I have a function that sits in one of my React components that's starting to get a bit long. I've decided to keep it in a separate file to keep my component a bit tidier. The issue is that the component has to refer to this in order to get functions and states that are mapped to the props through Redux. Here's how I call it in my component:  import {myFunction} from './functions/myFunction';  handleMyFunction(event) {     myFunction(event).bind(this) }  componentDidMount() {     this.handleMyFunction() }   Here is the function itself in './functions/myFunction':  export const captureSnapshot = (event) => {     console.log(this.props.someState) }   I would have thought that bind this would make all the props available in the imported function but instead I get:     Cannot read property 'props' of undefined   when I try to run the function. How can I pass "this" to the function properly?

I have a pretty good understanding of Javascript, except that I can't figure out a nice way to set the "this" variable.  Consider:  var myFunction = function(){     alert(this.foo_variable); }  var someObj = document.body; //using body as example object someObj.foo_variable = "hi"; //set foo_variable so it alerts  var old_fn = someObj.fn;   //store old value someObj.fn = myFunction;   //bind to someObj so "this" keyword works someObj.fn();               someObj.fn = old_fn;       //restore old value   Is there a way to do this without the last 4 lines?  It's rather annoying...  I've tried   binding an anonymous function, which I thought was beautiful and clever, but to no avail:  var myFunction = function(){     alert(this.foo_variable); }  var someObj = document.body;        //using body as example object someObj.foo_variable = "hi";        //set foo_variable so it alerts someObj.(function(){ fn(); })();    //fail.   Obviously, passing the variable into myFunction is an option... but that's not the point of this question.  Thanks.


in one of some configs files i have the next RegEx: /\.story\.jsx?$/ It's select all files with 'story.jsx' in name, but i also want ignore file if his name has 'template' word. How can i do this with single RegEx: if (.story.jsx && !template) ?

I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "<Regex for 'doesn't contain hede'>" input   Desired output:  hoho hihi haha


Say I've got this Dwarf, Dwarfnir. He has a +1 magic shield that he's pretty happy about. He gets into a big fight and decides that, while it's all fine and dandy to hit things with his warhammer, that he'd sure like to smack some faces sideways with his +1 magic shield, especially that weird thing with all the eyes that seems to be unharmed by his wimpy and totally-not-magic hammer.  Would such an attack benefit from the shield being a magic +1 shield the same way as if it were a magic +1 club (with +1 to attack and damage rolls, and bypassing nonmagic weapon resistances)?  I get an understanding from  how the shield bash would work and that proficiency wouldn't apply, but I'm wondering specifically about Dwarfnir getting that sweet sweet magic weapon bonus.

My Gnoll Paladin just got the Gauntlets of Ogre Strength from Phandelver the other day, and it got me wondering:    Would it be possible/make sense for punches using them to count as an improvised weapon? (Since I'm not punching with empty fists, I'm wearing magical gauntlets) If so, would punches from a person using them count as magical weapon damage?


Some time ago, I saw someone mention making a monstrum when asked about creating monster races. Supposedly it is a PC that is the child of a human and a monster, or something like that. I was wondering where I can find the rules for doing so. For example, a Half . It's like a half-elf, but instead of an elf, the non-human parent was a monster. The idea is that some of the monster's abilities would be passed down to the offspring but not all and in a weaker variation.  This is not a duplicate of , because that post is asking about making new races in general, not specifically tailored to monster-human offspring like mine is. If this is a duplicate then please explain to me where the overlap is located because for the life of me I can't see it. In the linked post I see creating a monster race and advance race guidelines (linked twice) neither of which answer my question.

I would like to create a new race which you can play as a PC without it being too overpowered for normal game settings. I would like one with wings, but are wings (even wings with clumsy maneuverability) (or gills or claws or a prehensile tail) potentially game-breaking? And what about racial traits and size categories and spell-like abilities-which ones are acceptable for PC use?


The excerpt below is taken from a web article I was reading.  The powerful machine LHC accelerates and steers billions of protons to collide with billions of other protons. The goal of this work is to answer fundamental questions to understand Nature. But what really happens when protons collide? Protons consist of quarks bound by gluons, and in a head-on collision between two protons it is the constituent quarks and gluons that collide. Inside each proton you can find a "sea" of quarks and gluons. Why so many? Haven't you learned that there are only 3 quarks inside a proton? Well, we say that a proton consists of 3 "valence" quarks, but also a whole bunch of “sea” or “virtual” quarks and anti-quarks stemming from gluons. When protons collide with such large energies as at the LHC, the collision results in a shower of all types of particles, the ones usual matter is made of, and others that only existed just after the Big Bang. The new particles are usually much heavier than the original colliding particles, thanks to the relation $E=mc^2$. To say it simply: All the energy we put into the collision can come out as mass instead!  Source:  I think that when protons collide with each other their kinetic energy is converted into matter in form of new sub-atomic particles and protons also get broken down though a quark cannot exist as an individual unit. Do those quarks get together again to make up a proton? Where do those quarks go? Why don't they use electrons instead of protons at CERN? I understand that an electron is an elementary particle which means, according to the current knowledge, an electron is not made up of any more basic particles. If electrons are used, their huge kinetic energy would also be converted into sub-atomic particles though the electrons themselves would remain intact. Perhaps, using electrons would not produce as many sub-particles since they are almost 1850 times less massive than protons so their kinetic energy would always be less than that of protons. Besides this, it might be possible that since electrons do not break down therefore, for some reason, this also limits the creation of new sub-atomic particles. Could you please help me with it? Helpful links:  Ars Technica. , YouTube, Oct. 16, 2018.  Seeker. , YouTube, Aug. 18, 2016.

Electrons   have a much bigger charge density as the protons (and especially lead nuclei), aren't compound particles as the protons (and especially lead nuclei) are able to get a much bigger energy with the same fields as the protons (and especially the lead nuclei).   Why seems common for the big colliders after the LEP to use protons (and much bigger nuclei)?  Reacting comments: Yes, to get good experimental data about quark matter they need a lot of hot quarks (= collided big nuclei). But to create new particles, the energy per degree of freedom needs to be maximized, and this maximum is at the single particle with the highest charge density, and this is the electron.


I am trying to set up a Ubuntu server on Raspberry Pi 2, but at the moment I am stuck with this:  sudo: unable to resolve host ubuntu   /etc/hostname says this:  ubuntu   /etc/hosts says this:  127.0.0.1 localhost  # The following lines are desirable for IPv6 capable hosts ::1 ip6-localhost ip6-loopback fe00::0 ip6-localnet ff00::0 ip6-mcastprefix ff02::1 ip6-allnodes ff02::2 ip6-allrouters ff02::3 ip6-allhosts   I have seen solutions where one can go into recovery mode and change the password and change the hosts, but I don't think I can do that on server version on Raspberry Pi 2. Or can I?  Thanks

And when I tried the following commands /etc/hostnames and /etc/hosts, it says:  bash: permission denied.


I was finally able to get the OS installed on my MSI Ghost Pro laptop (currently the only OS on the machine) only to discover that NONE of my networking drivers were working. ifconfig only shows the lo interface and nothing more. All of the troubleshooting guides I can find assume at least some method of being able to connect to the internet in order to make any fixes.   I know this question can be dependent on the specific drivers themselves, and was hoping someone could tell me if there is a way to get this particular ethernet driver working on Ubuntu 14.04, or any any other way of connecting this machine to the internet in order to make the necessary updates.  The particular Ethernet card on the machine is the 1969 ("Qualcomm Atheros"), device: e0a1 ("Killer E2400 Gigabit Ethernet Controller")

I have a new motherboard: MSI Z170A GAMING M5. This motherboard has an Atheros killer e2400 Ethernet controller. When I do lspci -nn, I get:  03.00.0 Ethernet controller [0200]: Qualcomm Atheros Device [1969:e0a1] (rev 10)   Google didn't seem to know the answer. Only a similar unsolved problem on the openSUSE forum.


$$\sum_{n=1}^{\infty}\frac{1}{n(n+1)\cdots(n+v)}=\frac{1}{vv!}$$ I am struggling to find a solution for this but no luck yet. How can I analyze it to get to second part?

Does anyone have any idea how to prove that  $$\sum_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)...(n+k)} = \frac{1}{kk!}$$


Usually on bash i did  shopt -s extglob rm !(filedontwantremove)   and remove all files except filedontwantremove  But if i want to remove all file except filedontwantremove and "antotherfilewithatotaldifferentname"?  There is a find solution,but i prefer i thing like rm !()

So, you can use the * as a wild card for all files when using cp within context of a directory.  Is there a way to copy all files except x file?


Is there a "geometrical" intuition behind L'Hospital's rule? I have recently found out the "geometrical" meaning of Taylor's approximation series and I was wondering if there is something analogous for L'Hospital's rule.

I understand perfectly well how to apply l'Hopital's rule, and how to prove it, but I've never grokked the theorem. Why is it that we should expect that $$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x \to a}\frac{f'(x)}{g'(x)},$$ but only when specific criteria are met, like $f(x)$ and $g(x)$ approaching $0$ as $x \to a$? I've never found the proof of the theorem to shed much light on this (thought this might be because I don't have much of an intuitive sense as to why the Cauchy Mean Value Theorem holds, either). I've always been mystified as to how l'Hopital (Bernoulli?) ever discovered this theorem, beyond accidentally discovering that it holds in some cases and then generalizing it to a theorem. So, if you have any ideas as to where the theorem came from, and why it makes intuitive sense, I'd appreciate it if you shared them!


I have a 4k display, so by default Spotify is incredibly zoomed out. To fix this, I had a look at , which recommends adding a command line option. This works when I launch Spotify through the terminal, however I want it to launch that way by default when I click on the icon. I attemped to follow the guidance in the rest of the solution, which mentions editing spotify.desktop, however whenever I try to edit it gedit says the file is read-only, even using sudo. First, I used sudo find . -name spotify.desktop and got the response of:  find: ‘./run/user/1000/gvfs’: Permission denied ./snap/spotify/21/meta/gui/spotify.desktop ./snap/spotify/21/usr/share/spotify/spotify.desktop find: ‘./proc/19908/task/19908/net’: Invalid argument find: ‘./proc/19908/net’: Invalid argument   Running sudo gedit /snap/spotify/21/meta/gui/spotify.desktop or sudo gedit /snap/spotify/21/usr/share/spotify/spotify.desktop opens gedit, but in read-only mode. Attempts to change the file permissions leads to chmod: changing permissions of '/snap/spotify/21/usr/share/spotify/': Read-only file system.  How should I best proceed?

