I wish to install the newest Ubuntu 14+ on a 32 GB USB Stick. I want to boot a fully operating ubuntu OS right but off the stick itself How do I do this? Thanks

If you are hurrying to reply, System → Administration → StartUp Disk Creator -- no, that's not what I'm talking about.   I want to try Ubuntu 11.04's Unity without touching my existing Ubuntu install.  To do this, I need to install the nVidia drivers first (sigh).  To do this, I need changes to persist a reboot.  To do this, I need to really install Ubuntu on a USB key.  How do you do that?    What I tried   I tried to make a USB key from , then boot from it, then choose "Install Ubuntu." The installer refused to install to the installation media itself. I tried, from my installed copy of Ubuntu:  sudo kvm /dev/sdb --cdrom .cache/testdrive/iso/ubuntu_natty-desktop-i386.iso   ...but the installer didn't detect the disk properly.


These books were in my middle school library.  It was a series of at least 2 (possibly more) books about a young man who was an alien.  He passed as human and only a few people knew, including some older man who seemed like a father figure.  Because he was an alien he had ESP-style psychic powers (telekinesis and others).  At some point he uses them to cause or stop or save someone from a car crash.  There was definitely a car or bus accident.  I believe the planet his people were from may have allegedly been a system orbiting a star in the Orion constellation.  It no longer existed, I believe -- I remember specifically the text making a point that the star it had orbited was gone, but that they could still see it up until a certain point in one of the books because speed-of-light, etc.  I should add that I remember it as being pretty much contemporary (roughly set in the 80's or 90's)--not set in the future.  There wasn't, apparently, much space travel or anything (even though there must have been, or how else did he get there).

I have been trying to find a book I read quite a few years ago. Well, there are 2, one being the sequel.  Now I'm sure my memory has been kind enough to mix parts of the 2 books, but I will do my best with the description.  The cover of the book had a hand print. As far as the story, a boy finds out he has some powers from some guy. I think he had a ring that allowed him to use his power. Later when training the boy, he has him learn to control his power by deflecting rocks or meteors or some rocky item. The boy ends up using too much force and shatters them, but eventually gets the hang of it. Another part close to the end, the boy has a vision, I think, of some other kid getting struck by lightning, so he figures out a way to save the kid, but gets struck by the lightning himself.  In the second book, I remember a part early on where a sign falls from a building toward some child, but the boy uses his power to save the kid; afterwards, no trace of the boy is found. A lady who witnessed it said something like it was her dead son (I'm guessing his mom from the previous book).   I'm having trouble remembering anything but that. I read them in '97 or '98, I believe. As far as the publication dates, I never checked.


I'm new for what about j2EE and I'm moving my first steps with servlet and EJB.  I use Netbeans, Glassfish. When I pass my data (I want to view in my JSP the data in the table Products on postgress and the connection I sure that works)  from servlet to JSP I have a strange Null Pointer Exception.  This is the processRequestMethod in the Servlet class:          protected void processRequest(HttpServletRequest request,HttpServletResponse response)         throws ServletException, IOException {           List<Products> list=new ArrayList<Products>();         list =  productsFacade.findAll();           request.setAttribute("list", list);          String arg = "/" + this.getServletName() + ".jsp";         RequestDispatcher dispatcher = this.getServletContext().getRequestDispatcher(arg);         dispatcher.forward(request, response); }   the method findAll():  public List<Products> findAll()     {       return em.createQuery("SELECT p FROM Products p").getResultList();     }   Instead the JSP is this:  <%@page import="java.util.ArrayList"%> <%@page import="entities.Products"%> <%@page contentType="text/html"%> <%@page pageEncoding="UTF-8"%> <%@page import="entities.Products_"%>  <%@page import="java.util.List"%> <%     List<Products> list=new ArrayList<Products>();     list = (List<Products>)request.getAttribute("list");  %>  <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"     "http://www.w3.org/TR/html4/loose.dtd">                 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">          <title>JSP Page</title>
Content of my Table
      <%            if (list != null)            { for (Products e: list)               { out.println(e.getName() + " " + e.getPrice() + "
"); }           }                   %>                 Why my list is NULL ?

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


I've been playing minecraft pocket edition for a while and got the new update recently. How do I stop the Invalid Name error when I join my little brothers server? I've already seen the no spaces or special characters in your name answers on this website, but they do not work for me.

I am having trouble getting onto a server in Minecraft PE on iOS. When I tap on the person's server it just says invalid name:    I have tried turning off and restarting the iPad, going to home screen and logging back into the server but I have had no luck and no change. Is there a reason why this is so?


I have a usb with my windows ISO loaded and ready. Problem is there is no ntfs partition on my hard drive for windows to load onto. I don't want to complicate things by running 2 operating systems. I’d like to go back to windows. I like Ubuntu more but I have no clue what I’m doing. I’m not a programmer.  I’ve tried booting from my usb with windows 7 loaded on as well as a CD with vista ultimate. Neither gave me an option to repair my drive. Both have the option to delete partition, and the CD gave me the option to format partition. The formatting failed and I’m afraid to delete the partition because I don't know what to do if I delete Ubuntu and the drive remains in ext4 format. Please help.

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


Ho can I make a figure like the following with tikz package?

Is there is an easy way to mark dimensions in a technical drawing with TikZ?    Is there a library or something?  Edit  I am using XeLaTeX.  Update  I chose Martin's answer because it serves me well for the moment. Ultimately the best solution would be a library that, in an easy and consistent manner, would allow to change the arrow/dimension lines styles, would support polar coordinates, would allow to choose 2 nodes and the vertical distance that you want the dimension to be typeseted etc.


I am facing problems in installing MiKTeX. My latest effort gave the following error log:  MiKTeX Setup 2.9.3959 Report  Date: Sunday, December 15, 2013 Time: 13:51:21 OS version: Microsoft Windows Vista Home Basic Edition, 64-bit (build 6000) SystemAdmin: yes PowerUser: false SharedSetup: yes Setup path: C:\as\u\tx\setup-2.9.3959.exe UserRoots: <none specified> UserData: <none specified> UserConfig: <none specified> CommonRoots: <none specified> CommonData: <none specified> CommonConfig: <none specified>  Installation: C:\Program Files (x86)\MiKTeX 2.9 Loading package database... starting package maintenance... installation directory: "C:\Program Files (x86)\MiKTeX 2.9" package repository: "C:\as\u\tx\MiKTeX 2.9 Setup" visiting repository "C:\as\u\tx\MiKTeX 2.9 Setup"... repository type: local package repository loading lightweight database... lightweight database digest: 9ac12380e9220f67d0db4465cc045262 going to install 75722 file(s) (2235 package(s)) problem: C:\Program Files (x86)\MiKTeX 2.9\miktex/bin\MiKTeX209-core-PS.dll does not exist problem: C:\Program Files (x86)\MiKTeX 2.9\miktex/bin\MiKTeX209-core.dll does not exist problem: C:\Program Files (x86)\MiKTeX 2.9\miktex/bin\MiKTeX209-packagemanager-PS.dll does not exist problem: C:\Program Files (x86)\MiKTeX 2.9\miktex/bin\MiKTeX209-packagemanager.dll does not exist extracting files from 12many.tar.lzma...  ***************  extracting files from yplan.cab... extracting files from yt4pdf.tar.lzma... extracting files from ytableau.tar.lzma... extracting files from ytex.cab... extracting files from zapfchan.cab... extracting files from zapfding.cab... extracting files from zed-csp.cab... extracting files from zefonts.tar.lzma... extracting files from zhmetrics.tar.lzma...  An error occurred:   source file: Libraries\MiKTeX\Core\fnamedb.cpp   source line: 594   message: File name database capacity exceeded.   info:

I am trying a complete installation of MikTex 2.9, using 64 bit installer, from a recently downloaded local package directory, all latest versions.  During installation, I run across this error "File name database capacity exceeded."  Does anybody know a solution to this problem. My complete log file can be viewed at


Im just curious but is it possible to build a bootable iso of my running 14.04 OS? Like if I could create an iso that upon running again would reinstall? I have to redo my system but I have so many files and shell scripts that I dont want to reinstall from fresh but reinstall the OS im using now.  Could this be possible?

I am new to linux, but had a question. I am getting in the business of buying old computers, putting Linux on them, then donating them to students who don't have their own computer at home. I have gone through and installed Xubuntu on my system, installed/uninstalled all the software that I want/need, and now want to know if there is a way that I could make an ISO of my system, and put it onto ANOTHER computer, and still have all of my tweaks, and programs ready to go after the ISO has installed. That way I don't need to go through and spend an hour or two on every computer.   What programs would you recommend for creating an ISO like this?   Thanks, Tobin


I have a dual-boot setup with MacOS and Arch Linux on my Macbook Pro mid-2009 17-inch.  I have  installed to my EFI System Partition as EFI/BOOT/bootx64.efi with a  that allows me to choose Arch Linux or MacOS on boot. Awesome!  Arch Linux is loaded via EFI stub and I have the ability to hibernate and resume to it by using a swap file and kernel parameter resume=.... I can even hibernate Arch Linux, turn on the computer, choose MacOS through rEFInd (or even through the built in boot manager by holding the option key), which boots MacOS, and I can later shut down MacOS and resume Arch Linux from hibernate by selecting it in rEFInd at the next boot.  What I would love is to be able to do the same thing with my MacOS side, that is, hibernate MacOS, boot Arch Linux, to later resume MacOS. However it seems that when I sleep my MacOS side to hibernate (see man pmset for how to tell MacOS to hibernate), when I turn the power on, the resume process bypasses any boot selection I can make! That is, holding option doesn't bring up the boot manager, and it begins MacOS resume right away.  I have tried ensuring that my EFI System Partition is the first choice of the boot manager by holding control and clicking the EFI System Partition at startup (after holding option to get into the boot manager), but this has no effect.   seems relevant, but doesn't explicitly discuss what you can do with how MacOS bypasses the boot manager on hibernation resume.

