I have set up my proxy server so that it works through the browser ( in firefox: edit > preferences > advanced < network < settings ).  I also got it working from the command line ( in system settings: network < network proxy ) which has been working fine for the last few weeks.  Suddenly connecting to the internet through the command line has stopped working but connecting through the browser still works fine.  Does anyone know why this could happen and how to fix it? Surely if I can access the internet through the browser, why can't I from the command line?   Many thanks.

Possible Duplicate:          I have tried changing my proxy settings in a terminal as:  export HTTP_PROXY=http://10.1.3.1:8080   and  export http_proxy=http://10.1.3.1:8080   but when I try to install a new package or update apt-get, apt-get starts displaying messages from which it seems it is trying to connect to a previously set proxy:  sudo apt-get update   0% [Connecting to 10.1.2.2 (10.1.2.2)] [Connecting to 10.1.2.2 (10.1.2.2)   I have tried setting the proxy via bashrc file but that din work either. As far as I remember 10.1.2.2 was set using GNOME GUI but I don't have access to the GUI right now so I am trying to set it from terminal.


Let $V$ a finite dimension space over $\mathbb{C}$ and $T:V\to V$, a linear transformation such that $T^k = Id$ for $k\ge 1$. Prove that $T$ is diagonalizable.   I'd be glad for an hint. How do I approach this question?  Thanks.

Say A is an n by n matrix over the complex numbers so that A raised to the kth power is the identity I. How do we show A can be diagonalized?  Also, if alpha is an element of a field of characteristic p, how do we show that the matrix A=[1, alpha; 0, 1] satisfies A raised to the pth power equals the identity I and cannot be diagonalized if alpha is nonzero.  Please be detailed. I really have no idea how to start on this one.


I'm not able to install Synaptic, please help me.  jhon@jhon-Inspiron-N5010:~$ sudo apt-get install synaptic [sudo] password for jhon:  Reading package lists... Done Building dependency tree        Reading state information... Done Package synaptic is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'synaptic' has no installation candidate

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


I want to know if I can have an inequivalent but weakly equivalent bundles over the Torus, i.e. if we can find explicitly an example of a bundle map $(\overline{f},f)$ where we require that $\overline{f}$ is an isomorphism from one fibre to another and $f$ an homeomorphism from the torus to the torus but such that $f$ is not the identity map (if this happens we will have an equivalence).        Notes    This restlessness is taken from Spivak's A comprehensive introduction to differential geometry,third edition,chapter 3.  I'm a beginner here so I don't know anything about cohomology, fancy differential geometry or that stuff thanks for your support.   Definition       A weak equivalence between two bundles over the same base space $B$ is   a bundle map $(\overline{f},f)$ where $\overline{f}$ is an isomorphism   on each fibre, and $f$ is a homeomorphism of $B$ into itself.     Example  When this curiosity came up to me it came up to me with two examples that are as follows. Imagine the Möbius strip and the infinite torus $\times \mathbb{R}$ then we mapped the Möbius strip to infinite jail cell and we project infinite torus $\times \mathbb{R}$ to only the infinite torus, this is for $E_1$ and for $E_2$ we only consider the maps the other way around.  Now, the other example was this. We pick the disjoint union of two circles and for $E_1$ we map the Möbius strip to one circle and $S^{1} \times \mathbb{R}$ to the other one, and again, for $E_2$ we only consider the maps the other way around. I cannot explain more because I am not very acquainted in this area but I can provide an image


I have recently upgraded Ubuntu 19.10 to latest LTS Ubuntu 20.04. After updating, I get serious artifacts on my screen. Every time I reboot (or log-in), my screen is fuzzy or scrambled (picture attached):     This is temporary. The fuzzy screen goes away when I change the background. But it reappears the moment I reboot or log back in.   I have Intel HD Graphics 520 (Skylake GT2).  The output of lspci -nn |grep -E 'VGA|Display' is:  00:02.0 VGA compatible controller [0300]: Intel Corporation Skylake GT2 [HD Graphics 520] [8086:1916] (rev 07)   Update:   On enabling Wayland in Ubuntu 20.04 and logging in to, these artifacts are however cured.   This is okay for now, but I am not sure about Wayland as I have not yet used it before.   Is there a way to correct the graphic issue with normal Ubuntu startup?


$${m+n \choose m+r} = \sum\limits_{k=0}^{m}{m \choose k}{n \choose r+k}$$ The problem makes sense to me, intutively, if I write out the left-hand side as: $${m\choose m}*{n \choose r}+{m\choose m-1}*{n \choose r+1}+...+{m\choose 1}*{n \choose r+m-1}+{m\choose 0}*{n \choose r+m}$$  You've introduced a group of size m to a group of size n and you have to pick m plus r in the first 'round', you simply pick every element from group m and get m elements, plus pick r elements from group n. Then the next time you don't pick one m and you pick an extra element from n, increasing in this way until you pick m+r elements from group n. The trouble is I have no idea how to write this out mathematically.   Please don't mark this as a duplicate of a post about Vandermonde's identity without explaining how this problem can be solved using Vandermonde's identity.

Prove that $$\sum\limits_{k=0}^m\binom{m}k\binom{n}{r+k}=\binom{m+n}{m+r}$$ using combinatoric arguments.   I prefer you to answer using an analogy to a combinatoric problem or else I'll have trouble understanding.  I tried:  Let $m$ represent a group of boys and $n$ represent a group of girls. We want to form a committee with the condition that there must be $r$ more girls than boys on the committee. There's two ways of doing this. (I'm having trouble with the right-hand side.)  The left-hand side is one way of doing this. So we split the problem to different cases. One such case is where there are no boys on the committee, and so, there's $\binom{m}0\binom{n}{r+0}$ ways of forming a committee. Next, we can have 1 boy on the committee. There's $\binom{m}1\binom{n}{r+1}$ ways to do this. We repeat this process until we have $\binom{m}k\binom{n}{r+k}$ ways of forming a committee. Summing up the cases will result in the right-hand side. However, as stated before, I don't really know how to explain the right-hand side. Maybe I used the wrong analogy?


Let $f \in \mathbb{C}[z]$ a complex polynomial such that $f(S^1) \subset \mathbb{R},$ where   $$ S^1 = \{ z \in \mathbb{C} : |z| = 1 \}. $$   Show that $f$ is constant.   My attempt is: define a function $g(z) = e^{if(z)}$ and plug some roots of unity in $g,$ but how can I conclude from this? I know that if $\Omega$ is open, connected and $f(\Omega) \subset \mathbb{R},$ then $f$ is constant.

I am preparing for qualifying exams, and this is a question from the Penn State Qualifying Exam for Fall 2015. It is stated as follows  Let $\epsilon > 0$ and let $f$ be holomorphic (analytic) on the disk $S = \{z \in \mathbb{C} \ | \ |z| < 1 + \epsilon \}$. Suppose that $f(z)$ is real valued whenever $|z| = 1$. Prove that $f$ is constant.  I have tried a few things in showing this to be true, but I keep finding holes in my logic. My largest issue is that the portion of the domain in which $f$ is real valued is not open, and so I'm not able to use many of the theorems I otherwise feel would be helpful (Open Mapping Theorem, Cauchy-Riemann Equations, Maximum Modulus, etc.).   Most of my attacks towards this problem have centered around showing things for the unit disk $\mathbb{D}$ instead of $S$, because I figure if I can show that $f$ is constant on $\mathbb{D}$, then I can use the Identity Theorem to extend it to $S$. However, since I don't know anything about the specific values that $f$ obtains, I can't use Schwarz' Lemma either.  I played with the idea, also, of suggesting that, if we consider the closure of $\mathbb{D}$, then $f(\partial{\mathbb{D}}) \in \mathbb{R}$. Since $\partial\mathbb{D}$ is closed and bounded and $f$ is analytic, it's image should also be bounded. That would put, for some $M \in \mathbb{R}$, $f(\partial{\mathbb{D}}) \in [-M,M]$, which is bounded and obtains a maximum (since $f$ is continuous and real valued here). I know that this set isn't open, but there is a Corollary in my text (Complex Analysis - Freitag) that says the following:  "If $K$ is a compact subset of the domain $D$ and $f:D \rightarrow \mathbb{C}$ is analytic, then the restriction of $f|K$ being a continuous function has a maximal modulus on $K$. By the Maximum Modulus Principle, we can moreover affirm that the maximal modulus value is necessarily taken on the boundary of $\mathbb{D}$."  The proof of that statement follows from the Open Mapping Theorem. Would it be appropriate to use that in this case, then? If $K = \partial \mathbb{D}$, even though it's technically not an open set, can I say that $f$ obtains its maximum on $\mathbb{D}$, state that it's constant, and then extend this to $S$ using the Identity Theorem? My issue here is that the constant itself isn't actually in $\mathbb{D}$,  I appreciate any help for this problem (or any tips for showing that complex functions will be constant, as these types of problems show up often).  Edit: My function $f$ is not necessarily entire, so Liouville's Theorem does not apply


If you have a dragon or a couatl and have it change shape into, say, the CR 3 knight, what among brave, multiattack, leadership, and parry is "not a class feature" and would therefore be available to the creature?  And, does it get racial benefits on top of the knight's stats? In which case, if you have it turn to a variant human with the Tough feat, would you count its "level" as its CR or its number of hit dice? If that feat is just unavailable, then what if it turns into a mage that specifies it's an "x-level spellcaster"?

It's well understood that Spellcasting in a creature's stat block is a class feature. For the purposes of Change Shape and similar abilities where the term "class features" has mechanical importance, are there any other class features in official monster stat blocks? The wording in Monster Manual implies that such things could exist, but do they, and if so how do we tell? Examples of creature stat blocks with named abilities that might be class features (vs classes where an equivalent ability is a class feature):  Kobold Scale Sorcerer's Sorcery Points vs Sorcerer? Would a shape changed Couatl be able to sorcerize its innate spells? Drow Shadowblade's Shadow Step vs Shadow Monk? Firenewt Warlock's Imix's Blessing vs Fiend Warlock's Dark One's Blessing? Githzerai Anarch's Psionic Defense and Unarmed Strike vs Monk? (I don't think we're in class feature any more.) NPC Assassin's Assassinate, Evasion, and Sneak Attack vs Assassin Rogue?


Im trying to draw the following graph: |x − 1| + |y − 1| ≤ 1  This is what I have:  \documentclass{standalone} \usepackage{pgfplots} \begin{document} \begin{tikzpicture} \begin{axis}[   xlabel=$x$,  ylabel={$y$} ]  \addplot {|x−1|+|y−1|≤1};  \end{axis} \end{tikzpicture} \end{document}   However this doesn't work. Would anyone be able to suggest why?