I have been trying for a long time to change Blender's icon, but no matter what I do, I am not allowed to edit anything in /snap/blender-tpaw/3/.  Here's what I tried:   Editing the files from nautilus without sudo. Editing the files from nautilus with sudo (sudo nautilus in terminal ). Using terminal commands such as cp or rm without sudo. Using terminal commands with sudo (such as sudo cp <source> /snap/blender-tpaw/3/ or sudo rm /snap/blender-tpaw/3/<filename.ext>) Doing everything above in a root terminal (using sudo -i)   In every case I get the following error:  cannot remove/copy '/snap/blender-tpaw/3/filename.ext': Read-only file system   where filename is the file and .ext is its extension.  This also applies to other snaps' files, not only Blender.  Am I doing something wrong here? Or is it just impossible to change those files? Although I don't think it is impossible because everything here from Ubuntu to Blender is open-source, so they have no reason to block us from modifying those files.  EDIT:  I used Main Menu (alacarte) to change the icon, but I still want to know why I cannot modify any snap file.


I want to format my system, but I don’t want to lose my updates and installed packages. I also want the same packages on other systems as well.

So I've been messing with thing that probably shouldn't be messed with trying to learn my way around Linux, and I seem to have messed something up. I'm getting a lot of error messages, reduced speed, and crashes, so I'm going to do a clean install.   However, I an using mobile broadband and don't exactly want to use all of it up again re-downloading updates.  Is there any way I can save all the packages installed now with their updates to an external hard drive?


In Mail on macOS Big Sur, I went to Preferences > Viewing > to show message-IDs in the header. The message-ID is a unique identifier for each email and looks something like this: <4E21D492-X12X-1234-93E5-271B1C901234@googlemail.com>  How can I get message-IDs to show in Mail on iOS?

Does Apple Mail under iOS support the ability to get the raw as-sent text of an email? Alternatively, is there a way to forward an email as an attachment?  I'd like to be able to report spam email to Spamcop.net, but I need all the headers and the raw source of the email, not just a copy of the rendered results.


Around one month ago I changed the name of one paper of mine on ArXiv. I noticed that on google scholar it still appear with the old name and that if I search on google with the new name it does not find anything.  Is there a workaround to fix this problem?

I know that new arXiv papers usually appear in Google Scholar within a few days or weeks. My question is: if someone submits a replacement of his/her arXiv paper, does the new version of the paper also appear in Google Scholar?


What if some person has access to someone else's Stack Exchange account (compromised credentials, open laptop, etc.) and goes ahead and posts something useless or even offensive garnering multiple downvotes and thereby negatively affecting that person's reputation?  Can the original user be awarded his rep back on an appeal/request? This is, of course, keeping in mind the question asked is not a "bad" question; mainly spam.

In an answer on Meta Stack Overflow, Brad Larson ♦ ,  In the vast majority of cases where the 100-point penalty is applied and a moderator notices, the account is also destroyed.... The few outlier cases tend to be when you have an otherwise good account that all of a sudden posts something bizarre. Sometimes it's a compromised account, sometimes people leave themselves logged in at a shared computer, etc.  In the cases where a contributing user does get hacked, and the hacker starts making red-flaggable posts (e.g. Spam, nonsense, or personal attacks), is there a procedure for separating out the penalties due to the hacker and negligence penalties applicable to the original account owner once the owner regains control? That is, if someone hacks my account and spams with it, am I "stuck" with the applicable black marks against my account (-100 rep penalty for each post, suspensions, question bans, etc.), or is it normal or expected for such posts to be disassociated or at least have applicable penalties reversed? For example,  I have disassociated the three Spam posts that the hacker made with your account, which will refund the 300 rep you lost as a result and lift your question ban. Unfortunately, it seems that you are not entirely innocent because you left your account logged in at a public library where the spammer found and took advantage of it, so I am Suspending you for a week so you can spend some time thinking about best practices in information security. Come back in a week to continue contributing.  At first I thought that it would be normal, natural, and just for all penalties to be reversed against the hacking victim upon submission of proof of victimhood, but then I remembered that I have dealt with some organizations other than Stack Exchange that have had Terms of Service clauses that more or less said "You agree to keep your login credentials secure and will be held solely responsible for any actions taken using your account", but I haven't been able to find such as clause for .


I want to install python 2.7.2.tgz on Ubuntu, downloaded from .  so, what the next step?

I have downloaded tar.gz files. But I don't know how to install it. How do I install this kind of file?


In the chemistry setting, a doped semiconductor is a crystal lattice with holes/extra electrons in it.   In the band/quantum mechanical picture, these holes/extra electrons can be seen as the amount of missing/excess charges from a full band of energy states.   Therefore, in a pure silicon crystal, with full covalent bonds and thus no holes or extra electrons, the valence band is completely full, and the conducting band is completely empty.   Which means that Silicon is an insulator, since the Fermi level lies above the valence and below the conducting band. What are the holes in my reasoning?

I'm tutoring senior high school students. So far I've explained them the concepts of atomic structure (Bohr's model & Quantum mechanical model) very clearly. Now the next topic to be taught is semiconductors.  I myself am not conviced with the concept of electron holes. If there is no electron then there is no electron. How can it be a hole. We define a hole when there is some thing every where except at a place. But inside an atom how can we define a HOLE.  Kindly explain it with the help of Bohr's model. What was the need of introducing such abstract concept in semi conductors?


If the electric field strength is $E_x=x, E_y=E_z=0$, then by $\nabla\cdot E=\frac1{\epsilon_0}\rho_e$ where $\rho_e$ is the density of charge, we get $\rho_e=-1$ for any point in the space. But if $\rho_e=-1$ for any point in the space, then the distribution of charge in space is completely symmetric, so we shouldn't get a $\vec{E}$ which only have $E_x$ component. I am really confused. Can you explain it for me?

This is a question from the second chapter (Problem 2.55) of Griffiths 'Introduction to Electrodynamics' fourth edition. The question says that if in a region, the electric field $E$ exists such that, $E_x = ax$ where $a$ is a constant, $E_y=0$ and $E_z=0$, what is the charge density. The charge density is given by the differential Gauss law, where, $\nabla.E = \dfrac{\rho}{\epsilon_0}$. This gives $\rho=\epsilon_0a$. Since $a$ is a constant, the charge density is uniform everywhere in the region. Now Griffiths further asks how could this uniform charge density produce an electric field that is parallel to just $X$ axis?  My intuitive answer is if there is an infinite slab like uniform distribution of charge where the slab has infinite length and breadth but a finite thickness, if the thickness is along the $X$ axis, the electric field will be along $X$ axis given as $E_x = ax$, $E_y=0$ and $E_z=0$.  However Griffiths himself answers this question in the instructors solution manual as given below.  While I also agree to Griffiths on a broader picture, I want to know if my intuitive solution of an infinite slab of finite thickness wrong?


I upgraded successfully. Now, when I run this:  dpkg --list | grep linux-image   I get this:  ii  linux-image-3.13.0-24-generic                               3.13.0-24.47                                                amd64        Linux kernel image for version 3.13.0 on 64 bit x86 SMP rc  linux-image-4.4.0-31-generic                                4.4.0-31.50                                                 amd64        Linux kernel image for version 4.4.0 on 64 bit x86 SMP ii  linux-image-4.4.0-34-generic                                4.4.0-34.53                                                 amd64        Linux kernel image for version 4.4.0 on 64 bit x86 SMP ii  linux-image-4.4.0-36-generic                                4.4.0-36.55                                                 amd64        Linux kernel image for version 4.4.0 on 64 bit x86 SMP ii  linux-image-extra-3.13.0-24-generic                         3.13.0-24.47                                                amd64        Linux kernel extra modules for version 3.13.0 on 64 bit x86 SMP rc  linux-image-extra-4.4.0-31-generic                          4.4.0-31.50                                                 amd64        Linux kernel extra modules for version 4.4.0 on 64 bit x86 SMP ii  linux-image-extra-4.4.0-34-generic                          4.4.0-34.53                                                 amd64        Linux kernel extra modules for version 4.4.0 on 64 bit x86 SMP ii  linux-image-extra-4.4.0-36-generic                          4.4.0-36.55                                                 amd64        Linux kernel extra modules for version 4.4.0 on 64 bit x86 SMP ii  linux-image-generic                                         4.4.0.36.38                                                 amd64        Generic Linux kernel image   So my question is: What do I do with all the extra modules? Do I trash them? If so, how? or do I keep them?

I occasionally update my kernel from this web site    I have been always downloading 3 deb files for installing  linux header all, linux image and linux headers. I noticed one more deb file recently for 64 bit kernel called Linux-image-extra.  I would like to know what does kernel file Linux-image-extra do and should I also install it?


I want to validate a string with alpha numeric values, but if the string contains -- (double dash) anywhere in the string, it should be invalid.  valid:   apple123 -apple-123 app-le123 a-p-p-l-e-1-2-3   invalid:   --apple123 app--le123       The above old post have the answer ^(?!.*bar).*$ which does the negation, but it does not work for same character repetition like --.  Can anyone help me to figure out to modify the ^(?!.*bar).*$ to identify -- as a string.

I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "<Regex for 'doesn't contain hede'>" input   Desired output:  hoho hihi haha


Several years back, I was on a backpacking trip with a guy whose whole family were huge fans of classic SF/Fantasy.  One of the fantasy books he brought for the long car rides piqued my interest, but I've lost the name.  General things I remember:   It's part of a series It's not very recent (certainly not in the last 20 years)   In particular, the logistics of the magic system intrigued me, and is the main reason for wanting to reread the first book and find the later ones.  Magic is granted by knowledge of words of power, of which there are a finite number in the world.  Knowledge of multiple words of power is possible and grants access to various tiers of abilities:   One word grants somebody a knack for a particular skill.  I don't recall the specifics, but I seem to remember that these were extreme enough to guide somebody's path through life without thoroughly defining it Two words makes somebody an adept, who excels at the acquisition of new skills when intensively trained.  In the book, one example described is that an adept who trained for a day with a master swordsman would be his equal by the end of the day Three words makes somebody a sorcerer.  I have very little knowledge of what this does, since there was only a brief encounter with one (if any).  Knowledge of four or more words isn't brought up, AFAIK. Finally,  the power of a word is slightly diluted by the number of people who know it.  People who know words of power may form agreements to share with each other, but these nearly always ended in one member killing the other(s), as one person could slightly increase their power by offing the other guy   The final detail I remember is that there is a set of individuals who share a space in the world.  These people all know the same word of power, and therefore are all adepts (there is a musician, a stereotypical brute, and maybe a thief?), but only one of them exists in the world at a given time.  I seem to remember that these people could switch out if they reached a consensus.

