How can you tell if something is a CFG or not? I am wondering if you could create a math/LaTeX parser using a parsing expression grammar (PEG), or not. Is this possible, and how can you tell?

I'm looking for a BNF grammar of the TeX language, does it exist?  EDIT  For those of us who are not computer scientists, a BNF grammar is one kind of formal description of a CFG: .  For those who don't know their Chomsky, a CFG is a , which means (very roughly) that substitutions can be made independently of their use context.


I am trying to make it so that when the cursor is hovered over an image, text will display at the center of the image. Text such as "Facials", "Skin Care Solutions" etc. should display at the center of their corresponding images when the cursor hovers on to it. A overlay effect where the images changes color when be hovered over has been added. Here is a picture for context.  HTML

SERVICES

Personalized Special Care

Facials

Skin Care Solutions

Lashes

Microblading

Eyebrow Treatment

  CSS #service{     width: 100%;     padding: 70px 0;     background: #b4edfa;     } .service-box{     width: 80%;     display: flex;     flex-wrap: wrap;     justify-content: space-around;     margin: auto; } .single-service{     flex-basis: 50%; /*get two services in 1 row*/     text-align: center;     border-radius: 7px;     margin-bottom: 15px;     color: #fff;     position: relative; } .single-service img{     width: 85%; /*resize image*/     border-radius: 7px; } .overlay{     width: 100%;     height: 100%;     position: absolute;     top: 0;     border-radius: 7px;     cursor: pointer;     background: linear-gradient(rgba(0,0,0,0.5),#93dced);     opacity: 0;     transition: 1s; }  .single-service:hover .overlay{     opacity: 1; } .service-desc{     width: 80;     position: absolute;     bottom: 0%;     left: 50%;     opacity: 0;     transform: translateX(-50%);     transition: 1s; } .service-desc h3{     line-height: 20% } .service-desc p{     font-size: 15px;     }  hr{     background: #fff;     height: 2px;     border: 0;     margin: 15px auto;     width: 60%; }  .singler-service:hover .service-desc{ /*create hovering effect that shows text*/     bottom: 40%;     opacity: 1; }

I want to overlay one image with another using CSS. An example of this is the first image (the background if you like) will be a thumbnail link of a product, with the link opening a lightbox / popup showing a larger version of the image.   On top of this linked image I would like an image of a magnifying glass, to show people that the image can be clicked to enlarge it (apparently this isn't obvious without the magnifying glass).


I wish to get all folders and subfolders starting with string mycobacterium in FTP. I couldn't find any information online how to do it. I have tried get mycobacterium*, mget mycobacterium* but they don't work.  What is the right way in retrieving the data in FTP? Thanks in advance.

I'm trying to ftp a folder using the command line ftp client, but so far I've only been able to use 'get' to get individual files.


This is the place which I am going to remove my item,  myhieararchy hierarchyforDisplay = null;      try {          hierarchyforDisplay = (myhieararchy)hieararchybefore.clone();      } catch (CloneNotSupportedException e) {          e.printStackTrace();      }      for (Project project : projectList) {      for (Program program : hierarchyforDisplay.getPrograms()) {          for (Project rootproject : program.getProject()) {              if(project.getId() != rootproject.getProjectId()){                  program.getProject().remove(rootproject);             }         }     }     }       return hierarchyforDisplay;   But I am getting this  org.springframework.web.util.NestedServletException: Request processing failed; nested exception is java.util.ConcurrentModificationException org.springframework.web.servlet.FrameworkServlet.processRequest(FrameworkServlet.java:656) org.springframework.web.servlet.FrameworkServlet.doGet(FrameworkServlet.java:549) javax.servlet.http.HttpServlet.service(HttpServlet.java:621) javax.servlet.http.HttpServlet.service(HttpServlet.java:722)   I can not imagine what is the reson because this is my first time I get this.. :(

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


If $\space$ $\forall$ $x \in \Bbb R$, $\space$ $f(f(x))=x^2-x+1$. Find the value of $f(0)$.  I thought that making $f(x)=0$ implies that $f(0)= 0^2 - 0 + 1 = 1$, but i think that this isn't correct, because the $x$ in $f(f(x))$ isn't equal to $f(x)$ .  Any hints?

Suppose that $f\colon\mathbb{R}\to\mathbb{R}$ without any further restriction. If $f(f(x))=x^2-x+1$, how can one find $f(0)$?   Thanks in advance.


*args is used to pass variable number of arguments that is when the number of arguments not known beforehand. But how it is working when it is passed as a parameter to a function?  In the code how arg1 identifies the first element of the tuple and not the second one and in the similar way arg2 points to the second element of the tuple not the first or third one .Why?  I saw a plenty of resources in the internet which explains *args and *kwargs but none of them explains how do they work when passed as a parameter.  def some_args(arg_1, arg_2, arg_3):     print("arg_1:", arg_1)     print("arg_2:", arg_2)     print("arg_3:", arg_3)  args = ("Sammy", "Casey", "Alex") some_args(*args)

In the following method definitions, what does the * and ** do for param2?  def foo(param1, *param2): def bar(param1, **param2):


I'm a Yemeni citizen with a Canadian permanent resident, and flying through turkey from Canada to Oman. Do I need a turkish visa? Note: I'm traveling with my Husband and three children who are all Canadian citizens.

I have an Indian passport and am planning to visit Germany with a valid visa. To book a flight for Germany (Mumbai – Dusseldorf), I came across some connected flights that stop at Istanbul.  Do I need to have visa for Turkey?  This is the first time I am travelling outside my country, and any information on this will be helpful.


In my textbook, the definition of normalizer is     $N_G(A)=\{g\in G \mid gAg^{-1} \subseteq A\}$   Many textbooks use this definition.     $N_G(A)=\{g\in G \mid gAg^{-1} = A\}$   I know that normalizer is subgroup of $G$.  There is no problem when $A$ is finite. Two things are the same.  But if $A$ is infinite, I know that there exists example such that  $ gAg^{-1}$ is strictly in $A$.  In that case, it can be shown that for $g \in N_G(A)$, $g^{-1}\in N_G(A)$?

Let $G$ be a group, $H\subseteq G$ a subgroup and $a\in G$ an element of the group. Is it possible that $aHa^{-1} \subset H$, but $aHa^{-1} \neq H$?   If $H$ has finite index or finite order, this is not possible.


Prove that there are infinitely many primes of the form $4k + 3$ (where $k$ is an integer).   Note that it is a special case of "Theorem 6 (Dirichlet). Let a and b be positive coprime integers. Then the sequence $b$, $b + a$, $b + 2a$, $b + 3a$, $b + 4a$, $b + 5a$, ....," contains infinitely many prime numbers  So far I got that suppose there are a finite number of primes   $p......p$  and if $4(p.....p)+3$ is prime it's a contradiction so the initial statement is proven?

This is the proof from the book:     Theorem. There are infinitely many primes of the form $4n+3$.    Lemma. If $a$ and $b$ are integers, both of the form $4n + 1$, then the product $ab$ is also in this form.  Proof of Theorem: Let assume that there are only a finite number of primes of the form $4n + 3$, say  $$p_0, p_1, p_2, \ldots, p_r.$$ Let $$Q = 4p_1p_2p_3\cdots p_r + 3.$$ Then there is at least one prime in the factorization of $Q$ of the form $4n + 3$. Otherwise, all of these primes would be of the form $4n + 1$, and by the Lemma above, this would imply that $Q$ would also be of this form, which is a contradiction. However, none of the prime $p_0, p_1,\ldots, p_n$ divides $Q$. The prime $3$ does not divide $Q$, for if $3|Q$  then $$3|(Q-3) = 4p_1p_2p_3\cdots p_r,$$ which is a contradiction. Likewise, none of the primes $p_j$ can divides $Q$, because $p_j | Q$ implies $p_j | ( Q - 4p_1p_2\cdots p_r ) = 3$, which is absurd. Hence, there are infinitely many primes of the form $4n +3$.   END  From "however, none of the prime ...." to the end, I totally lost!    My questions:   Is the author assuming $Q$ is prime or is not? Why none of the primes $p_0, p_1,\ldots, p_r$ divide $Q$? Based on what argument?     Can anyone share me a better proof?     Thanks.


Is there a way to tab through all active windows in Mac OS (Mojave 10.14.5) like in Win 7,8,10? I would like to do this on my work computer, so a native solution would be appreciated; rather than one where I would have to install a 3rd party service.  Sorry if this has been asked/answered before; I couldn't find a proper response.  Thanks

I opened two Google Chrome windows (because I am using multiple Gmails) and when I do the Cmd ⌘ Tab ⇥ shortcut it just shows me other applications that I opened but does not show me the other Chrome windows that are already opened.  How to switch to the other Google Chrome window that I opened using keyboard shortcut?


Ubuntu boot takes long time, and on boot I get these errors:    Similar errors appear on shutdown (which is also slow), however Windows 10 on the same SSD boots normally. I tried to reinstall Ubuntu, but that fixed nothing and same errors occur when I boot from live USB. What's the problem and how can I try to fix it?

I'm getting these errors ramdomly, and I don't know if its normal or not.   [39441.061856] ata3.00: failed to read SCR 1 (Emask=0x40) [39441.061866] ata3.01: failed to read SCR 1 (Emask=0x40) [39441.061892] ata3.15: exception Emask 0x10 SAct 0x0 SErr 0x280100 action 0x6 frozen [39441.061897] ata3.15: irq_stat 0x08000000, interface fatal error [39441.061904] ata3.15: SError: { UnrecovData 10B8B BadCRC } [39441.061910] ata3.00: exception Emask 0x100 SAct 0x0 SErr 0x0 action 0x6 frozen [39441.061917] ata3.01: exception Emask 0x100 SAct 0xe SErr 0x0 action 0x6 frozen [39441.061923] ata3.01: failed command: READ FPDMA QUEUED [39441.061933] ata3.01: cmd 60/a8:08:b0:48:62/00:00:00:00:00/40 tag 1 ncq 86016 in [39441.061940] ata3.01: status: { DRDY } [39441.061944] ata3.01: failed command: READ FPDMA QUEUED [39441.061953] ata3.01: cmd 60/a8:10:b0:49:62/00:00:00:00:00/40 tag 2 ncq 86016 in [39441.061959] ata3.01: status: { DRDY } [39441.061963] ata3.01: failed command: READ FPDMA QUEUED [39441.061972] ata3.01: cmd 60/58:18:58:4a:62/00:00:00:00:00/40 tag 3 ncq 45056 in [39441.061978] ata3.01: status: { DRDY } [39441.061987] ata3.15: hard resetting link [39441.608302] ata3.15: SATA link up 3.0 Gbps (SStatus 123 SControl 300) [39441.609090] ata3.00: hard resetting link [39441.929246] ata3.00: SATA link up 3.0 Gbps (SStatus 123 SControl 320) [39441.929333] ata3.01: hard resetting link [39442.249184] ata3.01: SATA link up 3.0 Gbps (SStatus 123 SControl 320) [39442.263242] ata3.00: configured for UDMA/133 [39442.277570] ata3.01: configured for UDMA/133 [39442.277725] ata3: EH complete   I'm also pasting smartctl -a for ,  and .  Thanks in advance for your help.