I am trying to draw the inequality plot of this inequality but did not mange to find a way. The plot I want is similar to the one that Mathematica produces. Anybody can help?     I tried this command   \addplot3 [surf,shader=interp,samples=45, domain=-2:6, y domain=-2:6] {(3*sqrt(x^2+y)+sqrt(4*x^3-3*x^2+y)-4)/(sqrt(y+1)+sqrt(3)*sqrt(4*x^3+3*y-  1)-4)};   and then view={0}{90} but it takes a lot of time to compile and I guess there should be a way to produce a 2D plot rather than changing the angle of a 3D plot.


In an exercise I am doing I have an abelian group $A$ and $a \in A$.  I have to find a homomorphism $$ f: \langle a \rangle \to \mathbb{Q}/\mathbb{Z} $$ such that $f(a) \neq 0$ and then extend this map to  $$ f': A \to \mathbb{Q}/\mathbb{Z}.  $$  I was trying to prove this by considering , but this seems to be not the right approach... I would appreciate explanation on how I can do this. Thank you.

Let $A$ be an abelian group.   I don't know how to construct a nontrivial map from $A$ to the group $\mathbb{Q}/\mathbb{Z}$.  Can anyone help me, please?


When I booted up my windows machine this morning my menus had switch from English to what I think may be Russian and I can't read the menu options. I have tried unistalling, rebooting and then reinstalling but this has not helped. Can someone please advise me how to change them back.  Thank you

I want the QGIS interface in English, in order to share information with the GIS community. Using another language, when chatting with the GIS community, makes things more difficult. When I installed QGIS, it automatically set the language to French. It's very frustrating not having the opportunity to select my preferred language.   I am using Windows XP in French, but I want QGIS in English.


The Gelfond–Schneider theorem only gives criteria for $a^b$ being transcendental so long as both $a$ and $b$ are algebraic, but further, that $b$ is irrational.  I could understand arranging it to the form of $(e^{i\pi})^{-i}$, since $e^{i \pi}$  and $-i$ are both algebraic, but then how the hell is $i$ irrational? It's only one integer unit away from the complex origin.

I have seen a proof of $\pi$ being transcendental by conclude that transcendental number powered by algebraic number must be transcendental and algebraic number powered by algebraic number must be algebraic.  So, from the equation $e^{i\pi} = -1$ and $i$ is algebraic so $\pi$ must be transcendental.  But then why is $e^{\pi}$ transcendental?


I have a table (in java) with numbers like this: (jTable1 has only one column)  Numbers   1   2   3   .   .   .  468  I would like to get data from this table and write it to the output with this code:         int rows=jTable1.getRowCount();        for(int j=0;j<rows;j++){             int data= Integer.parseInt(jTable1.getValueAt(j,0).toString());        }   When I run the code, it stops with NullPointerException. In first run at 410. row, and in the second run stops at 413 and sometimes at 430 and mark this row:  "int data= jTable1.getValueAt(j,0).toString();"  The table doesnt have empty row or cell and contains only numbers!!  If I change the "row1" variable to 450 then it is working well. If I increase the value of "row1" above 450, then it stops everytime at other row with this error.   Please anyone has experience with same problem?  Or maybe I have a basic problem but I do not see that.   Thank you so much for help.

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


Both a DSLR in live view mode and a micro 4/3 system camera use the main sensor for autofocus. However, on a DSLR it's embarrassingly slow.  This can't just be a software thing. How is it that one is so much faster?

With early 2013 cameras, it's generally accepted that using contrast detection autofocus on SLRs (ie live view on most SLRs) is something which is really suitable only for static, or close to static, subjects due to the slow focusing speed. On the other hand, the current best of breed mirrorless cameras (the Olympus OM-D E-M5 often being quoted here) have autofocus systems which are significantly quicker at achieving a focus lock, if not quite being up to the performance of phase detection autofocus systems.  My understanding is that both systems are using the same technology, so why is it the case that mirrorless cameras have much quicker autofocus systems than SLRs in Live View mode? Is it the case that the lenses for mirrorless systems are optimized for quick CDAF performance, and if so, what are those optimizations?  Edit: in response to one of the answers, I'm not thinking about how cameras like the Nikon 1 series or the Canon EOS M have quicker autofocus due to the use of phase detection elements in the sensor; I understand how using an entirely different technology will improve things - what I'm interested in here is how some manufacturers have made contrast detection autofocus much quicker than is apparently possible in SLRs. Similar reasoning applies to the Sony SLT series as that's again using PDAF rather than CDAF.


List li = new LinkedList();  for (int i = 0; i &lt; 100; i++) {     li.add(i); }  long start1 = System.nanoTime(); li.get(57);  long end1 = System.nanoTime(); long diff1 = end1-start1;  System.out.println("Time taken by LinkedList = "+diff1);  List al = new ArrayList(); for (int i = 0; i < 100; i++) {     al.add(i); }   What ever operations I perform on both the lists, when I print out the time taken,  ArrayList always runs faster than LinkedList.  Can somebody explain which performs better in terms of time taken? Also let me know if there is something wrong in the code. Thanks!

I've always been one to simply use:  List<String> names = new ArrayList<>();   I use the interface as the type name for portability, so that when I ask questions such as these I can rework my code.    When should  be used over  and vice-versa?


I'm thinking of applying for a PhD in Quantum Computing at Oxford. Suppose I later on decided that academia wasn't right for me. Would such a title still be useful for looking for jobs in different fields or would it be a waste of 3 years that would make me 'overqualified'?

This question follow's JeffE's comment :     In most industries, a PhD has negative value.   I am curious about what potential negatives there may be with having a PhD, particularly in industries.  For example, my PhD has applications for image sensors, and the potential of working in that field is appealing—would having a PhD be a potential barrier? Would it be a case of how explicit the practicalities of the PhD can be made?  Would this make any difference?


SO basically I am learning number theory chapter in the Discrete Maths. Now I really don't understand a proof here.  SO basically it is a corollary which says Let m be a positive integer and let a and b be integers. Then (a + b) mod m = ((a mod m) + (b mod m)) mod m and ab mod m = ((a mod m)(b mod m)) mod m.  Now the proof goes something like this. Proof: By the definitions of mod m and of congruence modulo m, we know that a ≡ (a mod m) (mod m) and b ≡ (b mod m) (mod m). Hence, Theorem 5 tells us that a + b ≡ (a mod m) + (b mod m) (mod m) and ab ≡ (a mod m)(b mod m) (mod m).  What i really can't get here is how is the a ≡ (a mod m) (mod m) and b ≡ (b mod m) (mod m)  I know about the reflexive property about mod but how come this two mod. what i know is a ≡ (a mod m) but how they are saying a ≡ (a mod m) (mod m)

For all $n \in \mathbb{N}$, $n > 1$ and $x,y \in \mathbb{Z}$ prove that      \begin{equation}   (x+y) \text{ mod } n   = ((x \text{ mod } n)+(y \text{ mod } n))\text{ mod } n. \end{equation}   Would this be a proof if I say:  Let $x = x' \text{ mod } n$ and let $y=y' \text{ mod } n$. Then  \begin{equation}   x+y = x'+y' \text{ mod } n. \end{equation}  Now, if we look at the current thing we want prove, this will follow:  \begin{equation}   x+y \text { mod } n = (x \text{ mod } n + y \text{ mod } n) \text{ mod } n. \end{equation}    I'm not sure if this is allowed or will count as a "proof" at all. Maybe you can show me some other ways of doing this, more precise ones?


when installing Ubuntu in UEFI mode alongside Windows 10 I don't know what the partition table should look like.  After this image:    what options will be presented?  Assuming no recovery partition for Windows, just that the whole drive is partitioned for Windows 10 with GPT and UEFI.  The  specify:  Manual partitioning      Choose "Manually edit partition table".     Listed will be your current partitions.     Select the partition you want to resize and press Enter.     Select "Size:", press Enter.     Select Yes, press Enter.     Type in a new size in gigabytes for your partition, it's recommended you free up at least 10 GB of free space for your Ubuntu install. Press Enter when happy with your changes. It may take some time to apply the changes.      Create a swap partition of at least your amount of RAM (if you don't know, 8000 MB is a good value).     Create a partition for your Ubuntu installation.      Create other partitions if necessary: see DiskSpace     Select "Finish partitioning and write changes to disk".    before I install what should the disk look like from fdisk or similar?  On my system lsblk shows:  thufir@doge:~$  thufir@doge:~$ sudo lsblk  NAME                  MAJ:MIN RM  SIZE RO TYPE MOUNTPOINT sda                     8:0    0 74.5G  0 disk  ├─sda1                  8:1    0  487M  0 part /boot ├─sda2                  8:2    0    1K  0 part  └─sda5                  8:5    0 74.1G  0 part    ├─ubuntu--vg-root   252:0    0   72G  0 lvm  /   └─ubuntu--vg-swap_1 252:1    0    2G  0 lvm  [SWAP] sr0                    11:0    1 1024M  0 rom   thufir@doge:~$    but before I press the button to install alongside Windows 10, what should it look like from fdisk or similar?  Assuming UEFI and GPT and that Windows 10 is on the first partition.  GPT:   and UEFI:

I'd like to see the full How-To on how to use manual partitioning during Ubuntu installation. The existing guides (at least those I found here) cover only automatic part and leave untouched the manual part (or extremely short and contain no pictures).  I'd like to cover such situations:     If your disk contains other systems:


Consider this example: \documentclass{article} \begin{document} \begin{equation}   \sum_i a \end{equation}  \begin{equation}   \frac{c}{ \sum_{i}b } \end{equation} \end{document}  How in equation 2 can I display the index under the sum sign as in equation 1?

I'm very familiar with how symbols display differently in inline mode (with $ ... $) vs. how display math shows them (with \[ ... \] or $$ ... $$).  Two examples would be with limits  $\lim_{n\rightarrow \infty}f(x)$   vs.  \[ \lim_{n\rightarrow \infty}f(x) \]   and with sums  $\sum_{n=1}^{x} n^2$   vs.  \[ \sum_{n=1}^{x} n^2 \]   My Question is:     How do you display these things in inline mode (with all the nice inline formatting) as if they were in display mode ?   The inverse -- how to display things in display mode as if they were in inline mode -- is also of interest.


I am looking for a book to study QFT in my vacations. I have all the standard maths on an undergraduate physics program level plus a little of group theory.  I found very good reviews from Quantum Field Theory for the Gifted Amateur, although there are a few harsh criticism. I was thinking to buy this book, but found to better to have some advice of more experienced physicists in the subject, given that books are really expensive from where I live. So, is it worth as a first book? Are there better alternatives?

I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page .  pdf ), a 24-page overview of the topic, very helpful for beginning study.  It all got me over the hump of learning the meaning of various terms associated with GR, most of which I had heard before without understanding.  It also outlined the most important examples.  Is there a similar document for quantum field theory, which presents the main equations, briefly describes the main ideas, and summarizes the most important applications and results so that the reader can feel the lay of the land before studying in depth?


