Every integer is congruent to the sum of its digits mod 9

This is a question from the free Harvard online abstract algebra .  I'm posting my solutions here to get some feedback on them.  For a fuller explanation, see  post.  This problem is from assignment 6.  The notes from this lecture can be found .     Prove that every integer $a$ is congruent to the sum of its decimal digits modulo 9.   Let $s$ be an $(n+1)$-digit integer given by $s=a_n\cdot10^n+\dots+a_2\cdot10^2+a_1\cdot10^1+a_0\cdot10^0$ with $a_i\in\mathbb{Z}$ such that $0\leq a_i\leq9$.  Then $ \begin{align} s\,\mathrm{mod}\,9&=\bar{s}\\ &=\overline{a_n\cdot10^n+\cdots+a_2\cdot10^2+a_1\cdot10^1+a_0\cdot10^0}\\ &=\overline{a_n\cdot10^n}+\overline{\cdots}+\overline{a_2\cdot10^2}+\overline{a_1\cdot10^1}+\overline{a_0\cdot10^0}\\ &=\overline{\overline{a_n}\cdot\overline{10^n}}+\overline{\cdots}+\overline{\overline{a_2}\cdot\overline{10^2}}+\overline{\overline{a_1}\cdot\overline{10^1}}+\overline{\overline{a_0}\cdot\overline{10^0}}\\ &=\overline{\overline{a_n}\cdot1}+\overline{\cdots}+\overline{\overline{a_2}\cdot1}+\overline{\overline{a_1}\cdot1}+\overline{\overline{a_0}\cdot1}\\ &=\overline{a_n}+\overline{\cdots}+\overline{a_2}+\overline{a_1}+\overline{a_0}\\ &=a_n\,\mathrm{mod}\,9+\cdots+a_2\,\mathrm{mod}\,9+a_1\,\mathrm{mod}\,9+a_0\,\mathrm{mod}\,9 \end{align} $  Again, I welcome any critique of my reasoning and/or my style as well as alternative solutions to the problem.  Thanks.


Not formatting a partition while installing Ubuntu but still data getting lost from that partition!

I'd Ubuntu 13.10 on my system with separate /home partition for my data. Now I reinstalled the same O.S. In the option while installing, I selected something else & there specified to format all partitions (/, /var, /tmp, /boot) except /home. Now when my system was installed, I found the data was lost on the home partition. I wondered as I had unchecked for formatting that partition while installation.  To test it again, I created a file in /home. Then using my bootable usb flash drive, I reinstalled the O.S. This time also I unchecked /home for formatting. But still afterwards I found the file I created on the home partition was lost.  Where am I thinking wrong? I thought it was a good method of installation to preserve home data but it's not working!!     EDIT#1   Yes I got clue from a comment. The problem is something else. Yes it's mounting on /home, that's no problem.  See what has happened! In the 1st system (Ubuntu 13.10) I'd logged in with the name of "ravi". I'd much data in the subdirectories of /home/ravi. Then I upgraded the system to 14.04 which didn't work, so I installed back the earlier O.S. (i.e. 13.10.) by keeping the same /home partition. This time while installing I changed the login name as "bholu". Now after getting installed & logging in as "bholu", I checked my home directory & subdirectories but didn't find any data. Then to further test, I created a file in home directory & reinstalled the O.S. with the same /home. Now this time I changed the login name to "bholua". Again now I didn't find the file I created earlier. So, I'd that doubt that the data are getting lost.  Now after reading a comment, it striked my mind & I checked my /home folder. There all the 3 names were present.  bholua@bholua-Aspire-5315:/home$ ls bholu  bholua  lost+found  ravi bholua@bholua-Aspire-5315:/home$   Now when I move to one username "ravi" , I see the below contents there.  bholua@bholua-Aspire-5315:/home/ravi$ ll total 12 dr-x------ 3 bholua bholua 4096 Jun 25 02:25 ./ drwxr-xr-x 7 root   root   4096 Jul 27 23:39 ../ lrwxrwxrwx 1 bholua bholua   56 Jun 25 02:04 Access-Your-Private-Data.desktop -> /usr/share/ecryptfs-utils/ecryptfs-mount-private.desktop* drwx------ 3 bholua bholua 4096 Jun 25 02:25 .cache/ lrwxrwxrwx 1 bholua bholua   30 Jun 25 02:04 .ecryptfs -> /home/.ecryptfs/ravi/.ecryptfs/ lrwxrwxrwx 1 bholua bholua   29 Jun 25 02:04 .Private -> /home/.ecryptfs/ravi/.Private/ lrwxrwxrwx 1 bholua bholua   52 Jun 25 02:04 README.txt -> /usr/share/ecryptfs-utils/ecryptfs-mount-private.txt   Now see the content of the other username "bholu". It's the same here.  bholua@bholua-Aspire-5315:/home/ravi$ ll /home/bholu total 12 dr-x------ 3 bholua bholua 4096 Jul 28 03:16 ./ drwxr-xr-x 7 root   root   4096 Jul 27 23:39 ../ lrwxrwxrwx 1 bholua bholua   56 Jul 28 03:13 Access-Your-Private-Data.desktop -> /usr/share/ecryptfs-utils/ecryptfs-mount-private.desktop* drwx------ 3 bholua bholua 4096 Jul 28 03:16 .cache/ lrwxrwxrwx 1 bholua bholua   31 Jul 28 03:13 .ecryptfs -> /home/.ecryptfs/bholu/.ecryptfs/ lrwxrwxrwx 1 bholua bholua   30 Jul 28 03:13 .Private -> /home/.ecryptfs/bholu/.Private/ lrwxrwxrwx 1 bholua bholua   52 Jul 28 03:13 README.txt -> /usr/share/ecryptfs-utils/ecryptfs-mount-private.txt   Now the point is how to access those data created under username of "ravi" & "bholu"! It seems I'd earlier enabled encryption of my home directory. linuxubuntu ravisingh1 is online now    Report This Post


What is the smallest sigma value (out of $1\sigma$, $2\sigma$, $3\sigma$, $4\sigma$, $5\sigma$, $6\sigma$) we can use when we want a less than 0.3% defect ratio? My idea is to use $68-95-99.7$ rule, and obtain $3\sigma$ as an answer. Is it correct approach, or has missing parts?


Getting coordinate system name from SpatialReference using GDAL/Python

In Python, using GDAL, I've extracted a raster's projection as a WKT string as follows:  wkt = dataset.GetProjection() # wkt is 'PROJCS["GDA_1994_Transverse_Mercator",GEOGCS["GDA_1994",DATUM["GDA_1994",SPHEROID["GRS_1980",6378137,298.2572221010002],TOWGS84[0,0,0,0,0,0,0]],PRIMEM["Greenwich",0],UNIT["degree",0.0174532925199433]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",0],PARAMETER["central_meridian",117],PARAMETER["scale_factor",0.9996],PARAMETER["false_easting",500000],PARAMETER["false_northing",10000000],UNIT["Meter",1]]'   Using the WKT string, I can create a SpatialReference instance as follows:  src = osr.SpatialReference() src.ImportFromWkt(wkt)   This is easy-peasy. I can extract several parameters of the projection from src such as the UTM zone, etc., easily enough. But I can't figure out how to extract something like the name of the projection, i.e. "GDA_1994_Transverse_Mercator". This has surely got to be possible, but the Python API documentation may as well be nonexistent for all the use it is.  How do I extract the names of the projection and the geographic coordinate system?


You are organizing a party.  However, the number of guests to attend your party can be anything from $a_1$, $a_2$, $\ldots$, $a_n$, where the $a_i$'s are positive integers.  You want to be prepared, so you want to cut a cake into smaller pieces.  The pieces are not necessarily of equal size.  The requirement is that, no matter how many guests come (which you will have known before distributing the cake), you will be able to give each of them some pieces of the cake without having to cut the cake any further so that everybody will get the same amount of cake.  What is the minimum number of pieces of your cake you will have to cut it into?     Trivially, if $n=1$, then the answer is $a_1$.  The answer is also known for $n=2$, which is $a_1+a_2-\gcd\left(a_1,a_2\right)$ (if you wonder why graph theory is in the tag, it is because the only proof known to me for the $n=2$ case is done via a graph-theorical argument).  I conjecture that the answer, in general, is $$m:=\sum_{j=1}^n\,(-1)^{j-1}\,g_j\,,$$ where $$g_j:=\sum_{1\leq k_1<k_2<\ldots<k_j\leq n}\,\gcd\left(a_{k_1},a_{k_2},\ldots,a_{k_j}\right)$$ for $j=1,2,\ldots,n$ (here, $g_1$ is simply $a_1+a_2+\ldots+a_n$).  It is easy to cut the cake into $m$ pieces to satisfy the required condition.  Apparently, the conjecture is false for $n>2$ (see ).  However, I expect that my guess is not far away from the correct answer.  EDIT: The $n=2$ case with $\gcd\left(a_1,a_2\right)=1$ appeared as a problem for the Spring Contest, A Level, of the Tournament of the Towns of 1990.  See  (page 35 of the PDF).  Related Topics:


First I am logged into root and executed this command:  # sudo su   Then:  # usermod -l lazybug peter   Getting this error:  usermod: user peter is currently used by process 19895   So I have killed the process   # kill 19895   It will come out of root and if I run the same command it will give the same error message. I am really confused and please help.


Why can't I refer to another cell with the value comparator field?

This is more a curiosity question than a fix to a problem, because I found a few ways to fix it already.  From what I could gather, if I want to apply a conditional formatting based on the value of another cell, I have to use a custom formula. However, in the list, there are a couple options that would seem to be much more relevant: "Greater than (or equal to)", "Lesser than (or equal to)", "Is (not) equal to", "Is (not) between". But I'm starting to think that they are not so useful.  Here I have a column of numbers ranging from 10 to 30; I want to highlight them in green if they're greater than or equal to a number (20) set in another cell. From a few other questions here and on SO, it would seem that I should use a custom formula as something like =K7>=K4, but instead I still wanted to try the options in the list that seemed more intuitive.    As you can see though, it does some weird things, where it consider 11 to be under 20 (which is true AFAIK), but everything else above 11 is either equal or greater than 20.  My guess is that putting =K4 in the "Value or formula" field didn't quite link to the actual K4 cell, but I can't figure out why it does what it does here.  If I put "20" in the field, it highlights the right cells (but it's not dynamic anymore).  Edit: putting =K$4 works like a charm. Quite literally, in this case.


I know that Word up! is a versatile expression and its meaning depends on different regions. But in a movie I came across this expression as in:     A: Hey, there's this big banquet for my university nomination, wanna come?     B: No, I have something to do.     A: There's an open bar there.     B: Word up!     I guess it's an enthusiastic exclamation but I'm not sure. Isn't it like saying Sweet! or Hot dog! when we express enthusiasm?


Making a tunnel in the Earth through its center

If I make a tunnel in the earth through its center from one place to the antipode place and throw a ball into the hole, what will happen? So far I can think, the ball will oscillate with SHM motion Making such a tunnel is not possible. I have just assumed it.


I want to see developers' opinions on the use of a certain language feature, where is the right place to ask that question?


Find the next month of a given date in javascript

I have a piece of code to find the next month of the given date.  var d = new Date('2018-03-31'); dt = new Date(d.setMonth(d.getMonth() + 1)); document.getElementById("demo").innerHTML = dt;   But i'm wondering what is wrong here since it adds one month to March & gives May instead of April?  DEMO:   var d = new Date('2018-03-31');  dt = new Date(d.setMonth(d.getMonth() + 1)); document.getElementById("demo").innerHTML = dt;


Are all lengths multiples of the Planck length?

If the Planck length is the smallest unit of length that has any physical meaning then is it true to think that all the lengths are multiple of the Planck length?