#include<iostream>  using namespace std;  class weapon { private:     int damage;     string name;  public:     weapon(const string& n, int d) {         name = n;         damage = d;     } };  class sword : public weapon { private:     int sharpness; public:     sword(const string& n, int d, int s) : weapon(n,d), sharpness(s) {} };  class gun : public weapon { private:     int capacity; public:     gun(const string& n, int d, int c) {         weapon(n,d);         capacity = c;     } };  int main() {     sword s("Katana", 72, 41);     gun g("AK-47", 74, 30);     return 0; }   in sword class, sword function is working fine with this syntax but in gun class gun function is giving me this error :  no matching function for call to weapon:weapon()

What are the C++ rules for calling the base class constructor from a derived class? For example, I know in Java, you must do it as the first line of the subclass constructor (and if you don't, an implicit call to a no-arg super constructor is assumed - giving you a compile error if that's missing).


A complex number $z$, in its nature, is nothing but an element $z \in \mathbb{R}^{2}$. Specifically, the imaginary unit $i$ is defined as $i = \left(0,1\right)$. Thus, our daily representation of a complex number $z = x + yi$ is abused in that, $x$ is a real number, and cannot be added to an element $yi \in \mathbb{R}^{2}$. In my understanding, $z = x + yi$ is actually the abbreviated form of $z = x\left(1,0\right) + yi = x\left(1,0\right) + y\left(0,1\right)$, where $\left(1,0\right)$ and $\left(0,1\right)$ are standard basis of $\mathbb{R}^{2}$. Thus, the $\mathrm{Re}\left(z\right)$ is the coefficient for $\left(1,0\right)$ while the imaginary is actually the coefficient for $\left(0,1\right)$. We should not see $i$ as something special. Is this understanding correct?

I haven't taken any complex analysis course yet, but now I have this question that relates to it.  Let's have a look at a very simple example. Suppose $x,y$ and $z$ are the Cartesian coordinates and we have a function $z=f(x,y)=\cos(x)+\sin(y)$. However, now I change the $\mathbb{R}^2$ plane $x,y$ to complex plane and make a new function, $z=\cos(t)+i\sin(t)$.  So, can anyone tell me some famous and fundamental differences between complex plane and $\mathbb{R}^2$ by this example, like some features $\mathbb{R}^2 $ has but complex plane doesn't or the other way around. (Actually I am trying to understand why electrical engineers always want to put signal into the complex numbers rather than $\mathbb{R}^2$, if a signal is affected by 2 components)   Thanks for help me out!


I am trying to keep an icon floated left on a liquid text container that has line breaks.  The problem is that when the line breaks, there is a large gap before the text ends and where the div ends. Which makes my floated element start where the gap ends.  Is there a way to make the div only the size of its contents?  Check this codepen:   Resize the output area to see the gap of space.  The button will auto resize it to see the gap.   *{ padding:0; margin:0; top:0; left:0;   }  #mainContainer{  width:100%;       border:black solid thin; }   #lt{  color: black;  background-color:gray;  tex-align:left;  max-width:90%; float:left;  } #icon{ width:20px; height:20px; background-color:blue; float:left; }

This is The information This is The information This is The information

   <input type='button' onClick='showBadSize()' value="click to auto resize to show gap" style='margin-top:20px;float:left; clear:left' />

I have a layout similar to:  <div>     <table>     </table> </div>   I would like for the div to only expand to as wide as my table becomes.


Let $G$ be a subgroup of $(\mathbb{R}, +)$. Prove that $G$ is dense in $\mathbb{R}$ or any element in $G$ has the form $a\mathbb{Z}$, with $a \in \mathbb{R}$. (We denote that a group $G$ is dense in $\mathbb{R}$ if any element in $\mathbb{R}$ is the limit of a sequence of elements from $G$)  I haven't done anything notable yet.  Thank you!

$\newcommand{\R}{\Bbb R}\newcommand{\Q}{\Bbb Q}\newcommand{\Z}{\Bbb Z}$ What are all the subgroups of R =  $(\R, +)$ and how can we categorize them?   I started thinking about this question last night after looking at the structure of the cosets of $\R / \Q$ . I did some searching on SO and google but didn't find anything giving a full categorization (or even a partial one) of the subgroups of $\R$.   Here are the subgroups that I came up with so far:   $\Z$ (there are no finite subgroups and $\Z$ is the universal smallest subgroup I think) n$\Z$ eg 2$\Z$ all even numbers a$\Z$ where a is any real number, including a in $\Q$ which "nest" nicely in each other $\Z$[a] - group generated by adding one real a to $\Z$ n$\Z$[a] which equals $\Z$[na] and so is just a case of the one above   eg a numbers of the form a/2b or similar subgroups such as a/3b, a/2b7c etc $\Q$ $\Q$[a] $\Q$[a in A] where A is a subset of $\R$ - could be finite, countable or uncountable. Group generated by adding all elements of A to $\Q$ eg  $\Q[\sqrt2]$   It is clear that the "n$\Z$ subgroups" n$\Z$ and m$\Z$ are related according to the gcd(n,m)  Also when H is a subgroup of R looking at the structure of the cosets of R / H. eg for H any of the Z subgroups we get R / H homomorphic to [0,1) or the circle. For H one of the Q subgroups it is more complex and I currently don't have ideas on the larger subgroup cosets  I am not clear how "big" a subgroup H can get before it becomes the whole of R. I do know that if it contains any interval then it is the whole of R. But what about H with dimension less than 1?  I am aware of one question on SO about the proper measurable subgroups of R having 0 measure , one on dense subgroups  and one on the subgroups of Q  but that is all my searching found so far.  Why is this question interesting? 1) there seem to be so many subgroups and they are related in many groupings 2) I think the subgroups related to the structure of the reals in some subtle ways 3) I know the result for the complete classification of all finite subgroups was a major result so wondering what has been done in this basic uncountable case.  If anyone has any insight, intuition, info, papers or theorems on subgroups of R and how they are interrelated that would be interesting.


I need to reinstall Windows 8 on my machine where I've installed ubuntu 15.04. I have no DVD drive and need to run it from a USB stick. Windows supports this but I cannot run the .exe windows file that creates the usb stick for rebooting from the USB. Hope someone have an idea on how to solve this.

I am unable to install WinUSB in Ubuntu 14.04 using command:  sudo apt-get install winusb  What is the correct way to install WinUSB in Ubuntu 14.04? Or is there any other application available to create Windows bootable USB in Ubuntu 14.04?


When I do ls -1, I get colours that I don't like:  These directories (folder1, folder2, folder3) have "anyone can do anything" permissions. (also called 777 permissions I think). I'm not partial to the the blue font with green background. How do I change the font colors for directories with these permissions?  OS: Ubuntu 19.04 Shell: Zsh

There are two directories shown by 'ls'.  Normally directories anywhere are blue on black background.  But the first one is blue on green and impossible to read.  Why is this?  How to make it blue on black, or at least something light on something dark?  This is on Ubuntu 12.04, using bash in Gnome Terminal.  In Konsole, the blue is slightly darker, and possible to read, though could be way better.


I'm trying to read from a json file in order to create visual images via processing. My code so far is:  public void generateShape(JSONObject file) {     //convert file to json object     JSONArray shapes = (JSONArray) file.get("shapes");     for (Object o : shapes) {         JSONObject json_shape = (JSONObject)o;         //getting shape id and function so we know which shapes to create         id = ((Number) json_shape.get("id")).intValue();         func = ((Number) json_shape.get("func")).intValue();         animate = ((Number) json_shape.get("animate")).intValue();         stroke_weight = ((Number) json_shape.get("stroke_weight")).floatValue();          JSONArray strokes = (JSONArray) json_shape.get("stroke");         Iterator<Float> iterator = strokes.iterator();         index = 0;         while(iterator.hasNext())         {             stroke[index] = ((Number)iterator.next()).floatValue();             index++;          }   stoke[] is an array of floats which will control the colour of the stroke. The json file im parsing from is   {    "shapes": [ {   "id":0,   "func":1,   "stroke":[143,50,200],   "stroke_weight": 70,   "animate": 1,   "jelly_func": 5,   "points":[268,330,400,333,74,210,90,300]    }    ] }   im getting the error at the line:       stroke[index] = ((Number)iterator.next()).floatValue();   I'm using the json.simple library and all solutions i've seen are for org.json library  I could hard code the values in the stroke array but I wanted to try iteration instead. Any tips/guidance?  full stack trace is  java.lang.NullPointerException at ImageLoader.generateShape(ImageLoader.java:35) at Sketch.setup(Sketch.java:48) at processing.core.PApplet.handleDraw(PApplet.java:2404) at processing.awt.PSurfaceAWT$12.callDraw(PSurfaceAWT.java:1557) at processing.core.PSurfaceNone$AnimationThread.run(PSurfaceNone.java:313)   where sketch is:   ImageLoader image = new ImageLoader();     JSONParser parser = new JSONParser();     try {         JSONObject file = (JSONObject) parser.parse((new FileReader("save_data.json")));         image.generateShape(file);      }     catch (FileNotFoundException e)     {         e.printStackTrace();     }     catch (Exception e)     {         e.printStackTrace();     }   eta: ok so upon removing the line causing the exception, and checking if my json values are even being read I can confirm the values being parsed are correct when I print them to console. I just now need to put them in an array

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


How exactly should I install ubuntu on my ultrabook so that I can use all my ultrabook hardware at its best? Since, I am new to Ubuntu, it will be really helpful if you can elaborate each step.  My laptop is Dell inspiron 14z ultrabook. I want to install solely ubuntu on it.

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


So this is my problem, spell caster with a bow.  Round 1   Equip bow as free object interaction (PHB.190) draw and load ammunition as part of ammunition property (PHB.146) attack end of round 1   Round 2   Release one hand from the bow ( ) Draw spell focus as a free object interaction cast a spell preforming its eventual somatic component with the same hand as the focus (Source: 5e System Reference document p.102) end of round 2   Round 3 (here the problem starts)   Sheathe spell focus as a free object interaction (could probably drop it but would rather not) RAW I would need to use a free object interaction to equip the bow two-handed again. but again according to  the intent is manipulating objects or picking objects up. All my character does is move his hand draw and load ammunition as part of ammunition property (this is also a part that requires the character let go of one hand of the bow to get the ammunition) attack end of round 3   What are your thoughts on this does the rule RAW or RAI (from credited sources) support this?

