What is the correct way to use WordPress functions outside WordPress files?

I read about 2 methods for initializing WordPress function outside of WordPress files so We can use these functions on any page or website outside the WordPress blog.  Which one of these 2 methods is the correct one? What are the use cases for each method if both are correct? What is the deference between using one method or the other?  Method 1:  <?php      define('WP_USE_THEMES', false);     require('./wp-blog-header.php'); ?>   Method 2:  <?php      define('WP_USE_THEMES', false);     require('./wp-load.php'); ?>


Hardy Hilbert space: Multiplication by $H^\infty$ function

If $H^2(\mathbb{D})$ is space of all analytic functions whose series of taylor coefficient is absolute square summable and $\phi$ is analytic in $\mathbb{D}$,then $\phi H^2 \subset H^2$  if and only if $\phi$ is in $H^\infty$.  Not able to solve it through elementary arguments. can't think of what theorem of functional analysis can i invoke. any hints ?


Getting from Halifax, Canada to the US by bus/train?

I'm considering going all the way across to Halifax, Nova Scotia, but am having trouble finding information on getting from there down to the USA (Boston in particular).  I gather it's 22 hours by train back to Montreal, and then I could bus down, but the train is only every few days.  I've tried Megabus and Greyhound but both sites won't show me how to connect to get to Boston in the USA, for example.  Is there a Greyhound connection to the US, or another bus company? Or do you have to backtrack all the way to Quebec/Montreal and cross the border there?


Why there are infinitely many positive integers n such that $1^5+2^5+...+n^5$ is a square?

I have no clue how to show some kind of positive integers has infinitely many. I guess perhaps I can use proof by contradiction? Say there is only a finite many, which means it will eventually stop at number $x$, and then show we can always find some integers after $x$, say $y$, such that $1^5 + ...x^5 + ... y^5$ is a square?   I am not sure it's the correct approach since I haven't figure out how to prove such y exists.  Thanks.


What is an example of $E/F,L/E$ are normal but $L/F$ is not.

Let $E/F,L/E$ be normal field extensions.  What would be an example such that $L/F$ is not normal?


I'm writing a technical documentation and I want to explain step-by-step how to go through various menus.  For example I used to write Open with > VLC media player.  That's how it looks in Windows 8:     What I want in Latex should looks similar to this: light grey box, dark grey border and black windows-like font.    I've seen , suggesting the package  - but it looks very old fashioned - are there any more modern approaches?


Find all number $n\in \mathbb N$ such that $\varphi (n)=14$   $\varphi (n)=p_1^{\alpha_1-1}\cdot p_2^{\alpha_2-1}\cdots p_n^{\alpha_n-1}(p_1-1)\cdots (p_n-1)=14$ so number that divide 14 $x|14$ is $x\in \{1,2,7,14\}$ so $p_i-1=1$ or $p_i-1=2$ or $p_i-1=7$ or $p_i-1=14$ $i\in \{1,2,\ldots n \}$ so $p_i=2, p_i=3, p_i=8, p_i=15$ since $8,15$ is not prime number then $p\in \{2,3\}$.  If we say that $n=2^{\alpha}$ then $\varphi (n)=2^{\alpha-1}=14$ so there is not such $\alpha \in \mathbb N$ that $\varphi(n)=14$ so $n\not=2^{\alpha}$  The same is for $n=3^{\beta}$ and $ n=2^{\alpha}\cdot 3^{\beta}$. So there is not exist $n\in \mathbb N$ such that $\varphi(n)=14$  Is this ok?


Probability Density Function of the Midrange of a Random Sample of Size 3 from a Uniform Distribution (0,1)

I defined another random variable $W = \frac{Y_3-Y_1}{2}$, then we get $Y_1 = Z-W$ and $Y_3 = Z+W$. I then used the change of variables method and get the joint pdf of $Z$ and $W$ is $h_{W,Z}(w,z) = 24w$, but I do not think this is correct since when I integrate everything out I do not get $1$.


This is from a multiple choice question with 4 options, but I narrowed it down to 2:     Select the best version of the following sentence:    (there is really no sentence after this, just the answer choices)         a) Each of the conference rooms has a computer display.   d) Each of the conference rooms have computer displays.      In my eyes these choices are both perfectly fine, I can't see anything wrong with either of them.


Let $f$ a concave function such as $f(0)=0$.  $$f :\mathbb{R^+}\rightarrow \mathbb{R}$$  I want to prove that, for all $x,y\in \mathbb{R^+}$: $f(a+b)\leq f(a)+f(b)$  My idea: Since $f$ is concave then for all $t\in [0,1]$, $f(t.a+(1-t)b \geq tf(a)+(1-t)f(b).$  And by taking $t=1/2$ then we'll have : $f((a+b)/2)\leq 1/2(f(a)+f(b)).$  and if we take $b=0$, then we'll have $f(ta)\geq tf(a)$  But I could not get to resault.


Rotate current selection of Objects .. Each object with a different Random Rotation ... Is this built into Blender?

Is such any such simple Object Mode feature/operation built into Blender? If yes what is the mechanism? It is certainly built in to rotate all the objects by the exact same rotation. The result might be for example each object has a random rotation about its own origin on the Y axis.  The rotation would be present in the object rotation entries. Trusted Addons are acceptable if they of age 3 months or greater. I checked the standard Addons.  I did not recognize anything.  Rotate has a proportional edit property though I did not see an explanation in the Blender documentation. Please exclude 🚫Particles and 🚫Pythons Scripts and 🚫Modifiers/Constraints/Keyframes and 🚫BAN.  I can write Script or use Particles if necessary.


Proving that the ring $R$ of $2\times 2$ matrices over $\Bbb{Q}$ contains only two ideals: $(0)$ and $R$.

There's a question in Herstein:      Prove that the ring $R$ of $2\times 2$ matrices defined over $\Bbb{Q}$ contains only two ideals: $(0)$ and $R$.   This seems to say that if I take any non-zero element, say $a=\begin{pmatrix} 1&1\\1&1\end{pmatrix}$, then $aR=R$.   This implies that for any $\begin{pmatrix} p&q\\r&s\end{pmatrix}\in R$, there exists $\begin{pmatrix} f&g\\k&l\end{pmatrix}\in R$ such that $\begin{pmatrix} f&g\\k&l\end{pmatrix}\begin{pmatrix} 1&1\\1&1\end{pmatrix}=\begin{pmatrix} p&q\\r&s\end{pmatrix}$.   It is clear that such a matrix $\begin{pmatrix} f&g\\k&l\end{pmatrix}$ need not exist in $R$, as the system of equations $f+g=p$ and $f+g=q$ does not have a solution unless $p=q$.      Is th question wrong then?  Thanks in advance!


A real variable solution of a problem posted on Terry Tao's Blog

On Terry Tao's blog I found the following problem:  I think I have a solution but I dont know how to write math on his blog so I posted my solution here.  Problem: Let $\{ a_n\}_{n\in \mathbb{N}}\subseteq \mathbb{R}$ be a bounded sequence. Suppose that the power series: $$f(x)=\overset{\infty}{\underset{n=0}{\sum}}\dfrac{a_n}{n!}x^n.$$ (which has an infinite radius of convergence) decays like $O(e^{-x})$ as $x\to\infty$ ($\underset{x\to \infty}{\lim}\dfrac{f(x)}{e^{-x}}=C$). Must the sequence ${a_n}$ be of the form ${a_n = C (-1)^n}$ for some constant ${C}$?


I'm getting a null pointer exception and I have no idea why, can you help me? Java

I've gotta create a bst and read in a text file to it so that the words of the file are recorded into that bst. I have to print the frequencies and probabilities of each word being searched however when i run my code i get an exception and I'm not really sure why. It's something having to do with my insert method I think. Here's my code:  import java.util.*; class Lepep3{     node root;     int counter;  class node{     String word;     int frequency;  //how many times the word shows up in the text file being read into the BST     double probability; //the probability that the node will be searched for      node leftLink, rightLink;   node(String w){         String word = w;         int frequency = 1;         node leftLink = null;         node rightLink = null;       }  }  Lepep3(){     root = null; }  void insert(String w){     if(root == null ){         root = new node(w);     }      else{         insert(w, root);     } }  void insert(String w, node t){     node parent = t;     while(t != null){         parent = t;         if(t.word.equals(w)){             t.frequency++;             return;         }          else if (w.compareTo(t.word) < 0)             t = t.leftLink;         else             t = t.rightLink;     }     if(w.compareTo(parent.word) < 0)         parent.leftLink = new node(w);     else          parent.rightLink = new node(w); }  void readInput(){     String x;     counter = 0;     Scanner inf = new Scanner(System.in);     while(inf.hasNext()){         x = inf.next();         insert(x);         counter++;     } }  double getProbability(node n){     double temp = n.frequency;     temp = temp/counter;      return temp; }  void printNodes(){     printNodes(root); }  void printNodes(node r){     if(root == null)         return;     printNodes(r.leftLink);     System.out.print(r.word + "   " + r.frequency + "   \n");     System.out.printf("%.4f\n", getProbability(r));     printNodes(r.rightLink); }  public static void main(String[] args) { System.out.print("\n Program to: find the frequency and probability of words form a given test file.");   System.out.print("\n Prepared by Lepe, Alfredo, Student ID: 109698093.");   System.out.print("\n Date: 3/8/2020");  Lepep3 ject = new Lepep3();  ject.readInput();  System.out.print("word   frequency   probability\n"); ject.printNodes(); }   }  Here's what my command prompt prints when i run the code:  C:\School\comp 282>java Lepep3 < p3.txt  Program to: find the frequency and probability of words from a given file.  Prepared by Lepe, Alfredo, Student ID: 109698093.  Date: 3/8/2020  Exception in thread "main" java.lang.NullPointerException      at Lepep3.insert(Lepep3.java:38)      at Lepep3.insert(Lepep3.java:31)      at Lepep3.readInput(Lepep3.java:58)      at Lepep3.main(Lepep3.java:88)


Probability that uniform random variables equal the natural numbers

I have random variables $X_{1}, X_{2}, \dots X_{n}$ that are each Unif$\{1, \dots, n\}$, and I want to calculate $$P(\{X_{1}, X_{2}, \dots X_{n}\}=\mathbb{N})$$  My intuition is that this means each $X_{n} = n$, which occurs with probability $\frac{1}{n!}$.  Does this seem correct?


How do I add a kernel boot parameter on live session itself?

I need to add boot parameter "pci=noaer" on my live persistent usb itself. Applying this command in terminal gave a error.  sudo update-grub   Error: /usr/sbin/grub-probe: error: failed to get canonical path of 'aufs'.  I am first time Linux user, my laptop is gone for repairs and I borrowed my dad's laptop. I just wanted to browse the internet. It took me 8 days and I am still not able to achieve this basic task. Actually I am having issue with wifi card "rtl8723be" ,its a known bug.  "sys.log" and "kernal.log" floads with pcie error and it basically fills my pendrive with those two large files which makes its unbootable. At this moment I hate Linux with passion. I willing to learn and understand more about Linux but I  need this system to work urgently. Please guys help me.


