Proof of Euclid's formula for primitive Pythagorean Triples

I have been reading about Pythagorean triples from the wiki page link .  It says that a pythagorean triple consists of 3 positive integer's $ a, b, c $ such that $ a^2 + b^2 = c^2 $.  Also if all the integers in a triple say $ a, b, c $ are relatively prime then the triplet is called Primitive Pythagorean triplet.  As I was reading more in this article it also described about generating  triple using Euclid's formula.  the formula is as follows :  $ a = m^2 - n^2, b = 2mn, c = m^2 + n^2 $ where $ m > n > 0 $  for any 2 values of $m$ and $n$ the above formula will give a Pythagorean Triple.  To get a Primitive Pythagorean triple, $m$ and $n$ have to co-prime and not both odd.  I wanted to understand the proof of this formula.  I don't understand this part of the proof which is also given in the wiki page.  "As ${{\tfrac {m}{n}}}$ is fully reduced, m and n are coprime, and they cannot both be even. If they were both odd, the numerator of ${\displaystyle {\tfrac {m^{2}-n^{2}}{2mn}}}$ would be a multiple of 4 (because an odd square is congruent to 1 modulo 4), and the denominator 2mn would not be a multiple of 4. Since 4 would be the minimum possible even factor in the numerator and 2 would be the maximum possible even factor in the denominator, this would imply a to be even despite defining it as odd. Thus one of m and n is odd and the other is even, and the numerators of the two fractions with denominator 2mn are odd. Thus these fractions are fully reduced (an odd prime dividing this denominator divides one of m and n but not the other; thus it does not divide m2 ± n2). One may thus equate numerators with numerators and denominators with denominators, giving Euclid's formula"


I just want to clarify something. Why is person1 and person2 still referring to the same object?  class Person{ private String name; Person(String newName) { name = newName; } public String getName() { return name; } public void setName(String val) { name = val; } }  class Test { public static void swap(Person p1, Person p2) { Person temp = p1; p1 = p2; p2 = temp; } public static void main(String args[]) { Person person1 = new Person("John"); Person person2 = new Person("Paul"); System.out.println(person1.getName()+ ":" + person2.getName());  swap(person1, person2);  System.out.println(person1.getName()+ ":" + person2.getName());  } }   Output would be:  John:Paul John:Paul   I was wondering why John and Paul didn't swap?


Paying USD 1000 towards the principal on my mortgage

I bought a home worth 200,000 paid 20% down, my interest rate is 4%, 30 yr fixed Remaining Loan 160,000. Initially, lets say I pay around 1000 USD (200 toward my principal and 800 towards my interest).(May not be accurate numbers) Now the balance left on my mortgage is 159,000.   If I pay additional 1000 USD towards my principal after paying my balance due this month, Starting next month when I have make my mortgage payment, would I be paying interest on 159,000 or 158,000.   I realized through internet that the additional payments would only cut the down the 30yr term. That is, instead of paying for 30 years, I might be paying for 29 years 11 months. But there would no change in the interest calculation.   Is that true? Appreciate your thoughts in advance.


Error in installing R on Ubuntu 18.04 bionic release

Running the command sudo apt install r-base:  E: Failed to fetch http://in.archive.ubuntu.com/ubuntu/pool/main/i/icu/libicu-dev_60.2-3ubuntu3_amd64.deb: Connection failed [IP: 91.189.88.152 80]   I have tried adding lines to the sources.list Also tried using aptitude.. Followed the steps on the link   Can someone help me ? Thank You.


Regarding black holes and the speed of light

Prior to a black hole reaching sufficient (size ) to stop radiating light (due to excessive gravity ) would the speed of radiation of light slow smoothly down to zero (as the hole draws closer to the critical size)


If $1+ab$ divides $a^2+b^2$ , prove that the quotient is a perfect square.   Tried to use the fact that $\displaystyle\frac{a^2+b^2}{1+ab}$ is an integer but I am stuck.


bijective function over $\mathbb{N}$ that isn't $f(X) = (X)$

I'm struggling to come up with a good example for a bijective function over $\Bbb N$. I've come up with:  $f(n) =\begin{cases}           1,& n=0\\          0, &n=1  \\        n, &\text{otherwise}\\ \end{cases} $  Firstly, can you confirm this is acceptable, and secondly, does anyone have any other examples? (Perhaps a more beautiful one!)


Why does the flagging dialogue think I've raised a flag I haven't?

The flagging dialogue tells me that I have raised a duplicate flag on that question. I haven't. I flagged it as off topic because instead of inline code it relied on a link (now broken).


Upload image not working after providing wrong URL

Drag and drop or click here to upload your image area is not working if error message is shown. If I try to add an image into a post and provide a wrong URL(not intentionally) which is not in the format recognized by SE sites it displays me,     Failed to upload image; the format is not supported | Close   This is okay. But the option,     Drag and drop or click here to upload your image (max 2 MiB)   shown above this error message is not responding on-mouse-click unless I click the Close to clear the error message shown below this message.     (i.e.) The local file upload window is not opening. However, the drag and drop functionality works fine even if the error message is shown. So the upload window works partially.   Expected behavior:  When I click the "Click here to upload your image", it should always open me the file upload window and clear any error messages shown below.  Tested on:  Firefox 39 and Chrome 44 in Windows 7 PC


What is the distribution of the ratio of two normals?

I need to use the ratio of two variables as the dependent variable in a regression. Both variables are normally distributed but with positive values. I can either center them or use as it is.  If I center them: the ratio of two centered normals is a Cauchy distribution. Is it therefore meaningful to do a "Cauchy" regression (e.g. using JAGS or Stan?)   If I leave as they are: What would be the distribution of their ratio?


How to check whether the linux system using a large disk space?

I am using VirtualBox. I installed a ubuntu system on it. At the beginning, I set default 8GB disk space. But it's not big enough so I want to add more space on it.  I used this way(add to 20GB):  VBoxManage modifyhd my_ubuntu.vdi --resize 20000   After I restart my ubuntu, I run these commands in the terminal:  $ df -h Filesystem      Size  Used Avail Use% Mounted on udev            1.3G     0  1.3G   0% /dev tmpfs           256M  4.4M  251M   2% /run /dev/sda1       5.3G  5.0G     0 100% / tmpfs           1.3G  224K  1.3G   1% /dev/shm tmpfs           5.0M  4.0K  5.0M   1% /run/lock tmpfs           1.3G     0  1.3G   0% /sys/fs/cgroup tmpfs           256M   48K  256M   1% /run/user/1000  $ lsblk NAME   MAJ:MIN RM  SIZE RO TYPE MOUNTPOINT sda      8:0    0 19.5G  0 disk  ├─sda1   8:1    0  5.5G  0 part / ├─sda2   8:2    0    1K  0 part  └─sda5   8:5    0  2.6G  0 part [SWAP] sr0     11:0    1 55.5M  0 rom   Why can't I see the addition space under df -h command? But can see it by using lsblk? And, is it really that my system is 20GB available and useful now?


Are there statistic/probabilty applications specifically made for card game designers?

I am developing a card game that involves building out sequences of matching symbol pairs and also has a lose state for a (different set) of symbols that is hidden to the player. Trying to create an atmosphere of paranoia.  I want to be sure I'm balancing the deck to create probably winning and losing sequences and can code a bit - but I was wondering if any of you used a specific application to run probabilities? Mac OSX would be great.


NullPointerException when calling MainActivity method in Fragment

There is setLocale method in MainActivity.class.  public void setLocale(String selected) {     Locale locale = new Locale( selected );     Locale.setDefault( locale );     Configuration config = new Configuration(  );     config.setLocale( locale );     getBaseContext().getResources().updateConfiguration( config, getBaseContext().getResources().getDisplayMetrics() );      SharedPreferences.Editor editor = getSharedPreferences( "LanguageSetting", MODE_PRIVATE ).edit();     editor.putString( "MyLanguage", selected );     editor.apply();  }   I want to call this method above in a Fragment below.  @Override     public void onItemClick(AdapterView<?> parent, View view, int position, long id) {         final String[] languageItems = {"English", "Polish"};         mainActivity = new MainActivity();         switch (parent.getItemAtPosition( position ).toString()){             case "Language":                 new AlertDialog.Builder( getContext() ).setTitle( R.string.nav_bottom_dialog )                         .setSingleChoiceItems( languageItems, -1, new DialogInterface.OnClickListener() {                             @Override                             public void onClick(DialogInterface dialog, int which) {                                 switch (languageItems[which]){                                     case "English" :                                         mainActivity.setLocale( "en" );                                         mainActivity.recreate();                                         break;                                     case "Polish" :                                         mainActivity.setLocale( "pl" );                                         mainActivity.recreate();                                         break;                                 }                                  dialog.dismiss();                             }                         } ).show();   It works when I have setLocale method and run it in MainActivity. I don't know why it doesn't work when I call the method in a Fragment showing NullPointerException Error like below.  There is no any error shown in Android Studio, does anyone know why??  E/AndroidRuntime: FATAL EXCEPTION: main     Process: org.language.languageapp, PID: 16894     java.lang.NullPointerException: Attempt to invoke virtual method 'android.content.Context android.content.Context.getApplicationContext()' on a null object reference         at android.content.ContextWrapper.getApplicationContext(ContextWrapper.java:118)         at org.techtown.techApp.MainActivity.setLocale(MainActivity.java:134)         at org.techtown.techApp.ui.fragment.Fragment01$1.onClick(Fragment01.java:74)   MainActivity.java:134 =>  getBaseContext().getResources().updateConfiguration( config, getBaseContext().getResources().getDisplayMetrics() );  Fragment01.java:74 => mainActivity.setLocale( "en" );


6-month UK visa from Russia refused. What to do?

This is a follow-up from a :  My girlfriend had a 6-month visa for the UK, which expired in December. She reapplied last week, and this time it was denied. Mainly it seems because her employment has changed, and admittedly the sums she presented didn't tally up.  It seems now the best thing to do is wait 6 months because then her employment and payslips will look consistent (her employer is going to help with this).  So is this the best thing to do, wait 6 months and reapply for same type of visa? With me down as the sponsor (last time she put herself down to pay for the trip, then her mum, then my details, and it seems my details and letter were largely ignored).  It seems that doing the form by herself and trying to be honest and transparent created a problem.  She has a Schengen visa which lasts through until the summer, so seeing her won't be impossible, but the strain is going to be tremendous. I am a UK citizen with full-time employment, and apart from going to see her in Russia and quick and expensive trips in Europe, I just don't know what I can do to make sure I've explored all options and done the best I can.  Anything at all in terms of advice is appreciated, but I guess mainly, would it change if I put myself as sponsor and fill in myself? Should I definitely wait? Is there anything I can do to have her here sooner? Or at least to ensure same problems don't arise again? If we were to go down the route, is marrying abroad and then having her come through a spouse application the most fail-safe way?  Thank you so much to all.


