In M. Ram Murty's paper Artin's Conjecture on Primitive Roots I am not able to understand a statement.  Let $k$ be the order of $a \bmod p$ where $p$ is a prime and also we have $a^{p-1} \equiv 1 \mod p$ then $k \mid (p-1)$ if $k \neq p-1$ then $k\mid(p-1)/q$ for some prime divisor $q$ of $p-1$.  I am not able to understand how the author was able to make the second claim i.e if $k \neq p-1$ then $k\mid(p-1)/q$ for some prime divisor $q$ of $p-1$.

So I'm first asked to compute, mod 19, the powers of 2,   $$2^{2},2^{3},2^{6},2^{9}$$  which I compute as   $$4,8,7,18$$  respectively.    I'm then asked to prove that 2 generates $(\mathbb{Z}/19\mathbb{Z})^{*}$ based on the above.  I'm not seeing how you can only look at these powers to know that 2 generates the group.  Of course I could compute the rest of the powers of 2 and show that all $1\leq a\leq 18$ are congruent to $2^{k}$ for some integer $k$, but I get the impression that this is not what I'm supposed to be seeing here.  What I am noticing is that I've basically computed $2^{2}$ and $2^{3}$ and then a few combinations of them.  Trivially I can get $1$ as $2^{0}$ and 2 likewise, and I'm allowed to take negative integer powers so I must get $2^{-1}$.  If I somehow knew that $2^{-1}$ were not $4, 8, 7,$ or $18$ then that would be nice, but I don't see how I can be assured of that without explicit calculation--and I get the feeling this is supposed to be an exercise in not explicitly calculating these.  Maybe this is supposed to be "half calculation", like showing that because I can get $4\cdot 8=32$ and $4\cdot 7=28$ I must therefore be able to obtain ... I don't know what.  Any hints?  Or am I over-thinking this and I should just calculate every power of 2?


It's striking to me that people can be banned from asking questions so seemingly trivially by an apparently dumb algorithm with no review, yet other, less important moderation functions need several actual humans to agree to the action.  I know that the Stack Exchanges are originally a programmers' site, and programmers think programming solutions are great, but I'd like to put forward that certain permanent moderation actions (such as banning users from participating) should be done by actual humans, especially since the post-ban algorithm is broken (as explained below).  A much more sensible solution is use some sort of pre-question ban queue.   A user passes a threshold which bans them from posting for a week or what have you.  They are put into a moderation queue. Other users have a week to vote / agree to make the ban permanent.     After a week is past, the user is banned or not.   As for why I think the question ban algorithm sucks, it has blocked me from asking questions on SuperUser after only two questions--one with no votes, another question with a single downvote, and my answer to my own question with a single downvote on it (after noone answered it).  By any reasonable tally, I think that a user being banned after 3 posts with two single downvotes on them is outrageous.

If you are reading this, you may have been affected by one of our post quality bans. If so, it is important that you  to understand what has happened and how to regain the permissions that you lost. While trying to ask a question, one could see:  We are no longer accepting questions from this account. See  to learn more.  Likewise, for answers:  We are no longer accepting answers from this account. See  to learn more.   Why am I getting this message? Are deleted posts taken into account too? Is a question/answer ban the same as a suspension? How do I avoid getting a question ban? How long do I have to wait before I can post again? What can I do to release the ban? How can I reactivate my account? Can I simply create a new account? I'll just ask somewhere else on the SE network, and they'll migrate my question to the correct site! Will a ban on one Stack Exchange site affect my standing on other sites in the network? Does this apply to meta sites too? My account is in good standing. Why am I still blocked?


Maybe I was just a bit unlucky: I got some down votes, one questions has been moved to Ask Different and another question has been closed as exact duplicate (and it's even not a duplicate!) and now I'm banned to ask questions.  Since it's of course impossible for me to determine the number of cases which are similar to mine I can't say if it's true: but in my opinion the question ban rule is a bit too strong.


After installation I am getting like this:  E: Failed to fetch http://archive.canonical.com/pool/partner/s/skype/skype_4.2.0.11-0ubuntu0.12.04.2_amd64.deb  404  Not Found [IP: 91.189.91.15 80]    E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?

I want to install Skype, but I can't locate it in Software Center or by using Synaptic Package Manager. Can anyone help me?


let's say I have a table with a column 'Name' and the user has set a column filter for 'Frank'. He currently sees some entries which match his search. This table is configured to accept new items via in-Table editing. If the user (with active filter) enters a new entry which does NOT match this filter (e.g. an entry with name 'Helen'), should the new entry... a) be disappearing instantly after the user entered it because it does not match the filter? OR b) stay visible although it does not match the current filter because the user explicitly entered it and it would be bad UX to pull it away from him? What do you think? I couldn't find any examples, so I am hoping on some UX advice here. All the best and have a nice day, Nadine

My project has a table with '+add' button and filtering. The add button opens a dialog to add item, and then to 'save' which closes it too Today I noticed the following flow:  Filter table on subject with value 'dummySubject'  Add new item with subject 'somethingelse'  save and close the new item ==> the new item is shown in the table   So the outcome is that an item that does not qualify the filtering appears in the table. When I asked around I got the following answer  We don't want the new item to 'disappear' on creation just because it does not qualify the filtering. So we display it If you filter again, it will disappear as it should  I can almost understand that logic, but still it sounds wrong. I would rather have like a toaster saying 'new item create' with a 'goto' link. My question is  is the current user experience considered a reasonable one? what is the best practice way to handle such scenario?      – Wireframes created with


I have recently used induction in solve a problem. But I am told that the proof is wrong. Below is the problem and solution.  I don't see any issue with this proof. What are the issues with this approach?     The population of every city in US is the same      The above statement is equivalent to: “For every n, if S is any set of   n cities in US, then the population of all cities from S is the same”.      Base Case:     Size of S is 1. There is only one city in S. Thus   population of every city in S is the same.      Inductive Hypothesis:       Let S be a set of m cities and assume that population of every city in S is the same.      Induction Step:       We will prove that if S is a set of m+ 1 cities, then the population   of every city in S is the same.       Let S = {c1, c2, · · · , cm, cm+1}. Consider the following two   subsets of S:        S1 = {c1, · · · , cm},      S2 = {c2, · · · , cm+1}      Note that both S1 and S2 are of size m. Thus by induction   hypothesis:      population(c1) = polulation(c2) = · · · = population(cm),   population(c2) = polulation(c2) = · · · = population(cm+1).      Since c2 appears in both sets, we have      population(c1) = polulation(c2) = · · · = population(cm) =   population(cm+1).      Thus for every set of m + 1 cities, their population is the same. By   induction principle, every city in US has the same population.   Are there any rules to decide whether to use Induction or not? What are the mistakes in the above approach.

Im trying to understand the solution about this, and all the other solutions are.. a bit weird for me and dont answer all my questions!  Reference :   Im using the answer there as reference, but my understanding is a bit different!     Find the error in the following proof that all horses are the same   color. CLAIM: In any set of h horses, all horses are the same color.      PROOF: By induction on h.      Basis: For h = 1. In any set containing just one horse, all horses   clearly are the same color. Induction step: For k > I assume that the   claim is true for h = k and prove that it is true for h = k + 1. Take   any set H of k + 1 horses. We show that all the horses in this set are   the same color. Remove one horse from this set to obtain the set H1   with just k horses. By the induction hypothesis, all the horses in H,   are the same color. Now replace the removed horse and remove a   different one to obtain the set H2 . By the same argument, all the   horses in H2 are the same color. Therefore all the horses in H must be   the same color, and the proof is complete.   Here's what i have come up with :  Suppose a set of 1 horse. $H_a = { horse_{1} }$  Obviously, all the horses in set $H_a$ are the same, since theres just 1 horse.  So using that as the Basis of the induction we can proceed and try to prove its true for $N$ horses.  -- I dont fully understand the part below   As an example : set $H_0$ :   $H_0 = { horse_{1}, horse_{2}, horse_{3}... horse_{n} }$  In my understanding, its because, I can make a subset  formed by 1 horse :  $K_1  = {horse_{1}}$ $K_2  = {horse_{2}}$ ...  I don't get it. I clearly know that this proof is a lie.  And for me, its because you cant claim theres a relation on a set with size $>= 2$ , since :  $H_1 = { horse_{1}, horse_{2}}$  Theres nothing that says $horse_{1}$ equals $horse_{2}$. The basis was for one horse. But that alone is not a proof.  So what should I do ?


How does one prove that $$\lfloor x \rfloor = \lfloor x/2 \rfloor + \lfloor (x+1)/2 \rfloor $$ where $\lfloor x \rfloor$ represents the greatest integer less than or equal to $x$?  I tried to do this by using inequalities but end up with $\lfloor x \rfloor + 1/2$ on the lhs. Can someone help?