How to combine GROUP BY and ROW_NUMBER ( ) OVER

I Have  CusID Name Country PhoneNo ------------------  1     JOHN USA     555555 1     JOHN USA     555554 2     MIKE CANADA  111111 2     MIKE CANADA  122222 5     JOHN UK      888888 5     JOHN UK      888889   I want to display output like this:  CusID Name Country PhoneNo ------------------  1     JOHN USA     555555                    555554 2     MIKE CANADA  111111                    122222 5     JOHN UK      888888                    888889   (or) any other methods in SQL?


Probability of winning when rolling a standard fair die with two players

We have two players, lets call them A and B, a fair die is rolled and if either player gets a 5 or a 6 they win, but if they get a 2,3 or 4 the game continues (until someone gets a 5 or a 6). If two 1's come up in a row the game ends in a draw, if A roll's first find the probability that A wins ?  I have considered the case where there are no draws ie getting a 1,2,3 or a 4 continues the game and this is simply an infinite geometric series. s.t   $P(A)=\frac{2}{6} + (\frac{4}{6})^2\times \frac{2}{6} +(\frac{4}{6})^4\times \frac{2}{6} +... $  but I am not sure how to do this when we consider draws?


Why is my dual-core CPU recognized as a quad-core one?

My processor is an . As you can see, it's 2 cores and 4 threads.  Although, both Ubuntu 11.04 and Windows 7 seem to think it's a quad-core CPU:      Why is this? Is it because there are 2 threads per core, dividing the CPU in 4 processing units?


Variation on how to combine values from multiple rows into a single row in Excel?

Hi I am trying to adapt the excellent VBA that was posted previously to go through data and take all lines with the same id in column 1 and add them all into one row for each. Trying to get from this:    To this    but the adapted code below only ever combines 2 rows even if there are more than two with the same id in column 1.  Sub CombineInvoices() Dim currentRow As Long Dim currentCol As Long Dim LastRow As Long LastRow = Cells(Rows.Count, 1).End(xlUp).Row  currentCol = 4 For currentRow = LastRow To 2 Step -1     If Cells(currentRow, 1) = Cells(currentRow - 1, 1) Then         Range(Cells(currentRow, 1), Cells(currentRow, 4)).Copy Destination:=Range(Cells(currentRow - 1, currentCol + 1), Cells(currentRow - 1, currentCol + 4))         Rows(currentRow).EntireRow.Delete     End If Next currentCol = currentCol + 4 End Sub   All help really gratefully received.


Determine the remainder, when $77^{200}$ is divided by $54$.

Is there any fast way to get the remainders of the division of large numbers? Like$-$ $$\frac{77^{200}}{54}$$


What does the math notation $\sum$ mean?

I have come across this symbol a few times, and I am not sure what it "does" or what it means: $\Large\sum$


In exercise 1.8 of chap I in Hartshorne algebraic geometry,       Let $Y$ be an affine variety of dimension $r$ in $\mathbf A^n$. Let $H$ be a hypersurface in $\mathbf A^n$, and assume that $Y \nsubseteq H$. Then every irreducible component of $Y \cap H$ has dimension $r-1$.     Let $I(H)={f}$. I saw a solution in which one of the steps was to prove that $\bar{f}$ is not a unit in $A/I(Y)$. How to prove this ?


What video conferencing software is available?

There 're somebody i want to talk with him in a video conference in Ubuntu, how can i do that?


What is the difference between the 18-55mm Nikon kit lens and the Nikon Nikkor Lens ‑ 35 mm ‑ F/1.8 ‑ Nikon F?

What advantages will a 35mm lens will give me if I already owe an 18-55mm. Isn't the 35mm somewhat included in the other one?  It may be a silly question, but I am new in photography and trying to understand the lenses.


Should I use "who" or "which" when referring to a specific animal species?

I'd like to know what option to use, specifically when referring to a species by its scientific name.


Let f be continuous on $[0, +∞)$  and differentiable on $(0, +∞)$. If $f(0) = 0$ and $|f'(x)| < |f(x)|$ for all $x > 0$, then $f(x) = 0$ for all $x ≥ 0.$  I tried using the Mean Value Theorem for this but can't get anywhere significant.


Can I edit a post as to delete a edited portion of it for good?

say I post something I realize afterward is embarrasing and/or inconvenient (say a password, a friend's phone number, ecc.).  May I ask to delete it, in strong sense to remove from the system? How?   If not, why?


Should flour be thrown out past its expiry date?

As the title says, is it safe to consume flour once its past its expiry date or should it be thrown away?


Best Practice for Forcing Garbage Collection in C#

In my experience it seems that most people will tell you that it is unwise to force a garbage collection but in some cases where you are working with large objects that don't always get collected in the 0 generation but where memory is an issue, is it ok to force the collect?  Is there a best practice out there for doing so?


My code is:  public void move() {     moveX();     moveY(); }  public void moveX() {     if(xMove > 0) {         int tx = (int) (x + xMove + bounds.x + bounds.width) / Tile.TILEWIDTH;          if(!collisionWithTile(tx, (int) (y + bounds.y) / Tile.TILEHEIGHT) && !collisionWithTile(tx, (int) (y + bounds.y + bounds.height) / Tile.TILEHEIGHT)) {             x += xMove;         }     } else if(xMove < 0) {         int tx = (int) (x + xMove + bounds.x) / Tile.TILEWIDTH;          if(!collisionWithTile(tx, (int) (y + bounds.y) / Tile.TILEHEIGHT) && !collisionWithTile(tx, (int) (y + bounds.y + bounds.height) / Tile.TILEHEIGHT)) {             x += xMove;         }       }  }  public void moveY() {     if(yMove < 0) {         int ty = (int) (y + yMove + bounds.y + bounds.height) / Tile.TILEHEIGHT;          if(!collisionWithTile((int) (x + bounds.x) / Tile.TILEHEIGHT, ty) && !collisionWithTile((int) (x + bounds.x + bounds.width) / Tile.TILEWIDTH, ty)) {             y += yMove;         }     }      if(yMove > 0) {         int ty = (int) (y + yMove + bounds.y) / Tile.TILEHEIGHT;          if(!collisionWithTile((int) (x + bounds.x) / Tile.TILEHEIGHT, ty) && !collisionWithTile((int) (x + bounds.x + bounds.width) / Tile.TILEWIDTH, ty)) {             y += yMove;         }     } }  protected boolean collisionWithTile(int x, int y) {     return room.getTile(x, y).isSolid(); }   but when I run it I get a NullPointerException with this StackTrace:  Exception in thread "Thread-0" java.lang.NullPointerException     at com.pixelandbitgames.entities.creature.Creature.collisionWithTile(Creature.java:69)     at com.pixelandbitgames.entities.creature.Creature.moveX(Creature.java:41)     at com.pixelandbitgames.entities.creature.Creature.move(Creature.java:27)     at com.pixelandbitgames.entities.creature.Player.tick(Player.java:19)     at com.pixelandbitgames.states.GameState.tick(GameState.java:23)     at com.pixelandbitgames.game.Game.tick(Game.java:72)     at com.pixelandbitgames.game.Game.run(Game.java:113)     at java.lang.Thread.run(Thread.java:748) I do not see where this is coming from as collisionWithTile has all its parameters filled. If anyone can help me that would be appriciated. if anyone needs any thing else to help I will deliver. My other classes seem fine and it is just this one. This happens when I try to move. my code for Room.getTile is here:  public Tile getTile(int x, int y) {     if(x < 0 || y < 0 || x >= width || y >= height)         return Tile.floorTile;     Tile t = Tile.tiles[tiles[x][y]];     if(t == null)         return Tile.floorTile;     return t; }   and this has no way to return null. Is solid is just a return true unless it is overridden.  public boolean isSolid() {     return false; }


Does "Markov Chain Monte Carlo" method really need "Markov Chain"?

I am studying MCMC with "Pattern Recognition and Machine Learning" Book by Christopher Bishop. In the chapter of MCMC, this book introduces Markov Chain also a little bit.   However, while reading the book, I wonder why Markov chain is needed. Because to conduct the Metropolis-Hasting algorithm, for every step I make sample from proposal distribution and then decide whether it is accepted or not.   For me, this Metropolis-Hasting algorithm is more like rejection sampling. Adopting proposal distribution that we can directly draw sample from and deciding the sample should be accepted or not are similar.   Where is the room for using Markov chain? Do I need to calculate 'transition matrix' for Metropolis-Hasting algorithm? At this my confusing  state, I feel that I can conduct Metropolis-Hasting sampling without need of transition matrix of Markov Chain.   I am very confusing now. This book just says "under some circumstances a Markov chain converges to the desired distribution". But it does not say how can I design the Markov chain to converge distribution I desire. And many of the materials in the Internet also seems to skip this part. I thought designing transition matrix of MC is important part to conduct MCMC. But now, I guess it is not necessary.   Thanks in advance.


Why do RAW images in Darktable have a lot of noise?

I installed the latest version of Darktable from the Ubuntu PPA from their homepage (1.6.8). When I import RAW ges from a folder they all seem to have a lot of noise.  I opened the exact same images in other programs (DigiKam and Corel Aftershot) and there, these images did not have as much noise. In comparison, it seemed also that Darkroom turned up the brightness or exposure as the images there seemed a lot brighter.  I looked over all the settings and none of them were turned on. Also, this is still the standard installation (I did not change anything after installing).  Also using the lens correction for my camera (Lumix LX7) makes the images even more bright and produces more noise.  Does anyone have a tip on how to remove this? I would really like to use Darkroom instead of Corel Aftershot or Digikam, as it seems to have all the features I want and it looks more stable than Aftershot.


What is the most concise way to insert or update a line?

I write a lot of adhoc scripts for adding lines to sudoers, sysctl.conf etc.  Usually I use the lineinfile ansible module. Sometimes, however, I don't get to do that so I use :  WHAT_I_WANT='my line of text = something' WHAT_TO_REPLACE='my line of text = .*' FILE_TO_EDIT=conf_file.conf if ( ! grep -q "^$WHAT_I_WANT\$" FILE_TO_EDIT ); then     echo  "$WHAT_I_WANT" >> FILE_TO_EDIT else     sed -i "s/$WHAT_TO_REPLACE/$WHAT_I_WANT/g' FILE_TO_EDIT fi   My guess is there's a more efficient way to do this. Ideally with one line and one language (and also in a way that allows regexp matching, removing commented out lines and backing up files)  But I don't know what that is.


Suggestion about Peltier Efficiency With Current Power Setup

I am currently using the very arbitrary TES1-4902 to cool water (small amounts) using a 5V 2.4A USB Battery Pack (2 Peltiers TES1-4902, 2 5V 2.4 A USB Battery Packs = 5V 4.8A)    Recently, it has come to my attention that a different Peltier setup may be able to increase my efficiency, thus giving me more "bang for my buck".    The current situation that I am in is that I need to achieve the maximum cooling power to cool small amounts of water as quick as possible; however, I need to reduce power consumption so that instead of buying two 5v 2.4A USB battery packs I can buy 1, 3.4 A USB battery pack to support my project and thus reduce my price.   I know that the more power you put into a peltier, the cooler it gets, so less power is counter-intuitive: so I will split my question into two parts:   1) Is there a more efficient Peltier (where the rated IMAX/VMAX/DT is more efficient than what I have) that runs on a 5V 2.4A batterry, that takes into account more power is needed to start the Peltier than to run it continuously?    How about a 5v 4.8A  battery?   2) Using a 3.4 AMP, 5V USB Battery pack, is there any way I can achieve a similar cooling effect than what I currently have (TES1-4902, 5V 4.8A (2 of them)? by using a more efficient peltier?    Thank you so much, while someone answers me I am learning how to read data sheets more efficiently; however, so many of you are much more knowledgeable than me I thought it may be useful to ask you guys who have been so helpful in the past.   Thanks!!!