Uniqueness of finite fields with $p^n$ elements.

It's well known there exists only one finite field with $p^n$ elements, up to isomorphism, where $p$ is a prime and $n \geq 1$. Let $n = m t$, where $m, t > 1$. Then $F = Z_p[X]/(f(X))$ is a field with $p^n$ elements, provided $f$ is some irreducible polynomial of degree $n$ in $Z_p$. By the same token, $G = Z_p[X]/(g(X))$ is a field with $m$ elements ($g$ irreducible of degree $m$). Then $G$ has $p^m$ elements. Finally let: $H = G[X]/(h(X))$ where $h$ is an irreducible polynomial of degree $t$ with coefficients in $G$. Now, in my understanding $F$ and $H$ have both $p^n$ elements. So my question is: Are $F$ and $H$ isomorphic?


I am miffed... This should work. I am using AWS and inside of a docker image but I would still expect this to work:  root@1e896e1e9c8e:~/shipamax/server# pgrep -d " " -f ^chromedriver 924 root@1e896e1e9c8e:~/shipamax/server# sudo kill -KILL 924 root@1e896e1e9c8e:~/shipamax/server# pgrep -d " " -f ^chromedriver 924   top's report of the process is:     924 root      20   0       0      0      0 Z   0.0  0.0   0:00.27 chromedriver


pyqgis - Load a PostgreSQL/PostGIS layer from a SQL query

With pyqgis I can load a vector layer from a PostgreSQL/PostGIS database :  uri = QgsDataSourceUri() uri.setConnection("localhost", "5432", "myBase", "myUser", "myPassword") uri.setDataSource("mySchema", "myTable", "geom") vlayer = iface.addVectorLayer(uri.uri(False), "myLayer", "postgres")   I want to apply a SQL query to load just a part of my features. With the  i've read i can add a simple WHERE clause :  uri = QgsDataSourceUri() uri.setConnection("localhost", "5432", "myBase", "myUser", "myPassword") uri.setDataSource("mySchema", "myTable", "geom", "name like 'Example'") vlayer = iface.addVectorLayer(uri.uri(False), "myLayer", "postgres")   But I'm not able to build a more complex syntax like st_intersects. For example :  uri = QgsDataSourceUri() uri.setConnection("localhost", "5432", "myBase", "myUser", "myPassword") uri.setWkbType(QgsWkbTypes.MultiPolygon) uri.setKeyColumn(u"idA") myQuery = """SELECT a.name FROM public.tableA a INNER JOIN public.tableB b ON st_intersects(a.geom, b.geom) WHERE a.name LIKE 'Example' AND b.name LIKE 'Something';""" uri.setDataSource("mySchema", myQuery, "geom") vlayer = iface.addVectorLayer(uri.uri(False), "myLayer", "postgres")   How can i use a full SQL query with a QgsDataSourceUri class ? Maybe with  ?


Create loop for 2000+ folders with incremental names to zip into archives with the same incremental names

I'm a total bash and SE beginner and in need some help, please. I have more than 2000 folders (their names are incrementals of 1000) on a Debian server, which I need to zip to separate store-only archives with the corresponding incremental names in the folder 1 level-up the hierarchy from the source. Then I need source files folders deleted after each archive is created. So, below code works for what I need but my current idea is to repeat the same line over 2000 times. I'd like to know if there is a better way to automate this process into just a few extra lines with the use of a loop and I guess a sub-folder variable? Any help appreciated, please. Thank you very much! #!/bin/bash  cd private/completed/0/ && zip -r -0 ../0.zip ./* && rm -R 0/ && cd - cd private/completed/1000/ && zip -r -0 ../1000.zip ./* && rm -R ../1000 && cd - cd private/completed/2000/ && zip -r -0 ../2000.zip ./* && rm -R ../2000 && cd - cd private/completed/3000/ && zip -r -0 ../3000.zip ./* && rm -R ../3000 && cd - cd private/completed/4000/ && zip -r -0 ../4000.zip ./* && rm -R ../4000 && cd - ....  cd private/completed/2800000/ && zip -r -0 ../2800000.zip ./* && rm -R ../2800000 && cd -  UPDATE: Thank you very much for the helpful link, Kusalananda (). I used the code from that related answer and slightly modified it to make it work exactly how I need it. I added the resulting code below: #!/bin/bash cd private/completed/ for i in {0..2800000..1000}; do echo "$i" ; cd "$i" ; zip -q -r -0 ../"${i%/}.zip" . && cd .. && rm -R "$i" ; done


Display header and footer in all PDF pages using VF

My vf page     <apex:page renderAs="pdf" Controller="testpdf1">

Header

Page  of

             <apex:repeat value="{!opp}" var="item">
                     {!item.Name}
             </apex:repeat>

 </apex:page>   Controller  public class testpdf1 {     public list<Account> opp{get;set;}      public testpdf1()     {         opp=[SELECT Name  from Account limit 50];     } }   I am getting all records in pdf format but able to get header in first page only and i am not getting header from second pages how can i display header to all pages.


How do I retrieve my forgotten passpharase on my PPC server?

So recently I installed Ubuntu server on my Power PC mac mini. But, now it takes me through  Yaboot and asks me to enter my passphrase so it can unlock the disk. I forgot my passphrase. Can I install a different flavor of linux or is there a workaround. Pressing shift during boot doesn't work. Please help.


In  to a question, I posted a link with a special character in.  Originally it was this:  > Q: Why did the chicken cross the [Möbius strip][1]?   > A: To get to the same side.  [1]: http://en.wikipedia.org/wiki/Möbius_strip   But the link didn't show. I have since changed it to /Mobius_strip since that URL works fine for Wikipedia, but just thought you might like to know.  Just testing to see if the link works by posting it raw:


I have a good quality scan of a document; such scan is in pdf format.  How can I add ocr information to the pdf, so that it becomes searchable? By searchable I mean that the goal is that when viewing the pdf with evince, CTRL-F actually allows me to search in the pdf content.


What effect does the Moon and Sun have on gravity?

I know that every object has a gravitational pull regardless of how far or how small it is. It's just that generally this force is negligible.  Does the force produced by the sun and moon have any non-negligible effect on the gravity we experience on earth? I imagine the two most extreme cases would be when the sun and moon are both directly overhead or directly below.  I imagine that all the other planets have far less of an impact than the sun and moon right?


Sogou is a Chinese search engine, which can search text, images, music and maps.  Is a comma required before "which" in the above sentence?


So I have a drop down list like this:  <select name="store-cost" class="target">     <option value = '100'>100</option>     <option value = '500'>500</option>     <option value = '1500'>1500</option> </select>   and jquery to see what the user has chosen  $( ".target" ).change(function() {     console.log($( this ).val()); });   and i have a button that calls jquery function:  Donate   How do I change the value in the function donateNow according to the user's option?  Many thanks  EDIT, sorry didn't make myself clear, I would like to change I would like to change the function donateNow() param according to the user's chosen option


Is there any mathematical contraction of the following factorial series function?  $$ F(n) = 1.1! + 2.2! + 3.3! + ...... + n.n! $$  I tried it by inspecting that $$ x.x! = x^2.(x-1)!$$  I need derivation of the series.


I was trying to setText for two views while parsing JSON from server but it gives me error when run. Here is my code:  protected void onPostExecute(String result) {             super.onPostExecute(result);             textView.setText(result);             newTextView.setText(result);         }   Here is my error:  FATAL EXCEPTION: main     java.lang.NullPointerException     at com.musicianfocus.ben.wordedfm.MainActivity$JSONTask.onPostExecute(MainActivity.java:254)     at com.musicianfocus.ben.wordedfm.MainActivity$JSONTask.onPostExecute(MainActivity.java:208)     at android.os.AsyncTask.finish(AsyncTask.java:631)     at android.os.AsyncTask.access$600(AsyncTask.java:177)     at android.os.AsyncTask$InternalHandler.handleMessage(AsyncTask.java:644)     at android.os.Handler.dispatchMessage(Handler.java:99)     at android.os.Looper.loop(Looper.java:137)     at android.app.ActivityThread.main(ActivityThread.java:4745)     at java.lang.reflect.Method.invokeNative(Native Method)     at java.lang.reflect.Method.invoke(Method.java:511)     at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:786)     at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:553)     at dalvik.system.NativeStart.main(Native Method)     06


Assume that $f(x),g(x)$ are positive and are in $L^1$. Moreover, they are differentiable and their derivative is integrable. Let $h(x)=f(x)*g(x)$, the convolution of $f$ and $g$. Does the derivative of $h(x)$ exist? If yes, how can we prove that $$ \frac{d}{dx}(f(x)*g(x)) = \left(\frac{d}{dx}f(x)\right)*g(x)$$  Thanks


Interpretation results seasonality in data R

I have a question about the results that I get from checking whether my data contains seasonality or not. I have a csv file which contains date, period and year. However, R reads the date as a factor and I didn't know how to deal with is.  So I extracted the frequencies per month, so I have very little points now.  My code:  k <- c(1110,989,1141,674,790,739,842,1004,751,765,1246,1045,        1106,1078,1012,965,978,991,856,703,784,639,821,518)  z <- ts(k, start =c(2012,1), frequency =12)  plot(decompose(z))     I really don't know how to read this.  Thanks in advance!!


Show that $\sum \limits_{i=1}^n $ log(i) = Θ(n log n)

I need to prove or disprove:  I start with the Big O notation:  $\sum \limits_{i=1}^n $ log(i)  = Θ(n log n)  $\sum$ log i ≤ $\sum$ log n = n log n   (dont know if this is enough or not)


\newcommand\whatever that ignores further \newcommand\whatever

Is it possible to define a command \foo such that further \newcommand\foo (I do not mean \renewcommand) are ignored and do not return errors?  For example:  \newcommand\foo[1]{\textcolor{red}{#1}} \newcommand\foo[1]{\textcolor{blue}{#1}} % to be ignored!  \foo{This should print in red.}   The reason why I am asking for this is that I have a document doc.tex of the form  \newcommand\foo[1]{\textcolor{blue}{#1}} \foo{Some text}   that I want to include in another document using \input{doc.tex}, and I'd like Some text to print in red (of course, in reality my problem is not about text color...).


Combinatorial sum identity for a choose function $\sum\limits_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$

I want to show that the following holds:  $$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}.$$  I have an idea of what is going on here. On the RHS we are selecting $r+s+1$ elements from the set $[m+n+1]$. Another way of doing this is to partition the set $[m+n+1]$ into two sets in several ways by shifting $k$ elements from one set to the other. For example, we can partition $[m+n+1]$ into a set with $m+k$ elements and a set with $n+1-k$ elements. From the set with $m+k$ elements we can select $r$ elements and from the set with $n+1-k$ elements we can select $s+1$. However, this is not matching the LHS. I believe the problem is that we don't know which $k$ elements are being shifted around.  I thought rewriting the sum as follows would help:  $$\sum_{k=0}^{m+n} \binom{k}{r} \binom{n+m-k}{s}.$$  I just don't understand why the "$+1$" on the top and bottom of the RHS disappear. I have spent several hours on this problem, and I have run out of ideas. Please help, I truly appreciate it.