I read a book of this series probably around 2000. I think the series was quite new then but not sure.  The main thing I remember about it is that magic is based on words of power. If you knew one word you got some extra ability, knowing two words gave you yet some other ability, and if you knew three words you became a very powerful wizard. Only one person at a time could know each word, and telling someone your word meant you died.  The main protagonist somehow gets hold of one word and then for some reason strives to learn more.  EDIT: I think that I accidentally picked up the second book of the series and never read the first one. From what I remember, the protagonist learned one word of power and got some kind of supernatural ability (cannot remember what though). He then ends up in some kind of challenge where he has to cooperate with another person who knows another word that gives super-strength.  Not very coherent memories, but I hope someone knows what series it is. It has been bugging me for years. (Not even sure if the series is good at all, but still would like to know the name.)  EDIT2:  I remember the world as being medieval-ish. I do not think there were dragons, but there may have been other humanoid races (I have a very weak recollection that there may have been an orc or similar in the story, but this could be completely wrong). The protagonist was male.


I am trying to implement a simple Quiz Game and when overriding toString method in my Question class I got a NullReferenceException. Where the problem comes from? This is my code in Question class      public class Question {         private String text;         private Answer[] answers;         private final static int ANSWER_SIZE_ARRAY = 4;          public Question(String text, Answer[] answers) {           this.text = text;           answers = new Answer[ANSWER_SIZE_ARRAY];           this.answers = answers;         }          public void setText(String text) {         this.text = text;      }       public void setAnswers(Answer[] answers) {           this.answers = answers;      }       public String getText() {          return this.text;      }       public Answer[] getAnswers() {          return this.answers;      }      //test toString     public String toString() {          String result = this.getText() + "\n";          for (Answer a : this.answers) {              result += a.getText() + "\n"; // HERE COMES THE PROBLEM          }          return result;      }   }   And my main method is like:      public class MainGameTestMethod {       public static void main(String[] args) {         Answer a1 = new Answer("Krisko", true);         Answer a2 = new Answer("Beatz", false);         Answer a3 = new Answer("Ivan", false);         Answer a4 = new Answer("Pesho", false);         Question q1 = new Question("Whats your name?", new Answer[] { a1, a2, a3, a4 });         System.out.println(q1.toString());     } }

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


I have an old iPad Air 2 that I forgot the passcode for. I want to unlock it without losing my data. I know it's probably impossible on the newer iPadOS but I want to know if I can downgrade the OS to an older version that has security exploits.  Can someone tell me if this is possible and if so how to downgrade and the bypass the passcode.

I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this?


I've been messing around with indefinite integrals. Watching some youtube videos and I found the Sinc function and that it has no finite Anti-derivative.  Desmos being my favourite program ever I decided to graph to the equations $y=\frac{\sin(x)}{x}$ and $y=\int_0^x\frac{\sin(a)}{a}da$ (only way I could do indefinite integrals in Desmos)  If you do this you might notice $y=\frac{\sin(x)}{x}$ looks very similar to $y =\sinh(x)$ and $y=\int_0^x\frac{\sin(a)}{a}da$ looks very similar to $y=\arctan(x)$  I wondered how we know that $\frac{\sin(x)}{x}$ has no finite anti-derivative because these simple functions give seemingly accurate approximations  Best approximation I could get for it in the short time I had was: $$\int \sinh(x)-\frac{d}{dx}\bigg[\frac{\sin(x)}{x}\bigg]-\frac{\pi}{2}$$ or $$2\arctan(e^x)+\frac{\sin(x)}{x^2}-\frac{\cos(x)}{x}-\frac{\pi}{2}$$ (In all the examples I'm assume $C=0$ because it's not important and I'm assuming any points with $\frac{0}{0}$ evaluate to their limits as $x$ tends to $0$)

I came across a list of functions in my calculus textbook whose indefinite integral cannot be found. It was written that the integral $$\int \frac{\sin(x)}{x} dx$$ cannot be evaluated without any explanation as to why.  I did some research over the internet and found out that the definite integral $$\int_{0}^{\infty} \frac{\sin(x)}{x} dx$$ can be evaluated using Laplace transformation and is equal to $\pi /2$. But I still couldn't find answer to my original question. I read somewhere that the integral cannot be expressed using 'elementary functions'. A little help is appreciated, I'm in Calc 1 going advanced than my course but I am sorry if my post shows lack of research. Thank you!


I was driving around and thinking about the sets that we commonly use in mathematical proofs such as $\mathbb{Z}$ or $\mathbb{Q}$. In many introductory proofs courses, these sets seem to be the building blocks of many definitions (such as what makes a number even or odd) or lemmas. In addition to having their own symbols, this sometimes gives off a perception to many introductory proofs students that these sets, while having infinite elements, are somehow singular and entities$^*$.  $^*$(I'm aware that some of these common sets are subsets of the others and aren't "singular" per se. I was trying to convey a description of their perception among students, including myself, due to their prevalent use which spurred this question to begin with).   It got me thinking, can you take a "reductionist" approach and fragment these common sets into an infinite mutually exclusive infinite sets of which the totality of their elements converges to these "special sets"? For example, to start simple, I was wondering if it was possible to have an infinite collection of infinite sets $n_1, n_2, n_3....n_j, n_{j+1}....$ such that:   $n_a\cap n_b=\emptyset$ for $a\neq b$, $\forall$ $a$ and $b$ that are indices to describe the infinite set. $\bigcup^\infty_{i=1} n_i = \mathbb{N}$

Can you partition an infinite set, into an infinite number of infinite sets?


How can I create a chart like the one below (taken from ) in LaTeX:

I am trying to reproduce a similar figure to the following one. My first guess was to use pgfplots but I didn't find any example that I could use as a starting point. At the moment I am unsure if pgfplots is actually the right package or I should rely on something else e.g. TikZ.   Since I don't really know where to start, I would appreciate any piece of code that points me in the right direction.    EDIT  Here is some dummy data for the plots.  plot1   plot2   plot3   plot4 0       0       0       0 3.466   2.058   0       0 4.262   2.976   0.001   0 3.822   3.168   0.006   0.008 2.953   2.936   0.019   0.063 2.065   2.492   0.046   0.265 1.332   1.977   0.092   0.734 0.797   1.478   0.164   1.508 0.443   1.045   0.268   2.44 0.228   0.698   0.412   3.219 0.107   0.438   0.598   3.524 0.046   0.256   0.831   3.219 0.017   0.138   1.109   2.44 0.006   0.067   1.429   1.508 0.002   0.029   1.78    0.734 0       0.01    2.141   0.265 0       0.003   2.479   0.063 0       0.001   2.736   0.008 0       0       2.808   0 0       0       2.465   0 0       0       0       0


Iam having trouble with a code coverage issue in one of my apex class code coverage please find the code below. Apex class: public class Executeapex {  public static void executethismethod(){          DELETE [SELECT Id, CC_ContractType__c, CC_Entity__r.Name, CC_ProductBook__r.Name, createdDate FROM CC_ContractEntityProductMatrix__c];  List<AggregateResult> l_epv = [SELECT CC_ContractType__c, CC_Entity__c, CC_Entity__r.Name E, CC_ProductBook__c, CC_ProductBook__r.Name FROM CC_EntityPropertyValue__c WHERE CC_ProductBook__r.Name != null AND CC_ContractType__c != 'All' AND CC_ProductBook__r.CC_Parent__c = null GROUP BY CC_ContractType__c, CC_Entity__c, CC_Entity__r.Name, CC_ProductBook__c, CC_ProductBook__r.Name]; List<CC_ContractEntityProductMatrix__c> l_cepm = new List<CC_ContractEntityProductMatrix__c>(); for(AggregateResult epv : l_epv){     CC_ContractEntityProductMatrix__c cepm = new CC_ContractEntityProductMatrix__c();     cepm.CC_ContractType__c = String.valueOf(epv.get('CC_ContractType__c'));     cepm.CC_Entity__c = String.valueOf(epv.get('CC_Entity__c'));     cepm.CC_ProductBook__c = String.valueOf(epv.get('CC_ProductBook__c'));     l_cepm.add(cepm); } insert l_cepm;     PageReference pageRef = new PageReference('/apex/Executeapex');     pageRef.setRedirect(true);     ApexPages.AddMessage(new ApexPages.Message(ApexPages.Severity.CONFIRM,'Pricing Calculation successful!'));      }  } Test class:     @isTest   public class Test_Executeapex {        public static testmethod void  test_executethismethod(){         CC_Entity__c e = new CC_Entity__c();         e.Name = 'Test';         e.CC_Country__c = 'FRANCE';         e.CC_DefaultLanguage__c = 'English';         insert e;                    SG_ProductBook__c pb = new SG_ProductBook__c();         pb.Name = 'Test Book';         insert pb;                    CC_ContractEntityProductMatrix__c epm = new CC_ContractEntityProductMatrix__c();         epm.CC_ContractType__c = 'Routine Maintenance';         epm.CC_Entity__c = e.Id;         epm.CC_ProductBook__c = pb.Id;                test.startTest();        // Executeapex exeap = Executeapex(epm.Id);         Executeapex.executethismethod();         test.stopTest();         //DELETE[SELECT Id, CC_ContractType__c, CC_Entity__r.Name, CC_ProductBook__r.Name, createdDate FROM CC_ContractEntityProductMatrix__c];                                }  }  I get a code coverage of 64 % only please find the image below.  Thanks.

This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, including more unit test resources, navigate to the  tag.  This canonical question is intended to address several classes of common questions by providing a quick summary and links to comprehensive resources:   How is code coverage obtained and calculated? How do I increase my coverage?  Why can't I cover these lines? Why isn't the body of my loop or conditional statement covered?


As objects move faster, their time slows down. I understand this, but what I'm having trouble with is intuitively grasping the concept of "time slowing down". A book I'm reading gave the following scenario:  Assume Person A is floating in space, while Person B flies past at a very high speed. If they were to communicate via radio (with electromagnetic waves moving at light-speed), Person A would hear Person B slurring their words.  Why does this happen?  Is it because Person B's time runs slower, and so from the reference frame of Person A, he talks slower? I'm sort of able to wrap my head around this, but I'm having a hard time doing it.  What would happen if Person A and Person B somehow had a conversation, while Person B was at their high speed and Person A was stationary (just as a thought experiment). When Person A spoke, would Person B take a long time to react (relative to Person A)? On the other hand, when Person B spoke, would it seem like Person A was speaking really fast (from B's perspective)?

don't get upset but I'm a total layperson and I'm not really understanding the twin paradox and I'm just wondering: If the twin who left earth in a rocket so that he wouldn't age as fast had a walkie talkie of some kind to contact the twin on earth with, would the twin on earth hear the spaceship twin's voice talking veeeeeeery slooooowly, and would the rocket ship twin hear the other twins voice squeaky and sped up?


