The following is taken from .     An imaginary number is a number whose square is less than or equal to   zero.   But I also heard that      An imaginary number is a number whose square is less than zero.   Which is the correct one?  Edit:  My doubt came from the fact that some mathematicians consider the imaginary numbers are on the vertical axis and the real numbers are on the horizontal axis. So the intersection point at the origin. As a result, zero is included in the imaginary number set.

A purely imaginary number is one which contains no non-zero real component.   If I had a sequence of numbers, say $\{0+20i, 0-i, 0+0i\}$, could I call this purely imaginary?   My issue here is that because $0+0i$ belongs to multiple sets, not just purely imaginary, is there not a valid case to say that the sequence isn't purely imaginary?


I want to have a variable that is a nested list of a number of empty lists that I can fill in later. Something that looks like:    my_variable=[[], [], [], []]   However, I do not know beforehand how many lists I will need, only at the creation step, therefore I need a variable a to determine it.  I thought about simple my_variable=[[]]*a, but that creates copies of lists and it is not what I want to have.   I could do:  my_variable=[]   for x in range(a):    my_variable.append([])   but I'm looking for a more elegant solution (preferably one-liner). Is there any?

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?


So I know that the period of a pendulum in a free falling elevator isn't going to change because there is no force acting on it since $$T = 2\pi\sqrt{\frac{\ell}{g}}.$$ So what happens to a pendulums period when it's going up in a lift in a constant speed, and what will happen to the period of a pendulum if it's accelerating up in a lift?

A simple pendulum suspended from the ceiling of a stationary lift has period $T_0$. When the lift descends at steady speed, the period is $T_1$. When the lift descends with constant downward acceleration, the period is $T_2$. Explain why $T_0 = T_1 < T_2$.  I know that for small angles of oscillations, $T \approx 2\pi\sqrt\frac{l}{g}$ where $l$ is the length of the pendulum. For the first two cases, since $\sum F = 0$, the value of $g$ is apparently the same. However, I am unable to explain why the period is largest for $T_2$. If $g$ is the same for all cases, shouldn't their periods be the same?


I have a table 'Route' with Id ,Name and Active columns. If Id = 0 I want to select all the Id's where Active = true.  If Id > 0 I want to select the data for particular Id where Active = true.  I tried with following Query. But not working. (here I passed 2 for a Id value.)  Can someone support me?  DECLARE @ID INT SET @ID = 2  SELECT  DISTINCT Id ,Name  FROM    Route  WHERE CASE WHEN @ID > 0  THEN Id = @ID AND Active= 1 ELSE Active=1 END   Sample Data Attached.

I tried searching around, but I couldn't find anything that would help me out.  I'm trying to do this in SQL:  declare @locationType varchar(50); declare @locationID int;  SELECT column1, column2 FROM viewWhatever WHERE CASE @locationType     WHEN 'location' THEN account_location = @locationID     WHEN 'area' THEN xxx_location_area = @locationID     WHEN 'division' THEN xxx_location_division = @locationID   I know that I shouldn't have to put '= @locationID' at the end of each one, but I can't get the syntax even close to being correct. SQL keeps complaining about my '=' on the first WHEN line...  How can I do this?


Lets say I have a flat 2D circle (bezier that's been filled). The node setup is simply a transparent BDSF + Diffuse BDSF going into a mix shader.  Is there a way that you can use nodes to make it so only a desired part of the circle appears transparent like in the image?    I don't necessarily want this exact pattern, I just made some random shape for the example,

So with my model, I've been struggling to create hair because it always looked weird or off and recently I discovered the "Bevel Curve" addon and it's an absolute lifesaver.   So I converted the bevels into mesh to colour it, except it lags blender like crazy and I need this model for a video game I'm currently developing called Candles(so I can't upload the model, sorry) but I was wondering, is it possible to put a texture on a bevel curve like you would mesh or any other method or giving it colour?


When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)?

Why is it that when you first fill up a balloon, it's hard to get air through, but after inflating it a bit, it becomes much easier to further inflate the balloon?


i need to have a function that has two arguments.  public void funx(string a, string b) {  // operations using string a and b }   is it by any way possible to call the method funx() with only the first argument 'a' . if  second argument 'b' is not entered during the function call, it should take a default value (for b) that can be set in fun x. in case i call funx() with two arguments a & b , then the values that i have provided in the function call should be used while skipping the  default values set( for 'b').  in simple words, 'b' is optional. if entered, its value should be used. if not entered, then a default value should be used

Note: This question was asked at a time when C# did not yet support optional parameters (i.e. before C# 4).  We're building a web API that's programmatically generated from a C# class. The class has method GetFooBar(int a, int b) and the API has a method GetFooBar taking query params like &a=foo &b=bar.   The classes needs to support optional parameters, which isn't supported in C# the language. What's the best approach?


Suppose that there is a real number $r$ such that $r+\frac{1}{r}$ is an odd integer.Then $r$ is irrational.   Let $r\in \Bbb Q$ then $r=\dfrac{p}{q}\implies \dfrac{p}{q}+\dfrac{q}{p}=$odd  $\implies \dfrac{p^2+q^2}{pq}$ is odd integer.  Since  $r+\frac{1}{r}$ is an odd integer$\implies pq\mid p^2+q^2$  How to derive a contradiction from here?