I'm doing some exercises on Apostol's calculus, on the floor function. Now, he doesn't give an explicit definition of $[x]$, so I'm going with this one:     DEFINITION Given  $x\in \Bbb R$, the integer part of $x$ is the unique $z\in \Bbb Z$ such that $$z\leq x < z+1$$ and we denote it by $[x]$.   Now he asks to prove some basic things about it, such as: if $n\in \Bbb Z$, then $[x+n]=[x]+n$  So I proved it like this: Let $z=[x+n]$ and $z'=[x]$. Then we have that  $$z\leq x+n<z+1$$  $$z'\leq x<z'+1$$  Then $$z'+n\leq x+n<z'+n+1$$  But since $z'$ is an integer, so is $z'+n$. Since $z$ is unique, it must be that $z'+n=z$.  However, this doesn't seem to get me anywhere to prove that  $$\left[ {2x} \right] = \left[ x \right] + \left[ {x + \frac{1}{2}} \right]$$  in and in general that   $$\left[ {nx} \right] = \sum\limits_{k = 0}^{n - 1} {\left[ {x + \frac{k}{n}} \right]} $$  Obviously one could do an informal proof thinking about "the carries", but that's not the idea, let alone how tedious it would be. Maybe there is some easier or clearer characterization of $[x]$ in terms of $x$ to work this out.  Another property is $$[-x]=\begin{cases}-[x]\text{ ; if }x\in \Bbb Z \cr-[x]-1 \text{ ; otherwise}\end{cases}$$  I argue: if $x\in\Bbb Z$, it is clear $[x]=x$. Then $-[x]=-x$, and $-[x]\in \Bbb Z$ so $[-[x]]=-[x]=[-x]$. For the other, I guess one could say:  $$n \leqslant x < n + 1 \Rightarrow  - n - 1 < x \leqslant -n$$  and since $x$ is not an integer, this should be the same as $$ - n - 1 \leqslant -x < -n$$  $$ - n - 1 \leqslant -x < (-n-1)+1$$  So $[-x]=-[x]-1$


I'm developing an Android app that fetch client mobile and send an SMS in the background; I want the sent messages to appear in the native SMS app. This is my code and it works fine sending the message.  public class AlarmReceiver extends BroadcastReceiver {      @Override     public void onReceive(Context context, Intent intent) {          // For our recurring task, we'll just display a message         Toast.makeText(context, "I'm running from AlarmReceiver", Toast.LENGTH_SHORT).show();          //         String no = "70625783";         String msg = "message";          //Getting intent and PendingIntent instance         Intent i = new Intent(context, MainActivity.class);         PendingIntent pi = PendingIntent.getActivity(context, 0, i, 0);          //Get the SmsManager instance and call the sendTextMessage method to send message         SmsManager sms = SmsManager.getDefault();         sms.sendTextMessage(no, null, msg, pi, null);          Toast.makeText(context, "Message Sent successfully!",                 Toast.LENGTH_LONG).show();     } }   For simplicity I have hard-coded the mobile and the message content.

I have written the below code for sending SMS messages.  SmsManager smsManager = SmsManager.getDefault(); smsManager.sendTextMessage(destAddr, null, mMessageText, il, null);   But this is not updating in my Inbox, I need to save the same message in Inbox, Or is there any way to invoke a native SMS application to send SMS ?


Question: Is the first one redundant and proper, or is it redundant and not necessarily correct?  (1) He is a friend of Doug's. (2) He is a friend of Doug.

As  shows, we nearly always use the possessive form of personal pronouns for friend of mine/his/ours/etc.  But when it comes to actual names, we prefer  without the possessive apostrophe. That preference is even more marked with, say, . Not that I think the usage itself is particularly American - it's much the same with .  Personally, I find friend of him grates. In general I've no strong feelings either way as to whether it's friend of Peter or friend of Peter's (though I deplore the possessive in ), but in line with many others, I really don't like the possessive in relation to things like countries.  Why is this?   Edit: Noting an apparent "progression" (pronoun -> person -> nation) marked by reduction in use of the possessive, I checked at a finer "granularity". NGram shows that although it does occur,  virtually "flatlines" against friend of mine. But the bias reduces through of you, of us, and by the time I get to  it's much less extreme. There seems to be something "egocentric" about the double possessive.  Presumably when babies learn to speak, they soon notice that possessive pronouns, possessive apostrophes, and the word "of", all do the same job. Parents would correct a child who says "of mine's", but probably wouldn't even notice the same "redundancy" in "of Peter's". Younger speakers are unlikely to even be talking about something "of America's". Perhaps as we mature we tend to discard the "double possessive" for the more "distant" things that only adults are likely talk about, but we keep it for "closer" people because that's how we spoke when we were younger.  EDIT2 I note that I'm a great fan of him is vanishingly rare compared to ...fan of his, but with ...fan (of John) the double possessive occurs far less often than ...friend (of John's). Usage seems to be affected by the noun before "of" as well as the one after it. This is getting complicated...


I have troubles with handling non hostile social interactions with NPCs that have information or items important for the story, but who are not willing to hand it out for free.    Imagine a situation where the party comes into a tavern and the owner knows some information the party would like to acquire.  My players are alined good and normally one of them starts talking to them to get some information. After recognising that the owner is unwilling to tell them what he knows they try to persuade him. Now I let them roll d20 and they fail on the check.   Then most of the time another one tries to persuade, bribe or intimidate him. Sometimes 3 or 4 of them try to persuade the owner one after another. How can I handle this situation?    Example situation:     PCs enter a tavern, I narrate it to them explaining the owner is behind the bar cleaning mugs.        PC1: "Maybe he has information about subjectX"        PC2 talks to him: "Good day Sir, we are travellers looking for accommodation and maybe you have heard of subjectX"        Owner: "Then you came to the right place, I have enough beds for you. And about subjectX...it depends on who is asking"        PC2 tries to persuade him; He talks a bit and I let him roll a check. He fails      Owner: "It's not worth getting in trouble for giving you this information"      PC1: "Let me try talk to him" - fails too       Now PC3, PC4 and PC5 will attempt the same   Edit: As previously discussed in the comments, I do not think this is a duplicate of:  and   as interacting with an NPC is different than interacting with an item

I could use some advice as a GM on how to handle rolls which get repeated by several players one after the other.  Example 1     The PCs stand in front of a locked door and try to force it open. The tough   guy: "Stand back, I'll handle this!" Gives it a try, fails his roll,   the door stands. Up comes PC number 2. "Okay, I throw myself against the   door". Rolls okay, but not sufficient; the door holds. Eventually, the   Elf with back pain or the paraplegic Halfling succeeds with a lucky   roll.   Example 2     The PCs come upon a strange herb that they found somewhere. First   player checks herbology, zip. Second player, "Maybe I know the   kraut?", rolls, nothing. Third player...   This happens kind of frequently in our game. I'm not entirely sure it is a bad thing, but somehow it feels wrong. Firstly it greatly changes the balance of skill checks: 'sneaking' rolls, for example, must be succeeded by everyone in the group, 'herbology' only by one out of many. Secondly, I feel it lessens the satisfaction of actually solving problems unless the players explicitly want their characters to work together (and somewhat act it out, maybe). It boils down to "Okay, you try it first, then you, then you, and you with 0.1% chance of succeeding, why don't you give it a shot as well?"  The problem is lessened in some situations:   Some skill checks can have bad effects if they go wrong (e.g. Surgery, First Aid). Others will take time/resources that not all PCs are willing to spend.   But in many cases there is no game mechanical or rational way why players should not do it.   Do you think this is an issue, i.e., does this bother you as a GM? How do you handle these kinds of situations? (Ignore it? Forbid rerolls by other players? Add penalties to consecutive tries?)   I am totally okay with answers involving just talking to your players, or suggesting they try this or that. I don't necessarily need a game-mechanical way to address this issue.


1) There has been a funeral, two weddings and three thefts since you left.  OR  1) There have been a funeral, two weddings and three thefts since you left.  2) There was a boy and two girls inside the room.  OR  2) There were a boy and two girls inside the room.  3) Two girls and a boy was murdered.  OR  3)Two girls and a boy were murdered.

It seems I put a   Bounty assigned by outside party, two lengthy, reference-citing answers, one "-1" (awarded the bounty), one "-2", two others scored "0" and "-2" respectively, the answers suggesting one or the other is correct, 73 comments and no consensus so far - and me, as the asker, lost without a clue what to think of the answers anymore -  this is no longer "Learners' Level" question, so I thought I'd bring it here and hear what the experts have to say.    Original question:  Plurality of verb depending on plurality of list elements  An edit was suggested to my sentence.     There was were an orange, some grapes, two apples and a small pile of cherries on the plate.   In my native language plurality of the verb always follows plurality of the first element on the list. There were an orange,... sounds awkward to me, no matter what follows up. My simple solution was reordering:     There were some grapes, an orange, two apples and a small pile of cherries on the plate.   But that's not the first time I faced this situation and I'd like to know what the rules of grammar say about that - was my editor overzealous or am I trying to copy rules of my language that don't apply in English?    Someone linked a  for negatives, where the situation is more clear-cut ("There is no..."). Same applies to connection with "or" apparently, per accepted answer there. Still, nothing for "and".  It seems there is a consensus that in that if the verb goes after the list, it will be plural.     an orange, some grapes, two apples and a small pile of cherries were on the plate.   There doesn't seem to be clear consensus for:     On the plate { was | were } an orange, some grapes, two apples and a small pile of cherries   Adding more to the confusion is the abbreviated form: "There's"     One last note. In North America, at least, there is a widespread use of using a singular form like "there is" and "there was", without regard for the subject item or items, and this "there is" is often shortened to "there's":           There's three apples on the table!      Could you please clarify this mess?


I have a VPS with Windows server 2012. When disconnecting the remote connection with my physical computer, the desktop of the VPS becomes inactive, it logs off. However, I need to keep the virtual desktop active because I have macro's running using mouse and keyboardstrokes.  Is this possible? Or do I have to create something like a virtual machine?  thx!

I connecting remotely using remote desktop to windows 7 client when i disconnect the session it automatically logged-out the user in the remote client. I want to keep the user logged-in on the remote client after i close the RDP session.  Thanks in advance


I was kind of baffled when I saw the following code did not work as expected.  I thought Java always passed variables by references into functions.  Therefore, why can't the function reassign the variable?   public static void main(String[] args) {    String nullTest = null;    setNotNull(nullTest);    System.out.println(nullTest); }  private static void setNotNull(String s) {   s = "not null!"; }   This program outputs null.

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?


I animated these 3 layers and than tried combining but couldn't do it. I know how to combine rendered images from different layers in compositor but I'm trying out animation. Please help.!!!

I would like to know which nodes can I combine this two render layers  width?    I've made this with alpha over node and transparent rendering. I want such an image but I don't want to lose the background (Sky texture).    Thanks for helping! :)


During my childhood, it was common to use magnifying glasses to burn paper and dead leaves.    But would it be a good idea to place a lens above a solar panel, making sure that all the magnified light hits every solar cell on the solar panel? I know that  to harvest more energy, but I was wondering if this is reliable and durable.   Wouldn't the magnified light burn the solar panel or would it be converted to electrical energy right away?

I was just wondering why Fresnel Lenses are not widely used in the production of solar electricity. Their use there would mean that you could produce heat within a fraction of a second, up to a few minutes and run a turbine to produce electricity.  Though it is used in welding, I am not sure what are the problems in producing electricity, as stated by :     New applications have appeared in solar energy, where Fresnel lenses can concentrate sunlight (with a ratio of almost 500:1) onto solar cells.