Is it possible to use the true hibernate system functionalities of Win 7 and OS X to create a kind of instant switching between the two? Imagine this when reading/writing the sleep images to a quick SATA-3 SSD.  Hibernate-corruption-fix: If this is made possible, make sure that your different partitions are not write-enabled from eachother. (e.g. make it so that Boot Camp Windows 7 cannot write to OS X partition and vice versa). This safety measure should make it impossible for your different systems to corrupt eachother when one is suspended into hibernation.  Edit: I realized that I'm not sure that this is how partitions work on a disk. The hibernated OS X kernel could have references to blocks on the disk which it will continue to write to when it is woken up again. Are disk blocks like these contained within a partition or are they assigned to a partition after they have been written on? Is it different on HDD and SSD? Does this affect the above hibernate-corruption-fix?  Ok let's move on:  Windows 7 already has an option "Hibernate" which allows you to boot back to your OS X partition, but OS X does not exactly offer the same.  With OS X it is possible to hibernate by changing the hibernatemode system variable.  Pre OS X 10.7     sudo pmset -a hibernatemode 2   OS X 10.7     sudo pmset -a hibernatemode 25   This makes your Mac go into hibernate when you put it to sleep. You can put it to sleep with:     sudo shutdown -s now   Ok, so far so good. So we can put both Windows 7 and OS X Lion into hibernation at will. But wait! There's more problems up ahead.  When you put OS X into hibernate it will automatically boot back into OS X when you power your Mac on again. This makes it impossible for us to use it for "hotswitching" between partitions.  Possible fixes: If you install  without rEFItBlesser you will get the rEFIt boot menu after OS X hibernation. On OS X 10.7 Lion however, this does not fully work, instead you get a black screen and have to hard shutdown your Mac. But hey! At least it interrupts the automatic OS X boot, right? Maybe it can be tweaked further from there.  As mentioned on earlier OS X:s the rEFIt boot menu actually does come up after hibernation shutdown + power on. This allows you to e.g. boot your Boot Camp Windows 7 partition instead.  There are problems here as well though. Apparently the OS X partition loses its hibernation flag if you follow this method, which means that the next time you boot into OS X, it will not return from its hibernation state. Instead it will do a clean startup. Why is this? Does OS X look for the existence of a sleep image to determine wether to wake up from hibernation or to do a clean start or does it have some kind of system variable/flag set?  Summary  When Win 7 goes into hibernate it shuts down completely and you can then boot into OS X on startup. On OS X however, hibernate forces you to wake up into OS X. Can you hack this so that you're allowed to select boot partition after OS X hibernates and still be able to return later to OS X and wake it up from its hibernate?  Let's see what we collectively can come up with!


I am having a problem getting to the parent window. I have a window that has 2 frames...one of the frame opens another window which in returns open a third window. In the third window I want to refresh the very first window by doing this  window.opener.window.opener.close();    it only works for non frame setup...what can I use for the frame. I am open to using jquery too

The client I am working with has a frameset like so...  <frameset rows="100,*, 0">   <frame name="theFrame" id="theFrame" src="blah.html" >   <frame name="theSecondFrame" id="theSecondFrame" src="foo.html" >   <frame name="importantFrame" id="importantFrame" src="myFrame.html" > </frameset>   When a certain action takes place I need my frame (importantframe which is currently hidden) to mostly take over the page and block any interaction with the other frames. I'm planning on blocking interaction using the jquery block UI plugin.  The problem is I can't actually change the foo.html or blah.html files. So the JS code cannot live there. What I need to do is execute my jquery code in the context of those frames. So just to recap, I need my JQuery code to live in myFrame.html but execute in the context of the other frames. How can I do that? Hope that makes sense.  Thanks CDR


I am using Geoserver 2.15.1 version to display PostGIS data as WMS layer at client side. There will be a rendering problem in my WMS layer, some dense areas are not visible in larger scale as marked in the below snapshot. Those area are getting generated when zooming closer to the particular location.  Is there any way in GeoServer to make the features visible at all scale levels? I have tried MinScaleDenominator and MaxScaleDenominator, but no luck.

I have a really strange problem which I don't know how to solve. I have shp file I've import into PostGIS using PostGIS Loader (made sure the srs is 4326 same is shp file) .  In geoserver (2.6.1) I've created a postgres store and published the table I've imported , set it SRS (WGS84) and style (default Polygon).  Now this is where things go weird and I have no idea how to approach this problem:   If I Preview the layer via WFS (KML/GeoJson/CSV etc...) I get the txt files with all features inside. If I try to preview via openlayers or any other WMS (like geotiff) either I see empty map or get error  When I create a store of shp files with the data I've imported , it shows fine as wms.    Here is example that I do see features via wfs (csv) but error in wms.  Any idea ?!    EDIT 1: It was pointed out in comments that "width=78450&height=330" is a strange size (although this is what geoserver auto generate in preview) so I've manually edited the request to :  http://localhost:8080/geoserver/Oakland/wms?service=WMS&version=1.1.0&request=GetMap&layers=Oakland:oakland180110&styles=&bbox=-122.502975463867,37.3532028198242,-121.66429901123,37.9185791015625&width=512&height=345&srs=EPSG:4326&format=image/png   and now I get empty image:   Since I do see the data in the shp files preview :  http://localhost:8080/geoserver/Oakland/wms?service=WMS&version=1.1.0&request=GetMap&layers=Oakland:Oakland180110&styles=&bbox=-122.491314021,37.379831195000065,-121.71847960399995,37.89508712800005&width=512&height=341&srs=EPSG:4326&format=image%2Fpng   I tend to think that the problem is somewhere from reading the data from PostGIS.    Last thing I did is comparing the shp layer settings to the postgis layer settings but I don't see anything that might hint on the problem I have:    Update 2:  I've checked geoserver log and noticed that the following query returns null:  SELECT encode(ST_AsBinary(ST_Simplify(ST_Force_2D("the_geom"), 0.002246433788820923)),'base64') as "the_geom" FROM datatable   Now , the_geom column is geometry type and is not null .  When running ST_Simplify it brings back null :  This is working :  SELECT ST_Force_2D("the_geom") as "the_geom" FROM "public"."datatable"   This brings the nulls :  SELECT ST_Simplify(ST_Force_2D("the_geom"), 0.002246433788820923) as "the_geom" FROM "public"."datatable"   Any idea why ?


Consider $R=\mathbb{Z}[x]$. Also let $p$ be a prime. Then we want to find all the prime and maximal ideals of $\mathbb{Z}[x]$. The prime ideals are $(0), (p), (x)$ and $(ap + bx)$. Then we see that the last one contains all the previous ones making it a maximal ideal for $\mathbb{Z}[x]$. Is this the correct way to think about it?  Also, since $(ap + bx)$ is a maximal ideal this means that $R/$(ap + bx)$ is a field. How can I see that this quotient is indeed a field?   Finally, how could I find the same for $\mathbb{Q}$ and then for a generic $k$?

Let $\mathbb{Z}[X]$ be the ring of polynomials in one variable over $\Bbb Z$.  My question: Is every prime ideal of $\mathbb{Z}[X]$ one of following types? If yes, how would you prove this?  $(0)$.  $(f(X))$, where $f(X)$ is an irreducible polynomial.  $(p)$, where $p$ is a prime number.  $(p, f(X))$, where $p$ is a prime number and $f(X)$ is an irreducible polynomial modulo $p$.


The question is to find the value of the definite integral: $$I=\int_{-2}^{2} \frac{x^2}{1+5^x}\,\mathrm{d}x.$$  This question appeared in this year's CBSE board exam.  Attempts:   Replace $x\to-x$ and we get $$I=\int_{-2}^{2} 5^x \frac{x^2}{1+5^x}\,\mathrm{d}x.$$ Now what?? Probably integration by parts? But I get stuck there too. Substitute $5^x=\tan^2\theta$, and then I get (after calculation): $$I=\left(\frac2{\log5}\right)^3\int_{\tan^{-1}(1/5)}^{\tan^{-1}(5)}\frac{(\log\tan\theta)^2}{\tan\theta}\,\mathrm{d}x.$$ But I still dont get the answer. It has become too complicated. Wolfram|Alpha gives me the value $$I=\frac83,$$ But I don't have a pro account so I can't see the steps.   So how do I solve it?

$$\int^2_{-2}\frac{x^2}{1+5^x}$$  How do I start to integrate this?  I know the basics and tried substituting $5^x$ by $u$ where by changing the base of logarithm I get $\frac{\ln(u)}{\ln 5}=x$, but I got stuck.  Any hints would suffice preferably in the original question and not after my substitution.  (And also using the basic definite integrals property.)  Now I know only basic integration, that is restricted to high school, so would prefer answer in terms of that level.


this must be a very stupid question but i came to this site by accident and now i'm somehow interested in this but i dont know how to start or where to play! Is there a online game of this or is this only table top? Because some posts sound like there is an online version. And generally how and where to start playing this game.  Excuse my lack of knowledge and thank you for your help!

I have been told that roleplaying is great fun. I've looked and looked and it all seems so complicated. Could anyone tell me a good place to start, and what sort of things you end up doing in roleplaying?


A math challenge for class asks us to take words (like five seven six three) and change that to an integer (like 5763) to use in a calculation within the program.  There are several examples of words2number that take words that spell out a number (like five hundred and sixty five, as if you're writing a check).  But I want to take the individual words and place them into their corresponding number.  nine nine five zero = 9950,  six three five = 635,  etc.

I need to convert one into 1, two into 2 and so on.  Is there a way to do this with a library or a class or anything?


Can I use a comma following a question mark (as part of a title), inside quotation marks?    It sounds like quite a complicated question, but all I want to do is correctly write the sentence:       "Leo Strauss, in his essay “What is Political Philosophy?,” takes a   radically anti-historical view, contradicting Nietzsche and relegating   Nietzsche's critique to the edges of meaningful discourse."

The American convention in quotations is (typically) to place punctuation inside quoted text. But I always run into situations where the punctuation of the quote interferes with the punctuation of the sentence. How would you punctuate this (American, non technical)?     When my friends ask, "What do you want for your birthday?", I never know how to respond.   It seems odd to place the last comma outside the quote simply because of the question mark. Is that the preferred (i.e. most often accepted) standard?


what are the odds from 5 persons, to at least 2 be born at the same day in the week?

What is the chance that at least two people were born on the same day   of the week if there are 3 people in the room?   I'm wondering if my solution is accurate, as my answer was different than the solution I found:  Probability that there are at least 2 people in the room born on the same day = 1 - (No one was born on the same day) - (Exactly one person was born on the same day)  There are (3 choose 2) different pairs of couples. Each couple has the same birthday as another couple with the chances of 1/7 and different with chances 6/7. Thus:  $$1 – (6/7)^3 – 3(1/7)(6/7)^2 = 0.0553$$  Thanks for any help!


Let $n\geq 1$ and define $$ S(n) = \binom{n}{0}\binom{n}{0} - \binom{n+1}{1}\binom{n}{1} + \binom{n+2}{2}\binom{n}{2} - \cdots + (-1)^n\binom{n+n}{n}\binom{n}{n} $$ In other words $$ S(n) = \sum_{i=0}^n (-1)^i\binom{n+i}{i}\binom{n}{i} $$     Then $S(n)=(-1)^n$   I am unable to make any progress.

Based on the binomial expansion of $(1+x)^n$, show that: $$\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n.$$  This is a question from a very old high school exam paper I came across. It looks like it involes the product of two binomial expansions but I cannot figure this out. Any help much appreciated.


I'm a manager in an office and need to wear shirt and tie every day.  I am also a keen commuter cyclist (5 mi cycle to station, train, 0.5 mi walk to office).  I've tried panniers, rucksack, rolling shirts up, trying to keep flat and folded...but as yet I still end up with more creases than I'd like.  Any advice on how to keep my shirts as crease free as possible?  (Oddly enough, my trousers always seem to come out nicely!)