I am using ArcGIS 10.2.   How to use ArcPy code to extract every row in the attribute table and save each row to separate shapefiles?

I have a feature class with over 2,000 features, and I need to make them all individual feature classes based on a field.   Is there a way to do this?


When I click on a link it works but when I click that link which is loaded with the help of of innerHTML then it works normally my jquery selector is not working at that time and link redirected to that link as usual some can tell what I should use?   $(document).ready(function() {  }); document.writeln("script load");``  $("a").click(function(e) {   //To prevent refresh   e.preventDefault();   console.log(e.isDefaultPrevented);   // Get the link in clicked anchor tag.   var link = $(this).attr("href");   console.log(link);   // Get that file in via ajax.   $.ajax({     type: "GET",     url: link,     success: function(data, status, xhr) {       history.pushState(data, document.title, link); //for pushing that page into history       document.querySelector("html").innerHTML = data; //change the page       }   }); });  // History handler window.addEventListener('popstate', function(event) {   console.log('popstate fired!');   updateContent(event.state); });  function updateContent(data) {   if (data == null)     return;   var full = document.querySelector("html");   full.innerHTML = event.state; } // very first page pushed into history. var soon = $("html").html(); history.replaceState(soon, document.title, document.location.href);

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


Why is this algebra calculus trick legal? $$ \frac{dy}{dt} = Ky$$ $$ \frac{1}{y}\frac{dy}{dt} = K$$ ...then my teacher did something illogical he decomposed the Differential operator $\frac{dy}{dt} $  into $\frac{1}{dt} *dy$ and used this "form" with the laws of arithmetic to "cancel" the  $\frac{1}{dt}$ by multiplying both sides by $dt$ $$ dt*\frac{dy}{dt}\frac{1}{y} = K* dt$$ $$ dy =K *y *dt$$ Why is this possible? Is it related to the chain rule?

I see an equation like this:  $$y\frac{\textrm{d}y}{\textrm{d}x} = e^x$$  and solve it by "separating variables" like this:  $$y\textrm{d}y = e^x\textrm{d}x$$ $$\int y\textrm{d}y = \int e^x\textrm{d}x$$ $$y^2/2  = e^x + c$$  What am I doing when I solve an equation this way?  Because $\textrm{d}y/\textrm{d}x$ actually means  $$\lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}$$  they are not really separate entities I can multiply around algebraically.    I can check the solution when I'm done this procedure, and I've never run into problems with it.  Nonetheless, what is the justification behind it?  What I thought of to do in this particular case is write  $$\int y \frac{\textrm{d}y}{\textrm{d}x}\textrm{d}x = \int e^x\textrm{d}x$$ $$\int \frac{\textrm{d}}{\textrm{d}x}(y^2/2)\textrm{d}x = e^x + c$$  then by the fundamental theorem of calculus  $$y^2/2 = e^x + c$$  Is this correct?  Will such a procedure work every time I can find a way to separate variables?


I want to get a more accurate track, but some of the makers seem to have a mind of their own and are bouncing all over. I am not sure if this problem is caused either by some of my settings, my footage, or just Blender not being able to do a good job. (Possible?)  My footage was shot using an iPhone 4, focal length of 35 I think (It changes whenever I solve to 41.14).   If my footage being too blurry is the problem (I think that it's not too blurry), I tried changing the Tracking Present to Blurry Footage and that didn't change anything that I noticed. Same with the rest of the presets.  What would fix the markers from jumping around?

Whenever I do camera tracking in Blender the reconstruction is always zooming out or not on the axis. I have a great quality camera, but the end results of the camera tracking always has the model sliding. If you have a solution please tell me.


I am not able to show that:     If $x+y+z=\pi$, show that $\tan(x) + \tan(y) + \tan(z) = \tan(x) \tan(y) \tan(z)$.

I want to prove  \begin{equation*} \tan A  + \tan B + \tan C = \tan A\tan B\tan C \quad\text{when } A+B+C = 180^\circ \end{equation*}  We know that   \begin{equation*} \tan(A+B) = \frac{\tan A+\tan B}{1-\tan A\tan B}~\text{and that}~A+B = 180^\circ-C. \end{equation*}  Therefore $\tan(A+B) = -\tan C.$ From here, I get stuck. Please help.


yarob@yarob-2184:~$ sudo add-apt-repository ppa:lutris-team/lutris  Stable releases for the Lutris client  More info: https://launchpad.net/~lutris-team/+archive/ubuntu/lutris Press [ENTER] to continue or Ctrl-c to cancel adding it.  Hit:1 http://deb.playonlinux.com cosmic InRelease Get:2 https://mega.nz/linux/MEGAsync/xUbuntu_20.04 ./ InRelease [2,441 B] Hit:3 http://ppa.launchpad.net/chrdevs/figma/ubuntu focal InRelease Hit:4 http://apt.postgresql.org/pub/repos/apt focal-pgdg InRelease Hit:5 http://archive.ubuntu.com/ubuntu focal InRelease Hit:6 http://ppa.launchpad.net/daniruiz/flat-remix/ubuntu focal InRelease Hit:7 http://ppa.launchpad.net/deadsnakes/ppa/ubuntu focal InRelease Hit:8 http://ppa.launchpad.net/graphics-drivers/ppa/ubuntu focal InRelease Err:9 http://ppa.launchpad.net/jonathonf/python-3.6/ubuntu focal InRelease   403  Forbidden [IP: 91.189.95.83 80] Hit:10 http://ppa.launchpad.net/js-reynaud/ppa-kicad/ubuntu focal InRelease Hit:11 http://ppa.launchpad.net/lutris-team/lutris/ubuntu focal InRelease Hit:12 http://ppa.launchpad.net/numix/ppa/ubuntu focal InRelease Hit:13 http://ppa.launchpad.net/papirus/papirus/ubuntu focal InRelease Reading package lists... Done N: Skipping acquire of configured file 'main/binary-i386/Packages' as repository 'http://apt.postgresql.org/pub/repos/apt focal-pgdg InRelease' doesn't support architecture 'i386' E: Failed to fetch http://ppa.launchpad.net/jonathonf/python-3.6/ubuntu/dists/focal/InRelease  403  Forbidden [IP: 91.189.95.83 80] E: The repository 'http://ppa.launchpad.net/jonathonf/python-3.6/ubuntu focal InRelease' is not signed. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.

I installed Ubuntu 18.04 and then while installing Virtualbox i get the 'i386' error message after I did:  $ sudo apt-get update Get:1 http://nl.archive.ubuntu.com/ubuntu bionic InRelease [242 kB] Hit:2 http://security.ubuntu.com/ubuntu bionic-security InRelease                                                                 Hit:3 http://ppa.launchpad.net/danielrichter2007/grub-customizer/ubuntu bionic InRelease                                          Hit:4 http://nl.archive.ubuntu.com/ubuntu bionic-updates InRelease Hit:5 http://nl.archive.ubuntu.com/ubuntu bionic-backports InRelease Get:6 http://download.virtualbox.org/virtualbox/debian bionic InRelease [4429 B] Get:7 http://download.virtualbox.org/virtualbox/debian bionic/contrib amd64 Packages [1426 B] Fetched 248 kB in 1s (209 kB/s)      Reading package lists... Done N: Skipping acquire of configured file 'contrib/binary-i386/Packages' as repository 'http://download.virtualbox.org/virtualbox/debian bionic InRelease' doesn't support architecture 'i386'   I found several answers on Askubuntu for the 'i386' message but I don't know how to apply this to my situation


I am trying to learn a C# and I am trying to use get and set with string. However, with various errors it either refuses to compile or crash with stack overflow using System; using System.Dynamic; using System.Security.Cryptography.X509Certificates;  namespace CshEssentials {     class Program     {         public string a         {             get             {                 Console.WriteLine($"Hello {a}"); return "0";             }             set             {                 a = value;             }         }         static void Main(string[] args)         {             a = Console.ReadLine();         }      } }

I know java and would normally put in getter/setter methods. I am interested in doing it in C# with the following code, but it throws a StackOverflow exception. What am I doing wrong?  Calling Code  c.firstName = "a";   Property Code    public String firstName; {     get     {         return firstName;     }     set     {         firstName = value;     } }


My need: As a teacher, regularly I need to annotate a pdf document of around hundreds of pages of maths. I need to be able to write maths myself in these annotations. Annotations tend to be "always the same" that is with around twenty to thirty annotations cover 90% of the needs. Therefore I build a list of annotations on a separate pdf, from which I select, paste and move around afterwards on the main pdf.  The present (unsatisfactory) solution: I create a list of pdfcomments in a separate document and paste, move and possibly edit them in the pdf pages.  Problems:   not all pdf reader render the comments, but I can cope with that by selecting the reader to be used I cannot write comments containing maths. I don't understand why, despite being in LaTeX, the math signs/operations are not taken into account. I use an HTML page that translate Latex to Unicode to cope with that but it is not satisfactory: long and for instance \frac{}{} is not well rendered.   (Some) PDF readers are capable of copying and moving comments around to find their place (through PDFcomment) . It is possible to have PDF comments including LaTeX math expression.  Question: Is there a way to mix both capabilities in the same comment ? LaTeX package(s) would be great or any other way is welcomed.

My goal : I correct copies from students that I scan to pdf. I wish I could make the annotations on the scanned copies rather than on the physical paper. Today, I have to scan the copies again to have my annotations transferable to students by email. Since most of the annotations are similar, I wish to have a stock of annotations I could transfer on the copies.  I went through a lot of technologies, including many "StackExchange Questions" here. I considered pdfcomment, cooltips, fancytooltips, the OCG family (ocgx, ocgp, ocg2, ...), etc.  Two tracks attracted more specifically my attention :    pdfcomments : I like the mouseover to see the comment, the capabillity to move the annotation around so I can have a stock on a pdf and I can copy it onto the scanned copies. This would be my choice if there was not a main drawback : it accepts only plain text when I need to use mathematical notations. (It needs selected pdf readers). Because you can move comments, you can put them on any pdf, even if it is not compiled from Latex or if you don't have the source. fancytooltips : I like the mouseover to see the comment, and the capability to use LaTeX mathematical formulas and images. Drawbacks : I can't move the annotation from a pdf document to the copies. (It works with very few pdf readers.) . I am not sure whether I can put tips on non Latex pdfs.   Is there a way to have pdfcomment have images/Latex mathematical formulas (or references to formulas that can show with a mouseover) ? Or is there a way to transfer fancytooltips to a non Latex pdf ? Or are there other techniques to achieve the goal ?