I have a halfling cleric of Bahamut who wears his holy symbol as an amulet around his neck as a spellcasting focus (so material components are not an issue). However, as per , this does not cover the Somatic component of any spells he casts.  He also wields a light crossbow as his only weapon, which has the two-handed weapon property. How does RAW handle Somatic casting when you're holding a two-handed weapon? Can I simply take a hand off my weapon, cast the spell, and re-grip all in the same action? If not, has anyone run into this problem at their table before and how did you handle it?


Using git, is there a command which I can reset a file to a specific commit in the commit log?  I know git checkout file can let me reset the file to HEAD, but how to reset to a specific commit version?

I have made some changes to a file which has been committed a few times as part of a group of files, but now want to reset/revert the changes on it back to a previous version.   I have done a git log along with a git diff to find the revision I need, but just have no idea how to get the file back to its former state in the past.


Every now and then I fail to track my mouse pointer on a large screen resp. multi monitor setup. MacOS has this nice feature to grow the mouse pointer when shaking the mouse for a bit. Is there any extension or tweak to have this accessibility feature inside Gnome 3?

Is there any software that does the same as the macOS feature "Shake to Find Cursor" for Ubuntu 18.04 LTS?


In Prometheus, towards the end the Engineer leaves his spaceship to pursue Dr. Shaw, and we last see him on the floor of the escape pod after an alien pops from his chest. In Alien, when examining the spacecraft, the crew finds the Engineer skeleton inside of a cockpit with a hole in it's side. Isn't this supposed to be the same Engineer that chased Shaw? How is he still in the cockpit?

At the end of , the alien that Elizabeth Shaw extracted from her womb kills the Engineer. Later on, a primary form of alien xenomorph is seen bursting out of the Engineer's chest. The scene takes place in Meredith Vickers' escape pod, stranded at a distance from the Engineers' crashed ship.  At the beginning of , the team that explores the derelict ship discovers the body of an Engineer pilot:    The corpse wears what we now know is some sort of armor, and his chest has been damaged by an alien xenomorph, as we later figure out.  Everything seems to indicate that the corpse in Alien is actually the Engineer in Prometheus. However, there are two major discrepancies:   The Engineer is killed in the escape pod, not in his pilot seat. The corpse in Alien is much taller than the Engineer in Prometheus.   What other theory could possibly explain how a (much taller) Engineer sat in the crashed ship and was killed by a xenomorph?


For all matrix $\mathbf{M} \in \mathbb{R}^{m,n}$ and $\mathbf{N} \in \mathbb{R}^{n,p}$, the inequality $\operatorname{rank}\mathbf{M} + \operatorname{rank}\mathbf{N} - n \leq \operatorname{rank}(\mathbf{M}\mathbf{N}) \leq \min(\operatorname{rank}\mathbf{M},\operatorname{rank}\mathbf{N})$ holds. What would be a proof of this theorem?

If $A$ is a $m \times n$ matrix and $B$ a $n \times k$ matrix, prove that  $$\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n.$$  Also show when equality occurs.


Simple question, title says it all. For example I have a few posts where the answers that are accepted are highly voted up by the community, which indicates they are, based on my questions, vastly right. Now I am not your copy, paste programmer who lives on SO, but I do use SO for understanding issues and problems and seeing new ideas and solutions to existing issues that I cannot figure out. Lets take an example post, call it "How to do x in x language" The question might have an answer with a vote of 100+, while other answers that still come in years later get instantly downvoted. Why does stack allow people to continue answering after a question has accepted what they deem to be the right answer based off the info provided, the votes and maybe the example solution (keyword: example). Why? I could see if there was no accepted answer, or every answer was below a certain threshhold in terms of voting. But questions after 6 months, regardless of accepted answer or not, should be closed - like GitHub. Thoughts?

My question concerns . I asked the question, and at the time selected the correct answer. However, time passes and libraries get updated, and now a different answer is actually correct.   I should probably select this new answer as the correct answer, but I feel bad for the person that will lose 15 reputation points even though is answer was the a good answer at that given point in time.  Any suggestions?


One of our servers has a 20gb / partition and it is getting full. Is there any safe way to take some space from the 2TB /home partition and allocate it to the / partition without losing data?  Thanks.

I just noticed that the root partition of my not-so-long-ago configured server is only 5gb  thats not much seeing as i allready use 4gb and still need to install a lot of things...  i was foolish enough to use the default config from OVH assuming they know their stuff :P  since i have some data on the data partition it would be a pain in the ... to backup and reconfigure it all  is it possible to repartition the drive to use a new part of the drive say 15-20gb without data loss ? by simply copying the root partition to a new place (from sda2) ? i can live with loosing the 5gb of the start of the drive :P    heres df -h  Filesystem            Size  Used Avail Use% Mounted on /dev/sda1             5.0G  3.9G  897M  82% / tmpfs                 998M     0  998M   0% /lib/init/rw udev                   10M  144K  9.9M   2% /dev tmpfs                 998M     0  998M   0% /dev/shm /dev/sda2             226G  7.2G  208G   4% /home   and fdisk -l  Disk /dev/sda: 250.1 GB, 250059350016 bytes 255 heads, 63 sectors/track, 30401 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x0000db26     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *           1         653     5242880+  83  Linux Partition 1 does not end on cylinder boundary.    <== now this is bad.. thx OVH :F /dev/sda2             653       30336   238426112   83  Linux /dev/sda3           30336       30401      526016   82  Linux swap / Solaris


I am having a little trouble with simple computation.  What is $\sum_{k=1}^\infty \frac{k^2}{k!}$?

I was exploring the fact that $$ \sum_{n=0}^\infty \frac{n^p}{n!} = B_pe,$$ where $B_n$ is the $n$th Bell number.   I found this result by exploring the series on wolframalpha and looking up the sequence of numbers generated. I have no experience with Bell numbers other than knowing that they represent the number of ways of partitioning a set.   What I tried  Looking at the base case we can verify $$\sum_{n=0}^\infty \frac{n}{n!} = \sum_{n=1}^\infty \frac{1}{(n-1)!} = e. $$  But then I realize that $n^2$ is going to be difficult.  Specifically what I want  I am doing this for fun, so I just want to glean some sort of lesson out of this. Resources that let me learn for myself are just as good!   An accepted answer will have any one of the following:   A proof that $\sum_{n = 0}^{\infty} \frac{n^2}{n!} = 2e$ (this interests me a lot) A description of why this series is related to Bell numbers and the number of partitions of a set A link to some resource that introduces Bell numbers and/or their connection to this series.


Currenly my issue with \includegraphics is as follows: \includegraphics{example.png} results in the following picture even though the example.png picture is present in the same directory as the main.tex file in Overleaf. . There is no error nor warning regarding the image name or path. Since e.g. the command: \includegraphics{exampleasdf.png} gives a warning that "File 'exampleasdf.png' not found on line", I am under the impression that the compiler finds the image file, but cannot read it? I changed my PDF viewer to native, but it did not resolve the issue. However, the exact same command in a dummy project gives out the desired output. . If I could I would share the the relevant .tex code, but as it is part of my thesis that uses a ready-made-format, I don't know what is and what is not important to share. That is, I would end up sharing pages upon pages of .tex code. It could be that the fault lies in some ready-made setting, but what to look for?

I'm working on overleaf v2. I wrote : \documentclass{article} \usepackage[utf8]{inputenc}  \usepackage[utf8]{inputenc}  % Accents codés dans la fonte \usepackage[frenchb]{babel}  % Les traductions françaises \usepackage{amsmath}  \usepackage{graphicx} \graphicspath{ {./images/} }  \usepackage{amsfonts}  \usepackage{biblatex} \begin{document} .... \begin{figure} \centering \includegraphics{comp_W_log.jpg} \caption{\textit{On compare la fonction de Lambert à $\log(x)-1$ dans un certain interval}} \label{fig:my_label} \end{figure}  .... \end{document}  But I just get, after compiling :  Can you help me plz ? Edit: png didn't work either


I know, it may sound as nothing but a provocative question, and probably it is. However I've been thinking about it for a while, despite being aware that the question itself may not have much sense. Consider the field $\mathbb{R}$. Each element can be defined univocally. First $0$ and $1$, then the integers, so the rationals and then all the others (for instance as equivalence classes of Cauchy sequences on $\mathbb{Q}$). Now we can define the complex field $\mathbb{C}$ as $$\mathbb{C} = \mathbb{R}[X]/(X^2+1)$$ where $\mathbb{R}[X]$ is the ring of polynomials with real coefficient. However here it becomes impossible to univocally define a root of the polynomial $X^2+1$ since it has two roots (which we will eventually call $\pm i$) and they are totally indistinguishable. I know that in practice it's not a problem, we just decide to call one of the two roots $i$ and the other $-i$. But what's going on exactly? Is it some kind of "axiom" the fact that we are allowed to choose one out of a set of two identical elements?

Today I learned that two roots of an irreducible polynomial are "algebraically indistinguishable."   In $\mathbb{Q}(\sqrt{2})$, define the conjugate of $a+b\sqrt{2}$ as $\overline{a+b\sqrt{2}} = a - b\sqrt{2}$.   My understanding/intuition on "algebraically indistinguishable" is that if $P$ and $Q$ are algebraic expressions (meaning using the ring operations only) in $\mathbb{Q}(\sqrt{2})$ with $P$ = $Q$, then then we also have $\overline{P} = \overline{Q}$ where $\overline{P}$ and $\overline{Q}$ are the algebraic expressions $P$ and $Q$ except every member of $\mathbb{Q}(\sqrt{2})$ in the expression is replaced with its conjugate.  For example,  $2(3+\sqrt{2})(4+\sqrt{2}) - (6-\sqrt{2}) = 22 + 15\sqrt{2}$  and indeed,  $2(3-\sqrt{2})(4-\sqrt{2}) - (6+\sqrt{2}) = 22 - 15\sqrt{2}$.  And in $\mathbb{R}(i) = \mathbb{C}$, we're guaranteed the same phenomenon:  $2(3+i)(4+i) - (6-i) = 16 + 15i$  $2(3-i)(4-i) - (6+i) = 16 - 15i$  But what I find interesting is that once I involve familiar operations outside of multiplication and addition, this will no longer hold for $\mathbb{Q}(\sqrt{2})$, but it still holds for $\mathbb{R}(i) = \mathbb{C}$.  For example, $(-\sqrt{2})^{-\sqrt{2}} \neq \overline{\sqrt{2}^{\sqrt{2}}}$ while on the other hand,$(-i)^{-i} = \overline{i^{i}}$.  My initial answer to this is that exponentiation viewed as a binary operation is not closed in $\mathbb{Q}(\sqrt{2})$, so I must view this as an operation on $\mathbb{R}(i) = \mathbb{C}$, but this is a larger field than extending $\mathbb{Q}$ to include the roots of $x^{2}-2$, so in this field with exponentiation, I can now distinguish $\sqrt{2}$ and $-\sqrt{2}$. On the other hand, exponentiation on $\mathbb{R}(i) = \mathbb{C}$ is closed, so even exponentiation does not allow us to algebraically distinguish between $a+bi$ and $a-bi$.