Please help me identify the icon encircled in my attached photo..thank you.

I am running Android 2.2 on HTC Legend. I have a LOT of applications installed on it.  Today, after I changed my mobile operator, a notification appeared in the top bar. When I click on it, it says that my connection to Google is wrong and asks for the password.  However, since this is a dialog overlay, I have no mean to know if it is an application that I can trust (like a native one), or some sort of scam.  Any idea on how to identify from which app/service this message comes from?


Looking at someone else's question, I had this book come to mind all of a sudden. I read it somewhere in the 1998 to 2002 timeframe while I was in Dayton, OH (probably 1999-2000 because I vaguely remember that the snow storm the day I read it shut down my Intro to Religion class, which I took in that timeframe). It was a paperback book, probably from one of the main publishers like DAW or Baen. It showed a girl on a mount, I think a horse, with animals also riding with her. I believe she was in a dress, maybe riding side-saddle. There might have been a decrepit knight (old, armor badly fitting, drooping lance) on the cover as well.  What little I remember of the plot was that the girl's mother died. A piece of black or brown bread was placed on her chest as she died and the daughter ate the piece of bread to consume her mother's sins to ensure she'd go to heaven (pretty standard "sin eater" plot point as per the Medieval practice) with the idea that she had her life ahead of her to atone for those sins. For some reason, she leaves the village immediately afterwards, accompanied with a bunch of animals that she could communicate with. The only one I recall distinctly (and she might have picked it up during her travel) was a turtle or tortoise (probably the latter). I mainly remember that because somewhere near the end of book, she's obtained her goal (which I don't remember what it was) and the tortoise has found a mate, and there's a description of the loud clacking that ensued as the tortoises mated and their shells collided.  I think maybe the half-remembered knight was a plot point, someone she met on her travels and accompanied her. Maybe he wound up as her romance? That part is a lot vaguer in my head.

I'm looking for a fantasy novel I read in the 90s. Heroine begins the story overweight and has to go on a long quest (don't remember why). Along the way she acquires a group of animal/spirit? sidekicks, including a smartass pig, I think. By the end of her quest she has lost weight - not the main point of the book of course, but it's a detail that sticks out.   I think she developed magical powers during her quest, which she may have been surprised to discover? That's about all I can come up with. Cover was a girl walking in typical fantasy/forest scene with the animals, as I recall.It was a humorous, lighter fantasy. Any ideas?


What is an example of a function which is not Riemann integrable on [0,1] but for which |f| is Riemann integrable on [0,1]? What is the upper integral and the lower integral of this function f, which are not equal, thus not Riemann integrable?

So i am stuck here.. how do i prove the first & second inequalities?  Also if |f| is Riemann integrable, then f is Riemann integrable.  I think it's ture but i dont know how to prove it.  any hints would be appreciated! Thank You


NOT cross-posting, of course. An idea came up in comments on  about cross-site asking.  That is, when a user is on one Stack Exchange site (Stack Overflow, for example), it may not be immediately apparent to them that they can ask questions on other, potentially more-relevant, sites (Programmers, for example). I see two ways to approach this:  Add an option to the Ask Question page to ask the question on a different site. Add a global Ask Question page to the main Stack Exchange site as a kind of launch pad to ask on any site.   Ask Question Page Option The Ask Question page is already full of useful information.  How to ask, related questions, etc.  But one thing it doesn't have is information about where to ask.  It occurs to me that a lot of off-topic questions (especially ones which used to be on-topic in the days of yore) may be avoided by adding some guidance to this page.  We don't want it to get in the way, of course.  So there's always going to be the remaining demographic of users who simply don't read it or don't bother.  But there's not much we can do about them.  (These are the same people who will move a wet floor sign that's in their way, slip and fall, and complain that the store should have done something about it.) My annotation on the above image is just a thinking-out-loud suggestion.  Admittedly, I'm not a UX expert by any means.  But essentially what I'm picturing is some kind of interface that says something akin to:  Want to ask this question on a different site?  Maybe this would be a better fit for another Stack Exchange community?  Take a look at these related sites:  This can be anything from a simple sidebar which links to the other sites (and perhaps also their FAQs), or it can be part of the form to actually post the question to that site instead of the current site and drive the user there. Over time we can potentially refine the usefulness of this by making the suggestion stronger based on tags used, etc.  We could also include the option in the question after it's been asked whereby the owner can migrate it to another site.  Hmm... I just asked this here.  But on second thought, I'm more likely to get useful information over there.  I'll just ask on both, nobody will mind.  But wait, what's this option?  Oh, I can move my question over there myself?  Cool, I'll do that.  Maybe later I'll also plant a tree, because I love helping the community.   Global Ask Question Page The main Stack Exchange site is a great place to find featured questions on a wide variety of subjects.  It highlights new SE 2.0 sites, it shows hot questions on the various sites, it provides a multi-site search, etc.  But one thing it doesn't do is provide a way to ask a question.  What I'm picturing here is an Ask Question page that's very similar to the one that the various Stack Exchange sites have, but with greater emphasis on the above suggestion of being able to choose a site.  (After all, one can't ask a question on the main Stack Exchange site.  It has to go somewhere.  So it would be a more prominent part of the form with more information.) The page could function much in the same way as the current Ask Question pages do.  For example, the selection of sites could perhaps be between the Title and the Body form elements.  Based on the title, sites can be suggested (with all sites as an expandable option beneath the suggested sites).  The site currently selected (radio button, no cross-posting, and no default or that site would probably get flooded with off-topic questions) can then further expand to show "Questions with similar titles" from that site just as the Ask Question pages do today. The main Stack Exchange site could use some work to make it more of a global entry point for the wide variety of Stack Exchange communities, and I think this would be a significant stride in that direction.  We are question and answer communities, and a great way to get started is to ask a question somewhere.

I've been a Stack Exchange contributor for a couple of years now, currently most active on . One thing that keeps coming up is questions that would appeal to audiences on two different Stack Exchange sites but there are almost no features taking advantage of these questions. On travel.SE we have crossover questions most often with  and possibly next most often with  - but it can happen with almost any SE site. Today alone we had  with  and  had . I am absolutely sure that this must happen all the time between arbitrary pairs of Stack Exchange sites but the only feature that takes advantage of it is the possibility of migrating off-topic questions which leaves the original question acting as a redirect across the two sites. I think there is a missed opportunity to build the network between sites where users of one site don't realize they could make valuable contributions to a sister site they have had so far little to do with. At the very least there could be a way to "advertise" a question on a second site that could be interested in it. Probably by listing it in the sidebar where there are also links to meta questions, linked questions, related questions, new blog posts, and But there could also be some kind of features that make some sort of acceptable crossposting. There could be gamification/badges added around building cross-site questions or whatever else you can think up. I think this is a great way for people to spread their expertise from their main site onto other sites, to make the network stronger and more cohesive, to bring more attention to questions that would have a divided audience between two sites. I can think only of positives and no negatives. Does anyone else have some ideas to add or think this is a bad idea for any reason?  Example crossover questions: Here are some links to some crossover questions I've been finding in the Stack Exchange network here. (This was previously posted as an answer, but more people wanted it to be part of the question.)   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :   ▶  :


So I am looking at the integral $$ \int_0^{2\pi} \frac{1}{a + \cos\theta} \mathrm{d} \theta$$ for $a > 1$. Evaluating the integral with complex analysis gives us $\frac{2 \pi}{\sqrt{a^2 - 1}} $ but I have failed to reproduce the result using standard substitution.  Here’s what I did: I found the antiderivative first, which is $$\frac{2}{\sqrt{a^2 - 1}}  \arctan \left(\sqrt{\frac{a - 1}{a + 1}} \tan\left(\frac{\theta}{2}\right) \right)$$ but substituting in the bounds would give us 0.   I used the standard substitution $t = \tan\left(\frac{\theta}{2}\right) $ to obtain the following result.  EDIT: Plotting the graph shows us that the area is definitely positive, so there’s no way the answer is $0$.  EDIT2: Is it because $2\pi$ corresponds to the second “cycle” so we should $\arctan 0$ to be $\pi$ for our upper bound instead?

I saw somewhere on Math Stack that there was a way of finding integrals in the form $$\int \frac{dx}{a+b \cos x}$$ without using Weierstrass substitution, which is the usual technique.   When $a,b=1$ we can just multiply the numerator and denominator by $1-\cos x$ and that solves the problem nicely.   But I remember that the technique I saw was a nice way of evaluating these even when $a,b\neq 1$.


Gandalf a Maia (Spirit) was sent to Middle-Earth in human form to help the free peoples fight the evil of Sauron. Is the same reason for the Saruman sent to Middle-Earth ?

Every wizard in The Lord of the Rings obviously had a purpose to be sent to Middle-earth, with Gandalf's being to help out in the defeat of Sauron and Morgoth's forces, etc. However, because Saruman was not returned to life after his death by Grima, he must have fulfilled his purpose.  I've read that Gandalf came back as the White in order to fulfill the purpose Saruman had failed in. So, obviously, Saruman had a purpose and failed it, but why? What was his purpose? And why was he not sent back to complete it, but instead Gandalf was sent in his place?


Do I get it right considering  'I am going to some shops' just as reporting a fact, and 'I am going down to some shops' as, say, I'am leaving my town residence for shopping in the country or my country or surbubian residence for downtown shopping?   More examples to look upon are  'We went down to the beach' and  'we went to the beach'.

I am travelling geographically down the country from north of the city of London. Do I state "I am travelling down to London" or do I state "I am travelling up to London" in reference to its capital city status?


This question was asked in a masters exam for which I am preparing and I was unable to solve this particular question.  In the group $G$ of all invertible $4\times 4$ matrices with entries in the field of $3$ elements, any $3$-Sylow subgroup has what cardinality?  Cardinality of group $G$ is $80 \times 78 \times 72 \times 54$. I thought $3$-Sylow subgroup has cardinality $3^n =81$ but this is wrong . Answer:   $$729$$  I am not able to think any other result which I can use it here. So, Can anyone please tell me right way to approach this question? Thanks!!

Let $p$ be a prime number . The order of a $p$-Sylow subgroup of the group $GL_{50}(F_p)$ of invertible $50\times50$ matrices with entries from the finite field $F_p$,equals which of the following    1.$p^{50}$ 2.$p^{125}$ 3.$p^{1250}$ 4.$p^{1225}$    I think order of this  group is $p^{2500}$  .A  sylow p-subgroup of order $P^k$ divides  order of the group but $p^{k+1}$  does not. I confused here how to apply these things .


Google recently announced the Bristlecone 72 qubit quantum computer. However, D-Wave already announced quantum computers featuring more than $2000$ qubits.  Why is Google's new device newsworthy then? Is it better than D-Wave's machine in some respects? If so, how?