This is not about keeping the picture or table close to where they have been mentioned.  It is about keeping the caption of the picture (or table) together with the picture. Otherwise the picture and the caption will be displayed in different pages (or columns). Then, how to do it?.  \documentclass[journal,twoside]{IEEEtran} \usepackage[spanish,english]{babel} \usepackage{circuitikz} \usepackage[justification=centering]{caption}  \begin{document} \title{Minimal Working}  \maketitle  \begin{center} \includegraphics[scale=0.2444]{MultiplierSimulationI.png} \captionof{figure}{\small Multiplier circuit x3.} \end{center}  \begin{center} \begin{circuitikz}[american] \draw (-0.5,-0.5) to[open, l=$Anode$] (0,-0.5); \draw (-1,0) to[D, v=$V_D$] (-1,-2); \draw (-1,0) to[open, o-o] (-1,-2); \draw (0,-0.5) -- (0,-1.3) to[short, i=$i_D$] (0,-1.5); \draw (-0.5,-2.3) to[open, l=$Cathode$] (0,-2.3); \end{circuitikz} \captionof{figure}{\small Ideal Diode.} \end{center}  \end{document}   This is how I insert pictures (correct me if I am wrong, I insert them like this to put them wherever I want and avoid that the position itself anywhere in the page, and to give them a location). Anyway, if you add forced spaces before the picture there is a time where the picture will stay in the first column and the caption in the first line of the second column (same situation with the circuit).


When can the constant of proportionality in an eq be set equal to 1 and when not?

In $F=kma$, $k=1$ but in $F=kx$, $k$ is not equal to 1?So what are the conditions for the constant of proportionality to be set 1?


Most efficient way to mass render tiles in java slick2D

So I am trying to make a tile based game, it is rendering about 40 tiles on the screen at once. I get about 40 FPS on an okay computer. When I tell it to not render the FPS jumps to around 400 so I know its something with the rendering. I was wondering if there is a more efficient way to render a lot of tiles. Here is the code for my Tile class :   public class Tile {     public static Tile empty;     public static Tile rock;     public static Tile flower;     public static Tile grass;  public static Tile[] tiles;   protected boolean solid,breakable;  public static final int TILE_SIZE = 32;  public static final int VOID_TILE = 0, ROCK_TILE = 1,GRASS_TILE = 2,FLOWER_TILE = 3;  private int width = 16,height = 16;  private SpriteSheet image; private int xCrop,yCrop; private String path; private boolean toRender = true; private int ID;  public Tile(int ID) {     this.ID = ID;     path = ("res/spritesheet.png");     if(ID == VOID_TILE) {         solid = true;         toRender = false;         width = height = 16;     }      if(ID == ROCK_TILE) {         solid = true;         breakable = true;          xCrop = yCrop = 1;         width = height = 16;          path = ("res/spritesheet.png");     }      if(ID == GRASS_TILE) {         xCrop = yCrop = 0;         width = height = 16;          path = ("res/spritesheet.png");     }      if(ID == FLOWER_TILE) {         xCrop = 1;         yCrop = 0;         width = height = 16;          path = ("res/spritesheet.png");     }     if(toRender) {         try {             image = new SpriteSheet(path,width,height);         } catch (SlickException e) {             System.out.println("Error Loading File : " + path);             e.printStackTrace();         }     }  }  public static void initTiles() {     empty = new Tile(VOID_TILE);     rock = new Tile(ROCK_TILE);     grass = new Tile(GRASS_TILE);     flower = new Tile(FLOWER_TILE);      tiles = new Tile[] {empty,rock,grass,flower}; }    public void render(int x,int y) {     if(image!=null)image.getSubImage(xCrop, yCrop).draw(x,y,TILE_SIZE,TILE_SIZE); }  public void update() {  }  public int getID() {     return ID; }  public void setID(int iD) {     ID = iD; }   }


How to enable "window snap" with OpenBox

Is it possible to enable a Windows 10-eque "window snap" in OpenBox? By this, I mean that windows will automatically resize by dragging them to the side and/or corner of the screen. I know that this is possible using keyboard shortcuts (and, indeed, there are at least a few questions on here regarding such). I'm looking for a solution using the mouse, if possible. Can this be done and, if so, how?


I read a lot about Hyper threading and how it works. One thing I still can't 'digest' is how is it more efficient than not using hyper threading at all? Hyper-Threading is where two threads are able to run on one single-threaded core. That also means that in that single core, there could be exactly 1 thread running. No matter if hyper threading allows 200 or 2 threads on single core, there would still be 1 thread running at a given time..and then slicing (but that is not my question). So, can someone make a point in how it improves our performance?


Consider:  I need to do this. I need do this.  My English grammar knowledge tells me that "need" doesn't have the same status as the modal verbs "may", "can", "should" and what not. Hence the second usage where two verbs appear consecutively is incorrect. But yesterday, my native English speaking friends (Americans) told me that "I need compute this." is a perfectly grammatical sentence, and one is simply omitting the "to". How can this be? Is it a colloquial usage but grammatically incorrect, or is it grammatically correct? If it is grammatically correct, is it because "need" is a semi-modal verb? EDIT: in particular, is it okay to use "need compute" in a scientific paper? EDIT2: the exact phrase that raised the question was "The advantage of this representation is that we need only compute sums and products"


I would like to compare the first column of file1 with the second column of file2 and only if they match it should display any matching lines in file2 only as the output. The columns are separated by |.  file1:  syfar03040k16.audc1.oraclecloud.com | syfar03040m02.audc1.oraclecloud.com | syfar03040m04.audc1.oraclecloud.com | syfar03040n11.audc1.oraclecloud.com | syfar03040n01.audc1.oraclecloud.com | syfar03040n02.audc1.oraclecloud.com | syfar03040n03.audc1.oraclecloud.com | syfar03040n05.audc1.oraclecloud.com | syfar03040n07.audc1.oraclecloud.com | syfar03040o11.audc1.oraclecloud.com | syfar03040o01.audc1.oraclecloud.com | syfar03040o02.audc1.oraclecloud.com | syfar03040o03.audc1.oraclecloud.com | syfar03040o13.audc1.oraclecloud.com | syfar03040o05.audc1.oraclecloud.com | syfar03040o04.audc1.oraclecloud.com | syfar03040o16.audc1.oraclecloud.com |   file2:     | LDAP                 | syfar03040o11.audc1.oraclecloud.com               |    | OIM                  | syfar03040o01.audc1.oraclecloud.com               |    | AUTHOHS              | syfar03040o02.audc1.oraclecloud.com               |    | APPOHS               | syfar03040o03.audc1.oraclecloud.com               |    | BI                   | syfar03040o04.audc1.oraclecloud.com               |    | ADMIN                | syfar03040o05.audc1.oraclecloud.com               |    | PRIMARY              | syfar03040o06.audc1.oraclecloud.com               |    | SECONDARY            | syfar03040o07.audc1.oraclecloud.com               |    | APPOHS_HA1           | syfar03040o13.audc1.oraclecloud.com               |    | PRIMARY_HA1          | syfar03040o16.audc1.oraclecloud.com               |    | SECONDARY_HA1        | syfar03040o17.audc1.oraclecloud.com               |    | OSN                  | syfar03040o09.audc1.oraclecloud.com               |   File3:     | LDAP                 | syfar03040o11.audc1.oraclecloud.com               |    | OIM                  | syfar03040o01.audc1.oraclecloud.com               |    | AUTHOHS              | syfar03040o02.audc1.oraclecloud.com               |    | APPOHS               | syfar03040o03.audc1.oraclecloud.com               |    | BI                   | syfar03040o04.audc1.oraclecloud.com               |    | ADMIN                | syfar03040o05.audc1.oraclecloud.com               |    | APPOHS_HA1           | syfar03040o13.audc1.oraclecloud.com               |    | PRIMARY_HA1          | syfar03040o16.audc1.oraclecloud.com               |


I really want to install  to my minecraft. Its an adventure map. I have looked at several youtube videos on how to install it but they all say the same thing, once I get to the "go to the saves folder" i get stuck cause in my minecraft i dont have a saves folder :( I found the hidden Library, and searched for my minecraft folder, but there isn't a saves folder inside. I'm on a Macbook Air, OS X Version 10.9.  What can I do so I can install this?


Destination Path Too Long - Windows 10 w/ Anniversary Update

I have a Windows 10 machine updated with the Anniversary update. When I try to copy a file from an external USB hard drive using windows explorer, I get the following Error :   Destination Path Too Long  The file name(s) would be too long for the destination folder.  You can shorten the file name and try again, or try a location that has a shorter path.  I found an article to enable long file names using the local group policy editor :    However, this doesn't work for me.  I do not see the option to enable.  SO, I manually edit the registry setting by adding the key and value.  Even after several reboots, this didn't allow the file to be copied.    The computer is part of a domain so I searched for the flag in the domain group policy editor but it is not listed.  The domain server is Windows Server 2008 R2 Standard.  Is there anything else I can do to get the file copied (in reality there are thousands of files I am trying to copy from an external hard drive to a Windows Surface Book).


I am trying to import pandas 0.20.3 in QGIS console but it's giving me this error. Could any one help me to solve this problem. I used pip to install pandas in windows and QGIS version is 2.14


2.9x Why can't I see my scripted print function results in the console?

import bpy print ("something")  When I run this script nothing happens, nothing appears. The only answers to where it prints I find are from 6 years ago. With 2.91 It's not in the Python Console output in the Scripting tab, so where does it display its print command? Using Windows.


Is there a better way to center horizontally an element?

Good day,  For my website, I have noticed that my div frame was not ideally centered on the screen - something that I haven't realised so far on my smartphone.   I was considering to customise the margin value in my css style file - but maybe that will not be ideal as I don't know the screen width of my users.  Do you have suggestions to have my frame better centered horizontally, as shown on the below picture?  Thanks a lot for your help.

           Les dates-cl&eacute;
Wedding Events

Party

                                          Samedi                     18.07.2020

                                          15:00                     01:00

Le lieu de r&eacute;ception sera r&eacute;v&eacute;l&eacute; d'ici au 15.03.2020.
En attendant, vous pouvez deviner o&ugrave; ce dernier aura lieu en participant au concours

Dress code : glamour chic

   CSS Code :  #fh5co-counter .event-wrap h3, #fh5co-event .event-wrap h3 { font-size: 20px; color: #fff; border-bottom: 1px solid rgba(255, 255, 255, 0.5); display: block; padding-bottom: 20px; text-transform: uppercase; letter-spacing: 2px; }  h1, h2, h3, h4, h5, h6, figure { font-family: "Work Sans", Arial, sans-serif; font-weight: 400; margin: 0 0 20px 0; }


The first time I applied for Schengen visa I was refused. And now, I'm confused whether I will appeal or re-apply.   The following are the documents I submitted:    Invitation letter from my cousin stating that he will take charge all my expenses Birth certificate as proof of relationship but not all were authenticated from National Statistics Office  Bank Certificate with only enough money for my round trip ticket Passport with stamp from my Singapore  travel last year Certificate of my employment stating my salary, position, length of service, compensation and benefits Company ID and 3 months payslip   I was refused due to "Your intention to leave the territory of the member state before the expiry of the visa could not be ascertained."


Lightning datatable in lwc to show multiple urls in single cell

Is it possible to add multiple links to a single Lightning Datatable cell. For example, as in the screenshot. it should be something like this


Recover Files from dead PC and Bitlocker Hardrive

I have a Laptop with a dead screen, I do not want to fix it but I need those files in it. The HDD have a BitLocker in it, how can I recover the files?