I have UK Passport and am Canadian Citizen. Flying to Mexico via Dallas. Do I need an ESTA or Visa?

In Europe usually you don't need to go through immigration to change planes (unless you are entering/exiting Schengen). Is it the case in the US as well? May I catch a connecting flight on one of the US airports if I don't have US visa?


Do I have to understand the sentence:     It has not been unchanged   .. as if the related subject actually changed, or whether there has been no change at all? In short, is this a double negative?

When I think of double negatives I think of phrases that grate on the ears, like:  I'm not going to do no homework. I'm never going to not go visit Graceland.  There are some phrases that appear to technically be considered a double negative, but seem more common and are, in my opinion, actually pleasing to the ear. And I've seen such uses in newspaper articles, magazine articles, and other edited content. I'm referring to phrases like:  It's not uncommon for two people to meet serendipitously. Baseball is not unlike golf - both are boring to watch without a beer in hand. It's not unusual to be loved by anyone.  Are the above examples of double negatives? Should their use be avoided?


I travelled from Philippines to UK transit in Istanbul. I bought some diamonds in Philippines properly declared with customs to bring out and will pay VAT in UK.  Q: Do I need to declare in Istanbul while transiting?

I have an Indian passport and am planning to visit Germany with a valid visa. To book a flight for Germany (Mumbai – Dusseldorf), I came across some connected flights that stop at Istanbul.  Do I need to have visa for Turkey?  This is the first time I am travelling outside my country, and any information on this will be helpful.


I tried a lot of ways like changing /etc/profile and /etc/apt/apt.conf file to use Internet for non browser applications.   I want to use the command sudo apt-get update but due to proxy I can't. How can I fix it?

During system installation from a Desktop LiveCD (10.10) I checked the "Download updates during installation" option.  Before starting the install I had configured an apt proxy server.  The proxy server was configured by writing  Acquire::http { Proxy "http://apt-proxy-server:3142"; };   to the new file /etc/apt/apt.conf.d/02proxy on the running system booted from the LiveCD.  This proxy was used correctly for my various package installs on the live system prior to launching the system installation GUI.  It accesses apt-cacher-ng running in non-transparent mode on the machine apt-proxy-server.  However, the downloads taking place during the installation are not using this proxy.  I verified that the file 02proxy had not been changed or removed.  Is there a way to force usage of an APT proxy during installation?


Does anyone know an easy way to check if an item is a member in a comma-separated list?  Something like this would be excellent:  \ifmember{elem1}{elem1,elem2,elem3}{true}{false}   The above would expand to true since elem1 is in the list.  Thanks

Is there a package that provides a command for testing whether a string is in a list?  I saw several answers that define their own commands to perform this or similar tasks, but I prefer a "self-evolving", and well-documented solution for this kind of tasks.  More precisely, the command should be something like this  \IfStringInList{string}{list}{DoThisIfTrue}{DoThisIfFalse}   For instance  \IfStringInList{Paul}{George,John,Paul,Ringo}{Beat it}{Roll it}   EDIT:  I'm not against defining commands.  I expected thas this natural functionality was present in a ready-to-use package, that can be accessed in a very simple way.


I was wondering if there is a way to have a figure in a slide that replace the previous figure. So if one has 5 figures then each figure will appear once and be replaced by the next figure. At the end of the slide, the last figure will be shown.  I have tried the following, but I am sure it's not the best way.  \begin{frame}     Here is an example. \begin{example}    Let a finite sequence of real numbers be $(1,2,3,4,5,6,7,8,9,10)$. \end{example} \pause \begin{minipage}{\textwidth}     \begin{itemize}       \item<1|only@1>\includegraphics[width=8cm]{figure1.png}       \item<2|only@2>\includegraphics[width=8cm]{figure2.png}       \item<3|only@3>\includegraphics[width=8cm]{figure3.png}       \item<4|only@4>\includegraphics[width=8cm]{figure4.png}       \item<5|only@5>\includegraphics[width=8cm]{figure5.png}     \end{itemize} \end{minipage} \end{frame}   The problem with above code is that the first figure is not shown and bullet points are also shown since it's a itemize environment.  I would appreciate any help or suggestion.  Thank you.

I would that the images would appeared for each overlay. Eg, in overlay 1 I have img1.pdf, in overlay 2 I have img2.pdf, and in overlay 3 I have img3.pdf. How I do this?  \begin{center}   \begin{tikzpicture}     \node (img1) {\includegraphics[width=.5\linewidth]{img1.pdf}};     \pause     \node (img2) {\includegraphics[width=.5\linewidth]{img2.pdf}};     \pause     \node (img3) {\includegraphics[width=.5\linewidth]{img3.pdf}};   \end{tikzpicture} \end{center}


I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


What is so important about the characters with the middle initial of D? It seems like they're the center of attention in One Piece and the middle initial of D seems to be of some significance. I don't want to actually know what the D stands for, just why people with the initial is important. And everybody should know that the meaning of something and how it is significant is two different things. Duh.

There are a lot of characters with the middle initial "D".  Is this an indication of something, or do they really all just have middle initials of the letter D?  If they are initials, do we know what they stand for?  Examples of names:     Monkey D. Luffy   Monkey D. Dragon   Portgas D. Ace   Monkey D. Garp   Gol D. Roger


Some tags are automatically created when a new child meta is spawned, including mod-only tags like  and mandatory tags like , as well as some ordinary tags like , , and .   Using  as an example: if you look at the  tag there, you can see that it exists even though there are no questions there, since it asks you if you would like to create a tag wiki for it. On the other hand, the hypothetical  tag does not exist at all, and hence does not ask you about creating a tag wiki.   I would like to know which tags, like , exist by default in the system. It would be particularly nice if this information was available in SEDE or the API, but if not, an answer here would work, too. Knowing this would help me know which tags on meta sites need to have tag wikis added to protect them from the script that deletes single-use tags after 6 months.   I could, I suppose, glean this information by inspecting the tag list on 's meta right after it launches, but I think it would be good to have this information on Meta.   EDIT: The  is no longer accurate. At minimum, it claims that delete is a tag that should be present on all child metas; however, as you can see at Meta.Japanese, .

Suppose a new user has a question to ask on a new meta site about badges. The meta site is too new to have a badges tag and the user is too new to have enough rep to create tags.  It would be useful if all of the per-site metas had a selection of generic tags from the start. As well as allowing low-rep users to use common meta tags, it would also make it easier for someone wanting to retrieve data on multiple meta sites from the data dump, as tags meaning the same things would have the same names across multiple sites.


I am using custom code for my website. Some delete all records from mysql database regularly after every week or 10 days. The deletion of records will also delete all the updates in db which has been made in this time frame. Kindly someone guide me how do I solve that issue.  I am using PHP and MySQL.  Thanks

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


Errors:   An object reference is required for the non-static field, method, or property 'Program.Quicksort(int[], int, int)'In Place Quicksort. An object reference is required for the non-static field, method, or property 'Program.ShowMyArray(string)'In Place Quicksort.   Lines:     Quicksort(MyArray, LBoundInteger, UBoundInteger);  ShowMyArray("Sorted Array");          LBoundInteger = MyArray.GetLowerBound(0);         UBoundInteger = MyArray.GetUpperBound(0);          outString = showLBoundStr + LBoundInteger.ToString() + Environment.NewLine + showUBoundStr + UBoundInteger.ToString();         Console.WriteLine(outString);         QSCallCnt = 0;         QSSwaps = 0;         Quicksort(MyArray, LBoundInteger, UBoundInteger);         ShowMyArray("Sorted Array");     }      private void Quicksort(int[] list, int min, int max)     {         int[] MyArray = { 65, 25, 75, 15, 85, 35, 95, 67, 48, 66 };         int pivot = 0;         int p = 0;         int temp = 0;         int QSCallCnt = 0;         int QSSwaps;         string round = "round";         string showMinOutstr = "min=";         string showMaxOutStr = "max=";         string showPivotOutStr = "pivot=";         string beginSortRecursion = "Begin Sort -Recursion ";         string pivotEnd = "Pivot to the end";         string QsCallcntStr = "QSCallCnt = ";         string QsSwapStr = "  QSSwaps = ";         string outString;          Random randomNumber = new Random();          QSCallCnt += 1;         QSSwaps = 0;         outString = showMinOutstr + min.ToString() + showMaxOutStr + max.ToString();         Console.WriteLine(outString, round, QSCallCnt);          if (min >= max)         {             return;         }          ShowMyArray(beginSortRecursion + QSCallCnt);          p = randomNumber.Next(min, max + 1);         pivot = list[p];          outString = showMinOutstr + min.ToString() + Environment.NewLine + showMaxOutStr + max.ToString() + Environment.NewLine + showPivotOutStr + pivot.ToString();         Console.WriteLine(outString);          temp = list[max];         list[max] = list[p];         list[p] = temp;         ShowMyArray(pivotEnd);          for (int i = min; i <= max; i++)         {             if (list[i] > pivot)             {                 for (int j = i + 1; j <= max; j++)                 {                     if (list[j] <= pivot)                     {                         temp = list[i];                         list[i] = list[j];                         list[j] = temp;                         QSSwaps += 1;                         ShowMyArray(QsCallcntStr + QSCallCnt + QsCallcntStr + QSSwaps);                         break;                     }                 }             }         }          for (int i = min; i <= max; i++)         {             if (list[i] == pivot)             {                 p = i;                 break;             }         }          if (p - min < 2)         {             Quicksort(MyArray, p + 1, max);         }         else if (max - p < 2)         {             Quicksort(MyArray, min, p - 1);         }         else         {             Quicksort(MyArray, min, p - 1);             Quicksort(MyArray, p + 1, max);         }      }      private void ShowMyArray(string msg)     {         string outString;         int[] MyArray = { 65, 25, 75, 15, 85, 35, 95, 67, 48, 66 };          outString = "      {";         for (int i = 0; i < MyArray.Length; i++)         {             outString += MyArray[i].ToString();             if (i == MyArray.Length - 1)             {                 outString += "}   ";             }             else             {                 outString += ",   ";             }         }         allOutString = allOutString + Environment.NewLine + outString;         Console.WriteLine(outString, msg);     } } }

Consider:  namespace WindowsApplication1 {     public partial class Form1 : Form     {         public Form1()         {             InitializeComponent();         }          private void button1_Click(object sender, EventArgs e)         {             //int[] val = { 0, 0};             int val;             if (textBox1.Text == "")             {                 MessageBox.Show("Input any no");             }             else             {                 val = Convert.ToInt32(textBox1.Text);                 Thread ot1 = new Thread(new ParameterizedThreadStart(SumData));                 ot1.Start(val);             }         }          private static void ReadData(object state)         {             System.Windows.Forms.Application.Run();         }          void setTextboxText(int result)         {             if (this.InvokeRequired)             {                 this.Invoke(new IntDelegate(SetTextboxTextSafe), new object[] { result });             }             else             {                 SetTextboxTextSafe(result);             }         }          void SetTextboxTextSafe(int result)         {             label1.Text = result.ToString();         }          private static void SumData(object state)         {             int result;             //int[] icount = (int[])state;             int icount = (int)state;              for (int i = icount; i > 0; i--)             {                 result += i;                 System.Threading.Thread.Sleep(1000);             }             setTextboxText(result);         }          delegate void IntDelegate(int result);          private void button2_Click(object sender, EventArgs e)         {             Application.Exit();         }     } }   Why is this error occurring?     An object reference is required for the nonstatic field, method, or property 'WindowsApplication1.Form1.setTextboxText(int)


How can I change the default text editor from gedit to vim? When I click on a text file, I want it to open in vim under the terminal instead of gedit.