So, @AndrewO mentioned recently that he has had 'encounters' with people wondering why D-Wave has a lot more qubits than IBM. Of course, this comparison is faulty, since the IBM and D-Wave's machine may both exploit quantum effects to a certain degree, IBM's machine matches the thing the TCS people call a 'Quantum computer' a bit more than D-Waves's alleged quantum annealer.   How do you explain to a novice why IBM is still reaching important milesstones, even though the D-Wave has a lot more 'qubits'. I understand that an easy answer is, 'well, you're comparing apples and pears', but that is merely relying on your possible authority and simply doesn't explain anything!   How can you explain that those devices are different, how can you dispell the myth that the number of qubits is not the only metric to judge quantum devices? (preferably to a layman, but assuming basic (undergrad?) physics knowledge is ok, if needed)


Just curious but are there any two words (possibly three in a tri-relationship) in the English language that define themselves with the other, therefore being subjected to a definition paradox? (They have to have no other meanings besides the other word.)  e.g.  (Not really a legit example, but what I am looking for) Compassion: The act of having pity. Pity: The act of having compassion.

How do definitions of words imbue meaning?   To give you a gist of what I try to discover, I'll define a collection of sets of words and show that their intersection contains all 'circular defined' words. How do these words gain their meaning? And how can definitions using these words be considered meaningful?  Let W be the set of words in a dictionary. Denote by w any word in W. The dictionary contains lemmas of each word it lists; for each word w, the lemma L(w) for word w is a subset of words in W. Let's say that the lemma is also the definition of the word w; for our purpose, we ignore examples of usage (otherwise most if not all words would have circular definitions).  Define the following collection of sets:   D(1) := {w in W | There is a w' in W such that w in L(w')}, the set of words used in definitions of other words. for n>=1, D(n+1) := {w in D(n)| There is w' in D(n) such that w in L(w')}, the subset of D(n) of words used in definitions of words in D(n). D := {w in W | For all n>=1 we have w in D(n)}, the intersection of all D(n).   We have constructed a nested collection of sets: if n>m then D(n) is a subset of D(m) by definition, and D is their intersection. D is the largest set of words which is such that each of its words occurs in the definition of (at least) one of its words.   Lemma. Since W is finite, D = D(n) for some finite n.  Proof. If not, it means that for each n, there is a D(m) such that D(m) is a strict subset of D(n) and we can construct an infinite collection of strict subsets. But there are only a finite number of words in W. Hence, there is an n such that D = D(n).  It follows that we can effectively determine D for any dictionary W by going through W, D(1), D(2), etc. creating the next D(n) until D(n+1) = D(n) = D.  If W is the English language, then D is not empty.   It contains the word 'an' (see , its lemma contains the phrase "an initial vowel").  It also contains cycles of length 2 or longer, such as {oak, acorn} and {foot, ankle}; these words are used in their mutual definitions.   The basic question is about the set D.  How do words in D gain meaning from their definitions?   They seem to be examples of words with 'circular definitions'.  Worse, words in D can occur in any definition (as they belong to D(1)), so how do they help define other words if their own meaning is ambiguous?  Finally, if words' meanings are ambiguous (for example if they have definitions including words in D), how can definitions succeed in taking away this ambiguity?


If we have a non-zero matrix $A\in\mathrm{Mat}_n(\mathbb{R})$ that is non-invertible. How do we prove that $A$ is both a left and right zero divisor?

Is every noninvertible matrix over a field a zero divisor?  Related to this: What are sufficient conditions for a matrix to be a zero divisor over a noncommutative ring?


I tend to install quite a lot of packages with ./configure --prefix=$HOME && make && make install. Why can't I do this as easily with dpkg or yum? Or if I somehow can, what is the way to do that?

From my research, I seem to notice that all package managers insist on being used as a privileged user and must be installed into /.  Typically, what I like to do is create a throwaway account, compile some software, and install to $HOME for that account. I can try a variety of setups and then when I'm done, just destroy the account.  However, compiling software becomes tedious.  My experience is really just limited to yum, but I don't understand why I wouldn't be able to drop a repo file into ~/etc/yum.repos.d and have yum install everything into a home account.  Is there any reason why package managers must be used as a privleged user to install software?


Translated  I'm looking for a similar solution to creating a bat file in Windows on Ubuntu 18.04, I have a java file in which I make the call via console with the command java -jar routine.jar however I would do the same routine to streamline with an executable like in bat files.  I made a file called backup.sh with the same internal command and I applied chmod+x and made the change via Nautilus giving the execution permission via software, still it is not executed via terminal, can you help me?  Original  Estou buscando uma solução semelhante a criação de um arquivo bat no Windows no Ubuntu 18.04, eu tenho um arquivo java no qual eu faço a chamada via console com o comando java -jar rotina.jar no entanto, gostaria de fazer a mesma rotina para agilizar com um executável como em arquivos bat.  Fiz um arquivo chamado backup.sh com o mesmo comando interno e apliquei o chmod+x e fiz a alteração via Nautilus dando a permissão de execução via software, ainda assim o mesmo não é executado via terminal, podem me auxiliar?

In Windows I can write a file containing commands for cmd (usually .cmd or .bat files).  When I click on those files it will open cmd.exe and run them commands the file contains.  How would I do this in Ubuntu?         I'm sure this is a duplicate, but I can't find my answer. Its similar to these questions, but they don't answer the question:


I have two Hard Drives a Samsung 750Gigs and a Western Digital Green 2 TB. My current partition scheme consists of only 3 NTFS partitions:  750:    C: 75 Gigs  Windows 7 Home Premium    D: 675 Gigs for Games and other stuff  2000:    E: 2 TB for remaining storage  and 4Gigs of RAM  I plan to dual boot Linux Ubuntu or a similar flavor of it (I assume they mostly have the space requirements)  My Question is mainly about the size of the Root partition and maybe also the SWAP partition. I plan to install a  root  swap and home partition on the 2 TB hard drive and leave the other HDD for windows 7 and windows games. But, I am slowly transitioning to Linux, hopefully completely and want to know how large should be the root partition if I plan to install a lot of software and Linux games from the repositories and maybe sourceforge and other sources so I would not need to resize the root in the foreseeable future ?   thank you in advance.

What partitioning scheme do you recommend for a desktop? I've always created three or four primary partitions -- root, swap, home, and sometimes a separate boot partition. Ubuntu's default install offers LVMs. I've never had to add additional drives or space, so it never seemed like a big deal. Whenever I do a fresh install, though, I always think there might be a better way.


I am pretty new to blender and I was experimenting with a subsurface scattering material and lighting on an imported object. But when I've rendered an image of the object with a material that has a subsurface scattering, it shows this weird "noise" or "blur" on the surface of the object.   I've also rendered the same object without subsurface scattering and the problem seemed to be gone.    The current version of Blender that I use is 2.83 but I've seen this problem in previous versions.

Since the Denoise feature was added to Blender I only use the default setting with it and it really does the work. But sometimes the denoise is noticable on some of my renders. How can I overcome the blurred effect? Denoising for me is a big help because my system is quite aged.


My fire simulation on a match tip is producing very weak flames so they aren't visible in the render. I'm not sure what is going wrong so I just included the entire file. Plz help, thank you.

I have been struggling to get a match tip to actually look like it's on fire and no matter what material shaders I try, I can't seem to achieve what everyone else does, I can in other scenes, just not this one. :(


I try to put up the Uppy Standalone Companion on a Scaleway instance. I managed to install Uppy and mananged to install Nginx with SSL but now I want the (sub)domain to load the Uppy Companion instead of the standard Nginx homepage.   I tried  location / {     proxy_pass http://127.0.0.1:3020; }   When I start companion it shows its running on 0.0.0.0:3020 so I also tried   location / {     proxy_pass http://0.0.0.0:3020; }   However, I won't get it to work. Below I've added my Nginx configuration file  # For more information on configuration, see: #   * Official English Documentation: http://nginx.org/en/docs/ #   * Official Russian Documentation: http://nginx.org/ru/docs/  user nginx; worker_processes auto; error_log /var/log/nginx/error.log; pid /run/nginx.pid;  # Load dynamic modules. See /usr/share/nginx/README.dynamic. include /usr/share/nginx/modules/*.conf;  events {     worker_connections 1024; }  http {     log_format  main  '$remote_addr - $remote_user [$time_local] "$request" '                       '$status $body_bytes_sent "$http_referer" '                       '"$http_user_agent" "$http_x_forwarded_for"';      access_log  /var/log/nginx/access.log  main;      sendfile            on;     tcp_nopush          on;     tcp_nodelay         on;     keepalive_timeout   65;     types_hash_max_size 2048;      include             /etc/nginx/mime.types;     default_type        application/octet-stream;      # Load modular configuration files from the /etc/nginx/conf.d directory.     # See http://nginx.org/en/docs/ngx_core_module.html#include     # for more information.     include /etc/nginx/conf.d/*.conf;      server {         server_name  companion.mywebsite.com;         root         /usr/share/nginx/html;          # Load configuration files for the default server block.         include /etc/nginx/default.d/*.conf;          location / {                 proxy_pass http://0.0.0.0:3020;         }          error_page 404 /404.html;             location = /40x.html {         }          error_page 500 502 503 504 /50x.html;             location = /50x.html {         }      listen [::]:443 ssl ipv6only=on; # managed by Certbot     listen 443 ssl; # managed by Certbot     ssl_certificate /etc/letsencrypt/live/companion.mywebsite.com/fullchain.pem; # managed by Certbot     ssl_certificate_key /etc/letsencrypt/live/companion.mywebsite.com/privkey.pem; # managed by Certbot     include /etc/letsencrypt/options-ssl-nginx.conf; # managed by Certbot     ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem; # managed by Certbot  }   # Settings for a TLS enabled server. # #    server { #        listen       443 ssl http2 default_server; #        listen       [::]:443 ssl http2 default_server; #        server_name  _; #        root         /usr/share/nginx/html; # #        ssl_certificate "/etc/pki/nginx/server.crt"; #        ssl_certificate_key "/etc/pki/nginx/private/server.key"; #        ssl_session_cache shared:SSL:1m; #        ssl_session_timeout  10m; #        ssl_ciphers HIGH:!aNULL:!MD5; #        ssl_prefer_server_ciphers on; # #        # Load configuration files for the default server block. #        include /etc/nginx/default.d/*.conf; # #        location / { #        } # #        error_page 404 /404.html; #            location = /40x.html { #        } # #        error_page 500 502 503 504 /50x.html; #            location = /50x.html { #        } #    }        server {     if ($host = companion.mywebsite.com) {         return 301 https://$host$request_uri;     } # managed by Certbot           listen       80 default_server;         listen       [::]:80 default_server;         server_name  companion.mywebsite.com;     return 404; # managed by Certbot   }}

I'm trying to run multiple Nodejs applications on Nginx server running on CentOS 7. I noticed that when I run a Nodejs app on some ports I get an 502 Bad Gateway error in the browser so I checked the error logs:  [notice] 12806#0: signal process started [crit] 12807#0: *13 connect() to 127.0.0.1:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://127.0.0.1:7777/", host: "myapp.com" [crit] 12807#0: *13 connect() to [::1]:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://[::1]:7777/", host: "myapp.com"   when I change the app to listen to 8008 for example everything is working fine. I checked permissions and if the process is running as root and everything seems ok. I played with the timeouts as well but no result. Can anyone help?