I have a class employee in which I have a static function with count number employee and and count to type of employee(e.g teacher ,assistant teacher,personal assistant etc) .For this purpose I have static class inside with I have a static count for number of employee and inside each subclass I want to access base class static method.  class Employee{     private static int emp;     //...code      static void IncreaseEmployeeCount()     {         emp=emp+1;     }  }  class Teacher : Employee{     private static int tchr;      //...code      static void IncreaseTeacherCount()     {         tchr = tchr + 1;     } }   How can I access base class static method using child class. It tried using following but fails with compile time error:  Teacher teacher = new Teacher(); teacher.IncreaseEmployeeCount();      'Employee.IncreaseEmployeeCount()' is inaccessible due to its protection level   Adding public access level still gives an error:     Member 'Employee.IncreaseEmployeeCount()' cannot be accessed with an instance reference; qualify it with a type name instead


Tips finding the gcd of $(n^2-3n-1, n-4)$

I need tips on how to find the $gcd(n^2-3n-1, n-4)$ for any $n \in \mathbb{N}$. I tried the two following methods (but got stuck):  Since I need to find the $gcd(n^2-3n-1, n-4)$, then there is a $q \in \mathbb{Z}$ which is the divisor of both $(n^3-3n-1)$ and $(n-4)$, giving each of them an answer of $q_1,q_2 ∈ \mathbb{Z}$ accordingly, therefore, it is possible to write them as follow: $n^2-3n-1 = q*q_1$ $n-4 = q*q_2$ Because $q,q_1,q_2 ∈ \mathbb{Z}$, multiplying them with each other produces another Integer (same with adding to them an Integer), so $n^2-3n = q_3$ , $q_3 ∈ \mathbb{Z}$ $n = q_4$ , $q_4 ∈ \mathbb{Z}$ With this method, I got stuck here (didn't find a way how to continue).  Another method I've tried is: According to the Euclidean Algorithm, $n^2-3n-1 = (n-4)*q + r, q,r ∈ \mathbb{Z}$ Use $q=n$, $n^2-3n-1 = (n-4)*n+r$ => $n-1=r$ $n^2-4n=(n-1)q+r$ (while $q=n$) => $-3n=r$ $n^2-n=-3n*n+r$ => $4n^2-n=4$ and so on...but also got stuck.. I'd appreciate any tips on how to continue with what I've tried or if I should try a different approach


Why don't electromagnetic waves need vacuum to move?

I understand that electromagnetic waves are caused by the oscillation of electric and magnetic fields. But how? Are there magnetic and electric fields in air, or in vacuum? How does this oscillation form a wave? Sorry, I am a new at this site, please simply put you answer so that I can understand.


How does the repositioning of starred messages work?

I just starred an already-starred message over at , and the message moved up by four spaces. Normally, I only see two or three spaces, but it was underneath a pile of highly-starred messages. This has confused me for some time; a good portion of me expects some linear algorithm, such as "one star means move up one space," but the behavior doesn't seem to follow any pattern I have yet found. And I'm not going to go star a bunch of random messages to figure it out (as much as I'd love to). Is there any way to tell how far up a message will move when I star it? For reference, the message I starred had two stars, and was bumped to three. It was underneath a message with five stars and another with three, and above that, two.


Word for someone who discriminates against left handed people

We have words like racist, bigot, xenophobe, etc. that we are all familiar with, but what would we call someone who discriminates against left handed people?


What is the correct formula for drift speed of electrons

These are the two formulae I came across for the drift speed of electrons in a circuit. Which one of them should I use for calculations? Which one is to be used for calculations?


In Hausdorff spaces, compact sets are closed

I've been stuck on this exercise for awhile. It was suggested that I fix a point in the compact set, but I didn't know what to do with that. Can anyone provide an answer?


Show that $a \cos \theta + b \sin \theta = \sqrt{a^2+b^2} \cos (\theta - \varphi)$

Show that:  \begin{align*}   a \cos \theta + b \sin \theta = \sqrt{a^2+b^2} \cos (\theta - \varphi) \end{align*}  fyi, the context is in studying the differential equation:  \begin{align*}   y''(t) + c^2 y(t) &= 0 \\ \end{align*}  which has general solution:  \begin{align*}   y(t) &= a \cos (ct) + b \sin (ct) \\ \end{align*}  My textbook says that this can easily be transformed into, where $\varphi \in \mathbb{R}$:  \begin{align*}   y(t) &= \sqrt{a^2 + b^2} \cos (ct - \varphi) \\ \end{align*}


How to change the python version in blender

I'm using Blender 2.71 and it comes with Python 3.4.0 even though the most recent version is 3.4.1. Is there any way to change this?


Best way to implement multi-language/globalization in large .NET project

I'll soon be working on a large c# project and would like to build in multi-language support from the start. I've had a play around and can get it working using a separate resource file for each language, then use a resource manager to load up the strings.  Are there any other good approaches that I could look into?


I don't know if this is a right place to ask this question, but a community dedicated to Data Science should be the most appropriate place in my opinion.  I have just started with Data Science and Machine learning. I am looking for long term project ideas which I can work on for like 8 months.  A mix of Data Science and Machine learning would be great.  A project big enough to help me understand the core concepts and also implement them at the same time would be very beneficial.


I need your thoughts. Worked on this 50s radio that I found in an antique market yesterday. I'm trying to do a mic to go with it. I've tried every possible shapes, cylinder, Square, stretch, beveled so on and it can't seem to get it. Is that something I would have to go in sculpting mode?


How can I seperate objects within objects (which are not touching each other) into independent ones?

^ I've got those beautiful cubes to run a physiks simulation, but obviously they are one object so I they can't move independently. I want each of them to be a single object. Is it possible to split all of them simultaneously?


Type of polynomial where leading coefficient is to the power of $6$

I need to identify the type of polynomial that a polynomial is based on the power of the leading coefficient. (Example $x^2$ = quadratic, $x^3$ = cubic, $x^4$ quartic). In this case, it is $x^6$. What is the name of the type for $x^6$? Thanks in advance.


boost::graph function with edge iterator passed by value and graph passed by reference

The following code appears in boost graph library manual available .    I have no problem understanding what the code does. My questions are:  (1)Why is the graph object passed as a constant reference. const Graph& g ?  (2)Why is the edge descriptor not passed similarly, but simply by value?  As I understand, the answer to (1) is that it imposes a constraint to ensure that the function is_self_loop() does not modify the object g and also that no copy is made of g within the function.  On the other hand, a copy is indeed made within the function of the edge_descriptor.  Is there any reason to accord these two different reasonings for the two passed objects? The function does not seem to alter e either, so why not pass it as a const and also to prevent a local copy, why not also pass it as a reference? Does this have to do with the sizes of g and e? That is, copying e is not a costly operation? If yes, how can the user figure out which object is "easy" to copy and which object is expensive to copy?


Normal Operator that is not Self-Adjoint

I'm reading Sheldon Axler's "Linear Algebra Done Right", and I have a question about one of the examples he gives on page 130. Let $T$ be a linear operator on $F^2$ whose matrix (with respect to the standard basis) is $$\begin{bmatrix} 2 & -3 \\ 3 & 2\end{bmatrix}$$ I can see why this operator is not self-adjoint, but I can't see why it is normal. I have to find $T^*$ and show that $TT^* = T^*T$. How would you do this?


How to algorithmically find only the edges of a high dimensional convex hull?

Given to me is a set of points $p_1,...,p_n\in\Bbb R^d$ in general position. I want to determine only the edges of the convex hull $C:=\mathrm{conv}\{p_1,...,p_n\}$, and this as efficient as possible. Especially, I do not want to compute the complete convex hull with all its faces and then extract only the $1$-faces from the result. This would be too much overhead.  In an abstract form, the problem states as follows:     For what pairs $(p_i,p_j)$ there exists a linear function $\Bbb R^d\to\Bbb R$ that takes its maximum exactly on $p_i$ and $p_j$?   We can assume that the origin is inside the convex hull, and that all points will be vertices of the convex hull.  A general algorithms would be welcome. However, for my specific use-case we can further assume that all the points are of the same kind, i.e. for any two of the points, say $p_i$ and $p_j$, there is a symmetry transformation $\phi$ of the arrangement, so that $\phi(p_i)=p_j$.    Appraoch  My previous approach was as follows. Given a pair $(p_i,p_j)$:   Compute $q:=p_i+p_j$. Find the points that maximize $\langle p_i,q\rangle$. If these are exactly the points $p_i$ and $p_j$ (not more, not less), then they form an edge. Otherwise, they do not.   The algorithm does not give false positives, however it gives false negatives. So it might find too few edges. I think it is about choosing $q$ in a better way. But I have no idea how to do this in general.    This question is different from my  on convex hulls, as here I ask for efficient algorithms instead of abstract techniques, and also I have other assumptions on the point set.  Further, I already have a specific algorithm in mind, where I would prefer to only hear about a better working choice for $q$. Of course, other approaches are welcome too.


SQL injection even when the variable is escaped

The sql injection will work only when my query looks like below sample  SELECT * FROM login WHERE id = $my_id_va;   Assume if my query is  SELECT * FROM login WHERE id = $my_id_va ORDER BY id DESC   Than I will get following error     #1064 - You have an error in your SQL syntax; check the manual that   corresponds to your MySQL server version for the right syntax to use   near 'order by id desc' at line 1   So, this 1 or 1=1; SHOW TABLES will not work, correct?  My site was hacked successively many times.  I want one quick answer: When my query looks like the following one, what ways or which types of query can they use to hack my site?  SELECT * FROM login WHERE id = $my_id_va ORDER BY id DESC   What are the ways to  execute the show table in the following query  SELECT * FROM login WHERE id = $my_id_va ORDER BY id DESC   I am  also using escaping function to handle the query string values, like mysql_real_escape_string($my_id_va). Yes, obviously this for single related hack, but not sure.  Added some more  SELECT EventActuallyCharged, EventDate FROM tblevent WHERE EventDate between '2011-07-21 or 1=1; SHOW TABLES --' and '2011-07-31' ORDER BY EventDate DESC   but show table not worked


Let G be a finitely generated abelian group and M a compact manifold,  I want to prove that $H_r(M,G)$ is finitely generated for $r\ge 0 $.  First I was thinking if  I could do induction over $r$ because for $r=0$, $H_0(M,G) \cong \bigoplus_{i=1}^nG$ where $n$ denotes the number of connected components of M.But for $r>0$ I can't see a way to relate $H_r(M,G$) and $H_{r+1}(M,G)$.  Then I tried to use the fact that for every compact surface there exists a finite cover $\{A_i\}_{i=1}^m$ such that the finite intersections of $A_i$'s are contractile.Let $\{A_i\}_{i=1}^m$ such cover for $M$.Then,using induction on $m$, we have :  -For $m=0$, $M$ is contractile and $G$ finitely generated then $H_r(M,G) $is finitely generated.  -For $m=r$ it's true by induction hypothesis.  -For $m=r+1$ now putting $A_{r+1}=B$ and $\cup_{i=1}^r A_i=A$, and using Mayer Vietoris we get:  $$ ...\rightarrow H_{r+1}(A\cap B,G)\rightarrow  H_{r+1}(A,G) \oplus H_{r+1}(B,G) \rightarrow H_{r+1}(M,G)\rightarrow H_{r}(A\cap B,G) \rightarrow...$$   Here I don't know what to do, maybe I'm missing some algebraic argument It's easy to see that $H_{r+1}(A\cap B,G)$ and $H_{r+1}(A,G) \oplus H_{r+1}(B,G)$ are finitely generated.But how can I argue that $H_{r+1}(M,G)$ is finitely generated? Any idea would be aprecciated.


How to leave ordering unchanged on equality using qsort

Straight from the qsort manual it says:     If two members compare as equal, their order in the sorted array is undefined.   However, I want qsort to leave the ordering unchanged on equality. That is to say, leave the ordering of two elements as they are in the original array if they have the same value used for ordering.   I'm not sure how to do this using qsort. I would rather not use an alternative sorting library/ roll my own.   Thanks  --  edit: now I know the distinction between stable and unstable sorts I realise this is a duplicate.


evaluating $ \sqrt {2+ \sqrt {3+ \sqrt{4+ \sqrt{5+\cdots}}} }$

How do we evaluate the infinite nested radical  $  \sqrt {2+ \sqrt {3+ \sqrt{4+ \sqrt{5+\cdots}}} } $ $\space $?   Please help   N.B. :- It is not a duplicate


Can I make a custom node from a group and have that available in other projects?

