Evaluate $$\int_0^{2a}\int_0^{\sqrt{2ax-x^2}}\frac{\phi'(y)(x^2+y^2)xdxdy}{\sqrt{4a^2x^2-(x^2+y^2)^2}}$$  Here I changed the order of integration but after that I am not able to think of the relevant substitution to proceed with the integration.  I have tried to substitute it with polar co-ordinates but didn't succeed in solving that either.  I have checked the solution provided here  , but this solution is very lengthy.  I am looking for a shorter way of solving this question which is more obvious to hit during exam and also considers the space constraint.  If someone could suggest what substitutions to make to solve it in lesser steps.

Change the order of integration in:  $$\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x }{\sqrt{4a^2x^2-(x^2+y^2)^2}}dxdy$$ and hence evaluate it.    I changed the order of integration and got the limits $y=0$ to $a$ and $x=a-\sqrt{a^2-y^2}$ to $a+\sqrt{a^2-y^2}$. I then tried changing to polar coordinates, but it is only making the integrand more complex.


I don't quite understand the definition of opposite category.  Wikipedia defines $\mathcal{C}^\text{op}$ to be the category formed by 'reversing' morphisms. So for instance, in Grps, given a groups $G,H$ and a homomorphism $f: G \to H$, what does reversing $f$ mean?  Do we reverse $f$ into a homomorphism $H \to G$?

Given some category ${\mathcal C}$, then the opposite category will consist of the same objects with the morphisms "turned around."  Given $f:A\rightarrow B$, for $A,B$ objects of ${\mathcal C}$, then in general do we have a canonical $f^{op}:B\rightarrow A$ which is induced by $f$?    Slight Motivation:  This is something that's just been bothering me recently, and I feel like I am thinking about this concept incorrectly.  To make this question slightly less vague, if we had, say, the category of rings and we had the mapping $f:{\mathbb Z}\rightarrow {\mathbb Z}/2{\mathbb Z}$ by $f$ sends even numbers to 0 and odd numbers to 1, then what is the corresponding map in the opposite category, $f^{op}:{\mathbb Z}/2{\mathbb Z}\rightarrow {\mathbb Z}$ induced by $f$?  Also, I always see this $f^{op}$ that I've mentioned just written as $f$; is this shorthand, or is there something deeper there?


I'm trying to apply a blue texture to a material, but the texture is not displaying in the 3D view port.    I'm using blender-2.80-387c1f2e0d5d-linux-glibc224-x86_64  What should I do? What I'm missing? Bellow is the .blend file.

I am creating a model of a glass and I would like to put a drawing on it (a png picture).  I know how to do it using Blender Render, but not with Cycles Render. Help :)


I got a notification that I need to install updates, and I clicked yes, but since then I am getting this stop sign on the top right corner because of unmet dependencies.  when i run:  sudo apt-get install -f   I get bunch of packages to be removed and then:  The following extra packages will be installed:   collada-dom2.4-sp-dev The following NEW packages will be installed:   collada-dom2.4-sp-dev   When I click yes:  Selecting previously unselected package collada-dom2.4-sp-dev. (Reading database ... 306874 files and directories currently installed.) Preparing to unpack .../collada-dom2.4-sp-dev_2.4.4.1-ubuntu1~trusty1_amd64.deb ... Unpacking collada-dom2.4-sp-dev (2.4.4.1-ubuntu1~trusty1) ... dpkg: error processing archive /var/cache/apt/archives/collada-dom2.4-sp-dev_2.4.4.1-ubuntu1~trusty1_amd64.deb (--unpack):  trying to overwrite '/usr/lib/cmake/collada_dom-2.4/collada_dom-config.cmake', which is also in package collada-dom2.4-dp-dev 2.4.4.0-ubuntu1~trusty1 dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Errors were encountered while processing:  /var/cache/apt/archives/collada-dom2.4-sp-dev_2.4.4.1-ubuntu1~trusty1_amd64.deb E: Sub-process /usr/bin/dpkg returned an error code (1)   when I run sudo apt-get autoremove I get:  You might want to run 'apt-get -f install' to correct these. The following packages have unmet dependencies:  collada-dom-dev : Depends: collada-dom2.4-sp-dev but it is not installed E: Unmet dependencies. Try using -f.   Any help would be appreciated, thank you.

For example:  $ sudo apt-get install curl Reading package lists... Done Building dependency tree Reading state information... Done You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies: bsh : Depends: libjline-java but it is not going to be installed groovy : Depends: libjline-java but it is not going to be installed rhino : Depends: libjline-java but it is not going to be installed E: Unmet dependencies.   Try 'apt-get -f install' with no packages (or specify a solution).   I get the same or similar errors when I attempt to install clojure1.3, leiningen, and several other packages.   When I try the suggestion made in the error message, this is what happens:  $ sudo apt-get -f install  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following packages were automatically installed and are no longer required:   diffstat linux-headers-3.2.0-26-generic linux-headers-3.2.0-26 dh-apparmor dkms html2text libmail-sendmail-perl libsys-hostname-long-perl Use 'apt-get autoremove' to remove them. The following extra packages will be installed:   libjline-java Suggested packages:   libjline-java-doc The following NEW packages will be installed:   libjline-java 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. 23 not fully installed or removed. Need to get 0 B/72.0 kB of archives. After this operation, 129 kB of additional disk space will be used. Do you want to continue [Y/n]? Y (Reading database ... 226243 files and directories currently installed.) Unpacking libjline-java (from .../libjline-java_1.0-1_all.deb) ... dpkg: error processing /var/cache/apt/archives/libjline-java_1.0-1_all.deb (--unpack):  trying to overwrite '/usr/share/java/jline.jar', which is also in package scala 2.9.2-400 Errors were encountered while processing:  /var/cache/apt/archives/libjline-java_1.0-1_all.deb E: Sub-process /usr/bin/dpkg returned an error code (1)  $ sudo apt-get upgrade Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt-get -f install' to correct these. The following packages have unmet dependencies:  bsh : Depends: libjline-java but it is not installed  groovy : Depends: libjline-java but it is not installed  rhino : Depends: libjline-java but it is not installed E: Unmet dependencies. Try using -f.


Some of the candidates that want to colonize Mars have the vegan trait. The description of the trait reads: "Don't worry. They'll tell you".   What are the benefits/drawbacks of having Vegan colonists?

One of the traits in Surviving Mars is Vegan. The description just says "don't worry, they'll tell you."  All of the food in the game seems to be plant-based so what, if anything, does Veganism do?


I just need to copy the value of data.notes. I have used below code. But still detailsOfCurrentNotes value changes according to the value of data.notes. So could you tell me how to do this?  notes :Note[]   const detailsOfCurrentNotes = Object.assign({}, data.notes);  //here data.notes changes  // detailsOfCurrentNotes also get that value

What is the most efficient way to clone a JavaScript object? I've seen obj = eval(uneval(o)); being used, but . I've done things like obj = JSON.parse(JSON.stringify(o)); but question the efficiency.  I've also seen recursive copying functions with various flaws.  I'm surprised no canonical solution exists.


As you see below I have two user account on my computer, and both of them have in  administrator group.     I want to run this below program :    When I log in with Abraham and double click on ELEnveloperGui it can't find my dongle that is connected to the computer :    But when I right-click on it and select Run as administrator it find my dongle !!!    Note: I have Windows-7 x64 professional  Q : What is the difference between Abraham and Administrator?     Update : I gave the program Full Permission, but problem still remain!

If my account is already a member of the administrator group why do some functions on Windows 7 require me to run them as administator? I kind of thought that was implied?


For my computer science course, we have an assignment in which we have to return to the user the popularity of a baby's name during a specific year. To sort through the most popular baby names, I made two arrays based on the gender (binary). I then fill these arrays up and then search through them depending on the gender entered. I use an if/else statement for that, however, it prints the else portion instead of the if portion.   import java.io.*;   import java.util.Scanner;  public class LAB08   {      public static void main(String[] args) {       Scanner input = new Scanner(System.in);       String[][] boysNames = new String[6][1000]; //this creates a 2 dimentional array that will have for each year it's own array for the boys names.     String[][] girlsNames = new String[6][1000];     getNames(boysNames, girlsNames);      //System.out.println(boysNames[0][0]);     System.out.println("Please enter the name you would like to search for. Enter the first letter capitalized ie Julia");      String searchingName = input.next();      System.out.println("Please enter the last digit of the year you would like to look for");     int searchingYear = input.nextInt();      System.out.println("Please enter if you are looking for a boy or a girl. Enter Boy, Girl case sensitive");     Scanner input2 = new Scanner(System.in);     String gender = input2.nextLine();     System.out.println(gender);      int rank = -1;     gender = "Girl";      if(gender == "Girl") {           rank = checkForName(searchingYear, searchingName, girlsNames);       } else if( gender == "Boy") {          rank = checkForName(searchingYear, searchingName, boysNames);      } else {          System.out.println("Sorry, you did not enter the information correctly.Please try again. Remember, Boy, Girl");      }     if (rank == -1) {           System.out.println("Sorry, the name was not found.");     } else {           System.out.println("You entered " + searchingName + " for the year " + searchingYear + " and the rank is " + rank +".");     }      }      public static void getNames(String[][] arr1, String[][] arr2) {          String filename = "";         //2 for loops are used to get the thing          for (int i = 0; i < 6; i++) {              filename = "babynameranking201" + i + ".txt"; //this uses the value created from the beginning.              try (Scanner input = new Scanner(new File(filename))) {  //attempts to read an input.                   for(int i2 = 0; input.hasNext(); i2++){                      input.nextInt();                     //System.out.println(input.next());                      arr1[i][i2] = input.next();                     arr2[i][i2] = input.next();                  }              }  catch (Exception is) { //catches if the file is unable to be read.                    is.printStackTrace(); //lets the user know what is wrong.               }           }       }     public static int checkForName(int year, String name, String[][] arr){          for (int i = 0; i < 1000; i++) {               if (name == arr[year][i]) {                   return i+1;               }           } return -1;       } }     Someone marked this question as a duplicate to a question that explains the equals method. This isn't an accurate duplicate because I wasn't aware of that previous notation as Java is not my primary language so I therefore wasn't aware that that was the problem. I believe a more useful approach would have been to let me know of that feature and letting me know that that was the problem. I am editing it so that it is made aware that it is not a duplicate.