This question was last answered 6 years ago: .   What has changed?  suggests not using Tor for Ubuntu. I'm running a 16.04 LTE. Is there any way to browse the internet anonymously for free? Are PrivateBrowser and Anonymox any good?

Could you please suggest me a good anonymous internet browsing application for Ubuntu?


Let us consider a cipher that works like the following:   Plaintext is encoded to Base64. The characters in the encoded plaintext are substituted with a randomly shuffled character set (a-z, 0-9, A-Z, /, +).   The shuffled alphabet are the key. How do I decipher it to get the base64 encoded string without knowing the shuffled character set?

Let's imagine a cipher that works like the following:   Plaintext is encoded to Base64. The characters in the encoded plaintext are substituted with a randomly shuffled character set(A-z, 0-9, -, _, =).  The shuffled alphabet is, in essence, the key.   Not particularly complex or even secure.  But...  What if I wanted to do frequency analysis?  For example, "RUNFORYOURLIFE" when encoded in Base64 is:  UlVORk9SWU9VUkxJRkU=  When the character set is shuffled, the final cryptext can look something like this:  xv24DYG9qxG2xYg6DYxf  The key being:   yhAc5bTOWeYvBXCpVuoMJLdg8P1jHN3ZIsi67SrK4E_D9-x2qRQmnlkwUaFt0G=zf  Which is a shuffled version of:  abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789-_=  Let's also assume that the character set in subsequent messages is in the same order(ie the key is re-used).  Since the bytes are basically split up resulting in different character units that may or may not correspond, is frequency analysis still feasible?  Does encoding plaintext this way before encryption add any form of security?  My question mostly pertains to longer messages, as my example may be too short for any sort of real analysis.


In programming languages like C, Go, and C++, the  is denoted using:  char *   What is the correct English pronunciation for this data type?   Is it /kɑr stɑr/, so with the ‹ch› of char pronounced as in character /ˈkerəktər/ and choir /kwɑɪr/?  Is it /tʃɑr stɑr/, so with the ‹ch› of char pronounced as in chair /tʃer/ and child /tʃɑɪld/?    My colleague has been arguing that the correct way is the second version, not the first version.  Who’s right?

In many programming languages, char is a type name for character values. The word character is pronounced with a [k] sound, but what about char?   While trying to find the answer elsewhere, I learnt that there is an English word char which is pronounced [tʃɑ:(r)], but it has nothing to do with characters.  How would you read the following piece of code out loud?  char a;   Is it [kær], [tʃær] or [tʃɑ:(r)]? I've always used the last but I have no idea whether it's correct.


Find all the ordered pairs $(x,y)$ such that $x^y=y^x$.   So the only ones that i find are when $x=y$ such as $(1,1)$ because $1^1=1^1$. However, I'm not very familiar with ordered pairs?  Any help?

We know that $2^4 = 4^2$ and $(-2)^{-4} = (-4)^{-2}$. Is there another pair of integers $x, y$ ($x\neq y$) which satisfies the equality $x^y = y^x$?


I am unable to add any field in my custom content type, when I click on save button or click on upload after adding images it gives me the following error and for the text field the error is simply Exception thrown without a stack frame in unknown on lne 0, after this a white screen appears. :  After this website appears to be blank until I import the database again.  UPDATED After adding following lines of code in the bottom of settings.php,   error_reporting(-1);  // Have PHP complain about absolutely everything  $conf['error_level'] = 2;  // Show all messages on your screen, 2 =   ERROR_REPORTING_DISPLAY_ALL. ini_set('display_errors', TRUE);  // These lines just give you content on WSOD pages. ini_set('display_startup_errors', TRUE);   I got the errors appears instead of white screen:

This is the error I am suddenly getting.  Additional uncaught exception thrown while handling exception.  Original PDOException: SQLSTATE[70100]: Unknown error: 1317 Query execution was interrupted...my query  Additional PDOException: SQLSTATE[HY000]: General error: 2006 MySQL server has gone away...my query   After doing some research it sounds like a custom module, which I have made, is attempting a query which is too big. A solution that seems to work for a lot of people is this:   Open my.ini Change "max_allowed_packet" from "1m" to "16m" (or larger) Save my.ini and restart MySQL   However, I am on a shared server, so I cannot edit my.ini, and although my provider has confirmed to me that the value is set to 1M, they won't increase it.  I also tried adding this: ini_set('mysqli.reconnect', 'on'); to settings.php. It didn't solve the problem.  Does anyone know of a another solution, or work around?  Thanks.


I have a server and client running on local server.   I read from the server this way:  br = new BufferedReader(new InputStreamReader(socket.getInputStream()));  public static String readResponse() throws IOException{     String response = "";     String line;     while((line = br.readLine()) != ""){         System.out.println("s: " + line);     }     return response;  }   And I get the response from server but the program stops and doesn't go anywhere from there:  Please enter option number: 1  c: MSGGET s: 200 OK s: Go for it now. The future is promised to no one.   And it just hangs here, when it is suppose to continue.  I also tried:  while((line = br.readLine()) != null){   It just keeps waiting. Is there anything maybe on the server that I have to change to tell the client that I am done transmitting data.   Please help! Thank you!

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I searched the web and I see people using the phrase:   Friend Group Friends Group   (notice the extra "s" at the end of word friend on the second entry) to refer to a group of people that are considered friends. So which one is correct?  The context that I am using the word friend is as follows:  Friend(s) Groups:   Family Acquaintances Not very nice etc   Thanks.

I’ve been looking over what has been posted regarding the use of ’s.   I used to be a Technical Writer (years ago). The title of one of our training documents was Users’ Guide.  Once, a coworker said every time he saw that title he expected users to start coming.    Never made any sense to me, but I have to admit that the majority of us didn't understand the use of s’ in place of ’s.  What is the difference?


> Context: On the other hand, Italian writers did well to draw on the Tuscan vernacular rather than the other vernaculars of Italy [1250] for the reasons that everyone knows and which we have stated pp.1246, end-47, beginning.     But it would be silly, absurd, pedantic, and ridiculous to conclude from this that only that vernacular can therefore be drawn on, that writers can only write in the manner and to the extent that that particular people speaks, that the Italian language and Italian literature wholly depend on the common people of Tuscany (when it does not even depend on the common people at all, but simply uses them when it so chooses), that in and outside of Tuscany, an Italian writer cannot create words or phrases that the Tuscan populace does not use, that, in short, someone who is not Tuscan, indeed, who is not Florentine, or not actually from the Old Market, is not Italian.   The questions would be:  1.There are two 'that' in line 3, would someone kindly explain this queer using of 'that'?  2.Is it acceptable writing in English using 'that' so many times in a single sentence? Wouldn't it be more appropriate if for example the first and second line: 'But it would be silly, absurd, pedantic, and ridiculous to conclude that only vernacular can therefore be drawn on'  3.If we decompile those 'thats' into multiple sentences, would it change the conveyed meaning?  Thank you!

Have you ever had a case where you felt compelled to include strange things like a double that in a sentence? If so, then what did you do to resolve this?  For me, I never knew whether it was acceptable grammar. However, what I did learn was that it was a logic distractor, could lead to confusion, and therefore should be reworded to avoid this.


It seems that they are quite different things but everybody uses the same term for them.

I know that they are both called 'virtual machines', but what is the exact difference?


My website has 3 section, header(navbar)+middle(content)+footer(sitemap etc).  My header is a fixed height, my footer contain sitemap which may update time to time, therefore the footer height may increase.   I want to apply 100vh on my middle. How do I use something like .middle{height: calc(100vh - footer.height);}?

I am working on a web application where I want the content to fill the height of the entire screen.  The page has a header, which contains a logo, and account information. This could be an arbitrary height. I want the content div to fill the rest of the page to the bottom.  I have a header div and a content div. At the moment I am using a table for the layout like so:  CSS and HTML    #page {     height: 100%; width: 100% }  #tdcontent {     height: 100%; }  #content {     overflow: auto; /* or overflow: hidden; */ }

...

...

     The entire height of the page is filled, and no scrolling is required.  For anything inside the content div, setting top: 0; will put it right underneath the header. Sometimes the content will be a real table, with its height set to 100%. Putting header inside content will not allow this to work.  Is there a way to achieve the same effect without using the table?  Update:  Elements inside the content div will have heights set to percentages as well. So something at 100% inside the div will fill it to the bottom. As will two elements at 50%.  Update 2:  For instance, if the header takes up 20% of the screen's height, a table specified at 50% inside #content would take up 40% of the screen space. So far, wrapping the entire thing in a table is the only thing that works.


Currently I am compiling a FAQ for my company on QGis, since some people feel the need to work more with QGis. I am the person to go to, when some specific problems appear, but I see a need to give people something to consult with instead of letting them blunder along.  Currently I have the following topics in my FAQ (either already fully explained or at least with some notes):   Limits of QGis Terms & User Interface, e.g. layer & layer properties, vector vs. raster, CRS, tools, snapping,  Data types, as shape, dxf, kml/kmz, csv, images, qgis-style, project files, geopackage, wms important, reoccurring tasks/workflows, as georeferencing, manipulating attribute tables, geometry validity, clip, dissolve, buffer, creating geometries   I also try to include all tricks I use regularly or built for others in my company, like automatically adding attributes to a newly created feature, or trying to determine if a polygon is about the desired size.

What topics do you think are essential in an introduction for QGIS?  The target audience is those with zero or rudimentary knowledge in mapping and geospatial software.


I had an interesting question asked for which I didn’t have any clue.  I have Googled around this about haven’t found any result of which help me answer this question. So here are the questions:   The OS Upgrades during installation puts a message “Do not shut down your machine”. If I shut it down the machine become unusable and I have to reinstall the OS? If the warning is just a caution with no harm done if I power down the machine, how does the update process do this?

My system has been stuck at "Configuring updates" for about an hour with the percentage stuck at 25%. If I do a hard reboot, what are the likely and worst-case consequences?


I'm trying to install different softwares found on Ubuntu Software Centre but I always get back the "Requires installation of untrusted packages" message after entering the pwd. That message pops up several times either after hitting "OK" or "Repair" button. The installation doesn't simply take place.  I tried the installation thru Terminal as suggested somewhere using the details in the error message but without success - here is the case of Stellarium software:  skround@HP-EliteBook-2530p:~$ apt-get install stellarium stellarium-data E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   Any suggestion? Thanks in advance

I get this error whenever I try to install programs using the terminal:  home@ubuntu:~$ apt-get install myunity E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   Also I'm unable to install updates using the terminal.