I have the bike, I have the best route; but now I want to know, how do I transport my clothing in each day? I typically wear suit pants and a business shirt, but not a suit jacket.   Am I better off leaving my clothes at work, or is there a special bag that would let me carry in shirt/pants without them getting crushed?


We built a website targeting different regions but with the same English language (Ireland, England and America). The content for the most part is the same set up on 3 different subfolders.  http://www.example.com/ - targeting the United States in WMT  http://www.example.com/ie - targeting Ireland in WMT  http://www.example.com/uk - targeting UK in WMT  Do I have duplicate content issues to be worried about?  If so, how do I get around this issue?   Also is there anyway of finding out if Google have in some way penalised these pages for having the same content on other pages trageting different countries? I have not received any messages from Google in WMT saying there is duplicate so I'm not sure if this is an issue.

I have organised my site by language using the following structure:  www.domain.com    #spanish language version homepage www.domain.com/en #english language version homepage   The site is of Spanish subject matter hence Spanish language takes priority at root of domain. Although the site is new at this stage I would hope searching for the domain from google.com and google.es would return English and Spanish versions respectively.  Are there any particular steps I need take to separate the two. Should I add them both as individual sites in Google's webmaster tools and also should I submit individual site maps for each 'site' or as a whole?   Thanks in advance.


This is Pinter $10.G.5$     Let:      $a \in G$      $\text{ord}(a) = n$      Prove: $\text{ord}(a^m) = \frac{\text{lcm}(m,n)}{m}$      Use $10.G.3$ and $10.G.4$ to prove this.   Here is $10.G.3$:     Let $l$ be the least common multiple of $m$ and $n$. Let $l/m = k$. Explain why $(a^m)^k = e$.   Here is $10.G.4$:     Prove: If $(a^m)^t = e$, then $n$ is a factor of $mt$. (Thus, $mt$ is a   common multiple of $m$ and $n$.)      Conclude that:    $l = mk \leq mt$   OK, let's begin.  By $10.G.3$:  $$ (a^m)^{\text{lcm}(m,n)/m} = e    \tag{5} $$  If $\text{lcm(m,n)}/m$ is the lowest number such that (5) is true, then:  $$ \text{ord}(a^m) = \text{lcm}(m,n)/m    \tag{9} $$  Let's assume that there is a number   $$ q < \text{lcm}(m,n)/m    \tag{7} $$  such that:  $$ (a^m)^q = e \tag{6} $$  By $10.G.4$ with (6):  $$ n \ \big|\ mq $$  $$ l \lt mq $$  $$ \text{lcm}(m,n) \leq mq $$  Isolate q:  $$ \text{lcm}(m,n)/m \leq q    \tag{8} $$  (8) contradicts assumption (7).  So (9) must be true.    That's how I approached it. If anyone notices any issues, I'd be happy to know about them.  Even if it is considered correct, do you feel there is a better way?

Let $G$ be a cyclic group of order $m$ generated by an element $a$.  I want to show that the order of $a^k$ is $m/d$, where $d:=\gcd(k,m)$.  I have a simple proof, but want to make sure I haven't overlooked anything since the other proofs I've seen (such as in Dummit and Foote) look more complicated.    The order of $a^k$ is the cardinality of the set $\{a^{ks}: s \in \mathbb{Z}\}$, which equals the cardinality of the set $\{a^{ks} a^{mt}: s,t \in \mathbb{Z} \}$ since $a^m$ is the identity.  But the set $\{ks+mt: s,t \in \mathbb{Z} \}$ is the set $d \mathbb{Z}$ by the basic properties of integers. So we have that the cardinality of the set is $| \langle a^k \rangle| = |\{1, a^d, a^{2d}, \ldots, a^{m-d} \}| = m/d$.


I'm looking for a simpler formula to calculate this sum:  $$n\cdot 1 + (n-1)\cdot 2 + ... + 2 \cdot  (n-1) + 1\cdot n$$ Alternate representation (but should be equal to the above): $$\sum \limits_{k=1}^{n}(n+1-k)\cdot k$$  Rationale behind requested formula  When  implementing a , the problem of how many substrings exists within a long text, and how many characters will the sum of all these substrings be came up. I found that the number of substrings is:  $$ n + n-1 + n-2 + ... + 2 + 1 = \frac{(n+1)\cdot n}{2} $$  Reasoning for finding number of substrings is that you have $n$ substrings of length $1$, $n-1$ of length $2$, and so on until the end where you only have $1$ substring of length $n$.  Using the same logic, to sum up the length of all these substrings, we arrive at the formula at the top, which I would like to have simplified. That is, multiply the count of substrings with the length of the substring, and sum all these.  I have found the article "", which seems to produce the number I want in the column for c3, with the $n$ enumerated as $rN$. But I can't read out of this article how the column is calculated, and what formula to use.

While thinking about  I found out that this equality might be useful there: $$n\cdot 1 + (n-1)\cdot 2 + \dots + 2\cdot (n-1) + 1\cdot n = \frac{n(n+1)(n+2)}6$$ To rewrite it in a more compact way: $$\sum_{k=1}^n k(n+1-k)=\frac{n(n+1)(n+2)}6.$$  This equality is relatively easy to prove: $$\sum_{k=1}^n k(n+1-k)= (n+1)\sum_{k=1}^n k - \sum_{k=1}^n k^2 = (n+1) \frac{n(n+1)}2 - \frac{n(n+1)(2n+1)}6  = n(n+1) \left(\frac{n+1}2-\frac{2n+1}6\right) = n(n+1)\frac{3(n+1)-(2n+1)}6 =  \frac{n(n+1)(n+2)}6.$$ (We only used the known formulas for the   and the .)   Are there some other nice proofs of this equality? (Induction, combinatorial arguments, visual proofs, ...)     EDIT: Now I found another question which asks about the same identity:  (I have tried to search before posting. But the answers posted here so far gave me some new ideas for good keywords to search which lead me to finding that question.) The questions are, in my opinion, not exact duplicates since the other question asks specifically about combinatorial proofs and my question does not have that restriction. But I agree that this is a very minor distinction. In any case, if you think that one of them should be closed as a duplicate, then you can vote to close. I will refrain from voting to close/reopen on this question. (If one of the two questions is voted to be a duplicate of the other one, they probably cannot be merged, since the summation variables are off by one.)


This has been asked quite a few times before but I want to add something extra hence a new question. Please take a moment before marking it as a duplicate.  I had dual booting with Windows 10 and Ubuntu 15.04 but later thought would replace it with only Ubuntu 16.04. I also had a partition on Windows to store personal data. While creating partitions for fresh Ubuntu installation I accidentally formatted the backup partition instead of the Windows partition.  I am now more keen to find out the list of files that I have lost in the process. I will be more or less okay if I can't recover the data.  From similar answers on data recovery it seems / is the tool of choice. But I want to know how I can effectively run this from a Ubuntu Live USB stick. When I tried to use Photorec I got an error saying - not enough free space available (I chose an external drive with 700GB free space). If I try using Testdisk it takes a lot of time analyzing the drive (1TB HDD deeper search). As of now my main requirement is to store the list of deleted files in a log or text file.  While I read the testdisk documentation if any expert can help me will be appreciated!  NOTE: Before format the partition was in NTFS and after EXT4

About two weeks ago I had a problem with my PC that my brother wrote a question about at .  I still haven't solved the problem, so my PC is unusable now.  Now I think that it would be simpler to re-install both Win7 & Ubuntu than repair them, but there're some data on their partitions. I want to recover this data.  These partitions are not mountable for some reason. I don't know why.  sudo fdisk -l about the problematic partitions:     Device    Boot      Start         End      Blocks   Id  System /dev/sda1            2048     147912703    73955328   83 Linux /dev/sdb2            206848   174079999    86936576    7  HPFS/NTFS/exFAT   And in GParted:      And the error of the mount command:  Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   And the exact same message for /dev/sda1  How can I recover my data from those HDDs?  EDIT     I have tried to specify the type of the drive:  $ sudo mount -t ext4 /dev/sda1 /olddisk mount: wrong fs type, bad option, bad superblock on /dev/sda1,        missing codepage or helper program, or other error        In some cases useful info is found in syslog - try        dmesg | tail  or so $ sudo mount -t ntfs /dev/sdb2 /olddisk NTFS signature is missing. Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   EDIT     sudo ntfsfix /dev/sdb2 returns:  Mounting volume... NTFS signature is missing. FAILED Attempting to correct errors... NTFS signature is missing. FAILED Failed to startup volume: Invalid argument NTFS signature is missing. Trying the alternate boot sector Unrecoverable error Volume is corrupt. You should run chkdsk.


Opening nautilus in administrator mode and then opening terminal in any directory is not functioning. Trying to open it always gives out the error.  I have Ubuntu 17.04 and Unity.

When using natilus as root, open in terminal used to work as using with any user. However, when I press open in terminal when using nautilus as root now, it does nothing.  How to solve it?  The error:  GLib-GObject-CRITICAL **: g_object_set_data: assertion 'G_IS_OBJECT (object)' failed


I'm attempting to solve a question which says that $ f: U \rightarrow \mathbb{C}$ is holomorphic on an open subset $U \subset \mathbb{C}$ and that $f'(a) \neq 0$ for some $a \in U$.  I'm asked to show that $f$ is injective on some disk around $a$ - I thought I had a proof but see now I only showed that $f(z) \neq f(a)$ for all $z$ in the disk with $z \neq a$, which obviously isn't good enough.  The section of the textbook I'm using that this exercise is in has covered the argument principle, Rouche's theorem, the open mapping theorem, and the inverse function theorem - so I assume that I'm supposed to use one of those to do so, but I can't see how.  Your help would be very much appreciated!

I am trying to solve the following problem:     Let $f:U\to V$ be a holomorphic function such that $f'(z)\neq 0$ for all $z\in U$. Show that for all $z_0\in U$, there exists a disc $D_\varepsilon(z_0)\subseteq U$ such that $f:D_\varepsilon(z_0)\to f(D_\varepsilon(z_0))$ is bijective.   Atempt:  I am trying to use Rouche's Theorem, but I am stuck on a particular step. Let $z_0\in U$. Since $f'(z_0)\neq 0$, there is a disc $D_r(z_0)\subseteq U$ such that $$f(z)=f(z_0)+(z-z_0)h(z),\quad\forall z\in D_r(z_0)$$ where $h$ is holomorphic on $D_r(z_0)$ and $h(z)\neq 0$ for all $z\in D_r(z_0)$.   Let $0<\varepsilon<r$ to be defined later and fix $w\in D_\varepsilon(z_0)$. To show that $f$ is injective in $D_\varepsilon(z_0)$ is to show that the function $f(z)-f(w)$ has exactly one zero in $D_\varepsilon(z_0)$. But $$F(z):=(z-z_0)h(z)$$ has exactly one zero in $D_\varepsilon(z_0)$, so we might want to apply Rouche's Theorem with $F$ and $$G(z):=f(z)-f(w)-(z-z_0)h(z)=f(z_0)-f(w)=-(w-z_0)h(w)$$ to conclude that $F$ and $F+G$ have the same number of zeros and hence $f$ is injective. But that means that we need to find $0<\varepsilon<r$ such that $|G(z)|<|F(z)|$ on $\partial D_\varepsilon(z_0)$. That is, $$|w-z_0||h(w)|<|z-z_0||h(z)|$$ for all $w\in D_\varepsilon(z_0)$ and $z\in\partial D_\varepsilon(z_0)$.  Can we find such $\varepsilon>0$?  It seems intuitive since if we expand $h$ in a power series at $z_0$, $h(z)=\sum_{n=0}^\infty a_n(z-z_0)^n$, then $$|w-z_0||h(w)| = |w-z_0|\sum_{n=0}^\infty a_n|w-z_0|^n < |z-z_0|\sum_{n=0}^\infty a_n|z-z_0|^n.$$ for $w\in D_\varepsilon(z_0)$ and $z\in\partial D_\varepsilon(z_0)$. But this is of course not a proof.