We are preparing a new paper and my supervisor tells me that we have to put the name of a person on our paper because he was involved in getting us the grant. He says it is because of future grants and that we want to show that he was involved in the research -- and obviously he was not. I think we are supposed to work with him on the last year of my PhD, but not now. My supervisor already knows that I am against it and tells me that this is an “order” and it is because of some sort of “politics”. I can reject but I am not sure what are the consequences. What a PhD student should do in such a situation?

There's a department at my university where the head of department is routinely put as author on papers he didn't contribute to, and where researchers from overseas who had no input (but who provide funding to the department) are put on papers.    As a pragmatic matter, how should a PhD student respond when they are told to put three names on a paper, when those people didn't contribute?  Assume that refusing to put the co-authors on is not an option, because:   There will be bad consequences if they do not, and  This practice is routinely done at a high level, and there is nobody at the university to complain to about it.   This is not a duplicate of , because its answer assumes that it is practical for the student to refuse.


When I add an object, it is invisible. When I change to evee, it turns black, and when I move around the view, it takes away from the black and makes it grey. Then when I turn to cycles it turns grey like in solid view. I've already tried rolling back my drivers, and it doesn't effect anything. I am using Blender 2.81. Everything was normal for a while, then all of the sudden I added an object and it was invisible. When I restarted my computer, it did the same thing but only when I was close. The origin and outline are still there. My clip start was set very low, but even when I change it it didn't change anything. One time when this was happening, I deleted everything, then added a new cube. It was displayed as one of the old cubes, but the outline was not in the right place. When I add more objects, some of them disappear and others display the wrong shape. This only happens in object mode, and going into edit mode fixes it. This only happens every so often, and seems to just magically be fixed.

I don't know why but now, when i go in material preview or rendered (in solid mode it works fine), my object is entirely gray, or invisible idk, because it has the same color of the background. I've been working for days on this project without having this issue, it suddenly showed up. I tried opening other old projects and suddenly they all do the same so i guess it is some blender program setting that applies for all the projects, but idk how it happened cuz i didn't change anything :/, anyone got any tips?


I am trying to define a new command representing a ternary operator \newcommand{\ternary}[1][2][3]{\textbf{if} \quad #1 \quad \textbf{then} \quad #2 \quad \textbf{else} \quad #3}  Do you see why this error occurs and how it could be fixed?

With newcommand I can define customized command like \ABC. Is there any way to define a command with arguments. For example I want \brat{A}{B} be the same as [\![A,B]\!].


Usually ~ is used to insert an unbreakable space, however, it is used to insert a normal space in LaTeX3, if I understand it correctly. So how do I insert an unbreakable space in this case? Just use the penalty to get the same affect?

I need to define a token list of the form  \tl_new:N  \g_silly_tl \tl_set:Nn \g_silly_tl { Text ~ and ~ a ~ tie:?? }   How do I do this?    More generally, is there a reference where one can see how to input characters 'normally' under expl3 syntax?


I have a dual boot system with Ubuntu 14 and Ubuntu 16 :/ don't ask me why.  I want to install a Ubuntu server and delete completely the previous OS. how can I do this?

I would like to see a full how-to guide on how to install Ubuntu.


The apps were all user-downloaded. Transfer size should have created generous internal storage "breathing room."  Details:  Samsung Galaxy S5 Android 5.0 Via Android App Manager(AAM) reported completion of each move 64GB Samsung SD Card (presumably undamaged) Internal storage 90-95% capacity. Phone was restarted after all the moves. Cleared each cache before moving.  Referred to the following, but it is dated and from a different platform.     Editorial: Why, if so little storage is gained with a move, are SD cards so recommended as near-crucial in Android? After 6 months, my "Let the buyer beware" factor is growing with each swipe at each of Android's supposed benefits. Seems I need a PhD to embark on just about any change.

I'm running very low on interal phone memory storage - I'm down to 5 MB of the 180 MB available. I understand that not all apps can be installed into SD card, and those will instead use up my internal storage. Luckily, those are rare.  However, I recently installed an app that is listed as being installed on the SD card, not internal storage. Even so, after installing it I'm now getting the "low on space" warning. The app takes up 16 MB, and I seem to remember I had a bit over 20 MB internal storage space before... So judging from the space, it looks like it's still taking up space on internal storage.  So my question: Should an app that's installed onto SD card take up any internal storage?  What could be causing this? Does the market store the installation files somewhere in internal cache or something as weird? Why on earth do I need to worry about apps consuming space, when I have gigabytes of free space for them on my SD card?  My device is GT-S5570 running 2.2.1.


How can I set up desktop defaults, much like most distributions do, for every new user? (ex. default wallpaper, apps, etc)

On Ubuntu 10.4 I have edited the /etc/bash.bashrc file to set some variables like the command history size (HISTSIZE=5000), however if I create a new users Ubuntu by default gives them a .bashrc file in their home directory with this set as HISTSIZE=1000 which is overriding mine. How can I change the default .bashrc file that is created?


I’ve read through many of the similar questions but I have not found the answer and I have more details. I’ve been looking for this book for almost 30 years. The main character is a youth and I believe a female human. Might be a male. One day, at school the kids are asked to draw a picture (it is implied that it’s some type of assessment). The main character draws the head of the societies leaders as a spider or in a web while in a relaxed state. (Subconsciously) We understand this is not appropriate - criticism of leaders. The society has many tunnels that run through the outer area of the living area (I don’t recall the living spaces to be squalid in anyway). The tunnels are filled with water. They are never mapped which allows each new generation of people to have the pleasure of discovering something new. It turns out the main character is special in that she is dissatisfied and feels something is being kept from her people by the leaders. I believe the story concludes with the fact that she is supposed to lead the ridged community back to the scary topside. If you know this story - I’d love to give it to my daughter for Christmas this year. P.s - I remember that the people have no hair. They’re naturally bald down on their heads. I also recall that the main character eventually meets a girl with long blonde hair from the top side. (Which is why I wonder if the main character was actually male). That may happen in the first book or there may have been a second book in the set. Thanks for reading.

I need an ID on a (probably young adult) sci-fi novel I don't remember finishing.  I read it sometime in the late nineties or early noughties. The library book didn't show any obvious indications of age that I recall. The book was in Finnish but I think it was a translation. The cover image was a person with long chains of cabled-together cylinders projecting diagonally upward from the back of their neck. It almost looked like they were hooked into something by those.  The main protagonist is a young nobleman, I think the term was "Lord", from a ruling family. This class of nobleman is characterized by having databank neural implants dangling from the back of their neck. These databanks are heavy enough to affect the wearer's posture, and the result was described as a lordly slouch.  The story starts with the main character's coming of age ceremony, where they get the databank implants. There's a scene where the character gets a new set of clothes for the occasion, with his family crest cleverly worked into the decorative patterns by his mother.  After the actual implantation, the ceremony is interrupted by a coup of some sort. The main character has some trouble evading pursuit because he is wearing his family crest prominently. Somehow, he ends up outside the city, which is on some sort of stilts. For whatever reason, he can't return to the city, maybe he locked himself out or he was hiding from the coup.  This results in the character's first experience of being outside. I remember a scene where he's looking at the moon and pulls the hard data on said celestial body from his databanks, and then decides to look up poetry instead.   Some time later, the main character ends up living in a village of outsiders. The last scene I remember is that one night he overhears the men in the village singing about how their people had once been slaves to the Lords. That's where my recollection of the plot ends.  It is not  by Walter John Williams; the story didn't mention splitting one's consciousness, and in the Aristoi setting the databank seems to be "in the cloud" rather than as external add-ons.


The polygon tool can be used to create power planes. This is the common use of it and I am not aware of any other application of it.  When power plane is created, we name the plane to have same signal name as the ground signal. Once the plane is drawn and we click rat's nest, the signal paths are made distinct from the plane by removing the copper around edges of the signal trace. The copper plane swamps any signals with same name as the plane itself.  I have 1 question:  If I create two small planes and then a big plan that then overlaps both of them, how do I keep them seperate? What I want to achieve is below. The blue color is copper. There are two small planes inside a big plane. I don't know how to achieve the white seperation. It seems that pressing rat's nest does make signal trace distinct from power but not overlapping planes.

I am trying to make separate signal planes in eagle using the polygon tool. The problem is that when I draw the first polygon, regardless of whether I draw it small or large once I name it to GND and hit the "Ratsnest" tool, it will just occupy the whole space of the PCB leaving no space for other planes. How can I fix that?  Also I need one of the planes to be exposed copper, by drawing a polygon on either the bstop or tstop layers, I am getting what I need. The problem is that I don't know how to connect it to another part (say a transistor)?


I added this line into my ~/.bashrc file.  alias myserver='ssh davidfaux@davidfaux.com'   However, when I open terminal and run myserver, terminal complains that  -bash: myserver: command not found   When I source my .bashrc file, however, (. .bashrc), the alias works.   Nonetheless, I do not want to source the file every time I open terminal for the alias to work. How do I make that happen?

I put some alias commands in my .bashrc file, so that they might be loaded everytime I open a new Terminal window. Yet this doesn't happen. I have to select run script: in the Terminal>Preferences>"MyDefaultTheme">Shell prefpane and add: source .bashrc && clear for it to work... This seems odd since many tutorials only say you just have to add to the .bashrc file and all is good. Note that I don't run in bash when using the terminal, I like the other (default) one (don't know what it is) better, because it show me where I am all the time eg: >>d54c6b47b:~ romeo$  in stead of: >>bash$  In bash all is loaded as should be. So my question is, why didn't my .bashrc file load automatically and did I have to add the option to call it everytime? Also some tutorial told me to do something like: $alias la=’ls -la’ >> ~/.bashrc  which should write the alias to my .bashrc, this doesn't work either... Note that I'm a UNIX novice, so be gentle.