How can I change my default text editor from gedit to Emacs?


I am fairly new to Linux and all I know for sure about the command echo is that when you type a word after it, such as echo Linux!, it prints out Linux!. Is there anything else echo does?  I don't think it is a duplicate.

man echo works. but out of curiosity, does echo have something similar to a --help flag/parameter?


I created an Google Apps business (free edition) account for my friend back in 2012. After that we never logged in to that account. Now today when tried logging back in we don't remember username or password. Google does not provide support if you're free business apps user.  How can I recover this account. I do not think I created any secondary email for that domain or I don't even remember recovery email address if I would have specified that time.

I have forgotten the password or username for my Google account, or I'm unable to access my account for other reasons.  How can I recover my account?  (This Q&A is meant as a general description for all Google and Gmail username/password questions. See: )


Nothing shown after logging in. Only Desktop picture (is it right? the purple one) is shown. that's all.  How can I do about this? I normally used Ubuntu 15.10. But Ubuntu 16.04 doesn't.  My system is  - Intel core-i7 6700k - Asus Z170-A - Samgsung DDR4 8GBx2 - Samgsung SSD 850 Pro 1TB - nVidia Geforce 970

When I login, nothing happens.   I am presented with my desktop wallpaper.    No Dash, no Launcher, nothing.


I am working in Alpine Linux and I cannot wrap my head around the following behavior of the sh shell: / # vsftpd /etc/vsftpd/vsftpd.conf > /dev/null 500 OOPS: bad bool value in config file for: hide_ids / # vsftpd /etc/vsftpd/vsftpd.conf 2> /dev/null 500 OOPS: bad bool value in config file for: hide_ids  Where is the message printed out? Was it stdout or stderr?

I got a program vsftpd which output doesn't seem to be either stdout or stderr (if that's even possible?)  My terminal output is:  ~# vsftpd 500 OOPS: SSL: cannot load RSA private key   I tried to redirect to a file but I get nothing in the file and the output still goes to the console:  ~#vsftpd > /tmp/out.txt 500 OOPS: SSL: cannot load RSA private key  ~#vsftpd &> /tmp/out.txt 500 OOPS: SSL: cannot load RSA private key  ~#vsftpd 2> /tmp/out.txt 500 OOPS: SSL: cannot load RSA private key   I'm actually trying to call this program from .Net Core from which I'm not able to get the StdOut/StdErr neither. And .Net Core crashes with The process cannot access the file because it is being used by another process. unless I enable StdIn-redirect, which I don't understand, I'm not parsing anything to StdIn and I never experienced this before with any other program calls.


I'm working on integration and change of variables. I'm not sure about how to do an exercise by using spherical and cylindrical coordinates. I think I can understand the process just seeing how it works for the spherical ones.  Calculate the volume of the set between the cone $y^2\sin^2a=(x^2+z^2)\cos^2a$ and the sphere $x^2+y^2+z^2=b^2$.  First, I've replaced $x=r\cdot \sin\theta\cdot \cos\phi$, $y=r\cdot \sin\theta\cdot \sin\phi$ and $z=r\cdot \cos\theta$ in both expressions and I've obtained: $0=-r^2\cdot \sin^2\theta\cdot \sin^2\phi-r^2\cdot \sin^2a$ for the cone and $r=b$ for the sphere. Then, I thought of finding the intersection between the cone and the sphere: $y^2=b^2-x^2-z^2\Longrightarrow(b^2-x^2-x^2)\sin^2a=(x^2+z^2)\cos^2a$. By using $\sin^2a+\cos^2a=1$, I've got: $b^2\sin^2a=x^2+z^2\Longrightarrow b^2\sin^2a=-b^2\sin^2a=-b^2\sin^2\theta \sin^2\phi-b^2$ I don't know how to go on to obtain the limits for $\theta$ and $\phi$ since I think I have the value of $r$ ($r=b$), and I don't know if it's ok what I've done neither. Thanks!

I'm trying to find the volume between the surfaces defined by the following equations: $$ x^2 + y^2 + z^2 = b^2 $$ $$ y^2 \tan^2 a = x^2 + z^2 $$ I need to find the volume using two different methods: the first one is by spherical coordinates and the second one by polar coordinates. The problem is I get two different results: Using spherical coordinates I found: $$ x = \rho \sin \phi \cos \theta \\ z = \rho \sin \phi \sin \theta \\ y = \rho \cos \phi $$ $$ V= \int_0^{2\pi}\int_0^{a}\int_0^{b}\rho^2\sin\phi \:d\rho d\phi d\theta = \frac{2\pi}{3}b^3(-\cos(a)+1) $$ and using polar: $$ x = r \cos \theta \\ z = r \sin \theta \\ y = y $$ $$ V = \int_0^{2\pi}\int_0^{b\sin a}\int_0^{\sqrt{b^2-r^2}}r \:dy dr d\theta = -\frac{2\pi}{3}b^3(\cos^3(a)-1) $$ So I know I have made a mistake at some point but I can't find it. If anyone can help I'd appreciate it. Thanks!


What is the point in Wizard creating  and , for example?  It seems like it would be a lot more efficient and cost effective to everyone involved if these basic land types were not specific to a set.  Wizard wouldn't have the cost of manufacturing (as many of) them and we wouldn't need to buy new ones just to stay legal.

Say, for example, you have a card that is still legal in standard but the version you have of it comes from a set that has since been rotated out. Can you still play the version from your older set?


It's well known that the Fibonacci sequence $\pmod m$ (where $m \in \mathbb N$) is periodic. I have figured out a proof for this, but upon googling, I found proofs online that were far more complicated. This leads me to suspect that my proof may be fallacious - that's why I am posting here.  Proof:  Let us list out the Fibonacci sequence modulo m, where m is some integer. It will look something like this at first (for $10$ at least):  $$ 1,2, 3,5,8, 3,1, 4, 5, 9, 4, 3, 7 {\dots}$$  Obviously, any number in the sequence is the sum of the last two numbers modulo $m$. Therefore, if at any point in the series modulo m a pair of numbers repeat, the numbers following that pair must repeat as well. eg. if at some point later we see the pair $1, 1$, then $2, 3, 5, \dots$ must follow that pair.  Now there are $m^2$ possible pairs in the series $\text{mod} m$. By the pigeonhole principle, after $m^2 + 1$ terms, a pair must repeat. If a pair repeats once, it must repeat again the same number of terms later. Therefore, the Fibonacci sequence $\pmod m$ is periodic $\forall m$ .  Is my proof correct?

About this Fibonacci sequence, is it true that the remainders when divided by three repeat along with the sequence like this:  Fibonacci sequence:  $1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946\cdots$  Remainder when divided by $3$ sequence:  $1, 1, 2, 0, 2, 2, 01, 00, 01, 01, 02, 000, 002, 002, 001, 000, 0001, 0001, 0002, 0000, 00002\cdots$  I made each one the same number of digits to align them to avoid confusion.  Is it true that it happens every eight numbers?  If so, how and why does this happen?


In several episodes of Assassination Classroom (animated version), characters develop spontaneous nosebleeds seemingly in response to becoming sexually aroused.  This occurs with a number of male characters, though I can recall at least one instance where it happens to a female character as well.    Here's an example on Youtube:    Is this a common trope in anime, or something that's unique to Assassination Classroom?  And in either case, is there any rational explanation behind using this seemingly bizarre method of depicting arousal?

In a similar spirit to my , I wonder who was the first artist to feature a nose-bleed when thinking, shall we say, "provocative thoughts"?  Did it become popularized in anime/manga because of the popularity of the artist's work or because it is a common belief in japanese folklore?


Coming from Languages without a GC (C/C++/Rust..) i am wondering what exactly is happening if an array is reallocated.    if we're in a c++ like language(pseudo code), this is considered bad:   Obj *x = xarr[2]; xarr.push(new Obj(12)); do_with(x);   running example in c++   after the push, x may point to freed memory due to reallocation of xarr.  x is basically just a pointer sized integer storing the memory address of xarr[2].  if i do the same in java. this is working just fine and i am wondering why?  List<OBJ> list = new ArrayList<>();     list.add(new OBJ()); list.add(new OBJ()); list.add(new OBJ());  OBJ x = list.get(2); for (int idx = 0; idx < 1000000; idx++) {     list.add(new OBJ());     } do_it(x);   what exactly is x and how and why is the memory address of x changed after  the array is seemingly reallocated?  obviously java is not deepcopying the array because x2 could not change x like in this code as you can see, the address of x is changing, too.  private static class OBJ {     int one;     String two;      public OBJ() {         this.one = 1;         this.two = "two";     } }  public static void do_it(OBJ o) {     System.out.println("o.two is: " + o.two);  }  public static void main(String[] args) {      List<OBJ> list = new ArrayList<>();     list.add(new OBJ());     list.add(new OBJ());     list.add(new OBJ());      OBJ x = list.get(2);      printAddresses("Address x", x);      for (int idx = 0; idx < 1000000; idx++) {         list.add(new OBJ());         }      OBJ x2 = list.get(2);     x2.two = "haha";      printAddresses("Address x", x);      do_it(x);  }    should not print out this  Address x: 0x525554440 Address x: 0x550882b80 o.two is: haha   full working example can be found here   so that begs the question how is the address of x changed after the reallocation of the list. And what exactly is the so called "reference"? I thought the so called "reference" in Java is just an ordinary pointer with something like autodereference and no pointer arithmetic because in Java everything is passed by value and not by reference. this is clearly evident in this code   public static void test1(OBJ o) {     o.one = 2; }  public static void test2(OBJ o) {     o = new OBJ();     o.two = "no reference"; }  public static void main (String[] args) throws java.lang.Exception {     OBJ x = new OBJ();     test1(x);     test2(x);      System.out.println("x.one: " + x.one + " x.two: " + x.two); }      printing out   x.one: 2 x.two: two   so it seems like x is behaving like a pointer but somehow java is redirecting it if necessary. How does this work? The term "reference" is extra confusing, why is it called like that?