How do I know that the quantity of salt is enough for a given amount of flour?

When making bread during Ramadan, I can't taste the flour.  Is there a known ratio of salt to flour when making bread?


I'm having trouble setting up TauDEM to work in the processing tools of QGIS 2.0.1.  I download TauDEM from  and select "TauDEM 5.2 Command Line Executables for 32 bit Windows PC". I extract them to a directory called "C:\work\taudem".  I then go into QGIS processing menu > "Options and configuration" under TauDEM I set the "TauDEM command line tools folder" to "C:\work\taudem".  When I execute a TauDEM tool I keep getting errors saying:     Oooops! The following output layers could not be open.


Blender App opens in worst resolution and the info bar is invisible

Blender opens on a worst resolution, the the info bar isn't visible and edges of the app overlaps on the screen, I have attached the picture below.  Drivers are updated. Here are my machine specs   Windows 10 Pro 64 bit Core™ i5-7200U Integrated Intel® HD Graphics 620 8GB RAM     EDIT: I have Intel HD 620, and i real dont have a clue what drivers version works perfect with blender as for , its the (Intel HD 530 version 15.45.19.4678) that was causing problems.


I have a really weird error when trying to \cite. I watched several video tutorials on how to create a bibliography and after doing so created a .bib file (named "sqwg2)" with the following content:  % Encoding: ISO-8859-1  @ARTICLE{Keldysh,   author = {L. V. Keldysh},   title = {Ionization in the field of a strong electromagnetic wave},   journal = {Soviet Physics Jetp},   year = {1965},   volume = {20},   pages = {1307-1314},   owner = {Chris Ferris},   timestamp = {2014.02.18} }   After doing so, I went to my .tex file and created the bibliography as normal:  \bibliography{sqwg2} \bibliographystyle{eeh}   To make sure the citation would appear, I used   \citep{Keldysh}    at some random text passage. However, the citation shows only "(?)" and I get an error message saying "Citation Keldysh on page 1 undefined".   What makes this error even more weird is that when I type in "\citep{" I can see "Keldysh" in the drop-down list. Since it clearly recognizes the .bib file, I do not understand why it tells me that it is undefined...  Can anyone help me please? A google-search regarding this problem didn't help me.


A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.

The question is Q4.1.17(a) in Hungerford's Algebra:  If $R$ has an identity and $A$ is an $R$-module, then there are submodules $B$ and $C$ of $A$ such thatt $B$ is unitary $RC = 0$ and $A = B \oplus C.$ [Hint: let $B = \{ 1_{R}a | a \in A \}$]  But I can not see why $1_{R}a$ will be equal a and hence $B$ will be unitary or is it because of that $R$ has identity (a very trivial justification ), could anyone clarify this for me please?


How can I add a new screen resolution to an old laptop?

I have an old laptop (Esprimo Mobile). I am new to Ubuntu. I ran xrandr -q and the only option available is 640 x 480  $ xrandr -q  xrandr: Failed to get size of gamma for output default  Screen 0: minimum 640 x 480, current 640 x 480, maximum 640 x 480 default connected primary 640x480+0+0 0mm x 0mm  640x480 73.00*  1240x800_60.00 (0x288) 80.750MHz -HSync +VSync  h: width 1240 start 1304 end 1432 total 1624 skew 0 clock 49.72KHz  v: height 800 start 803 end 813 total 831 clock 59.84Hz –    This makes my windows on screen way too big. How can I fix them?  EDIT: Since posting I have managed to create a new screen resolution option. When I applied the 1240 x 800 resolution it made things worse, all the windows became even wider and the top bar stretched out so I couldn't see the far right corner. I switched back from the 1240x800 (3:2) to the 640 x 480 but i am back where I started. What do I need to change?


How can I start learning about political philosophy?

I'm interested in learning about political philosophy. What are the best ways to start? Are there any websites for beginners? Are there any books such as the "For Dummies" series? Are there any audio or video introductions to familiarize myself with the terminology?


Proof that the covariance equals to zero

let $(X,Y)$ is a random point.  $(X,Y)\in\{ (x,y): x^2 + y^2 \le 1\}$. Prove that the $\text{Cov}(X,Y)=0$. My approach was to use the covariance formula, and then try to write $Y$ as a function of $X$, but I got stuck because it's $\le$ and not $=$.


Should we do something about the [anonymous] and [anonymous-visitors] tags?

On Meta Stack Exchange, there are two tags,  and . These two tags are synonyms since the tag wiki of  says "This tag is for questions regarding anonymous users". The  tag, on the other hand, doesn't have any tag wiki, but I think that regarding its name it's fairly obvious that that tag is also about anonymous users.  I think that we should keep  because although it's less popular than , its name is less ambiguous. I've seen several cases where  was used in questions about the fact that voting is anonymous that have nothing to anonymous users. Here are a few examples:        I therefore suggest that all questions about anonymous users that are tagged  should be retagged to  (I personally think that it would have been better to call it  but since we already have  we might as well use it). The  tag could be made a synonym of  or simply burninated. If  becomes a synonym of , questions tagged  that aren't about anonymous users could be retagged manually (this shouldn't be too difficult since  only has 65 questions).


Matter and Antimatter (Hypothetical question)

What will happen if we somehow create an "anti-sodium "element and react it with "hydrogen"(not anti)?  I am specific about ANTI-SODIUM and HYDROGEN. Not just plain matter and antimatter.


Hadn't encounters with the Borg already occurred in the Neutral Zone prior to Q Who?

In the episode Q Who, at the end, Guinan says that the encounter with the Borg happened before it should have. Picard says "they will be coming" in response to Guinan saying that they are now aware of The Federation's (or humanity's) existence implying this was the Borg's first contact with them as well.  However, earlier in the episode, after Q first sends the enterprise light years away, when scanning a Class M Planet Worf comments that the suspected industrialized civilization that had been there there appeared to have been ripped away from the planet identical to what happened to the outposts along the Neutral Zone in the episode The Neutral Zone.  This made me think that in both cases the perpetrators were the Borg and that the Federation and the Romulans have encountered the Borg already.....just that no one's survived to report back.   If that is the case then didn't the Borg already know about the Federation? If Guinan was expecting the Federation to encounter the Borg much later, was she not aware that the encounter had already happened and they are already seen as they are just raw material for the Borg?


Bad URL check performed on edit, but not on initial question submission?

I am not sure if this is a bug or a design error, but I came across this issue on SE Information Security. I assume that the same code is employed across the various SE sites, so I am posting my question here.   I was trying to edit the question, , when I noticed that I could not submit the edit, due to a URL containing mydomain.net, which I had not added.    However, the question was obviously asked and entered with this URL in the body text, so was the same URL check not performed when the question was initially submitted? Here is the question containing the erroneous URL


How to add common Java Script function to all div generated dynamically?

How to add javascript function to all div, which are generated dynamically. In _data_grid.html, div bucket is generated dynamically with id forloop.counter0. I want to add common javascript function. Like Show and hide the some portion of div. All division are different and Want JavaScript function work separatel. How I will do that.   _data_grid.html
       {% for row in rows%}
             {{ row.render }}
         {% empty %}                                          {{ table.get_empty_message }}             {% endfor %}
   All division will work separately. Please see the following figure, If I click on hidecontent on 1st div then It will hide 1st div on other will hide, If I click on 2nd div then It will hide the 2nd div, no other div will hide.


Pathfinding for a destination that is more than 1 tile

I have a 2d grid, and there are situations where the player selects the 3d model of an exit (like a gate) so they could leave, but in reality, the exit is comprised of multiple tiles in the grid:  In this example, the exit is 4 tiles. Right now, I'm just thinking of brute-forcing it and doing pathfinding for each exit tile (that means, in the example, 4 times), and just choose the one with the shortest path, but I'm wondering if there is a more efficient way to do this. Maybe do it only on the extremities of the tile group (in the example, Exit 1 and Exit 4)? Maybe edit my A* code such that each tile being searched through has multiple heuristic scores (one for each possible destination tile)? Or maybe the heuristic score I assign is the average of all heuristic scores for each destination tile? I also want to take into consideration other situations in the future where the exit tiles are not necessarily adjacent to each other, even if collectively they are considered one single exit, like this:  So it should figure out that Exit 5 is the shortest path.


I have never even got 4 bio-hazards before.  What's required to get 5 bio-hazards when you win?


I am trying to implement a visual representation of linked list using tikz library.  The code written so far:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{shapes,arrows}  \begin{document} \tikzstyle{box}=[draw, fill=pink!10, text centered] \begin{figure}   \centering   \begin{tikzpicture}[node distance=0cm,outer sep = 0pt]     \node (A) [box,minimum height=7mm, minimum width=7mm] {\textbf{12}};     \node (B) [box,anchor=west,minimum height=7mm, minimum width=7mm] at (A.east) {\textbf{\textbullet}};      \node (C) [box, anchor=west, minimum height=7mm, minimum width=7mm] at ([xshift=10mm]B.east) {\textbf{98}};     \node (D) [box,anchor=west,minimum height=7mm, minimum width=7mm] at (C.east) {\textbf{\textbullet}};      \draw[thick,->] (B.center) edge [bend left=0]  node {} (C);   \end{tikzpicture} \end{figure} \end{document}   Things are looking good except the arrow getting out from node B (first bullet) has also a tip. How can I get rid of this?


First paper published, follow-up paper rejected by editor as out of scope?

I published an article few months ago in a journal. I sent another article to the same journal, in which I improved the design idea and enhanced the computation. I was told that my second article was sent to Prof. X (name was provided) as a topic editor.   After about 70 days, I got an editorial rejection due to the article not being within the scope of the journal. In the online submission site, it said that my article was under review for the last 70 days. In the end, my article was not even sent to referees... is that normal?


Switch to Console in Ubuntu 18.04 - How to Leave GUI?

To install the graphics driver I need to exit GUI / Gnome and go to the terminal. How can I do this in Ubuntu 18.04? Ctrl(STRG)+Alt+F1...F7 does not work, neither on the desktop, nor on the login screen...


Why limits give us the exact value of the slope of the tangent line?

Limits tell us how functions behave at $x\to a$, not how they behave at $x = a$. However, in limits we plug $x = a$ as an approximation of $x\to a$, so: why the limits give us the exact value of slope of the tangent line, despite being just an approximation of what happend around $x$?


Installing Eclipse IDEs for Java and C/C++

I'm running an Ubuntu 14.04 and want to install the Eclipse IDE for both Java and C/C++ programming. I installed the separate installation files from their official website. I followed this thread . (The top answer)   The steps helped me install the Java IDE but I don't know what changes I should make to the procedure to install the C/C++ IDE.   Another thread , recommended to install eclipse-cdt but the Eclipse version installed is outdated. (Doesn't allow me to install Pydev)   I have TWO questions:   Can the C/C++ libraries be downloaded from within eclipse, like Pydev? If not, how do I install both IDEs without interfering with each other?   P.S. I commented this query in the first thread but got no reply, that is why I'm asking a fresh question!


(C++) What are the Differences between these 3 type conversion methods?