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


tests:  1. 'Product: aab bbc; Product: xyz pqr; Junk1: jjkk jjuu; Junk2: nnnkk junk; Junk3: lkie rnier rae' 2. 'Product: Fuasdcsen' 3. 'Product: marlwaw Swwō' 4. 'Product: aab bbc abc xyz; Product: xyz pqr; Junk1: jjkk jjuu; Junk2: nnnkk junk; Junk3: lkie rnier rae'   output:  1. ['aab bbc', 'xyz pqr'] 2. ['Fuasdcsen'] 3. ['marlwaw Swwō'] 4. ['aab bbc abc xyz', 'xyz pqr']   I want list of only Product name. so, far i have came up with r'Product:\s*(.*)(?:;|$)' this regex but it only works with single Products(case 2 and 3). can somebody suggest general solution for all. I am trying to extract details between : and ;(if present).  In [10]: reg_str = 'Product: marlwaw Swwō xyz abc'  In [11]: re.findall(r'Product:\s*(.*)(?:;|$)', reg_str) Out[11]: ['marlwaw Swwō xyz abc']

I have this gigantic ugly string: J0000000: Transaction A0001401 started on 8/22/2008 9:49:29 AM J0000010: Project name: E:\foo.pf J0000011: Job name: MBiek Direct Mail Test J0000020: Document 1 - Completed successfully  I'm trying to extract pieces from it using regex. In this case, I want to grab everything after Project Name up to the part where it says J0000011: (the 11 is going to be a different number every time). Here's the regex I've been playing with: Project name:\s+(.*)\s+J[0-9]{7}:  The problem is that it doesn't stop until it hits the J0000020: at the end. How do I make the regex stop at the first occurrence of J[0-9]{7}?


$f:[0,1]\to \mathbb{R}$ is a continuous function such that $$\int_0^1 f(x)^2dx=\int_0^1 f(x)^3dx =\int_0^1 f(x)^4dx$$ Find all such $f$ My approach: Clearly $f=0,1$ are solutions (and only possible constant functions). Now let $f$ to be a non constant function. By CS inequality we have, $$\int_0^1 f(x)^2dx \times \int_0^1 f(x)^4dx \ge ( \int_0^1 f(x)^3dx )^2$$ Equality holds here.So $\int_0^t f(x)dx =k \int_0^t f(x)^2dx$ for all $t\in (0,1]$ for some $k$ . I don't know what to do from here 😅 Please help.

Let $f : [0,1] \to \mathbb{R}$ be a continuous function such that   $$\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$$   Determine all such functions $f$.   So far, I've managed to show that $\int_0^1\!{f(x)^t\, \mathrm{dx}}$ is constant for $t \geq 2$. Help would be appreciated.


Suppose I'd like to find the coefficient of $x^{l}$ in the expansion of  $(1+x+x^{2}+...+x^{n})^{m}$, where $n$ and $m$ are given positive integers, for some given integer $l$ such that $n < l < mn$. Is there a straightforward formula (in terms of some multinomial coefficient, or similar)?

The literature defines multinomial coefficients (or extended bnomial coefficients) as   $$ \binom{n}{r_1,r_2,\cdots,r_l} = \frac{n!}{r_1!r_2!\cdots r_l!}$$ where $$ r_1+r_2+\cdots+r_l = n$$  Which is the coefficient of $x_1^{r_1}x_2^{r_2}\cdots x_l^{r_l}$ in expansion of $(x_1+x_2+\cdots+x_l)^n$.  Question: How do we call the coefficients of $x^r$ in expansion of $(x+x^2+\cdots+x^l)^n$. Is it bad to name them multinomial coefficients?  In case of binomial coefficients the two are same in expansion of $(x_1+x_2)^n$ and the expansion of $(x+x^2)^n$. Obviously the two are different for multinomial expansion.   Example: As $(x_1+x_2+x_3)^2= x_1^2+2 x_2 x_1+2 x_3 x_1+x_2^2+x_3^2+2 x_2 x_3$. The coefficients are $\{ 1,2,2,1,1,2 \}$. Are these MULTI-NOMIAL?  $ As (x+x^2+x^3)^2=x^2 + 2 x^3 + 3 x^4 + 2 x^5 + x^6$. The coefficients are $\{1,2,3,2,1\}$. Are these too the MULTI-NOMIAL?  I prefer different terminologies to avoid confusion. Therefore want to know how these are distinguished in existing literature.


I wonder whether instead of 'Reply' and 'Close' I can have other options like 'Trash' or 'Archive' or 'Mark as Read' in notifications coming from the Mail app on macOS.

Is it possible to customize the alerts or badges (either will be okay) for the Mail application so that it displays Delete upon a mouse-over instead of Options --> Delete? I receive a lot of mails daily which I need to delete etc and it will be very handy to have such a simple feature. I am using MacOS Big Sur on MacBook Air M1. .


I have two strings, one is inputted by the user and one is the name of a thread. I inputted the name which should be the same as the thread. To verify this I have the program output  System.out.println("DS:" + DeamonMain.threadNameFinal + "CN:" +getName());   Which prints   DS:Thread-66CN:Thread-66   Now these appear to be the same string. However, when I have it test the validity of this using   boolean factChecker = DeamonMain.threadNameFinal == getName(); System.out.println(factChecker);   it prints false...  Why is this? Does this have to do with getName()? How are the string different and why so?


I have a Maven project with certain set of dependencies. One of the dependencies is:  <dependency>     <groupId>net.java.dev.jna</groupId>     <artifactId>jna</artifactId>     <version>4.5.0</version> </dependency>   As long as I work in Eclipse, all is good. But when I package and try to use the resulting jar file(from command line if that matters), I get this error message:  Exception in thread "main" java.lang.NoClassDefFoundError: com/sun/jna/NativeLibrary   while this class is definitely accessible in IDE.  My guess is that Maven is not packaging project's dependencies by default but in that case why don't I get more error messages complaining about more classes that were not found?

I want to package my project in a single executable JAR for distribution.  How can I make a Maven project package all dependency JARs into my output JAR?


A topological space is $T_B$ if each compact subset  is closed.  A topological space is called a US-space provided that each convergent sequence has a unique limit.  A topological property $\mathcal{R}$ is contractive if $(X,\tau)$ has property $\mathcal{R}$ and if $\tau^{\prime} \subset \tau$, then (A, $\tau^{\prime}$) has property $\mathcal{R}$.  A topological space is called a C- C-space provided that  the  compact subsets  are precisely the closed sets.     Is property C-C , US contractive,  hereditary?      Is property $T_B$  contractive?

A topological property $\mathcal{R}$ is contractive if $(X,\tau)$ has property $\mathcal{R}$ and if $\tau^{\prime} \subset \tau$, then (A, $\tau^{\prime}$) has property $\mathcal{R}$.  A topological space is $T_B$ if each compact subset  is closed.  A topological space is called a US-space provided that each convergent sequence has a unique limit.  A topological space is called a C- C-space provided that  the  compact subsets  are precisely the closed sets.     Is property C-C , US contractive,  hereditary?      Is property $T_B$  contractive?


A couple of weeks ago a teacher of mine (I'm taking mathematics) was giving a final inspiring lecture about how fundamental Math is to every possible universe. During the lecture though, he said that what the current physics theories tell us is that the Universe originated from a point. Not a really small point, but an actual mathematical point, one with 0 dimensions. I've heard the concept of a singularity before, but even in theory, can it happen in Nature?  EDIT: My question is not the same as . I'm not interested in how the Universe expanded, I want to know if the Universe was compressed into an actual point.

TV documentaries invariably show the Big Bang as an exploding ball of fire expanding outwards. Did the Big Bang really explode outwards from a point like this? If not, what did happen?


I'm trying to record my screen and the audio only coming from my Mac.   When I do a screen recording with quicktime, with audio settings: internal microphone, it records the video but with a lot of external noise (like cats).  How do I make sure that the audio of what is being played on the screen (like music being played on my Mac) is recorded in the video file?   I don't care if I'll have to record the screen and audio separately, or plug in earphones etc, I'd like to have a simple answer.   I have already tried the suggestions in these other questions:        Sadly their solutions don't work for me, as my recordings still capture external noises on macOS Catalina.  What software or setup can do this?

I would like to know If I will be able to record using quick time player or other application you may suggest, both audio and video on my Macbook Air with head phones connected !!  When headphones are not connected, there is no problem, i go to setting on the recording screen and i choose built-in microphone  But what i want is while i'm using my headphones, when i want to record a video, i want it to capt the audio from that video rolling on my mac, not the sound of outside


I have SharePoint enterprise server 2013 with SP1, and i check my timer jobs and many of them are showing "N/A" beside their last run time, as follow:-    now i run the following command :-  Start-SPAdminJob -verbose   and i got the following :-     VERBOSE: Leaving BeginProcessing Method of Start-SPAdminJob.   Start-SPAdminJob : The administration service is running so all   administration jobs will be run in the timer service. At line:1 char:1   + Start-SPAdminJob -verbose   + ~~~~~~~~~~~~~~~~~~~~~~~~~       + CategoryInfo          : InvalidData: (Microsoft.Share...etStartAdminJob:    SPCmdletStartAdminJob)   [Start-SPAdminJob], SPException       + FullyQualifiedErrorId : Microsoft.SharePoint.PowerShell.SPCmdletStartAdm    inJob      VERBOSE: Leaving ProcessRecord Method of Start-SPAdminJob. VERBOSE:   Leaving EndProcessing Method of Start-SPAdminJob.   so can anyone adivce what is causing this problem ? and even if i manually run the timer jobs i will keep receiving "N/A" for their last run time. I also checked the search schedule job and the search job will not get started . where i specify that the incremental search should run each 20 minutes. but the search will never start , only its "next incremental search" time will get updated ..

I tried to publish some content types inside my site collection hub, but the content types were not published correctly, as they did not appear under custom content types at the other site collections. now i checked Content Type Subscriber status and it showed its last run =N/A as follow:-    Now i checked the "Content type publishing error log" under the site collection hub , but it did not show any errors .  and when i checked the Content Type hub job , i find that the web application is set to N/A, as follow, although the managed metadata is connected to the web application :-    so can anyone advice how i can fix this problem ?


Take  recent (and highly irritating) bug for example. Our one and only Oded fixed it quickly but for the fix to actually have any effect, code must be "deployed" first, action that might take even days, especially now with SQL playing tricks on the team.  Until the fix is deployed, the bug still exists.  Two options:   Mark  since as far as the dev is concerned, it's fixed and it's just matter or time until all we enjoy it. That's by far the norm here in Meta. Bug exists so don't put any tag and wait until the fix is actually out there (maybe even wait for OP to confirm) before tagging as completed. Concern here is forgetting to tag leaving bug reports open even though they're actually fixed.   Personally I prefer #2 though it's really not that crucial. Can anyone see more aspects or reasoning in addition to what I brought here?