I've found some neat combinations of nodes to create certain effects, so I'd like to make them a group and then have that node available on my list of available nodes, even when I reload the startup file. How would I do that?


I'm working on a book project using LaTeX and am stuck on a very fine point of style in the index. The publisher wants page ranges in the index to appear in the form 145--52 (rather than 145--152), page range elision. I have no idea how to to get a LaTeX indexing package to do this. At the moment I'm using imakeidx and the project has two indices (Names and Subjects). I've put together a minimal working example. I'd be grateful for any advice,  \documentclass{article} \usepackage[utf8]{inputenc}  \title{Index elision problem} \date{July 2019}  \usepackage{imakeidx}  \makeindex[name = person,title=Name Index,columns=2] \makeindex[name = subject,title=Subject Index,columns=2]  \begin{document}  \maketitle  \index[person]{Mr. T} \index[subject]{vans} \clearpage Space \clearpage filler \clearpage Space \clearpage filler \clearpage Space \clearpage filler \clearpage Space \clearpage filler \clearpage Space \clearpage  Mr. T, vans \index[person]{Mr. T|(} \index[subject]{vans|(} \clearpage filler \clearpage Space \clearpage filler \clearpage Space \clearpage filler Mr. T, vans \index[person]{Mr. T|)} \index[subject]{vans|)}  \printindex[person] \clearpage \printindex[subject]  \end{document}


Ways to say “someone who messes with forces they don’t understand”

I want to describe a character who experiments with sciences they don’t understand, at a great peril they are unaware of. A hypothetical example of such a person would be a scientist who, in an attempt to study atomic behavior, splits an atom (obvious logistical challenge aside).


If I double a bread recipe do I double the salt?

I think it was my mom who gave me the rule of thumb that when you double a recipe you double everything except the salt.  I'm willing to defer to her wisdom for the sorts of soups and stews she liked to make, but she didn't do much baking, and I never saw her make bread leavened with yeast.  I know salt and yeast aren't friends and I'm trying to double a rustic ciabatta recipe.


What is the best book or resource to start Learning about Quantum Computing?

What is the best book or resource to start Learning about Quantum Computing ?


A theorem about oscillation in Arnold's mathematical methods of classical mechanics

There is a theorem in page 100 of , which says that:     If $\cfrac{dx}{dt} = f(x) = Ax + R_2(x)$, where $A = \cfrac{\partial f}{\partial x}|_{x = 0}$,  $R_2(x) = O(x^2)$, and $\cfrac{dy}{dt} = Ay$, $y(0) = x(0)$, then for any $\vphantom{\cfrac12} T>0$ and for any $\xi > 0$ there exists $\delta > 0$ such that if $|x(0)| < \delta$, then $\vphantom{\cfrac12}|x(t) - y(t)| < \xi \delta$ for all $t$ in the interval $0 < t  < T$.   How can I prove this theorem rigorously?    Cross-posted at physics.se .


I've just got  on Stack Overflow.        But it is not displaying in my badges. Badge count is also not increasing. :'(


Make `hostname -f` return fully qualified hostname

How can i make hostname (i.e. the unix commandline tool hostname, invoked in terminal) return a hostname including the domain information?  At the moment, hostname, hostname -f and hostname -s return the same name, all without the domain information, but host <hostname> returns the full hostname:  $ hostname > jvf-imac $ hostname -f > jvf-imac $ hostname -s > jvf-imac $ host jvf-imac                                                                                > jvf-imac.fritz.box has address 192.168.178.31   The question is not about how I can get the full hostname in general. Some scripts I use rely on hostname -f to get the fully qualified hostname, so I need to make hostname -f return the correct hostname. Anyone any idea?  Updates  System Overview   System Version: OS X 10.10.5 (14F27) Kernel Version: Darwin 14.5.0 Computer Name: jvf_imac   Content of resolv.conf (shortened)  domain fritz.box nameserver 192.168.178.1   DNS Setup (shortened)  $ scutil --dns                                                                                resolver #1   search domain[0] : fritz.box   nameserver[0] : 192.168.178.1   if_index : 4 (en0)   flags    : Request A records   reach    : Reachable,Directly Reachable Address  resolver #2   domain   : local   options  : mdns   timeout  : 5   flags    : Request A records   order    : 300000  resolver #3   domain   : 254.169.in-addr.arpa ...  ...  resolver #7   domain   : b.e.f.ip6.arpa ...  DNS configuration (for scoped queries)  resolver #1   search domain[0] : fritz.box   nameserver[0] : 192.168.178.1   if_index : 4 (en0)   flags    : Scoped, Request A records   reach    : Reachable,Directly Reachable Address


How to refresh the parent window after opening a pop up window from inline page?

I opened a Popup from an inline VF page in SFDC and then after some action I was able to close the window but needed a refresh of the Top window from inline frame .  My code is as below for opening a pop up.Note this is inline page   <apex:page standardController="Account" extensions="Accountctrl">  <apex:form >  <script>    function openwindow(){       window.open("/apex/pagereal", "myWindow", "width=200, height=100");    }  </script>  <apex:pageBlock >  <apex:pageBlockSection columns="1" id="Test" >     <apex:inputcheckbox value="{!test.istest__c}" label="Same as Above">     <apex:actionSupport event="onchange" rerender="Test" /> </apex:inputcheckbox>   <apex:outputPanel rendered="{!NOT(test.istest__c)}">  <apex:inputField value="{!test.Campaign__c}" /> <apex:inputField value="{!test.cust_vendor__c}" /> </apex:outputPanel> <apex:commandButton value="Tetete" onclick="openwindow();"/>   </apex:pageBlockSection>  </apex:form> </apex:page>   And my popup page code is as below and I want to redirect top frame from inline page  <apex:page >    <script>    function test(){      alert('hello');      window.opener.top.location.href='https://googleflowauth-dev- ed.my.salesforce.com/001900000096agv';   }     </script>    <apex:form >     <!-- End Default Content REMOVE THIS -->      <apex:commandButton onclick="test()" value="Test"/>     </apex:form>   The error is pretty much I know that it is for security browsers dont allow        Unsafe JavaScript attempt to initiate navigation for frame with URL '' from frame with URL ''. The frame attempting navigation is neither same-origin with the target, nor is it the target's parent or opener.   I am happy if i get workaround for same


Preventing Quantum Attacks on Cryptography

With the advancement of technology in quantum computing, it's becoming more evident that we need to start thinking about protecting the future integrity of our cryptographic standards.  What can we do on binary computers to prevent attacks on cryptographic related items such as password hashes, private keys, and asymmetric key exchange?


Consequences for a tenured person of not getting grants

As far as I heard in (some of) the universities a person having a tenure track position who fails to get grants may not get tenure.      I am wondering what might be consequences of not getting grants for a tenured professor. (Say may he or she get more teaching load? more administrative load? What will happen if he or she will not agree for that?)   In your answers please indicate about what country are you talking about.


Classify the non-abelian subgroups of order 20.

$20=2^2\times5 $  My initial reaction was to write direct products between an abelian and non abelian groups — for example, $Z_5\times D_2$. However, I realized they are both abelian so I am a little stuck. I can't think of any subgroup that is not abelian. Could it be a semidirect product or something? If so, could you give me a hint? My knowledge of semidirect products is sketchy to say the least.


What's the best way to clean dust from film negatives?

Every time I scan my 35mm negatives, there is always a lot of dust, even after using a rocket duster and wiping with a microfiber cloth. What sort of equipment exists in order to get rid of the dust? I’m using a dedicated 35mm scanner that has IR dust removal, but that too isn’t that great. I try deleting every dust particle manually in Photoshop, but as you might imagine, it takes hours and is far from completely effective, especially with larger particles. Do you think it would be better just to make prints with an enlarger and then scan those?


Python pythonw subprocess check_output not working

I have a problem regarding pythonw. I'm making a program which should be executed in background. When it starts, it's supposed to send the computername, the username and the result of a check to see if the program has admin rights. Here's the relevant piece of the client code:  computername = subprocess.check_output("echo %computername%", shell=True).decode(sys.stdout.encoding).splitlines()[0] username = subprocess.check_output("echo %username%", shell=True).decode(sys.stdout.encoding).splitlines()[0] isadmin = ctypes.windll.shell32.IsUserAnAdmin() sleep(0.5) s.send(computername.encode() + ";;".encode() + username.encode() + ";;".encode() + str(isadmin).encode())   And this is the piece of server code that's supposed to receive it:  data = conn.recv(1024).decode().split(";;") print(data) clientcount += 1 clientlist.append({"conn": conn, "ip": ip, "id": clientcount, "name": data[0] + "\\" + data[1], "isadmin": int(data[2])})   (the print line is just for debug) So here's the problem. When I execute the client code as client.py, everything works normally, I get this output:  ['DESKTOP-#######', '######', '0']  and the code can go on. But when I execute the program as client.pyw, as it's supposed to be, I get:  ['']  So of course I get an IndexError. I'm guessing something goes wrong with the subprocess.check_output. Is it normal? With what could I replace it, so it works in background?  (I'm using python 3.5)  Thanks


Does this set of vectors span the space of all polynomials of degree at most 3?

I'm having trouble understanding this homework problem.   Suppose four polynomials are defined by the following:   $ p_{1}(x) = x^3 - 2x^2 + x + 1 \\ p_{2}(x) = x^2 - x + 2 \\ p_{3}(x) = 2x^3 + 3x + 4 \\ p_{4}(x) = 3x^2 + 2x + 1 \\ $  Does the set $S = $ { ${p_{1}, p_{2}, p_{3}, p_{4}}$ } span $P_{3}$ (the space of all polynomials of degree at most 3)?  So if I start with the polynomial $y = ax^3 + bx^2 + cx + d$ I understand(I think) that in order for $S$ to span $P_{3}$ then $y$ must be a linear combination of $S$ but I'm not sure where to go from there.   EDIT:   $$ A =  \begin{bmatrix} 1 & -2 & 1 & 1\\  0 & 1 & -1 & 2\\  2 & 0 & 3 & 4\\  0 & 3 & 2 & 1 \end{bmatrix}  \sim  \begin{bmatrix} 1 & 0 & 0 & 0\\  0 & 1 & 0 & 0\\  0 & 0 & 1 & 0\\  0 & 0 & 0 & 1 \end{bmatrix} $$  So $\operatorname{rank}(A) = 4$ which means the vectors in the set are linearly independent because there are only 4 column vectors in the matrix (AND there is only the trivial solution to the matrix) and therefore we span $P_{3}$?