How to convert a photo to a black and white image by ImageMagick?

How can I convert a JPEG photo to black and white (not grayscale) image like output of a FAX scanner, by ImageMagick?


I'm not that into dynamic programming languages but I've written my fair share of JavaScript code. I never really got my head around this prototype-based programming, does any one know how this works? var obj = new Object(); obj.prototype.test = function() { alert('Hello?'); }; var obj2 = new obj(); obj2.test();  I remember a lot discussion I had with people a while back (I'm not exactly sure what I'm doing) but as I understand it, there's no concept of a class. It's just an object, and instances of those objects are clones of the original, right? But what is the exact purpose of this ".prototype" property in JavaScript? How does it relate to instantiating objects? Update: correct way var obj = new Object(); // not a functional object obj.prototype.test = function() { alert('Hello?'); }; // this is wrong!  function MyObject() {} // a first class functional object MyObject.prototype.test = function() { alert('OK'); } // OK  Also these  really helped a lot.


Why is inset producing different results on horizontal to vertical faces?

For years I've worked with inset to make many shapes and objects, most notably guns and other game asset-type things. However recently inset has stopped working as I need it to, when using it on vertical faces. On horizontal faces however it works fine.  Refer to the attached images.


Has anyone tried installing Ubuntu Desktop on the ?    The essential specs are:   Intel Core i5-8259U Quad-Core Intel Iris Plus Graphics 655   Does it work (partially)? And if not everything works, what does work?


how do i clear up space because my phone is almost full?

Can i sweep the storage. Is this data i don't want or the data that runs my phone. Not sure exactly what my huawei phone stores in storage. Whats miscellaneous?


Is there a Windows 10 privacy checklist?

I would like to know what settings should be changed on a new Windows 10 (Pro, but a canonical answer covering all editions would be nice) installation to disable as much of the built-in telemetry/tracking as possible.  I am looking for both GUI-solutions as well as GPO/Registry modifications.  The duplicate doesn't answer my question as I'm also looking for hidden settings only accessible via GPO/registry, like for example disabling the start menu's web search (impossible via the normal GUI after the anniversary update).  Regards.


expalin output of the below java program

Please have a look at the code below :  public class SampleClass{         String name;         public SampleClass(){          }         public void setName(String s){             name = s;         }         public String getName()         {             return name;         }         public static void main(String d[]){             PojoClass p = new PojoClass();             SampleClass s = new SampleClass();             s.setName("jack");             System.out.println(s.getName());             p.setSample(s);             System.out.println(p.getSample().getName());             s.setName("Fgk");             System.out.println(p.getSample().getName());             p.recMod(s);             System.out.println(p.getSample().getName());             p.changeVal(s);             System.out.println(p.getSample().getName());         }     }      class PojoClass{         SampleClass s;         public void setSample(SampleClass d){             s=d;         }         public SampleClass getSample()         {             return s;         }         public void recMod(SampleClass s){             SampleClass g = new SampleClass();             s=g;             //g.setName("FGH");             s.setName("hjk");         }         public void changeVal(SampleClass s){             s.setName("hjkjkl;k;k");         }      }   I am trying to run this code but unable to get why we get the output as Fgk when we call recMod() method. Also if I uncomment g.setName("FGH") then also the output remains the same.


External FTP File Transfer Activity Error in Automation Studio

I configured a Data Extract (Data Extension Extract) and a File Transfer (Safe House to External FTP which is also an SFMC FTP ).  Unfortunately, File Transfer fails without giving a proper error.   ERROR:  An undefined error occurred. Contact your account representative if the error persists.  Salesforce Support is asking me to whitelist Stack 1 IP Address on my Internal Network when the operation is done within SFMC Servers. I have ask them to escalate this to Tier 2 support.    Have you come across this issue in the past? What have you done to resolve this issue?


(Feels strange that this does not seem to have been brought up before, I have searched for a duplicate but could not find any)  It's nice that MSO/MSE got split up finally. However, I do feel that it's a bit awkward that  is completely empty.  I assume this is because MSE doesn't have elected moderators (whether it should have elections or not is a completely different topic).  It would be helpful if  showed... some moderators.


I'm trying to solve the question:     Ten people are standing are standing in a circle. Find the number of ways to choose $3$ people such that no $2$ of them are consecutive.    I have got the answer to be ${10\choose1}{6\choose2}$, but I'm not sure if this is right.   Please tell me if my answer is correct! If it's not, then where did I go wrong?


addslashes() function in PHP is not able to replace all ' in my string

I am trying to use txt file hosted at  in php. I am saving all individual words in a database using mysql. I am using addslashes() function like this  $txtFile = addslashes(file_get_contents('http://terriblytinytales.com/test.txt'));   But after successfully saving in the database, the ' in the string I got by file_get_contents('http://terriblytinytales.com/test.txt') is not replacecd.  only the first ' in we're is replaced and others are same. Please help


Can something travel faster than the speed of light?

I understand this is a very complicated question to answer as no one really knows. However if gravity exerts an infinite force in the singularity of a black hole, then can't it travel faster than the speed of light?  I mean, wouldn't it also have to have infinite mass? I was thinking that if gravity exerts a force that eventually puts an accelerating object at terminal velocity - what if the gravity was infinite? Such as in the singularity of a black hole. It was just an abstract thought but wondered any one else's take on it.


str='filename=1817616353&realname=Arguments%20for%20&%20against%20protection%20.pdf&code2=pds' ptn='(?<=realname=).+(?=&)' re.search(ptn,str).group()   well, when i run this code i'm expecting to get  'Arguments%20for%20'   as the match, but instead it gives me  'Arguments%20for%20&%20against%20protection%20.pdf'   i thought the match should occur at the first occurrence of '&', which is right after 'for%20' part, so i have no idea why it's going all the way down to 'pdf'. what am i doing wrong?


Hi all im a noob on Ubuntu/Linux World,  So i need some that give a full tutorial to How to install  from apachefriends.org correctly on Ubuntu 11.10 + all beyond Ubuntu for 32 bit and also 64 bit Desktop Version.. and also i need this:   Make a Folder on Your Home Folder and Linked to htdocs from Apache Web Server Make a GUI interface for Xmapp Start Xampp when Ubuntu Boot Up or Start Ubuntu   (Note: i ask it for both X86 and X64 so people in the further can see the tutorials)    New Data:  What i did was i download from  for now and i also what to say that I'm currently running Ubuntu 11.10 X64 bit for Dell Studio 1558 processor intel i3  i will let you know guys which solution was the best, and it is for a Desktop Version of Ubuntu 11.10 (Laptop 15 inch screen ^_^ ) not Server Ubuntu


I'm trying to redirect a single port to a local server via IPtables.  Currently I have the following rules:  iptables -t nat -A PREROUTING -p tcp -m tcp --dport 55555 -j DNAT --to-destination 10.188.44.125:3306 iptables -t nat -A POSTROUTING -j MASQUERADE   When I have these rules in place, my rsync process of ssh fails.  I'm assuming something here is conflicting, but I'm not sure what.  Any suggestions?  Thanks!  Update: Here are the rules I have in place to allow the rsync over ssh connection.  My input policy is set to drop.  Other policys are set to accept.  iptables -A INPUT -p tcp -m tcp --dport 22 -j ACCEPT iptables -A INPUT -p tcp -m tcp --dport 80 -j ACCEPT iptables -A INPUT -p tcp -m tcp --dport 443 -j ACCEPT iptables -A INPUT -m state --state RELATED,ESTABLISHED -j ACCEPT iptables -A INPUT -p icmp -j ACCEPT iptables -A INPUT -s 127.0.0.1/32 -d 127.0.0.1/32 -i lo -j ACCEPT   Update 2  Here are the results of iptables-save for the nat:  *nat :PREROUTING ACCEPT [8:468] :INPUT ACCEPT [7:408] :OUTPUT ACCEPT [2:134] :POSTROUTING ACCEPT [0:0] [0:0] -A PREROUTING -p tcp -m tcp --dport 53306 -j   DNAT --to-destination 10.183.42.125:3306 [2:134] -A POSTROUTING -j MASQUERADE COMMIT


I am trying to run Citrix receiver on the Xenial version of Ubuntu, but I am getting this error below  ERROR: Cannot connect to "0.0.0.2 - Remote Desktop Connection" Unknown error 1000119. Verify your connection settings and try again.  What should I do?


re.search searches for last part of the string


Target player holding specific item with testfor

I am trying to make this command where a lightning bolt will be summoned at every arrow shot from a specific bow, and I need it to work on multiplayer. I have tried to use the /testfor command but cannot figure out how to target the exact player shooting the bow. Does anyone know how to do this?


How to continue: Show that there are infinite prime numbers $1 + 2mp$, $p >2$ prime and $m > 0$ integer.

What I tried. First of all, let $a > 1$ integer and $p > 2$ prime. Consider $a^p + 1$. Let $q$ a prime divisor of $a^p + 1$. Then $q$ divides $a + 1$ or $q \equiv 1\pmod p$. I obtained this form: Let $q$ a prime divisor of $a^p + 1$. Then $a^p \equiv - 1 \pmod q$. Then $|a|$ the order of $a$ is in $\{1,2,p,2p\}$. It can't be $1,$ or $p$, so if $|a| = 2$ then $q$ divides $a+1$. Otherwise, $q \equiv 1 {\pmod {2p}}.$  So, suppose that there are just finite primes of the search form. Construct the number $N = (2p_1\ldots p_r)^p + 1.$ We have that $N$ is odd. Then, it has one prime divisor $q$. But, what now? If $q$ has the form $q = 2np + 1$ for some $n$ we are done, but, what if $q$ divides $(2p_1\ldots p_r) + 1$? Then we don't have any contradiction... Whats next?


I know how to show $[0,1] \times [0,1]$ is not homeomorphic to $(0,1) \times (0,1)$ by a compactness argument. Is there such an argument that shows $[0,1) \times (0,1)$ is not homeomorphic to $(0,1) \times (0,1)$? If not, what is the best way to show that they're not homeomorphic?


Multiple extensions Chromium not working after update to 13.10

It seems like after updating to Ubuntu 13.10 and Chromium 29.0 multiple extensions have stopped working. Reddit Enhancement Suite and Smoothscroll are among them. Some extensions partially work, like Adblock. Others, like Webtimer and Collusion still work as they did before.  I realize this might be slightly off topic if the problem lies with the new version of Chromium. However, it may very well be something about the new version of Ubuntu, or perhaps a bit of both.


As a queen, what must I do to take the son of my husband's dynasty out of succession line?

I have two sons now, one is of my former husband's side and older than the second son of my side from matrilineal marriage. The first son won't leave the succession line. I can't conspire to murder him since he's my child.  What must I do to take him out and bring my second son forward?  EDIT. A bit of update, that stupid non-dynastic heir somehow inherited a petty kingdom nearby, meaning he was not of my court anymore, there was nothing I could do. I could not ask him to take the vows (since he's not my courtier), couldn't imprison him though I was willing to suffer the opinion penalty. I tried to fabricate claim and declare war with hope to capture him as POW but wasn't a success. He took over the kingdom after my passing, leaving my dynasty to oblivion shame and putting an end to yet another noble house that couldn't survive the feudal hardship.