In several scenarios, including two today ( and ), we have had bugs set to  simply because the fix has been checked in. Just because the code portion has been completed does not mean the work is done, and this can be confusing for users who come across the same problem. Until then it really is  or maybe a tag that doesn't yet exist (status-checked-in?).  Particularly in times like this week, where the stability of the system is a priority, I don't think this status should be set merely because the code has been checked in - it should happen when the code is actually deployed and verified. Currently the devs are being very good about telling us that the code is done but they're not sure when it will be deployed, but I think that is because of the stability issue.


Ok, so I have looked this question up and gotten scrambled answers and I dont know what is right. I just got a paycheck from catering a wedding and I dont know if it would expire or if I can hold onto it and use it as a bond.

Do personal checks expire in the US?  Also, if I stamp the following on it:     VOID if not claimed within 60 days.   Will that be honored by most banks?    Related


I would like to insert a linkedin logo to my document that also acts as a link to my profile.  Here's my code  \documentclass{article}  \usepackage{hyperref} \usepackage[demo]{graphicx} \usepackage{wrapfig} \usepackage{lipsum} \usepackage{fontawesome} \usepackage{setspace}  \begin{document} \begin{wrapfigure}{l}{25mm}      \includegraphics[width=1in,height=1.5in,clip,keepaspectratio]{AuthorImage} \end{wrapfigure}\par \textbf{Author A} \lipsum[1]    \begin{figure}     \centering     \href{http://www.google.de}{%         \scalebox{0.1}{             \parbox{\textwidth}{                 \centering                 \includegraphics{LinkedinImage}}         }     } \end{figure} \end{document}   I'm trying to inert LinkedIn logo just after Author A or at the end of the paragraph.  Thanks

Can an image be included in TeX so that the resulting PDF is clickable leading to a reference?


What is the idiom or single word for a person who just talks high-flying to show himself important and powerful? But, in actuality, he is not what he tries to portray himself as.

I'm looking for a single word to most aptly describe a person possessing the following "qualities":   Appears to be superior in every technology/skill under the sun, which he deems worthy of knowing On being questioned/assigned the task, is found to have only superficial/no knowledge of the said skill. Inherent tendency to "one-up" anyone and everyone - example: "I didn't work hard at all in my undergrad days, but yet I have better/equal grades than you have! "   Could someone help?  Edit: I've got some very good responses, but despite popular opinion for "braggart", I'm going with "pretentious" as it suits what I was looking for more aptly IMHO.


I'm searching a simple and cost-less way to remove the fisheye effect by:   adding a material (additional corrective lens) or find the right software (free if possible) to remove the fisheye effect on my pictures

Can you recommand me a software for doing this job? I shoot using Sigma 8mm lens and I would like to be able to obtain a normal image out of that. The camera is canon 550D.


I'm a little bit confused about the nature of symmetrical reference frames and how they relate to time dilation. To clarify my question, I've written a scenario.  Bob stands on a platform as a train moving at some high velocity goes by. He observes that while his own watch measures 10 seconds elapsed, the train's clock measures 15 seconds elapsed. The train stops, its clock 5 seconds ahead of Bob's.  However, since from the train's point of view, Bob was moving at the same velocity, the passengers measure his watch to have measured 15 seconds while their clock measures 10. When the train stops, Bob's watch is ahead of the train's clock by 5 seconds.  How are these reconciled?

There is a problem with my logic and I cannot seem to point out where. There's a rocket ship travelling at close-to-c speed v without any acceleration (hypothetically), and there is an observer AA with a clock A on Earth, and there's another observer on the rocket BB with a clock B and these two clocks were initially in sync when the rocket was at rest with a FoR (frame of reference) attached to Earth. Now, this rocket's moving and AA tells us that B is running slower than A by a factor of$$ \gamma = 1 /(1-v^2/c^2)^{1/2} $$ $$ t_A/t_B = \gamma $$ where v is the relative 1d- velocity between the two i.e the earth and the rocket! That would mean the time elapsed on A is greater than that on B but this will happen only in the FoR of AA? So $t_B$ in this equation must be the time on B as observed by AA? Is this correct? What do the terms mean in the equations? If the symmetry holds and BB doesn't accelerate, then BB could say that $$ t_B/t_A = \gamma $$ right? where $t_B$ and $t_A$ are the times on B and A with respect to FoR of BB? But I was solving this problem and I took the earth FoR of A, but the prof took the rocket FoR of B? Like how will I know which FoR to solve the problem from? It'd greatly help if the terms in all the above equations were laid down neatly! DO we even need these FoRs?? Because in all the solved problems the prof is't specifying any and is using random ones! Please help!!!! This is the question where I messed up. The first rocket bound for Alpha Centauri leaves Earth at a velocity (3/5)c. To commemorate the ten year anniversary of the launch, the nations of Earth hold a grand celebration in which they shoot a powerful laser, shaped like a peace sign, toward the ship.  According to Earth clocks, how long after the launch (of the rocket) does the rocket crew first see the celebratory laser light?  This must be 25 years. My reasoning is: If v = 3c/5 10v + vt = ct where t is time taken by the light to reach the rocket from Earth as calculated from Earth.. and I solved that for t. and added 10 years to that because the time starts at the launch of the rocket!  According to clocks on the rocket, how long after the launch does the rocket crew first see the celebratory laser light?  This is 20 years. Here, I say: If it takes 25 years as observed by clocks on earth for the laser to reach the rocket, what should be the corresponding time as seen on a clock on the rocket? Using the formula: 25 = $\gamma$t where $\gamma$= 5/4 solved for t!  According to the rocket crew, how many years had elapsed on the rocket's clocks when the nations of Earth held the celebration? That is, based on the rocket crews' post-processing to determine when the events responsible for their observations took place, how many years have passed on the rocket's clocks when the nations of Earth hold the celebration?  For this, I did the following: 10 years on earth = T years on rocket ship where T must be lesser than 10 as observed from Earth FoR! Therefore, T= 4(10)/5 years = 8 years! But, prof says, 10 years on Earth = T years in rocket ship where T must be GREATER than 10 as observed from the rocket FoR??? Therefore, T = 10(5/4) years = 12.5 years!! What does this question actually want?


Let $d_1 = 1 < d_2 < . . . < d_k = n$ be all the positive divisors of the positive integer n, and let $d = \sum_{i=1}^{k-1} d_id_{i+1}$.  Show that $d < n^2$.

IMO 2002 P4 Let $n\geq 2$ be a positive integer with divisors $1=d_1<d_2<\cdots<d_k=n$. Prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k$ is always less than $n^2$, and determine when it is a divisor of $n^2$  I am trying this question but I run out of ideas, could someone give a little hint or a suggestion? Please, without giving me the solution. I am trying to use the fact that the product of $d_i$*$d_{i+1}$ is a divisor of $n^2$ (and they are all different) and maybe try to use the formula for the sum of divisors to see if this specific sum is less than $n^2$


Let us suppose we have a triangle with base $j$ to $j-1$ and height of $1/j$ for $j=2,...,n$. Then, $$\frac{1}{j}(j-(j-1))\lt\int_{j-1}^{j}\frac{1}{x}dx$$ Why $\frac{1}{j}(j-(j-1))\lt\int_{j-1}^{j}\frac{1}{x}dx$?

In an Econometrics - Time Series textbook (Hamilton), I saw the claim, without proof: Consider the sequence $ \psi_j $, then, for $ x > j $, $ \frac1j > \frac1x $, and therefore: $$  \frac1j > \int_{j}^{j+1} \frac1x dx $$ for $x$ > $j$. When I plug in numbers for $j$, I see that this is indeed satisfied. But I'd like to know the intuition behind this or a proof.


I need to proof that $$\int_{0}^{\pi}xf(\sin(x))dx=\frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))dx$$ The problem says that the substitution $u=\pi-x$ is useful. Following their advice $u=\pi-x,du=-dx$ $$-\int_{0}^{\pi}(\pi-u)f(\sin(\pi-u))du$$ What do I do next, this the first time I encounter integrals writeen like this and I am not that familiar with proof thanks in advance !

Let $f(\sin x)$ be a given function of $\sin x$.   How would I show that $\int_0^\pi xf(\sin x)dx=\frac{1}{2}\pi\int_0^\pi f(\sin x)dx$?


Every time I go to render this, it comes out totally blank. I'd also like to note that it's rendering REALLY fast. Not sure if that has anything to do with it [the render just keeps coming out like this .    I tried the stuff from  post but it didn't work.

A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [


I am a graduate student of Informatics.  Studying mathematical logic I've just started discovering it connection to philosophy. Following this way I started reading something about old and modern philosopher. My first source of information is internet, especially Wikipedia, but I am meeting a lots of difficulties because of the use of terms  I don't know the meaning.   So, I want to ask you  a suggestion of a minimal set of books to read in order to get the main concepts related to philosophy.  I am mainly interested in the explanation of the meaning of the more general terms ( e.g. judgment, subject, object, extension, ecc.. ) I am also interested about a pan on the thoughts of the main philosopher.  Thank you.

I've been searching the questions posed here, and don't seem to find one that gives the answers I am looking for. I've proposed to start a  on meta but no one proposed anything, so I feel I must ask this question: What are some books generally regarded as good for a general introduction on philosophy? By this I mean good books that can introduce you to philosophy in general and throughout the times, not to some philosophy or period in particular.   almost answers mine, except for the fact that most things proposed there are not books, thus not giving me much options to weigh upon.  regards contemporary philosophy in particular. And  has the same problem as the first one, plus the fact that it asks for layman's terms, which is not what I am looking for.  I've been tempted to buy Will Durant's , but am not sure if it is the best book to get started on philosophy (plus, the book has some mixed reviews). I also checked , which seems to be unanimously good, but has the format of dictionary/encyclopaedia, which is not exactly what I am looking for (at least as a main source).  also seems to be a good introduction regarding how to do philosophy, rather than to its history and ideals (this also interests me, but I'd rather learn about the philosophers and their theories first).   It is also important to point out that I have little notions (or none at all) on philosophy. I would like to read something that covers from classical to contemporary philosophy generally (although I do not know if there is such a book), so that from there I could pick some author, period or branch of philosophy in particular to read further on. So, to sum up, I would like to 'hear' your opinions on what are some books generally regarded as good for a general introduction on philosophy.