I don't understand the motivation of the transpose (or better yet, I haven't even seen one). It feels like just something pulled out of a hat. Thinking about it makes it seem  like a product of being able to write a matrix using either columns or rows 'first'. E.g., when we 'reflect down the diagonal' we are really keeping all the information of our old matrix, just changing rows to columns.   This is much like how $f \text{  from} \{1,2,...,m-1,m\} \times \{1,2,...,n\} \text{ to some field } \mathbf{F}$ is an $m \times n$ matrix, ● if we switch the order of the product, so that we would define: $g \text{ is a map from } \{1,2,...,n\} \times \{1,2,...,m - 1, m\} \text{ to } \mathbf{F}$ ● but allow $f(i,j) = g(j,i)$. Then we somehow get a 'natural' map from the space of $m \times n$ matrices to $n \times m$ matrices.  Is that what transpose is - a 'natural' map for those spaces? What do I even mean by natural here (serious question, I'm not being mysterious)? If I had to guess, it is a linear bijective map? Is that close enough?  Moving away from this, does the transpose have any useful application in Euclidean geometry (other than orthogonal matrices being defined in terms of transposes?).

I can follow the definition of the transpose algebraically, i.e. as a reflection of a matrix across its diagonal, or in terms of dual spaces, but I lack any sort of geometric understanding of the transpose, or even symmetric matrices.  For example, if I have a linear transformation, say on the plane, my intuition is to visualize it as some linear distortion of the plane via scaling and rotation. I do not know how this distortion compares to the distortion that results from applying the transpose, or what one can say if the linear transformation is symmetric. Geometrically, why might we expect orthogonal matrices to be combinations of rotations and reflections?


i need to proof the following formula by math. induction  $ \sum_{k=1}^n k!*k=(n+1)!-1  $   n ∈ N  I dont know how to start and there to end, i would appreciate any help.

I am trying to prove the following by Mathematical Induction:  $$\sum_{i=1}^n i\cdot i! = (n+1)!-1\quad\text{for all integers $n\ge 1$}$$   My proof by Induction follows: First prove $P(1)$ is true,  $$\sum_{i=1}^1 i\cdot i! = (1+1)! - 1$$  Then, for all integers $k >= 1$, if $P(k)$ is true then $P(k+1)$ is also true,  $$ \sum_{i=1}^k i\cdot i! = (k+1)! - 1$$ Then, we must show that $P(k+1)$ is true   $$ \sum_{i=1}^{k+1} i\cdot i! = ((k+1)+1)! - 1\\ \sum_{i=1}^{k+1} i\cdot i! = (k+2)! - 1$$  I am currently struggling with the next step to show that $P(k)$ is equal to $P(k+1)$. How would I finish this prove by induction?


Let $ f : \mathbb{C} \rightarrow \mathbb{C} $   such that $ |f(z)| \leq |sin(z)| $ for   every $ z \in \mathbb{C}$. Prove  that  there  exist $ C \in \mathbb{C}$ such that $|C| \leq 1$   such that $ f(z) = C sin z $ for  every $ z \in \mathbb{C}$. How  to  proceed?

Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.  Half an hour ago I asked the same question for $|f(z)|\leq |z^2-1|$  but this time I cannot say something like $$|f(z)|\leq M|z|^m$$ so I don't know how to start. The problem is that $$ \sin(z) = \frac{e^{iz}-e^{-iz}}{2i} $$ gets really large if $z$ gets large.


I am a beginner in this of neural networks and automatic learning and I understand that the network learns training data, but I do not understand what the validation data are.  Validation data is a set of training data?  Can you give me an example of training data vs validation data

I found this confusing when I use the neural network toolbox in Matlab. It divided the raw data set into three parts:   training set validation set test set   I notice in many training or learning algorithm, the data is often divided into 2 parts, the training set and the test set.  My questions are:   what is the difference between validation set and test set?  Is the validation set really specific to neural network? Or it is optional. To go further, is there a difference between validation and testing in context of machine learning?


Consider a body of mass $m$ on a smooth inclined plane with the normal force and weight labelled as shown:  Now, usually when the forces are broken into its components, we get an FBD like this:  From this we can obtain the equation: $$ \Sigma F_\perp = 0\quad \implies\quad N = mg\cos(\theta) \tag1$$ However, I tried resolving the forces along the x and y axes and obtained a diagram like this:  But this time I got a different equation: $$ N\cos(\theta) = mg \tag2$$ Clearly, equation (1) and (2) aren't the same. So what am I missing here?

Suppose we are given the free-body diagram above, with a mass on an incline at an angle $\theta$. If my coordinate axes are taken to be the regular $x-y$ plane rotated an angle of $\theta$ (i.e. the x axis is parallel to the direction of $mg \sin \theta$ and the $y$ axis is parallel to $mg \cos \theta$), then if there is no vertical motion, $N = mg \cos \theta$. Now suppose I take my coordinate axes to be the $x-y$ plane but NOT rotated by any angle (i.e. the $x$ axis is parallel to the base of the triangle and the $y$ axis is parallel to the adjacent side), then if I want to resolve my weight $mg$ in the direction of $N$, wouldn't I need to make it $\frac{mg}{\cos \theta}$? (since in this case I would have to find the force whose vertical component is $mg$) If this is the case, no vertical motion would imply that $N = \frac{mg}{\cos \theta}$. Does this mean that $N$ depends on my choice of coordinate axes? I might be making a mistake, but I'd appreciate if someone could point out the mistake in my logic.


I've seen many boads with weird zig-zag shaped tracks just like the one below. Why are they designed like that?

On some PCB designs, specific traces are routed in curious ways. This probably has to do with high frequency design considerations and general signal behavior that I am not familiar with.  Let's take this PCB (somewhere from the web) as an example. It shows part of a PCIe card with SATA routing and DDR2 RAM:    I highlighted 4 areas that qualify as unusual trace layout (from my perspective).   What are those shapes supposed to achieve? How do designers come up with what pattern is required? Another example of wave shaped, antenna like routing. This is fairly rare. But obviously the designer deliberately avoided 45° traces. Why? Curves again and a single "pulse" within the trace. How can this have any significant effect?   So what are the use cases and benefits of this techniques?   I want to be able to take those into consideration when doing future PCB designs.


I have a database containing components with about 20 properties. To find out if an update is needed I want to check if all properties for the two objects, except DateCreated and Id, matches.  If all matches no update, if not, update db.  Component comp_InApp = new Component() {     Id = null,     Description = "Commponent",     Price = 100,     DateCreated = "2019-01-30",     // Twenty more prop };  Component comp_InDb = new Component() {     Id = 1,     Description = "Component",     Price = 100,     DateCreated = "2019-01-01",     // Twenty more prop };  // Check if all properties match, except DateCreated and Id. if (comp_InApp.Description == comp_InDb.Description &&     comp_InApp.Price == comp_InDb.Price     // Twenty more prop     ) {     // Everything up to date. } else {     // Update db. }   This works, but it's not a very clean way with 20 properties. Is there a better way of achieiving the same result in a cleaner way?

This is what I've come up with as a method on a class inherited by many of my other classes. The idea is that it allows the simple comparison between properties of Objects of the same Type.  Now, this does work - but in the interest of improving the quality of my code I thought I'd throw it out for scrutiny. How can it be better/more efficient/etc.?  /// <summary> /// Compare property values (as strings) /// </summary> /// <param name="obj"></param> /// <returns></returns> public bool PropertiesEqual(object comparisonObject) {      Type sourceType = this.GetType();     Type destinationType = comparisonObject.GetType();      if (sourceType == destinationType)     {         PropertyInfo[] sourceProperties = sourceType.GetProperties();         foreach (PropertyInfo pi in sourceProperties)         {             if ((sourceType.GetProperty(pi.Name).GetValue(this, null) == null && destinationType.GetProperty(pi.Name).GetValue(comparisonObject, null) == null))             {                 // if both are null, don't try to compare  (throws exception)             }             else if (!(sourceType.GetProperty(pi.Name).GetValue(this, null).ToString() == destinationType.GetProperty(pi.Name).GetValue(comparisonObject, null).ToString()))             {                 // only need one property to be different to fail Equals.                 return false;             }         }     }     else     {         throw new ArgumentException("Comparison object must be of the same type.","comparisonObject");     }      return true; }


Harem anime and manga has become pretty popular since the 90s. The first harem anime I saw was Tenchi, but I think that studio might've had an earlier, similar show. I think the definition of a harem anime or manga might be a bit subjective, so I will try to be specific here.  To me, a harem anime or manga is one where multiple female characters surround a male lead.   At least two must be attracted to him.  The female characters who are attracted to the lead must appear regularly.  What is the first anime or manga that fits this description?

Harem is genre in Anime and Manga involving a Male protagonist surrounded by girls who have feelings for him  Harem is a popular genre in the anime/manga industry but what are the origins of how it become one of Anime and Mangas popular genres?


How to use the fact that $f:E\to F$ is an homeomorphism, if $cl(A)=E$ then $ cl(f(A)) =F $  I know that f is continuous then $f(cl(A))\subset cl(f(A))$ but how to continue? and where is used the fact that $f^{-1}$ is continuous?   thank you

Let $(X,T_1),\,(Y,T_2)$ be topological spaces and $H$ be a homeomorphism from $X \to Y$. If $C$ is a dense subset of $X$, is $H(C)$ necessarily dense in the $Y$?  I thank you in advance.