So I'm developing a soap webservice and I need to check the request Headers, I've spent the last 30 minutes searching how to do this but couldn't find an answer, is it possible to check the request headers and if so how? Service example: webservice static AccountAddressResult UpdateAccountAddressInfo(AccountAddress accountAddressInfo, String addressType, String addressCategory) {     //Check Headers here     (...) }

<soapenv:Header>   <wsse:Security SOAP-ENV:mustUnderstand="1" xmlns:SOAP-ENV="SOAP-ENV">      <wsse:UsernameToken wsu:Id="UsernameToken-1" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd">         <wsse:Username>oneview</wsse:Username>         <wsse:Password Type="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-username-token-profile-1.0#PasswordText">oneview123</wsse:Password>      </wsse:UsernameToken>   </wsse:Security>     Here is how my header is structured in request .By default when my stub is generated from WSDL no information regarding  header in WSDL .So is there any code in apex i can start and include in my stub class and create this kind of header.  Update:  <wsp:Policy wsu:Id="UsernameToken" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd" xmlns:wsp="http://schemas.xmlsoap.org/ws/2004/09/policy">     <wsp:ExactlyOne>         <wsp:All>             <sp:SupportingTokens xmlns:sp="http://docs.oasis-open.org/ws-sx/ws-securitypolicy/200702">                 <wsp:Policy>                     <sp:UsernameToken sp:IncludeToken=".../IncludeToken/AlwaysToRecipient"/>                 </wsp:Policy>             </sp:SupportingTokens>         </wsp:All>     </wsp:ExactlyOne> </wsp:Policy>   The WSDL has wsp and policy .Do WSDL to apex support this.Any help appreciated


I'm having a bit of a dilemma currently. Basically I applied (with my own research proposal) to three universities for a PhD. Whilst I was accepted at all three, I got no offer for funding from one, placed on the reserve list for funding for another, and offered funding for the third.   The university I was placed on the reserve list for was basically my dream university to go to for a PhD but after hearing nothing for 2 months I accepted the offer from the other university. I accepted about two weeks ago and have spoken to the people who will be my supervisors and they're both lovely people.   However, this evening I received an email from my preferred university offering me full funding. Obviously I would love to accept but I don't know how bad it looks to reject the other offer now? I would feel terrible, but one of my main concerns is also that people say the academic community is very tight-knit and obviously these academics all research a similar topic. I want to work in academia following my PhD and wouldn't want to start this career already having academics not a fan of me!   Any advice would be massively appreciated.

I have accepted a PhD offer from a very good university to do a project very close to my interests. I have told the project supervisor I accept it. In the meanwhile I have managed to secure a PhD offer from another 2 universities much better in world rankings and with better research groups and better faculty. Additionally these 2 universities do research exactly on what I want to devote my PhD research.  My only commitment to the first university is a mail confirming I accept. Nothing else. I understand declining the offer after already having accepted it is quite dishonest but it is a huge decision that will affect my future in a very significant level.   I would like your opinion and I would also like to ask for possible consequences of such an action. As far a postdocs concerned, in the first university there is no chance I ever get a postdoc since they do not actually do research on my area (except for the prospective supervisor and even he not as much).  UPDATE I have decided to do as I was afraid to. I have decided to choose a different university than the first one that I have already accepted the offer. My offer acceptance included:    An online "I accept" statement. An e-mail I sent stating "I accept the scholarship and this University is my first option"   I do not have any legal commitments since I have not signed anything. The supervisor of the first university though is really nice to me and continuously was sending me mails. How do I very nicely tell her I will not be joining in the end? Additionally the place I will go in the end will be for research in Mathematics and not Physics. Can I use this as a part of a sensical excuse?  WHAT I HAVE CHOSEN AND WHAT THE CONSEQUENCES WERE  I think that I should let people, especially other beginning grad students know what happened with my case. I have chosen to nicely tell the first university I got accepted that I will not be attending and will not be pursuing a PhD there since I decided I have different research interests (which is true). I had applied there in the first place since I was not sure what I wanted to do and because it was a nice program. Despite that, I got an offer from a World top university to work on 100% my research interests. I explained this to them, the first uni, and they happily let me go and wished me good luck, especially the supervisor who faught a lot secure me funding. I was lucky.


I have an example of what I mean, for this I use a cube adding a simple cycles material I select toon  How do I bake this material, thanks for reading.  Cheers!

I'm currently working on a project with Unity 3D, and my plan is to design everything with Blender. But I didn't know until today that Cycles renderer is meant for animations and HD images.  Can I use Cycles for a game in Unity as well?  I've heard about baking, but I don't know how it works, other than creating a UV image with light impact to the mesh of an object. But would this mean that moving an object around the scene will make it look like the light is till glued to the object?  This doesn't sound that good if objects in a game are supposed to move around.


It's normal when using terminals that pressing up and down cycles through previous commands entered chronologically.  I learned from a site how to add to that behaviour by autocompleting what I'm typing at the cursor based on previously entered commands when pressing up and down.  For example, let's say I typed the following commands in this order:   ls Videos ls Vids lsomething ls Videos/Funny/Old vi file ls Music   If I haven't typed anything, pressing up and down will cycle through all of the lines just like normal. But, if I've typed ls, pressing up and down cycles through all commands where the first 2 characters are ls (lines 1,2,3,4,6 above). Entering ls (with a space after) though, will only let up and down cycle through lines 1,2,4,6. Similarly, ls Vid lets the arrows cycle through lines 1,2,4 but ls Videos just allows cycling between lines 1 and 4.  It's pretty useful to complete values specific to commands that you need to enter over and over again without having to cycle through every single unrelated command you've entered between them. For example, I'm trying to test the effects of env values, like locale, on things:  env [many different values] [command] [insert many different commands here] env [slightly different values from before] [command] [doing other stuff]   I'd only have to press up a few times after typing env to cycle between the values I've tried.  I apologize if it's a bit of a long way to describe it. I don't know what it's called. My terminals used to have this behaviour, but they seem to have lost it and I can't find the site I learned it from. I think it has something to do with editing ~/.bashrc.

I have searched, but not found anything on this. I am looking for a functionality in bash, using a terminal.  Way back when, I had a user on a debian system, and a friend set me up with a convenient history search feature (I believe I used tcsh then), where I would type the beginning of a previous command, hit up-arrow, and it would do a search, based on the partial string.  E.g. if my history is:  ./script.pl ./script.pl arg1 cat output cat output | grep yada   And I type ., and press up-arrow, it would show me: ./script.pl arg1. Press it again and it would show ./script.pl, etc.  Very much like it would perform a grep on .bash_history. Is there a way to get this functionality?


I am trying to install one program named TecDoc Catalog. I am using Lubuntu 17.10 whit installed 32 bit Wine, winetricks and configured  wineprefix(installed dotnet452).   When i try to run the Install.exe whit Wine it shows this error:     This application could not be started. You must enable the .NET   Framework from Windows Features dialog box (from Control Panel, choose   Programs, Turn Windows features on or off).      Do you want to view information about this issue?   If i click "yes" it leads me here:   In terminal the error looks like this:  fixme:ntdll:WinSqmIsOptedIn (): stub wine: cannot find L"C:\\windows\\system32\\fondue.exe"   I have installed .net framework(dotnet452),  i'm asking how to enable it? Please tell me how to do it by terminal.  Thanks!  tip: Before install dotnet452 the error was "This app require installed .net framework..." Now i need to enable it somehow.

I wanted to install osu!, but it doesn't work when you go on PlayOnLinux (error message and nothing happens).  Then, I followed .  As the video showed (at 2:44,) I clicked on Run a .exe file in this virtual drive then I clicked on osu!install.exe and then I get this message:    Can you tell me how to install this?


I’m a minor 17 and I’m from Peru. I have requested a visa for the UK for a short-term study less than 6 months and I didn’t realize that they wrote in there only acc by/ father/. I’ll be entry the country with my father but I will not leave with him. I’ll return alone. If I present at the moment to leave the country a letter consent where both of my parents sign that I’m allowed to leave and entry the country without them. Will they let me leave the UK? Please I’m really worried about it

My daughter who is just under 18 has a child accompanied visa to the UK. I am traveling with her to the UK for a few days. We return from UK on the same day except that she returns to India and I am heading to San Francisco an hour later on the same day.   Is that okay or will we have an issue at immigration into the United Kingdom?


I have a Windows 10 computer and am running Windows 10 in the virtual machine (Virtual box). If i wanted to download lots of viruses to screw with the virtual machine, could they infect the host? I know about turning shared folders off. If they can infect the host, is there any way to make it so they can't, but i still want to be able to browse the internet in the vm. Thanks!

If I am running a Windows 7 virtual machine on a Windows 7 host using VMWare or VirtualBox (or anything else) and the virtual machine is completely overloaded with viruses and other malicious software, should I worry about my host machine?  If I have an anti-virus program on host machine will it detect any problems?


How can I explain that $A\cup(B\cap C) = (A\cup B)\cap(A\cup C)$ is true?

I've only the definition of union, intersection, subset, and complement available to me.   $$(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$$  $(X \cap Y) = \left\{a: a \in X, ~ a \in Y\right\}$  $$\begin{eqnarray} (X \cap Y) \cup Z &=& \left\{a: a \in X ~ \text{or} ~ a \in Y\right\} \cup \left\{a: a \in Z\right\}\\ &=& \left\{a: a \in X ~ \text{or} ~ a \in Y, ~ \text{and} ~ a \in Z \right\} \tag1 \\ &=& \left\{a: a \in X~ \text{and} ~ a \in Z, ~ \text{or}, ~ a \in Y ~ \text{and} ~ a \in Z \right\} \tag2\\ &=&\left\{a: a \in X~ \text{and} ~ a \in Z\right\} \cap \left\{a: ~ a \in Y ~ \text{and} ~ a \in Z \right\}\tag3\\ &=& (X \cup Z) \cap (Y \cup Z)\tag4 \end{eqnarray}$$  I numbered those last few lines to make it easier to point out my blunders. I've never proven anything with sets before, so it probably doesn't make any sense. Many thanks in advance.


Through the photoelectric effect among many others we learn that light is actually comprised of discreet quanta of energy. That's because of the energy of the emitted electrons as well as the minimum frequency of incident light that is able to start the process. A photon of frequency (energy) less than the threshold frequency is not able to free the electron from the surface. However if the required energy to free the electron was greater than this frequency by an integral value why couldn't the electron simply absorb two photons or three photons (or any required number of photons) so as to be released? In this case even with frequencies lesser than the threshold frequency there would be photoelectric effect.