Edit : Note that it is not yet possible to migrate from 16.04.05 LTS to 18.04.1 LTS. Today is Tuesday, August 7.... The release of 18.04.1 LTS took place on July 26... They must have simply forgotten to enable the "For long-term support versions" option in "Notify me of a new Ubuntu version", in the "Software Updater" options... Someone absolutely must tell them please.    This documentation  indicates, in the part titled "Upgrade from 16.04 or 17.10 to 18.04 > Upgrading Ubuntu Desktops to 18.04 (Recommended)" that in order to migrate from 16.04 (16.04.5 LTS for me) to 18.04 (18.04.1 LTS in fact), we must confirm the "Notify me of a new Ubuntu version:" option is set to "For any new version", and change it if otherwise.  My question is : why not to keep it set at its default value, which is : "For long-term support versions" ? 18.04(.1) is indeed an LTS version ! So this option should also enable the migration.  I have another question: in addition to allowing the change from 16.04(.5) to 18.04(.1), what are/will be the other (potentially bad) consequences of choosing the "For any new version" option, recommended by the above documentation?  Am I making a mistake ?  Important  This migration is really impossible when "For long term support versions" is chosen. It's possible when "For any new version" is chosen.

I understand that the first point release of Ubuntu 18.04, namely 18.04.1 is now available and that my system should now offer it as an update.  My current OS version is 16.04.5 LTS. In System Settings/Software and Updates I have set 'Notify me of a new Ubuntu version' to 'For long term support versions'. I have tried both the main server and the server for United Kingdom, neither offers an update when Software Updater is clicked or via the Ubuntu Software icon.  Can anyone please tell me why I don't get the option of updating to 18.04?  Edit:  I don't remember the details exactly, but I think that my last LTS point release update was offered automatically a lot sooner after the published release date than where we are now with 18.04.1.  Edit 10th August  It appears that there has been some problem with the update process and that it should be fixed next week, see:    Edit 14th August 18.04.1 LTS now available from UK server,


public class contactCreation{     integer i;     list<contact> conlist = new list<contact>();      public void createContacts(list<contact> contacts){          for(i=0; i<=20; i++){             contact c = new contact(lastname = 'contact'+i);             conlist.add(c);         }         insert conlist;     } }

I am trying to call my Apex class from a trigger:  trigger newCrossSellAccounts on Account (before insert) {    crossSellModule.insertAfterAccount2(trigger.new); }   On the class I have:  public void insertAfterAccount2(list<account> accountList){   When I try to save trigger I get error:  Method does not exist or incorrect signature: crossSellModule.insertAfterAccount2(LIST<Account>) at line 2 column 4    Now from  it says .new "Returns a list of the new versions of the sObject records." I tried to change the function on class to:  public void insertAfterAccount2(sObject<account> accountList){   But I get error:  Invalid type: sObject<account>    Should I loop thru and create a list in trigger first? Or is there are workaround. Also, how one would test such trigger/class combination?


I had already asked a nearly identical question   I am using biblatex with biber from TL2018 for my PhD thesis. Due to various reasons, I am forced to use Mendeley for citation managements and cannot switch to another tool now. Mendeley is capable of generating a bib file - but it is compatible with only the classic natbib/bibtex combo (although it correctly escapes special characters).  I understand that with biblatex/biber combo, the month field is not a string, but rather must be an integer.  So, as expected and discussed , I get the warning      WARN - month field 'jan' in entry 'Guo2012' is not an integer - this will probably not sort properly.   (this time for jan  wherein unlike my original question, the month does not begin with captial J).  For tackling the original question, I used the regex given in that question in my preamble (given below)   \DeclareSourcemap{     \maps[datatype=bibtex]{         \map[overwrite]{             \step[fieldsource=month, match=\regexp{\Ajan\Z}, replace=1]             \step[fieldsource=month, match=\regexp{\Afeb\Z}, replace=2]             \step[fieldsource=month, match=\regexp{\Amar\Z}, replace=3]             \step[fieldsource=month, match=\regexp{\Aapr\Z}, replace=4]             \step[fieldsource=month, match=\regexp{\Amay\Z}, replace=5]             \step[fieldsource=month, match=\regexp{\Ajun\Z}, replace=6]             \step[fieldsource=month, match=\regexp{\Ajul\Z}, replace=7]             \step[fieldsource=month, match=\regexp{\Aaug\Z}, replace=8]             \step[fieldsource=month, match=\regexp{\Asep\Z}, replace=9]             \step[fieldsource=month, match=\regexp{\Aoct\Z}, replace=10]             \step[fieldsource=month, match=\regexp{\Anov\Z}, replace=11]             \step[fieldsource=month, match=\regexp{\Adec\Z}, replace=12]         }     } }   How can this be modified suitably to handle this lowercase situation?

I am using biblatex with biber from TL2018 for my PhD thesis. Due to various reasons, I am forced to use Mendeley for citation managements and cannot switch to another tool now. Mendeley is capable of generating a bib file - but it is compatible with only the classic natbib/bibtex combo (although it correctly escapes special characters).  I understand that with biblatex/biber combo, the month field is not a string, but rather must be an integer.  So, as expected and discussed , I get the warning   [784] Utils.pm:193> WARN - month field 'Apr' in entry 'coolauthor2012' is not an integer - this will probably not sort properly.   Taking inspiration from a tangentially related question , I used the following month -> integer hand-conversion in the preamble.  \DeclareSourcemap{     \maps[datatype=bibtex]{         \map[overwrite]{             \step[fieldsource=month, match={jan}, replace=${1}]             \step[fieldsource=month, match={feb}, replace=${2}]             \step[fieldsource=month, match={mar}, replace=${3}]             \step[fieldsource=month, match={apr}, replace=${4}]             \step[fieldsource=month, match={may}, replace=${5}]             \step[fieldsource=month, match={jun}, replace=${6}]             \step[fieldsource=month, match={jul}, replace=${7}]             \step[fieldsource=month, match={aug}, replace=${8}]             \step[fieldsource=month, match={sep}, replace=${9}]             \step[fieldsource=month, match={oct}, replace=${10}]             \step[fieldsource=month, match={nov}, replace=${11}]             \step[fieldsource=month, match={dec}, replace=${12}]         }     } }   I have two nagging questions now.    Will this work? I don't see any more of the aforementioned warnings, but I wonder if the citations are correctly sorted, and the month replacement was indeed accounted for and handled correctly. Is there a better way to handle this problem? Clearly, hand-mapping each month to an integer is not efficient.   This will help all folks who want to use mendeley especially for re-using their existing mendeley library for manuscript submissions to publishers who are mostly stuck behind in natbib/bibtex era.


Exercise 2.12(a) from Leinster:     Show that for any adjunction, the right adjoint is full and faithful if and only if the counit is an isomorphism.   Note: The exercise is given before the chapter on representables and the Yoneda lemma, so I wouldn't like to use those. There is a  which partly covers what I'm asking, but the answer uses the Yoneda lemma and other stuff from  (whereas this exercise is from Chapter 2).    Suppose $F:\mathscr A\to \mathscr B,\ G:\mathscr B\to\mathscr A$ are functors and $F\dashv G$. So there is a bijection $$\mathscr B(F(A),B)\cong\mathscr A(A,G(B))$$ denoted by $f\mapsto \bar f$ in either direction. The counit of adjunction is the natural transformation $$\epsilon: FG\to 1_\mathscr B$$ whose component at $B\in\mathscr B$ is   $$\epsilon_B=\overline{1_{G(B)}}:FG(B)\to B.$$  The question asks to prove that $G$ is full and faithful iff $\epsilon$ is a natural isomorphism. The latter happens iff $\epsilon_B$ is an isomorphism in $\mathscr B$ for all $B\in\mathscr B$. So it suffices to show that $G$ is full and faithful iff each $\epsilon_B$ is an isomorphism.    I really don't see how to prove either direction. For example, suppose $G$ is fully faithful. Then there is a bijection $$\mathscr B(B,B')\cong \mathscr A(G(B),G(B'))$$ for all $B,B'\in\mathscr B$. Thus there is also a sequence of bijections  $$\mathscr B(B,B')\cong \mathscr A(G(B),G(B'))\cong \mathscr B(FG(B),B')$$ (the cited question calls these bijections natural isomorphisms, but at this point Leinster doesn't even interpret the adjunction bijection (the second bijection above) as a natural transformation (he only gives some "naturality conditions" which at this point are not interpreted as a natural isomorphism; and I also treat the first $\cong$ above as a mere bijection).   So every arrow $g:B\to B'$ corresponds in a unique way to an arrow $FG(B)\to B'$. But (1) I don't know any explicit formula for this correspondence (the first $\cong$ is just applying $G$; the second is taking bar, but there is no explicit definition of a bar in Leinter's text), and (2) even if I knew the explicit correspondence law, I don't see how it would help me.  The other direction is also not clear.  Addition: the naturality conditions in Leinster's notation:

Let $C,D$ be categories and $F:C\to D,G:D\to C$ be such that $F$ is a left adjoint of $G$. Prove that $F$ is fully faithful iff the unit is an isomorphism.   (This is an exercise from the book by T. Leinster)   I think I can do one direction:  $\impliedby$: If we let $\eta$,$e$ be unit/counit then as $\eta:\text{id}_C \implies GF$ is an isomorphism, it follows that the composite  $$ \text{Hom}(x,y)\to\text{Hom}(F(x),F(y))\to\text{Hom}(GF(x),GF(y)) $$  for all $x,y\in C$ is an isomorphism, which implies that $F$ is faithful. But $F$ must be full since the composite  $$ G=G\circ \text{id}_D \implies GFG \implies G $$  is an identity transformation (I'm rather skeptical about this).  But I don't have any idea regarding reverse direction, in which I have to show that the arrow $x\to GF(x)$ has an inverse for all $x\in C$.


Use the result $1 + z + z^2...+z^n=\frac{z^{n+1}-1}{z-1}$ to sum the series to n terms  $1+\cos\theta+\cos2\theta+...$  also show that partial sums of series $\sum \cos (n\theta)$ is bounded when $0<\theta<\pi/2$  My attempt  so z  can be written as $e^{i\theta}$ which means:  $1+ \cos \theta + \cos 2\theta ....+\cos n\theta + i(\sin \theta+\sin 2\theta+....+\sin n\theta)=\frac{z^{n+1}-1}{z-1}$  after this.. i dont know

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series:  $$\sum_{k=0}^{n-1}\cos (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \cos \biggl( \frac{ 2 a + (n-1)\cdot d}{2}\biggr)$$  There is a slight difference in case of $\sin$, which is: $$\sum_{k=0}^{n-1}\sin (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \sin\biggl( \frac{2  a + (n-1)\cdot d}{2}\biggr)$$   How do we prove the above two identities?


In the help center under the moderator tools privilege, there is an interesting screenshot.    I assume that this picture was taken while logged in as Jeff Atwood on Meta Stack Overflow.  In this picture, I can see "print" and "transmogrify" buttons beneath the question. It's pretty obvious what "print" means, but what about "transmogrify?" And what privilege levels do you need to see these buttons?