$!/bin/sh if grep "$1" /etc/passwd 2>/dev/null               #Search username at beging of line1 then          echo "Pattern found - Job Over" else           echo "Pattern not found"  fi

Just looking for the difference between   2>&- 2>/dev/null |& &>/dev/null >/dev/null 2>&1   and their portability with non-Bourne shells like tcsh, mksh, etc.


I want to get all fields that have null values but i aint even getting any fields:    [Serializable()] public class BaseClass {     [OnDeserialized()]     internal void OnDeserializedMethod(StreamingContext context)     {         FixNullString(this);     }      public void FixNullString(object type)     {         try         {             var properties = type.GetType().GetFields();               foreach (var property in from property in properties                                      let oldValue = property.GetValue(type)                                      where oldValue == null                                      select property)             {                 property.SetValue(type, GetDefaultValue(property));             }         }         catch (Exception)         {          }     }      public object GetDefaultValue(System.Reflection.FieldInfo value)     {         try         {             if (value.FieldType == typeof(string))                 return "";              if (value.FieldType == typeof(bool))                 return false;              if (value.FieldType == typeof(int))                 return 0;              if (value.FieldType == typeof(decimal))                 return 0;              if (value.FieldType == typeof(DateTime))                 return new DateTime();         }         catch (Exception)         {          }          return null;     } }   And then i have a class :      [Serializable()] public class Settings : BaseClass {     public bool Value1 { get; set; }     public bool Value2 { get; set; } }   But when i comes to    var properties = type.GetType().GetFields();   then i get 0 fields, it should find 2 fields.  Is type.getType().GetFields() wrong to use ? or am i sending in the wrong class to the base class?

Given this class  class Foo {     // Want to find _bar with reflection     [SomeAttribute]     private string _bar;      public string BigBar     {         get { return this._bar; }     } }   I want to find the private item _bar that I will mark with a attribute.  Is that possible?    I have done this with properties where I have looked for an attribute, but never a private member field.  What are the binding flags that I need to set to get the private fields?


To copy the property values from one object to another, we usually achieve with following syntax:  ca.pro1 = cb.pro2; ca.pro2 = cb.pro2;   where ca and cb are of the same class.   Is there any simpler synatx or utility method to help us to achieve the same effect?  Thank you.

I want to do something like:  MyObject myObj = GetMyObj(); // Create and fill a new object MyObject newObj = myObj.Clone();   And then make changes to the new object that are not reflected in the original object.  I don't often need this functionality, so when it's been necessary, I've resorted to creating a new object and then copying each property individually, but it always leaves me with the feeling that there is a better or more elegant way of handling the situation.  How can I clone or deep copy an object so that the cloned object can be modified without any changes being reflected in the original object?


So I hava a TOSHIBA laptop (64 bit) with Windows 7 Home Premium. First I downloaded wubi.exe and I installed it to my laptop. The only problem with this when I start Ubuntu I always get an error: Prefix is not set.The ubuntu boot up succesfully after 1 minute but it is very slow.  So I want to reinstall ubuntu from a CD. I burnt a Windows 7 Home Premium (english version) iso for a Verbatim DVD-R and an Ubuntu 12.04 (desktop edition) (amd64) iso for a Sony CD-R. Okay I'm a beginner. Please anyone write me the method step by step: how to dual boot Windows 7 with ubuntu 12.04  I have the Installation disks, what is the step 2?

I need my pre-installed version of Windows 7 (or any other version of Windows), how could I install Ubuntu without erasing it?


I have this ul element
                                     <?php for($i= 1 ; $i <= $total_items ; $i++ ) : ?>                                        <li id="rmv_cam<?= $i ?>"><button type="button" id="rmv_cam<?= $i ?>"  class="btn btn-error btn-sm remove_cam"> </button>  פריט מחסן  :&nbsp<input type="text" name="cam[]" id="get_prod<?= $i ?>" data-i = "<?= $i ?>" class="form-control w-25 mt-3 prod"  >
<span class="prd_info" id="pdr_info<?= $i ?>">

                                     <?php endfor; ?>
   and I have this script that creates a new li on change   $( "li" ).last().on('change',function () {     num++;     $('#cams_ul').append('
<button type="button"  id="rmv_cam'+num+'"  class="btn btn-error btn-sm remove_cam"> </button>  פריט מחסן  :&nbsp<input type="text" name="cam[]" id="get_lens'+num+'" data-i = "'+num+'" class="form-control w-25 mt-3 prod"  >

'); } );   my problem is that when the new li is created the last function is not responding to the last append elemet that created

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


This is on a virtual CentOS host which I access via terminal ssh, and have sudo rights on.   wget works fine. Neither ping nor git can see the internet at all. Since wget is able to resolve host names while fetching pages, it doesn't seem to be DNS related.  I checked the iptables command as suggested below; no relevant protocols seem to be blocked.  How do I go about troubleshooting the cause?

When I ping www.google.com and 8.8.8.8, I get no reply:  # ping www.google.com PING www.google.com (216.58.221.228) 56(84) bytes of data. ( no response)  # ping 8.8.8.8 PING 8.8.8.8 (8.8.8.8) 56(84) bytes of data. ( no response)  20 packets transmitted, 0 received, 100% packet loss, time 19006ms   There has been no response. But, both curl and wget are OK. My OS is CentOS 7.  Here is my network configuration file:  # cat /etc/sysconfig/network-scripts/ifcfg-ens33  TYPE=Ethernet #BOOTPROTO=dhcp BOOTPROTO=static DEFROUTE=yes PEERDNS=yes PEERROUTES=yes #IPV4_FAILURE_FATAL=no IPADDR=192.168.42.12 NETMASK=255.255.255.0 GATEWAY=192.168.42.129 DNS1=192.168.42.129 DNS2=114.114.114.114 IPV6INIT=no IPV6_AUTOCONF=no IPV6_DEFROUTE=yes IPV6_PEERDNS=yes IPV6_PEERROUTES=yes IPV6_FAILURE_FATAL=no NAME=ens33 UUID=e7328f29-6313-4382-8023-b7740ed4f7ad ONBOOT=yes   Here is ip  and route information:  # ip addr 1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN      link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: ens33: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast state UP qlen 1000     link/ether 00:0c:29:4d:df:bf brd ff:ff:ff:ff:ff:ff     inet 192.168.42.12/24 brd 192.168.42.255 scope global ens33        valid_lft forever preferred_lft forever     inet6 fe80::20c:29ff:fe4d:dfbf/64 scope link         valid_lft forever preferred_lft forever 3: tun0: <POINTOPOINT,MULTICAST,NOARP,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast state UNKNOWN qlen 100     link/none      inet 10.8.0.1 peer 10.8.0.2/32 scope global tun0        valid_lft forever preferred_lft forever # ip route default via 192.168.42.129 dev ens33  proto static  metric 100  10.8.0.0/24 via 10.8.0.2 dev tun0  10.8.0.2 dev tun0  proto kernel  scope link  src 10.8.0.1  192.168.42.0/24 dev ens33  proto kernel  scope link  src 192.168.42.12  metric 100      cat /etc/sysctl.conf | grep echo   outputs nothing.  I see, not be able to connect to Google because of the firewall:GFW.  traceroute output:  # traceroute -T www.google.com traceroute to www.google.com (216.58.197.100), 30 hops max, 60 byte packets  1  gateway (192.168.42.129)  0.541 ms  0.378 ms  0.294 ms  2  * * *  3  * * *  4  * * *  5  * * *  6  * * *  7  * * *  8  * * *  9  * * * 10  * * * 11  * * * 12  * * * 13  * * * 14  * * * 15  * * * 16  * * * 17  * * * 18  * * * 19  * * * 20  * * * 21  * * * 22  * * * 23  * * * 24  * * * 25  * * * 26  * * * 27  * * * 28  * * * 29  * * * 30  * * *   traceroute with www.vim.org output:       # traceroute -T www.vim.org traceroute to www.vim.org (216.34.181.97), 30 hops max, 60 byte packets  1  gateway (192.168.42.129)  0.447 ms  0.419 ms  0.287 ms  2  * * *  3  * * *  4  * * *  5  * * *  6  * * *  7  * * *  8  * * *  9  * * * 10  * * * 11  * * * 12  * * * 13  * * * 14  * * * 15  * * * 16  * * * 17  * * * 18  vhost.sourceforge.net (216.34.181.97)  229.060 ms  214.904 ms  220.727 ms   But , ping www.vim.org  also have no response.   # ping www.vim.org PING vhost.sourceforge.net (216.34.181.97) 56(84) bytes of data. (no response)   Thank you for any advice.


I'm very new to brewing, and I'm making a couple test batches of cider as we speak. However my accessibility to things like wine or champagne yeast, so i'm stuck with baking yeast.   My question is when i'm done if i'm not happy with the taste is it possible for me to freeze my cider and add sweetener? Would sugar work or would I have to use a honey or other substitute?

I've just finished my primary fermentation and have produced a cider that is coming in at 5.2%. I am about to bottle my cider and add some priming sugar to give it a bit of a fizz. I would like to try and flavor some of the ciders with a fruit coulis. am I correct in thinking that the natural sugar in the fruit should give the cider a natural fizz and I don't need to add any sugar? Also, I am a fan of a sweeter cider, I have been advise not to add more than a teaspoon of priming sugar, and to use a sugar substitute at the same stage if i wish to sweeten it. I have purchased Xylitol, I plan on trying a few combinations with the priming sugar/Xylitol & no additive fruit coulis. Does this all sound like it makes sense or am I just going to ruin my cider.


Solve for positive integers $x,y,z$  $$\frac{4}{13}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$$  I tried to solve it by some generel work but it didn't help.

Solve for $x,y,z\in\mathbb{N}$  $\frac{4}{13}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$  I tried by some general methods but they didn't help me.


Humans, animals and birds all have two eyes. Why? In addition to why two instead of one, why aren't there more than two?

We have two eyes, but we don't have two hearts. Why do humans have two of some organs, but not all?


Consider $n$$(>1)$ spots created around a circle. A man jumps from one spot to another in the following manner. He starts from some selected spot. From there, he skips exactly one spot in the clockwise direction and jumps to the next one. Then skips two spots and jumps to the next and then three spots and so on. He is allowed to visit the same spot more than once. Suppose that after some time he ends up visiting all the spots. Is it possible for the value of $n$ to be odd?   Well, the answer is obviously no. I tried to assume that it is odd and then take "$\mod n$" to prove that all possible remainders will not come. Though that seems to be the right path, I am not able to conclude. Please help!