Either of below methods gives me the same value when I use it on a char type variable. So what are the differences between them?  (int)c int{c} static_cast<int>(c)


What happens to tags with no associated questions?

There are some tags on that do not have any questions associated with them.   Are these tags deleted? Does having an excerpt or description change anything? When does this happen? Does the reputation for tag exceprt/description disappear after the tag is deleted?


What is $(65!)^2$ congruent to mod $131$?

So I'm trying to find a solution for the equation $$(65!)^2\equiv x\:(\text{mod}\: 131)$$ I'm given the hint to use Wilson's Theorem which states, that for a prime $p$ we have $(p-1)!\equiv -1\:(\text{mod}\:p)$.   The only thing I've managed to so far is insert my number in Wilson's Theorem: So I get $(130!)\equiv -1\:(\text{mod}\: 131)$. From here on I have no idea what to do.   Any help would be appreciated. Apologies for any english errors.


I am getting this error: System.LimitException: Too many SOQL queries: 101

I am getting this error System.LimitException: Too many SOQL queries: 101 when I run the class bellow. It seems like it is affecting all the triggers linked to NRProducts__c Object(This object has 45,000 records but the SOQL query should only return 7,000 ). I have a SetInterval JQuery function in the VF Page that clicks the a button every 20 seconds. My question is if I am making any mistake in the Classs code, or any ideas why this is happening. Thank you!  this is the whole error message:    System.LimitException: Too many SOQL queries: 101    Error is in expression '{!CreatePlan}' in component <apex:commandButton> in page   inventoryamzipa    Trigger.InventoryAdjCountsONProducts: line 4, column 1   This is the class:      public class InventoryAMZAPIController2{     public String Debug{ get; set; }      public InventoryAMZAPI2.CreateInboundShipmentPlanResult NewPlan{ get; set; }     public List<InboundShipmentPlanRequestItem> RemainingItems{ get; set; }       public void CreatePlan(){       Date target_date = date.today();       List<NRProducts__c> details = [SELECT NRName__c, AMZ_Inventory_Update__c, Active__c, isFBA__c  FROM NRProducts__c WHERE isFBA__c=true AND Active__c = true AND AMZ_Inventory_Update__c != :target_date  LIMIT 10];         Map<String, InboundShipmentPlanRequestItem> itemsMap = new Map<String, InboundShipmentPlanRequestItem>();         if(!details.isEmpty()){             RemainingItems = new List<InboundShipmentPlanRequestItem>();             for(NRProducts__c rl : details){                 InboundShipmentPlanRequestItem item = new InboundShipmentPlanRequestItem(rl.NRName__c);                 itemsMap.put(rl.NRName__c, item);                 RemainingItems.add(item);             }              //request values                 NewPlan = InventoryAMZAPI2.CreateInboundShipmentPlan(                 RemainingItems,                 'Basic'             );              Map<String, String> soDetailSkuMap = new Map<String, String>();               for(InventoryAMZAPI2.InboundShipmentPlan p : NewPlan.InboundShipmentPlans){                 soDetailSkuMap.put(p.SellerSKU, p.InStockSupplyQuantity  );               }              //Assign values to products             List<NRPRoducts__c> nr = [Select NRName__c FROM NRProducts__c Where NRName__c  IN: soDetailSkuMap.keySet()];             for(NRPRoducts__c detail : nr){                 detail.AMZ_Inventory__c = soDetailSkuMap.get(detail.NRName__c );                 detail.AMZ_Inventory_Update__c= date.today();                  update detail;                }           } else{          Debug = 'Done';          }      }      public class InboundShipmentPlanRequestItem extends InventoryAMZAPI2.InboundShipmentPlanRequestItem{         public InboundShipmentPlanRequestItem(String sellerSKU){             super(sellerSKU);         }     } }


Does the weight of iOS devices change based on storage size?

I don't think this is just true of Apple products but the weight advertised for iOS device model of varying storage size is always same.  For example . Is this the same for all models?  Does an increase in storage size add extra weight?  Is the weight difference so minuscule that it is not mentioned?


I am soon finishing my thesis and need some advice on how to create the cover/wrapper that surrounds the thesis (cover page + spine + back). Since it will be printed I also need to add some X's in the corners, so the printing comany will know where to cut the pages and finally I need 3mm of extra page color all the way around the page. I have tried to illustrate what I need to create here:    As you can see, I need 1 page that includes all (front, spine, back, crosses) and it should have a size of Width: 43.6cm height: 30.3cm.  Can you adwise me on how to proceed with this task? I also Wonder if there are some other tools for this, however, my thesis is written in with latex.  UPDATE I have tried to follow the other examples gives, but I cannot get it to Work. I hope some of you can see the problem :)  Here is a working sample:


Download OS update only once for all home computers

I want to upgrade all my home computers (4 macbooks running 10.8) to the new Mavericks OS.   I have a download cap, so i dont want to download it 4 times. How can i download it once and install it on all computers?


How long does it take for cows to grow up in Minecraft?

The title says it all, how long does it take for a cow to go from baby cow to cow. I'm using minecraft 1.7.2. Is there anyway to speed it up or slow it down? Thanks for you help.


It is well-known that $\sum_{n=0}^\infty x^n=1/(1-x)$. However, it seems difficult to find $\sum_{n=0}^\infty x^{n^2}$. A natural problem is study its behavior around $1$. A problem states that $$\lim_{x\to 1}\sqrt{1-x}\sum_{n=0}^\infty x^{n^2}=\sqrt{\pi}/2.$$  How can we prove this? Abel summation formula? Any others? I have no idea.


Question removed as spam, but title still remains in HTML, content visible elsewhere

Got a laugh over this one    ()  (just realized I screwed up my Freehand Circle--you can see the original title in the tab, as is shown by the html below)  The spam isn't scrubbed from various parts of the html, notably the header  <title>produce her with endless orgasms - Meta Stack Exchange</title>  <meta name="twitter:title" property="og:title" itemprop="title name" content="produce her with endless orgasms" /> <meta name="twitter:description" property="og:description" itemprop="description" content="[Edit: product name removed - OP] this can be a fashionable aphrodisiac native to Malaysia. In recent years, it has been shown to supply sexual enhancement effects in men because of its ability to boost testosterone " />   and answer sort tabs       active      oldest    I think at a minimum the title needs to be scrubbed. Scrubbing the title slug may also be warranted.


How to get the location of the program you're running and store it in a File object

I'm trying to find a way to reference my java program in order to check whether or not it's up-to-date, and I was wondering whether or not there is a special way of referring to it? For example, the person runs the program (I don't know where it is) and I want to compare it to a file I have on my web server to make sure it's up-to-date, but to do this I must have it stored in a File object in order to compare it to the one on my web server, how do I go about doing that? Is there a special way to find the location of the program that's being run?  Something like this:  File thisProgram = new File(?);   Not sure what to put inside the parenthesis in order to reference the program itself.


What does Linux accent-grave command do?

In a bash shell (A), typing an ` (accent-grave) will start another shell prompt (B). The output of any command entered in B is a command for A.   $ ` > whoami` -bash: Joe: command not found   (If my username were Joe.)   $ man ` > ` What manual page do you want?   Is there a man page for this, preferably with some examples?


How can I change the OS name from Ubuntu to something else?

I want that applications like System Monitor and Conky display the name MYOS instead of Ubuntu 11.10.  Also, I want lsb_release -a and etc. to show MYOS only.


I am using a custom UITableViewCell which has some labels, buttons and image views to be displayed. There is one label in the cell whose text is a NSString object and the length of string could be variable. Due to this, I cannot set a constant height to the cell in the UITableView's heightForCellAtIndex method. The cell's height depends on the label's height which can be determined using the NSString's sizeWithFont method. I tried using it, but it looks like I'm going wrong somewhere. How can it be fixed?  Here is the code used for initializing the cell.  if (self = [super initWithFrame:frame reuseIdentifier:reuseIdentifier]) {     self.selectionStyle = UITableViewCellSelectionStyleNone;     UIImage *image = [UIImage imageNamed:@"dot.png"];     imageView = [[UIImageView alloc] initWithImage:image];     imageView.frame = CGRectMake(45.0,10.0,10,10);      headingTxt = [[UILabel alloc] initWithFrame:   CGRectMake(60.0,0.0,150.0,post_hdg_ht)];     [headingTxt setContentMode: UIViewContentModeCenter];     headingTxt.text = postData.user_f_name;     headingTxt.font = [UIFont boldSystemFontOfSize:13];     headingTxt.textAlignment = UITextAlignmentLeft;     headingTxt.textColor = [UIColor blackColor];      dateTxt = [[UILabel alloc] initWithFrame:CGRectMake(55.0,23.0,150.0,post_date_ht)];     dateTxt.text = postData.created_dtm;     dateTxt.font = [UIFont italicSystemFontOfSize:11];     dateTxt.textAlignment = UITextAlignmentLeft;     dateTxt.textColor = [UIColor grayColor];      NSString * text1 = postData.post_body;     NSLog(@"text length = %d",[text1 length]);     CGRect bounds = [UIScreen mainScreen].bounds;     CGFloat tableViewWidth;     CGFloat width = 0;     tableViewWidth = bounds.size.width/2;     width = tableViewWidth - 40; //fudge factor     //CGSize textSize = {width, 20000.0f}; //width and height of text area     CGSize textSize = {245.0, 20000.0f}; //width and height of text area     CGSize size1 = [text1 sizeWithFont:[UIFont systemFontOfSize:11.0f]                         constrainedToSize:textSize lineBreakMode:UILineBreakModeWordWrap];      CGFloat ht = MAX(size1.height, 28);     textView = [[UILabel alloc] initWithFrame:CGRectMake(55.0,42.0,245.0,ht)];     textView.text = postData.post_body;     textView.font = [UIFont systemFontOfSize:11];     textView.textAlignment = UITextAlignmentLeft;     textView.textColor = [UIColor blackColor];     textView.lineBreakMode = UILineBreakModeWordWrap;     textView.numberOfLines = 3;     textView.autoresizesSubviews = YES;      [self.contentView addSubview:imageView];     [self.contentView addSubview:textView];     [self.contentView addSubview:webView];     [self.contentView addSubview:dateTxt];     [self.contentView addSubview:headingTxt];     [self.contentView sizeToFit];      [imageView release];     [textView release];     [webView release];     [dateTxt release];     [headingTxt release]; }   This is the label whose height and width are going wrong:  textView = [[UILabel alloc] initWithFrame:CGRectMake(55.0,42.0,245.0,ht)];


I want to develop a functionality for creating no more than one record per day. If more than one record is created should show error. How should I do this?