Let $f(x) =7x^{32}+5x^{22}+3x^{12}+x^2$. Then find its remainder in the following cases.

Let $f(x) =7x^{32}+5x^{22}+3x^{12}+x^2$. (i) Then find the remainder when $f(x)$ is divided by $[x^2+1]$. (ii) Also find the remainder when $xf(x)$ is divided by $[x^2+1]$. Given both the remainders will be of the form $4(ax+b)$. The 'polynomial long division method' can be applied, but that won't be logical enough, because its too long a process. Can you tell me any other shorter & easier process? Thanks.


Error when installing: "unable to find a medium containing a live file system"

Error message:  (initramfs) unable to find a live medium containing a live file system   I got this error while trying to install Ubuntu 10.10 from a bootable USB stick on to Asus X64J series laptop. After getting this error the installation fails to start.  I have used the same USB stick on some other laptops and the installation started as usual. Any help will be appreciated.


How the current of a wire pass so quickly if it has that less drift velocity of electrons.?

The rate of flow of electrons is known as current. When we switch on a light bulb, then it lights immediately. If drift velocity of electrons is so small--at least on the supply on 220V (supply of my home)--then why does the light bulb light up so quickly?


Is there a way to play Bejeweled blitz on Facebook with ubuntu? I am not really used to the os and am not sure if there is something I am missing or not.


I m not able to choose a nickname for me in the game so which type of nickname I should try?


Evalute integral of Brownian motion $E[(\int_0^tB_sds)^2]$

Can someone explain me how to compute this expectation?  $E[(\int_0^tB_sds)^2]$  I know that the result is $t^3/3$


why float and double does not identify 0 in decimal places

setlocale(LC_ALL, "Portuguese");  double var = 1.0; cout << var << endl;   system("pause"); return 0;   output:  1    Press any key to continue . . .


serial redirect from 12.04 server usb installer

I have downloaded 12.04.4 LTS server iso (64 bit) and used netbootin to create a bootable usb thumb drive for the purpose of installing ubuntu server on a dell r620.  I have serial console connected and working for the host (I can see bios post, etc).  I can boot from the usb thumb drive and get to the unetbootin menu where I select install ubuntu server.  Once I select that option (or any of the others - expert install etc), I don't see any output on my remote console connection.  I do however see output on my direct connected monitor/keyboard (crash cart).  It is my assumption that the serial redirect setup is not done on the files on the thumb drive version of OS.  My ultimate goal is to be able to get hw to a datacenter, have it racked and cabled, have serial connection setup, have one of these usb thumb drives attached and from there I can do the install etc.  This is sort of a one off and I don't want to install via our usual pxe/kickstart method.  Can someone point me to a guide to "unpack" the iso files, add the serial redirection bits I need and then "repack" into an iso so I can then burn the iso to the thumb drive (using unetbootin)?  Or is there a different/better way?


If two linear transformations are one to one, is the product of them also one to one?

Example:  Let $T : V \to W$ and $S : W \to U$ be two one to one linear transformations.  Would $S \circ T$ also be one to one?


includes function not working for plotly trace - js

I have an array of Plotly traces. console.log(traces): traces: [{…}] 0: name: "temprature" type: "scatter" x: (7523) [1527581340000, …] y: (7660) [15.68, …] __proto__: Object length: 1 __proto__: Array(0)  At an event, I want to check if a newly created trace is on the list or not. Firstly, I check it with the includes function but it didn't work, then I found  on how to check the availability of an object in an array in js. function contains(a, obj) {         for (var i = 0; i < a.length; i++) {             if (a[i] === obj) {                 return true;             }         }         return false; }  but it seems not to work for me. $("#temprature").change(function () {         var trace_temprature  = {                             x: index,                             y: temprature,                             name: document.getElementById('temprature').name,                             type: 'scatter'         };          if (document.getElementById('temprature').checked) {             if( !traces.includes(trace_temprature) ){                 traces.push(trace_temprature);             }             console.log('trace in the add ', traces);                        console.log('temperature trace: ', trace_temprature) // this line prints the same object on the previous list                      } else {             console.log('if condiiton: ', contains(traces, trace_temprature)); // this line print False             if( contains(traces, trace_temprature) ){                 var ind = traces.indexOf(trace_temprature);                 traces.splice(ind, 1);             }          }            });  any ideas?


From Finan:  Let $\sigma\in{S_n}$, define the $\mathbf{order}$ of $\sigma$ to be the smallest positive integer such that $\sigma^m=(1)$.  Prove that if $\sigma$ has order $m$ then $\tau\sigma\tau^{-1}$ has order $m$ for all $\tau\in{S_n}$.  So $\tau$ can have its own order, so let $order(\tau)=p$.  Thus $\tau^p=(1)$.  If $(m,p)=1$, then $order(\tau\sigma)=mp$.  But doesn't $order(\tau^{-1})=p$?  Thus $order(\tau\sigma\tau^{-1})=pmp$.  So them this implies $(\tau\sigma\tau^{-1})^{pmp}$...  Not sure where to go with this.


How to convert an image file of lines into a lines shapefile in QGIS?

I need to convert the following image into a line .shp file. I can make the image into whatever type of image file it needs to be before converting. For context, I had started mapping an area by drawing over the map in photoshop but then came across QGIS and finished the project by mapping over the image using lines shapefile layers. I'm now trying to run the lines through a matlab code and the code can only use shapefiles.  I haven't used QGIS extensively.


when using tabularx and X, how to make the text vertically centered?

\documentclass[a4paper]{article} \usepackage[landscape,hmargin=2cm,top=1.5cm,bottom=1.6cm,headsep=1mm,headheight=3cm]  {geometry}  \usepackage{multirow} \usepackage{tabularx} \usepackage{microtype} \usepackage{siunitx}  \begin{document} \noindent \begin{tabularx}{\textwidth}{|*{7}{c|}X|*{5}{c|}p{35mm}|}     \hline     &&&&suface quality&&&The financials crashed and burned during the 2008 meltdown but have since been in recovery mode with the rest of the market. This article will explore the risks and rewards associated with these Financial ETFs to identify which have been the best performers.&check&\SI{100}{\percent}&continueous&&worker& The Best Financial ETFs \\     \hline \end{tabularx}   \end{document}    As the above code show,the text can't in the center vertically,how to improve it?


Customized citation for secondary quotes ("quoted in")

i'd like to customize the citation style for secondary citations. At the moment it looks like this:  but i want to look the citation like this:   Is there any chance to create a citation style which is doing this? Here is an minimal example of the code i'm using including the customization for using 4 letters and the "-" for the cite.  \documentclass[fontsize=11pt, oneside, parskip=half+, numbers=noenddot]{scrreprt} \usepackage[ngerman]{babel}  \usepackage[utf8]{inputenc}  \usepackage{filecontents}   \begin{filecontents}{Minimalbeispiel.bib}  @book{Bechte.1984,     author = {Bechte, Wolfgang},     year = {1984},     title = {{Steuerung der Durchlaufzeit durch belastungsorientierte      Auftragsfreigabe bei Werkst{\"a}ttenfertigung. Diss. Univ. Hannover}},     address = {D{\"u}sseldorf},     volume = {2},     number ={70},     publisher = {VDI-Verlag},     series = {{Fortschritt-Berichte}} }  @book{Wiendahl.2005,     author = {Wiendahl, Hans-Peter},     year = {2005},     title = {{Betriebsorganisation f{\"u}r Ingenieure}},     address = {M{\"u}nchen},     edition = {5. aktualisierte Aufl.},     publisher = {Hanser},     isbn = {3446228535}     } \end{filecontents}   \usepackage[babel, german=quotes]{csquotes} \usepackage[ backend=biber,  style=alphabetic,  pagetracker=true,  maxbibnames=99, backref=false,  natbib=true,  firstinits=true,  sorting=nyt,  isbn=false, url=false, doi=false]{biblatex}   \AtBeginBibliography{%      \renewcommand*{\mkbibnamefamily}[1]{\textsc{#1}}     \renewcommand*{\labelnamepunct}{\addcolon\addspace} } \DeclareNameAlias{default}{last-first}  \DeclareLabelalphaTemplate{     \labelelement{         \field[final]{shorthand}         \field{label}         \field[strwidth=4,strside=left,ifnames=1]{labelname}         \field[strwidth=2,strside=left,ifnames=2]{labelname}         \field[strwidth=1,strside=left]{labelname}     }     \labelelement{          \literal{-}      }      \labelelement{         \field[strwidth=2,strside=right]{year}     } } \renewcommand*{\labelalphaothers}{}    \addbibresource{Minimalbeispiel.bib}   \begin{document} Interesting stuff. \cite{Bechte.1984} quoted in \cite[S. 266f.]{Wiendahl.2005}  \par  Interesting stuff. [Bech-84 quoted in Wien-05, S. 266f.]  \printbibliography \end{document}


Among the effects of Wild Shapes, these two:     Your game Statistics are replaced by the Statistics of the beast, but   you retain your alignment, personality, and Intelligence, Wisdom, and   Charisma scores. You also retain all of your skill and saving throw   proficiencies, in addition to gaining those of the creature. If the   creature has the same proficiency as you and the bonus in its stat   block is higher than yours, use the creature's bonus instead of yours.   If the creature has any legendary or lair actions, you can't use them.      You retain the benefit of any features from your class, race, or other   source and can use them if the new form is physically capable of doing   so. However, you can't use any of your Special senses, such as   Darkvision, unless your new form also has that sense (PHB p.67, "Wild Shape")   Seem to come into conflict with each other when things like Draconic Resilience:     When you aren't wearing armor, your AC equals 13 + your Dexterity   modifier. (PHB p.102, "Draconic Bloodline")   How would this resolve?


Move pdf files from one library to folder within library in sharepoint 2013

I want to move files from the Library into its folder (Which is in the same library). How can I do this using sharepiont Designer 2013


This is the line C-3PO speaks when he meets BB-8 in The Force Awakens (2015):  C-3PO: Come along, BB-8, quickly. Yes, I must get my proper arm reinstalled.  That means they know each other even before.


How to copy only new files AND only those that are modified after a certain date?

I would like to copy files from one drive to another, but I only want to copy source files that are newer than the destination file.  BUT, I also want to only copy source files that have been changed after a certain date.  I know I can use xcopy to do either one of these things, but I would like to do both at the same time.  So for example, I want to copy all source files dated on or after 3/1/2013, but in addition I only want the file copied if the source file is newer than the destination.  So ideally I would like to do something like this:    xcopy c:\*.* e:\*.* /D:03-01-2013   combined with something like this:  xcopy c:\*.* e:\*.* /D   Can this be done with xcopy or Robocopy?


how to change # of tag posts on /tag page?

I have my blog page limited to 5 posts on the main page, which I'm happy with.  However, I want my tag pages to list much more, maybe 15 or so.  How do I most easily make this change?  There's no option on the reading page.  thx!


Why the pins of a port in some microcontrollers are not in order?