Lotus leaves are arranged around a circle.      A Frog starts jumping from one leaf in the manner described below.   In the first jump it skips one leaf,next jump it skips two,three the next jump and so on.      If the frog can reach all the leaves, show that number of leaves cannot be odd.


I got really confused reading conflicting grammar rules for sentences such as below:   First  one:     A number of people is/are going to the party.   Here, the subject is "A number". Since "A number" is plural, the the correct answer must be     A number of people are going to the party.  Second one:     His collections of music is/are good.   Here, the subject is "Collections of music". Since "collections" is a plural, the correct answer must be:     His collections of music are good.  Third one:     His collection of music is/are good.   Going by my previous rule, since the subject here is "collection of     music", which is singular, the correct answer must be:     His collection of music is good    But I have seen answers that state the right answer to the second one is "His collections of music is good".   Can someone please elucidate this?  Thanks in advance!

Formally, is it correct to write:     A number of questions has been asked here.   or:     A number of questions have been asked here.   As a non-native speaker of English, I would prefer the former: the subject seems to be "number", therefore the verb ought to be singular, I'd say. However, the latter seems more common, and therefore I believe that my gut feeling is just plain wrong — but I would really like to have a definite answer.  Moreover, is it the same for "a myriad of", "a plethora of", and so on?


Let us say we have a mighty man crossing a bridge, carrying 4 bags of concrete, each of which weighs 50 pounds.    Let us say, for the sake of the argument, that the mighty man himself weighs 300 pounds.  The support capacity of the bridge $x$ is less than the 500 pounds they weigh together - therefore, the mighty man cannot carry the concrete in a stack across the bridge - it will fall.  However, the mighty man does have the ability to juggle all the concrete bags so that he is only in contact with one of them at a time.    Is there such a value of $x$ possible that he can cross the bridge juggling all four bags of concrete at once, or will the bridge necessarily exceed its support capacity?

A friend offered me a brain teaser to which the solution involves a $195$ pound man juggling two $3$-pound balls to traverse a bridge having a maximum capacity of only $200$ pounds. He explained that since the man only ever holds one $3$-pound object at a time, the maximum combined weight at any given moment is only $195 + 3=198$ pounds, and the bridge would hold.  I corrected him by explaining that the acts of throwing up and catching the ball temporarily make you 'heavier' (an additional force is exerted by the ball to me and by me onto the bridge due to the change in momentum when throwing up or catching the ball), but admitted that gentle tosses/catches (less acceleration) might offer a situation in which the force on the bridge never reaches the combined weight of the man and both balls.  Can the bridge withstand the man and his balls?


Here  var a = {}   When  if(typeof a.b == "undefined"){   console.log("undefined"); }  if (!a.b){   console.log("undefined"); }   both return "undefined" and when  if(typeof c.b == "undefined"){   console.log("undefined"); }  if (!c.b){   console.log("undefined"); }   both raise error c is not defined  It looks like 2 if-else statements above are working the same. So which way is better?

How do I check if an object has a specific property in JavaScript?  Consider:  x = {'key': 1}; if ( x.hasOwnProperty('key') ) {     //Do this }   Is that the best way to do it?


I need to prove that $$\cos\dfrac{\pi}{11}+\cos\dfrac{3\pi}{11}+\cos\dfrac{5\pi}{11}+\cos\dfrac{7\pi}{11}+\cos\dfrac{9\pi}{11}=\dfrac{1}{2}$$  How to do it?


I am new to Linux. I have a Dell Inspiron 15 with a 1st generation Intel Core i3 and Ubuntu 12.10.  My laptop gets heated quickly which doesn't happen on Windows. Also the battery is discharged faster than in Windows. Please help.

Last year I purchased a Dell Inspiron 5315 laptop shipping with Windows 7 preinstalled. I installed Ubuntu 10.10 alongside it with dual-booting. On upgrading to Ubuntu 11.10, I was upset to find I now get less than one hour of battery life! Windows 7 gives me 2.5 hours of running time.  Is there any possible explanation why  my battery is running out faster with Ubuntu? Can anybody tell me better power options?


I have the following strings having pattern which given below:  1)click on http://www.google.com  2) click onhttp://www.google.com".  3) click on www.google.com  4) click onwww.google.com  5) click on www.google.com#xyz  6) click onwww.google.com#xyz   I need to convert all these string to below manner with using of regular expression:  click on http://www.google.com  click onhttp://www.google.com  click on www.google.com  click onwww.google.com  click on www.google.com#xyz  click onwww.google.com

I have the following string:  "Look on http://www.google.com".   I need to convert it to:     "Look on "   The original string can have more than 1 URL string.  How do I do this in php?  Thanks


I don’t get it. if let’s say Uranium undergoes fission to produce Barium and Krypton. Barium and Krypton will have a greater binding energy per nucleon meaning they require more energy to hold the nucleus in place. if that’s the case where does the energy released from fission come from? Shouldn’t the total energy of the reaction decrease as energy is absorbed?

The nuclear binding energy, is the energy that is needed to seperate the nucleons in a nucleus. And binding energy is also defined as the energy given out when a nucleus forms from nucleons.   Also the larger the nucleus is, the more energy is required to break it apart, so why doesn't that mean that larger nuclei are more stable? I mean Uranium has a lower binding energy per nucleon than Iron, but there are many many more nucleons in Uranium that Iron so the total binding energy is going to be much greater.   Basically I don't understand why whether an element gives out energy by fusion or fission (why the lighter element provide energy by fusion not fission and vice versa for heavy elements) depends on binding energy per nucleon and not "total" binding energy


I'm trying to solve this integral in terms of elementary functions but my result does not seem to match up with Sage's or WolframAlpha's.   $\int \frac{1}{x^4+1} = \frac{x}{1+x^4}+\int \frac{4x^4}{(1+x^4)^2}$   Where:  $4\int \frac{x^4}{(1+x^4)^2} = 4\int \frac{u-1}{u^2} = 4\log u + \frac{4}{u}$  So the original integral is  $\int \frac{1}{x^4+1} = \frac{x}{1+x^4} + 4\log (1+x^4) + \frac{4}{1+x^4}$  Where did I go wrong here? Thanks.

I don't know how to integrate $\displaystyle \int\frac{1}{x^{4}+1}\mathrm dx$. Do I have to use trigonometric substitution?


Since security is always something that is a concern, is it fine to just use the following method whenever I need to clean data that I don't know is safe?  function clean_data($input) {   return mysqli_real_escape_string($cxn, htmlspecialchars(strip_tags(trim($input)))); }   Or is something that I shouldn't do?

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


I need help or an explanation as to how I would shorten this code?  I thought about just combining the two, but when I tried, I just keep getting errors  Any ideas?  Thank You!  import random  fave_word = 'hello' + "world"  rand_num = random.randint(0,3)  if rand_num == 0:     fave_word += ''  elif rand_num == 1:     fave_word += 'Bob' elif rand_num == 2:     fave_word += 'BobBob' elif rand_num == 3:     fave_word += 'BobBobBob' else:     fave_word += '' print(fave_word)  fave_word_2 = 'csc108' + "world" if rand_num == 0:     fave_word_2 += '' elif rand_num == 1:     fave_word_2 += 'Bob' elif rand_num == 2:     fave_word_2 += 'BobBob' elif rand_num == 3:     fave_word_2 += 'BobBobBob' else:     fave_word_2 += '' print(fave_word_2)

I want to write a function in Python that returns different fixed values based on the value of an input index.    In other languages I would use a switch or case statement, but Python does not appear to have a switch statement.  What are the recommended Python solutions in this scenario?


I was thinking of decimal expressions for fractions, and figured that a fraction of the form $\frac{1}{p}$ must be expressed as a repeating decimal if $p$ doesn't divide $100$. Thus, $\frac{p}{p}$ in decimal would equal $0.\overline{999\dots}$ for some number of $9$s, thus there must be some amount of $9$s such that $p | 999...$ in order for a decimal representation of $\frac{1}{p}$ to be possible.  Furthermore, the question could be rephrased to "an infinite number of" since if it divides $999\dots$ where there are $k$ nines, it also divides when there are $2k, 3k, \dots$ nines.  Is this reasoning correct? If so, this is how I thought about proving it:  We can reduce the set to $\{1, 11, 111, 1111, \dots\}$ since $p=3$ obviously works.  Let $a_k = 111\dots$ where there are $k$ ones. This satisfies the recursion $a_k = 10a_{k-1} + 1$  But I'm unsure what to do past this point (tried looking at modular cases or something but wasn't able to get anywhere). Am I on the right track at all? Is this "conjecture" even correct?

A curiosity that's been bugging me. More precisely:     Given any integers $b\geq 1$ and $n\geq 2$, there exist integers $0\leq k, l\leq b-1$ such that $b$ divides $n^l(n^k - 1)$ exactly.   The question in the title is obviously the case when n = 10. This serves as a motivating example: if we take b = 7 and n = 10, then k = 6, l = 0 works (uniquely), and if we calculate $\dfrac{n^k - 1}{b}$, we see that it turns out to be 142857 - the repeating part of the decimal expansion of 1/7. A (very sketchy, but correct!) sketch proof, which I've included for completeness:   Notice that $\dfrac{1}{99\dots 9} = 0.00\dots 01\; 00\dots 01\; 00\dots 01\dots$. Notice that $1/7$ must have either a repeating or a terminating decimal expansion: just perform the long division, and at each stage you will get remainders of 0 (so it terminates) or 1, 2, ..., 6 (so some of these will cycle in some order). It turns out the decimal expansion is repeating, and the 'repeating part' is 142857. This has length (k=)6. $\dfrac{1}{10^6 - 1} = 0.000001\;000001\dots$, so $\dfrac{142857}{10^6 - 1} = 0.142857\;142857\dots = 1/7$, and so $7\times 142857 = 10^6 - 1$. And we can do the same thing with $\dfrac{1}{10\dots 0} = 0.00\dots 01$ and terminating decimals. And the same proof of course holds in my more general setting.   But this (using the long division algorithm after spotting an unwieldy decimal expansion) feels a little artificial to me, and the statement is sufficiently general that I'm sure there must be a direct proof that I'm missing. Of course, the $n^k$ part is easy, but the $n^k-1$ part has me a little stumped. My question is: is there a direct proof of the latter part?  Thanks!


I'm compiling a source code that generates following error:  checking for avcodec.h... no checking for libavcodec/avcodec.h... no checking for ffmpeg/avcodec.h... no checking for libav/avcodec.h... no checking for ffmpeg/libavcodec/avcodec.h... no checking for libav/libavcodec/avcodec.h... no configure: error: avcodec headers not found! Install FFmpeg or Libav.   Installing ffmpeg package didn't help me. Which package should be installed?