I am thinking of two circular gears with radii $R_1$ and $R_2=2R_1$. Gear 1 initially spins at $\Omega_1=10$ $rpm$ while the Gear 2 is at rest. After the gears come into contact, Gear 2 angularly accelerates and eventually reaches the steady speed $\Omega_2=20$ $rpm$. Gear 1 applies a torque $\tau_1=F_1 R_1$ on the second gear, correct? Why doesn't torque $\tau_1$ continue to increase the speed of the Gear 2? Why does $\Omega_2$ stop at 20 rpm? After all, an unbalanced torque should continue to provide angular acceleration... Angular speed is amplified from $10$ $rpm$ to $20$ $rpm$ but the torques are $\tau_2<\tau_1$. Is torque $\tau_1=R_1F_1$ the torque acting on Gear 1 or on Gear 2? Is the force $F_1$ acting on Gear 1 to keep it spinning at $\Omega_1$? Or is $F_1$ the force acting on Gear 2 to make/keep it spinning at $\Omega_2$? I am confused. Is $\tau_2=R_2F_2$ the torque that Gear 2 could apply to a 3rd hypothetical gear, if it came in contact with it, or is it the torque acting on Gear 2 itself? Thank you


Editing the "Self-Learner" Badge Description

Stemming from  the text for "Self-Learner" badge is pretty easy to get confused by.  Current Text     Answered your own question with score of 3 or more    Issue  The person in the above question was confused as they thought they needed to answer their own question, and that the question had to have a score of 3 or more. What it actually means is that they have to answer their own question, and the answer needs to have a score of three or more. The way it is phrased is ambiguous, so why not make it clear?  Suggestion  Edit the text as follows:     Provide an answer with a score of 3 or more to your own question   No more confusion.


Bascom uses a special format to comment out blocks of code. I want a RegEx that matches this block to be used in SyntaxHighlighter.  These comment blocks starts with '( and ends with '). Yep, it's so stupid.  Example input:      bla     '(     test     test     ')     blubb   I tried:     '\(.*?\)' and many others without success.  Expected return after replace:      bla     #####     blubb   where ##### is the replacement.  Basically just like C++ & similar /* .. */ rule. But I can't get it working.  Thanks in advance!


Would Harry still be a Parselmouth at the end of the Deathly Hallows?

Near the end of Harry Potter and the Deathly Hallows:      Voldemort "kills" Harry, destroying the part of his own soul that was in Harry.   Dumbledore tells us before this that:     Part of Lord Voldemort lives inside Harry, and it is that which gives him the power of speech with snakes, and a connection with Lord Voldemort's mind that he has never understood.   Given the above, does that mean that Harry would have lost his ability to speak with snakes at the end of the book? Or would his own mind have learnt Parseltongue from the thing that gave it to him, so that when that thing was gone he would still know how to talk to snakes? I don't think any mention of this is made in the book, but I'm very curious to know. It would be a shame if Harry was no longer a Parselmouth.


Scripted SQL Deployment in a Transaction with Rollback

Note: I believe this differs from other questions simply due to the size of the creation script I want to run under a single transaction.    Background  I'm working on automating the deployment of the data side of an application. I'm working with the team's existing scripts. They seem to drop everything and recreate. I don't have much time to make it perfect.  I'm thinking of running their drop-all script outside of a transaction, but running a single long "genesis" creation script inside a transaction at least so if that part should fail, its at a clean point and easier to recover from.  Genesis.sql contains 34k lines and seems to all be CREAT(ions) of functions, procedures, tables, types etc.  Question  Can I do this:  SET XACT_ABORT ON BEGIN TRAN  # Genesis!  COMMIT TRAN   ?  What's really confusing everyone is the impact of the GOs in the script with some saying that it will commit the transactions and other people (on the web) saying GO is just an instruction for the client to send a batch.  Follow-up  So far, this hasn't worked, new stuff is written and I see this message:     The COMMIT TRANSACTION request has no corresponding BEGIN TRANSACTION.   However, I think its mostly due to syntax errors in one or two scripts (that all get concatenated to 30k lines) and the parser is thrown out.  It seems I'll need to dummy run the scripts into an empty, local DB first, to discover syntax errors, then attempt against the target environment server.


If mastery of the Force is hereditary, how are the Jedi so numerous?

I can't seem to find a satisfactory answer to this anywhere on the web. While  poses a related question, I don't think it sufficiently answers mine...  During the opening chapters of Jedi Search, Luke addresses the new Senate on the need to find new Jedi talent, or Force sensitive individuals. During this proposal, he cites that the most fruitful leads of Jedi potential are in the descendants of Jedi Knights: as Force sensitivity is hereditary. The book even discusses the notion that Leia should be comparatively well attuned to the Force, due to her being the child of Anakin Skywalker.  I understand that the concept of the Jedi as a totally celibate and monastic order was something that was retconned into the lore after Episode II: Attack of the Clones, and that there are examples of entire nuclear Jedi families exist (such as Andur Sunrider and Plo Koon)...  But if Force-manipulative ability is passed down genetically (as a potentially mutative property of their genetic makeup), why would the Jedi order be so numerous if they practice Chastity?  Even if procreation is not expressly forbidden (as in the pre-retcon Expanded Universe): why would Jedi need special permission to produce more Jedi potential children?  How are more Jedi created, if not through procreation? Has their profusion been deliberately retarded, and if so why? is there another explanation for their (pre-empirical) plenitude?


How do beam weapons pass through a stargate differently to Puddle Jumpers?

Forgive me, I'm a late bloomer with regards to the Stargate TV series (loved Universe when originally shown, but never watched SG1 or Atlantis, until now, thanks to streaming services have begun binge watching) Was always a fan of the original Stargate movie. That background aside...   In Atlantis a puddle jumper gets stuck in a gate and it is said that nothing rematerializes at the other end until the entire object passes completely into the event horizon from the origin side. Yet a continuous beam is able to be fired through a stargate to attack the Atlantis' shields and must still be passing into the stargate while the front is emerging from the destination end.   How is this possible? does this not contradict the previous episodes? I know you could argue that the beam is made up of discrete packets of particles (pulses perhaps) but if that were the explanation then there would be no reason why the windscreen of the puddle jumper and the front crew couldn't rematerialize as they themselves were "discrete packets" compared to the puddle jumper's hull.   Is there an explanation in the series that I've missed or is this a plot loophole?


Connect 12V digital LED strip to Arduino

How to connect a T12V-10L-30LED-W LED strip to an Arduino?     is the strip specification. And here the actual image of the strip:   The package says: VCC: RED GND: WHITE DAT: GREEN  My question now is: Does the DAT input take 12V or something else? And how to wire this with an external 12V power source?


Problem adding difference of two timestamps in txt file in python

I have the following error when i try to add the difference of two timestamps in txt file in python TimeStamp3 = TimeStamp2 - TimeStamp1 TimeStamp3_str = TimeStamp_3.strftime("%d (%H:%M:%S.%f)") LogFile.write('Total time: ' + TimeStamp3_Str + '\n')   AttributeError: 'datetime.timedelta' object has no attribute 'strftime


Let $X,Y$ be topological spaces and $f \colon X \rightarrow Y $ continuous surjection. If $X$ is separable, is $Y$ separable?  I'm not sure if this is valid statement. I tried to show it directly but I got stuck. Then I tried to think of an counterexample but I couldn't. Any hint helps! P.S.


11 weeks and concern of THC in babys system at birth

I was a heavy weed smoker for the past 3 years, up until I found out I'm pregnant. I've completely stopped smoking now. So far, it's been 30 days and I'm 11 weeks pregnant but I recently took a drug test and it still came out positive. My concern is even if I've completely stopped smoking will my baby test positive for  at birth?


Should training data in each batch size be resample only one time or at each epoch when using mini-batch

I saw some related question regarding to the fact is one should use sampling with resampling or without when using minibatch.  However my question is different.  Let's assume that I use sampling witouth replacement. Meaning that for each epoch one training example can only belong one 'batch size' group.  I want to know if one should only resample the training data (into the different batch size) only 1 time or before to start to update the parameters before each epoch.  For instance suppose I have 20 'batch size' group. Suppose at the first iteration I have sampled picture A in group 2 and picture B in group 4.  If so should picture A always stay in group 2 and picture B in group 4. Or should I resample it before to start a new epoch (e.g. at epoch 2 put picture B in group 6 and picture B in group 20).


Finding a probability measure such that the time-shifted Brownian motion is also a Brownian motion

Let $T<\infty$, $(\Omega,\mathcal F,P)$ a probability space carrying a standard $d$-dimensional Brownian motion $(B_t)_{t\geq 0}$ and $(\mathcal F_t)_{t\geq 0}$ the natural $\sigma$-algebra filtration generated by $(B_t)_{t\geq 0}$, $\mathcal F=\mathcal F_T$. $(A_t)_{t\in[0,T]}$ is a continuous $R$-valued and strictly increasing $(\mathcal F_t)$-adapted processes satisfying $A_0=0$.  If we define $\tilde B_t:=B_{A_t}$ and $\tilde{\mathcal F}_t:=\mathcal F_{A_t}$, then we have that $\tilde B_0=0$, $E[\tilde B_t]=0$ for each $t$, and $\tilde B_t-\tilde B_s$ is independent of $\tilde{\mathcal F}_s$, but $E[\tilde B^2_t]\neq t$. So $(\tilde B_t)$ is not a Brownian motion under $P$.  I am wondering that if we can find an appropriate probability measure $\tilde P$ to make $\tilde B$ a standard Brownian motion under a new probability space $(\Omega,\tilde{\mathcal F},\tilde P)$?  My attempt: To make $(\tilde B_t)$ a Brownian motion, we only need to make it satisfy the Gaussian distribution $G$, so define the corresponding probability measure $\tilde P(\tilde B_t\in A):=G(A)$ for each $A\in\mathcal B(R^d)$.   I reffere to Theorem 3.4.6 in pp.174 of Brownian motion and stochastic calculus authored by Ioannis Katatzas and Steven Sherve, second edition. By this result, $(\tilde B_t)$ is a sandard Brownian motion if $(A_t)$ is a $\mathcal F_t$-martingale. Without this restriction, I can not obtain my desired result.


It is well known that the power set of a countably infinite set is uncountable. Therefore, if a power set is countable, then the cardinality of the set must below "countable". Formally, if $2^A$ is $\aleph_0$, then $A$ must be below $\aleph_0$.  However, I think $\aleph_0$ is the lowest possible cardinality? Are there any possible cardinalities between a finite set and a countable set?      From existing information we can only conclude that if $2^A$ is countable, then $A$ is “below countable”. How to prove that if $2^A$ is countable, then $A$ must be finite?


I installed YAPF formatter for Python code. Installation was successfull, no errors. Python 2.7.12  pip install yapf   Can't figure out how to run it: when run yapf -h, I get error 'unknown command'. Same when run python yapf -d file.py  Output of test commands:  $ type -a pip yapf pip is /usr/bin/pip bash: type: yapf: not found  $ echo $PATH /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin  $ ls -l {~/.,/usr/}local/bin/yapf ls: cannot access '/usr/local/bin/yapf': No such file or directory -rwxrwxr-x 1 username username 213 Jul 25 00:17 /home/username/.local/bin/yapf


Finding the Integer part of $\sum_{k=2} ^{9999}\frac{1}{\sqrt k}$

Question from Model Question Paper for B.Math/B.Stat:  by   Q. Assume the following inequalities for positive k:  $$\frac{1}{2\sqrt{k+1}}< \sqrt{k+1}-\sqrt k<\frac{1}{2\sqrt k}$$  The Integer part of:  $$\sum_{k=2} ^{9999}\frac{1}{\sqrt k}$$ equals:  A. $198$  B. $197$  C. $196$  D. $195$  My approach:  $$S=\sum_{k=2} ^{9999}\frac{1}{\sqrt k}$$ $$S=\frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+ \cdots + \frac{1}{\sqrt{9999}}$$ $$S=2\left(\frac{1}{2\sqrt 2}+\frac{1}{2\sqrt 3}+ \cdots + \frac{1}{2\sqrt{9999}}\right)$$ $$S\approx 2\left((\sqrt 2- \sqrt 1) + (\sqrt3- \sqrt2)+\cdots +(\sqrt{9999}-\sqrt{9998})\right)$$ $$[S]\approx2(\sqrt{9999}-\sqrt1)$$ $$[S]\approx 2(98)$$ $$[S]=196$$  I know my method is not an efficient one. Also I don't know if the answer is correct. Any help will be appreciated.