In some ICs the pin numbers are not in proper order. For example, in msp430x12x2 series (following pic).   In the pic, why don't P2.0 be available at pin 20 (or adjacent to P1.0 ??)  Why is that few pins of both ports P2 and P3 are on either sides of the IC?


Denied entry to the UK after having student visa refused a week earlier, what are my options now?

On the 1st of September my Tier 4 student visa application was rejected but I made the mistake of thinking I was still entitled to enter the UK with my US passport. I had already purchased a Eurostar ticket to London so I thought I could put it to use to visit some friends (one of them being my boyfriend) for two weeks before their school years started. On the 9th, I was detained in Paris and refused entry to the UK on the grounds that I recently showed "intention to live and study in the UK" and they weren't convinced I would be leaving when I said I would. Additionally, I didn't carry any documents aside from my passport, my Swiss residence permit and a copy of my passport. I am also unemployed but I am still completely financially dependent on my parents. Staying with my boyfriend was the cherry on top.  In hindsight, I acknowledge that I raised every red flag. It was like a twisted skit. However, the last time I traveled outside of Schengen was when I was 15 (I'm 19) and any recent travel I've done was by rail so I didn't anticipate the seriousness of crossing the border. It was my first time traveling alone but I suppose that level of cluelessness warrants learning the hard way.   At this point, I'm wondering what my next move should be. How long do I have to wait? I definitely want to visit the UK some time soon because I now have an unexpected gap year lying in front of me. My intentions were strictly for leisure and I wouldn't attempt anything along the lines of volunteer work while I'm there. I just want to visit my friends/boyfriend for 1-2 weeks at most. Should I apply for a visitor visa this time or can I try traveling there again but making sure I have as many documents as possible? I'm worried about getting denied entry again and having an even more "tarnished" record, so that's the main thing I want to avoid. I tried contacting the UKVI by email but they haven't responded.  Keep in mind, I'm planning on reapplying for a student visa next summer so I have no idea what I can and can't do - I really don't want to compromise anything.


Why is a very small percentage of the swap being used when my ubuntu is almost freezing?

My Ubuntu gets very slow because of too many apps, but when i check the system monitor, Ram use is 80% but swap is less than 5%. How do you let ubuntu use the swap more effectively?


C++/CLI: " Button^ button1; " what is ^ meaning here?

I created a WindowsForm class in C++/CLI with one button and onClick event. I looked into the source code and saw this:  public ref class MyForm : public System::Windows::Forms::Form { public:     MyForm(void)     {         InitializeComponent();         //         //TODO: Add the constructor code here         //     }  protected:     /// <summary>     /// Clean up any resources being used.     /// </summary>     ~MyForm()     {         if (components)         {             delete components;         }     } private: System::Windows::Forms::Button^  button1;      ...  private: System::Void onClickButton1(System::Object^  sender, System::EventArgs^  e) {          }  }   I would like to ask: what is the meaning of the ^ operator when declaring the button (Button^ button1;) in the class?


i need to excute posts from 2 search keywords & put all in one loop to showing by using WP-Query i have trying array_merge but this not worked for me so my last code is:  please note: i  need to excute posts from 2 seprated keywords not one keyword containing 2 words & put the posts from keyword1, keyword2 in the same loop  $argssss=array('s'         => 'keyword1'); $argsss=array( 's'         => 'keyword2', 'orders'    => 'DESC',  'showposts' => 60 ); $argss=array_merge( $argssss, $argsss );     $queryy = new WP_Query($argss);  if ( $queryy->have_posts() ) : while ( $queryy->have_posts() ) :     $queryy->the_post();     $do_not_duplicate = $post->ID;     the_title( '<p>', '</p>' ); endwhile;  wp_reset_postdata(); endif;       i have also tried to put s in array but not worked like this array('keyword1','keyword2')  so how can i excute posts from 2 different keywords  this answer is very very good it solved my problem by merging 2 wp_query in one    another note this answer is very very good because it is really merged the two wp_query in one but i can't figure it with my filter   but how can i use pagenavi with my custom query


Java does not return string from scanner input

I'm practicing Java and I've run into a little odd issue or should I say issues.  When I compile the below code it says java line # :error:       missing return statement.    If I remove the comment where I have return "not valid", it compiles.   Now this is where the other issue comes in. When I pass the init_config and final_config string that I input as A and B, it returns the not valid. But when I pass "A" and "B" to other function (other("A", "B") the specific return which is "C" is returned/printed.  I am not sure if the the issue lies with my input method. The data I input for my init_config and final_config should be string values, correct? I'm not sure if Scanner is a good string input method. However, if I print the two inputs it works fine so I'm not sure if it is data loss or the string reference is lost when it is passed.   I also tried replacing init_config = in.next() with init_config = in.nextLine() but it did not make any difference.  Is it necessary to compile the code with the return "not valid" at the end of the function or can I bypass this by some method? And how can I pass String data using Scanner input method without any loss?  Here is my code:  import java.util.Scanner; public class towerGen {     public static void main(String[]args)     {         Scanner in = new Scanner(System.in);         String init_config, final_config;          System.out.print("Enter initial configuration: ");         init_config = in.next();          System.out.print("Enter final configuration: ");         final_config = in.next();          System.out.print(other(init_config, final_config));      }      public static String other(String src, String dest)     {         if (src=="A" && dest=="B")              return "C";         if (src=="B" && dest=="A")             return "C";         if (src=="B" && dest=="C")             return "A";         if (src=="C" && dest=="B")             return "A";         if (src=="A" && dest=="C")             return "B";         if (src=="C" && dest=="A")             return "B";     //return "not valid";     } }


When I'm on  mobile and I vote to close a question, my pudgy fingers often click the links instead of selecting the close reason.  Can we disable these links, please?


Why is $ \sum_{n=0}^{\infty}\frac{x^n}{n!} = e^x$?

I am trying to see where this relationship comes from: $\displaystyle \sum_{n=0}^{\infty}\frac{x^n}{n!} = e^x$ Does anyone have any special knowledge that me and my summer math teacher doesn't know about? He went over generating functions a few days ago and I did not know exactly what he was talking about. In the middle of his lecture he wrote this generating function. He explained that in this case $a_{n} = \frac{1}{n!}$ for $\displaystyle \sum_{n=0}^{\infty} a_{n} x^n$.   Is the relationship a definition or can it be derived using $\displaystyle \sum_{n=0}^{\infty} x^n $?


how can i change language of onbeforeunload message?

i have a typical web application with multi language ( french , english and Nederland ) and I'm using a page unload trigger to warn the user of unsaved changes while leaving the page/closing the tab/etc... and this works fine.  My problem is how can i change language of onbeforeunload message with title of dialogbox and the 2 bottons "leave this page" and "stay on this page" without changing language of the browser?


Data Not Backed Up, Partition Type: FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF

I was trying to install Linux on my MacBook for class when I bricked my computer, which now in an unbootable state.   I made my partition too small, so I was going to delete and create a larger one. However, Disk Utility did not allow me to delete the small partition. I followed the instructions from   However, not only was I still unable to delete it, but upon restarting I realized my primary partition (located on the same disk) changed into FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF, and I had no options to boot.  (I am sure I performed the command on the correct disk and partition)  I saw some similar threads, but my main bootable drive is the one that got corrupt.   I don't want to lose any data. I'm not the most terminal savvy, so ANY help is appreciated, and I will kindly provide any additional information!  (Disk 0, partition 2 is my main partition, and that only one I care about)  Below are the results of  $ diskutil list and $ gpt -r show disk0.        UPDATE: :  I have followed @klanomath 's instructions. At the last step I received the following error:  Checking prerequisites Checking the partition list Checking for an EFI system partition Checking the EFI system partition's size Checking the EFI system partition's file system Problems were found with the partition map which might prevent booting Error: -69766: The partition map needs to be repaired because there's a problem with the EFI system partition's file system Underlying error: 8: POSIX reports: Exec format error    FINAL UPDATE: SUCCESS!  I just wanted thank @klanomath for helping me through this entire process. He spent 11 hours TeamViewing with me until not only my files were accessible, but until I could access my computer as could before this whole debacle (and this was after 5 hours of email correspondence).   To any future reader with this problem: PLEASE don't give up, it can be fixed!


How do we prove that when $\int_a^b f = 0$, f(x) = 0 for all x $\in [a, b]$

Let $f:[a,b] \mapsto \mathbf{R}$ be a continuous function such that $f(x) \geq 0$ for all x $\in [a, b].$ Suppose $\int_a^b f = 0.$ Show that $f(x) = 0$ for all x $\in [a,b]$


How do command authorization codes work in Star Trek?

In Star Trek franchise there are command codes that seems to give you access to the ships systems, can you change or at least disable them?  In one episode of ST:VOY the captain, B'Elana and Tuvok are assimilated but something goes wrong and and the Borg Queen gains access to Tuvok's memories including his access codes?  So can you change or disable access codes or is the crew of ST:VOY totally stupid?


Book about a boy thats transported into a medieval fantasy computer game

This is a long shot but I'm really in need of help for this because it was an amazing book. It was either a kid's or YA book. A guess from what year it was published would be 90s-mid 2000s, as I read it around 2008-2011.  The book cover was in first person view, with the main character holding a weapon, and was a 3D rendered image inside a dungeon or cave (that was very reminiscent of early 90s CGI animation), though there may be variants.  It would have been set around when computer games were mainstream (maybe around the same time as when it might've been published) It's about a teenage boy who is bored at home, so he looks through an old family computer to play a game and finds one that he has never seen before. When he plays it he gets transported into the game which is a fantasy-medieval setting.  All that I can remember about the game and story is that the main character is on a quest, he rides horses a lot, (to the point where he can ride horses perfectly in real life), at one point he eats food at an ingame tavern/restaurant? and he tosses the ingame coin currency at the server because he's in a hurry, (don't know why I remember that bit specifically haha), and he meets a gnome/dwarf character who is helping him on his journey, who has a home in an ingame mountain, and that time goes faster in the game. (For example, if he spent 5 minutes in the real world, 3 in-game days would have passed)  Sometimes as he's playing something stops him from being able the play the game for a few weeks, maybe a concerned parent because he's playing too much or there's a family vacation. I remember during the time when he's not playing the game he's on a farm and knew how to ride the horses there.  There was a character in the real world who was the main character's sibling, relative or friend. They were like a rival and was also very whiny (to some extent). They were on the farm as well with him and questioned how the main character knew how to ride a horse when he had never done it in real life. This is all I can remember but if you need more specific information I can try and answer. It is definitely not Space Demons or Demons Don't Dream. If anyone knows anything remotely similar please mention it, I would really appreciate it. Thank you!!


Why is $(-1) \times  (-1)=+1$ ?  What is the intuitive concept ?  My second question :  How can I show that no triangular number can be of the form $3n-1$ ?


Can one ever say for certain a word does not exist?

Can it ever be concluded that an alleged word is not actually a word? Obviously, if a word is not in a particular dictionary, it does not mean the word is any less of a word than the ones that do appear in the dictionary.  What about words like irregardless or administrate, which seem to be self-contained logical fallacies? Can one conclude definitively that they are not "real" or "proper" words?  In other words is the statement     "xyz" is not a word   always false?