Hello ive read about 10 tutorials, but i keep getting errors all the time,this is my Makefile file and errors

LNode : Linked List Node  LList : Linked List  Eleman : Linked Lists value type  Kontrol : All main codes  Program : main , contains kontrol()   g++ -I "./include" -c ./src/Program.cpp -o ./lib/Program.o g++ ./lib/LNode.o ./lib/LListe.o ./lib/Kontrol.o ./lib/Program.o ./lib/Eleman.o -o ./bin/program ./lib/Kontrol.o:Kontrol.cpp:(.text+0x3e): undefined reference to `LListe<Eleman>::LListe()' ./lib/Kontrol.o:Kontrol.cpp:(.text+0x1ad): undefined reference to `LListe<Eleman>::pushBack(Eleman  const&)' ./lib/Kontrol.o:Kontrol.cpp:(.text+0x1de): undefined reference to `LListe<Eleman>::end()' ./lib/Kontrol.o:Kontrol.cpp:(.text+0x2fc): undefined reference to `LListe<Eleman>::pushBack(Eleman  const&)' ./lib/Kontrol.o:Kontrol.cpp:(.text+0x3fa): undefined reference to `LListe<Eleman>::pushBack(Eleman  const&)' ./lib/Kontrol.o:Kontrol.cpp:(.text+0x44e): undefined reference to `LListe<Eleman>::end()' ./lib/Kontrol.o:Kontrol.cpp:(.text+0x587): undefined reference to `LListe<Eleman>::pushBack(Eleman  const&)' ./lib/Kontrol.o:Kontrol.cpp:(.text+0x68e): undefined reference to `LListe<Eleman>::pushBack(Eleman  const&)' ./lib/Kontrol.o:Kontrol.cpp:(.text+0x711): undefined reference to `LListe<Eleman>::begin()' collect2.exe: error: ld returned 1 exit status Makefile:3: recipe for target 'program' failed mingw32-make: *** [program] Error 1


On guidelines to tagging and avoiding unnecessary tags

I wasn't able to find guidelines as to how generally tagging is done on SO (and possibly other SE sites).  Not that we want to have a long list of rules or rule-likes but something tags such as  AND  are unnecessary and sometimes may cause non-ideal behavior.  Take, for example, users who have an interest in  but have no interest in . Tagging a question both means such users will also be distracted to such a question via the highlighting system. But if one follows a principle that since  implies , it doesn't mean they need to also tag with .    In other words,  being a subset (in terms of interest, so-to-say) of , people interested in  are not necessarily interested in .


Regex to find a value after a specific word with Google App Script

I have a string and I wrote following code to extract "NewUsers19" from that.    function getNoOfUsers() {    var noSpace = "UserRejectedOrderCount25NewUsers19FundedNewUsers14DepositAmount($)43165.23DepositCount75WithdrawAmount($)53510";   var regex = /(?:NewUsers)([0-9]+)/;   var value = regex.exec(noSpace);   return value;    }     The regex worked fine in online editors but I don't know why it does not work in Google App Script. Any help will be appreciated.


Being able to join chat rooms from the Android app would be a plus! It would truly make us connected on the go, instead of having to sit down at our desks and open a browser window. This will allow more users to fully utilize the chat system and join events no matter where they are.


Graphics Card Not Avalible in Blender Internal

For some reason Blender does not use my GPU when rendering, even though I have my card selected in the user preferences   When I render, my CPU usage goes up to 100% and MSI Afterburner shows no increase of GPU usage. It also doesn't show an option to change my compute device in the system area or whatever   However, when I switch to Cycles Render, it gives me the option to use my GPU, but not when I am in normal Blender Render. Is there a way to fix this or is it set like this for some reason?


Are Linux VirtualBox images legal to distribute?

I have a website with adsense. Can I share Linux distro VirtualBox images with users? Is this legal? Will it affect my adsense account?


When does a .com domain become available after it expires? (With status clientTransferProhibited)

the domain I want is taken and according to ICANN it expires on 2021-01-05. The only status it has is "clientTransferProhibited". I am not sure how to interpret this domain status... Does this status prohibit me from getting the domain once it has expired? And can I acquire the domain as soon as it expires according to the expiry date on ICANN?


What is impeding current when voltage is stepped up in a transformer?

What is physically impeding electric current when a transformer steps up voltage? Is there some EM field along the conductor impeding electron movement?  FYI, I'm not asking about losses or leakage. (assuming ideal transformer) I'm trying to get an electromagnetic explanation of how increasing turns on the secondary winding exchanges current for voltage.  Thank you.


Why doesn't lord Voldemort just trace and Kill harry in an ambush?

I'm aware that between books 1-4 Voldemort was vaporized and didn't have a physical body, but why doesn't he just visit Harry after he gained a physical body in books 4-7? Did Voldemort have travel restrictions? Was Hogwarts or Little Whinging protected against Voldemort? I know this would be a plot-twist but there must be a reason...


Is the Wilcoxon rank-sum test the right test to see if total donations differ?

Background:  My software asks users for optional donations of any amount.  I split test donation requests among users to find the best way to ask: 50% get request version 1, 50% get request version 2, and we see which one does better.  Almost all users give $0, but a few donate.  The results might look like this:           Number of users  Number of donations   Dollar amounts donated GROUP A  10,000           10                    40,20,20,20,15,10,10,5,5,5 GROUP B  10,000           15                    50,20,10,10,10,10,10,10,5,5,5,5,5,5,5   I want to know if one group is a winner, or if it's a tie, or if we need a larger sample to be sure.  (This example, kept simple for discussion, almost certainly needs a larger sample to get significant results.)  What I measure already:   Did one group have a significantly larger number of donations?  How much larger?  I measure this p value and confidence interval using , using only the number of donations and number of users, ignoring dollar amounts.  Its methodology is described in the "What are the underlying statistics?" section of that link.  (It's over my head, but I believe it calculates the confidence interval by taking the difference between donation rates as normal random variables on the Agresti-Couli interval.) Did one group donate a significantly different amount of total money?  I measure this p value by performing a permutation test: repeatedly re-shuffling all 2N subjects into 2 N-subject groups, measuring the difference in total money between the groups each time, and finding the proportion of shuffles with a difference >= the observed difference.  (I believe this is valid based on this  doing the same thing for crackers instead of dollars.)   R's wilcox.test:  A few questions now about wilcox.test() in R:   If I fed wilcox.test(paired=FALSE) the above table of data, would it answer any new questions not already answered by my tools above, giving me more insight with which to decide whether to keep running my test/declare a winner/declare a tie? If so, what exact question would it answer?


How can I limit the amount of memory available to a running process?

In Windows 7, is it possible to somehow prevent an already-running process from consuming more than a given amount of memory? Microsoft's , as far as I can tell, only allows manipulation of processes launched through it, so it's not helpful in the case of a process that's already been started.


Class with templated class from different header wont compile

I have multiple errors with my class, either "string", a variable, or the template class isnt declared. Not sure whats wrong with my header files or how I'm setting it up.   Now my program uses 2 classes, one is a templated class that uses dynamic arrays in the private member, and the other class uses that templated class in the private member.  In the .cpp  #include <iostream> #include <ostream> #include <string>   #include "Classroom.h" using namespace std;  bool Classroom::addStudent(const string& name){        return (classRoom.insert(name)); } bool Classroom::removeStudent(const string& name) {       return (classRoom.remove(name)); } bool Classroom::containsStudent(const string& name) {       return (classRoom.contains(name)); } string Classroom::listAllStudents() {      string name;     string data;     unsigned int i;     for (i=0;i<classRoom.size()-1; i++){           if (classRoom.at(i,data)){                  name += data;                 name += ", ";            }           }     if (i<classRoom.size()){        if (classRoom.at(i,data)){                  name += data;            }         }     return (name); }   In the .h   #ifndef CLASSROOM_H #define CLASSROOM_H  #include "UniqueVector.h"  class Classroom { public:     /*— If a student named name is not already on the     classroom roster, adds a new student named name to the classroom roster and returns true;     otherwise, returns false.*/     bool addStudent(const std::string& name);      /* — If a student named name is on the classroom     roster, removes the student named name from the classroom roster and returns true; otherwise,     returns false.*/     bool removeStudent(const std::string& name);     /* — If a student named name is on the classroom     roster, returns true; otherwise, returns false. */     bool containsStudent(const std::string& name);     /*— Returns a string containing the names of the students in the     classroom, separated by commas.*/     std ::string listAllStudents();      private:     UniqueVector<string> classRoom; };  #endif   I'm getting templated argument 1 invalid or classRoom from the private member of Classroom isn't declared.   Also an error about I UniqueVector classRoom; with string not declared   I tried using std:: UniqueVector classRoom; is there way so that I dont have to include std:: in every instance of string?


Overbrace/underbrace without extending brackets/parentheses

I'm using \overbrace to explain  a part of an equation, like this:  \begin{align} a\left[\frac{d\cos y}{e} + \overbrace{\frac{b\sin x}{c}}^{\text{second bit}}\right] \end{align}   But the overbrace increases the height of the brackets unnecessarily:    Really, what I'd like is for the height of the brackets to be unrelated to the overbrace, like this:    Is this possible?


How do I get to Orgrimmar from Silvermoon?

I'm new to the Horde and I'm a death knight but I'm not quite sure how to get back to the horde main city, I'm in silvermoon city and I just don't know how to get there as dumb as it sounds, could someone help me?


Is it better to have 4GB RAM in dual channel or 6GB as single channel?

I know there a lot of posts about ram but I'm still confused about it. I'm building a new system and because it was cheaper, I bought a 6GB kit from Corsair. So I'm wondering if I would be better off just using 4GB of it in a dual channel configuration or just add all 6GB (3 DIMMS) in a single channel configuration.   Thanks


is it common to use " you done? " instead of " are you done? "

in the above video someone use " you done? " instead of " are you done " is it common in English?


A trigonometic integral with complex technicals

Let $a,b \in \mathbb{R}^+$. Show that $$\int_0^{2\pi}\frac{1}{a^2\cos^2(t)+b^2\sin^2(t)}dt=\frac{2\pi}{ab}$$ Help please! Thanks.


Do I need to submit a sitemap to Google with new filename everytime I have new URLs?

I just submitted my first sitemap to Webmaster Tools a few days ago. Now I just added some new pages to my site and I'm not sure that I should create a new sitemap or just extend the existing.   So which option is the right?   Adding the new URLs to my existing sitemap (sitemap1.xml) and doesn't change anything. Creating a new sitemap called sitemap2.xml and submitting it as well to Webmaster Tools.    Or maybe it doesn't really matter and I can choose the option I like? Is there any SEO related danger if I delete the old sitemap and submit the new one (with a new name and URL)?


Better latest version or the package for rkhunter and chkrootkit?

The rkhunter version of the ubuntu package is currently 1.4.0, while the installer is version 1.4.4  The repo version of chkrootkit is 0.49, while its installer is 0.52  Since security is a major concern for servers, what would be the best choice: install the latest version or my distribution's package, even if outdated?


Interface - different ways to create object

I have a question regarding interfaces. If I have an interface Printable which has (for example) a method "print", and I create a class Book which implements the interface, I can create an object of Book in two different ways:  Book b = new Book(); Printable b1 = new Book();   I know that I can only reach the methods declared in the interface Printable if I create the object using the second method, but why do we have this option? In which cases would one want to only access the methods declared in the interface, and not be able to access the other methods that are specific to the class in question? Maybe a stupid question, but I don't understand the use of the second option shown above.


A method to search questions on more than one criteria (not tag)

Quick basic question.  Is there a method to search questions on more than one criteria?   example, oldest, unanswered, with zero answers (as opposed to >0 answers, but no accepted answer)?  Where is, or how do we find the way to modify our search criteria  nb this is not about tags as such  I do not need a solution for the example


Does localisation commute with Hom for finitely-generated modules?

