these two are identical statements algebraically?  I have done study on my own on this subject, but haven't had formal training in it. Any help is appreciated.


I am getting this error when using apt-get command

mayank@mayank-Compaq-15-Notebook-PC:~$ apt-get install android-tools-adb E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?


My profile shows this:    but the toolbar shows this:    It looks like the 24-pixel generated mini-avatar on imgur is broken:    but other sizes are OK:    I realize that this is probably an imgur bug, but I thought it was worthwhile posting it in case other people have this problem. Uploading it again fixed it.


Was Harry making a big mistake with his plan for Elder Wand?

At the very end of Deathly Hallows, after Harry repaired his own wand with the Elder Wand, he tells Dumbledore's Portrait in the office:     “I’m putting the Elder Wand,” he told Dumbledore, who was watching him with    enormous affection and admiration, “back where it came from. It can stay there. If I die a    natural death like Ignotus, its power will be broken, won’t it? The previous master will    never have been defeated. That’ll be the end of it.   Now, this seems incredibly foolish to me.  "The previous master will never have been defeated" would only have been assuredely true if Harry had died right after depositing the Elder Wand back into Dumbledore's Tomb.   If not, Harry (the Wand owner) would still be alive, and at the risk of being Disarmed (as was shown with Harry and Draco Malfoy, it doesn't matter if the Elder Wand's owner is defeated by death or simple disarming, AND it's not even required that the Disarming would involve the Elder Wand!).  So, if Harry merely put the Elder Wand back into the Tomb, and some years later, someone would disarm him (or, even worse, kill him) - then that someone would become the Elder Wand owner, either by accident or by design:    By accident - Harry is likely to get into plenty of magical duels in the future. Even discounting friendly one (teaching people the Expelliramus), he plans on becoming an Auror!  By design - plenty of people have been in the Great Hall hearing Harry explaining to Voldemort that he, Harry, was now the owner of the Elder Wand, so the fact of his ownership would most assuredly NOT remain a secret, inviting countless people tempted by owning the Deathstick to hunt Harry down. Oh, and the location is now also known!   So "its power will be broken" is quite unlikely to come true!  Is Harry hopelessly wrong? Or am I missing something in the above logic? Was this addressed in canon/JKR info?


My php code is not successfully inserting records to my database. Mysql is giving me a syntax error on the line where I specify INSERT INTO     $conn = mysqli_connect($dbhost, $dbuser, $dbpass) or die ($dberror1);       $select_db = mysqli_select_db($conn, $dbsel) or die ($dberror2);      $sql = "INSERT INTO `lit_order_table` (`email`,  name_first,name_last,company,address,apt,city,state,postal_code,country,ord_options,quantity,message)  VALUES ($email,$name_first,$name_last,$company,$address,$apt,$city,$state,$postal_code,$country,$ord_options,$quantity,$message)";   $conn->close();


What are some good tips on how to extrude text in Adobe Illustrator?

I'm bit of a newbie in Adobe Illustrator and have been learning the application by trying to follow some tutorials and recreating some cool stuff I come across on the web.   That being said, I'm having trouble replicating the effect found in the following image using the standard 'Extrude & Bevel' options. I've also tried copying + pasting the text in front, back, in place and that came out even more horrendous. 'Extrude & Bevel' gives me a nice approximation but nothing that pops out like in the example.   Any tips on how to fine tune my 'Extrude & Bevel' settings or an entirely different method of achieving a similar effect would be very much appreciated. Thanks for your time and help!  How can I create a 3D effect on my text similar to the one in the following image, using Illustrator's Extrude and Bevel tools?