Simple enough question: is there some shell command (or GUI method) I can use that, given the path to a file on my system, tells me what package put it there? Assuming the file did in fact come from a package, that is.  Bonus question: what if it's a file that isn't installed on my system? Is there, say, a website that will let me look up a file and see what packages, if any, provide it?


I found this chart in one of the questions here. Additional to this:  When making a measurement and getting 2 Measures of Latitude, for example  51.1901354 and 51.1901359. Is it then possible to say that these points are 5.55 cm apart? Also, I am using this formula to get meters rather then degree:  Northing = (Latitude-Base_Latitude)*(6378137*pi/180)  Easting =(Longitude-Base_Longitude)*(6378137*pi/180) * cos(Base_Latitude*pi/180)  Is the Chart above usable with this Convertion?

I have latitude and longitude as 19.0649070739746 and 73.1308670043945 respectively.   In this case both coordinates are 13 decimal places long, but sometimes I also get coordinates which are 6 decimal places long.   Do fewer decimal points affect accuracy, and what does every digit after the decimal place signify?


Let $ A $ be subset of of $ \{ 1, 2, ... 2n \} $, such that: $ Card(A) = n + 1$.  Prove that there exist at least two distinct elements $a,b$ in $ A $ such that: $ a \mid b $.    We have:  $$ \{ 1, 2, ... 2n \} =  \{ 1, 2, ... n \} \cup  \{ n+1, n+2, ... 2n \} $$  Intuitively, I know that every subset $ A $ of $ \{ 1, 2, ... 2n \} $ with $ n + 1 $ elements contains at least 2 elements $ a $ and $ b $ such: $ b = 2a $.  I don't know how to prove it mathematically. Thank you for your help.

Let $n$ be greater or equal to $1$, and let $S$ be an $(n+1)$-subset of $[2n]$. Prove that there exist two numbers in $S$ such that one divides the other.   Any help is appreciated!


I have a snippet of code kinda/sorta like this:   world" ; </script>   This barfs and displays and renders the span. The problem is caused by the " value in the variable.   I have worked around it by escaping the \ and changing it to      This works fine. This seems really, really hokey. There has to be a better way to do this??

Why do some sites (or advertisers that give clients javascript code) employ a technique of splitting the <script> and/or </script> tags up within document.write() calls?  I noticed that Amazon does this as well, for example:  <script type='text/javascript'>   if (typeof window['jQuery'] == 'undefined') document.write('<scr'+'ipt type="text/javascript" src="http://z-ecx.images-amazon.com/images/G/01/javascripts/lib/jquery/jquery-1.2.6.pack._V265113567_.js"></sc'+'ript>'); </script>


There is large space between the compound name and compound . I used arrow[0]{,0} also and cyclohexane is not aligned properly at center :(  picture explains clearly :(   How do i remove distance between c1 and benzene as well as c4 and cyclohexane .  How ever the main problem is adding [0.8ex] fixes for some compounds with names like the screenshot below .   You can see at c1 c2 there is no problem but in second c1 and c4 there is huge distance :(  Here is my Latex Code .  \documentclass[11pt]{article}  \usepackage{chemfig} \usepackage{siunitx}  \def\benzene{\chemname[0.8ex]{\chemfig{**6(------)}}{Benzene}}  \def\nitrobenzene{\chemname[0.8ex]{\chemfig{**6(----(-NO_2)--)}}{Nitro Benzene}}   \begin{document}  % #1 \schemedebug{true}  \vspace{5mm}         \schemestart                 \benzene                  \arrow{0}[,0] \+                  \chemfig{3Cl_2}                  \arrow{->[sunlight][uv]}                  \chemfig{C_6H_6Cl_6} \arrow{0}[,0]  \, \, \, \,  or                  \chemname[0.8ex]{\chemfig{*6((-Cl)-(-Cl)-(-Cl)-(-Cl)-(-Cl)-(-Cl)-)}}{Benzene Hexachloride(BHC)}           \schemestop   % #9 \vspace{5mm}         \schemestart                 \benzene                  \arrow{0}[,0]                  \+ \chemfig{3H_2}                  \arrow{->[\chemfig{Ni}][$\Delta$,Pressure]}[0,2,]                   \chemfig{C_6H_{12}} \arrow{0}[,0]  or \chemname[0.8ex]{\chemfig{*6(------)}}{Cyclohexane}           \schemestop  \end{document}

I'm trying to put a number of different molecule structures into one document with the help of the chemfig package. The package also allows to add the name of the compound to the structure as a caption via the chemname command. As far as I understand the distance of the label from the structure is measured by the package and to avoid overlaps the largest spacing found is used for all subsequent labels. This leads to the effect of a large distance if the following molecule structure is small.   Is there a way to reset the distance measured between the \chemname commands?  Thank you very much for your help and please also see the example code below.  Thomas  \documentclass{article} \usepackage[english]{babel} \usepackage[utf8]{inputenc} \usepackage{chemfig} \begin{document} \chemname{\chemfig{-[7]-[1]P(=[2]O)(-[6]-[7])-[7]-[1]}}{Triethylphosphine oxide}  \chemname{\chemfig{-[1](-[2]OH)-[7]}}{Isopropanol}  \chemname{\chemfig{H_2N-[1](=[2]O)-[7]NH_2}}{Urea} \end{document}


Let $U\subset\mathbb{C}$ be simply connected, and let $\phi:U\rightarrow\mathbb{D}$ be a conformal map with $\phi(z_0)=0$ and $\phi'(z_0)>0$. If $f:U\rightarrow\mathbb{D}$ is analytic with $f(z_0) = 0$ then $|f'(z_0)|\leq\phi'(z_0)$, with equality only when $f$ is a constant multiple of $\phi.$ Can we use Schwarz Lemma to prove the statement? Since we know $f$ is analytic, it remains for us to show other requirement to apply Schwarz Lemma, if using Schwarz Lemma was the right call. But I am having trouble translating statement to $f'$ and showing we have everything to apply the Lemma. Here is the Schwarz Lemma: Let $f(z)$ be analytic for $|z|<1$. Suppose $|f(z)|\leq 1$ for all $|z|<1$, and $f(0)=0$. Then $|f(z)|\leq|z|$ for $|z|>1$. Further, if equality holds at some point $z_0\neq 0$, then $f(z)=\lambda z$ for some constant $\lambda$ of unit modulus.

Let $z_0$ be a point in an open set $U \subset \mathbb{C}$.  Let $f,g:U \to \Delta(0,1)$ where $g$ is a bijection such that $g(z_0)=0$ and $g'(z_0)\neq 0$. Suppose that $f(z_0)=0$, then $|f'(z_0)|\leq |g'(z_0)|$  I am not even sure how to start this.  I was assuming Schwarz lemma.


In my bachelor courses, we have defined the space $C^1(\mathbb{R})$ as $$C^1(\mathbb{R}) = \{f: \mathbb{R} \rightarrow \mathbb{R}~|~f \text{ is differentiable}~\land~f' \text{ is continuous}\}.$$ However, I really do not understand why it is required that $f'$ must be continuous. Indeed, if $f$ is differentiable at $a \in \mathbb{R}$, then the limit $$\lim_{x \rightarrow a} \frac{f(x) - f(a)}{x - a}$$ does exist. Isn't it equivalent to the fact that our function $f'$ is continuous in $a$ ? I asked my teacher for an example of a function that would be differentiable at a point but whose derivative would not be continuous at this point. He gave me the function $$f(x) = |x| \quad \text{at zero.}$$But I disagree with him, it's not that the derivative is not continuous in zero, it doesn't even exist because these two limits don't agree $$- 1 = \lim_{x \rightarrow 0^-} \frac{f(x) - f(0)}{x - 0} \neq \lim_{x \rightarrow 0^+} \frac{f(x) - f(0)}{x - 0} = 1.$$ Therefore, $f$ is not differentiable at $0$. Could someone explain to me the definition of $C^1(\mathbb{R})$? Is there an example of a differentiable function whose derivative is not continuous? Thank you very much!

Suppose $f$ is continuous on $[a,b]$ and differentiable on (a,b). Does it follow that $f'$ is continuous on $(a,b)$?


is it somehow possible to add a dictionary for two different foreign languages to the Dictionary app? I am using macOS 10.15 "Catalina" in English and I would like to add a Spanish to German dictionary. Adding a Spanish and a German dictionary is possible. Also also the Dictionary app allows us to add english to german and English to Spanish, but I do not see the the option to add German-Spanish. Can someone help if this is even feasible? When yes, how can I add this dictionary? Here is the list of options I have.

For quite a while now, I have been looking for English and Spanish conversion dictionaries (both ways) for Apple's native Dictionary application. So far I have not had any success.    Is there any free, decent quality solution such as "New Oxford American Dictionary" and "Dictionnaire de l'Académie Française"?   Any links or information would be highly appreciated.


I'm currently working through Principles of Mathematical Analysis, and I'm thoroughly enjoying it, but I wanted to know from some of you who've read it before, what's the best approach to get the most out of Baby Rudin?  I'm hoping to complete most, if not all of the exercises in it, that I'm sure of. No questions there.  What I'm not so sure about is note taking, currently I'm taking truly copious amounts of notes, to the point where I've copy-pasted almost everything in the first chapter into my own book.   It would be completely illogical to rewrite the whole book out just for the sake of it, and it would take me forever to complete the book that way.   I know as I'm typing this, that this is a very subjective matter, and some people prefer to take copious amounts of notes, while others prefer to take none at all, but since this is my first true Definition-Theorem-Proof style book (if you can call it that), I want to find out what's the best way to tackle the book.  For those of you who've read Baby Rudin, and more generally for all Definition-Theorem-Proof style books, how do you go about taking down notes?    Do you copy-paste most of the stuff (i.e as I did)? Do you only take down notes on proofs and use the book as a reference for definitions and theorems? Do you take down all the definitions and theorems? Do you take down any of the exposition stuff (comments etc.)? Do you take as little notes as possible and only worry about doing the exercises? Do you try and reprove everything and not worry about notes as much?   I know that each person studies in their own way, and this may be the softest of soft questions on Math.SE, but I'm highly interested to see how others have gone about working through Baby Rudin.

What are/ were some of your good mathematician's study habits that you found really worked for you?  I'm a CS major at a respected school and have a solid GPA...  However, I definitely lack when it comes to getting great grades in relatively higher level maths (300 and 400 level).  I feel that even though I study a lot, I perhaps don't study effectively enough.  I would like to ask for any tips/ tricks as to how you keep yourself focused, motivated etc that could perhaps help me or others.  Thanks in advance.


What do we do if we come across a question that could have malicious intent behind it. I found  and don't know what the normal practice regarding these questions is. Do we flag them? Not answer them? Not worry about them? Related

How should we treat questions that are, or have seeds of, evil or malicious purposes and actions, such as writing spambots and malware?    Should they be answered like regular "everybody keeps their pants on" questions? Or should there be some other type of response to this bad behaviour lot?