I need to find the summation of:  $$\begin{align*} &\sum_{i=0}^{\infty} iar^{i} &\text{if }|r|\lt 1 \end{align*}$$  I found this result: $$\begin{align*} \frac{a}{1-r} &= \sum_{i=0}^{\infty}ar^i &\text{if }|r|\lt 1\\ \frac{d}{dr}\frac{a}{1-r} &=\frac{d}{dr}\sum_{i=0}^{\infty}ar^i&\text{if }|r|\lt 1\\ \frac{a}{(1-r)^2} &= \sum_{i=0}^{\infty}\frac{d}{dr}ar^i &\text{if }|r|\lt 1\\ \frac{a}{(1-r)^2} &= \sum_{i=0}^{\infty} iar^{i-1}&\text{if }|r|\lt 1\\ \frac{a}{(1-r)^2} &=\sum_{i=1}^{\infty} iar^{i-1} &\text{if }|r|\lt 1 \end{align*}$$  However I do not get the last step. Shouldn't it be:  $$\begin{align*} \frac{a}{(1-r)^2} &= \sum_{i=0}^{\infty} iar^{i-1}&\text{if }|r|\lt 1\\ \frac{ar}{(1-r)^2} &=\sum_{i=0}^{\infty} iar^{i} &\text{if }|r|\lt 1 \end{align*}$$  Thank you

How can I evaluate $$\sum_{n=1}^\infty\frac{2n}{3^{n+1}}$$? I know the answer thanks to , but I'm more concerned with how I can derive that answer. It cites tests to prove that it is convergent, but my class has never learned these before. So I feel that there must be a simpler method.  In general, how can I evaluate $$\sum_{n=0}^\infty (n+1)x^n?$$


Give an example of a function $f\colon\Bbb R\rightarrow \Bbb R$ such that $f\circ f\circ f=f\circ f\neq f$, that is, $f(f(f(x))) = f(f(x))$ on $\Bbb R$ but $f(f(x))\ne f(x)$ for some $x\in\mathbb R$.

Create an example of a function $f: \mathbb{R} \to \mathbb{R}$ such that $f(f(f(\mathbb{R}))) = f(f(\mathbb{R})) \neq f(\mathbb{R})$.


I hovered the mouse over the deleted message by tripleee, whose content used to be  :46713033 still up   Well now, message 46713033 is highlighted. But it shouldn't. The message that refers to it is deleted already.  I've confirmed that any user (including anonymous users - unlogged-in) can see the highlights, after page refresh.  Note that this is not a duplicate of , as that one is a bug report that has been considered by design, this is a feature request asking that the design be changed.

If a user posts a message in chat that links directly to another chat message like  12345689: You smell funny!  The chat rightly highlights message 12345689 when you hover over User: You smell funny!  If the user or a moderator deletes the You smell funny! message, the text changes to (removed), which again is expected.  However, hovering over (removed) still highlights the previously referred-to message, in this case 12345689.  I have to assume this is unintentional behavior for a message that is ostensibly deleted.


I wanted to create a new material using an image texture.  It worked fine, but then it suddenly turned purple.  Is there any switch that I might have accidentally turned on that causes this behavior?

I made a character, and its one of my first times texturing, and I saved my character into a new folder, and when I came back to the model ALL the textures were pink, I used to know what to do, but I stopped texturing, how do I bring my textures back?


Let $ f $ be a function that is differentiable on a deleted neighborhood of $x_0 ∈ R$ and continuous at $x_0$. Show that if $\lim \limits_{x \to x_0} f'(x) = L$ then $f'(x_0) = L $

Let $f$ be a real-valued function continuous on $[a,b]$ and differentiable on $(a,b)$. Suppose that $\lim_{x\rightarrow a}f'(x)$ exists. Then, prove that $f$ is differentiable at $a$ and $f'(a)=\lim_{x\rightarrow a}f'(x)$.    It seems like an easy example, but a little bit tricky. I'm not sure which theorems should be used in here.    ==============================================================  Using @David Mitra's advice and @Pete L. Clark's notes I tried to solve this proof. I want to know my proof is correct or not.  By MVT, for $h>0$ and $c_h \in (a,a+h)$ $$\frac{f(a+h)-f(a)}{h}=f'(c_h)$$ and $\lim_{h \rightarrow 0^+}c_h=a$.    Then $$\lim_{h \rightarrow 0^+}\frac{f(a+h)-f(a)}{h}=\lim_{h \rightarrow 0^+}f'(c_h)=\lim_{h \rightarrow 0^+}f'(a)$$   But that's enough? I think I should show something more, but don't know what it is.


Why is the following table wider than the page?!  After comments from two members from this site, I included more code from the original file.  It seems that the tabular environment in the first problem is prompting TeX to artificially stretch the table in the last problem.  \documentclass{amsart}   \usepackage{tikz} \usetikzlibrary{calc,intersections}   \usepackage{makecell}   \begin{document}   \noindent \textbf{1.) }Compute the following differences. Express each difference as a fraction for which the only common divisor of the numerator and denominator is 1. \\ \\ \noindent \hspace*{2em} \setlength{\tabcolsep}{0.75in} \setlength{\extrarowheight}{3ex} \begin{tabular}{@{}r@{}lr@{}lr@{}l} \textbf{i.) }   &   $\displaystyle{\frac{1}{2} - \frac{1}{3}}$ & \textbf{ii.) }  &   $\displaystyle{1 - \frac{1}{3}}$ & \textbf{iii.) } &   $\displaystyle{\frac{11}{18} - \frac{22}{45}}$ \\[1.2\normalbaselineskip] \textbf{iv.) }  &   $\displaystyle{\frac{27}{14} - \frac{12}{35}}$ & \textbf{v.) }   &   $\displaystyle{\frac{16}{27} - \frac{32}{81}}$ & \textbf{vi.) }  &   $\displaystyle{\frac{21}{10} - \frac{21}{100}}$ \end{tabular} \vskip0.25in  \vfill \pagebreak   \noindent \textbf{14.) }What is the perimeter of the following triangle? \vskip0.2in  \noindent \hspace*{\fill} \begin{tikzpicture}   %Triangle ABC is drawn. The lengths of AB, AC, and BC are to be 8, 10, and 12, respectively. %(The measure of the angle between AB and AC is arc cos(1/8).) \coordinate (A) at (0,0); \coordinate (B) at (5,0); \coordinate (C) at ({acos(1/8)}:4); \draw (A) -- (B) -- (C) -- cycle;    %The lengths of the sides of the triangle are typeset. \node[anchor=north, inner sep=0, font=\footnotesize] at ($($(A)!0.5!(B)$) +(0,-0.15)$){$10$}; \node[anchor={acos(1/8)-90}, inner sep=0, font=\footnotesize] at ($($(A)!0.5!(C)$) +({acos(1/8)+90}:0.15)$){$8$}; \draw let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in node[anchor={\n1-90}, inner sep=0, font=\footnotesize] at ($($(B)!0.5!(C)$) +({\n1+90}:0.15)$){$12$};   \end{tikzpicture} \hspace{\fill} \vskip0.25in  \noindent The following table, describing the Preston City workforce, is missing some data entries. Based on the information in the table, how many women in the Preston City workforce are unemployed? \begin{tabbing} \hspace*{3em} \= \hspace{2.5in} \= \kill \> \textbf{a.) }500     \> \textbf{b.) }1000 \\ \> \textbf{c.) }1500    \> \textbf{d.) }2000 \\ \> \textbf{e.) }2500 \end{tabbing} \vskip0.2in  \noindent \hspace*{\fill} \setlength\extrarowheight{2pt} \begin{tabular}{|| c | c | c !{\vrule width0.8pt}c ||} \hline \multicolumn{4}{|| c ||}{{\bf Residents of Preston City}} \\ \Xhline{0.8pt}             &   Employed    &   Unemployed  &   Total \\ \hline     Men     &   27,000      &               &   \\ \hline     Women   &               &               &   21,500 \\ \Xhline{0.8pt}     Total   &   48,000      &               &   50,500 \\ \hline \end{tabular} \hspace{\fill}  \end{document}

I have a table that I want to insert on a page, but at least one (perhaps both) of the following conditions are met:   The table is too wide to fit within the text block or page. That is, I'm exceeding some horizontal restriction. The table is too tall to fit within the text block or page. That is, I'm exceeding some vertical restriction.   What are my options to make this table fit? If it doesn't fit, regardless of my attempts, what other options exist?


int a=870,b0=-20, b1=120, a0=0, a1=3584;             double d=(b0 + (b1 - b0) * ((a - a0) / (a1 - a0))); Console.Write(d);   It gives a result as -20. I want it precisely upto few decimal places.  whats wrong with c#??

I think there's a lot for me to learn about data types. Why this happens  double result = ((3/8)*100).ToString();   it gives zero .. should be 37,5 ... :(