Question. Let $R$ be a ring, $\mathfrak{p}$ a prime, $M$ a finitely-generated $R$-module, and $N$ any $R$-module. Is the natural map $$\textrm{Hom}_R(M, N)_\mathfrak{p} \to \textrm{Hom}_{R_\mathfrak{p}}(M_\mathfrak{p}, N_\mathfrak{p})$$ an isomorphism (of $R_\mathfrak{p}$-modules)?  I can prove this in the case when $M$ is finitely presented: indeed, let $S$ be any flat $R$-algebra, and let $$R^m \to R^n \to M \to 0$$ be a right-exact sequence; tensoring with $S$ gives another right-exact sequence $$S^m \to S^n \to M \mathbin{\otimes_R} S \to 0$$ and applying hom functors, we get left-exact sequences $$0 \to \textrm{Hom}_R(M, N) \to N^n \to N^m$$ $$0 \to \textrm{Hom}_S(M \mathbin{\otimes_R} S, N \mathbin{\otimes_R} S) \to (N \mathbin{\otimes_R} S)^n \to (N \mathbin{\otimes_R} S)^m$$ and $S$ is flat, so tensoring the first sequence yields $$0 \to \textrm{Hom}_R(M, N) \mathbin{\otimes_R} S \to (N \mathbin{\otimes_R} S)^n \to (N \mathbin{\otimes_R} S)^m$$ but extending the sequences by $0$ to the left, and putting in vertical maps between the last two, we conclude that $\textrm{Hom}_R(M, N) \mathbin{\otimes_R} S \cong \textrm{Hom}_S(M \mathbin{\otimes_R} S, N \mathbin{\otimes_R} S)$ by the five lemma (modulo checking commutativity of diagrams). This is essentially the proof Eisenbud gives [Commutative Algebra, Prop. 2.10].  The trouble with extending it to a proof for finitely-generated modules is that we have to replace $R^m$ with a potentially arbitrary submodule $K$ of $R^n$, and that may not be free or even finitely-generated without some additional assumptions on $R$. I can't see an abstract nonsense proof of the claim, but I admit I haven't tried a bare-hands proof. However, is the claim even true?


Can I attach a callback function to a built-in operator?

I'd like to run some of my code when the bpy.ops.object.duplicate() operator is called. Is there a way to attach a callback function to this built-in operator? Or is there a way to create a custom handler?


If sequences $\{a_k\}$ and $\{b_k\}$ are related by $a_k = \sum_{r=0}^k \binom{k}{r} b_r$, can I compute $b_k$s in $O(1)$ time?

I have two series, say $\{a_k\}$ and $\{b_k\}$ for $k=0, 1, \ldots$.  They are related to each other as  $$\sum_{r=0}^k \binom{k}{r} b_r = a_k.$$  I want to compute $b_k$'s.  Of course, I can do this using the following recurrence relation  $$b_k = a_k-\sum_{r=0}^{k-1}\binom{k}{r} b_r.$$  But this is quite time consuming as $k$ increases because the number of operations is $O(k)$.  Is there a possibility that we can have a recurrence relation to obtain $b_k$ in $O(1)$ time?


Some Subgroup of Dihedral Group is Normal

I ran into this question when I was studying for my abstract algebra midterm.     Show that the subgroup $H$ of rotations is normal in the dihedral group $D_n$. Find the quotient group $D_n/H$.   I'm not quite sure where to begin. I know that for a Dihedral group of $n\geq 3$, then $r^n=1$ where $r$ is a rotation, and $s^2=1$ where $s$ is a reflection, and $srs=r^{-1}$. I was not sure how to prove something is a normal subgroup from here. Any advice, thanks!


Understanding the asterisk "*" in functions/parameters

I'm trying to understand if there is any difference between:  bool String_Init(String *str, char * s, uint32_t len){};   and  bool String_Init(String *str, char *s, uint32_t len){};   Also,  const char * String_GetCString(const String * const str){};   and  const char *String_GetCString(const String * const str){};   Thank you!


Prove the identity $\sin\theta/(1+\cos\theta)=(1-\cos\theta)/\sin\theta$

I'm stuck on the equation $$\frac{\sin\theta}{1+\cos\theta}=\frac{1-\cos\theta}{\sin\theta}$$   I just can't figure how to start. I need to flip the equation and change the signs but I'm not sure where to start.


finding path to libgsl2:i386 in ubuntu 16.04LTS

I needed to install gsl in Ubuntu 16.04 to run a cosmological simulation, however, I tried the command in terminal  sudo apt-get install libgsl0ldbl   in returned me :  Package libgsl0ldbl is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it:   libgsl2 libgsl2:i386  E: Package 'libgsl0ldbl' has no installation candidate   So I typed instead:  sudo apt-get install libgsl2 libgsl2:i386   and it seems it installed successfully, however I need to know that path where it has been installed. so I did:  which gsl2:i386   and it returned me nothing.  Anyone have any idea how to find that path ?


Today a new version of vscode was available, so I went to  and downloaded the .deb file. I clicked the downloaded file, it opened in the Ubuntu Software Center and I clicked install to update my current version. So far this is a very user friendly process IF the installation would actually work :-)   What actually happened:  If I go to the Software Center after the installation it still shows me the old version of VSCode:   If I click the downloaded .deb file again it still shows me that I can install it and NOT launch it, even if the installation was successful (I can check it by opening VSCode from the dock and check the version).    My questions are:   What happened here?  Why is Ubuntu not showing me the updated version in the Software Center? Why does Ubuntu still show me that I can install the .deb file even if I have just installed it How can I show this post to Canonical, so they can finally implement a NOT buggy installation/update process?


Suggested starting place for Ghost in the Shell

As the title suggests, I want to start watching Ghost in the Shell. But I have seen many different ones and dont know if they're all part of the same series etc.  What are some suggestions for where to start the series?


Why the Pink textures? Not Packed but called from a source file

So I wanted to make a Blender game and I've been working on the exterior now suddenly after about three days of working on it, Blender will no longer call the textures I need it to and I wind up with this, which is completely undesirable. The textures for some reason show in the materials tab but not in the textures tab nor in the Materials viewing pane. Is there a way to fix this? Preferably permanently so that it doesn't happen again?


What are the possible dimensions / sizes / units LaTeX understands?

I know there are different ways of expressing sizes or dimensions in LaTeX such as points (pt), inches (in) and ex.  As some commands, such as \hspace , I would like to have a reference or complete list of possible dimensions or sizes including a description of what they mean.


I have been running Kubuntu 15.10 32-bit for a while, and although I love the KDE enviroment, I would like the option of having Unity. So, I did the following:  sudo apt-get update sudo apt-get install unity   I then rebooted, and when I was at the login screen, I tried to switch from plasma to unity, but the only options were "Plasma" and "Failsafe". When i run:  sudo apt list | grep gnome   or:  sudo apt list | grep unity   I am presented with several packages saying "Unity-8-desktop", or something along those lines, so I know Unity is installed, I just can't reach it. Can anyone help me?


What's the old guy (Chuck?)'s problem in the end of Better Call Saul episode 4 of season 1

In Better Call Saul episode 4 of season 1 (the one aired on Feb 23, 2015), there's an old guy (Chuck?) in the end, who James hid the newspaper from, and apparently can't go outside without a shield thing. Does he have some sort of disease, if yes, what is it?


Java Scanner String Input If statement not working

I am very new to java, and this seems very simple, perhaps I am missing something.   Below is a little bit of my code, what it should do is have the user enter the a password, which is stored in userinput, unfortunately if I type admin which I have it set to == "admin" it will not work, even if I do all caps or all lowercase like I have it.   I even tried pre-setting a variable such as String password = "admin"; and having it set to be if (userinput == password) but that did not seem to work either. Please help!      }     public void protect(){         Scanner input = new Scanner(System.in);         System.out.println("Enter password: ");         String userinput = input.nextLine();         if (userinput == "admin"){             System.out.println("Correct!");         } else if (userinput != "admin"){             System.out.println("Wrong!");         }     } }   Quick summary, no matter what password I type, even if it is "admin" it goes right to wrong.


Expressing a factorial as difference of powers: $\sum_{r=0}^{n}\binom{n}{r}(-1)^r(l-r)^n=n!$?

The successive difference of powers of integers leads to factorial of that power. Here's the formula:     $$\sum_{r=0}^{n}\binom{n}{r}(-1)^r(n-r)^n=n!$$   Can anyone give a proof of this result?  Note: The original question was to prove the more general     $$\sum_{r=0}^{n}\binom{n}{r}(-1)^r(l-r)^n=n!$$   for an integer $l$, which some of the answers address.


Emails from my server are considered as spam on hotmail

Well all is in the title. How to be removed from their spam list? We don't use external email provider for now. We respect emails good practices: signed email, unsubscribe link, dest email...  Here are different tests, nothing bad reported:         Can we contact Microsoft for a manuel check?


I'm looking for a short story that's a dialogue between a researcher and an AI. The AI is told it's a person waking up in a dark room, and slowly comes to realize it's actually just a machine with no physical body.   The setting would be the lab they're in. I vaguely remember some plot twist where the one you think is the researcher is actually the AI, but I really don't remember.   I read the story online ~2 years ago, but I don't know the publish date. I don't know the name of the AI. The researcher was male. I don't think it was a well-known author.


How can my content script access element from an HTML web accessible resource page?

I'm working on a chrome extension, where I have an iframe pop up when user is on a certain website. I have the iframe html document saved as a web accessible resource, and I'm trying to figure out how I can access and manipulate an element in that iframe document from the content script. Basically I want to be able to update information on the iframe popup based on the web page the user is on. Is there a way to somehow access it directly from the content script? Or can I have a separate js file manipulating information on the html page? Looking for any ideas/guidance anyone can offer. Thanks! Edit: This is what I'm trying, I can't figure out where it's going wrong. iframe.html               <title>My extension</title>                  <meta charset="UTF-8">         <meta name="viewport" content="width=device-width, initial-scale=1.0">

Trying to get some text here!

        iframe.js var testHeaderElement = document.getElementById("testHeader"); console.log(testHeaderElement.innerText);  In iframe.js, it's telling me that it can't log testHeaderElement.innerText because it's null. Why isn't it finding the element?


How to show that a set with injections into and from $\mathbb{N}$ is uncountable?

Let's say we have two injective functions $u : \mathbb{N} \to A$ and $v : A \to \mathbb{N}$.  How can I demonstrate that $A$ is uncountable ?  If there is an injective function $u : \mathbb{N} \to A$ and $v : A \to \mathbb{N}$, consequently there is a bijection between $\mathbb{N}$ and $A$. But what can I do from that?  Thanks!


Automatic bounty awarding - votes count up to which point considered?

In the accepted answer to the question  it says,   If the author offered the bounty, and accepted an answer that was posted during the bounty period, that answer is awarded the full bounty.     Otherwise, all or half of the bounty is awarded to the highest-scored   answer out of those which...         were posted after the bounty was started, and    have a score of at   least +2, and    were not written by the bounty starter.      Here the score of at least +2 votes means the number of votes it had at the moment bounty period is ended or at the moment calculation for automatic award is done? Lets say an answer had a score of 2 when the bounty period is ended and later it gets a downvote and score become 1. but its still the highest scoring answer. Will it get the bounty by automatic bounty award mechanism?


How to disable global menu and have always visible menu bars

Is it possible to get menus to be shown in always visible menu bars in 14.04, rather than in window title bars?


I was doing the the following problem- Prove that $$\frac { \sqrt { a+b+c } +\sqrt { a }  }{ b+c } +\frac { \sqrt { a+b+c } +\sqrt { b }  }{ c+a } +\frac { \sqrt { a+b+c } +\sqrt { c }  }{ a+b } \ge \frac { 9+3\sqrt { 3 }  }{ 2\sqrt { a+b+c } }. $$ I normalized this to $a+b+c=1$ and simplified to get- $$\frac { 1 }{ 1-\sqrt { a }  } +\frac { 1 }{ 1-\sqrt { b }  } +\frac { 1 }{ 1-\sqrt { c }  } \ge \frac { 9+3\sqrt { 3 }  }{ 2 }.$$ By Titu's lemma, $$\Rightarrow \quad \frac { 1 }{ 1-\sqrt { a }  } +\frac { 1 }{ 1-\sqrt { b }  } +\frac { 1 }{ 1-\sqrt { c }  } \ge \frac { 9 }{ 3-(\sqrt { a } +\sqrt { b } +\sqrt { c } ) } .$$ However the RHS is maximized when  $\sqrt { a } +\sqrt { b } +\sqrt { c } $ is maximized which is at $\sqrt { 3 } $, $$\Rightarrow \quad \frac { 1 }{ 1-\sqrt { a }  } +\frac { 1 }{ 1-\sqrt { b }  } +\frac { 1 }{ 1-\sqrt { c }  } \ge \frac { 9 }{ 3-(\sqrt { a } +\sqrt { b } +\sqrt { c } ) } \le \frac { 9 }{ 3-\sqrt { 3 }  } =\frac { 9+3\sqrt { 3 }  }{ 2 } .$$ What went wrong? You can view the rest of the problems .