Chrome GUI is too big as of 43.0.2357.124-1

Last night, I updated my version of Google Chrome from 43.0.2357.81-1 to 43.0.2357.124-1. The most visible change is that the UI elements are way too large. Here's a comparison with Chrome (top), Firefox (center) and my system fonts (bottom); only Chrome is wrong:    This isn't a page zoom issue. Chrome thinks my zoom is at 100%. I can shrink the page elements by zooming out, but the UI is still too large.  I can fix this by launching Chrome with the --force-device-scale-factor flag. However, this isn't really a great fix; I'd have to change my launcher shortcuts and any programs that launch Chrome (e.g., web servers that auto-launch a browser, like Racket's). Using this flag also causes Chrome to start with a very small window size.  I checked in chrome://flags and didn't see anything interesting matching the grep for "scale."  If relevant, my desktop environment is Cinnamon on Linux Mint 17.1 64-bit. My screen resolution is 1920×1080, on a normal 14-inch (157 dpi) display.


Recurring crash from Google app with error message "EXCLUSIVE background task UPDATE_HOTWORD_MODELS crashed"

My mom's Xiaomi phone started displaying the error message:  The Google application has suffered an error again. Please send a report to Xiaomi.  The code under the "see more" button is extensive, but the gist of it is that the "EXCLUSIVE background task UPDATE_HOTWORD_MODELS crashed". The error message pops up every 2 seconds. What should I do to help my mom return her phone to a usable condition? Restarts do not help; I purged the settings of Google apps, that did not help either.


Showing that the fiber of a morphism of schemes over a point is homeomorphic to the preimage

Suppose I am given a morphism of schemes $f: X \longrightarrow Y$ and suppose that for any point $y \in Y$, $\kappa(y)$ denotes the residue field. I would like to show that the fibered product $$X \times_{Y} \text{Spec}(\kappa(y))$$ is homeomorphic to the preimage $f^{-1}(y)$ in the induced topology.  The following is my attempt so far:  The question is obviously affine on the target, so without loss of generality we reduce to the case of a morphism $f: X \longrightarrow \text{Spec }A$. Then we have  $$ f^{-1}(\text{Spec }A) = \bigcup_{i \in I} \text{Spec }B_{i} $$ via morphisms $$ \phi_{i}: A \longrightarrow B_{i}. $$ We can then write, \begin{align*} f^{-1}(\text{Spec } A) \times_{\text{Spec } A}\text{Spec } \kappa(y) &= \bigcup_{i \in I} \left( \text{Spec } B_{i} \times_{\text{Spec }A} \text{Spec }\kappa(y) \right) \\  &= \bigcup_{i \in I} \text{Spec }  \left( B_{i} \otimes_{A} \kappa(y)  \right). \end{align*} Now let $\mathfrak{p}$ be the prime ideal of $A$ corresponding to the point $y \in \text{Spec } A$. Then $\kappa(y) = (A/ \mathfrak{p})_{\mathfrak{p}}$. Then for any of the $B$ (dropping the index for brevity), we have \begin{align*} B\otimes_{A} (A/ \mathfrak{p})_{\mathfrak{p}} &\simeq B \otimes_{A} A / \mathfrak{p} \otimes_{A} A_{\mathfrak{p}} \\ &\simeq B_{\mathfrak{p}} \otimes_{A} A / \mathfrak{p} \\ & \simeq B_{\mathfrak{p}} / \mathfrak{p}B_{\mathfrak{p}} \end{align*}  Now the prime ideals in $B_{\mathfrak{p}} / \mathfrak{p}B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B_{\mathfrak{p}}$ containing $\mathfrak{p}B_{\mathfrak{p}}$. Further, the prime ideals of $B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B$ contained in $\phi(\mathfrak{p})B$. That is, we have \begin{align} \text{Spec }B_{\mathfrak{p}} &= \{  \mathfrak{q} \subseteq B :  \phi^{-1}(\mathfrak{q})  \subseteq \mathfrak{p}  \} \\ &=  \{ \mathfrak{q} \subseteq B : f(\mathfrak{\mathfrak{q}}) \subseteq \mathfrak{p}      \}. \end{align} Note that in the very last line we have abused notation slightly: There is not really any notion of being "inside" $\mathfrak{p}$ when it is being treated as a point in the scheme. So really we mean that $f(\mathfrak{q})$ is a point in the scheme whose corresponding prime ideal is a subset of $\mathfrak{p}$. Now as we said above, the prime ideals of $B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}$ are the following $$ \text{Spec }(B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}) = \{ \mathfrak{q} \subseteq B : f(\mathfrak{\mathfrak{q}}) \subseteq \mathfrak{p}      \text{ and } ???  \} $$ This is the point at which I get stuck. Ideally I would like to make some argument from the statement "Now the prime ideals in $B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B_{\mathfrak{p}}$ containing $\mathfrak{p}B_{\mathfrak{p}}$" to conclude that the question marks are the condition $\mathfrak{p} \subseteq f(\mathfrak{q})$. Could someone point me in the right direction as to how to get this condition?   Is the proof up until this point correct? Different sources online seem to do this many different ways, so it's difficult for me to check.


I am trying to create a custom theme using Wordpress 3.4's customization options. I would like to create an option to change the theme's logo, but I would like to also display a default logo image.   I am using the following code in my function.php page:  $defaultbranding = "get_bloginfo('template_directory') . '/images/logo.png";      $wp_customize->add_setting( 'change_branding', array(         'default' => get_bloginfo('template_directory') . '/images/logo.png',     ) );      $wp_customize->add_control( new WP_Customize_Image_Control( $wp_customize, 'change_branding', array(         'label'   => 'Image Control',         'section' => 'theme_settings',         'settings'   => 'change_branding',     ) ) );   And in the theme's header.php page:  src='<?php echo get_theme_mod( 'change_branding' , 'default' ) ?>'   I would like the 'default' value on the front end to be:  get_bloginfo('template_directory') . '/images/logo.png'   Is there some way I can achieve this?  Thanks in advance for any help.


How do I determine the variance of a collection of groups?

I’m trying to compute the variance of how much pumpkins weigh across pumpkins from 125 farms. However, I only have, for each farm, three pieces of data: (1) the variance of weights for pumpkins from that farm (2) how many pumpkins the farm has (3) the total weight of the pumpkins from the farm.  How can I compute a “weighted variance” of how much a pumpkin weighs across farms? Can I just compute a weighted average of the individual variances?


I am facing a very specific problem when trying to implement a generic queue in C++. Here is the code:  template <class T> class Queue  {      private:         T * queue;         int front;         int back;         int MAX_SIZE;      public:         Queue(){             Queue(SOME_PREDEFINED_CONSTANT);         }          Queue(int size){             queue = new T[size];             MAX_SIZE = size;             front = 0;             back = 0;             cout << "inside constructor:" << " back= " << back <<  " front=" << front << endl;          }          void push(const T entry){              if(back < MAX_SIZE){                 queue[back] = entry;                 back++;             }         }          T peek(){              return queue[front];          }          void pop(){              if(size() > 0){                 front++;             }             if(front==back){                 front = 0;                 back = 0;             }         }          int size(){             cout << "size:" << " back=" << back <<  " front=" << front << endl;             return (back-front);         } };   When I am initializing the queue, like this: Queue <int> q;, I get the correct values of back and front inside the constructor; The output:     inside constructor: back=0 front=0   But when I am asking for the size of the queue, like this: q.size() (without any push/pop operation), I get very weird values of back and front. One sample output:     size: back=32766 front=-746749592   Can anyone please point out what I am doing wrong here?


How big can the deck get while still allowing this puzzle to be solvable?

Here's a classic puzzle (I think Martin Gardner talks about it somewhere, though I'm not sure exactly where):     Alice and Bob are co-conspirators. Alice is dealt five random cards from a standard deck; she looks at the cards, and then shows four of them to Bob in some chosen order. Using only the four cards and the order they are shown in, Bob must determine the identity of the fifth card.   The solution that I know of is:      Alice and Bob agree on an ordering of the $52$ cards, and a bijection between $S_3$ to $\{1,\dots,6\}$. With this information, an ordering of any three cards gives an integer between $1$ and $6$ inclusive. Now, Alice uses the pigeonhole principle to find two cards of the same suit. Without loss of generality, their ranks are $r_1$ and $r_2$ where $r_1+a \equiv r_2 \pmod{13}$ and $1 \leq a \leq 6$ (if they weren't originally, swap $r_1$ and $r_2$). Alice puts the card of rank $r_1$ first (naming the suit) and then orders the other three cards in a way that tells Bob $a$ (naming the rank).   Notice that $52$ cards is the maximum possible number that this solution works for, since it depends heavily on there being only four suits and thirteen cards in each suit. However, it seems like it wastes a fair amount of information whenever     the suit distribution isn't 2-1-1-1.   Is there a method to do this which works on a deck containing more than $52$ cards? The obvious upper bound on deck size is that Bob sees a list of four ordered cards and can deduce from it the original five cards Alice was dealt, so it it works for a deck of size $n$ we must have $$ 4!\binom{n}{4} \geq \binom {n}{5} $$ or $n \leq 124$. But that still leaves quite a gap...


Java NullPointerException on concatenating Double types but not on String types

Double d1 = null;      Double d2 = null;      System.out.println(d1+d2);//throw NullPointerException      String s1 = null;      String s2 = null;      System.out.println(s1+s2);//doesn't throw any exception prints nullnull   Since both Double and String are of type Object then why Double types throw exception??


Let $n \in \mathbb{N}$. Proving that $13$ divides $(4^{2n+1} + 3^{n+2})$

Let $n \in \mathbb{N}$. Prove that $13 \mid (4^{2n+1} + 3^{n+2} ). $  Attempt: I wanted to show that $(4^{2n+1} + 3^{n+2} ) \mod 13 = 0. $ For the first term, I have $4^{2n+1} \mod 13 = (4^{2n} \cdot 4) \mod 13  = \bigg( ( 4^{2n} \mod 13) \cdot ( 4 \mod 13 ) \bigg) \mod 13. $ But still I don't know how to simplify the first term in the large bracket.  Any help/suggestions?


My wife has a US CR1 visa with her maiden name on it. Her Philipines passport has her married name on it. Should she have any issues flying to the US for the first time because of the name difference? She will take her old passport with the maiden name and her marriage certificate with her for backup as well.   Thank you


maximize volume of triangle in given perimeter

question: Find the triangle with perimeter 2a given that, when we rotate it around one of its sides, the solid obtained have the maximum volume.  suppose we have a triangle of sides x,y,z such that $x+y+z=2a$ and $h$ is the height,  we rotate it around the side with size z, we want to get the solid with maximum volume. $Area = \sqrt{a(a-y)(a-y)(a-z)}=\frac{1}{2} zh$ but i was confuse why the volume is $(\frac{1}{3}\pi h^2z)$  if it is cone why not  $(\frac{1}{3}\pi z^2h)$??  and is it better to use Lagrange multipliers or substitution method? thankyou


Convert column values to grouped comma-separated string

I am using SQL Server 2008. I have a table like below:  ID  Name  1   a 1   b 2   c 3   d   I want output like below:  ID  Name 1   a,b 2   c 3   d


How to reduce the heat from peppers in my tomato soup?