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


I am wondering if someone can tell me how I can make a folder in windows that will automatically delete any files within that have been there for more than 'n' days, say maybe 7 for a week.  I have found a similar question that was answered well , though im not sure if it works on windows 10.  Also, would this be a '.bat' file? And, how do I make the batch file run automatically?  Thanks!  Edit:  I created a .bat file, starting with the mentioned answer:       forfiles /p "C:\what\ever" /s /m *.* /D -<number of days> /C "cmd /c del  @path"       Which I changed to:  forfiles /p "F:\Movies" /s /m *.* /D -<1> /C "cmd /c del @path"   exactly, to test it.  The folder 'Movies' has a bunch of things whos date modified is from very long ago.  I created a task with Task Scheduler (Thanks Thomas)  and it didnt delete anything.  I also tried running the batch manually, tried changing it to 1 minute, tried putting it in the folder that its deleting from, and ran it as admin.  Nothing worked.  I have permissions on the folder.  Does anyone have any suggestions?  Did I do something wrong with the code?

I am looking for a way to delete all files older than 7 days in a batch file.  I've searched around the web, and found some examples with hundreds of lines of code, and others that required installing extra command line utilities to accomplish the task.  Similar things can be  in just a couple lines of code. It seems that something at least remotely easy could be done for batch files in Windows. I'm looking for a solution that works in a standard Windows command prompt, without any extra utilities. Please no PowerShell or Cygwin either.


Does my Schengen Visa allow me to re-enter the Schengen zone after I've completed my initial visit to the issuing country? My visa is still valid for about a year. I'm intending on visiting a different country in the Schengen zone other than the one who issued it and don't intend on visiting the issuing country on this occasion. As my Schengen is still valid, that should be fine?

In case, if I get a multiple-entry Schengen visa in one of the embassies in Ukraine, Kyiv - should my first trip be to the country which issued the visa?  Any there any requirements of this sort? Does this condition vary depending on embassy which issued the visa?  What are the possible consequences on not visiting that country first? Does it somehow depend on country where the embassy is (i.e. non-Schengen and not EU members)?


I am new to blender and trying to render . Trying to render using script gives a very different result (everything purple) as compared to what I see in Blender GUI. What am I doing wrong? Here is the script I am using import os import bpy  bpy.ops.wm.open_mainfile(filepath="materials.blend")  VIEWS = 1 RESOLUTION = 200 RESULTS_PATH = '.' DEPTH_SCALE = 1.4 COLOR_DEPTH = 8 FORMAT = 'PNG' RANDOM_VIEWS = True UPPER_VIEWS = True CIRCLE_FIXED_START = (.3, 0, 0)  fp = bpy.path.abspath(f"//{RESULTS_PATH}") if not os.path.exists(fp):     os.makedirs(fp)  # Render Optimizations bpy.context.scene.render.use_persistent_data = True  # Set up rendering of depth map. bpy.context.scene.use_nodes = True tree = bpy.context.scene.node_tree links = tree.links  # Add passes for additionally dumping albedo and normals. # bpy.context.scene.view_layers["RenderLayer"].use_pass_normal = True bpy.context.scene.render.image_settings.file_format = str(FORMAT) bpy.context.scene.render.image_settings.color_depth = str(COLOR_DEPTH)  # Background bpy.context.scene.render.dither_intensity = 0.0 bpy.context.scene.render.film_transparent = True  # Create collection for objects not to render with background objs = [ob for ob in bpy.context.scene.objects if ob.type in ('EMPTY') and 'Empty' in ob.name] bpy.ops.object.delete({"selected_objects": objs})  def parent_obj_to_camera(b_camera):     origin = (0, 0, 0)     b_empty = bpy.data.objects.new("Empty", None)     b_empty.location = origin     b_camera.parent = b_empty  # setup parenting      scn = bpy.context.scene     scn.collection.objects.link(b_empty)     bpy.context.view_layer.objects.active = b_empty     # scn.objects.active = b_empty     return b_empty  scene = bpy.context.scene scene.render.resolution_x = RESOLUTION scene.render.resolution_y = RESOLUTION scene.render.resolution_percentage = 100  cam = scene.objects['Camera'] cam.location = (0, 4.0, 0.5) cam_constraint = cam.constraints.new(type='TRACK_TO') cam_constraint.track_axis = 'TRACK_NEGATIVE_Z' cam_constraint.up_axis = 'UP_Y' b_empty = parent_obj_to_camera(cam) cam_constraint.target = b_empty  b_empty.rotation_euler = CIRCLE_FIXED_START scene.render.image_settings.file_format = FORMAT scene.render.filepath = fp + '/r_0' bpy.ops.render.render(write_still=True)  # render still  Output of blender --background --python script.py  Screenshot of Blender GUI

I made a character, and its one of my first times texturing, and I saved my character into a new folder, and when I came back to the model ALL the textures were pink, I used to know what to do, but I stopped texturing, how do I bring my textures back?


I was once shown a shortcut that I can't recall/ find. After pinging an ip, then attempting to ssh into it - the ip was saved into to a variable automagically.  Something like:      ping 10.1.23.4     ...     ssh root@$!   and the ip was replicated in the second line replacing $! without further ado.  So does this ring a bell as to what the actual syntax is? Or was this some special configuration? I believe this was running centos if that is related. tia

For example, if I do a   mkdir thisismyfolder912   I remember there is some easier way to switch to thisismyfolder912 than having to do a  cd thisismyfolder912   What is that way and how does it work? Also, what are the other ways I can use this?


if you have 5 black marbles and 1 white marble in one bag,  when randomly selecting 4 out of the 6 marbles at once without replacement, what is the probability of the white marble being included in the 4 marbles selected

If you have 5 marbles in a bag, 2 of them are red and 3 of them are white, what is the probability that you take out 2 red marbles out of the bag back to back? No replacement.


I am fairly new to AI and still learning. Like the title stated, i would like to know how to fill the shape with  gradient colors (or so i dont actually know how to call it) such as this. I tried with blend tool and it worked but i would like to know if there is any faster way to fill it directly rather than  using  blend tool. Thank in advance !

I'm trying to create something like this:  (Ignore the gray diagonal line) I have the female symbol and the rainbow flag. I know how to add stroke, create clipping masks, and create interlocking solid-color shapes with the live paint bucket, but I can't put everything together to make this design. The logical way, I think, would be to "bring forward" or "send backward" a part of a shape by selecting nodes, but I don't think that's possible. How should I go about doing this?


user has serial up-voting reversed, but he still have badge Mortarboard.   Is it correct behavior of badges? I suppose it should be reversed too.  And will this 200 daily reputation (2012-03-20) score for the Epic, and Legendary badges?

What are badges? How do users get badges? How can users get tag badges? Can badges be lost/revoked/taken away after they are awarded? If so, how and when? How can I suggest a new badge?   For more information, see "" and the  in the .


What is a simple proof that $\sin 1^\circ$ is irrational?    I have no idea how to solve this problem.

In university last semester I was asked to prove that $\sin1$ (1 radian that is) is irrational,  and ended up simply using the Taylor Series Expansion. This method provides a very quick solution, but I am curious as to whether anyone has a method for proving this without making use of the Taylor Series Expansion. I feel as though doing so must be possible using some number theory, but am low on ideas as to an alternative approach to the question.  Note:  If anyone is interested in my solution using Taylor Series Expansion (although it is not the focus of my question), here it is :      From    $$ \sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} -  \dots$$   We see that    $$ \alpha = \sin 1 = 1 - \frac{1^3}{3!} + \frac{1^5}{5!} -  \dots $$   Given integers $a$ and $b$, if $\alpha = \frac{a}{b}$ then it follows that $b!\alpha \in \mathbb{Z}$, and $b!\alpha = C + D$ where $C \in \mathbb{Z}$ and we have :   $$ D = \begin{cases} \pm(\frac{1}{b+1} - \frac{1}{(b+1)(b+2)(b+3)} + \dots) \text{    if $b$ is even}\\ \pm(\frac{1}{(b+1)(b+2)} - \frac{1}{(b+1)\dots(b+4)} + \dots ) \text{ if $b$ is odd}\\ \end{cases} $$   In each case we can see that $0 < D < 1$, giving us a contradiction.    Thus, we have that $\sin 1 $ is irrational.    $$ \blacksquare $$


Recently my cat died. He escaped my house and was attacked by a dog. Sadly he didn't survive.  I emailed a male acquaintance ( were not close friends, live long distance, communication is not daily). He's offered a listening ear if I need one. I told him the above ,and that I was feeling sad.  His response by email "My goodness. My heartfelt condolences."  My goodness is expressing surprise?

Why do we say my goodness?  It doesn't sound appropriate for the contexts in which it is used.  Both the my and the goodness don’t seem to bear on a surprising or startling situation.  When was it started, and why?


I am executing the following code in java but i got two different answers for what should be the same number mathematically.  public class TestClass {      public static void main(String[] args) {          double a=0.01;         double b=4.5;         double c=789;                System.out.println("Value1---->"+(a*b*c));         System.out.println("Value2---->"+(b*c*a));           } }   Output:  Value1---->35.504999999999995 Value2---->35.505   Please tell me why I get this result.

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


I want to draw a diagram like this. Could you please help me?