In the last image of the , there is a button named "transmogrify". What does it mean?    The dictionary entry makes it more confusing:     trans·mog·ri·fy      Verb   Transform, esp. in a surprising or magical manner.   In addition to the image on MSO, the SO image seems to have the print and transmogrify text as well.


I want to show that $$  a_n = \frac{3^n}{n!} $$ converges to zero. I tried Stirlings formulae, by it the fraction becomes $$  \frac{3^n}{\sqrt{2\pi n} (n^n/e^n)} $$ which equals $$  \frac{1}{\sqrt{2\pi n}} \left( \frac{3e}{n} \right)^n $$ from this can I conclude that it goes to zero because $\frac{3e}{n}$ and $\frac{1}{\sqrt{2\pi n}}$ approaching zero?

Why is     $$\lim_{n \to \infty} \frac{2^n}{n!}=0\text{ ?}$$   Can we generalize it to any exponent $x \in \Bbb R$? This is to say, is     $$\lim_{n \to \infty} \frac{x^n}{n!}=0\text{ ?}$$     This is being repurposed in an effort to cut down on duplicates, see here: Coping with  duplicate questions.  and here: .


import java.math.*;  public class PowerDigitSum {     public static void main(String[] args) {         double[] digits ;         digits = new double[302];         double i = Math.pow(2, 1000);         double c = 301;         double c1 = 0;         double d = 0;         while(c>=0) {             c1 = Math.pow(10, c);             d = Math.floor(i/c1);             i = i - d*c1;             digits[(int)c] = (int)d;             c = c-1;         }         double sum = 0;         c = 0;         while (c<302) {             sum = sum+digits[(int)c];             c= c+1;         }         System.out.println(sum);     } }   The output is 1281 but that's not correct according to projecteuler. What am I doing wrong?

2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.  What is the sum of the digits of the number 2 power of 1000 (2^1000)?  Can anyone provide the solution or algorithm for this problem in java?


I came across a combinatorial identity today but have no idea how to handle the $\frac{1}{i+1}$ term:  $$\sum_{i=0}^m {m \choose i} (-1)^i \frac{1}{i+1} = \frac{1}{m+1}$$  How would I prove it?

Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$.  Writing out several terms, I think the answer is $1/(n+1)$, but I'm struggling to prove this. I would greatly appreciate it if someone could show how to prove this.


I am attempting to change the URL of my site, to make it more user friendly.  Currently users must navigate to www.domain.com/client/client/. I wish to display this as just www.domain.com/client. However, I still require the file path /client/client to exist (IE: there are files in /client/client that use ../folder, and I need these to still work)  Does anyone know if RewriteRule can accomplish this, or how else to accomplish this?

This is a  about Apache's mod_rewrite.   Changing a request URL or redirecting users to a different URL than the one they originally requested is done using mod_rewrite. This includes such things as:   Changing HTTP to HTTPS (or the other way around) Changing a request to a page which no longer exist to a new replacement. Modifying a URL format (such as ?id=3433 to /id/3433 ) Presenting a different page based on the browser, based on the referrer, based on anything possible under the moon and sun. Anything you want to mess around with URL   Everything You Ever Wanted to Know about Mod_Rewrite Rules but Were Afraid to Ask!  How can I become an expert at writing mod_rewrite rules?   What is the fundamental format and structure of mod_rewrite rules? What form/flavor of regular expressions do I need to have a solid grasp of? What are the most common mistakes/pitfalls when writing rewrite rules? What is a good method for testing and verifying mod_rewrite rules? Are there SEO or performance implications of mod_rewrite rules I should be aware of? Are there common situations where mod_rewrite might seem like the right tool for the job but isn't? What are some common examples?   A place to test your rules  The  web site is a great place to play around with your rules and test them. It even shows the debug output so you can see what matched and what did not.


I'm developing a Tamil web app (using PhoneGap) where I use unicode to display the Tamil language. The problem is, it is working fine in Android Emulator and in web (Firefox), but the fonts are not displaying in a Galaxy S device. I'm sure that I have used the following in my HTML file      <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />     <meta name="viewport" content="width=device-width, initial-scale=1">      <link rel="stylesheet" href="http://code.jquery.com/mobile/1.2.0-alpha.1/jquery.mobile-1.2.0-alpha.1.min.css" />     <script src="http://code.jquery.com/jquery-1.7.2.min.js"></script>     <script src="http://code.jquery.com/mobile/1.2.0-alpha.1/jquery.mobile-1.2.0-alpha.1.min.js"></script>   I really don't know what I'm missing.

Please excuse the length of this question. I need to explain all this to help others and to avoid helpful contributors to provide answer without asking clarifications.  My requirement in one line: "to enable an Android phone to display Tamil characters properly".  Elaboration: Tamil, like any other Indian language has complex character rendering system. Unlike English or other Latin based script, it has glyph (what you see in screen) composed of more than one character.  Android does not have ability to render such complex scripts (with exceptions). My aim is to know how I can provide such an ability to an Android phone or tablet.  Little background that I gathered so far: To display a glyph in screen, Android first needs a suitable font file.  Android device has a folder /system/fonts which has few of them.  The most interesting file in that folder is the DroidSansFallback.ttf.  As the name suggests, when Android's system fails to find a character in system fonts (that could be DroidSans.ttf or DroidSans-Bold.ttf etc) it falls back to search it in DroidSansFallback.ttf.  By replacing a suitable font file from PC (Latha.ttf or Lohit-Tamil.ttf - these are fonts for Tamil) and DroidSansFallback.ttf will enable to display Tamil characters in the device. It is not so easy to replace and it involves rooting the device and mounting the system as writable.   In spite of those troubles, even if the DroidSansFallback.ttf is replaced, the Tamil characters that are displayed are not rendered properly.  The Tamil character "தி" is a conjunct of two characters and instead of getting displayed as "தி", it will be displayed as "த ி" without space in between. Though this is enough to read short messages, it cannot be used to read books etc.  From Android 4.0 on wards, Tamil and other few languages are supported through browser as said in Android 4.x API overview as seen below.  Support for Indic fonts (Devanagari, Bengali, and Tamil, including the complex character support needed for combining glyphs) in WebView and the built-in Browser   The words to notice is "in WebView and the built-in Browser", which means that Tamil characters will be rendered perfectly if it is rendered as HTML content and will not be rendered otherwise.  Opera and other few browsers did this even before Android 4.0 by substituting image instead of character.  I noticed that in few devices that target Indian market (ex: LG Optimus One, most of Samsung phones and tablets) are able to display Tamil properly both in browser and even in places out of browser like in contacts, text messages, file names etc.  To my surprise they do this even in Android 2.3 onwards.  I also noticed that the same model targeting non-Indian country running same version of Android does not support Tamil character display.  This made me to investigate further and reached a conclusion that Android (as other Linux based OS) depends on a font rendering engine to display such complex characters.  The two engines that I came across are Skia and Harfbuzz. I noticed LG uses skia and Samsung uses Harfbuzz libraries in their devices to bring this ability.  I came across many websites suggesting to replaces these libraries and fonts. It did not work and results in freezing.  Fortunately I backed up using clockworkmod and hence I restored my phone.  Though I had explained this with Tamil, this is applicable for most of the Indian languages.  Here comes my question (if you are still reading;) ) Now, far sure it is clear that a TTF file should be present to provide characters and an appropriate libraries (libskia.so or libharfbuzz.so) are required to render them correctly.  Does any one know how these manufacturers are able to provide the ability? I am even ready to build my own ROM from AOSP (Android Open Source Project).


I mean, there's many other spells he could've cast, but why choose to launch a snake of all things?

In Chamber of Secrets, in the first Duelling Club class, Snape suggests Malfoy use the Serpensortia spell against Harry. This of course reveals that Harry is a Parselmouth, but how could Snape anticipate this? Was there any reason for Snape to suspect Harry is a Parselmouth? Or was it just a way to laugh at how Harry would get frightened?


My wife makes my wholemeal bread as she insists. She says every recipe lists 5 grams of salt otherwise the bread will end up having missing patches in baked form- it has happened with early loaves. We live in Japan and the loaves here are rather small. The bread tastes salty. What are my options to reduce the salty taste while maintaining the result of a decent loaf of wholemeal bread?  I have heard that soy sauce can reduce salty taste in other foods. This recipe includes 50% wholemeal flour and 50%  self-raising flour.

I've been doing a lot of yeast bread baking as of late and I got to wondering what the salt in the bread was for.  Upon doing some research it turns out (aside from perhaps some flavor) the purpose is to "Control" the yeast during the rise.  This got me to wondering if it was possible to make a yeast bread with no salt at all.  My first attempt was met with defeat, and upon some more experimentation I was able to get the salt down 75% with success.  Its the last 25% that alludes me.  Is it possible to make a yeast bread with no salt?


I have an MVC 4 web application and I need to enter and validate some email addresses, without sending an email to the user's email address.  Currently I am using basic regex email validation with this pattern:  [RegularExpression(@"\A(?:[a-z0-9!#$%&'*+/=?^_`{|}~-]+(?:\.[a-z0-9!#$%&'*+/=?^_`{|}~-]+)*@(?:[a-z0-9](?:[a-z0-9-]*[a-z0-9])?\.)+[a-z0-9](?:[a-z0-9-]*[a-z0-9])?)\Z",         ErrorMessage = "Please enter correct email address")]   Although this is validating email addresses, it passes 1@1.1 as a valid email address. For the moment I have a validation that requires symbols @ symbols . symbols where the symbols can be numeric/alphabetic and ._- .    I need more standard email validation for my MVC 4 application. How do I do that?

Over the years I have slowly developed a  that validates MOST email addresses correctly, assuming they don't use an IP address as the server part.  I use it in several PHP programs, and it works most of the time.  However, from time to time I get contacted by someone that is having trouble with a site that uses it, and I end up having to make some adjustment (most recently I realized that I wasn't allowing 4-character TLDs).  What is the best regular expression you have or have seen for validating emails?  I've seen several solutions that use functions that use several shorter expressions, but I'd rather have one long complex expression in a simple function instead of several short expression in a more complex function.


im trying to make a 338CM X 70CM sign in illustator, the design contain vectors and images. The printing place wants it to be 1:10 scaling size and im trying to understand one thing: if im sending him a 1:10 pdf file (33.8 cm X 7 cm instad of 338 cm X 70 cm) how the images wont be ruined after he will print it in the actual size? Also, when i open a 1:10 file, how do i set the bleeds in it? doing 1:10 also? (instad of 0.3 cm im doing 0.03 cm?) Thanks for the help

For wall-sized graphics and large banners (e.g. 3m × 5m), what is an acceptable PPI for print? As I understand it 300 ppi is the typical for 'small' artworks (esp. for clean text resolution). However, for small artworks, the audience usually engages at a much closer distance. Therefore, in the interests of keeping a bitmap file down to a reasonable size, can you get away with a much-reduced PPI for a large format/banner print?