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


I'm interested in expressions for the second fundamental form of an implicit surface $f(x,y,z) = 0$, in terms of the first and second derivatives $f_x, \ldots, f_{yz}$. I am not looking for the expressions of a function in Monge form, $z = h(x,y)$. That is I don't want to assume that I can rewrite the expression locally in the form. I have access only to $f$ and its derivatives. As a concrete example, suppose I have a function $x^2+y^2+z^2 - 1 = 0$, and I want to compute the coefficients of the second fundamental form $L, M, N$ in terms of the available derivatives, without rewriting $f$ in parts such as $z = \sqrt{1-x^2-y^2}$.

Let $U\subset\mathbb R^3$ be an open set, and $f:U\to \mathbb R$ be a smooth function. Suppose that the level set $S=f^{-1}(\{0\})$ is non-empty, and that at each $p\in S,$ the gradient $\overrightarrow \nabla f(p)$ is not the zero vector. Then $S$ is a smooth two-dimensional surface in $U$, and $p\mapsto \overrightarrow \eta(p)=\frac{1}{||\overrightarrow \nabla f(p)||}\overrightarrow \nabla f(p)$ defines a smooth unit-length normal vector field along $S$. At each $x\in U,$ write $H(f)_{(x)}$ for the $3\times 3$ Hessian matrix specified by $$(H(f)_{(x)})_{ij}=\frac{\partial^2f}{\partial x_i\partial x_j}(x).$$   Show that, at each $p\in S$, the second fundamental form $II_p: T_p(s)\times T_p(s)\to \mathbb R$ is the symmetric bilinear map    $$II_p(\overrightarrow v,\overrightarrow w)=\frac{-1}{||\overrightarrow \nabla f(p)||}\overrightarrow v\cdot H(f)_{(p)}\overrightarrow w,$$for all $\overrightarrow v ,\overrightarrow w \in T_p(s)$.       (Here, we view the tagent space $T_p(S)$ as the two-dimensional subspace $(span\{ {\overrightarrow \eta(p)}\})^{\bot}$ of $\mathbb R^3$.      Edit: Actually my question is why the second fundamental form under the usual definition can be written in this way.      Definition: The quadratic form $II_p$, defined in $T_p(S)$ by $II_p(v)=-<d  N_p(v),v>$ is called the second fundamental form of $S$ at $p$, where $dN_p:T_p(S)\to T_p(S)$ is the differential of the Gauss map.   Hopefully, I express this problem explicitly. I was just wondering how to prove this statement.   I took a diffrential geometry class last semester, and when I organized my notes this morning, I found this statement, but there was no proof...  Looking forward to an understandable explaination. Thanks in advance.     Edit 2:Furthermore, show that, at each point $p\in S$, the expression   $$\phi_p(z)=det\pmatrix{-H(f)_{(p)}-zI_{3\times 3} & \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)& 0}$$   (the underlying matrix here is $4\times 4$) defines a second-degree polynomial whose roots $\lambda_1$ and $\lambda_2$ are $||\overrightarrow \nabla f(p)||k_1$ and $||\overrightarrow \nabla f(p)||k_2$, where $k_1$ and $k_2$ are the principal curvatures of $S$ at $p$.      Also, if a non-zero vector $\pmatrix {\overrightarrow v \\c}$ lies in the kernel of the $4\times 4$ matrix $$\pmatrix{-H(f)_{(p)}-\lambda_jI_{3\times 3} & \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)& 0},$$   then $\vec v$ is a non-zero element of $T_p(S)$ and lies in the "principal direction" corresponding to $K_j$.


I have a c# int array that contains numbers from 1 to 100 that means that  myArray[0] = 1; myArray[1] = 2; .... myArray[99] = 100;   But I want to rearrange them in this array randomly, is it possible in c# ?

What is the best way to randomize an array of strings with .NET? My array contains about 500 strings and I'd like to create a new Array with the same strings but in a random order.  Please include a C# example in your answer.


Given that the eigenvalues of a Hamiltonian operator $H$ are bounded below, will a Hermitian operator $T$ exist such that $[T, H] = i\hbar{\bf 1}$ identity operator?

In Quantum Mechanics, position is an observable, but time may be not. I think that time is simply a classical parameter associated with the act of measurement, but is there an observable of time? And if the observable will exist, what is an operator of time?


I'm trying to dual boot my laptop with windows 8 and linux. Can someone supply me with instructions of an easy way to do this? Thank you.

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


I had Windows 7 and Ubuntu 12.04 installed in my system. I removed Ubuntu and installed it again. When I restarted the system, it showed:  Error : Unknown filesystem  grub rescue >    When I use the ls command I am getting this   (hd0),(hd0,msdos8),(hd0,msdos7)(hd0,msdos6)(hd0,msdos5) (hd0,msdos4)(hd0,msdos3)(hd0,msdos2)(hd0,msdos1)   But when I run ls (hd0)/ it's saying unknown partition. The same case for all the others (hd0,msdos1) to (hd0,msdos8).  I tried booting a new OS from USB, and I am getting   Error loading operating system   I also tried Super Grub from USB, but I still get the same error Error loading operating system.  Please let me know what to do now.

I have a multiboot system set up. The system has three drives. Multiboot is configured with Windows XP, Windows 7, and Ubuntu - all on the first drive. I had a lot of unpartitioned space left on the drive and was reserving it for adding other OSes and for storing files there in the future.  One day I went ahead and downloaded Partition Wizard and created a logical NTFS partition from within Windows 7, still some unpartitioned space left over. Everything worked fine, until I rebooted the computer a few days later.  Now I'm getting:    error: unknown filesystem.   grub rescue>   First of all I was surprised not to find any kind of help command, by trying:    help, ?, man, --help, -h, bash, cmd, etc.  Now I'm stuck with non-bootable system. I have started researching the issue and finding that people usually recommend to boot to a Live CD and fix the issue from there. Is there a way to fix this issue from within grub rescue without the need for Live CD?  UPDATE  By following the steps from , I was able to boot to initramfs prompt. But not anywhere further than that.  So far from reading the manual on , I was able to see my drives and partitions using ls command. For the first hard drive I see the following: (hd0) (hd0,msdos6) (hd0,msdos5) (hd0,msdos2) (hd0,msdos1)  I now know that (hd0,msdos6) contains Linux on it, since ls (hd0,msdos6)/ lists directories. Others will give "error: unknown filesystem."  UPDATE 2  After the following commands I am now getting to the boot menu and can boot into Windows 7 and Ubuntu, but upon reboot I have to repeat these steps.    ls ls (hd0,msdos6)/ set root=(hd0,msdos6) ls / set prefix=(hd0,msdos6)/boot/grub insmod /boot/grub/linux.mod normal   UPDATE 3  Thanks Shashank Singh, with your instructions I have simplified my steps to the following. I have learned from you that I can replace msdos6 with just a 6 and that I can just do insmod normal instead of insmod /boot/grub/linux.mod. Now I just need to figure out how to save this settings from within grub itself, without booting into any OS.  set root=(hd0,6) set prefix=(hd0,6)/boot/grub insmod normal normal   UPDATE 4  Well, it seems like it is a requirement to boot into Linux. After booting into Ubuntu I have performed the following steps described in the :  sudo update-grub sudo grub-install /dev/sda   This did not resolve the issue. I still get the grub rescue prompt. What do I need to do to permanently fix it?  I have also learned that drive numbers as in hd0 need to be translated to drive letters as in /dev/sda for some commands. hd1 would be sdb, hd2 would be sdc, and so on. Partitions listed in grub as (hd0,msdos6) would be translated to /dev/sda6.  UPDATE 5  I could not figure out why the following did not fix grub:  sudo update-grub sudo grub-install /dev/sda   So I downloaded  based on an answer from  post. That seemed to do the trick after I picked the "Recommended Repair (repairs most frequent problems)" option.


How can I improve, in a way ideally not requiring manual (automatic may be OK!) tinkering with (half) linewidths and scaling factors, the look of this axis intersection:  Here's what I have (left), and what I want (right):     And here's my MWE:  \documentclass[tikz,border=3pt]{standalone} \usepackage{tikz,pgfplots} \begin{document} \begin{tikzpicture}     \begin{axis}[         axis x line = middle,         axis y line = middle,         xtick = \empty,         ytick = \empty,         xmin = 0,         xmax = 1,         ymin = 0,         ymax = 1,         width = 2cm,         height = 2cm,     ]\end{axis} \end{tikzpicture} \end{document}

The 2nd page of the .pdf file generated by the following .tex file:  \documentclass{beamer} \usepackage{pgfplots} \begin{document} \begin{frame}   \framezoom<1><2>(0cm,5.5cm)(0.5cm,0.5cm)   \begin{tikzpicture}     \begin{axis}[%       axis x line=bottom,       axis y line=left,       ymin=0,       xtick=\empty,       ytick=\empty,       ]       \addplot {1} ;     \end{axis}   \end{tikzpicture} \end{frame} \end{document}   points out a notch at axes intersection:    How could I get rid of this notch?  Note that this question is similar to:    but is concerning more specifically pgfplots than tikz,  but is concerning axes instead of plot lines.


My graduate school requires the appendices to be after the bibliography but still numbered A,B,C, etc.  I'm running into a problem because I am using \backmatter before calling the bibliography but this turns off chapter numbering so then all appendices are numbered as .1 and so forth.  For example, I'd like to do the following:  \documentclass{book}  \begin{document}  \frontmatter \tableofcontents  \mainmatter \chapter{foo} \section{Donald}  \backmatter \bibliographystyle{bibstyle} \bibliography{exampleBiB}  \appendix \chapter{bar} \section{Mickey}  \end{document}   and have the Mickey section labeled A.1.  I know that backmatter turns off chapter numbering so I realize this is the problem, but without it then the bibliography is incorrect.  Any help is appreciated.