As very first task in our analysis I class we got the following task which gives (only) 1 of 16 points. I add the points in order to calculate the needed effort to solve this task...      So let $n,m\in\mathbb{N}$ and $a_n:=\sqrt[n]{b_1^n+...+b_m^n}$, with $b_i\geq 0$ and $i=(1,...,m)$ We have to prove if this sequence converges and determine the limit (by using $\epsilon$ definition).     After running a simple R simulation I found out, that this sequence seems to converge against m.     As I have learned so far, the first step is to determine an $N\in\mathbb{N}$ so that $\forall n\in\mathbb{N}, n\geq N : |a_n-m|<\epsilon$, but while searching for that $N$ I began to struggle. $|a_n-m|=|\sqrt[n]{b_1^n+...+b_m^n}-m| < \epsilon \Leftrightarrow ... \Leftrightarrow b_1^n+...b_m^n<(\epsilon+m)^n$. After some research I found, that the LHS can be expressed by polynomials using . At this point I am afraid to be on the wrong track.     Can somebody give me a hint which respects the limitations (having only 1 lecture and it is the first task regarding sequences)?  The R-Code    m_max = 20 m=seq(1,m_max) sumOfPowers=function(n){sum(m^n)} n_max = 50 n=seq(1,n_max) temp=sapply(n,sumOfPowers) a_n=nthroot(temp,n) print(data.frame(n,temp,a_n))

Let $m\in \mathbb{N}$ and $c_1,c_2,\ldots,c_m \in \mathbb{R}_+$. Show that $$\lim_{n\rightarrow \infty} \sqrt[n]{c_1^n+c_2^n+\ldots+c_m^n} = \max\{c_1,c_2,\ldots,c_m\}$$  My attempt: Since $$\lim_{n\rightarrow \infty} \sqrt[n]{c_1^n+c_2^n+\ldots+c_m^n} \leq \lim_{n\rightarrow \infty}\sqrt[n]{\max\{c_1,c_2,\ldots,c_m\}} = \lim_{n\rightarrow \infty} \sqrt[n]{n}\sqrt[n]{\max\{c_1,c_2,\ldots,c_m\}}=\lim_{n \rightarrow \infty} \max\{\sqrt[n]{c_1^n},\sqrt[n]{c_2^n},\ldots,\sqrt[n]{c_m^n}\}=\lim_{n \rightarrow \infty}\max\{c_1,c_2,\ldots,c_m\}=\max\{c_1,c_2,\ldots,c_m\}$$  it follows that $\lim_{n\rightarrow \infty} \sqrt[n]{c_1^n+c_2^n+\ldots+c_m^n}$ is bounded, but I don't think it's monotonically decreasing, at least I can't prove this. Can anybody tell me whether the approach I have chosen is a good one, whether what I have done is correct and how to finish the proof?


I have a question about the use of Cloudflare Flexible SSL and the settings in Google Search Console.   Say I use Flexible SSL on my website example.com. I have wrote a redirect from http to https in my .htaccess so every request on http://example.com redirects to https://example.com.  What do I need to register on Search Console? Right now I have registered all four possible URLs, meaning http://example.com, https://example.com, http://www.example.com and https://www.example.com.

In my site I'm redirecting everything (http://, http://www., https://) to https://www.example.com.  Google webmaster tools says: Make sure you add both "www" and "non-www" versions for your site. Also, if you use the HTTPS protocol, add those variations as well.  So I've added all the FOUR versions to google webmaster tools. Is this a correct process?


does 'I introduce someone as something' mean 'I introduce someone as I am something' or 'I introduce someone as he is something'?

I come up with the sentence "I don't like him as a pianist, but as a judge" when considering "him" as a pianist. But can this sentence have two meanings when "as a pianist" refer to both "I" and "him"? Or can it only refer to the closer "him"?


I'm on Cent OS 7 and I have installed fresh apache(httpd) server. There is 16 GB memory installed in the server. I created a simple API in PHP at /var/www/html called testAPI.php. PHP code is as bolow. Note that it has 5 second delay in it. <?php        $age = '{"Peter":"Good", "Ben":37, "Joe":43}';        header('Content-Type: application/json');         sleep(5);         echo $age; return; ?>  I did a simple load test with Apache jmeter and I couldn't go beyond 100 TPS. How can I configure the webserver to serve 2000 TPS with reasonable delay profile?

This is a  about capacity planning for web sites. Related:      What are some recommended tools and methods of capacity planning for web sites and web-applications? Please feel free to describe different tools and techniques for different web-servers, frameworks, etc., as well as best-practices that apply to web servers in general.


I'm trying to prove the inequality below using induction: $\dfrac{2^{2n}}{n+1} < \dfrac{(2n)!}{(n!)^2} \,\, (n > 1)$ The base case is ok, but I'm not able to see how I can proceed in the induction step. I'm reaching a dead end, either multiplying by 2 or adding $\dfrac {1} {k + 1}$ to both sides of the inequality. Any tips?

I would like to prove by induction the following inequality:  $\frac{4^n}{n+1} < \binom{2n}{n}$, for all natural numbers n > 1.  Any hints?


The equation is the following:  $$ {d^2 x(t) \over dt^2} = {k \over (x(t))^2} .$$ I used the software Maple to try and solve it, it can't. I did some research and this equation is obviously second order, and maybe of type "missing x", even if I don't know what that really means. I also found this substitution: $$ v = {d x(t) \over dt} $$ but nothing really came out of it. Also, none of my teachers are able to solve it, I have asked three of them. This equation comes the Newton's law of gravitation.

I conceived the following second order nonlinear ordinary differential equation:  $$\frac{d^2y(x)}{dx^2}=\frac{k}{(y(x))^2}$$  I can tell it's nonlinear because of the $\frac{k}{(y(x))^2}$ term and second order because of the second order derivative.   Also, I did some research and concluded that it is of the type "missing x". In this category we use the relation,  :  $$\frac{d^2y(x)}{dx^2}=v\frac{dv}{dy} (1)$$  by making v equal to $$\frac{dy(x)}{dx} (2)$$ and then, using the chain rule, simplify to obtain equation (1).  Despite all that, I can't seem to find a logical solution to my ODE. I would appreciate any help or clue! Thanks!


I am interested in adding a continuous color ramp legend with numerical labels like the following example to place on the layout view of arcmap:    I am quite new to arcMap so I'm not sure how I can do this. On the symbology tab, I used graduated colors with a preset color ramp from ArcMap. There are 60 classes, so when I insert a color ramp, the result becomes this:

I'm using ArcMap 10.3.1.   Is there a way to show, on the legend, just the color ramp as a single patch instead of with each group of values?   I don't really need to show those values on the legend.  This is what it looks like now:    I would prefer to have it look like the ramp in the properties window and somehow note that the green area is less concern, while red is more concern.   Such as this:


Any suggestions for a field Isomorphism $f:\mathbb{C} \rightarrow \mathbb{C}$ other than the identity map?

I read about so called "wild" automorphisms of the field of complex numbers (i.e. not the identity nor the complex conjugation). I suppose they must be rather weird and I wonder whether someone could explain in the simplest possible way (please) how I could imagine such wild automorphisms.  E.g. I suppose they are completely discontinuous. E.g. are the real rational numbers fixed or any other set of complex numbers? Can such an automorphism be pictured in a model?


How can I select which section I want to compile and which section I do not want to compile? I am using XeLatex to compile the document. Sometimes the text in each section is long and I don't want to comment and uncomment all of the text inside the section every time I run the script. Every time I am running, need to compile different set of sections. It would be easier to have an easy way to do it. Or just comment/uncomment a particular section line instead of comment/uncommenting the whole text inside.  The question , suggests to break the file in to multiple files and then run the main script (within the main script one can choose the desirable file(s) to compile). However, I am interested to know is it possible to do it within a single file?  \documentclass[a4paper,10pt]{article}  \usepackage{xunicode,xltxtra,url,parskip} \usepackage[usenames,dvipsnames]{xcolor}  \usepackage[big]{layaureo} \usepackage{hyperref}  \definecolor{linkcolour}{rgb}{0,0.2,0.6}  \hypersetup{colorlinks,breaklinks,urlcolor=linkcolour,linkcolor=linkcolour}  \usepackage{titlesec}  \titleformat{\section}{\Large\scshape\raggedright}{}{0em}{}[\titlerule] \titlespacing{\section}{0pt}{3pt}{3pt}   \usepackage{tabularx}             \begin{document}  \pagestyle{empty}   \section{Personal Data}  some text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text here   \section{Education} some text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text here  \section{Work Experience}  some text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text here   \section{Hobbies} some text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text here  \section{Interests} some text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text here  \section{Skills} some text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text here  \section{MISC} some text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text heresome text here  \end{document}

I see that there a number of questions (, , , , ) on best practices, none of them answer the issue I am going to talk about.  We all need to prepare large documents (or slides) from time-to-time. And once you have reached a certain number of pages, you find that compiling the whole document takes a substantial time, which you need to do to check that the part you have written is error free, specially if it contains a number of images.   To circumvent the situation, I have used the following practices over years to keep compile time at minimum.   Divide the document in to many chapters: The chapters are put in separate files. Only the one I am working one is uncommented.  \documentclass{book}  \begin{document}  %\input {chapterone.tex} \input {chaptertwo.tex} %\input {chapterthree.tex} %\input {chapterfour.tex}  \end{document}    The above technique can also be used for \include.   Keep a preamble replica of the main file in a temporary file (build file): I use this technique when I am preparing a presentation with many slides, say a hundred. Prepare a main file, copy it to another build file. Delete everything between  \begin{document} and \end{document} in the build file. Prepare a slide (or a group of slides) in the build file. Cut and paste the contents between \begin{document} and \end{document} in the build file to relevant location in the main file only when satisfied with the output (image locations, overfull boxes etc.)     We can hear your inputs about the best practices you practice when a you are preparing a document or presentation from scratch.    Now, I have failed to find a good answer in the case when you have finished the whole document or presentation and now you need tweaking the small things, may be edit a text here, add an image there. What will be your best practice?  Perhaps, again keeping only one chapter uncommented will be usable here. But what about large presentations? May be adding a \end{document} just after the point-of-change will be beneficial, but only if you can put that before midpoint of the file.  Commenting a part of the file will also work, but that is error-prone, at least for me.


I have a Nikon d3400 with kit lens 18-55 mm af-p DX. What is the right camera settings for northern lights photography?

A friend has been kind enough to lend me a DSLR for a few months.  It's my first foray into DSLR photography, or indeed any kind of photography beyond simply aiming my Canon IXUS at something and clicking the button.    Over the last few weeks, I've been busy studying, practising and trying to learn as much as possible ahead of a planned trip to Norway where I hope to see, and get some photos of, the Aurora Borealis.  I currently have:   Canon Rebel Xsi (450D) Canon 50mm f/1.4 L  Canon 18-55m kit lens Aluminium full height tripod with ball head Cable release Spare battery & memory cards   I'm prepared to spend the night wrapped up outdoors, in the hope that they will make an appearance. I'd like some advice on how to get the most out of this kit for the trip:   How should I go about setting up to get pics of the Aurora?  How might I achieve optimum focus? From what I've read, I'll need to use the tripod and cable release, with IS turned off, on continuous shooting mode with long exposure times. But I'd like some more specific tips in terms of which aperture and ISO settings might work best? Should I use one of the lenses above, or would it be worthwhile renting a better, wide angle lens; if so, which would you recommend?