I am trying to find a regex that matches brakets that may contain other brakets.  Example:  Match1(Match2())   I want the output to be: Match1:     $0 => 'Match1(Match2())'      $1 => 'Match1'      $2 => 'Match2()' Match2:     $0 => 'Match2()'      $1 => 'Match2'      $2 => ''  Is there a way to get it done, e.g. \w+\(.*?\)

Is it possible to write a regular expression that matches a nested pattern that occurs an unknown number of times? For example, can a regular expression match an opening and closing brace when there are an unknown number of open/close braces nested within the outer braces?  For example:  public MyMethod() {   if (test)   {     // More { }   }    // More { } } // End   Should match:  {   if (test)   {     // More { }   }    // More { } }


When I try to write  \begin{equation} {\hat{a}_{1}^{\dagger}}^{2} \end{equation}   I am getting this error  ! Double superscript. l.4 {\hat{a}_{1}^{\dagger}}^                             {2} ?    So what is the proper way of writing

When I write {{\tilde{C}}^{0}_{har}}^{\Gamma} (or the same with fewer curly brackets) in Tex I obtain a double superscript error and I can't solve it. Does someone know how to fix this?


I have a package of Great Value Hot & Spicy Beer Battered Jalapeno Slices that state that they are best if used by February of 2020. It is January 2021. What is your opinion of whether or not they are still good? They have been in the freezer the entire time.

How do I know if a given food or ingredient I have is still good, or if I should discard it?  How can I best preserve a food or ingredient?     This broad question is intended as a "general reference" question to quickly answer many how long will food keep for? questions. Please feel free to edit this question to expand and clarify as needed.


I would like to upgrade my Ubuntu 11.04 from the command line (this is a remote machine I can only SSH into). I am following . I am getting 404's from many commands I am trying to run such as:   sudo apt-get install update-manager-core  sudo apt-get update sudo apt-get install libkrb5-dev   What can I do to apt-get install these things without 404s from the command line? I can only use the command line.  Here is an example of the 404.  $ sudo apt-get install update-manager-core [sudo] password for melissa: Reading package lists... Done Building dependency tree Reading state information... Done The following NEW packages will be installed:   update-manager-core 0 upgraded, 1 newly installed, 0 to remove and 95 not upgraded. Need to get 165 kB of archives. After this operation, 1,294 kB of additional disk space will be used. WARNING: The following packages cannot be authenticated!   update-manager-core Install these packages without verification [y/N]? y Err http://archive.ubuntu.com/ubuntu/ natty-updates/main update-manager-core amd64 1:0.150.5.4   404  Not Found [IP: 91.189.91.13 80] Err http://security.ubuntu.com/ubuntu/ natty-security/main update-manager-core amd64 1:0.150.5.4   404  Not Found [IP: 91.189.91.14 80] Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/u/update-manager/update-manager-core_0.150.5.4_amd64.deb  404  Not Found [IP: 91.189.91.14 80] E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?

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


On one of the StackExchange sites, I have changed my display name from pacoverflow to something else. Recently there was a question on that site in which a lot of people left comments, including me. I just noticed that all of the comments on that question were moved to chat. So I went into the chat room, and the comment that I left actually has "pacoverflow" next to it, not my site-specific username. This seems like a bug.

I was using multiple SO sites,like many others, under my one email address. Later I decided to break one my account on one SO site (lets call it X.SE) because I did not want to have public profile on that account. The SO staff helped me create a separate account, with some restrictions, that is   I must not login using my old email address. If I do my account may automatically get merged again. I will lose some of my important gadgets that I worked hard for.   Now I understand this feature is not fully supported and I am fine with. But the problem I am facing now is when I chat on this site X.SE, my SO username is shown instead of my X.SE user name. Can this be fixed at least so I can stand independent on that site and get invoved in healthy discussions?


I've just read somewhere about "Dirty Cow" bug, and I'm a new user of Ubuntu 1604.    How can I know my kernel version? How to fix this bug? Am I in danger of hacking?   Thanks you all for your helps.

I've just heard of this bug "Dirty COW" that allows any user with read access to files to also write to them and gain administrative access. How do I protect against this bug?


Suppose you have multiple graphs in a pgfplot whose y ranges are [0 y1] [0 y2] etc, y1 < y2 < .... I want to divide all graphs by max(yi), so that the plot would be in the y range [0 1] (but maybe y axis range in [0 1.2] to have a nice display).  In other words, I want to normalize the y axis, to compare the plots on a relative basis.  I used scale y tick=manual:{}{\pgfmathparse{#1/120}}, but it needs to know the maximum 120. Even if I put the correct maximum value, the plot is normalized to  [0 0.97]. Is there a way to do it automatically, without having to look up data? Let's say I now which graph contains the maximum. There should be a simple solution to this.  Here is a MWE.   \documentclass{standalone}  \usepackage{tikz,pgfplots} \begin{document}  \begin{tikzpicture} \begin{axis}[     xmin=0,      xmax=4,      ymin=0,      ymax=3.2,     xlabel=$x$,     ylabel=$y$] \addplot[smooth,mark=*,blue] plot coordinates {     (0,2)     (2,3)     (3,1) }; \addlegendentry{Case 1}  \addplot[smooth,color=red,mark=x]     plot coordinates {         (0,0)         (1,1)         (2,1)         (3,2)     }; \addlegendentry{Case 2} \end{axis} \end{tikzpicture}  \end{document}   For instance, in this example I want to divide all y numbers divided by 3. The actual data file can be quite complicated; it's preferred that the pgfplots fins this maximum and normalizes all y axis by that.

I am new to pgfplots and would like to get your help on my question. Basically I need to read y value from a file that only contains a list of data (in one column), normalize each value by y=(y-min(Y))/(max(Y)-min(Y)) where max(Y) is the maximum value in the list and min(Y) is the minimum value in the list and plot them. For example, if I have {1,2,3,4} then on the plot, the value of y will be {0, 1/3, 2/3,1}.   I use \addplot table [x expr=\coordindex, y index = 0] {filename}; to draw x and y on the plot. What's the normalization expression for y? Is there existing function to do that? If not, can we extract the max(Y) and min(Y) in pgfplots?


1.He has been watching TV.  What does this sentence mean?  Does it mean that the person started watching TV sometime before and still watching it or the person started watching TV sometime before and has stopped watching it? does it mean something else rather than my options?

Non-native speakers often get confused about what the various tenses  and aspects mean in English. With input from some of the folk here I've put together a diagram that I hope will provide some clarity on the matter.  I offer it as the first answer to this question. Consider it a living document. Input is welcome, and good suggestions will be  incorporated into the diagram.    Nota bene: What this is not is a discussion of whether there are  more than two tenses in English. , to which this question is not intended to supply arguments one way or the other.  Here, the aim is to provide an overview of what constructions English-speaking people use for conveying information about actions referring to past, present, and future, and to provide it first and foremost to precisely the people who are likely to use "tense" as a catch-all term in their search, rather than to linguists who know better.  Breaking News There is now an excellent ELU blog article titled  . It is highly recommended reading.


I know how to set up KDE so that I can initially login without a password.  But is there a way to enable login without a password following a logout?

I've been using Ubuntu 12.04 LTS since release and am trying to figure out a couple things about all of these passwords and key-ring prompts that I've just been living with for a while.  Ever since install it seems that every time I boot up my computer and want to do anything (ie. use the internet, use a internet browser, install something, delete something, pick my nose) I'm always prompted for either a normal password entry or a key-ring password entry.  Is there anyway to turn off all of this "security" and tell my Ubuntu that it can trust what I'm doing and go take a shower?


Find the greatest common divisor of $2^{2004}-1$ and $2^{2002}-1$.   Using Euclidean algorithm:  $$2^{2004}-1=4(2^{2002}-1)+3$$ $$2^{2002}-1=x\cdot 3+y$$  The solution manual says that $2^{2002}-1$has the remainder $0$ when divided by $3$, that is $y=0$ so GCD is $3$. But how do I find that remainder?


I need to find the biophysical parameters(biomass) from the LiDAR point cloud data. For that I need the height of the trees from the data. Currently I am having the general height with respect to sea level(400 range).   I tried with lasheight, and also tried to create dem and dsm and from them chm but nothing is working with the data set. I have attached my las data too below.    I tried with lasheight, and took the output, its supposed to give the height information as 0 for ground and for the trees for example 10m or something. but I'm getting the same 400 range values for ground and trees.         I tried with las2dem and tried to save its output as tif image.(I am programing using R), while reading that tif image to R. Its giving error. Its not taking that tif image

How I can get Digital Height Model (only object heights, DSM - DTM = DHM)?  Many applications can do this, but they convert it to GRID or TIN format. I was wondering if it was possible to keep the data as point clouds.


I've got a fixed layout page and the client has asked for it to have "shades of blue". What colour would you recommend for the background, page wrapper background, text, dropdown menu and the buttons on the side?

No matter how nice the composition, flow, and lines of my design are, if I am not copying directly from nature, I have a very difficult time picking a decent color scheme.  It either looks too drab, or too garish.  Is there a good resource that will help me to choose a color scheme that has 2 or 3 colors, and the colors do not clash?  I'm not looking for specific colors or color schemes.  What I need is a resource that will help me choose a color (or colors) that go nicely with, or provide a good accent to, whatever main color I am working with on the design.


How do companies do this typically? Is there any metadata linkage between test cases and code components covered?

How do companies clean up test cases? If I have 5000 tests in my library and 1000 of them are deprecated because we have cleaned up the code associated originally, how do we ensure that the tests are removed?