I am trying to design a neural network for time series forecasting using LSTM neurons.  I am stuck because the many different configurations that I tried so far are not performing well (actually they perform really really bad).  So I am starting to think that I'm missing something :).  This is the time series that I am using for training. I have a similar time series for testing (the training consists in 2016 data and test is 2017):   What I want is to take T steps of my time series and predict the following P steps, so I converted the problem in a multi-output regression problem in order to solve it using supervised learning: suppose I want to predict the series from time a+1 to time a+P, the features of my dataset are the steps from a-T to a, (by consequence my ys for training are the steps from a+1 to a+P)  As only preprocessing step, I applied different types of scaling (using scikitLearn:  stdscaler = StandardScaler() minmaxScaler = MinMaxScaler(feature_range=(-1, 1)) robustscaler = RobustScaler()   Sometimes I combined these methods, but I have always got bad results in term of network performance.  After preprocessing and reshaping, I designed the following network:  # create and fit the LSTM network model = Sequential()  model.add(LSTM(NODES_L1, return_sequences=True, input_shape=(1, SEQ_LEN), stateful=True, batch_size=BATCH_SIZE)) model.add(Activation(ACTIVATION_L1)) model.add(Dropout(DROPOUT_L1))  model.add(LSTM(NODES_L2, stateful=True)) model.add(Activation(ACTIVATION_L2)) model.add(Dropout(DROPOUT_L2))  model.add(Dense(OUTPUT_TIMESTEPS, activation='linear')) adam = Adam(lr=0.0001) model.compile(loss='mean_squared_error', optimizer=adam)  callbacks = [     EarlyStopping(monitor='val_loss', min_delta=0.00001, patience=5, verbose=0, mode='auto') ]  model.summary()  model.fit(     trainX,     trainY,     shuffle=False,     batch_size=BATCH_SIZE,     epochs=EPOCHS,     validation_data=(validX, validY),     verbose=2,     callbacks=callbacks)   Two LSTM layers and one dense at the end to predict the time steps. The validation loss and the loss are descending quite well; what I see when I train the network is the following output:  4s - loss: 3.8233 - val_loss: 0.6118 Epoch 2/100 3s - loss: 3.4985 - val_loss: 0.6668 Epoch 3/100 3s - loss: 3.1761 - val_loss: 0.6724 Epoch 4/100 3s - loss: 2.7586 - val_loss: 0.5258 Epoch 5/100 3s - loss: 2.3404 - val_loss: 0.3424 Epoch 6/100 3s - loss: 2.0137 - val_loss: 0.2554 Epoch 7/100 3s - loss: 1.7479 - val_loss: 0.1697 Epoch 8/100 3s - loss: 1.5935 - val_loss: 0.1564 Epoch 9/100 3s - loss: 1.3824 - val_loss: 0.1206 Epoch 10/100 3s - loss: 1.2645 - val_loss: 0.0699 Epoch 11/100 3s - loss: 1.1752 - val_loss: 0.0619 Epoch 12/100 3s - loss: 1.1283 - val_loss: 0.0711   And so on (until early stop kills everything).  After the training step, I try to do some predictions, here the results:     Not even close.  I tried to find the best hyperparamters with hyperopt, here the configuration I used (maybe I am wrong on the dimension of the network):  fspace = {         'SEQ_LEN': hp.choice('SEQ_LEN', range(5, 48)),         'NODES_L1': hp.choice('NODES_L1', range(1, 80)),         'NODES_L2': hp.choice('NODES_L2', range(1, 80)),         'DROPOUT_L1': hp.uniform('DROPOUT_L1', 0.05, 0.8),         'DROPOUT_L2': hp.uniform('DROPOUT_L2', 0.05, 0.8),         'BATCH_SIZE': hp.choice('BATCH_SIZE', range(25, 150)),         'ACTIVATION_L1': hp.choice('ACTIVATION_L1', ['relu', 'tanh']),         'ACTIVATION_L2': hp.choice('ACTIVATION_L2', ['relu', 'tanh']),         'EPOCHS': hp.choice('EPOCHS', range(15, 1000))     }   Where SEQ_LEN is the number of T timesteps used as features.  The question is: how can I improve my process? What I am doing wrong? I double checked my code and all data seems to be loaded correctly, so I think it's a methodological problem.  Thank you for any clue ;)

I'm training a neural network but the training loss doesn't decrease. How can I fix this?  I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my network's performance doesn't improve on the training set.    This question is intentionally general so that other questions about how to train a neural network can be closed as a duplicate of this one, with the attitude that "if you give a man a fish you feed him for a day, but if you teach a man to fish, you can feed him for the rest of his life." See this Meta thread for a discussion:   If your neural network does not generalize well, see:


In tellling-time constructions like the following:  It's half past ten. It's a quarter to two.  What is commmonly used in AmE before past and to? My guess is that only half, a quarter and numbers 0 through 29 [possibly followed by minute(s)] are used. How far off from the actual American usage am I?

I don't know if this is a good question. But as far as I know, and as I do it, American English also say "after" other than "past" in expressing times.   For example, a quarter after six instead of, a quarter past six as in British English.  The other difference I know, so far, is that the British use dots to separate "hour" and "minute" in digital times like "08.35" while Americans use a colon e.g; "08:35".  So is what I know, so far, correct? Or are there any other differences that I don't know about?


W: An error occurred during the signature verification. The repository is not updated and the previous index files will be used. GPG error: http://repository.spotify.com stable InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 13B00F1FD2C19886 W: Failed to fetch http://repository.spotify.com/dists/stable/InRelease   W: Some index files failed to download. They have been ignored, or old ones used instead.   How can I fix spotify?

I added some extra repositories with the Software Sources program. But when I reload the package database, I get an error like the following:     W: GPG error:  trusty InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 8BAF9A6F   I know I can fix it using apt-key in a terminal, according to the official Ubuntu documentation. But I would have liked to do it graphically. Is there a way to do this without using a terminal?


So, I have o convert a .csv file from ANSI encoding to UTF-8 in windows, using a .bat file. Basically a program capable of doing this conversion without needing Notepad++ nor excel and etc. Do you have any idea of how to do it?

We have a text file which is in default ANSI format and that needs to be converted into UTF-8 format. Is there any way we can use the general windows DOS commands to convert the file? We can use the PowerShell but only this command line has to be run from a different batch process.


why i got error:  undefined control sequence <argument> luatexversion                          <95 l.924   for this simple example:  \documentclass{article} \usepackage{animate} \begin{document} here is nothing to animate! \end{document}   when compiling with pdfLateX. closing compilation editor open file pdfbase.sty.  I have recent 64-bit MikteX and this test has been working no so far ago.

I am using pdflatex on a fresh (and current) MikTex 2.9 install with the following MWE:  \documentclass{article} \usepackage{animate} \begin{document}  Test \end{document}   Pdflatex throws the error:  Package: pdfbase 2017/03/23 v0.14 driver independent access to low-level PDF fe atures \g_pbs_page_int=\count175  ! Undefined control sequence. <argument> \luatexversion                            <95 l.924 }   I have read the other posts containing the offending control sequence, especially  but the solutions offered there didn't help in my case.  This problem might have arisen with a recent MikTex update. I have now completely uninstalled, redownloaded, reinstalled and updates MikTex -- with no success.


I had been trying to prove that any positive integer can be uniquely expressed as $$a = 3^m + 3^{m-1}b_{m-1} + \cdots + 3^0b^0 \text{ where each b = -1, 0 or 1 and } a \in \mathbb{Z}^+$$ This is a problem from Niven's Introduction to Theory of Numbers.  My Attempt:  Proof by Strong Induction.  Let $P(n) ::= n = 3^m + 3^{m-1}b_{m-1} + \cdots + 3^0b^0 \text{ where each b = -1, 0 or 1 }$.  Base Case: P(1) is true. Since $1 = 3^0$.  Assuming $P(1), P(2), \cdots, P(n-1)$ is true to prove it for $n$.  Considering cases:  Case 1: $n = 3m$ $$\implies n = 3(3^m + 3^{m-1}b_{m-1} + \cdots + 3^0b_0)$$ $$\implies n = 3^{m+1} + 3^{m}b_{m-1} + \cdots + 3^1b_0 + 3_0*0$$  Case 2: $n = 3m+1$ $$\implies n = 3(3^m + 3^{m-1}b_{m-1} + \cdots + 3^0b_0) + 1$$ $$\implies n = 3^{m+1} + 3^{m}b_{m-1} + \cdots + 3^1b_0 + 3_0*1$$  Case 3: $n = 3m-1$ $$\implies n = 3(3^m + 3^{m-1}b_{m-1} + \cdots + 3^0b_0) - 1$$ $$\implies n = 3^{m+1} + 3^{m}b_{m-1} + \cdots + 3^1b_0 + 3^0*(-1)$$  This is how I've managed to prove the above proposition(I am not sure though). Is my proof correct? Please report even the slightest mistake. Also, how can I prove that they are unique.  Could you prove the above proposition in some other way without using induction and by using number theory because I feel I haven't used it? I believe there must be other techniques of proving this by using some number theory concepts.  Thanks.  My question includes proof verification alongwith other questions and it is hence not a duplicate.

show that every nonzero integer can be uniquely represented in the form  $e_k3^k + e_{k-1}3^{k-1}+ … + e_13+e_0$ where $e_j= -1, 0, 1$ for $j = 0,1,2,…k$ and $e_k \neq 0$


When you join a chat room on chat.SE without being logged in (or using incognito mode), the message telling you that "You must be logged in to talk." is very dark and therefore pretty unreadable except the links (dark grey on dark blue).      In my opinion, the text should get modified by CSS to set to a more visible color, #FFF for example looks fine.

If you visit a chat room attached to a beta site while logged out, the log in message is all but unreadable, being dark grey on a dark blue background. For example, visit  while logged out or in private browsing mode.


I can see the general solution.. but I was wondering if the wizards here could help me along. :) Given an ellipse with a known major and minor axis.  Take a known r(T) such as, the major or minor axis, and a known arc length A. I'd like to determine any r(t) given any r(T) and A. Numerical approximation is 100% ok, as this is for an applied problem.

Is it possible to determine the angle in degree of an arc in ellipse by knowing the arc length, ellipse semi-major and semi-minor axis ? If I have an arc length at the first quarter of an ellipse and I want to know the angle of it, what is the data that I will need it to use it and what is the exact method to use it?  Please take a look at this picture:    Actually I know how to determine the arc length of a ellipse . but I want to do the obverse.


As we many of know that we have to include external jsscript file at the end of page. for performance and usability purpose.  I want to know the correct place where to place it.  means  <boby> <!--html here -- > <script src= ""> <!--  here ???  -- > </body> <script src= ""><!--  here ???  -- >   before the closing of script tag or after the closing of script . Is there any avantage of putting inside or outisde of body tag.  Thanks in advance..

When embedding JavaScript in an HTML document, where is the proper place to put the <script> tags and included JavaScript? I seem to recall that you are not supposed to place these in the <head> section, but placing at the beginning of the <body> section is bad, too, since the JavaScript will have to be parsed before the page is rendered completely (or something like that). This seems to leave the end of the <body> section as a logical place for <script> tags.  So, where is the right place to put the <script> tags?  (This question references , in which it was suggested that JavaScript function calls should be moved from <a> tags to <script> tags. I'm specifically using jQuery, but more general answers are also appropriate.)


which of these two phrases is correct?  A - The man, WHOM from now on we will refer to as Jim, approaches the table and stands next to the lady.   B - The man, WHO from now on we will refer to as Jim, approaches the table and stands next to the lady.   None of my native English speaker friends do not agree on which one is correct.  Thanks.

I can never figure out whether I should use who and whom. Most people use who for both colloquially, but some people say this is not correct.  What’s the rule for using who and whom correctly?


I'm working on a complicated building which my goal is to keep the multiple objects in their respective groups and scale all objects at once. Instead of using Ctrl+J function to group everything into 1 object and scale it.   Appreciate some advice. Thanks.

I've never been quite able to figure out how groups work in Blender (at least not since 2.5/6x). Is it possible to group several objects and then manipulate them (scale, rotate, translate) as one?


I have an HP laptop with planned HDD to SSD migration with Windows 8 installed.   Source - HDD - 500GB - SATA - I can put this in my server and save it to a file. Destination - SSD - 120GB - M.2 - I can't put this into my server.   I plan on doing the following in a few days:   Delete the two HP partitions at the end of the disk. Shrink the system (C:) partition using some software for Windows below 100GB. Using Linux computer and pv utility as follows:  pv < /dev/sourceDrive > /dev/destinationDrive   Making 1:1 copy of the drive.  Expecting it to fail of course at the end of the SSD drive, i.e. at 120 GB. But since there will be no data on the source disk there, that is no problem, right?   That's about it. Is it a sound idea?