The problem:  Construct an explicit bijection $f:[0,1] \to (0,1]$, where $[0,1]$ is the closed interval in $\mathbb R$ and $(0,1]$ is half open.  My Thoughts:  I imagine that I am to use the fact that there is an injection $\mathbb N \to [0,1]$ whose image contains $\{0\}$ and consider the fact that a set $X$ is infinite iff it contains a proper subset $S \subset X$ with $\lvert S \rvert = \lvert X \rvert$ (because we did something similar in class). I also have a part of proof that we did in class that I believe is supposed to help with this problem; it states the following: Start with an injection $g: \mathbb N \to X$ and then define a set $S=F(X)$ where $F$ is an injective (but NOT surjective) function $X \to X$ with $F(x) = x$ if $x \notin \text{image}(g)$ and $f(g(k)) = g(2k)$ if $x=g(k) \in \text{image}(g)$. Honestly, I'm having a lot of trouble even following this proof, so I could be wrong. Anyway, any help here would be appreciated. I feel really lost on this one. Thanks!

How to define a bijection between $(0,1)$ and $(0,1]$?   Or any other open and closed intervals?   If the intervals are both open like $(-1,2)\text{ and }(-5,4)$ I do a cheap trick (don't know if that's how you're supposed to do it): I make a function $f : (-1, 2)\rightarrow (-5, 4)$ of the form $f(x)=mx+b$ by \begin{align*} -5 = f(-1) &= m(-1)+b \\ 4 = f(2) &= m(2) + b \end{align*} Solving for $m$ and $b$ I find $m=3\text{ and }b=-2$ so then $f(x)=3x-2.$  Then I show that $f$ is a bijection by showing that it is injective and surjective.


I have problem removing duplicate values from an array I have the following:   $input = explode(' ', $term_single->name); $result = array_unique($input); print_r($result);   I got the same value twice   Array ( [0] => QA ) Array ( [0] => QA )   What am I missing?

How can I remove duplicate values from an array in PHP?


I have two groups which are about their departments in college (For example, group1=faculty of x, group2=faculty of y). However, the size of the group1 is 12 and size of the group2 is 99. There is a big gap between the group size. My intention is to test their perceptions based on their departmen. Is it appropriate to compare them? I will use independent t-test.

I have two independent groups: from one I have drawn a sample of size less than 30 due to its small population, while the second group has sample size 100.  Is it appropriate to use an independent samples t-test in this case?


Are there any solutions for the diophantine equation $x^2+y^2=n$ ?  For $n \in \mathbb{P} \wedge n \equiv1\pmod4$  solutions are widely known.  Can we generalize a bit?

Problem   Let $n = p_1.p_2.p_3 \cdots p_k.m^2$, where $p_1, p_2, p_3 \cdots p_k$ are distinct primes. Prove that n is sum of two squares if and only if $p_i$ is either 2 or $p_i \equiv 1 \pmod{4}$   For $p_i = 2$ , this is trivial case since $2m^2 = m^2 + m^2$. For $p_i \equiv 1 \pmod{4}$, I tried to use the fact that the product of a number of the form $4k + 1$ is also in this form. So I come up with: $$n = (4k + 1) \cdot m^2 = 4km^2 + m^2$$ Apparently, $m^2$ is a square, but I could not figure out how to prove $4km^2$ is a square, since k is in unknown form. Any idea?    Thanks,


Let's say some US company declares the ex-divided-date as Sep 30, 2020. Now at which time exactly does this ex-date start? When this stock is traded in stock exchanges world wide, is the UTC time taken? So UTC Sep 30. 2020 00:00:01 AM is the first second of the ex-date?

Is the ex-dividend date linked to the time zone of the market it is bought at? Let's imagine an American firms stock traded at NASDAQ and a German market, the ex-Dividend day being the 1st February. This announcement is made on their American website, without specifying a time zone. I want to get the dividend.  1) The German market opens at 8am on February 1st local time, which would be 2am on February 1st New York time. I sell my shares at 8am. So the trade would have been made on ex-dividend day, with NASDAQ being closed. Will I get the dividend?  2) Let's imagine a bigger time difference, where the market I sell the stock is 8am in the morning of February 1st local time, but New York Time is sill 11pm on January 31. Will I get the dividend?   Or phrased differently, is the Ex-dividend linked to a date, independent of time zones, or is it linked to a local time zone?


I am looking to install .deb files that have been encrypted and then decrypted. During this process the names of the original files have been dropped and instead are a temporary gibberish value. I can install using 'dpkg -i' without issue but I was looking to use 'apt-get install' to avoid having to perform any cleanup for dependency issues. I did not see any options for apt-get to allow this type of functionality. Does anyone know if this is possible?  I.E - original package:  something-something-version-amd64.deb       decrypted package: blahblah    'dpkg -i blahblah' - success   'apt-get install blahblah' - unrecognized file   Thanks!

Say, I have foo-1.2.3.deb which depends on perl and python, however, running command:  dpkg -i ./foo-1.2.3.deb   won't install these dependencies. So I must apt-get install perl python by hand.  How to make dpkg -i install these dependencies for me automatically?


I charge my phone using my PC all the time, and it's been only a week that since I bought my iPhone 5. Now I can't charge my phone with my PC.  What could be the problem thats causing my phone to not charge while connected to my PC?  The USB charger is new.

On a Windows 8 machine, I've connected an iPhone 4s. Windows makes a audible chime for 'device connected', but doesn't allow charging in any USB port.  iTunes isn't installed, and cannot be installed at this time under corporate policy.  The iPhone shows as a generic device / toaster under Control Panel's Devices as below. The iPhone does NOT show as charging.  Is there a driver to install to ensure the iPhone is detected and can charge via USB without installing iTunes?  I've tried:   forcing Windows Update


This question is prompted by the Eldritch Claw Tattoo which can allow your attacks to "reach a target up to 15 feet away from you..." and specifically relates to Attacks of Opportunity.  You can make an opportunity Attack when a Hostile creature that you can see moves out of your reach.  In a situation where I have a Glaive, and have activated the Eldritch Claw Tattoo, do I have 3 different reaches?  Unarmed Strike (5 feet) Glaive (10 feet) Glaive & Unarmed Strike (15 feet, thanks to the Eldritch Claw Tattoo)  Or, does the Eldritch Claw Tattoo's effect make all of those attacks' reach only 15 feet? Is this accurate, and can I make an Attack of Opportunity with any of them, where someone leaves that specific attack's reach?

Assume I wield a Whip in one hand and a dagger in the other.  If a creature moves from 5ft to 10ft it has technically moved out of my reach (dagger), but at the same time it is still inside my reach (whip). When does it provoke opportunity attacks from me?  I am fully aware that this would not enable me to make off-hand attacks since the whip is not a light weapon, just to cut that issue out of the question.


There are plenty of people who still raise this concern, Since I too use such editors, I’ve compiled this list of best LaTex editors  with good facilities and features. Here are the top ones that I could recommend:  TEXMAKER  Website:   TEXSTUDIO  Website:   LYX  Website:   TEXWORKS  Website:   TEXNIC  Website:   LED  Website:  Source:  I hope this information helps you. Cheers!!

What editors/IDEs are available for easing the process of writing TeX/LaTeX documents? Please state some useful features like code completion, spell checking, building final DVI or PDF files, etc.  This question is undergoing a systematic refurbishment, see  on Meta. If you’d like to see another editor feature covered here or to take care of an editor that’s not covered yet, share your ideas in that meta question.  List of editors Links to answers.


In Outlook, How can I list cancelled/declined meetings?   I happen to use Outlook 2010 at the moment.

I accidentally clicked "decline" on an Outlook invitation and now I can't reverse it -- the event has completely disappeared from my calendar!  How can I get back the event invitation and change my "Decline" to "Accept" or "tentative"?


I know it has something to do with triangle medians and pythagorean theorem since there's a 2/3 and a square root in there, but I don't exactly know why.

How do I calculate the height of a regular tetrahedron having side length $1$ ?  Just to be completely clear, by height I mean if you placed the shape on a table, how high up would the highest point be from the table?


I'm picturing the  formation, where soldiers were arranged in rows and the men in Row B or even Row C could attack the enemy by thrusting their spears between the soldiers in Row A. Can you do that with a Reach weapon in DnD 5e? Attack an enemy even though there's an ally (or even a row of allies) directly between you and them?

You can move through an ally's position (as difficult terrain), but can you attack through it at no cost?   If you have 10' reach, but there is an ally between you and the target, does the target get the +2 cover or is that ignored as friendly ally who could move away?


While Wave says Grand Chariot is stronger, Incursio(Tatsumi) has more abilities, from what we see, and has the ability to adapt to any weather or situation, because of the beast used to make it. Its user, Tatsumi, also relies on his personal skill most of the time, Incursio there to just bail him out when he is in serious trouble, while Wave relies on Grand Chariot more than anything. But I could be wrong, so let me know your opinions.

Wave states with great confidence that Incursio is weaker than Grand Chariot, because Incursio was a prototype for Grand Chariot, etc.  The early clashes between Wave and Tatsumi can lead the viewer to such conclusion, but Incursio's has the ability to evolve (from the beast it was made of), while Grand Chariot doesn't.  If you watched to the finale, we can see that      Tatsumi causes Incursio to evolve so much during the fight against Shikoutazer that it even gains the ability to fly. While it is enough to defeat the emperor, unfortunately not enough to save Tatsumi's life.   Considering this, I don't think that Incursio was the weaker one. Is it so?


I have several layers (shapefiles) that have data in groups. Each group has a distinct group name. I am trying to number each item in the layer based on its distinct group name.     So, for each group I want to add a serial number for each object. For example group "broadst" = 1....7, group "crew" = 1......6 and so on.     Manually this can be done by sorting and selecting each group and adding a sequential number using rownumber.  But I have a large dataset and it will take a long time. Is there a plugin or would it be possible to use the field calculator using some form distinct filter based on group name?

Is there a way to fill the table with a row number so that count will restart as new group (identified by a separate column) starts? As a result, "row number" column will restart the count when the new attribute value for a group is found, and will produce row number (1,2,3 etc.) record within this group.  seems to answer my question, but SQL in QGIS does not allow such statements (DENSE_RANK) (or it does but I don't know how?).


and I dont know how to get back. Actually I intended to cut the sphere into half by box selecting one half. Accidentely I pressed CMD B instead of just B. Redo not possible, the rest of the model is not visible anymore.

When looking at my objects in 3d view I'm seeing a gray cone that seems to be hiding other objects.   Can anyone help me turn this off and explain what it is please.  Screenshots attached.


How to record the output of a bash script from terminal without suppressing the terminal output like $ ./bash-script.sh >> terminal.txt ? and I want to record the resulting output to text and keep it in the terminal as well.