I'm trying to get the figures and labels in my appendices to have the same format as the rest of the document.  In my main thesis.tex file I use:      \backmatter % book mode only     \appendix     \include{Appendix1/appendix1}   and then in the appendix1.tex file I have:      \chapter{Appendix A - Data}     \label{ch:App1}   This produces my appendices as I wish, displaying "Appendix A - Data" in the table of contents etc.  However, it also restarts the numbering of figures and tables.  So for example I would have Figures 5.1, 5.2, ... in Chapter 5, presently I have Figures 1, 2, 3, ... in Appendix A, whereas I would rather something along the lines of Figure A.1 etc.  The same applies to Tables.  Also, when I reference the appendix in an earlier chapter using:      Appendix \ref{ch:App1}   It is referenced as "Appendix 7" (I have 6 preceding chapters) as opposed to "Appendix A" as listed in the contents.  Any help would be greatly appreciated.


I have a group of 16 people that are working together on a committee. We want to get to know each other better by splitting into smaller groups of 4 for icebreakers. I believe if we did this 5 times, every member would be able to meet every other member, with nobody meeting the same person twice. I can't figure out the formula for this. Can you help?

I found this hard to word in the title, so let me give an example. I have 16 students, and I want to split them up into 4 groups of 4. However, I want to make sure that every time I have a new combination of groups, that a student has never been with any of their new groupmates before. I found info on how to separate objects into groups, but not in only unique ways as I've described above. I think I figured this out the rote way, by assigning each student a number and then finding the unique combinations, and got 3. But I'd like to know the math behind it, and how it could be applied to other configurations (20 students w/ 4 groups of 5?). Thanks for any help you can give!


I executed the command below in a BASH shell.  export PROMPT_COMMAND='echo "$BASH_COMMAND" >> $HOME/my_bash_history'   but everytime I type something in the shell and hit return, I just get one more line my_bash_history file which fills up with:  echo "$BASH_COMMAND" >> $HOME/my_bash_history echo "$BASH_COMMAND" >> $HOME/my_bash_history echo "$BASH_COMMAND" >> $HOME/my_bash_history echo "$BASH_COMMAND" >> $HOME/my_bash_history echo "$BASH_COMMAND" >> $HOME/my_bash_history echo "$BASH_COMMAND" >> $HOME/my_bash_history   anybody know why that's happening?

Why when I enter this command the prompt changes to my directory?  PS1='$(pwd)'   I am using single quotes, which means no interpolation , a.k.a echo '$(pwd)' ——→ $(pwd)  Furthermore, say that we clarified why this works... why is it functioning differently from PS1=$(pwd) ? (no quotes at all)  By different I mean that if I use the quotes then the prompt will keep changing to my current directory as I navigate through the terminal. But if I don't use quotes, then the prompt will always remain the directory that I was in when I first entered the command PS1=$(pwd)  why?


I'm working on adding ssh authentication to a fresh Linode Ubuntu 12.04LTS deployment. I followed  to the letter up to the point where I need to ssh into the box with my now freshly added ssh key, but I instead get:  "Error: agent admitted failure to sign using the key"   Which is fine, the  says that all you need to do is to run  ssh-add   on the server and you'll be golden. Except when I do that I get   Could not open a connection to your authentication agent.   I double-checked the processes and indeed it does look like ssh-agent is already running (in fact twice, because I tried , which didn't work at all):  alex@mybox:~$ ps aux | grep ssh root      2645  0.0  0.1  49948   776 ?        Ss   Mar13   0:00 /usr/sbin/sshd -D alex     16989  0.0  0.0  12492   324 ?        Ss   Mar13   0:00 ssh-agent root     18986  0.0  0.7  73360  3564 ?        Ss   09:03   0:00 sshd: alex [priv]    alex     19119  0.0  0.3  73360  1676 ?        S    09:03   0:00 sshd: alex@pts/0     alex     19785  0.0  0.0  12492   316 ?        Ss   09:59   0:00 ssh-agent root     20026  0.0  0.7  73360  3568 ?        Ss   10:02   0:00 sshd: alex [priv]    alex     20184  0.0  0.3  73360  1680 ?        S    10:03   0:00 sshd: alex@pts/1     alex     20325  0.0  0.1   9384   924 pts/1    S+   10:13   0:00 grep --color=auto ssh   As I mentioned, the eval approach managed to make ssh-add work once, but when I tried to log in again, the system reported the same error I listed above. I also now have two instances of ssh-agent.   What is the proper way of addressing this?

I'm using Ubuntu server 10.04.   ssh-add /foo/cert.pem gave the following output:     Could not open a connection to your   authentication agent.   These are my running processes:  ps -aux | grep ssh Warning: bad ps syntax, perhaps a bogus '-'? See http://procps.sf.net/faq.html root      1523  0.0  0.0  49260   632 ?        Ss   Dec25   0:00 /usr/sbin/sshd root     10023  0.0  0.3 141304  6012 ?        Ss   12:58   0:00 sshd: padmin [priv] padmin   10117  0.0  0.1 141304  2400 ?        S    12:58   0:00 sshd: padmin@pts/1 padmin   11867  0.0  0.0   7628   964 pts/1    S+   13:06   0:00 grep --color=auto ssh root     31041  0.0  0.3 141264  5884 ?        Ss   11:24   0:00 sshd: padmin [priv] padmin   31138  0.0  0.1 141264  2312 ?        S    11:25   0:00 sshd: padmin@pts/0 root     31382  0.0  0.3 139240  5844 ?        Ss   11:26   0:00 sshd: padmin [priv] padmin   31475  0.0  0.1 139372  2488 ?        S    11:27   0:00 sshd: padmin@notty padmin   31476  0.0  0.0  12468   964 ?        Ss   11:27   0:00 /usr/lib/openssh/sftp-server   These are my environment variables:  $ env | grep SSH SSH_CLIENT=192.168.1.13 42626 22 SSH_TTY=/dev/pts/1 SSH_CONNECTION=192.168.1.13 42626 192.168.1.2 22   What is wrong? Why can't I add any identities?


I have an application that minimizes to icon state when user press close. I want to make application show again when user tries to open the app, instead of just opening the app again. I thought of using settings: A boolean value, true if the app is opened and false if it isn't but that would mean you should set it to false when user closes app and true in the load function. But since close event doesn't run when program crashes, that would make program un-openable (:D?), and i have no idea how to call events between two programs. TL;DR: Show the app to user instead of opening it twice when user opens program again, just like Discord. Thanks!

Using C# and WPF under .NET (rather than  or console), what is the correct way to create an application that can only be run as a single instance?  I know it has something to do with some mythical thing called a mutex, rarely can I find someone that bothers to stop and explain what one of these are.  The code needs to also inform the already-running instance that the user tried to start a second one, and maybe also pass any command-line arguments if any existed.


Fairly certain it's from the 70s and that the author is American or British. IIRC, the first book starts with a very old man travelling to the place, and when he eventually goes through the portal to a zone which is when other people have been transformed, he comes out the other side, says "Oh, of course," and moves on.  Other people are transformed into   Walking trees that reproduce by getting bigger, developing a second brain and consciousness, and then splitting A centaur-like race   You have the sense that the world in question is both very old, and now neglected by its makers.  Could swear "world" was in the title, at least of the first one.

I read this book at least ten years ago.  Any help identifying it would be appreciated.  Characters are teleported to an artificial world where each take over the mind of a different species.  I remember a moving sentient plant, a faun-like character, and a wasp-like character.  The planet is subdivided into different zones designed for each species.  One of the characters had long sharp fingernails with poison in them.  Thanks for any help, steve


I just installed dual-boot (Windows 10 + Ubuntu 18.04). On Windows I have download speed like ~60 Mbit/s on Ubuntu it looks like this:  Download: 0.71 Mbit/s  I tried both: Home WiFi and also mobile hotspot (works the same in both cases)  None of solutions that I found worked for me.  Some info:  Bus 001 Device 009: ID 0bda:8178 Realtek Semiconductor Corp. RTL8192CU 802.11n WLAN Adapter   @Update 1: lspci -knn:   @Update 2: lsusb and lspci results:   SOLUTION: Looks like I fixed this. This helped me:  Thanks @GabrielaGarcia for help. It's still not as fast as on windows but speed is good enough (Download: 25.77 Mbit/s).

On windows downloading a 100 MB file takes less than a minute while on Linux it is taking me 1 hour.  Why is there such a big difference and what do I do to speed it up?   I am using a wireless network adapter made by belkin and since it is working fine on windows I suspect its some driver issue or something.   I will edit this post with outputs of a command if desired!  --- Output of lsusb ---  Bus 004 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 003 Device 003: ID 046d:0990 Logitech, Inc. QuickCam Pro 9000 Bus 003 Device 002: ID 04d9:fa50 Holtek Semiconductor, Inc.  Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 003: ID 050d:2103 Belkin Components F7D2102 802.11n N300 Micro Wireless Adapter v3000 [Realtek RTL8192CU] Bus 001 Device 002: ID 413c:2003 Dell Computer Corp. Keyboard Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub   --- Output of lsmod | grep rtl ---  rtl8xxxu              122880  0 rtl8192cu              65536  0 rtl_usb                20480  1 rtl8192cu rtl8192c_common        53248  1 rtl8192cu rtlwifi                77824  3 rtl_usb,rtl8192c_common,rtl8192cu mac80211              761856  4 rtl_usb,rtlwifi,rtl8192cu,rtl8xxxu cfg80211              581632  2 mac80211,rtlwifi


When I add a new item (sphere, cube etc) the lower left hand editing box is no longer activated....it is clouded over and unresponsive. For example: I add a UV Sphere but can no longer change the segments, rings, size etc. It was working in the past which makes me wonder if I have inadvertently turned it off....I have closed and reopened Blender but cannot rectify this issue.

I have lost functionality in the tool shelf. When I click on a selector or something in the bottom part of the tool self that you can hide and unhide, nothing happens. I can see the options but when I click it doesn't work. See screenshot where it says "Add Cylinder".


I've got a website I'm developing, and it's database driven.  If I use SQL Server Development Edition as the back end, is that "legal"?  I'll be the only developer using the software, but it will be accessed/queried by dozens/hundreds/thousands of other people.  I apologize if this seems rudimentary, but I've never done this outside of a company so I don't really understand product licensing.