Ok, I want to do a "paranoid" migration from a a HDD to a SSD. There will be no shrinking involved.  For the moment this is what I know/have:   Connect SSD and create an 1MB aligned partition, at least the size of the C: from the HDD Clone C: to SSD using Easeus DiskCopy in DOS mode Use a small linux distro and byte-compare source and clone: cmp /dev/sda1 /dev/sdb1 just to make sure that everything is perfectly copied. (I've personally encountered a situation where Macrium Reflect Free did not clone byte perfect, after comparing manually the files.)   Now here comes the part which I don't know:   Make the new cloned partition bootable, since the alignment was changed. How? I've seen these, but not sure:  bootrec /fixboot bootrec /fixmbr bcdboot c:\windows  Change the disk ID, so there will be no collisions in case you connect both the HDD and the SSD at the same time Are there other things to consider?   I'm aiming to make this as safe and as reliable as possible, so any advice is welcome.


I am trying to redirect HTTPS www request to non-www but I can't get it to work. What line of code would I have to change to achieve the redirection?  server {     root /var/www/mydomain.com/html;     index index.html index.htm index.nginx-debian.html;      server_name mydomain.com www.mydomain.com;      #gZip stuff here...     #Certbot stuff here... }  server {     if ($host = www.mydomain.com) {         return 301 https://$host$request_uri;     } # managed by Certbot      if ($host = mydomain.com) {         return 301 https://$host$request_uri;     } # managed by Certbot      listen 80;     listen [::]:80;      server_name mydomain.com www.mydomain.com;     return 404; # managed by Certbot }

Hi this must be a basic question but I haven't seen an answer with cerbot considerations (if there are any considerations). How do I get https www to redirect to non-www instead of timing out?  The https www version of my site times out instead of redirecting to non-www, whereas all other versions (http and https non-www) work fine.  Preferably I would like to future proof so that I can renew the certs through certbot and not need to manually change the nginx config afterwards.  The nginx server config is shown below:  server {     listen 80 default_server;     listen [::]:80 default_server ipv6only=on;     server_name www.mydomain.com mydomain.com;      listen 443 ssl; # managed by Certbot     ssl_certificate <path_to_cert> # managed by Certbot     ssl_certificate_key <path_to_key>; # managed by Certbot     include /etc/letsencrypt/options-ssl-nginx.conf; # managed by Certbot     ssl_dhparam <path_to_this>      if ($scheme != "https") {         return 301 https://$host$request_uri;     } # managed by Certbot }


If I have an ideal wire and I connect a battery to it, then the potential drop is zero along the wire, right? So, all its points must be at the same potential. Well, that means charges ( which are initially assumed to be at rest) will not go from one point to another in the wire. There's one more question to it. I've read in books that if the terminals of a battery are connected by an ideal wire, then all the points on the wire have the same potential as the potential of the positive terminal of the battery. But why don't all the points of the wire have the potential same as that of the negative terminal of the battery instead by similar logic? (because all the points of the wire are also connected to the negative terminal with zero resistance, and hence, zero potential drop along the way).  Here's how I tried to explain it. Please tell me if I'm wrong: Even if all the wire has zero resistance, then still charges are transferred through it because it's points are not at the same potential even if the wire has zero resistance. Yes, there is no potential drop due to resistance but there is a potential drop due to the kinetic energy gained by the charges as they more along the wire. So, it's points are at different potentials even with no resistance, because, at the end of the day, what we're talking about is the usual electric field, which will push charges to points of lower potentials even if there is no resistance along the way.  But according to this explanation of mine, a potentiometer would never work, because if my explanation is true, then charges would still be transferred along the wire containing the galvanometer even if both the points of that wire are at the same potential. So, where am I wrong?  It's not a duplicate. I've asked one more question in the details.

According to , if there is a potential difference, $V$, across a resistor then there is a current, $I$, flowing through it.   Since we assume that points along the connecting wire are at the same potential, how can current, $I$ flow between points at the same potential, $V$?


I just read about the L-U decomposition method to decompose matrices to upper and lower triangular ones. And I saw some examples of solving systems of equations using this method. My question: with what conditions can we safely use this method to solve the system of equations? For example should the coefficient matrix be necessarily a square matrix? In other words when can one write the matrix $A$ as $LU$ ?

When can we split a square matrix (rows = columns) into it’s LU decomposition?  The LUP (LU Decomposition with pivoting) always exists; however, a true LU decomposition does not always exist.  How do we tell if it does/doesn't exist?  (Note: decomposition and factorization are equivalent in this article)  From the :     Any square matrix $A$ admits an LUP factorization. If $A$ is invertible, then it admits an LU (or LDU) factorization if and only if all its leading principal minors are non-zero. If $A$ is a singular matrix of rank $k$, then it admits an LU factorization if the first $k$ leading principal minors are non-zero, although the converse is not true.   This implies that for a square matrix:     LUP always exists (We can use this to quickly figure out the determinant). If the matrix is invertible (the determinant is not 0), then a pure LU decomposition exists only if the leading principal minors are not 0. If the matrix is not invertible (the determinant is 0), then we can't know if there is a pure LU decomposition.     The problem is this third statement here. “If $A$ is a singular matrix of rank $k$, then it admits an LU factorization if the first $k$ leading principal minors are non-zero”, gives us a way to find out if LU decomposition exists for a singular (non-invertible) matrix.  However, it then says, “although the converse is not true”, implying that even if a leading principal minor is 0, that we could still have a valid LU decomposition that we can't detect.  This leads us back to the question: is there a way of truly knowing whether a matrix has an LU decomposition?


So i have these partitions on my drive, i would like to shrink down sda1 to increase sda5. How could i do that?  If i reduce sda1 it does not give me options to increase sda5

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


I have created a new HashMap Object say. Now I pass this object to a method where I change the reference of the variable to some other hashmap object .The reference to this new object is not reflected once the method is completed   Example :  Map<String, Boolean> map = new HashMap<String, Boolean>(); changerefofMap(HashMap<String, Boolean>() map) { map=methodwhichreturnSomeMap(); System.out.println(map.size());  //returns 2 } System.out.println(map.size());  //returns 0   I don't understand why the reference is not getting changed.

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


In chat last night a user and I were discussing the "physical" meaningfulness of the notion of lebesgue measure. In particular, we were curious as to whether physicists can "make do" without it. I mentioned that the dominated convergence theorem is needed to prove certain theorems in statistics that would be needed in areas like statistical thermodynamics, where you want to know that when dealing with a huge quantity of particles things like velocity/energy are approximately normally distributed (Central Limit Theorem). We were then surprised to find a proof the CLT that no only was free of the DCT, but formulated entirely in terms of the Riemann Integral.  My question is: Are there any specific areas in physics that rely on the notion of the lebesgue measure? (either directly or indirectly via theorems for which this notion is needed to prove). To the point of being necessary and not merely useful?

is fine for physics in general because the functions dealt with tend to be differentiable and well behaved. Despite this, it's possible that  can be more powerfully used even in physical situations that can be solved by Riemann integration. So my questions is:  In solving physics problems, when is Lebesque integration useful over Riemann integration?


$$\forall x, y, n \in \mathbb{Z},    x=y  \ \implies x \equiv y\ (mod\ n)\ $$ I am not sure if I am doing this properly and I don't know if I can show my proof like this: Suppose x = y which means x = x x ≡ x mod n n | x - x kn = x - x kn = 0 and since x ≡ y mod n jn + y = x jn = x - y and since x = y, y=y and x=x jn = 0 kn = jn

Let $m \in \mathbb{N}$. Show that $\,a \text{ R } b \Leftrightarrow a \equiv b \text{ }(\text{mod } m)\,$ is an equivalence realtion.   We need to show 3 things:  (i) reflexive: $\forall a \in \mathbb{Z}: a \equiv a \text{ mod } m$  (ii) symmetric: $\forall a,b \in \mathbb{Z}: a \equiv b \text{ mod } m \text{ } \Rightarrow b \equiv a \text{ mod } m$  (iii) transitive: $\forall a,b,c \in \mathbb{Z}: a \equiv b \text{ mod } m \text{ } \wedge b \equiv c \text{ mod } m \Rightarrow a \equiv c \text{ mod } m$  So I tried it like this:  (i) $m \text{ | } 0 \Rightarrow m \text{ | } a-a \Rightarrow a \equiv a \text{ mod } m$  (ii) $a \equiv b \text{ mod } m \Rightarrow a \text{ mod } m = b \text{ mod } m \Rightarrow b\text{ mod } m = a \text{ mod } m \Rightarrow b \equiv a \text{ mod } m$  (iii) $a \equiv b \text{ mod } m \text{ } \wedge \text{ }b \equiv c \text{ mod } m \Rightarrow m \text{ | } (a-b) \text{ } \wedge \text{ } m \text{ | } (b-c) \Rightarrow m \text{ | } (a-b) + (b-c) \Rightarrow m \text{ | } a-c \Rightarrow a \equiv c \text{ mod } m$  Because every condition is fulfilled, we are done (?)  Please help me and tell me if it would be correct like this? Maybe there is better way to prove it?


After finishing the first part of an adventure and leveling up, the party continued to the next part but all of them died. Now, we are trying the adventure again but without redoing the first part which would be tedious and time consuming.   On their way to level 2, the player characters found multiple items (like potions, equipment, or even items that are just meant to be sold). These items, even though they may have little value at higher levels, at their current situation may provide some much needed help in their adventure. But because the whole party died, all the items are lost with the dead party and I can't just tell them "Your new characters have the same items as the old ones had when you died before" as that would take away from the "immersion".   I know that there is starting equipment depending on class and I did see the answer in , but that's exactly my problem. The DM Guide says that starting at levels 1–4 they still only get starting equipment, but in this particular situation, I feel that the characters should own something extra  So is there a guideline to award each character with any sort of items or is it completely up to the DM to decide? Is there a more helpful guideline than the one in the DMG?

The PHB only gives starting wealth for Level 1 PCs. Based on my experience in other games, specifically Pathfinder, I would expect to get more at higher levels. Where can I find an appropriate table or calculation?


Is there an easy way how to characterize the groups with exactly two automorphisms?  I was able to find the following finite groups with exactly two automorphisms: $\mathbb{Z}_3$, $\mathbb{Z}_4$, $\mathbb{Z}_6$.

Which groups $G$ have precisely two automorphisms, i.e., precisely one non-trivial automorphism?  Examples: $G= C_3, \mathbf{Z},\ldots$.  I think $G$ has to be abelian. In fact, we have $ \vert G\vert \geq 3$. Therefore, if $G$ is not abelian, we have at least two non-trivial inner automorphisms.  If we can show that $G$ is cyclic the above examples are all of them.