I am working on my Project in Netbeans entitled Car reservation system. I've encountered an error in my log in form codes. Once I clicked the login button java.lang.NullExceptionPoint error showed up.  Any suggestions for my codes? thanks  Here is my code:  private void cmdloginMouseClicked(java.awt.event.MouseEvent evt) {                                               // TODO add your handling code here:         String sql = txtusername.getText() + "'select * from tblelogin where username='" + "' and userpass='" + txtuserpass.getText() + "'";         try {             pst = conn.prepareStatement(sql);             rs = pst.executeQuery();             if (rs.next()) {                 JOptionPane.showMessageDialog(null, "Correct");              } else {                 JOptionPane.showMessageDialog(null, "Invalid username or password");             }          } catch (Exception e) {             JOptionPane.showMessageDialog(null, e);         }     }


How to hide dotted files when they reappear after closing file manager?

I have hidden my folders. They hide when I rename it starting with a  dot and enter ctrl+h. But when I close file manager and reopen it my hidden folders are shown automatically. So I want an answer so that I can keep my dotted folders hidden as most of them are confidencial. I have tried Nautilus but it did not work.


How to set up TrueCrypt "traveler disk" using Mac OS X?

I managed to encode my USB device having installed TrueCrypt on my Mac. I want to use the device with other Windows/OS X computers that may not have a version of TrueCrypt installed.  How do I get my USB to have the traveler disk setup that seems to be easily achievable through Windows, but apparently only there?


Irreducible polynomial which is reducible modulo every prime

How to show that $x^4+1$ is irreducible in $\mathbb Z[x]$ but it is reducible modulo every prime $p$?   For example I know that $x^4+1=(x+1)^4\bmod 2$. Also $\bmod 3$ we have that $0,1,2$ are not solutions of $x^4+1=0$ then if it is reducible the factors are of degree $2$. This gives that $x^4+1=(x^2+ax+b)(x^2+cx+d)$ and solving this system of equations $\bmod 3$  gives that $x^4+1=(x^2+x+2) (x^2+2x+2) \pmod 3$. But is there a simpler method to factor $x^4+1$ modulo a prime $p$?


How can I align the handles of control points from a curve?

I made a curve but part of the same curve doesn't fit in a regular line, I need to align the points/vertices with each other, how can I do this? I need to put those in order.


Regex for string which can contains either numbers, letters or a combination of both. Do not include symbols or special characters

I need to validate Username for an user for below condition.  username can contain letters, numbers or combination of both. Username must not contain any special characters such as @ $ % ^ & * () + = ‘ ~ - _"  Valid Examples: Test123 123Test T123est Invalid Examples: Test@%^&123 @#$Test Test123@#$%^ Below is the expression I tried: /[a-zA-Z\d]+/ /[^@$%^&()+=‘~-_"]/


Exception in thread "main" java.lang.NullPointerException in JBox2d

I'm trying to make a simple game in java with Box2D but it crashes 50% of the time.  Exception in thread "main" java.lang.NullPointerException     at Enemy.<init>(Enemy.java:41)     at Game.<init>(Game.java:27)     at Game.main(Game.java:110)  Process finished with exit code -1   Here's the function:  public Enemy(int size, World world, Player p) {         super(ID.Enemy,size);          Random rand = new Random();         Vec2 pos = new Vec2();         do pos.set(rand.nextInt(Game.width),rand.nextInt(Game.height));         while(pos.sub(p.body.getPosition()).length()<100.0);          BodyDef bodyDef = new BodyDef();         bodyDef.type = BodyType.DYNAMIC;         bodyDef.position.set(pos.x/10f,pos.y/10f);         this.body = world.createBody(bodyDef);         CircleShape shape = new CircleShape();         shape.setRadius(size/10f);         FixtureDef fixtureDef = new FixtureDef();         fixtureDef.density = 1;         fixtureDef.restitution = 0;         fixtureDef.shape = shape;         body.createFixture(fixtureDef);         body.setUserData(this);          this.target = p.body.getPosition();         this.dir = new Vec2();      }   The compiler says the problem is on the line  body.createFixture(fixtureDef);


Iphone 5s Activation no Sim card installed?

hi i buy iphone 5s in uk but my mobile not Activate. That error is saying no sim card installed. now I'm in India i don't have sim card how to activate my Iphone. That Iphone not asking Apple ID.


ESTA return, does the “clock” reset when travelling across Panama - Cuba?

I'm currently staying in the US under the ESTA, but later on I'll travel to Panama, then to Cuba, and from there through Mexico back to Miami, where I'm catching a flight back to London. The thing is, my ESTA 90 days period will end during my visit in Cuba, but as far as I know, visiting Panama should be reseting the 90 days “clock”. My question is, is the ESTA trip period going to be reseted despite of coming back to US through Mexico which doesn't apply for the 90days count reset? Will I have to proove that I've visted Panama as well?  Thank for any advices and sorry for the long post!


I'm new to PHP and programming, but I started building my own website, which will need a registration site woth the following PHP code:  <?php $fnameErr = $lnameErr = $emailErr = $pwErr = $pw_confErr = ""; $fname = $lname = $email = $pw = $pw_conf = "";  function test_input($data) {   $data = trim($data);   $data = stripslashes($data);   $data = htmlspecialchars($data);   return $data; }  if ($_SERVER["REQUEST_METHOD"] == "POST") {   if (empty($_POST["fname"])) {     $fnameErr = "(Please submit first name)";   }    else {     $fname = test_input($_POST["fname"]);   }    if (empty($_POST["lname"])) {     $lnameErr = "(Please submit last name)";   }    else {     $lname = test_input($_POST["lname"]);   }    if (empty($_POST["email"])) {     $emailErr = "(Please submit email address)";   }    else {     $email = test_input($_POST["email"]);     if (!filter_var($email, FILTER_VALIDATE_EMAIL)) {       $emailErr = "(Email address is not valid)";      }   }    include ("email_compare.php");    if (empty($_POST["pw"])) {     $pwErr = "(Please submit password)";   }    else {     $pw = test_input($_POST["pw"]);     $pwHash = password_hash($pw, PASSWORD_DEFAULT);   }    if (empty($_POST["pw_conf"])) {     $pw_confErr = "(Please confirm password)";   }    else {     $pw_conf = test_input($_POST["pw_conf"]);   }    if ($_POST["pw"] !== $_POST["pw_conf"]) {     $pwErr = "(Please confirm password)";     $pw_confErr = "";   }     if (empty($fnameErr) && empty($lnameErr) && empty($emailErr) && empty  ($pwErr) && empty($pw_confErr))   {     include ("db_add.php");      header('Location: register_success_en.php');     exit;   } } ?>   I just found out, that data, that should be included into MYSQL should be escaped by mysqli_real_escape_string, but I already use my test_input function, which, in my opinion, has the same effect.  So my question: is the test_input function sufficient or should I also use mysqli_real_escape_string?   Thanks in advance!


Globally customizing the style of figure captions

Is it possible to globally alter the way figure captions are rendered? For example, I might want to wrap all captions in \textit to better distinguish captions from regular text.


Remove votes to close question X as a duplicate of Y if question Y is closed as a duplicate of X

I just happened across , which has one close vote suggesting that it be closed as an exact duplicate of .  This suggestion is perfectly correct: these are exactly identical questions asked by the same user.  However, there's not much point in closing question A as a duplicate of B, since question B has already been closed as a duplicate of A.  Yet the close vote remains, doing nothing but wasting reviewers' time.  This is not the first time I've seen this happen, so I'd like to suggest that the Stack Exchange software should do something about it.  In particular, I'd like to suggest the following feature:     When a question Y is closed as an exact duplicate of another question X, any votes or flags to close X as a duplicate of Y should be automatically discarded.   Actually, I'm kind of surprised that the SE software doesn't do that already.  If anyone else thinks that this constitutes an actual bug, feel free to retag it.


Can Mann Whitney U test be used for uneven sample sizes?

N1=240 N2=260  Also a reference to your answer would be great please!


How to create 3 columns from 2 columns with SQL query?

I have the following table, Table1:  Id, Speed, Power 1, 1000, 100 1, 2000, 150 1, 3000, 200 2, 1000, 125 2, 2000, 175 2, 3000, 225   I would like to know SQL syntax to return the following:  Speed, Power600V, Power750V 1000, 100, 125 2000, 150, 175 3000, 200, 225   I tried this:  SELECT Speed, Power as Power600V From Table1 WHERE Id=1 UNION SELECT Speed, Power as Power750V From Table1 WHERE Id=2   It isn't returning the data the right way though.


Lots of tags breaks mobile responsive layout

I really hope this is a duplicate.  Here is a screenshot:  When a post has lots of tags on the mobile responsive layout ('full site' in the footer), they don't wrap round and you end up with horizontal scroll bars. Expected The tags wrap nicely onto the next row. Actual They don't.


Why is my MacBook Pro already using swap memory?

I have a late 2013 MacBook Pro 13" with 8 GB of memory. Lately my MacBook Pro uses swap memory, when it has enough free memory. Is this normal and can I do something about it? Also when I only have safari and let's say Xcode open it uses 99% of the RAM. Is this normal behavior?


The campingList JavaScript controller isn't setting the 'item' as a parameter or saving the record correctly

I have been through several posts on workarounds to this issue where the code works, but the challenge is not passed, none of the proposed solutions seem to work for me:      in the last one Jeff Douglas seems to mention some code change/enhancement to the trailhead module.  Here is my handleAddItem function from the CampingListController.js:      handleAddItem: function(component, event, helper) {     var addItm = event.getParam("item");     helper.createItem(component, addItm);  },   and createItem from the helper:  createItem: function(component, newItem) {     var action = component.get("c.saveItem");     action.setParams({         "item": newItem     });     action.setCallback(this, function(response){         var state = response.getState();         if (component.isValid() && state === "SUCCESS") {             var items = component.get("v.items");             items.push(response.getReturnValue());             component.set("v.items", items);             component.set("v.newItem",{'sobjectType':'Camping_Item__c',                                'Name': '',                                'Quantity__c': 0,                                'Price__c': 0,                                'Packed__c': false});         }     });     $A.enqueueAction(action);       I posted the images of the rendered component after submitting the form and the record that is created from the apex method to the DB.  Any idea why the challenge is not passed?


List all Points within Polygon using QGIS?

Complete newbie to QGIS and can't seem to find how to do this.  I have created a map with 84 different polygons.  Then I've imported approx. 8000 points.  What I want to do is now query my map and get it to tell me the polygon each Point is in and then be able to extract this into a text or CSV file.  Can anyone help?


What is the etymology of the 'here' in the expression 'these here'?  I am unable to find a dictionary definition, although I believe the expression could also be simply these, or even those.  So why did the 'these here' construct come about? It sounds like dialect, which isn't always explainable, but I'd appreciate any actual references to why and where it came about. An example is:     Probably she was one of these here New Women. (The Wheels of Chance, H.G. Wells)     It also can be formed with other demonstrative determiners, while using either adverb 'here' or 'there', for example:        This here   Those here   That there


How to find all subgroups of a direct product?