Do you use SQL Server Developer Edition on server-class machines in DEV and STAGING environments?  I am working on a large project where (if it passes the proof of concept stage) we will have several large geographically distributed enterprise class database servers running SQL Server 2012 Enterprise Edition.  We will have a production environment will initially have 3 servers, our Staging environment will have a minimum of 3 servers, and our Development environment will have 1 server (hosting three instances).  I was under the impression that we would only need to acquire Enterprise licences for the actual production servers, and we could get by with developer edition in our developer and staging environments because they are not "production".  Other sources have told me that we need to have an enterprise licence on all of the above mentioned machines, and that the developer edition is only meant for a single developer on their workstation.  Since developer edition has all the sexy features of Enterprise, I can't really see the value of it on a workstation class machine, especially for developing and testing the type of high availability system we are building.  If we have to fork out Enterprise licences for a dev server, that will just about kill our proof of concept stage, thus killing the project.  Forcing an enterprise licence on a staging environment will make management just want to skip staging altogether.


I bought a model that has .obj, .fbx and .max formats. I use Mac, so I'm not able to use .max, so I decided to import .obj in Blender. After I imported the file, I saw that a part of it hidden as if there was a gray wall or a portal to another universe. It's hard to explain it, better check the gif:    I'm totally new to Blender, so I have no idea what it is.

I'm having an odd issue - When I try to zoom in on a detail using my MMB, the "camera" in the 3D view seems to be cutting off the exterior surface of my object and showing me the inside instead. I'd expect this behavior, but only when I was much more zoomed in.  If I zoom out a bit (one click on the scroll wheel) then I can see the exterior as I intend.  Is there any way to adjust this behavior?  Thanks!


\documentclass{article}  %\usepackage{filecontents} \begin{filecontents*}{references.bib} @misc {dg,   author = {{Detroit Gazette}},   note   = {1817--1830. Microfilm edition, Detroit Gazette Collection,              c.~123, XYZ University Library, University Town, State}, } \end{filecontents*}  \usepackage[authoryear,round]{natbib} \bibliographystyle{plainnat} % choose a bibliography style that suits your needs  \begin{document} \dots{} as the Ohio Canal fund \citep[Dec~11 1827,p.~2, c.~5]{dg}\dots \bibliography{references} \end{document}   the result is:     . . . as the Ohio Canal fund (?, Dec 11 1827,p. 2, c. 5). . .

I've browsed the forums and found a number of posts that have addressed this issue, but none of the solutions seem to work for me. I have the following script that I just copied from the bibtex home page to get familiar with it. Instead of the citation number I get a question mark. I compile using Latex+Bibtex+Latex+Latex+PDFLatex+ViewPDF just as has been previously suggested and the problem persists.   \documentclass[11pt]{article} \usepackage{cite}  \begin{document}  \title{My Article} \author{Nobody Jr.} \date{Today} \maketitle  Blablabla said Nobody ~\cite{Nobody06}.  \bibliography{mybib} \bibliographystyle{plain} \end{document}   My bibliography (Bib.bbl)  @misc{ Nobody06, author = "Nobody Jr", title = "My Article", year = "2006" }    Looking at previous posts one thing that is concerning is that my .bbl looks empty as shown below. Further, I don't have a .blg  \begin{thebibliography}{}  \end{thebibliography}


I'm trying to achieve real time reflections in the game engine, possibly using the render to texture module if needed, but am not sure exactly how to go about it. Faking reflections using cube maps, etc, are simple enough, but that doesn't achieve a true reflection. I want to be able to see a true reflection of my character if he/she moves in front of the mirror.  If you're still confused, take a look at a real mirror. That is what I want to simulate. Any tips are appreciated.

A google search found this demo of a mirror in the BGE  but I can't find out how to setup the material. Unlike in the BI renderer the option Mirror isn't available when in BGE.  What tricks do I need to know?


I have used the following script-  Let's consider That you are constructing \bf{rational numbers}for the first time using natural numbers and so we don't have any idea about the \bf{division operator}   And the ouput produced is -  Let’s consider That you are constructing rational numbers for the first time using natural numbers and so we don’t have any idea about the divi sion operator .  But I want only want the characters in between \bf{} to have bold font. How to do it ??

Is either of these considered better/more readable/more "proper"/more conventional than the other for making text bold? If so, what is the reason?  I like my text \textbf{bold}   versus:  I like my text {\bf bold}


As the title suggests what is the nature of the Vulcan Romulan divide?  Is it biological, are the Romulans biologically distinct enough to be considered a different species ?  For example would a medic treating injuries in war time need to check if the patient was from Romulus or Vulcan in order to provide adequate care ?  Or is it political with the only thing separating them is their differing philosophies ?

I know that Vulcans and Romulan come from the same parent race. But beyond that, how did they branch off? For how long they have been apart? Are they more different than human and chimps? Can they breed?


The following code  template <typename T, class ContainerType> ContainerType<T>::iterator elementIteratorAt(ContainerType<T> container, size_t index) {     return container.end(); }   generates a compile error at the function's return type (ContainerType<T>::iterator):      error C2988: unrecognizable template declaration/definition   Why does it happen and how to write this properly? I'm not even instantiating the template, just compiling.

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


I downloaded eclipse via snap and no longer want it in my system. I used snap remove eclipse and the IDE was removed but if I do the reverse process snap install eclipse --classic , the IDE is restored again without delay. I want to completely purge a snap program and how do I do that?

When I install a snap with snap install <SNAPNAME> then it is being downloaded and mounted. When I remove it with snap remove <SNAPNAME> then 'everything' is being deleted like the snap, user settings dependecies and so on. But when I re-install the snap after removing it, it has no download time so the snap must be stored somewhere. How can I clear the cache of snapd with all uninstalled snaps?


Without assuming the Axiom of Choice, is the following proposition provable?  If $A$ is countable, and $|A \cup B|=|\mathbb{R}|$, then $|B|=|\mathbb{R}|$.

I'm currently reading a little deeper into the Axiom of Choice, and I'm pleasantly surprised to find it makes the arithmetic of infinite cardinals seem easy. With AC follows the Absorption Law of Cardinal Arithmetic, which states that for $\kappa$ and $\lambda$ cardinal numbers, the larger infinite and the smaller nonzero, then $\kappa+\lambda=\kappa\cdot\lambda=\max(\kappa,\lambda)$.  I was playing around with the equation $k+\aleph_0=\mathfrak{c}$ for some cardinal $k$. From the above, it follows that $\mathfrak{c}=k+\aleph_0=\max(k,\aleph_0)$, which implies $k=\mathfrak{c}$.  I'm curious, can we still show $k=\mathfrak{c}$ without the Axiom of Choice? Is it maybe possible to bound $\mathfrak{c}-\aleph_0$ above and below by $\mathfrak{c}$? But then I'm not quite sure such algebraic manipulations even mean anything, or work like that here. Certainly normal arithmetic does not! Thanks.


Please may you help with the following question:  let E be a non-empty subset of R. Let E' be its derived set(the set of all the limit points of E). How to prove that E' is a closed set.  closed set is the set containing all its limit points. limit points p of a set A  are points p in which all deleted neigborhoods intersect A  Thank you

Let $X$ be a Hausdorff space and $A\subset X$.  Define $A'=\{x\in X\mid x\text{ is a limit point of }A\}$.  Prove that $A'$ is closed in $X$.  Relevant information:  (1.) Every neighborhood of a point $x\in A'$ contains a point $y\in A'$ distinct from $x$ (in fact, in a Hausdorff space, every neighborhood of $x$ contains $\infty$-many points of $A$ distinct from $x$)  (2.) In a Hausdorff space, every sequence has a unique limit.  On first glance, it should be an easy proof, but I've made little progress.  I was planning on showing $\overline{A'}=A'$.  Firstly, $A'\subset \overline{A'}$ trivially.  To show $\overline{A'}\subset A'$, proceed by contradiction.  Assume there exists $x\in\overline{A'}$ such that $x\not\in A'$.  This should yield an easy contradiction but I don't see it.  In particular, I'm unsure if the fact that $x\in\overline{A'}$ implies that there actually exists a sequence in $A'$ converging to $x$.  By (2) we know all sequences have unique limits, but do we know that elements in the closure are limits of sequences?  If this is true, it should yield an easy contradiction.  Any help?


/****************pair.h******************/   #include<iostream>     using namespace std;     template<class T1,class T2>     class Pair     {     private :       T1 first;       T2 second;     public  :       Pair(T1,T2);       Pair(){};       Pair<T1,T2>  make(T1  a , T2  b);       void operator=(const Pair& other);       friend ostream& operator<<(ostream& out ,const Pair<T1,T2>& A);      };   /*******************main.cpp*********************/  #include<iostream> #include<utility> #include"Pair.h" using namespace std;  int main()  {   Pair<int,int> A=make(10,20);  cout << A ;   return 0; }   /***********************pair.cpp******************/  #include"Pair.h"  #include<ostream>  using namespace std;  template<class T1, class T2>  Pair<T1,T2>::Pair(T1 a,T2 b){    this->first = a;    this->second = b;  }   template<class T1, class T2> void  Pair<T1,T2>::operator=(const Pair& other)  {     this->first = other.first;     this->second = other.second;  }   template<class T1, class T2> ostream& operator<<(ostream& out ,const Pair<T1,T2> A) {   out<<"("<<A.first<<" , "<<A.second<<")";   return out; }   template<class T1, class T2>  Pair<T1,T2> make(T1   a , T2   b) {   return (Pair<T1,T2> (a,b)) ;     }   it gives me an error in function make ; as it was not declared in the scope of main and i don't understand why.     Also there is a problem when it comes to all friend functions and template. The program doesn't want to be compiled.

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


Let $A$ be a set of all continuous functions $f:[0,1] \to \mathbb R^+ \cup \{0\}$ that satisfies the following condition:      $$\int_{0}^{x}f(t)dt \ge f(x), \forall x\in [0,1].$$      Which of the following statements is true?      (A)  $A$ has cardinality $1$.      (B) $A$ has cardinality $2$.      (C) $A$ is infinite.      (D) $A=\phi$   Case 1  $\int_{0}^{x}f(t)dt =f(x)$, differentiating on both the sides. We get, $f'(x)=f(x)\implies f(x)=Ke^{x}$. hence option (C) is correct. Am I correct? Please check my steps. how it is wrong?