I just made tomato soup with two cans of tomatoes with jalapeno peppers in it.  The soup has turned out to be too spicy.  How can I reduce the spicy (heat) level of the soup?


Proof concerning regular space: there exist a closed set contained in any open set containing $x$

I was given a claim:     Let $(X, \mathfrak{T})$ be a topological space. Then $X$ is a regular    space iff $\forall x \in X, \forall U \in \mathfrak{T}$ s.t. $x \in  U$, $\exists V$ such that $x \in V \subseteq \overline V \subseteq U$   Regular is defined as (similar to wiki):     If, given any point $x$ and closed set $F$ in $X$ such that $x$ does   not belong to $F$, they are separated by open disjoint neighbourhoods   I was stuck on a minor part of the proof and need some help!    $(\Rightarrow)$ Let $(X, \mathfrak{T})$ be a regular space. Then $\forall x \in X$, $F \subset X$, $F$ is closed and does not contain $x$, there exists open sets $U$ and $W$, such that $x \in U, F \subset W$ and $U \cap W = \varnothing$.  Since $U$ is open, for all points $X$, there exists an open set $V$ such that $x \in V \subset U$. (We have just produced $V$ in the claim)  Let $y \in F \subset W$ be another point. Then by definition of regular, $y$ is separated from any closed set. Consider the closed set $\overline V$, then we have $y \in W, x \in V \subseteq \overline V \subseteq U$. And since $U \cap W = \varnothing, y \notin \overline V$  ($\qed$ $\eop$ <--- how to generate end of proof symbol?)       There is something terribly wrong in the second last line of the proof   which I stated:      " $x \in V \subseteq \overline V \subseteq U$"      There is no insurance that such $\overline V \subseteq U$.  It is very likely that $U \subseteq \overline V$ instead.      How do I correct this line?


Give a description of Loop Quantum Gravity your grandmother could understand

Of course, assuming your grandmother is not a theoretical physicist.  I'd like to hear the basics concepts that make LQG tick and the way it relates to the GR. I heard about spin-networks where one assigns Lie groups representations to the edges and intertwining operators to the nodes of the graph but at the moment I have no idea why this concept should be useful (except for a possible similarity with gauge theories and Wilson loops; but I guess this is purely accidental). I also heard that this spin-graph can evolve by means of a spin-foam which, I guess, should be a generalization of a graph to the simplicial complexes but that's where my knowledge ends.  I have also read the  but I don't find it very enlightening. It gives some motivation for quantizing gravity and lists some problems of LQG but (unless I am blind) it never says what LQG actually is.  So, my questions:        Try to give a simple description of fundamentals of Loop Quantum Gravity.   Give some basic results of the theory. Not necessary physical, I just want to know what are implications of the fundamentals I ask for in 1.   Why is this theory interesting physically? In particular, what does it tell us about General Relativity (both about the way it is quantized and the way it is recovered from LQG).


What does it mean to have "Web browser is waiting for data from the server" high on a speed test site. I have 21560.1s in wait time?

The web page took 22792 ms to load, used 119 requests, and weighed in at 1.7 MB.  The Google Page Speed performance grade for this web page is 70/100.  I'm looking to decrease my load times, but am unsure of what further I can do. I believe my images are as low as I can get them without compromising any more quality.     Any help is appreciated.   TIA


Converting JavaFx project to .exe and .app in Netbeans

I am developing a desktop app in JavaFx for mac and windows and want to distribute it to users but not as a .jar file. I want to distribute it as an installer file for both mac and windows.  I have read at some forums and in stackoverflow also that we can export a project a .exe for windows and .app for mac using Neatbeans but I am not able to find how to do it.  Is it possible through netbeans to create .exe and .app files ??  I have neatbeans 8.  I can see some ways to convert it to .exe using some apps, but for .app or .dmg I am not able to find anything.


I've created a working bootable USB stick! Now how do I "finish it"?

Before posting this, I looked at 24 different duplicate questions including: . I couldn't find a single question that dealt with this. So, please don't mark duplicate unless there truly is another question asking this...  Now that I've followed the , and it works flawlessly, how do I make it permanent, rather than a trial/installer?     I believe this will help Windows users too. My ultimate goal is to have a single USB stick that I can use on Mac or PC, but in the end may have to carry 2   The directions I linked above are excellent! It worked perfectly. I'm not one of those people who can't follow directions. The problem is that the directions ended too soon.  Here is what I mean by "make it permanent"   When I boot off the USB stick, I get GRUB menu offering "Try Ubuntu without installing", "Install Ubuntu", "OEM install (for manufactures)", and "Check disk for defects"   I want this to boot straight into a full Ubuntu Install.  When I boot into "Try Ubuntu", the drive is very small.   I want to make the full space of my 32GB USB stick available I don't want to waste my precious little space on tools for installing Ubuntu on another drive. (This is my drive!)  The drive seems to be in a Guest/Read-only-ish mode.   I tried to remove the media files in the Examples directory linked on the Desktop and got an error I tried to downloaded the , but...   the Ubuntu GUI installer doesn't even seem to try to open it. dpkg -i won't install it because of 3 dependencies. apt can't locate any of the 3 dependencies. none of the answers on  work for me.  [ I fully realize that the Chrome issue may be a  ]    Let me clarify my criteria   EDIT: I can't believe I'm doing this again, but here we go... Let me take the big bold question at the top, and break it down phrase by phrase...   Now that I've followed the ,   If you are calling this question a duplicate of another and the other does not specifically address following those directions, it is a different question  and it works flawlessly,   If you are calling this question a duplicate of another and the other is about failing to follow those directions, it is a different question  how do I make it permanent,   The key word there is it. What does that pronoun refer too? A USB drive that was created in about 2 minutes by dding an ISO on to it. What does it NOT refer too? A USB drive that created over the course of hours by using it as the target of the GUI Ubuntu installer. If you are calling this question a duplicate of another and the other does not populate the USB drive via dd or , it is a different question  rather than a trial/installer?   If you are calling this question a duplicate of another and the other produces the Live CD/trial/installer, it is a different question   I want my hard drive to be untouched. I don't want to make an Ubuntu USB "install disk". I do want to Ubuntu installed on a USB disk. The answer may very well be that it's not possible to do.   REMINDER: My question is in bold at the top The answer may be that I have to try something else  This question is not a duplicate.   If the answer turns out that I have to try something else, that's okay. But marking the question as a duplicate prevents smart people from considering the question.    Please don't be nasty  Before you vote to close this, put it on hold, mark it duplicate, or kill my dog, post a comment and lets see if we can improve the question to your satisfaction. I'm doing this for posterity. Please don't be nasty.


LIGO flawed by the identical expansion of laser wavelength and arms in presence of a gravitational wave?

, Laser Interferometer Gravitational-Wave Observatory, is a large-scale physics experiment aiming to directly detect gravitational waves. The device measures the phase shift laser beams.  If I understand this well, the measurement assumes that a suitable gravitational wave reduces and prolongs one of the tubes and the extension will take effect in the phase-shifting laser beams.  But I think if there's a gravitational wave that passes through it, it will affect everything, even the laser beam. This means that when the wave lengthens or shortens the tube, it also lengthens or shortens the wavelength of the laser beam.  In my opinion, therefore, this device does not work. Or am I wrong?


I didn’t know about the <button> tag until today.


Finding $\frac {d(\tan \theta)}{d\theta}$

I was reading Needham's Visual Complex Analysis, and could not figure out how we get length $Ld\theta$ here:


Prove, for  every $n\in\mathbb{N}$, that       a) (done) $\displaystyle\int_0 ^{\pi/2} \sin^nx\,dx=\frac{n-1}{n}\int_0^{\pi/2}\sin^{n-2}x\,dx$, $n\geq2$.      b) $\displaystyle\int_0^{\pi/2} \sin^{2n+2}x\,dx\leq\int_0^{\pi/2} \sin^{2n+1}x\,dx\leq\int_0^{\pi/2} \sin^{2n}x\,dx.$   So, using part (a)  $$\displaystyle\int_0^{\pi/2} \sin^{2n+2}x\,dx =\frac{2n+1}{2n+2}\int_0^{\pi/2}\sin^{2n}x\,dx\leq\int_0^{\pi/2}\sin^{2n}x\,dx$$  But I don't know how do reduce the expoent in only one unit, since part (a) reduces two units per once.


What if quantum mechanics and general relativity are not connected?

The main objective in modern physics research is to find a way to unify quantum mechanics and general relativity thorugh a series of theoretical approaches called "quantum gravity theories"  But what if quantum mechanics and general relativity are not connected/related? What if we never find evidence of such connection?


How to block specific websites without using Parental Controls?

I know I can block websites in Parental Controls, but accessing that option requires the "Limit Adult Websites" option, which I find to be overly strict.  Is there a way to block specific websites without third-party software?  I'm running High Sierra on my laptop.


extrapolation in graph editor in blender 2.8

I wanted to create a spiral rotating at constant speed. I created my spiral, made two keyframes with linear interpolation and then wanted to add linear extrapolation, but for some reason, when I right click on the channel in graph editor, all the options under extrapolation are greyed out. I am not sure, whether this is just blender 2.8 thing, or I just made some stupid mistake or overlooked something... What could be the cause of this? Or is there some workaround or something? Thanks in advance.


Allocate Disk Space FROM Ubuntu for Windows

I want to dual boot Windows and Ubuntu from my computer, which has only Ubuntu installed. I have done dual booting before but in that case, Windows was installed first. Here are my Ubuntu partitions:    And I want to free up some 60GB space for my Windows. How do I do that?


I am trying to replace >>> with "" in file  cat table_files.md | egrep ">>>$"                                  \>>>   \>>> \>>> \>>> \>>> \>>> \>>> \>>> \>>>   replace it with sed  cat table_files.md | sed "s\>>>$\\g" > table_files.md   Unfortunately, all my data gone, it feedback to me a blank file. I check this should be done using -i option in place.  How could that happen, is it possible to recover the data?


Over on stack-overflow, I have 2 or 3 questions that have over 1000 page views and its hard for me to believe that they only have 1 up-vote each. I am not saying my questions deserve it, but I have seen some really stupid questions that have way more, with less views. No examples at the moment, but I am sure you have all seen them...  This is either due to my questions not being useful at all except for myself, or there are a lot of lurkers out there that find them in search but never take the time to sign and up-vote if they were helpful.  SO should implement a sign in after X amount of web site visits or something similar. That feature is really annoying but if cache isn't cleared then the login will persist... I don't think questions are getting represented accurately enough both positively and negatively. Who knows, maybe all my questions suck and I would be getting 100 down votes.


I know that electric charge is lorentz invariant quantity and I can easily think of experiment to check that. Is a though experiment that can prove that also?


$X,Y,B$ are sets  Prove:  $X\cup B=Y\cup B$ if and only if $X\setminus B=Y\setminus B$  I have no idea how to do it.


I used Fermat’s Little Theorem and was able to turn the equation into $x^{44} = 1 \pmod {23}$ but still was not able to find a solution from that.


Installing flash images on an unrecommended device

I want to install the Nexus Hammerhead flash image on my Samsung Galaxy S Duos. Is this possible and if so is it safe?