I am wondering how do we find all subgroups of a direct product? Is there a method to find it?  For example, how can we find all the subgroups of $\mathbb{Z}_2\times\mathbb{Z}_2$?  There is the answer: $\{(0, 0), (1, 0)\}, \{(0, 0), (0, 1)\}, \{(0, 0), (1, 1)\}$, and the improper and trivial subgroup. But I do not know the method how to find it.   All I can think about is the following: since the order of $\mathbb{Z}_2\times\mathbb{Z}_2$ is $4$, the order of a subgroup of it can be $1,2$ or $4$.   If order is $1$, then it is trivial, and if order is $4$, it is proper. Then, the order of a subgroup is $2$. We know all the elements of   $\mathbb{Z}_2\times\mathbb{Z}_2$, so we try all the pairs.   Is that the method?   But what if we are given a bigger order product, such as $\mathbb{Z}_2\times\mathbb{Z}_8\times\mathbb{Z}_3\times\mathbb{Z}_9$? It looks very long to try all possibilities.   Can anyone help?  Thanks


How to remove the "mystartsearch" browser redirect malware?

I keep deleting the search engine on Firefox, yet every time I restart Firefox it shows up again.  I am setting Google as default.  How can I remove "mystartsearch"?  This is not something similar with removing virus. This is removing annoying setting that don't get off the easy way. And I already know the answer.


Does "snapshot" command exist like in Linux Redhat?

I used to use "snapshot" command to capture screen shots in the Linux Redhat environment. Is there the same or similar command with ubuntu 12.04 LTS?


Download a file using C# from a URL into a MVC.Net Application directory

How Can I download a file from a url, let's say:   https://example-my.sharepoint.com/personal/Documents/MyExample.docx   using c# and save it in a folder into my MVC Application on the server. Is there any way to do it?  Thanks.


Is there a way to randomly choose value from hashmap by key?

Suppose that I have two ImageButtons, a HashMap, and pictures in drawable(resources) that are placed in this HashMap as a value. I need to randomly choose a value from the HashMap by key using Randomizer and then assign this value (that is a picture) to the ImageButton as it's background. For example, if the first button is clicked, the second button's background will be randomly changed.  So this is what I already have:    public class MainActivity extends Activity {    final Resources res = getResources();   final Random random = new Random();    final ImageButton imgButt1 = (ImageButton) findViewById(R.id.imageButton1);   final ImageButton imgButt2 = (ImageButton) findViewById(R.id.imageButton2);    @Override   protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     setContentView(R.layout.activity_main);      Drawable coub1 = res.getDrawable(R.drawable.coub1);     Drawable coub2 = res.getDrawable(R.drawable.coub2);     Drawable coub3 = res.getDrawable(R.drawable.coub3);     Drawable coub4 = res.getDrawable(R.drawable.coub4);     Drawable coub5 = res.getDrawable(R.drawable.coub5);     Drawable coub6 = res.getDrawable(R.drawable.coub6);     Drawable coub7 = res.getDrawable(R.drawable.coub7);     Drawable coub8 = res.getDrawable(R.drawable.coub8);     Drawable coub9 = res.getDrawable(R.drawable.coub9);     Drawable coub10 = res.getDrawable(R.drawable.coub10);      final Map<Integer,Object> someHashMap = new HashMap<Integer,Object>();     someHashMap.put(1, coub1);     someHashMap.put(2, coub2);     someHashMap.put(3, coub3);     someHashMap.put(4, coub4);     someHashMap.put(5, coub5);     someHashMap.put(6, coub6);     someHashMap.put(7, coub7);     someHashMap.put(8, coub8);     someHashMap.put(9, coub9);     someHashMap.put(10, coub1);      imgButt1.setOnClickListener(new OnClickListener() {          @Override         public void onClick(View v) {              Object[] values = someHashMap.values().toArray();             Object randomValue = values[random.nextInt(values.length)];             int drawableID = values.;             imgButt2.setBackgroundResource(drawableID);         }     });      imgButt2.setOnClickListener(new OnClickListener() {          @Override         public void onClick(View v) {              Object[] values = someHashMap.values().toArray();             Object randomValue = values[random.nextInt(values.length)];             int drawableID = myImages.getResourceId(randomInt, -1);             imgButt1.setBackgroundResource(drawableID);         }     });   } }


Is the curvature of spacetime in General Relativity instantaneous?

Assume one initially has perfectly flat Minkowski vacuum. At some point in this Gedankenexperiment a point mass spontaneously appears at some location in Minkowski creating a Schwarzschild geometry. At some interval from the location of this point mass, how much proper time does it take for the space to appear Minkowski? Is there some sort of gradual change in the metric from Minkowski to Schwarzschild or does this change occur instantaneously?


Problems with fglrx driver on AMD Radeon 8000M series on Trusty

I have tried installing proprietary drivers from the "Software & Updates dialog" and also from ATI's latest driver .   The problem I am facing is that the binaries aren't in the path, and trying to run them with the full path gives me the following error.  atoulan@atoulan-laptop:~$ sudo /usr/lib/fglrx/bin/aticonfig  Unable to open /etc/ati/control, please reinstall the driver. /usr/lib/fglrx/bin/aticonfig: No supported adapters detected   Here is the output from lspci:  atoulan@atoulan-laptop:~$ lspci | grep VGA 00:02.0 VGA compatible controller: Intel Corporation 4th Gen Core Processor Integrated Graphics Controller (rev 06) 01:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] Mars [Radeon HD 8670A/8670M/8750M] (rev ff)   and uname:  atoulan@atoulan-laptop:~$ uname -a Linux atoulan-laptop 3.13.0-29-lowlatency #53-Ubuntu SMP PREEMPT Wed Jun 4 21:27:51 UTC 2014 x86_64 x86_64 x86_64 GNU/Linux   According to AMD's page my card should be supported by this driver. Of course every time I try out a new driver I purge the old ones.   Can anyone tell me how to install this driver properly ?  Thanks.


At which level does a Glamour bard cast the Command spell when they activate Mantle of Majesty?

At level 6,  gain the Mantle of Majesty feature (XGtE, p. 14):     At 6th level, you gain the ability to cloak yourself in a fey magic that makes others want to serve you. As a bonus action, you cast command, without expending a spell slot, and you take on an appearance of unearthly beauty for 1 minute or until your concentration ends (as if you were concentrating on a spell). During this time, you can cast command as a bonus action on each of your turns, without expending a spell slot.   However it doesn't really mention at what level you cast command at. Do you use it as a level 1 spell, or at the highest spell slot you can cast at your level?


How to ignore an output of a multi-output function in Python?

Suppose I have a function:  def f():   ...   ...   ...   return a,b,c   and I want to get only b in output of the function. Which assignment I have to use?  Thanks.


Let a, b and c be natural numbers. If a^2 = bc and gcd(b, c) = 1, then there exist natural numbers s and t such that b = s^2 and c = t^2 .

We were given this proof under our Fundamental Theorem of Arithmetic section and it is supposed to involve prime factorization. I'm totally lost so far and could use any help you can offer.


How to show that $\langle a \rangle$ is a subgroup of a group $G$, where $a$ is in center of the group $G$

How to show that $\langle a \rangle$ is a subgroup of a group $G$, where $a\in Z(G)= \{x \in G ∣  xg = gx ~ \forall g \in G\}$, the center of the group $G$.  I am unable to show this result. Although I know that $Z(G)$ is a subgroup of $G$.


Why were these items on the Millennium Falcon?

The Falcon appears to contain       another copy of the Jedi sacred texts   How did they come to be located on the ship?      Did Obi-Wan leave it there when he was aboard? Did Han and/or Chewie pick it up at some point? Did they know what they had?


What is the origin of "a cut above/below the rest"?

Where did the phrases "a cut above the rest" and "a cut below the rest" come from? I'm supposing they came from the same source. I feel it something very obvious, but I don't know what.


Was warp technology ever used as a weapon?

In any Star Trek canon, was warp technology ever used to intentionally damage something? According to physics as we know it, the ability to deliver a payload (even a relatively small one) at relativistic speeds would be devastating to virtually any target (trust me, don't stand in the way of the LHC beam). Since warp drive allows ships to travel even faster than light, one would think that would only increase the damage it could do if slammed into another ship.  Was warp drive ever used to propel a projectile (or even a full ship) into a target? If no, is there any reason given as to why not?


This is a question from Stein & Shakarchi's complex analysis book.  Show that if $\rho$ is fixed with $Im(\rho)>0$, then the Jacobi theta function $$\theta(z|\rho)=\sum_{n=-\infty}^\infty e^{\pi in^2\rho}e^{2\pi inz}$$ is of order 2 as a function of z. And here's the hint from the book:  $-n^2t + 2n|z| \le -(n^2t)/2$ when $t \gt 0$ and $n \ge 4|z|/t$  I've been teaching myself complex analysis with Stein's book but it's pretty difficult to do so. I can't quite figure out the steps to do a problem. Any help?


One source of light is, IIRC my high school physics, when an excited electron jumps back to its normal position. This jump generates a photon. How can an event like that shoot of a particle at the speed of light? Why isn't it this photon moving much slower? Other particles can move at almost the speed of light but typically is much slower..


How to grant Windows 8 admin rights without admin account?

Unfortunately I derp'ed and locked myself out of my admin account. I have a non-admin account that I can still log onto. I don't have access to another computer to try some of the many other methods of getting past and reseting the admin passsword, but I need to either grant myself admin rights so I can get back on or reset the admin password from a non-admin account.  Is there any way to do this? Any sort of registry editing I can do as a regular user?  Thanks.


Unable to match results that contain apostrophe

I have a db table that contains some business names.  I need to query by name and usually have no problems unless the name contains an apostrophe.   (" SELECT* FROM t1 WHERE bus_name = '".$busName."'  ")   I've experimented and tried using static value, like this:  (" SELECT* FROM t1 WHERE bus_name = \"Bob's store\"  ")   and it worked. Tried:  (" SELECT* FROM t1 WHERE bus_name = \"".$busName."\"  ")   and it doesn't. What am I missing?


How to change the value of a div dynamically on each click

I have got a task to create a game. For that I need some help... How can I change the value of a div by clicking on it?

Two

   js code :   $( ".block1" ).click(function() {           $( "#one" ).css('display','block');           $( "#two" ).css('display','none');           $( "#three" ).css('display','none');           $( "#four" ).css('display','none');               });


Why do we use "if" in the definitions instead of "if and only if"?

I often write my notes as logical statements and constantly wonder why people use only the "if" direction in the definitions instead of the "if and only if". Consider:  "A homomorphism $\phi$ is said to be an isomorphism if it is an injection  and a surjection." would translate to:  $homomorphism(\phi) \wedge injection(\phi) \wedge surjection(\phi) \implies isomorphism(\phi)$  By adding the following statement consistent with the previous one:  $homomorphism(\phi) \wedge \neg injection(\phi) \wedge surjection(\phi) \implies isomorphism(\phi)$  we could deduce  $homomorphism(\phi) \wedge surjection(\phi) \implies isomorphism(\phi)$  which is obviously not what we intended to express in the definition, however the intention does not imply the deed.  From the strict logical perspective do you agree that all definitions of this form are "flawed" owing to the lack of the attention to details? Or is there some reason which I have not managed to observe that explains why "if" is used in lieu of "if and only if"? Would you accept if I write in papers definitions in the iff version? I.e. "A homomorphism $\phi$ is an isomorphism if and only if it is an injection and a surjection."