Static inner class extending abstract outer class in java

I saw this pattern today and it confused me a lot:  abstract class A {     // does something      static class B extends A {         // does something as well     } }   Two weird things I found about it:   Static class can be initialised using new A.B(). Static class is not unique in the application (therefore, not really static), as each initialisation creates a new object.   I am still perturbed as to why to use such a pattern? And does static class in this context mean, that you can access it's constructors statically, without needing to create an instance of A, but not really it being a unique in any way in the app?  EDIT:  OK, so I think my understanding of static classes came from C#. I am clear on the staticness of java classes now. But when would you use such a pattern (where inner static class is extending outer abstract one) and why?


Why can't a null-reference exception name the object that has a null reference?

It seems to me that a lot of my debugging time is spent chasing down null-reference exceptions in complex statements. For instance:  For Each game As IHomeGame in _GamesToOpen.GetIterator()   Why, when I get a NullReferenceException, can I get the line number in the stack trace, but not the name of the object that equals null. In other words, why:  Object reference not set to an instance of an object.   instead of  _GamesToOpen is not set to an instance of an object.   or  Anonymous object returned by _GamesToOpen.GetIterator() is null.   or  game was set to null.   Is this strictly a design choice, meant to protect the anonymity of the code or is there a compelling reason in compiler design not to include this information in the debug-time exception?


Providing a callee response to a "call to undefined method" error?

I'm learning my way into some more advanced programming with PHP.  I've seen that calling an non-existent method produces "call to undefined method" error.  PHP being quite flexible is there a technique that allows to intercept this error ? If so, how is this usually done ?  Edit: To clarify, I want to actually do something when the error occurs like send a reply back, not necessarily prevent it. Forget to mention that this is in the context of a class. Of course, methods only apply in the context of a class ;)


How can I switch to Unity/Ubuntu mode from xbmc kodi?

I selected the xbmc default mode via switch user. Now my computer directs me to xbmc. I want to switch to my default Ubuntu 14.04 desktop. I tried to exit, but it starts again in xbmc.


Is there a site already for SEO questions or is this maybe a subject I should take to Area 51?  This company has a site for virtually every other computing discipline, but I don't seem to see a place where SEO questions can be asked. Is it maybe on-topic at the ?


What are the differences between 2.5" and 3.5" hard disks?

What does the 2.5"/3.5" value indicate? The thickness?  I want one of my friends to buy 1TB hard disk for me. I know I want a 1TB capacity and 7200rpm, but don't know how to choose between 2.5" and 3.5"; I am worried that the 3.5" drive may be physically too big.  Also, aside from the measurements, are there any other differences that may cause compatibility or usability concerns?


Why left continuity does not hold in general for cumulative distribution functions?

Definition: The c.d.f. $F$ of a random variable $X$ is a function defined for each real number $x$ as follows:$$F(x)=\Pr(X\leq x) \text{ for } -\infty<x<\infty$$    Let $$F(x^-)=\lim_{y\rightarrow x,\,y<x}F(y)$$ and $$F(x^+)=\lim_{y\rightarrow x,\,y>x}F(y)$$       Property of cumulative distribution function: A c.d.f. is always continuous from the right; that is , $F(x)=F(x^+)$ at every point $x$.        Proof: Let $y_1>y_2>\dots$ be a sequence of numbers that are decreasing such that $$\lim_{n\rightarrow \infty}y_n=x.$$Then the event $\{X\leq x\}$ is the intersection of all the events $\{X\leq y_n\}$ for $n=1,2,\dots$ .Hence, $$F(x)=\Pr(X\leq x)=\lim_{n\rightarrow \infty} \Pr(X\leq y_n)=F(x^+).$$     Now I think the left inequality can also be proved in the similar way as:  Let $y_1<y_2<\dots$ be a sequence of numbers that are increasing such that $$\lim_{n\rightarrow \infty}y_n=x.$$Then the event $\{X\leq x\}$ is the union of all the events $\{X\leq y_n\}$ for $n=1,2,\dots$ .Hence, $$F(x)=\Pr(X\leq x)=\lim_{n\rightarrow \infty}\Pr(X\leq y_n)=F(x^-).$$  Where am I wrong?


graphicx: including files with multiple . in filename

I load the package with:  \usepackage{graphicx}   I use it as follows:  \includegraphics{inc/2 aanbod/inc/doc/Vormingplus/inc/img/2 jpg/p. 04-05.jpg}   This is the error I get:    LaTeX Warning: File `inc/2 aanbod/inc/doc/Vormingplus/inc/img/2 jpg/p. 04-05.jp g' not found on input line 444.   ! LaTeX Error: Unknown graphics extension: . 04-05.jpg.  See the LaTeX manual or LaTeX Companion for explanation. Type  H <return>  for immediate help.  ...                                                l.444 ...c/Vormingplus/inc/img/2 jpg/p. 04-05.jpg}  ?      I think the solution for this problem is clear. graphicx should start seeking at the END of the specified filename, seek to the left for the FIRST APPERANCE OF A DOT.  Could this please be solved?


How can i prove this problem about Cauchy integral?

Let $V$ be an open connected subset of $\mathbb{C}$.  Let $f:\rightarrow \mathbb{C}$ be a function continuous on a contour $C$.  Define $F(z)=\int_C \frac{f(\zeta)}{\zeta - z} d\zeta$ on $V$.  My question is:   How can i show that $F$ is analytic at every point except $C$? How can I show that  $F'(z)=\int_C \frac{f(\zeta)}{(\zeta - z)^2} d\zeta$ where $z$ not in $C$?


Do I need a transit visa for a 12 hours transfer from Narita to Haneda airports?

I'm arriving at Narita airport at 9:30 pm, and departing from Haneda airport at 9:30 am the following day. I am a Filipino citizen working in The Bahamas.  Will I still need a transit visa?


I want to develop iOS application with swift in windows 8.  Is it possible?  Thanks in advance for helping.


I'm new to D&D and RPGs in general, but have wanted to play for a long time. Jumping into the new edition, If I purchase the starter set I'm trying to figure out where we would go after we finish.  Should I just create a campaign without the help of the core books (that release in August, September and November)? Or is there material to adapt I can adapt first (on the internet or from other editions that are adaptable), instead of creating it all from the ground up?


I cannot delete answers on Stack Overflow

Sometimes I misinterpret questions and like to remove my irrelevant answer.   For the past few days I could not delete my own answers anymore on Stack Overflow. The following dialog appears after clicking the delete button:     Vote to delete this post?   Bug or new feature?


My Xbox freezes when I play Minecraft for a few minutes

Why does my Xbox freeze when I play in my Minecraft world for about two minutes? The whole Xbox freezes but I can still hear music and in-game sound.  If I take out the game it sends me to the dashboard and it all happens again if retry with the disc. It is not the console because I have also played Skyrim, Far Cry 3 and Thief and none of those crash my Xbox. My hard drive also has 195 GB remaining.


In viewing the weekly list of rep change, I see  on top: razpeitia2 5 16  member for: 2 years, 7 months link #1 week rank +8529 change 727 total reputation 2,286 week reputation    How can someone with 727 total have 2286 for the week with no bounties?  Call me curious.  Is this a bug or something else here?


Equation with factorial, exponential and Sum

I need to prove that : $\mathrm{\sum_{n=0}^{\infty} {p^n\over n!} |p-n| = 2{p^p\over(p-1)!}}$ Knowing that $\mathrm{\sum_{n=0}^{\infty} {p^n\over n!} = exp(p)} $ I've tried many ways : $\mathrm{\sum_{n=0}^{\infty} |p-n| = \sum_{n=0}^{p-1} (p-n) + \sum_{n=p+1}^{\infty} (n-p) }$ $\mathrm{ \Longleftrightarrow ... \Longleftrightarrow \sum_{n=0}^{\infty} |p-n| = \sum_{n=0}^{p} n + \sum_{n=0}^{\infty} n }$ Also tried to use ln()... But nothing seems to be leading to a result... I have spent more than 3 hours just on this one... Can anyone show me the answer and the way I need to proceed in such exercises ?


hi when i format  micro SD card to fat32 and after that copying executable file to SD card , permission of  file that sent changes to read only and can not be executed even i use  chmod777 -R with no error but dose`not works i tried many ways but automatically  changes to no executable


A difficulty in understanding the definition for limit superior of ${x_{n}}$

The definition is given by the following formula:  $$\limsup_{n \rightarrow \infty} x_{n} := \lim_{n \rightarrow \infty}(\sup_{m\geq n} x_{m}) $$  I could not understand the meaning of $(\sup_{m\geq n} x_{m})$ and why we have this number m and why it must be $\geq n$, could anyone explain this for me please?


Caption titles in List of tables and List of figures overlapping subsection number

I need to show the numbering of my tables and figures up to subsection which makes the numbering have four digits (e.g. Table 1.2.3.4). When I create the List of tables or the List of figures the title of the caption overlaps with the last digit of numbering. See image:  I only find ways to add vertical space between entries, but not to add horizontal space within the entry. Any idea would be appreciated, especially if it doesn't change the spacing of the ToC. MWE \documentclass[11pt, a4paper, oneside]{report}  \usepackage{chngcntr} % to be able to change the numbering "depth"     \counterwithin{figure}{subsection} % make figures show subsection number     \counterwithin{table}{subsection} % make tables show subsection number  \begin{document}  \listoftables \newpage   \chapter{chap1} \section{sec1.1} \subsection{subsec1.1.1}  \begin{table}[!htb] \centering \caption{caption.} \begin{tabular}{lll} \hline Hola & Hello & Hallo \\  Adéu & Bye   & Tchüs \\ \hline \end{tabular} \end{table}  \begin{table}[!htb] \centering \caption{caption.} \begin{tabular}{lll} \hline Hola & Hello & Hallo \\  Adéu & Bye   & Tchüs \\ \hline \end{tabular} \end{table}  \begin{table}[!htb] \centering \caption{caption.} \begin{tabular}{lll} \hline Hola & Hello & Hallo \\  Adéu & Bye   & Tchüs \\ \hline \end{tabular} \end{table}   \end{document}


Q: Let R be a commutative ring with unity. Prove that if A is an ideal of R and A contains a unit, then A=R.  This is my attempt at an answer: It suffices to show that all the elements in R are in A.  Let a be and element of A, and r be an element of R. Since A is an ideal of R then all elements ar and ra must be in A.   We know that A has a unit say 1, then we know 1r and r1 for all r in R, are in A.  Thus all elements in R are in A, therefore A=R.