I'm using BibLaTeX with biber and the authortitle style and I want to omit the "p." when citing an entry in my .bib-file BUT ONLY for entries with a non-empty shorthand field. I managed to do so by changing the postnote bibmacro in the following way:  \renewbibmacro*{postnote}{%   \iffieldundef{postnote}     {}     {\setunit{\postnotedelim}%      \iffieldundef{shorthand}        {\printfield{postnote}}        {\DeclareFieldFormat{postnote}{##1}%         \printfield{postnote}}}}   This seems to work. But if I do it like this: \DeclareFieldFormat{postnote}{#1} I get an error message. Why is that the case? What is the difference between {#1} and {##1}?  Here is the MWE:  \documentclass{article}  \usepackage[style=authortitle,backend=biber, firstfull=true]{biblatex}  \renewbibmacro*{postnote}{%   \iffieldundef{postnote}     {}     {\setunit{\postnotedelim}%      \iffieldundef{shorthand}        {\printfield{postnote}}        {\DeclareFieldFormat{postnote}{##1}%         \printfield{postnote}}}}  \usepackage{filecontents}  \begin{filecontents}{\jobname.bib}  @Book{A1,   Title                    = {Title1},   Author                   = {AuthorA},   Year                     = {1900},   Shorthand                = {GuI} }  @Book{B2,   Title                    = {Title2},   Author                   = {AuthorB},   Year                     = {1900} }  @Book{C2,   Title                    = {Title2},   Author                   = {AuthorC},   Year                     = {1900} } \end{filecontents}  \addbibresource{\jobname.bib}  \begin{document}  "Some citation of a shorthand title"\parencite[][34]{A1}  "Some citation of the same shorthand title in a footnote"\footcite[][34]{A1}  "Some citation of the same title from another page"\footcite[][70]{A1}  "Some citation of a non-shorthand title"\footcite[][12]{B2}  "Some citation of the same non-shorthand title from another page"\footcite[][15]{B2}  "Some citation of the same non-shorthand title from another author"\footcite[][15]{C2}  \printshorthands  \printbibliography  \end{document}

I've seen sometimes that people use a double pound sign (##) when defining/using arguments.  What is the difference between the normal argument, #1, and the double sign one, ##1? Are there any restrictions for its use? Can you list the good practices, if any, for this type of arguments.


I am nowhere close to a physicist so please correct me anywhere I am wrong   From what I understand about the observer effect, when we measure one intrinsic property of an electron such as position, the mere act of observation instantly alters another property of that electron such as momentum, so we can never accurately measure both.  Continuing, the reason observing an electron changes one of these properties is because when we use electronic instruments to sense/measure these properties, we are shining light upon the electron which has enough energy itself to alter that electrons properties in that instant, so what was before the observation is different from what is observed in that moment.  So, my question is:   Isn't the problem that we just don't have the technology that could sense/measure the properties of an electron without disturbing it? Theoretically if we did have such a device as the aforementioned, doesn't this mean that a particle's state is determinable and particles don't actually exist in multiple states simultaneously?

From what I understand, the  states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on equipment but just a natural phenomenon.  However, isn't this just an observational limit? There is a definite velocity and momentum, we just don't know it. As in, we can only know so much about the universe, but the universe still has definite characteristics.  Considering this, how do a wide range of quantum mechanical phenomena work? For example, quantum tunneling - its based on the fact that the position of the object is indefinite. But the position is definite, we just don't know it definitely. Or the famous light slot experiment? The creation of more light slots due to uncertainty of the photon's positions?  What I am basically asking is why is a limit on the observer, affecting the phenomenon he is observing? Isn't that equivalent to saying  because we haven't seen Star X, it doesn't exist? It's limiting the definition of the universe to the limits of our observation!


There seems to be a mix up with my login account credentials. Whenever I go to a site that wants me to use Stack Exchange to login, that site will not accept my email as a valid login.  I use the one that is represented in my account profile page, but "Get Code Done" for example, does not recognize the email as a Stack Exchange email.

Enter email id in login box and press login button, without entering the password.        Then click on g+ login you will get an error that 'The password is incorrect. Which is a bug, it should redirect to g+ login screen'


Windows 10 seems to want to control everything while I attempt to install Ubuntu. How can I set up a separate partition for Ubuntu and keep Windows 10?  Please don't suggest deleting Windows 10. I don't like 10 but I don't want to lose it now either.

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


One of my colleagues has a name that ends in an apostrophe, namely Faee'. Recently when sending an email I realized I wasn't sure how to refer to something that belongs to them using the typical " 's " possessive structure and ended up rewriting my sentence to avoid this. My question is whether I am safe to just use " 's " in the future or if I should be doing something different.

I am an editor editing a book review, and I'm not sure how to deal with this:    Serhii Bilokin’’s book    The author has chosen to transliterate with the apostrophe at the end of the name, but it looks very odd with the English possessive tacked on at the end. I know that  the the apostrophe in Ukrainian language/names changes the pronunciation of the surrounding letters, but that's about it, so I'm not sure how integral the apostrophe is to the name. (I've seen it transliterated with and without, so I assume there are multiple right ways, but I'd prefer to respect the author's choices.) I'm having a terrible time trying to find precedents to base my decisions on here. I assume the issue is extra-grammatical. Any insight is appreciated! This type of thing fascinates me, but it's also very confusing.


Given that $f$ is continuous on $[0,1]$, differentiable on $(0,1)$, and $f(0)=0$, $f(1)=1$, prove   $$\text{There exists $c_1 \lt c_2$ such that $\frac{1}{f'(c_1)}+\frac{1}{f'(c_2)} =2$}$$ and    $$\text{There exists $c_1 \lt c_2$ such that $f'(c_1)f'(c_2)=1$} $$   I have already proven that there exists $c \in (0,1)$ such that $f'(c)=1$ and there exist $c_1 \lt c_2$ such that $f'(c_1)+f'(c_2)=2$. I tried using these to help to prove the existence of the above.    I've just learned Mean Value Theorem, Rolle's Theorem and Intermediate Value Theorem, which I've used to answer the first two parts. Given the mark allocation for these two questions, they're supposed to be easy. However, I can't seem to find my way around.  Please advise me on what I should do to simplify the problem. Thank you!

Given $g$ is continuous on $[0,1]$ and differentiable on  $(0,1)$,   $g(0)=0$, and $g(1)=1$.        1) Prove that there exist $0<c_1<c_2<1$ such that   $$\frac{1}{g'(c_1)}+\frac{1}{g'(c_2)}=2.$$       2) Prove that there exist $0<c_1<c_2<1$ such that    $$g'(c_1)g'(c_2)=1.$$   I am thinking if Mean Value Theorem would help, but Mean Value theorem could only prove that in interval (0,1) there exists $g'(c)=1$.


I am about to buy clothes to cosplay Pansy Parkinson- but... what were clothes like in the wizarding world? Parkinson is a blood supremacist so she wouldn't wear muggle clothes, and since so many wizards are pureblood, what do they wear? is it linked to a specific time?

In the Harry Potter films, Harry, Ron, Hermione, and the other students wear muggle clothing while not in classes at Hogwarts:    Even "purebloods" like Draco Malfoy wear muggle clothes, albeit more expensive and distinguished ones:    In the books, do students wear this kind of clothing while not in classes at Hogwarts?


I'm trying to write a minimax algorithm for connect 4 in Java, but am getting an error while trying to iterate through a list of possible moves.   It says that      Exception in thread "main" java.util.ConcurrentModificationException     at java.util.ArrayList$Itr.checkForComodification(Unknown Source)   at   java.util.ArrayList$Itr.next(Unknown Source)   I've looked around online, and have found some things (about updating an object within the iterator), but am not quite sure what to do.  Here is my code.  public class AI {        public Move minimax(Board board, int depth, int alpha, int beta, String           player, Move move) {          if(depth == 0 || board.getScore() >= 512) {             return move;         }          else if(player.equals("computer")) {             Move maxMove = new Move(0,0);             maxMove.moveScore = -1000000;             Iterator<Move> it = board.possibleMoves.iterator();             while(it.hasNext()) {                 Move m = it.next();                 board.putPiece(player, m.yMove);                 m.moveScore = board.getScore();                 if (board.getScore() < minimax(board, depth-1, alpha, beta,      "human", m).moveScore) {                     maxMove = m;                 }                 else {                     maxMove = minimax(board, depth-1, alpha, beta, "human",     m);                 }                 board.removePiece(m);                 alpha = Math.max(alpha, maxMove.moveScore);                 if (alpha >= beta) {                     break;                 }              }              return maxMove;         }          else {             Move minMove = new Move(100, 100);             minMove.moveScore = 1000000;             for(Move m : board.possibleMoves) {                 board.putPiece(player, m.yMove);                 m.moveScore = board.getScore();                 if (m.moveScore < minimax(board, depth-1, alpha, beta,      "computer", m).moveScore) {                     minMove = m;                 }                 else {                     minMove = minimax(board, depth-1, alpha, beta,     "computer", m);                 }                 board.removePiece(m);                 beta = Math.min(beta, minMove.moveScore);                 if(alpha >= beta) {                     break;                 }              }              return minMove;         }     } }   Any and all help is appreciated.   Thanks,

We all know you can't do the following because of ConcurrentModificationException:  for (Object i : l) {     if (condition(i)) {         l.remove(i);     } }   But this apparently works sometimes, but not always. Here's some specific code:  public static void main(String[] args) {     Collection<Integer> l = new ArrayList<>();      for (int i = 0; i < 10; ++i) {         l.add(4);         l.add(5);         l.add(6);     }      for (int i : l) {         if (i == 5) {             l.remove(i);         }     }      System.out.println(l); }   This, of course, results in:  Exception in thread "main" java.util.ConcurrentModificationException   Even though multiple threads aren't doing it. Anyway.  What's the best solution to this problem? How can I remove an item from the collection in a loop without throwing this exception?  I'm also using an arbitrary Collection here, not necessarily an ArrayList, so you can't rely on get.


I was browsing  looking for gems I could learn some stuff from.  In this list you can only see the title of the question, it would be nice to see the tags as well. In the titles shouldn't be the tags, which is good in my opinion, but then it's hard to find the questions that are interesting to you here.

I'm trying to get the Weed-Eater hat on Stack Overflow. To do so, I'm looking at the list of questions . The problem is, no tags show up there, and so it's rather difficult to see which ones I have a shot at. Any chance of showing the tags on this page?  I realize that getting this before Winter Bash is over would be difficult, but it would be good to keep such things in mind for the future.


Do you know why we say study window not study's window although we mean the window which belongs to study(room)?

Do you know why we say study window not study's window although we mean the window which belongs to a study(room)? I want to know the reason.


Here is my problem: I'm trying to install steam and I got this error:  sudo apt-get install steam-launcher  The following packages have unmet dependencies: steam-launcher : Depends: curl E: Unable to correct problems, you have held broken packages.   So I try to install curl and i got this:  sudo apt-get install curl  The following packages have unmet dependencies: curl : Depends: libcurl3 (= 7.34.0-1ubuntu1) but 7.35.0-1ubuntu2 is to be installed E: Unable to correct problems, you have held broken packages.   I have the latest version of libcurl3 (7.35).    So how can I install an old version of libcurl3 (7.34)?  I searched  but have not found anything.

After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.