It's the first time I'm using Tikz on Latex. I have to draw this block diagram (this is a low resolution snip from a paper)   In Tikz I have done this:   That is very similar but I need some adjustments, like the u_i arrow and the node sum after the H(s) block.  Is there anybody that can help me with this?  my code:      \tikzstyle{block} = [draw, fill=white, rectangle,  minimum height=2em, minimum width=3em] \tikzstyle{sum} = [draw, fill=white, circle, radius=1mm, node distance=1.5cm] \tikzstyle{input} = [coordinate] \tikzstyle{output} = [coordinate] \tikzstyle{pinstyle} = [pin edge={to-,thin,black}]  \begin{tikzpicture}[auto, node distance=2cm,>=latex'] \node [input, name=input] {}; \node [input, above of=input](input1) {}; \node [sum, right of=input] (sum) {}; \node [block, right of=sum] (controller) {$K(s)$}; \node [sum, right of=controller] (sum1) {}; \node [block, right of=sum1] (filterinv) {$H^{-1}(s)$}; \node [block, right of=filterinv] (system) {$G(s)$}; \node [output, right of=system] (output) {}; \node [output, above of=output] (output1) {}; \node [block, below of=filterinv] (filter) {$H(s)$}; \node [block, above of=controller] (delay) {$D(s)$}; \node [sum, below of=sum1] (sum2) {};  \draw [->] (filterinv) -- node[name=u] {$u_{i}$} (system); \draw [draw,->] (input) -- node {$s_{i-1}$} (sum); \draw [->] (sum) -- node {$e_{i}$} (controller); \draw [->] (system) -- node [name=q] {$q_{i}$}(output); \draw [->] (q) |- (filter); \draw [->] (filter) -- node {} (sum2); \draw [->] (controller) -- node {} (sum1); \draw [->] (sum1) -- node[name=xi] {$\xi_{i}$} (filterinv); \node [input, below of=sum1](input2) {}; \draw [draw,->] (input2) -- node {$r_{i}$} (sum2); \draw [->] (sum2) -| node[pos=0.99] {$-$}      node [near end] {$\tilde{s}_i$} (sum); \draw [->] (delay) -| node[] {}      node [near end] {} (sum1); \draw [draw,->] (input1) -- node[pos=0.15] {$u_{i-1}$} (delay); \draw [->] (u) |- node[pos=0.99] {$u_i$}      node [near end] {} (output1);  \end{tikzpicture}


I know commands for setting specific time and/or date, but can't find ones which move the time relative to the current time.  What are the commands to move the time forward/backward x seconds/minutes/hours? (And possibly also days/months/years?)

How to change the system date in Linux ?  I want to change:   Only Year Only Month Only Date Any combination of above three


As stated in the title, I want to evaluate the integral $$\int_0^\infty \frac{\tan^{-1}(t)}{e^{2\pi t}-1}\,\mathrm{d}t$$ Because of the $e^{2\pi t}$, it seems that complex analysis techniques are required for this one, which I am not so familiar with. I have tried some substitutions and integration by parts. Besides, I tried using the property $$\int_0^\infty f(t)\,g(t) \,\mathrm{d}t =\int_0^\infty \mathscr{L}[f](s)\cdot \mathscr{L}^{-1}[g](s)\,\mathrm{d}s$$ But no luck here. I would like a solution without complex analysis techniques, if that's possible. Thank you!

I want to calculate $$ \int_{0}^{\infty} \frac{\arctan{2t}}{e^{2\pi t}+1} \, {\rm d}t $$ and am wondering if there at all is an analytical expression for the result. I haven't tried much so far, but expressing the denominator as the geometric series and then substituting $z=2\pi t (n+1)$. Equivalently I get $$ \sum_{n=0}^{\infty} \frac{{\rm si}\left(\pi(n+1)\right)}{2\pi (n+1)} $$ where $$ {\rm si}(x) = -\int_{x}^{\infty} \frac{\sin(t)}{t} \, {\rm d}t $$ is the shifted ${\rm Si}(x)$ function. The value is approximately $0.03618247146$, in fact I know from comparison with something else that it is exactly $\frac{\ln \pi -1}{4}$, but there should be some (direct) derivation, or?  Thanks for your input if you have any.  Edit: I tried to follow your instructions, but am now stuck. So I wrote $$ {\cal L}^{-1} \left(\frac{\psi(t)-\psi(1)}{t-1}\right)(s) =\sum_{n=0}^{\infty} \frac{e^{-sn}}{n+1} = e^s \int_s^\infty \frac{{\rm d}x}{e^{x}-1} $$ and taking the Laplace-transform \begin{align} \psi(t) &= \psi(1) + (t-1)\int_0^\infty {\rm d}s \, e^{-s(t-1)} \int_s^\infty \frac{{\rm d}x}{e^{x}-1} \\ &= \psi(1) + (t-1) \int_0^\infty {\rm d}x \int_{0}^{x} {\rm d}s \, \frac{e^{-s(t-1)}}{e^{x}-1} \\ &= \psi(1) + \int_{0}^{\infty} {\rm d}x \, \frac{1-e^{-x(t-1)}}{e^x-1} \tag{1} \\ &= -\frac{1}{t} + \psi(1) + \int_0^\infty {\rm d}x \, \frac{1-e^{-tx}}{e^x-1} \tag{2} \\ &= \dots \\ &=-\sum_{k=0}^{n} \frac{1}{t+k} + \psi(1) + \int_0^\infty {\rm d}x \, \frac{1-e^{-(t+n)x}}{e^x-1} \\ &\stackrel{(\rm{2})}{=} -\frac{1}{2t} + \ln(t) - \int_0^\infty {\rm d}x \, \left\{ \frac{1}{2} - \frac{1}{x} + \frac{1}{e^x-1}\right\} e^{-tx} \tag{Binet 1} \end{align} where $\psi(1)=-\gamma$.  Now we integrate over $t$ from $1$ to $y$ yielding $$ \ln \Gamma(y) \stackrel{({\rm 1})}{=} \psi(1)\,(y-1) + \int_0^\infty {\rm d}x \, \frac{y-1+\frac{e^{-x(y-1)}-1}{x}}{e^x-1} $$ but what now? Substitute?


I have a problem proving this inequality but I can't get anywhere after the inductive step.  $$(x_{1}+x_{2}+...+x_{n})^2\leqslant n(x_{1}^2+x_{2}^2+...+x_{n}^2)$$ Maybe some hints would help.

Stuck, help please, I am really new to this. I opened the 2-norm and multiplied by $n$, then I am thinking to square both sides. The problem is that I do not know how to open $(x_1 + x_2 + ... + x_n)^2$ $\|x\|_1 \leqslant \sqrt n\cdot \|x\|_2$


I'm making this dinosaur, and I'm making certain parts certain materials. For some reason, some faces do this. They are set to be the tan material, but show some red. I'm pretty new to this so it may be a simple answer, maybe not. If you need anymore information, just ask. This is also my first time using this site.

How do you add more than one material to a mesh?   I have tried adding two materials to the object, and then assigning one of the materials to a vertex-group, but I could not find a place to assign it.  I am making a striped bouncy ball that I want to deform, so adding a different material by separating the mesh into different objects would not be ideal.


What do you call the method what you use when you know what to say but not exactly how to say it but use another method to do so?  You have an idea you have to explain to people, you know what you want to say but not how to articulate it correctly. So you end up using examples, sayings to help the person to understand what you are trying to convey, to help to get to the meat/jist of it until you get an "aha"moment that is what I'm trying to say     The  stackexchange english language user knew what he wanted to ask in an indirect way but didn't know the exact words to ask it correctly so he used examples to trying get the question in a "roundabout" way.   or     Pete wants directions to the arcade. He asks a passerby but forgot the word " arcade" so instead he asks "can you give me directions to the place in the mall where the 12-year old kids hang out?" He used  workaround way to explain where he wanted to go. He didn't say the correct word but the passerby knew the place he meant.   What method did Pete use?     For the above Pete can't explain the word succinctly so he uses a [...] way or expresses it []   Words that don't fit exactly:  convoluted means. Convoluted means difficult to understand or complex where I'm trying to instead convey it's an "other"  way to ask to get there.  non-succinct way also is similar to the above  Inarticulate method coveys he isn't clear which is untrue since he is using another method  parallel conveys the two ways that are the same, where instead I want to say the the other method is instead an out of the norm way  Roundabout,Workaround is probably the closest I can think of   This might be a better explanation of the context     The computer system user asks a question but the support ticket was closed with explanation "Your question is convoluted". The user believes the reason is unfair as he believed he question in isolation might be phrased without the correct technical terms but he additionally used a specific example to explain  what he was trying to achieve which left no room for ambiguity to understand what he was asking. He escalates it to their manager saying his question was not convoluted as he used used a [got to the jist of it] way to explain which the helpdesk should have understood and that he feels they were intentionally being pedantic.

What is it called when you use many words to describe the word you want to use?  I know there is a technical word that's used in foreign language acquisition that means using many words to describe a word you don't know.  I'm doing it now, just talking and beating around the bush until someone can tell me the word I'm looking for.


I was changing file permissions and I noticed that some of the permissions modes ended in @ as in -rw-r--r--@, or a + as in drwxr-x---+. I've looked at the man pages for chmod and chown, and searched around different help forums, but I can't find anything about what these symbols mean.

I am using Mac OSX. When I type ls -l I see something like   drwxr-xr-x@ 12 xonic  staff    408 22 Jun 19:00 . drwxr-xr-x   9 xonic  staff    306 22 Jun 19:42 .. -rwxrwxrwx@  1 xonic  staff   6148 25 Mai 23:04 .DS_Store -rw-r--r--@  1 xonic  staff  17284 22 Jun 00:20 filmStrip.cpp -rw-r--r--@  1 xonic  staff   3843 21 Jun 21:20 filmStrip.h   What do the @'s mean?


I know that affine equalities such as  $$a_1 x_1 + a_2 x_2 + a_3 x_3 = b_3$$  are convex. I'm wondering whether there are nonlinear equality constraints, for instance something like  $$a_1 x_1 + a_2 x_2 + a_3 x_3 = b_3 + x^{2p},\quad p \in N$$  or even something like  $$x_1 = x_2^2$$  Are these kinds of equality constraint also convex? Can you give me any other example showing non-affine convex functions? Thanks!

In convex optimization, the feasible region is convex if equality constraints $h(x)$ are linear or affine, and inequality constraints $g(x) \leq 0$ are convex. Does this mean that if $h(x)$ is nonlinear, then the optimization problem is non-convex? Is there any special case where $h(x)$ is nonlinear and the feasible region is still convex?


Let's say that both int and float are 4-byte aligned. According to ISO C99 6.3.2.3 p.7:     A pointer to an object or incomplete type may be converted to a   pointer to a different object or incomplete type. If the resulting   pointer is not correctly aligned for the pointed-to type, the behavior   is undefined.   According to this, the following code should not invoke UB:  #include <stdio.h> #include <stdlib.h>  int main(void) {     int i = 7;     float *f = (float *) &i;     exit(0); }   I noticed that GCC is not always good at catching strict aliasing rules violation attempts but here in can correctly warn that dereferencing *f  will break will break strict-aliasing rules what is illegal according to 6.5 p. 7:     An object shall have its stored value accessed only by an lvalue expression   that has one of the following types:         a type compatible with the effective type of the object,     a qualified version of a type compatible with the effective type of     the object,     a type that is the signed or unsigned type corresponding to the     effective type of the object,     a type that is the signed or unsigned type corresponding to a     qualified version of the effective type of the object,     an aggregate or union type that includes one of the aforementioned     types among its members (including, recursively, a member of a     subaggregate or contained union), or     a character type.      $ gcc  -Wall -fstrict-aliasing -Wstrict-aliasing=2 so1.c -Wcast-align so1.c: In function ‘main’: so1.c:7:2: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing] so1.c:7:9: warning: unused variable ‘f’ [-Wunused-variable]   So does it mean that this code may invoke UB only when *f will be dereferenced and it's 100% correct in current shape?  EDIT:  One more thing - would this cast be also legal if float had a different size from int but alignment would still be the same for both types? I think yes because this is what C standard says but I don't understand why alignment is the most important here and not size. Why does alignment matters when converting pointers and only when dereferencing?