How do I save the output of a command to a file?  Is there a way without using any software? I would like to know how.


I would like the "AB" subscripts in my formula to be vertically aligned with each other--ideally, by adjusting the second subscript to match the current placement of the first.   MWE:  \documentclass{article}  \usepackage{braket} \begin{document}     \begin{equation}         \rho_{AB}=\ket{0}_{AB}\otimes_{AB}\bra{0}     \end{equation} \end{document}   I have attempted to use \vphantom to remedy this in the following way:  \documentclass{article}  \usepackage{braket} \begin{document}     \begin{equation}         \rho_{AB}=\ket{0}_{AB}\otimes\vphantom{\ket{0}}_{AB}\bra{0}     \end{equation} \end{document}   However, this did not produce a discernible difference, so I'm stumped at the moment.  Proposal for another MWE (Manuel Kuehner)  Even with a full \phantom the vertical position changes...  \documentclass{article}  \usepackage{braket} \begin{document}     \begin{equation}         \rho_{AB} = \ket{0}_{AB} \otimes_{AB} \bra{0}     \end{equation}     \begin{equation}         \rho_{AB} = \ket{0}_{AB} \otimes\ket{0}_{AB} \bra{0}     \end{equation}     \begin{equation}         \rho_{AB} = \ket{0}_{AB} \otimes\phantom{\ket{0}}_{AB} \bra{0}     \end{equation}         \end{document}

The superscripts position is exactly the same for these two statements:  \vphantom{\int}^S and {}^S  How can I get the superscript higher up?  Edit  The \intis just an example. Here is another one: \vphantom{)}^S and )^S.


Can anyone explain what is meant by recursive locking in Java?   Many thanks

POSIX allows mutexes to be recursive. That means the same thread can lock the same mutex twice and won't deadlock. Of course it also needs to unlock it twice, otherwise no other thread can obtain the mutex. Not all systems supporting pthreads also support recursive mutexes, but if they want to be .  Other APIs (more high level APIs) also usually offer mutexes, often called Locks. Some systems/languages (e.g. Cocoa Objective-C) offer both, recursive and non recursive mutexes. Some languages also only offer one or the other one. E.g. in Java mutexes are always recursive (the same thread may twice "synchronize" on the same object). Depending on what other thread functionality they offer, not having recursive mutexes might be no problem, as they can easily be written yourself (I already implemented recursive mutexes myself on the basis of more simple mutex/condition operations).  What I don't really understand: What are non-recursive mutexes good for? Why would I want to have a thread deadlock if it locks the same mutex twice? Even high level languages that could avoid that (e.g. testing if this will deadlock and throwing an exception if it does) usually don't do that. They will let the thread deadlock instead.  Is this only for cases, where I accidentally lock it twice and only unlock it once and in case of a recursive mutex, it would be harder to find the problem, so instead I have it deadlock immediately to see where the incorrect lock appears? But couldn't I do the same with having a lock counter returned when unlocking and in a situation, where I'm sure I released the last lock and the counter is not zero, I can throw an exception or log the problem? Or is there any other, more useful use-case of non recursive mutexes that I fail to see? Or is it maybe just performance, as a non-recursive mutex can be slightly faster than a recursive one? However, I tested this and the difference is really not that big.


The mysql table record:  definitionID = 1, term = alert('Hello World'); , definition = Javascript pop-up box   I am having some issues querying the definition field from the above example. Everything has already been through mysqli_real_escape_string as part of its form input method/validation.  The term is assigned to a variable earlier in my PHP. I think this worked fine.  //So, $term = alert('Hello World');  $definitionQuery="SELECT definition FROM definitionTable WHERE term='".$term."'"; $definitionArray = mysqli_query($dbc,$definitionQuery); $row = mysqli_fetch_array($definitionArray); $answer = $row['definition'];  /*In addition, document.getElementByID('test'); as a term doesn't work either but the following do. Gotta be something to do with single quotes but cant figure out what. Whilst the quotes are in a variable and not processed by PHP, might they be processed in mysql?*/  <script></script> or, document.getElementByID("DOUBLE");   The PHP error is:  mysqli_fetch_array() expects parameter 1 to be mysqli_result, boolean given

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?


My 2014 MacBook Air just recently updated to macOS Catalina 10.15 today. After the update I did a routine check on what's new & in the Disk Utility app something caught my eye for the volumes... there are now have two instead of the usual one. Usually I would only see "Macintosh HD", but now there's "Macintosh HD - data" as well:    Why exactly do I have a "Macintosh HD" & a "Macintosh HD - Data" as volumes in Disk Utility?

I created a second bootable volume called "Beta" in order to install the macOS Catalina beta. I successfully installed and booted to this new volume, but when I returned to the first volume (which has macOS Mojave installed) I was surprised to see a third volume.    The "Beta - Data" seems to have been created during the installation process. This third volume is also not visible when I return to the "Beta" boot volume, only having the "Beta" and "Panther" volumes. The "Beta" volume when booted into it also seems to have the combined size of the "Beta" and "Beta - Data" volumes.   I originally created the "Beta" volume with a quota of 256GB as well, but that quota is gone from that volume and the "Beta - Data" volume seems to have inherited it.  The "Beta" volume seems to contain the system install; containing the home, Library, System and Users directories (though the Users directory only contains the Shared directory, and not the home folder for the user I created). While the "Beta - Data" volume has the user-specific data; having the Device, private and Users directories (with the home folder for the user I created within, as well as another Shared directory).  I have never tried dual booting on a Mac before, so this could be more common than I am aware of, but I couldn't seem to find any information on why this would happen or where this volume came from. Could this be a new "feature" (or bug) from macOS Catalina? Or did I just do something wrong when I created the new volume?


After pressing the log in button it would said updating minecraft and after that it said Failed to launch Fatal error occurred (4): null I have forced an update and updated Java but it still doesn't work. Not even the demo works.

Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved.


Till 16.04, when I press Print Screen, we used to get the "Save to" option which enabled us to save the screenshot into a desired folder. Now, with 18.04, pressing Print Screen saves the screenshot directly in the Pictures folder. I am unable to find a way to save the screenshot into the desired folder.  I have tried binding Print Screen with gnome-screenshot -i. However, this option currently requires me to go through two steps (press Print Screen and then again press "Take screenshot" button) instead of a single step (just Print Screen) to get the "Save to" dialogue box.   Any help is appreciated in this regard.

I take screenshots a lot. I usually take screenshot of an area, I then recheck if I have the desired area and then copy it to clipboard.  I want to change this behaviour so that immediately upon  pressing Shift+PrntScr the screen capture application allows me to select an area, and immediately afterwards it provides me with the option to save to a particular location or clipboard.  I want Shift+PrntScr to bring up a pop-up screen like this:


What happens to the singularity within a black hole when a black hole evaporates? If there is a point in space which is both infinitely dense and small, do they simply evaporate as well?

Does it just vanish into space leaving nothing behind or does it expel some material?    Also, talking more about black holes, as far as I understand the term "temperature", it is defined by the amount of kinetic energy of the particles of a body and from what I have read, there are no particles inside a black hole, I know that you can find the temperature of a black hole by analyzing its Hawking radiation but I cant really understand how the term "temperature" can be applied to a black hole. Does it mean that whatever is that it is inside a black hole has kinetic energy? Have physicist already experienced the death of any regular black hole (by regular I mean space-sized black holes not micro ones created in labs)? Also, where is the Hawking radiation form? Because if it is released by the black hole I bet it must have formed outside the event horizon, but how exactly?


Sorry to throw a question with such little information.  Hardware:  Overall - 500S-14ISK Laptop (ideapad)  Wifi Card - I'm very keen to find out but the manufacturer seemed to let out little information, so I'm keen to find out what is it exactly. I think it is Broadcom. here's a link to its windows driver   Software: fresh install of Ubuntu 16.04 LTS  I'm taking notes from  but not sure how to start - total newbie here.  I'm also trying to use  but lspci -nn actually showing a network controller as Qualcomm Atheros Device, with no wireless device insight it has [168c:0042] (rev 30) labeled.  So appreciate any help I can get and I'm more than happy to post any diagnostics here.  Thanks!

I bought an Acer laptop and installed Ubuntu 14.04LTS but WiFi drivers are not available for it. So I am trying to install a windows driver using wifidocs/driver/ndiswrapper.  On doing lspci -vvnn, it gives:  Network controller ［0280: Qualcomm Atheros Device ［168c:0042］ (rev 30)   Then I also disabled the atheros drivers. Using lspci and lspci -n, I can say PCI id is 168c:0042. But Acer website has three atheros drivers. I could not figure out which one to download but downloaded one on a windows PC and pasted the zip file on my desktop then unzipped it from the terminal using unzip <filename>.zip. The page says you have to go to control panel system hardware and all that on the windows system. I did not do it. Windows computer not being mine, I am afraid I should not install any additional driver on it. After unzipping it has one .inx file and one .bin file but no .sys file. I don't know whether I am completely right till here or have I missed something? And if I am right then how to proceed from here? I also made a new directory and copied the unzipped .inx and .bin files in it. Then in that directory I ran the ndiswrapper -i <filename>.inf but it says ndiswrapper not installed and when I do sudo apt-get install ndiswrapper-common, I get the reply that ndiswrapper-common is already the latest version. What to do? here is my dmesg | grep ath10k result  [   7.882758] ath10k_pci 0000:03:00.0: pci irq msi-x interrupts 8 irq_mode 0 reset_mode 0 [    8.190016] ath10k_pci 0000:03:00.0: Direct firmware load for ath10k/cal-pci-0000:03:00.0.bin failed with error -2 [    8.334587] ath10k_pci 0000:03:00.0: Direct firmware load for ath10k/QCA9377/hw1.0/board-2.bin failed with error -2 [   10.140677] ath10k_pci 0000:03:00.0: qca9377 hw1.0 (0x05020000, 0x003820ff sub 105b:e09a) fw WLAN.TF.1.0-00267-1 fwapi 5 bdapi 1 htt-ver 3.1 wmi-op 4 htt-op 3 cal otp max-sta 32 raw 0 hwcrypto 1 features ignore-otp [   10.140682] ath10k_pci 0000:03:00.0: debug 0 debugfs 0 tracing 0 dfs 0 testmode 0 Here is the output of lspci -nnk | grep -iA2 net  02:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [10ec:8168] (rev 15)     Subsystem: Acer Incorporated [ALI] Device [1025:098a]     Kernel driver in use: r8169 03:00.0 Network controller [0280]: Qualcomm Atheros Device [168c:0042] (rev 30)     Subsystem: Foxconn International, Inc. Device [105b:e09a]     Kernel driver in use: ath10k_pci


The basic question is "why light travels at slower speed in a medium?" I mean what's the full second quantization quantum mechanical explanation of the phenomenon? I'm looking for the explicit calculations on this, not only the "by words" explanation. I'm interested on visible light, so eV energy scale. I've often heard that "the photon receives an effective mass" and "Maxwell equation modifies in the medium" and I indeed agree with theese kind of explanation, but the single little "simple" building blocks of the phenomenon remains obsure in my opinion. How we pass from the single photon view to a medium exitation? What's the basic QED phenomenon? Compton scatter? By who?  The effective mass raises more questions than answers: How the transition is made? Do we use Proca's equation inside the medium? In this case should be the longitudinal polarization of the quasiparticle, right?   I have also some related questions, in random order:   Does exist "simple" solvable models? maybe for diluite gas, perfect cubic lattice solid or something else What phenomenology does them reproduce? on which hypothesis? Does it depend on a thermodynamic limit of the medium (gas, liquid, solid)? Fixing enviromental conditions (temperature, pressure etc.), does single photons interact always in the same way, if not absorbed or diffused? If not, why? and how much? Does exists books or ref on such argument?   Thank you!