Why is moment of inertia minimum about centre of mass of any rigid body?


How do I disable the blank console "screensaver" on Ubuntu Server?

How to disable blank screensaver on Ubuntu Server?  There's no desktop or X, only console (command-line interface).


I am studying on websites manual test. I haven't any idea about making a bug report for developer by MS word, excel, powerpoint, PDF, video, screenshot etc. That they can understand easily my report & absence of me they fixed bugs. How to create a report, specially bugs report for developer. Developers need clean & easy report for understanding & also fixing those bugs. Which report will be clean & that report will have details about bugs. Step by step every bug & their fixing issue.  I need some idea with examples that I can understand & created by myself. If anybody know about any tools & websites about manual bugs reporting so please details information to me.


How to find out WHERE a PG error/warning/log happened?

I have PostgreSQL CSV-log its "errors" according to this structure:  It doesn't include the file path to the script which ran the query, so I have no idea where it occurred besides the vague, essentially useless hint from the "application_name". How do I make it log which file caused the error/warning/log? My first thought was to just add my own column to the table, called file_path, but then I realized that this won't help, since my script which does the COPYing of the csvlog data into my table has no idea from where the entries origin, since they are not logged by PostgreSQL. Without knowing where the error occurs, I might as well not have a log at all. How do I make it log the file path and not just the application_name? I'm baffled as to why this is lacking in the table structure/CSVlog dump format. The "detail" column is almost always empty, so there are no file paths there for me to extract.


How can I find a past roundtrip airfare from Detroit to Nashville, leaving Detroit on 4/5/14 and returning on 4/8/14?


Can't read InputStream after creating jar

I can't really wrap my head around what's going on with my program. Everything works fine before building the jar file. When running the jar file I get Exception in thread "main" java.lang.NullPointerException  The NullPointerException happens when I call System.out.println(FileHandler.readInputStream(path));  Exception in thread "main" java.lang.NullPointerException     at java.io.Reader.<init>(Unknown Source)     at java.io.InputStreamReader.<init>(Unknown Source)     at java.util.Scanner.<init>(Unknown Source)     at RaspberryPiServer.FileHandler.FileHandler.readInputStream(FileHandler.java:17)     at RaspberryPiServer.Client.<init>(Client.java:47)     at RaspberryPiServer.Main.main(Main.java:277)   The important parts. Testing the relevant parts:  String path = "Client\\key.txt"; System.out.println(FileHandler.readInputStream(path));  // RaspberryPiServer.FileHandler class: public static String readInputStream(String path) {     InputStream input = RaspberryPiServer.Utils.ResourceLoader.loader(path);     java.util.Scanner s = new java.util.Scanner(input);     s.useDelimiter("\\A");     String streamString = s.hasNext() ? s.next() : "";     s.close();      return streamString; }  // RaspberryPiServer.Utils.ResourceLoader class public static InputStream loader(String path) {      InputStream input = ResourceLoader.class.getResourceAsStream(path);      if (input == null) {         input = ResourceLoader.class.getResourceAsStream("/" + path);     }      return input; }   I also did jar tf RaspberryPi.jar to confirm that the key.txt file exists within the jar file.  META-INF/MANIFEST.MF Client/ Client/key.txt log4j.properties Logging.log META-INF/ RaspberryPiServer/ ... ...


Do I really need cdn for video delivery?

If I'm going to create video delivery site for big country (Russia), should I use CDN for video? I believe, that store video in two places, Tokyo (for East part of country) and Frankfurt (for West part of country) for example much cheaper than load videos to CDN. However, I'm a bit worry about video load speed, but should I? UPD. Sorry I'm not really good in this kind of questions. So, as for the tecnical details. I suppose that, it's will be quite big service. Most part of users based in one country. Our own servers output speed about 220Gb/s. From answer below, I understand that most likely I'll need cdn, but what parameters should I keep in mind while choosing?


Just upgraded to Mac OS X.9 Maverick and XeTeX (at least us used from TexWorks, which is all I've tried) now seems to be broken though it was working before. Error message when I try to typeset with ConTeXt/XeTeX:     /System/Library/Frameworks/Ruby.framework/Versions/2.0/usr/lib/ruby/2.0.0/rubygems/core_ext/kernel_require.rb:45:in   'require':   /usr/local/texlive/2013/texmf-dist/scripts/context/ruby/base/switch.rb:501:   invalid multibyte escape: /\xFF/ (SyntaxError)    from   /System/Library/Frameworks/Ruby.framework/Versions/2.0/usr/lib/ruby/2.0.0/rubygems/core_ext/kernel_require.rb:45:in   'require'     from   /usr/local/texlive/2013/texmf-dist/scripts/context/ruby/texexec.rb:11:in   `'   Anyone else having this? Any ideas?  (I'm relatively new to both TeX and Macs, as well as this site, so apologies if this is inappropriate, poorly asked or a stupid question. :) )  Edit: The problem occurs even on minimal files with both ConTeXt/XeTeX and ConTeXt/pdfTeX but not with ConTeXt/LuaTeX. Complete reinstallation of MacTeX has not helped.


What will affect the value of Young's modulus?

What will affect the value of Young modulus? Is it a constant for every material no matter how you change the length or area?


Additive set function on a semiring of sets

A semiring $\Pi$ on a set $X$ is a non-empty family of subsets of $X$ with the following properties.     1) $P \cap Q \in \Pi$ whenever $P\in \Pi$ and $Q\in\Pi$.      2) $P - Q$ is a finite disjoint union of members of $\Pi$ whenever $P\in \Pi$ and $Q\in\Pi$.   Let $\lambda: \Pi\rightarrow [0, \infty]$ be a non-negative extended real-valued set function such that $\lambda(\emptyset) = 0$. Suppose $\lambda$ is additive, i.e. if $P, Q_1, Q_2$ are members of $\Pi$ and $P = Q_1\cup Q_2$ is a disjoint union, then $\lambda(P) = \lambda(Q_1) + \lambda(Q_2)$.  Then $\lambda$ is finitely additive? In other words, if $P, Q_1, \cdots, Q_n$ are members of $\Pi$ and $P = \bigcup_{i=1}^n Q_i$ is a disjoint union, then $\lambda(P) = \sum_{i=1}^n \lambda(Q_i)$?  I came across this problem when trying to solve this question:   I also found this is an exercise in Halmos's Measure Theory, Ch. II, sec. 7. It has some hints, but I was unable to solve it.


How do I understand if an indefinite integral is not solvable in terms of elementary functions?

Many indefinite integrals cant be solved in terms of elementary functions.e.g.-$$\int \frac{\sin(x)}{x}dx$$ But many hard looking ones are still solvable by weird substitutions and other tricks. Is there a test(like there are tests of solvability/convergence.etc in mathematics) of whether it is solvable or not by which I can see beforehand without wasting hours of time after which I come to know that it is not even solvable?


The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel

Let $H$ be the normal subgroup of $G$.   Is it true that $(H[G,G])/H$ is isomorphic to $[G/H,G/H]$?  If so, I want to make a surjective homomorphism $\phi\colon H[G,G]\to [G/H,G/H]$ with Kernel $H$ to prove it.  But, if I define $\phi(h[g_1,g_2])=[g_1/H,g_2/H]$ then I have some trouble.


I have a request to display all related opportunity records for a particular product2 using a visualforce page on thé product2 object


Equation: 1/(1*2) + 1/(2*3) + 1/(2*4) + ... + 1/(n*(n+1)) = n/(n+1)  I need help with solving this equation. I cannot seem to be able to do anything with (n+1)/(n+2) that I get on the right side after induction step.


Create logical volume again on Ubuntu after deleating it

I have a Ubuntu 16.04 Server and used these two commands which accidently deleted my logical volume:  lvchange -an -v /dev/sda5/xyz-vg and  lvremove -vf /dev/sda5/xyz-vg  I did so from an Ubuntu Live CD, in order to decrease the size of the partition where the lv was located using gparted. It would not work otherwise. In the end resizing  worked fine, but now I cannot boot anymore.   At startup I get an error message Failed to find logical volume "xyz-vg/root"  sudo pvdisplay from the live CD indicates that the PV is called /dev/sda5 and the VG name is xyz-vg.  sudo lvmdiskscan gives me that I have three partitions of which one is a LVM phyiscal volume.   I followed steps indicated as linked in the comment section :   pvcreate --restorefile /etc/lvm/archive/ --uuid dev/sdX vgcfgrestore -f /etc/lvm/archive/ --verbose thisVG vgdisplay -v /dev/thisVG && vgchange -ay /dev/thisVG mount /dev/thisVG/missingLV /mnt   This recreated my volume group. The output of vgdisplay from the livecd is now:  root@ubuntu:/home/ubuntu# vgdisplay   --- Volume group ---   VG Name               xzy-vg   System ID                Format                lvm2   Metadata Areas        1   Metadata Sequence No  9   VG Access             read/write   VG Status             resizable   MAX LV                0   Cur LV                0   Open LV               0   Max PV                0   Cur PV                1   Act PV                1   VG Size               439.45 GiB   PE Size               4.00 MiB   Total PE              112499   Alloc PE / Size       0 / 0      Free  PE / Size       112499 / 439.45 GiB   VG UUID               Ii03eE-fP5g-1Mjm-yC0T-F9Yl-5vqW-XYUBID   However, this still does not bring me back the logical volume. lvdisplay gives no output, so I guess I need to recreate it? How do I do that without deleting all the data that is still on the disk?


Are there any prime ideals in the ring $C[0,1]$ of continuous functions $[0,1]\rightarrow \mathbb{R}$, which are not maximal? Perhaps, I duplicate smb's question, but this is an interesting problem! Could you give me any hint or give a link to some literature?


What is the difference between French and British cuts of beef?   I am told they just butcher the animals dfferently. Certainly the cuts don't seem the same. For example is faux fillet really exactly the same as British sirloin and is entrecôte really the same as rib steak?  Here is a picture of British beef cuts.


When can the limit of a sum be the sum of a limit?

If I have a limit of an infinite sum, can I bring the limit inside the infinite sum? If so, why?


How to set watermark width and height same as video width and height using ffmpeg?

I want to set watermark width and height same as video width and height.    String[] cmd={"-i",margefilePath,"-ignore_loop","0","-i","/storage/emulated/0/Download/light2.gif","-i","/storage/emulated/0/Download/04 - Aa To Sahi - DownloadMing.LA.mp3","-filter_complex","[1:v]format=yuva444p,scale="+800+":"+720+",setsar=1,rotate="+angle+":c=black@0:ow=rotw("+angle+"):oh=roth("+angle+") [rotate];[0:v][rotate] overlay=0:0:shortest=1[v]","-map","[v]","-map","2:a:0","-c:a","aac","-shortest","-y","/storage/emulated/0/Movies/video_gif_light2.mp4"};   If I try to scale using constant value it's not work all time. Please tell me how to scale watermark dynamically?


I am experiencing an identical problem to the one in:   However this thread in unanswered and unresolved  My internal drive can format to everything except APFS, I have tried troubleshooting via linux, and simple disk utility. Fsck and first aid both report no problems and this is driving me insane!! help desperately needed!