I have two examples in Beamer, Example 1 and Example 2. I then would like to have Example 1 (ctd) after Example 2. The following is not working:  \documentclass[notheorems]{beamer} \usetheme{Pittsburgh} \setbeamertemplate{theorem}[ams style] \setbeamertemplate{theorems}[numbered]  \makeatletter \ifbeamer@countsect   \newtheorem{theorem}{\translate{Theorem}}[section] \else   \newtheorem{theorem}{\translate{Theorem}} \fi   \theoremstyle{example} \newtheorem{example}{\translate{Example}}    \setbeamertemplate{theorem begin}{% \begin{center} \begin{minipage}{0.9\textwidth} \begin{\inserttheoremblockenv} {%   \inserttheoremname   \inserttheoremnumber   \ifx\inserttheoremaddition\@empty\else\ (\inserttheoremaddition)\fi% }% }  \setbeamertemplate{theorem end}{% \end{\inserttheoremblockenv} \end{minipage} \end{center} } \makeatother  \addtobeamertemplate{theorem begin}{% \setbeamercolor{block title}{fg=green}% \setbeamercolor{block body}{bg=gray}% \setbeamerfont{block title}{size=\small,series=\bfseries}% }{}  \newtheoremstyle{examplec} {\topsep} {\topsep}% {\upshape}% Body font {}% Indent amount (empty = no indent, \parindent = para indent) {\bfseries\scshape}% Thm head font {.}% Punctuation after thm head {1em}% Space after thm head (\newline = linebreak) {\thmname{#1} \thmnumber{ #2}\thmnote{#3} (ctd)}% Thm head spec \theoremstyle{examplec} \newtheorem*{examplec}{\translate{Example}}  \begin{document} \begin{frame} \begin{example} This is the first example.\label{myexample} \end{example}  \begin{example}  This is the second example. \end{example}  \begin{examplec}[\ref{myexample}]  Continuing first example. \end{examplec}  \end{frame} \end{document}   This will produce the following:    What I want is: instead of Example (1), having Example 1 (ctd).  I noticed the solution at  but it does not seem to work if I keep my configurations in the preamble (which is why MWE is a bit long) -- I want to keep the (ctd) part.   Your help is much appreciated. Thanks!


Connected component of $GL_n(\mathbb{R})$

The set of $n\times n$ matrices can be identified with the space $M_n(\mathbb{R})$. Let $G$ be a subgroup of $GL_n(\mathbb{R})$.  I would like to show that the set of matrices that can be joined to the identity $I$ forms a normal subgroup of G.


Possible to run "Merge shapefiles to one" algorithm from Python script?

Developing a python script in QGIS 2.2, I can run algorithms from the Processing plugin fine such as those from QGIS geoalgorithms and SAGA.   Can you do the same for the algorithm "Merge shapefiles to one" from the Vector menu and how can you call it from the Python console?  The "Merge shapefiles to one" algorithm is from the Ftools plugin.  Found a link which might be useful:


Is it possible to access a history of your clipboard in Ubuntu?

Every time I copy and paste something I save it to my clipboard. Is it possible to access a record of what I have copied and pasted on Ubuntu?


In any calculus course, one of the first thing we learn is that $(uv)'=u'v+v'u$ rather than the what I've written in the title. This got me wondering: when is this dream product rule true? There are of course trivial examples, and also many instances where the equality is true at a handful of points. Less obvious though, is the following:     Are there non-constant $u,v$ such that there exists an interval $I$ where   $(uv)'=u'v'$ over $I?$   I have a feeling there should be, but I am having trouble constructing such a pair.


I'm studying for actuarial exams, but I always pick up mathematics books because I like to challenge myself and try to learn new branches.  Recently I've bought Topology by D. Kahn and am finding it difficult.  Here is a problem that I think I'm am answering sufficiently but any help would be great if I am off.  If $d$ is a metric on a set $S$, show that  $$d_1(x,y)=\frac{d(x,y)}{1+d(x,y)}$$ is a metric on $S$.  The conditions for being a metric are $d(X,Y)\ge{0}, d(X,Y)=0$ iff $X=Y$, $d(X,Y)=d(Y,X)$, and $d(X,Y)\le{d(X,Z)+d(Z,Y)}$.  Thus, we simply go axiom by axiom.  1)  Since both $d(x,y)\ge{0}$ and $1+d(x,y)\ge{0},$ it is clear that $d_1(x,y)\ge{0}$.  (Is this a sufficient analysis?) 2) $d_1(x,x)=\frac{d(x,x)}{1+d(x,x)}=\frac{0}{1+0}=0$. 3) $d_1(x,y)=\frac{d(x,y)}{1+d(x,y)}=\frac{d(y,x)}{1+d(y,x)}=d_1(y,x).$ 4) $d_1(x,y)=\frac{d(x,y)}{1+d(x,y)}\le{\frac{d(x,z)+d(z,y)}{1+d(x,z)+d(z,y)}}=\frac{d(x,z)}{1+d(x,z)+d(z,y)}+\frac{d(z,y)}{1+d(x,z)+d(z,y)}\lt\frac{d(x,z)}{1+d(x,z)}+\frac{d(z,y)}{1+d(z,y)}=d_1(x,z)+d_1(z,y).$  However, #4 is strictly less, not less than or equal to, according to my analysis, so where did I go wrong?


This particular statement was one of the options in a question which was to be chosen if Right and I was unable to think how to reason it . So  I am asking here.  If G is cyclic then Aut(G) is cyclic or not?  CAn you please tell how to prove it or Give some counteexample if it can't be proved. Thanks!!


Awesome papers that were initially rejected?

Recently I heard from a senior student that the celebrated adaBoost  was originally rejected by a conference.   Are there any other instances of seminal papers (in any field) which initially could not warrant a publication?


reflecting direct light on glossy surface in Cycles

Working in Cycles.  Say I have a "disco ball" with a glossy shader. I'm pointing a spot light to it, and I'm trying to have the reflections of that light illuminate the diffuse material on the walls with the patterns from the ball.    I get this:    but I'd like to get something like:    For the illustration I placed a point light inside the ball an removed faces. But what I'd like to do is move the light around the ball so that the light reflected from it changes like it would do in real life.   Is that possible at this point?  EDIT:  Just for the record here's the image rendered in LuxRender (yet another program to learn...)


How do I add values to the app.config or web.config's appSettings section in C#?


what is asymptotic behavior of $\sum \frac {1}{\sqrt[\alpha] k}$

Asymptotic behavior of $$\sum \frac {1}{\sqrt[\alpha] k}$$  for $\alpha=1$? is $\ln k$ what about $\alpha > 1$ ?    the suggested link is for $\alpha > \frac{1}{2}$ my question is about $ 0< \alpha < \frac{1}{2}$


"L'Hôpital's rule" vs. "L'Hospital's rule"?

I know this is not strictly a mathematical question, and I considered putting it on Linguistics SE, but I decided that seeing as this is most probably a mathematical history question, it would be better placed here on math SE.  My question is:     Why is "L'Hôpital's rule" often referred to as "L'Hospital's Rule" in english mathematical literature?   I am aware that the translation from French to English of "L'Hôpital" is "The Hospital", but I haven't seen any cases of other french names which correspond to proper nouns being translated into english, so why the special case here?  Again, sorry if this is completely the wrong place to put this question, and moderators feel free to migrate this question to a more appropriate SE board if one exists, but as I said, I believe this to be the most appropriate board.


What should you do if you think an asker has evil intent?

got me thinking. There have been cases, very occasionally, where upon reading the question I get the sense that the asker is looking to do something evil: spam, black-hat hacking, mass email scraping, rootkits and so on.  Typical signs are a new user, asking about a precursor to a sketchy task (for example, ), without contextual details or further explanation.  Judging by the disparity in the ones I'm seeing and the ones I was able to find in search, usually these questions get closed and deleted or go unanswered. Some are answered, though.  I'm curious as to the community's thoughts -- is it our job to be judging askers on their perceived intent? Should we flag for this if we have sufficiently strong evidence the answer will clearly be used for evil purposes, if it's otherwise an on-topic Stack Overflow question?  (It's not as clear-cut as you might think -- as an security researcher I blur this line all the time, and thus have strong feelings about the ethical responsibilities of people who play with that particular fire. There have been times when I've written up a full, complete, multi-paragraph answer, read the question through a few more times, sighed, and deleted the whole thing because I didn't like what I might be helping someone do. I'm curious if anyone else has had this experience, and what they've done: sometimes I've left a comment, but mostly I just move on.)


Is it true that $\forall \epsilon > 0 , a \leq b + \epsilon \Rightarrow a \leq b$?

Is it true? I see a lot of inequalities like that in proofs, but i don't understand why it should be true.


I am writing a console application. UI would be like this.  Please input :  to learn java to learn VB.NET to quit   if user enters 1 it will go for java learning, if enters 2 it will go for VB learning, if enters 3 program will quit. For all other inputs the program will show the above message again. I implemented this in below way : import java.io.BufferedReader; import java.io.IOException; import java.io.InputStreamReader;  public class DriverTest {  public static void main(String[] args) {     new DriverTest().takeOver(); }  public void takeOver() {     BufferedReader inputScanner = new BufferedReader(new InputStreamReader(System.in));     System.out.println("Please enter:");     System.out.println("1. to learn JAVA");     System.out.println("2. to learn VB");     System.out.println("3. to quit");      try {         int actionKey = Integer.parseInt(inputScanner.readLine());         switch (actionKey) {         case 1:             System.out.println("Welcome to JAVA learning");             break;         case 2:             System.out.println("Welcome to VB learning");             break;         case 3:             System.exit(0);             break;         default:             System.out.println("Please select a proper action :");             takeOver();         }     } catch (NumberFormatException | IOException e) {         System.out.println("Some error occured please try again. :(");         takeOver();     } }  }  Now if user continuously provide invalid input, it will result eventually into StackOverflow error.(You can test it, copy the class in folder.complie it : javac DriverTest.java, create one text file input.txt and write anything except 1,2 and 3. e.g. hgsad, now run java DriverTest < input.txt) Please suggest, if there is any better solution of the problem.


$_ vs !$. Last argument of the preceding command and output redirection

The question is about special variables. Documentation says:     !!:$      designates the last argument of the preceding command. This may   be shortened to !$.        ($_, an underscore.) At shell startup, set to the absolute pathname used  to invoke the shell or shell script being executed as passed in the    environment or argument list. Subsequently, expands to the last argument to the previous command after expansion. Also set to the full pathname  used to invoke each command executed and placed in the environment    exported to that command.    There must be some difference I cannot catch, because:  $ echo "hello" > /tmp/a.txt $ echo "!$" echo "/tmp/a.txt" /tmp/a.txt  $ echo "hello" > /tmp/a.txt $ echo $_ hello   What is the difference?


I currently have the following object in php:   "Direction": "Please choose the direction"   "Media": "Please choose the stock"   "Coating": "Please choose the coating"  I then loop through it with a foreach foreach ($product as $key => $att) { // is there away I can get the index?  Meaning 0, 1, etc? }  In the foreach is there away I can get the index?  I need a numerical index value.


YA Book (series?) - Trying to find a SF story about a young girl raised by a robot on an alien world?

I was at a Science Fiction Convention in February and at a panel a writer was talking about Young Adult Genre crossing over into SF Genre with the focus on identity.  Since that is a common theme in YA books he brought up a book that he mentioned 'might not be in print any longer' so as it sounded very interesting I had made note of it, but somewhere along the line I lost the info.    In this book a young girl raised by a robot on an alien world and while she saw herself as human something had happened to her ( I think the robot might have used some kind of re-engineering on her so she could survive on the planet or perhaps she was disfigured or maybe she's not human, I'm not really sure ) so that she didn't look human.  As a result she was never allowed to look at herself in a mirror, or something, so when other humans finally found her it was hard for them to see her as human, ergo the identity aspect of the book: What makes one human? Is she human if she believes she is?  A few other details that I recall: She lived in a harsh world, everyone else in her group or settlement or whatever was dead and I had the impression they may have lived in a cave or something (though that could be wrong).   Now I never read this book and am not sure if I'm explaining it very well, I'm not even sure if it's from the 50's 60's 70's or 80's but I don't think it's more recent then that, so I hold no real belief that I can find the answer to WHAT IS THIS BOOK? even here...    Still I thought I might give it a shot as the story sounded very interested.