As I learned today in school, my teacher told me that when light enters a glass slab it slows down due to the change in density and it speeds up as it goes out of the glass slab. This causes a lateral shift and the light emerges out from the point different than that from where it should have actually emerged from.  Okay so what I mean to ask is, when light enters point A on glass slab and emerges from point C why does the light speed up? Where does it get the energy it has lost when it entered the glass slab?  P.S.: Also, if I place a very very very large glass slab and make a beam of light pass through it will the light never come out as all the energy was lost in place of heat?


In Python everything is object, but some methods are not called as attributes, but you pass them the instance of object as parameter. For instance:  function len() expects object - len(str) seems logical, because it clearly shows that strings are immutable.  But why then str.find() is called as attribute of str?  I thought that it is because len excepts more then just one type of object, but this could be solved with polymorphism, right?  Is there any reason for some functions to be called as func(obj) and some as obj.func()?

I know that python has a len() function that is used to determine the size of a string, but I was wondering why it's not a method of the string object.  Update  Ok, I realized I was embarrassingly mistaken. __len__() is actually a method of a string object. It just seems weird to see object oriented code in Python using the len function on string objects. Furthermore, it's also weird to see __len__ as the name instead of just len.


I am still pretty new to Stack Exchange. I have posted a couple of questions that have not gotten very good answers. If I post an question on one site, and it does not a good solution, is it acceptable to post a duplicate question on another community?  Example:  I posted an issue I was having with the OS X terminal and finding the right port on Stack Overflow. I got a few answers, but nothing that good. The problem was with an Arduino port, so is it acceptable to post a duplicate answer on the  or  since they would know more about Arduinos and terminal issues?

It is possible to migrate a question from one Stack Exchange site to another by closing, but if I have a question that I think is on-topic for multiple Stack Exchange sites, is it OK to post it on both (multipost)?   For example, I have a question that's earned me the tumbleweed badge on SO and I'm not sure what the best thing to do with it is. It's about a web server so it might be answerable on Server Fault but it's really more of a programming thing, hence the posting the question on Stack Overflow.    Is there any way to make the question visible on multiple sites (crosspost) and then accept the answer wherever it came from?


If $p+q+r=0$, prove that   $$\begin{vmatrix} pa&qb&rc\\ qc&ra&pb\\ rb&pc&qa \end{vmatrix}=pqr\begin{vmatrix} a&b&c\\ c&a&b\\ b&c&a \end{vmatrix}$$  My attempt is as follows:-  Taking $p$ common from first row, $q$ from second row and $r$ from third row  $$pqr\begin{vmatrix} a&\dfrac{qb}{p}&\dfrac{rc}{p}\\ c&\dfrac{ra}{q}&\dfrac{pb}{q}\\ b&\dfrac{pc}{r}&\dfrac{qa}{r} \end{vmatrix}$$  $$pqr\begin{vmatrix} a&\dfrac{-bp-br}{p}&\dfrac{-cp-cq}{p}\\ c&\dfrac{-pa-qa}{q}&\dfrac{-qb-rb}{q}\\ b&\dfrac{-qc-rc}{r}&\dfrac{-pa-ra}{r} \end{vmatrix}$$  $$pqr\begin{vmatrix} a&-b-\dfrac{br}{p}&-c-\dfrac{cq}{p}\\ c&-a-\dfrac{pa}{q}&-b-\dfrac{rb}{q}\\ b&-c-\dfrac{qc}{r}&-a-\dfrac{pa}{r} \end{vmatrix}$$  $$pqr\begin{vmatrix} a&b+\dfrac{br}{p}&c+\dfrac{cq}{p}\\ c&a+\dfrac{pa}{q}&b+\dfrac{rb}{q}\\ b&c+\dfrac{qc}{r}&a+\dfrac{pa}{r} \end{vmatrix}$$  $$pqr\left(\begin{vmatrix} a&b&c\\ c&a&b\\ b&c&a\end{vmatrix}+ \begin{vmatrix} a&\dfrac{br}{p}&c\\ c&\dfrac{pa}{q}&b\\ b&\dfrac{qc}{r}&a\end{vmatrix}+\begin{vmatrix} a&b&\dfrac{cq}{p}\\ c&a&\dfrac{rb}{q}\\ b&c&\dfrac{pa}{r} \end{vmatrix} \right) $$  $$\left(pqr\begin{vmatrix} a&b&c\\ c&a&b\\ b&c&a\end{vmatrix}+ \begin{vmatrix} pa&br&pc\\ qc&pa&qb\\ rb&qc&ra\end{vmatrix}+\begin{vmatrix} pa&pb&cq\\ qc&qa&rb\\ rb&rc&pa \end{vmatrix} \right) $$  Now I am left with two other determinants and their sum should come out zero.  I am getting no way to simplify those determinants, if you open those determinants, expression would be quite large.  Is there any better way to solve this problem?

If $p+q+r=0$, prove that the value of the determinant $$ \Delta= \begin{vmatrix} pa & qb &rc \\  qc & ra &pb\\  rb& pc & qa  \\  \end{vmatrix} =-pqr \begin{vmatrix} a & b &c \\  b & c &a\\  c& a & b  \\  \end{vmatrix}$$  My Try:Since $p+q+r=0$ we have $$a(p+q+r)+b(p+q+r)+c(p+q+r)=0$$ $\implies$ $$(ap+qc+rb)+(qb+ra+pc)+(rc+pb+qa)=0 \tag{1}$$ Now applying $C_1 \to C_1+C_2+C_3$ and then applying $R_1 \to R_1+R_2+R_3$ for $\Delta$ we get $$\Delta=  \begin{vmatrix} 0 & qb &rc \\  qc+ra+pb & ra &pb\\  rb+pc+qa& pc & qa  \\  \end{vmatrix}$$ Any clue here?


I wonder if i try this calculation on scientific calculator, i am getting 6/2(2+1) = 1   and in mobile device, online and normal calculators it gives me,  6/2(2+1) = 9   from my knowledge and what i get taught, first one (answer = 1) was correct... but how normal calculator provide this? i am confused. please clarify..  i searched about this, found something called BODMAS rule was the reason for first one.. is it correct or anything else?

Possible Duplicate:          Sorry if this has already been asked, my searches were fruitless...  There's been a buzz lately about the different results given by two different Casio brand calculators .  It would seem that there's debate on this issue.  The expression is thus:     6 ${\div}$ 2 (1 + 2)   It would appear that the debate is between the scope of the division operator in the equation.  Now, as a software developer, I'm accustomed to well-defined operator precedence.  The compiler knows exactly in what order terms will be evaluated.  Thus, above, the answer is 9.  However, it would appear that the two calculators differ because there's debate about that division operator regarding whether it divides the entire expression or only the first two terms.  Rather, is it:     (6 ${\div}$ 2) (1 + 2)   or is it:     (6) ${\div}$ (2 (1 + 2))   Is there an official answer regarding the operator precedence for mathematics in general, outside the realm of computer programming and compilers?


I am writing a method which requires reading a file and putting all its contents into a string variable.  This is what I have tried:  unsigned int ShaderHandler::CompileShader(unsigned int shaderType, const std::string& sourceFilename) {      std::string sourceCode;         std::string line;     std::ifstream shaderFile;      shaderFile.open(sourceFilename);      while (getline(shaderFile, line)) {         sourceCode << line;     }      shaderFile.close();       std::cout << sourceCode;  }   And this is the error I get:  ShaderHandler.cpp:30:20: error: invalid operands to binary expression ('std::string' (aka 'basic_string<char, char_traits<char>, allocator<char> >') and 'std::string')         sourceCode << line;         ~~~~~~~~~~ ^  ~~~~   Instead of sourceCode << line, which is obviously wrong, what shall be used?

How do I read a file into a std::string, i.e., read the whole file at once?  Text or binary mode should be specified by the caller. The solution should be standard-compliant, portable and efficient. It should not needlessly copy the string's data, and it should avoid reallocations of memory while reading the string.  One way to do this would be to stat the filesize, resize the std::string and fread() into the std::string's const_cast<char*>()'ed data(). This requires the std::string's data to be contiguous which is not required by the standard, but it appears to be the case for all known implementations. What is worse, if the file is read in text mode, the std::string's size may not equal the file's size.  A fully correct, standard-compliant and portable solutions could be constructed using std::ifstream's rdbuf() into a std::ostringstream and from there into a std::string. However, this could copy the string data and/or needlessly reallocate memory.    Are all relevant standard library implementations smart enough to avoid all unnecessary overhead?  Is there another way to do it?  Did I miss some hidden Boost function that already provides the desired functionality?     void slurp(std::string& data, bool is_binary)


Is $A=\lbrace{ \frac{1}{n}, n \in \mathbb{N} \rbrace}$ dense set in $\mathbb{R}$ with cofinite topology ?  I think it is dense because all infinite subspace are dense sets under cofinite topology but I don't know how to prove.

Let $X$ be an infinite cofinite space and let $A \subset X$ be infinite. Then $\overline A = X$  I am having a tough time in trying to understand this. Why is every infinite set in an infinite cofinite space dense ?


An art gallery has the shape of a simple $n$-gon. Find the minimum number of watchmen needed to survey the building, no matter how complicated its shape be.  I failed to solve the problem. Please help in details.

Given a polygon with $n$ vertices, what is the minimal number of points inside the polygon such that for each interior point there exists at least one point such that the segment between them lies inside the polygon?  If the polygon is convex, one point is enough (any point inside the polygon).


I have a problem calculating improper integrals, this one for example, can you please help me solve it? $$\int_0^\infty t^3(e^{-t^2})dt$$ thanks in advance.

$\int e^{\frac{x^2}{2}} \cdot x^{3} dx=?$  I tried to do the substitution $du = x^3dx$, so that $u=\frac{x^4}{4}$. Then, $\int e^{\frac{x^2}{2}} \cdot x^{3} dx= \int e^{\sqrt{u}} du$  However, I would have to do a second substitution ($v = \sqrt{u}$) which would give a product again.  How should I proceed?