In Mexican Spanish (not sure if other Spanish speaking countries use the word too) we call "tocayo" to those people that share the same name as us (but not necessarily the same last name i.e., Juan Gonzalez and Juan Carlos Castillo are tocayos).  I was wondering if an equivalent for this word exists at all in English or maybe even an expression?

If a person shares my name, in Dutch there is the word "naamgenoot", meaning roughly 'member of the same name'.  John A: Hi, my name is "John"  John B: O, then we're insert solution word here!  Similarly,  'classmate' is 'klasgenoot' in Dutch 'roommate' is 'kamergenoot' in Dutch  I'm pretty sure I cannot call someone with the same name as mine a 'namemate' :)  Edit Because sceptics appear to be frustrated mightily by an apparent lack of research, there was  in chat, with no satisfactory conclusion. /Merriam Webster namesake appears to be linked to intentional name correspondance (being named after someone). There may be a US/UK English divide there.  "I was named after my grandfather. I am his namesake." -   Also, the introduction seems to hint at much broader meaning:  "Namesake is a term used to characterize a person, place, thing, quality, action, state, or idea that has the same, or a similar, name to another"   Do you know of a better word/phrase to describe this succinctly?


Say I have a project that I've done in 30 FPS.  I now want to re render it for final use at 60 FPS to match my destination project (shot at 60fps).  My current project (at 30FPS) is 2 seconds long. Of course, if I set the project to 60, it will need double the frames. So my current 60 frame project must be "expanded" to 120 frames. If I have key frames at, let's say, 15 and 30 frames (I have more too), is there an easy way to just tell it to scale all the key frames to fit my new project length and frame rate?

How can I change the animation fps when I already have finished making an animation? I already did an animation and I don't want spend some time recalculating the time by hand, is there a easy way to change the frame rate without making the animation speed up or slow down?


Find all monic complex polynomials $P(x)$ such that $P(x)|P(x^2)$.  My progress so far is that I have find that for degree 1, $P(x)=x, x^2$ are the only ones. For degree 2, they are $P(x)=x^2+x+1, x^2, x^2-1, x^2-x, x^2-2x+1$. I also prove that these are only solutions for degree 1 and 2. However I do not see how this generalizes. Any help please?

The Factor Square Property (FSP) is the divisibility of the polynomial $f(x^2)$ by $f(x)$.   Is $x^2+x+1$ the only FSP irreducible polynomial of degree $2$ ? Are there other linear polynomial besides $x$ and $x-1$ with FSP? Do we have other FSP irreducible polynomials of degree $3$ or $4$? Any of these have integer coefficients?? Are there any other observations you can make about polynomials with FSP?


I need to get a retrun value from dynamically calling java class by passing a variable values to that calling method. I try to use the java.lang.reflect.Method;  PredictionManager pm = new PredictionManager(); Class invokeclass = pm.getClass();  Class[] cArg = new Class[1]; cArg[0] = Integer.class;//Instances.class;  Method lMethod = invokeclass.getMethod("showLong", cArg); Object aaa= lMethod.invoke(pm, cArg);   in there I need to pass the value as a argument. but this method needs to give the parameter type. not the parameter value.  What can I do?

If I have two variables:  Object obj; String methodName = "getName";   Without knowing the class of obj, how can I call the method identified by methodName on it?  The method being called has no parameters, and a String return value. It's a getter for a Java bean.


I have conducted PCA that has reduced the dimensions of my data from more than 20 to 7 (7 PCAs explain about 85% of the total variation). As a second step, I have to cluster my data based on these new 7 PCAs. My question is: how I should reconstruct/transform my data (cbind/rbind)? As I understand, each PCA is a weighted mix of the original variables. So should I just replace the old variables with the PCAs? Also, how should I interpret the final results? If there was no PCA, each cluster would incorporate all variables in some proportion. But after PCA, how would I describe each cluster? For instance, cluster 1 contains 40% of PCA 1 and PCA 1, in turn, has xxx loading scores? Something like this? Would greatly appreciate any help on interpreting this. Thanks!


I was corrected in the middle of a conversation because I used "John and I are friends" as opposed to  "John and me are friends."  I think the former sounds correct, but am not sure. Could someone help?

I have two sentences:          John, Jane, and I went to the party.     He and I went to the party.    But I think there is a rule that says a pronoun at the end of a list should be in a special form (for "I", the special form is "me").  So, my sentence 1 and 2 should be rewritten like this:        John, Jane, and me went to the party.     He and me went to the party.    But in a lot of writing, sentences like sentence 1 and 2 are used instead of sentence 3 & 4.  Is there a special rule that allows not using "me" for sentences similar to 1 and 2 for casual writing?


I would love to have a nice tikz-version of this drawing of a binomial tree.  and my lines are not that nice, can anybody help me So far I've made the following: \documentclass{standalone} \usepackage{graphicx} \usepackage{subfig} \usepackage{pgf,tikz} \usetikzlibrary{positioning} \begin{document}   % Set the overall layout of the tree \tikzstyle{level 1}=[level distance=2cm, sibling distance=2cm] \tikzstyle{level 2}=[level distance=2cm, sibling distance=2cm] \tikzstyle{level 3}=[level distance=2cm, sibling distance=2cm]  % Define styles for bags and leafs \tikzstyle{bag} = [text width=2em, text centered] \tikzstyle{edge from parent}=[draw] \tikzstyle{end} = [text width=3em, text centered] %\tikzstyle{every node}=[fill=red!30,rounded corners]    % The sloped option gives rotated edge labels. Personally % I find sloped labels a bit difficult to read. Remove the sloped options % to get horizontal labels.   \begin{tikzpicture}[grow=right, sloped, edge from parent] \node[bag] {$S_{0}$} % First bag child{node[bag] {$S_{0}d$} % Step 1 down    child{node[bag]{$S_{0}d^{2}$} % step 2 down        child{node[end]{$S_{0}d^{3}$}} % step 3 down        child{node[end] {}} % step 3 up        }    child{node[bag] {} % step 2 up        child{node[end]{}} %step 3 down        child{node[end] {}} %step 3 up            }   }    child {node[bag] {$S_{0}u$} % step 1 up       child{node[bag]{$S_{0}ud$}           child{node[end]{$S_{0}ud^{2}$}} % step 3 down           child{node[end]{}} % step 3 up           } % step 2 down         child{node[bag ]{$S_{0}u^{2}$} % step 2 up            child{node[end]{$S_{0}u^{2}d$}} % step 3 down            child{node[end]{$S_{0}u^{3}$}} % step 3 up        }   };   \end{tikzpicture}    \end{document}

For a class in derivatives pricing I would like to find a way to quickly and efficiently draw recombining binomial trees. The class involved quite a few of those trees and it would be immensely helpful to come up with a way that would allow me to semi-automate the process.  Here's an example (excuse the low resolution; it's the best I've been able to find):   I want to achieve this look by specifying only the number of periods (i.e. horizontal levels); the probability p of going upwards from any node; and the possible values for all nodes. The probabilities p  and 1-p should then automatically be displayed above the connecting lines upwards and downwards respectively (as shown in the example). All values for the nodes themselves should be entered manually and their number of course depends on the number of levels.  I am of aware of the possibility of specifying node locations manually in order to achieve the recombining tree but my experience does not suffice to build something to automate this. My question is not about drawing recombining trees in general; it is about finding a way to do it very quickly, as I use LaTeX for my lecture notes.


I am using this format for my section and subsection headings (it is centered and numbers have dots):  \documentclass[12pt]{article} \usepackage[center]{titlesec}  \titlelabel{\thetitle.\quad} %dots after title number   But I cannot unbold it by using most of the unbold commands because centering changes in most of them. Is there way to unbold the section and subsection headings with this format?

How do I specify the fonts, and general font size, for the titles, chapters and sections in my document  Update:  I can see how my question is confusing.  I use \section and \chapter etc. to organise my document, and I would like to change the way the section and chapter titles are displayed.


I have a Scenario, were I need to place help icon inside a modal window, Even though I have help icon on screen i.e... behind modal window. Is it is ok to have Help icon inside modal window, If not is there is any good reason for not to have that inside modal window.

Using bootstrap modals, I keep running into the issue of having an info modal with content inside of it, but there's a need to have a "confirm your decision" modal/popup on top of the initial modal.   E.g. I have a page with a list of users. You can click on a user to open a modal with user info inside of it. Then there will be maybe a "remove user" button in the modal that requires a "confirm remove user" modal.  Is it ever a good idea to have a modal on top of another modal or am I using modals wrong? Should I use actual pages instead?


I would like to have the full control on the Windows 10 updates. I have already searched on the Internet and I have found this Github repository:   I need to know if those PowerShell scripts are enough or if I need to do some extra stuff.

We've upgraded some machines to Windows 10 and realized there were some updates which updated as required. However, I realized there was no option available to stop the download similar to that on Windows 7 and 8.1. The only way I could stop the download was to stop the Windows Update service.  My question is does anyone know of a way to stop auto updates or is stopping the service is the only solution?


There is a black hole, called Gargantua, featured in the recent blockbuster Interstellar. I understand why the accretion disk is bright (friction), but why does it seem to be flowing in two perpendicular directions?   I acknowledge it may just be a design-based decision made by the special effects team to make things look pretty, but perhaps there is an in-universe explanation I cannot conjure.

I was expecting a whirlpool in 3D and the matter glowing from friction as it nears the center, as I expected a event horizon to be negligible visually.  How does this depiction work? How big is the central sphere? I am puzzled by the perpendicular circles. Are they the event horizons if they are both visible? What would be a path of a particle as it gets swallowed into the singularity?


When I compile this code the error that appeared is LaTeX Error: File '1053817122' not found.  I wish for this image (that is not found) to appear in my pdf with a  height of 4 centimeters and a width of 3 centimeters.    This is the code I have Used  \documentclass[11pt,a4paper,sans]{moderncv}  \usepackage[spanish,english]{babel} \usepackage[utf8]{inputenc}  \moderncvstyle{casual}  \moderncvcolor{blue} \usepackage{lipsum}   \usepackage[scale=0.75]{geometry}   \firstname{Juan Pablo} % Your first name \familyname{Muñoz Diaz} % Your last name  \title{Hoja de Vida} \mobile{321 643 9819} \email{jpmunozd@unal.edu.co}  \photo[70pt][0.4pt]{1053817122}   \begin{document}  \makecvtitle % Print the CV title \end{document}

In order to insert an image in LaTeX, I do as follows, but I get an error telling that the file 'me.jpg' is not found.  Where should I save my image files to do this?   \documentclass{article} \usepackage{graphicx} \begin{document} \begin{figure}[h]    \centering   \includegraphics[width=0.2\textwidth]{me.jpg}   \caption{Some figure} \end{figure} \end{document}