I'd like to open a website at regular intervals per day, i.e., the browser should open and automatically navigate towards a pre-set URL.  I looked at options like scheduling to open browser, but I can't figure out how to open it with a default URL. (No I do not want to make this my start page)  Any help is appreciated


Is it possible to have a magnet which looks like a hollow cylinder and who's north is interior and south is exterior?  What then happens as the cylinder gets longer?  Would that affect the strength of the magnetic field?   Cut side view:       .  Approximated axial view:                       .          South          .       South    ______________     .       _____    |______________|    .     / _____ \                        .    / /     \ \        North          .   | | North | |    ______________     .    \ \_____/ /   |______________|    .     \ _____ /        South          .       South    I think it should be possible, but when extruding it longer, its properties get fuzzy to me.  I would assume that there would be a lot of stress on the structure as it gets longer, to try and break the cylinder apart.  EDIT But what would happen to the strength of the field as the cylinder got longer?  Would the field strength at the ends of the cylinder get stronger or approach a maximum?  Further, what would happen if the cylinder became bent around so that the ends touch?  Would there only be a south visible on the outside?  AFAIK, there must be a magnetic field line that goes from the south to the north from the same physical object, so would that mean that the field would try and reenter the physical object and cancel out the field?  (EDIT According to  post, it would cancel out)  Also, what would happen to the field lines as the ends approach each other?  Is there some way of visualizing the field as this occurs?  A sim programme perhaps?


Schengen tourist visa right after student visa expires (South Korean passport holder)

I have a passport from South Korea, and I have a student visa from the Czech Republic valid from January 2017 to september 2017. I moved to Germany on  31st of August and I'm still here. (6th September)   I'm planning to go back to Prague end of this month to apply for a Czech work permit with my boss (it is after my student visa expires, and this month i'm staying in Germany, so meanwhile I need either a temporary residence permit here in Germany or 3 months visa free status(tourism purpose)).  -i know SOUTH KOREAN national applies to 90/180 days schengen visa free tourism system/law.  I asked Ausländeramt (foreigner office) if I can get a temporary residence permit after explaining my situation, but then the guy said I can stay for 90 days, which is until November without visa/residence permit as a tourist.   Since my Korean and Japanese friends told me that I need to get out of the Schengen area and come back, I thought he didn't understand my situation so I explained again and again. He kept saying I am fine.  And from some posts from here the answers said it will be fine as well.  I am afraid of asking the Ausländeramt guy again (in case I'll need to get a temporary residence permit and if he gets fed up with my emails, he won't give me that lol. yup. Germany).  So my question is, am I entitled to that 3 months(tourism purpose) visa free status in Germany right after the expiration of my student visa from the Czech Republic?   (Just in case you are curious what the foreigner office guy said, this is the last email I got from him (I know what he said in this email.) after explaining my situation and he also has a scan of my passport and visas).  Ein aller letztes Mal. Sie hatten ein tschechisches Nationalvisum, sind dann am 31.08.2017 in die Bundesrepublik Deutschland eingereist. Was bedeutet, dass Sie sich in dieser zu touristischen Zwecken bis zum 29.11.2017 aufhalten können ohne ein Visum zu benötigen. Sollten Sie planen über diesen Zeitraum hinaus in der Bundesrepublik zu bleiben, so brauche ich die bereits von mir angeforderten Unterlagen von Ihnen. Eine andere Möglichkeit besteht nicht.)


Closed form expression for for $\sum\limits_{i=0}^{\infty} i^2\cdot x^i$

I understand that $\sum\limits_{i=0}^{\infty} x^i$ is $1/x-1$ and I know that $\sum\limits_{i=0}^{\infty} i\cdot x^i$ is $x/(x-1)^2$ but the $i^2$ in the original problem throws me off and I don't know how to differentiate to get it. Can someone show me the solution?


OSX (Yosemite) Make 2 sided printing the default for *all* applications

I'd like to make double-sided printing the default for all applications.  This  tells how to set it for one application, but by experimentation it only affects that application, not others.  I Googled, looked in the system prefs, looked on this site - no luck.  Is there a setting somewhere?


I'm trying to find the distance between two bluetooth beacons which are typically in the distance of 60cm or less. Direction is not an issue, I'm only looking to figure out the distance between the beacons and there will be no interferences such as walls/objects in between. Is it possible to detect the distance through RSSI Measurements? and if so what will be the expected accuracy?


How to know where to put bias terms in neural nets?

I've read different places that talk about bias terms in neural nets like this    But I still have trouble understanding what it is used for and how it affects the neural network.  In a neural network, where would you place it? There can be hundreds of neurons, how do you know which one to link it to? And how many bias terms do you need? How do you know you need one?  Can anyone explain?


find an injection $h:\{\mathbb{N}\to\{0, 1\}\} \to A$ while A = {f : N → Z|∀n, m ∈ N.(n > m) → (f(n) < f (m))}

How can I find an injective function from $h ∈ (\mathbb N → {0, 1}) → A$. $A = \{f : N → Z|∀n, m ∈ N.(n > m) → (f(n) < f (m))\}$?  I was trying to define it as follows:  $h=-n-f(n)$, but I know that doesn't work since it only maintains $f(n) \leq f (m)$ but not $f(n) < f (m)$.  Would love to hear your thoughts.


How does Hogwarts manage to track the Dursleys' and Harry's movements in "The Philosophers Stone"?

In the seventh book, Harry wonders if 'the trace' is still on him after his seventeenth birthday, as the Ministry of Magic/Death Eaters keep managing to track him, Hermione and Ron down. It is later revealed that Voldemort's name has been "tabooed", so that the location of anyone speaking it will be revealed, and the However, in the first book, 'the trace' would only have worked if Harry was using magic- which, aside from setting a Boa Constrictor on Dudley, does not happen. The address(es) on the Hogwarts acceptance letter(s) sent to Harry are very specific:  "Mr H. Potter, The Cupboard under the Stairs, 4 Privet Drive, Little Whinging, Surrey"   "Mr H. Potter, The Smallest bedroom, 4 Privet Drive, Little Whinging, Surrey"   "Mr H. Potter, Room 17, Railview Hotel, Cokeworth"  At first I thought that the Anthony Horowitz book "Groosham Grange" (which was published a decade before Harry Potter and ) might help provide an answer, as in the book a black crow is sent by the school to watch David. However, there are no mentions of Owls/other birds except for the ones delivering the (already addressed) mail. It's possible that professor Trelawney used a crystal ball or her prophecy powers to watch Harry's movements, however, in 'The Prisoner of Azkaban', Dumbledore comments:  'Do you know, Harry, I think she might have been,' he said thoughtfully. 'Who'd have thought it? That brings her total of real predictions up to two. I should offer her a pay rise…' (PA22)"  As her first real prediction was the prophecy "neither shall live while the other survives", and the second was the one about "the servant returning to his master". Crystal-ball-gazing doesn't seem to extend to present events as such, and in any case, Dumbledore admitted in the quote that she wasn't a great seer, so what I'm wondering is: How did the Hogwarts professors know (and in such great detail) where Harry was, and; Why couldn't this method be replicated in later books (such as when the Death Eaters wanted to track Harry)? Additionally, does anyone have any idea how (Wizarding-world) Owls can manage to track people with no addresses written on them? E.g, in book 4, (aside from being a super-smart bird) how is it that Hedwig can easily find where Sirius is?


I have recently come across awk seen option. I can see it is removing duplicates in files. But unsure how it works tried google but didnt find any results, need help in clarification for the same. cat tes 1 2 3 1 1 1 3 4  with awk seen output cat tes | awk '!seen[$0]++'  1 2 3 4


Is this form of epsilon delta version of Limit valid?

Just a thought came in my mind , i understand the original def of epsliom delta version of limit . Why cant the limit definition be based on" for every delta there exits epsilon thing such that..."? Why the mathematicians give def for "every epsilon there exists delta such that..", was there some kind of contradiction in that def for some  functions where it was not valid? Hence the epsilon to delta was selected ?


Do opposite counters coexist or cancel each other out?

Nuance abounds nowadays; whereas it was commonplace to mentally coalesce opposing counters on a permanent, I imagine doing so is incorrect.  Scenario 1 Suppose one Sengir Vampire has amassed five +1/+1 counters from having sent five creatures to the graveyard, and it is now blocking a Regeneration-enchanted Putrefax, a 5/3 whose infectious damage is dealt in the form of -1/-1 counters.  Does Sengir Vampire have zero counters, or ten counters?  Scenario 2 Rabid Wombat, green 0/1, which gains +2/+2 for each enchantment on it, enchanted with Unstable Mutation, which gives it +3/+3, and gives it a -1/-1 counter during controller's upkeep. Is this accurate?  Consecutive Turns: 0/1. Rabid Wombat cast. 5/6. RW+Unstable Mutation. 3/4 + a 2/2 counter 4/5. 3/4 + a 2/2 counter + -1/-1 counter 3/4. 3/4 + a 2/2 counter + (2 x -1/-1 counters) no cancellation here? 2/3. 3/4 + a 2/2 counter + (3 x -1/-1 counters) ... .. etc. correct?  Scenario 3 Rock Hydra comes into play with casting-time X +1/+1 counters, and receives damage in the form of loss of the counters. If it becomes infected by Putrefax, which deals damage as -1/-1 counters, is the infection essentially redundant to Rock Hydra's normal life cycle? Or does the state-based action's removal of the counter count as damage which then removes another head?  Is reduction of a creature's toughness due to counter-based actions considered damage?


What's this? What is it? but not What's it? - Why?

Can anyone give a cogent, simply described explanation of why the verb BE in:  What is it?  ... doesn't seem to be able to be contracted with the subject:  What's it? *  Compare the sentences above with:  What's this? What's that?  These are perfectly fine. In fact, the contractions here should be expected in almost all examples of spoken English. Answers with references to authoritative vetted sources would be greatly appreciated.


Ubuntu installer and grub don't see Windows installation

On a system with nvme memory, I installed (K)ubuntu 19.04. The installer did not detect the preinstalled Windows 10 installation and only offered a complete wipe. So I prepared the disk with parted and did a manual install.  Disklabel type: gpt  Device             Start       End   Sectors   Size Type /dev/nvme0n1p1      2048   1026047   1024000   500M EFI System /dev/nvme0n1p2   1026048   1288191    262144   128M Microsoft reserved /dev/nvme0n1p3   1288192 283981890 282693699 134,8G Microsoft basic data /dev/nvme0n1p4 283983872 285702143   1718272   839M Windows recovery environment /dev/nvme0n1p5 285702144 498561023 212858880 101,5G EFI System /dev/nvme0n1p6 498561024 500117503   1556480   760M Linux swap   However, update-grub can't detect the windows installation (even when the windows partition is mounted) and I can't boot into Windows any more.  I've tried boot-repair with different options, but no avail. Here is my updated bootinfo generated by boot-repair:   Questions:   Why is Windows not in the GRUB menu? How can I revive Windows 10?   How come the installer doesn't offer the "install alongside windows" option? Why is boot-repair failing? Can it handle nvme media? Is it outdated?   It doesn't seem these questions are answered in