I'm working on rewriting a software package my employer uses for system health checks from Windows Batch to Python. Is there an easy way to include a Python 2.7 installation with this package, that can be moved around? Or will I have to install Python on the machines I'm running the scripts on each time?  I've looked into Portable Python, but it seems like more of a portable dev environment then a portable installation I can run scripts off of.

I need to package my Python application, its dependencies and Python into a single MSI installer. The end result should desirably be:   Python is installed in the standard location the package and its dependencies are installed in a separate directory (possibly site-packages) the installation directory should contain the Python uncompressed and a standalone executable is not required


Do particles ever touch each other during a collision?  My understanding is that they can get really close to each other but never actually touch, is that true?  Another thing I've read about is, the closer the particles get to each other the greater the density of virtual particles until they reflect or particle pair creation occures due to the high energy density. If true, how does that work?

If you've ever been annoyingly poked by a geek, you might be familiar with the semi-nerdy obnoxious response of      "I'm not actually touching you! The electrons in the atoms of my   skin are just getting really close to yours!"   Expanding on this a little bit, it seems the obnoxious geek is right. After all, consider Zeno's paradox. Every time you try to touch two objects together, you have to get them halfway there, then quarter-way, etc. In other words, there's always a infinitesimal distance in between the two objects.   Atoms don't "touch" each other; even the protons and neutrons in the nucleus of an atom aren't "touching" each other.  So what does it mean for two objects to touch each other?   Are atoms that join to form a molecule "touching"? I suppose the atoms are touching, because their is some overlap, but the subatomic particles are just whizzing around avoiding each other. If this is the case, should "touching" just be defined relative to some context? I.e, if I touch your hand, our hands are touching, but unless you pick up some of my DNA, the molecules in our hands aren't touching? And since the molecules aren't changing, the atoms aren't touching either?  Is there really no such thing as "touching"?


This may be a trivial question but not for non-native. It is a bit confusing whether I should use the before internet or not.     heavy reliance on internet services in people's daily life   OR     heavy reliance on the internet services in people's daily life

As a proper noun, and as something commonly referred to in everyday life, I've heard both "the internet," and "internet" when using it as a noun. Ex:     I went on the Internet   Vs.     I found my answer via Internet   Although the second of the two sounds more awkward when saying it out loud, is it still acceptable?


I'd been living in the UK for a few years as a student when I got denied entry some 25 years ago.  I did appeal but after all it wasn't successful and consequently I was removed (deported).  I have no documents on my refusal kept with me and frankly I do not remember all the details after such a long time.  Now that I'm wondering if my refusal/deportation record is still kept by the UK Immigration Office?  Since I'm from one of the countries whose citizens are allowed to travel visa-free to the UK, I've been completely baffled all these years that if or how I can obtain "Entry Clearance" (I think that's what the IO advised me to when I was refused).    What on earth is Entry Clearance??  Do they mean a visa??  If it is, again, citizens of my country don't need a visa to enter the UK and I'm not sure if I'd still need a visa or what type of visa I should apply for to enter as a general visiter/tourist.  Could I travel visa-free with no trouble by now?  I'd appreciate any assistance/help and feedback on this...

I am a very recently naturalized America citizen. I want to visit the the UK but leaning towards flying in to France, and attempt entry into the UK via Calais by road on my US passport, so that if I am refused entry I can just go back to Paris and continue my vacation in France instead of flying direct into the UK from USA and risk being sent back to the USA directly.  I don’t intend to apply for a visitor's visa ahead of time. My reason being UK visitor's visa applications are evaluated purely based on the documentation you mail in without having the opportunity to talk/explain to the officer, while my current plan of going physically to the UK would mean at the very least I will have the opportunity to petition for admission face to face.  Some background for my dilemma:  In November 2015, while a permanent resident in the USA, I applied for a simple 6-month visa to visit the UK for one week and indicated I had $3,500 of spending money. I was refused under V4.2E.  His explanation for my refusal is I presented a Bank of America account with a balance of over $20k, which shows huge deposits (of $25k+ each) and withdrawals not in line with my biweekly pay deposits of about $5k. Now of course because UK visas are purely by mail and without appeal, I was unable to explain to him those funds come from my own brokerage account. I chose not to submit a new application with additional financial documents to clarify the  because of time, my vacation to Europe was about to start in a couple of weeks plus I have zero intention of providing her majesty with more in unnecessary visa fees.  I have been legally resident in the USA since 1998. I am married, have a well paying job as an engineer here in the USA, have traveled several times to the UK and never stayed more than ten days. Previously I had two different five-year multiple entry UK visas (the last of which expired in 2014), visited several other countries in Europe, own my own home and I'm financially secure. I have never overstayed a visa in any country and travel extensively.  So basically I want to travel with all my financial documents plus a copy of the previous refusal as if I were applying for a visa, and present my case if questioned at entry. I assume as an American I am allowed to travel visa free to the UK, despite my previous visa refusal.  Is this better than applying for entry clearance ahead of time, bearing in mind obtaining entry clearance ahead of time does not mean I will automatically be allowed entry into the U.K.  UPDATE 1 on March 15 2017  See my answer below to find out how it unfolded at Heathrow.  UPDATE 2 on July 8 2017  Follow-up visit after my detentiion in March.  UPDATE 3 on July 3 2018  Second visit after the initial detention.  UPDATE 4 on March 3 2019  Third visit after the initial detention and removal of stop flag from my profile.


I am writing report using Latex software but I got stuck while using tags.  consider  a statement( for example):     for any A ∈ Γ, B ⊆ A implies B ∈ Γ. The traditional (t, n) threshold secret sharing [3 - 9] is a special case of general secret sharing.Their qualified subsets are those that have at least a certain, per-determined number of participants.   And my latex code :  for any A \in T, B  \subseteq A implies B \in T.The traditional (t, n)  threshold secret sharing [3 - 9] may be a special case of general secret sharing. Their qualified subsets area unit those who have a minimum of an exact,  pre-determined variety of participants.   The output generated in the PDF look like:     for any A ∈ T;B ⊆ AimpliesB ∈ T.Thetraditional(t,n)thresholdsecretsharing[ 3-9]maybeaspecialcaseofgeneralsecretsharing:T heirqdeterminedvarietyofparticipants.   My questions is when I am using some tags, after using tags text occurring after that tag is  displayed without space between them as you can see in the latex output above.  I have referred latex pdf also but I am not getting my answer. so please suggest to me some way so I can display my text in original form as you can see in example statement.

I have a definition:  \newcommand{\arnold}{Arnold Schwarzenegger}   When I refer to it by:  \arnold is a   it is rendered as:   Arnold Schwarzeneggeris a    In order to have a space in front of "is" I would need to write  \arnold\ is a   Is there some other shorter way?


I'm struggling to figure out the best way to prove some extremal combinatoric ideas. If I have a set $\{1,2,...,n\}$ a collection of subsets $A_1, A_2,...A_m$ where $|A_i|$ is even $\forall i$ and $|A_i \cap A_j|$ is odd when $i \neq j$, then how should prove that $m\leq n$? I understand the proof that uses linear algebra to prove that if I had two subsets $A_1,..A_m$ and $B_1,..B_m$  and the same constraints but for $|A \cap B|$ but I am struggling to see how I can leverage this proof to show it for just $A$.

Let assume facebook has $n$ users. Mark Zuckerberg decided that people are allowed to open groups under the following restrictions:      1) No two different groups can exactly the same participants.      2) The number of users in each group is even.      3) Every two group has an odd number of common users.      Denote by $m$ the maximal number of groups that can be formed in facebook under the restrictions mentioned above. Prove $m \leq n$.   I tried solving this by defined a matrix, multiplying it by its transpose and using some rank considerations I thought I could derive the bound, but I didn't succeed. Could you please give me a hint?  The question had anther subsection : prove that in the case that $n$ is even than we have stron inequality


However, most assets are still subject to some price volatility and inflation, even those considered a strong store of value, such as gold.   Is ”even those considered a strong store of value” a misplaced clause? Or is the sentence wrong for some other reason?

My case here is that I was writing something for school, and my teacher explained an error which I really can't see. She referred to articles about "dangling participles", which was previously unknown to me. I find it hard to relate the examples I've found about it to my situation. So this is a text I've written and the bold part is where the problem arises: (You could read only the bold part if you please)  Wandering, and lost in his thoughts, there is a deep despair occupying the mind of this man. He is barely aware of his surroundings, except for those few moments when the loud blissful voices break through the protective barriers, developed by his immense sadness and grave frustration, into his mind. ”How can they all possibly be so happy?” he thinks to himself. Staring blindly, with his head low, as he walks in a slow pace, whispering ”Mary, Mary, my Mary,” over and over again. Yesterday was her funeral. She had passed away from a severe type of cancer, at a relatively young age. It was his wife. They had been together since high school and were greatly attached to each other. Having spent nearly half his life by her side, we cannot but imagine his grief. Indeed, he could hardly picture a life without her. So, alone he roams in the midst of all the seemingly incessant cheering and noises, drowned by his sorrow.  Her comments on that part was:  we is slightly out of place here – see my comment below These few sentences are about him and his emotions, so ‘we’ seems out of place. If the sentence starts: ‘Having spent nearly half his life by her side’, the reader expects it to continue: ‘he’. After all we have not spent half our lives by her side.  Is she right? If so, could anyone try to explain why?


I don't remember anything from school, so please what do you say about the title?

Could someone experienced in the field tell me what the minimal math knowledge one must obtain in order to grasp the introductory Quantum Mechanics book/course?  I do have math knowledge but I must say, currently, kind of a poor one. I did a basic introductory course in Calculus, Linear algebra and Probability Theory. Perhaps you could suggest some books I have to go through before I can start with QM?


In directories Dmoz has special preference for directory listing.   I had submitted 60 days back in dmoz still it not displaying my site, what is the problem with my site or still I have to wait?

I have a new website that I tried to list in DMOZ, but as of now it's still not listed.  Please tell me what I have to do so that my website will get listed in DMOZ.


My external hard drive fell.  After that I plug it in and it lights up but doesnt blink, the HD spins then stops.  The WD icon in the top right of my screen shows it there as plugged in but it doesnt ever switch to showing data on it. It never shows as an available drive to use.

Today as I was using my WD HDD, it fell off my corner. After I fixed the thing, I plugged it into the Mac and it loads the HDD but it's very very very very slow. It also does not work sometimes. The entire laptop just hangs  Tried running Disk Utility First Aid but it won't work.  It says some error and hangs  Can someone advise me on what I can do in this case?