When asking about , people sometimes refer to the strict aliasing rule. What are they talking about?


I've currently got a DataGrid which is bound to a List. This List is populated through a database query. Now, I'd like to be able to select an item in the DataGrid, and move it up or down, and at the same time having it move in the List.  I thought about LinkedLists, because I also need to have the ability of inserting above or below specific spots in the list. However, I've only ever heard of LinkedLists and I'm not even sure where to start. Looking at the MSDN for it, there doesn't seem to be a built in MoveUp()/MoveDown() methods. I figure, if I can move it in the list, then getting it to move in the DataGrid will be simple.  My question is: Is there a way to move items up and down in a LinkedList or List?

So I have a generic list, and an oldIndex and a newIndex value.  I want to move the item at oldIndex, to newIndex...as simply as possible.  Any suggestions?  Note  The item should be end up between the items at (newIndex - 1) and newIndex before it was removed.


Suppose that we have a population of N= 1000 people and they want to select 5 items (for simplicity) {A, B, C, D, E} (but actually the number of items is in the order of thousands). Number of selections for items is {3, 142, 52, 633, 800}. Each person (selector) is free to select as many items as they want. Selecting one item may affect the selection of another item by one person. For example, if items are goods in a supermarket, the first person may select items A and C. The second person may select all items. Each person can select each item just once. We want to find “the minimum number of selections”, named T, so that if the number of selections for an item is larger than T, we can say that item is interesting or popular for the population since at least T people have selected that item. We want to find this number (T) by “a statistical method”. Thanks.

Suppose that we have a population of $N= 1000$ people and they want to select 5 items (for simplicity) $\{A, B, C, D, E\}$ (but actually number of items is in the order of thousands). Number of selections for items is $\{3, 142, 52, 633, 800\}$. Each person (selector) is free to select as many items as they want. Selecting of one item may affect for selection of another item by one person. For example, if items are goods in a supermarket, the first person may select items $A$ and $C$. The second person may select all items. We want to find “the minimum number of selections”, named $T$, so that if number of selections for an item is larger than $T$, we can say that item is interesting or popular for the population since at least $T$ people have selected that item. We want to find this number ($T$) by “a statistical method”. As an another example, for each item, we can assign a value to it by the percentage of people who have selected that item. So, we have a range of 0 (no person has selected it) to 100% (all people have selected that item). Definitely, 100% means popularity or significance for that item for the population. But We want to find what is the minimum percentage so that we can say that item is still popular. In other words, is the range of popularity from 20-100% or 10-100% or ....? We want to find a statistical measure for defining popularity of significance. Thanks.


I have a number of specific questions regarding the design of a high write throughput data ingestion stack into a highly relational database.   Where can ask high level software architecture questions on Stack Exchange sites relating to this project?

There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.


Some days ago I've said that "people in the gym work out hardly", then someone told me that when I say "hardly" in this context, then the meaning is in fact opposite of what I want to say (that their workout takes a lot of power).   Then my question is what is the adverb that can replace the incorrect adverb "hardly" to some other correct word in this context?

His degree was hard earned.     His degree was hardly earned.    Which is right?


Is there a way to get an image in Javascript? By this, I mean, get an image by URL, and then be able to draw it in an HTML canvas using the ctx.drawIamge() function? I'm using this to make a chess game, and wanted to use custom images for this. Here's my code so far: let ctx = document.getElementById("gm").getContext("2d"); let board = [   ["bR", "bN", "bB", "bQ", "bK", "bB", "bN", "wR"],   ['bP','bP','bP','bP','bP','bP','bP','bP'],   ['','','','','','','',''],   ['','','','','','','',''],   ['','','','','','','',''],   ['','','','','','','',''],   ['wP','wP','wP','wP','wP','wP','wP','wP'],   ["wR", "wN", "wB", "wQ", "wK", "wB", "wN", "wR"]   ] function fillSquare(color, x, y) {   ctx.fillStyle = color;   ctx.fillRect(x, y, 64, 64); }  function drawGrid() {   color = "#3c9653";   x = 0;   y = 0;   for (let x1 = 0; x1 <= 7; x1++) {     for (let y1 = 0; y1 <= 7; y1++) {            fillSquare(color, x * 64, y * 64);       if (color == "#3c9653") {         color = "#d2dba2";       }       else {         color = "#3c9653";       }       x++;     }     if (color == "#3c9653") {       color = "#d2dba2";     }     else {       color = "#3c9653";     }     y = y + 1;     x = 0;    }     } function drawPieces(grid) {   let px = 5;   let py = 5;   for (row of grid) {     for (piece of row) {       if (piece == "wR") {         piece_img = require("./imgs/white/wrook.png");         console.log(piece_img);         ctx.drawImage(piece_img, px, py);       }       px = px + 64;      }     py = py + 64;   } } drawGrid(); drawPieces(board);  The way I tried to do this, is using a require() function, but that cannot be used in normal JS, (or according to the error I got): ReferenceError: require is not defined     at drawPieces (/script.js:52:9)     at /script.js:63:1

How can I fetch images from a server?  I've got this bit of code which allows me to draw some images on a canvas.                     <canvas id="canv" width="1024" height="1024"></canvas>                      Instead of looping over document.images, i would like to continually fetch images from a server.  for (;;) {     /* how to fetch myimage??? */     myimage = fetch???('http://myserver/nextimage.cgi');     ctx.drawImage(myimage, x, y); }


I understand that for instance on a Windows system that when you delete a file that in fact it is not deleted as such immediately, but that the file is just marked meaning that other files can override it. This means then that some deleted files can then be recovered after their deletion.  Is there a similar system on Ubuntu? And if so is there a way to get it so that the deleted files, before their actual deletion, are encrypted or something so that if they are recovered then they cannot be read?  I am running Ubuntu 14.10.

Is there a way to make sure that a deleted file can not be recovered?   As you know, deleting a file by pressing shift-del or using trash doesn't mean that file is gone forever. It resides somewhere in the computer.  In day to day life, law enforcement or thieves use recovery programs to reveal our private data or something else.   They can recover all data that resides on hard disk, in RAM, and even USB.  To protect us from these people, what should one do? Which program should one use?  Note: I don't want an answer like first use a recovery program then erase that file with shred. With just one program, I want to erase all unused/deleted files on my computer.


I am very enthusiastic about learning QFT. How much group theory would I need to master? Please could you recommend me a textbook on group theory, which would help me to start QFT?

I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.  Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated?


Given the current covid-19 situation where the home country (India) has stopped all international flights, how can one (65+ year old) extend their B2 visa or stay after I-94 extension? Any help is appreciated.  I called up USCIS regarding the same and they told me it usually takes around 6 months to process these applications. My main concern is what if the application is rejected and the applicant has already overstayed their original VISA expiry date, will it be considered illegal? What happens if it is considered illegal?  The BringIndiaHome Initiative, is an initiative by Indian and American Indian lawyers to assist stranded Indian citizens to return to India. The petition seeks the relief of directing the Government to formulate a scheme to identify Indian Nationals in distress in the US and airlift them, specially in view of the WHO travel advisory which advised nation States not to impose disproportionate and excessive travel bans.If anyone interested please mail :  or fill up this form :   P.S. Please don't remove the Airlift details I have added here, last time someone edited my posting and removed those details.It's an important info, don't delete it.

My mom has come to US on a tourist visa and her I-94 expires on the first week of May.   Due to the coronavirus, travel restrictions have been imposed in our home country (India). Also we want to avoid the risk of traveling in flights at this time.  Is there an easy way to to extend her stay in the US by one or two months?  I am aware that we should fill out an  to extend our stay. But in-order to submit the online application it requires a fee of $370.    Is filing I-539 the easiest way to extend her stay at this time? If so, is it possible to waive the fee due to the coronavirus situation?  After filing I-539 should she wait for an approval to continue her stay? Or is the receipt good enough?   Can you please help me with these? Thanks!  [Edit 1]:  With the current situation of the virus, traveling anywhere sounds like a very risky operation, especially for elders.   That is the main reason behind this question. If the US government will allow visitors to overstay until Covid-19 settles down!


Here $2^A$ is the set of all functions from $A$ to $\{0,1\}$.  This is evidently true if one of $A$, $B$ is finite.  To me it seems like it should be true for infinite $A$, $B$, but a proof is oddly hard to come by.  Is there a quick proof or counterexample?

In a lecture recently one of my lecturers was proving something to do size of basis or something (I can't remember exactly) and somewhere near the end of the proof we had the following:  $2^\alpha=2^\beta\Rightarrow \alpha=\beta$  Now this was just in a proof about finite (or possibly countable) things so everything is cool here but this rang a bell a a results that may be independent of ZFC or something which I couldn't quite recall. I had a look but I couldn't find anything about it?  Thanks for the help


This has eluded and frustrated me for too long.   After adding objects like a Sapling or a gear you get a panel inside the tools menu-bar with options to control the object that you just added.   If you select another object, make changes in the same object(rotate, scale, etc.) or click anywhere in the viewport, the panel disappears. I've never been able to find it once it's gone. I've been trying to follow this tutorial and this happened multiple times and each time I have to start over. So,  Where is the panel and how do you get it panel back?

When you first add a cylinder, you have the option to change the number of vertices, etc, but once you do anything else in blender, it seems you no longer can edit those parameters.   Is there a setting anywhere or an add-on that allows these parameters to be edited later on? If not, how easy would such an addon/feature be to create for anyone reading this?


Claim: $p\neq q$ are primes, $m\in\mathbb{Z}$, $N=pq$ So: $m^{\varphi(N)+1} \equiv m \pmod N$. I was hinted that $\gcd(N,m)\in \{1,p,q,N \}$, and that for the case $\gcd(N,m)=1$ I should use Euler's theorem (that part I understood), but for the other cases I should use CRT. I can't see how to apply CRT in these cases. Thanks for your help :)

I want to know a proof of an alternative form of Fermat-Euler's theorem   $$a^{\phi (n) +1} \equiv a \pmod n$$   when $a$ and $n$ are not relatively prime.   I searched some number theory books and a cryptography book and internet, but there were only proofs of the original theorem  $a^{\phi (n)} \equiv 1 \pmod n$ or in case n=pq which is used for RSA. So I would be very thankful if someone show me a proof or book I should read.