Let $\varphi$ be a nonnegative and continuous function on $[0,\infty)$ and such that $$\varphi(x)\le\int_0^x\varphi(t)dt$$ for all $x\in[0,\infty)$. Can we infer from here that $\varphi\equiv0$.  By taking limit on both sides, I got $\varphi(0)\le 0$. As $\varphi$ is nonnegative, I can say $\varphi(0)=0$. But what then. I could have progressed if I could show that $\varphi(x)\le \varphi'(x)$, but it is not quite evident from the given condition.


Let $\mathbb{Z}_n$ be the cyclic group of $n$ elements and $1$ the trivial group. I'm looking at the following extension:  $$1 \to \mathbb{Z}_2 \to \mathbb{Z}_4 \to \mathbb{Z}_2 \to 1$$  Because every action of $\mathbb{Z}_2$ on itself is trivial, the only split extension of $\mathbb{Z}_2$ by $\mathbb{Z}_2$ is the direct product $\mathbb{Z}_2 \times \mathbb{Z}_2 \cong V$ (the Klein group). But given that:  $$\mathbb{Z}_2 \cong \mathbb{Z}_4/\mathbb{Z}_2 = \{ (1 \bmod \mathbb{Z}_2), (x \bmod \mathbb{Z}_2)\} \text{ with } (x \bmod \mathbb{Z}_2)^2 = 1$$  A homomorphism $\psi: \mathbb{Z}_4/\mathbb{Z}_2 \to \mathbb{Z}_4$ that sends $(x \bmod \mathbb{Z}_2) \mapsto y$ (consider $y$ the generator of $\mathbb{Z}_4$) isn't a splitting of the above sequence? Because going through $\psi$ and then back through the projection sure is the identity mapping.  I'm sure I'm missing something deeper, because I also can't answer the general case: given that $G$ is a extension of $N$ (normal) by $K$, and that $K \cong G/N$, doesn't the injection $K \to G$ which maps $(x \bmod N) \mapsto x$ always splits the sequence? I'm sure not, but why?

I am stuck in the following problem:  Show that every group of order 4 is an extension of $\mathbb{Z}_{2}$ by $\mathbb{Z}_{2}$. Which of the exact sequences splits?  Ok, i have to consider two cases for a group of order 4: $\mathbb{Z}_{4}$ and $\mathbb{Z}_{2}\times \mathbb{Z}_{2}$, so i get two exact sequences:  $0\rightarrow \mathbb{Z}_{2}\overset{\psi }{\rightarrow}\mathbb{Z}_{4}\overset{\varphi }{\rightarrow}\mathbb{Z}_{2}\rightarrow 0$  and $0\rightarrow \mathbb{Z}_{2}\overset{\tilde{\psi} }{\rightarrow}\mathbb{Z}_{2}\times \mathbb{Z}_{2}\overset{\tilde{\varphi} }{\rightarrow}\mathbb{Z}_{2}\rightarrow 0$  For both cases i checked the conditions of exact sequence and proved that these are exact sequences. Now i have a problem how to show if they split or not.  We say that an exact sequence splits if for the first sequence there exists a group homomorphism $\pi :\mathbb{Z}_{2}\rightarrow \mathbb{Z}_{4}$ with $\varphi \circ \pi =id_{\mathbb{Z}_{2}}$ and for the second $\tilde{\varphi} \circ \tilde{\pi} =id_{\mathbb{Z}_{2}}$, right? But how to show if these group homomorphisms exist or not?  Can anybody help me, please? I would appreciate any hints and comments. Thank you in advance!


I have heard that a 'vitamin B17' can cure cancer, but that the medical industry never talks about it, since making it legal would cause them loss of billions. But I have never found a reliable report on whether B17 really works or not. There is a question on 'vitamin B17' deficiency as a cause of cancer (see ), however, not on 'vitamin B17' as a possible medication for cancer. What are the proposed mechanisms? And is there evidence that 'vitamin B17' really works in curing cancer?

I have read in an article on the internet that cancer is caused due to deficiency of vitamin B17 which has been removed from our diets long ago in the western food. But some people say that vitamin B17 does not work. So, is it deficiency of vitamin B17 which causes cancer i.e. can this vitamin really be used to cure cancer?


I am trying to use LSTM to predict a time series data as you can see in the following image, the predicted graphs is very noisy:    The original data is looking like this:   That I normalized it like this and fed it to the LSTM network:    Is there a way to get better result with less noise?  EDIT: I use keras implementation of LSTM and sklearn.preprocessing.normalize library for normalization.

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:


Prove that if $H$ is a subgroup of group $G$, $H\circ x=H$ if and only if $x\in H$.   Not sure how to start this proof about the right coset.

Does the closedness of a subgroup $H$ of $G$ imply that for $h\in H, g\in G \setminus H: hg \not \in H$?  I'm new to abstract algebra and this would appear to be a useful result. However, by definition, a subgroup is nearly closed, and I don't think this directly implies that for any element $g$ from $G$ not in $H$, the composition $gh \not \in H$.  Is this in fact a true statement?


As we know moving objects have a shorter length as seen from a rest frame. $$L=L_0 \sqrt{1-  \frac{v^2}{c^2}   }$$ The first question that arises, is length contraction real or just imaginary for an observer in the rest frame? Secondly what about atomic distances, do they also get shorter as the object moves faster and faster? Atomic distances also effect the intermolecular forces, how do they get balanced? Many quantum problems have length as a parameter, how do you justify that the results will be the same? And finally, does length contraction mean space contraction? As in muon half life problems, one explains in the muon frame the distance travelled by the muon will be shorter.

I was in argument with someone who claims that length contraction is not "real" but only "apparent", that the measurement of a solid rod in its rest reference frame is the "real length" of the rod and all other measurements are somehow just "artificial" and "apparent". Seemed to me like a bad conversation about poorly defined words and not really relevant to physics, but then some quotes were offered:  ...so that the back appears closer to the front. But of course nothing has happened to the rod itself.  (Rindler)  The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.  (Resnick & Halliday) At the same time, the  insists that length contraction and time dilation are "real", with observable consequences:  Time and space dilation are often referred to as ‘perspective effects’ in discussions of STR. Objects and processes are said to ‘look’ shorter or longer when viewed in one inertial frame rather than in another. It is common to regard this effect as a purely ‘conventional’ feature, which merely reflects a conventional choice of reference frame. But this is rather misleading, because time and space dilation are very real physical effects, and they lead to completely different types of physical predictions than classical physics. [...] However, this does not mean that time and space dilation are not real effects. They are displayed in other situations where there is no ambiguity. One example is the twins' paradox, where proper time slows down in an absolute way for a moving twin. And there are equally real physical effects resulting from space dilation. It is just that these effects cannot be used to determine an absolute frame of rest.  I went through a lot of Einstein, Minkowski and Lorentz original material, and didn't find anything about what is "real" and what is not. Finally, I know about muons, where the effects of SR seem to be very real (from , but I had seen it in a physics class before):  When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and muon neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the speed of light. Although their lifetime without relativistic effects would allow a half-survival distance of only about 456 m (2,197 µs×ln(2) × 0,9997×c) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.  So which is which? Why do Rindler, Resnick & Halliday use the word "apparent"?


I am new to relativity ,So please correct me If I am wrong. In the case I have mentioned, In a gravity free space, Let us assume a stationary observer and an observer moving with a velocity 'V' w.r.t to the stationary observer.  The stationary observer looks at an event taking place very far away('X') at time 't' So the moving observer's reference (the event is taking place far away for the moving observer as well) of space time can be calculated using Lorentz transformation. if 'V' is considerably small compared to speed of light, then the transformation for space will be similar to Galilean transformation, but since the distance of the event taking place is very large the time transformation will not be Galilean. ( because of the term (V*X)/C^2)  A light year being of the order 10^16 and all objects in universe being beyond this distance, does that mean an observer moving with a speed of 10 m/s will have relativistic effects in significant form recording an event like star explosion, wobbling effects, light variation etc?

I have been studying causality (specifically why there is no such thing as a simultaneous instant of time across all observers) recently and I keep hearing references to the Andromeda paradox. Can anyone tell me what it is and how it is resolved?  I've tried reading what  says about it, but I could really use someone's explanation.  Edit Ok, after reading the related question, now I'd like to know does this imply there is some sort of privileged reference frame, in which there exists absolute velocity and absolute time? I ask because the answer for the other question seemed to indicate that the actions seem to be at different points of simultaneity but that in fact the person not moving is getting it right. But this seems strange to me because if we accelerated our galaxy to a different speed, we would still perceive our stationary observer as being right even though they'd see something different than before the acceleration.  So who is right? In what frame can we be sure that our present is Andromeda's present?


I'm trying to define some static constant strings in C++ and reference them from different files.  Here's how I have the information set up this far:  structClass.h  namespace test {      typedef struct customstructure{           static const std::string stringA;       } customstructure; }   structClass.cpp  namespace test {      static const std::string customstructure::stringA = "This is String A"; }   Now I'm wondering how I would call this in a third file?  execute.cpp  void printStringA(){     printf("stringA is: %s", test::customstructure::stringA.c_str()); }   gives me a compile error that says:  undefined reference to 'test::customstructure::stringA'

Can anyone explain why following code won't compile? At least on g++ 4.2.4.  And more interesting, why it will compile when I cast MEMBER to int?  #include <vector>  class Foo {   public:       static const int MEMBER = 1;   };  int main(){       vector<int> v;       v.push_back( Foo::MEMBER );       // undefined reference to `Foo::MEMBER'     v.push_back( (int) Foo::MEMBER ); // OK       return 0; }


I have heard two pronunciations for the word tissue. Tishoo and Tisyou. Tishoo is of course the one in common use but what is the current status on Tisyou ? It ''feels'' like an archaic way of pronouncing tissue but that might not be true. It also ''feels'' more British and more formal. I found myself using Tishoo for paper and Tisyou for organic tissue. As in skin tissue. What is the status/useage of the tisyou pronunciation ?

Just a curious question: Why is "assume" pronounced so funny by many native speakers? I can't think of any other word where "ss" is pronounced like that. A bit hard to explain via text, but it's like "sh" with something like a speech impediment. You probably know what I mean. Is there even a phoneme for this?