Can sum of a rational number and its reciprocal be an integer?   My brother asked me this question and I was unable to answer it.   The only trivial solutions which I could think of are $1$ and $-1$.  As to what I tried, I am afraid not much. I have never tried to solve such a question, and if someone could point me in the right direction, maybe I could complete it on my own.  Please don't misunderstand my question.   I am looking for a rational number $r$ where $r + \frac{1}{r}$ is an integer.


I have this sentence:     In our software we ask the user to specify some elements by clicking on the <highlighted / being highlighted / active ...> HTML element   My purpose for the sentence: Suppose you move the mouse over some elements and the border of each element under the mouse gets highlighted as the mouse enters it.   The element is not highlighted before the mouse enters it The element gets highlighted as the mouse enters it   If I say "highlighted element", one can't know if it was highlighted before or it gets highlighted as the mouse enters it.  Which phrase can be used instead of "highlighted" to convey this only-present-not-past-tense relation?

Why is it grammatically correct to use these -ing adjectives:   annoying habit exciting news   and NOT these -ed adjectives:   annoyed habit excited news


It's my first time doing this kind of task, so I'm a little unsecure if my method is right.   Heres my setup and what I`ve done so far.  I`m using a PCAN USB (Peak System) + PCAN View tracing a J1939 Network using extended identifiers. The application has no numerical indication about the bus load, only status like bus ok, heavy bus... So I decided to convert the trace record into a CSV and then analyzing it with Python.  Once I had it converted, I was interested in get 4 fields of information: message ID, data size (how many data bytes in that message), how many times that message was sent, and the message itself.  Cycletime was calculated as the total recording time divided by how many times that message was sent.  Message Size was calculated considering:  Start of Frame - 1 bit  Identifier A - 11 bits  Identifier B - 18 bits  Substitute Remote Request - 1 bit  ID Extension Bit - 1  Remote Transmission Request - 1  Reserved Bits - 2  Data Length Code - 4  Data Field - 0-64 bits  Cyclic Redundance Check - 15  CRC Delimiter - 1  ACK Slot - 1  ACK Delimiter - 1  End of Frame - 7  ________________________________TOTAL (considering a 8 byte message): 128bits Load was calculated as 128bits*1000/cycletime  % of Bandwidth was calculated as Load/250000  Am I Missing Something?  Is there another method that's more accurate?

I have a few questions regarding CAN bus load  Is there any derived equation/formula to calculate the bus load?  I need transmit below frames(Assume Standard frame format) at baud rate 500 kbps on the bus 5ms  ----- 50 frames. 10ms ----- 10 frames. 100ms ---- 30 frmaes. Event messages ---- 10 frames.   How to calculate bus load, does anyone knows kindly illustrate the same?  What is the maximum bus load on CAN bus?


Python doesn't support multidimensional arrays, but I thought this workaround would be easy enough. It's just not working though. Here's my code  mat = [ [ None ] * 3 ] * 3 mat[0][0] = 1 return mat   Output  [[1, None, None], [1, None, None], [1, None, None]]   Why is it changing mat[1][0] and mat[2][0]? If I ask it to print mat[0][0] it just gives me 1 like it should.

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?


I recall watching this film as a kid in the mid 80s and it really scared me at the time. It was to do with scientists making a machine that made monsters (that apparently exist all the time but we cannot see) become visible. There was a part where one of the main characters grows some kind of small eye on a stalk that comes out of his forehead. It was quite a gory film - at one point he tries to eat a womans brain (using her eye socket as entry point). It was so many years ago I just cannot recall the name of the film and I would quite like to see it again to see how badly it has aged. Can anyone recall this from the vague description above?

From what I can remember of the movie, it features an increasingly isolated loner building or inheriting a machine in his Attic that starts bringing back monsters from outside reality when he turns it on.  I think it was from the early 80s and it had a Lovecraftian vibe to it.  The movie is like 'The Fly' in that it features a story that slowly descends into dark horror.  Does anyone have any clue what I'm talking about?  I'll try to add more details if I can remember anymore.


I'm implementing collision detection with the map for my platformer. I have a method that generates a polygon on every tile and checks if the player hits it -- that's all fine. The problem is that when ever a player touches a wall in front of him the d key which moves him to the front gets disabled so he can't walk any further that way.  This method works great for preventing him from walking into walls, but I also want him to be able to jump on the walls and there is the problem. So he falls on the tile(polygon) the game senses that and applies the same method for the d key, preventing the character from walking left or right, because the game thinks it is hitting the tile in the front but it is hitting from above.  Long story short, the game handles collision from above same as from the front or back. How do I make it recognise collisions from the side separately from above?  My code is along these lines:  if(PlayerPolygon.interesects(TiledPolygon) && dKey==1) {          moveX = 0; } if(dKey==1) {   player.x +=moveX }

After , I need some more help.  How can I find out which side of a rectangle a collision came from and react accordingly?      The blue arrows are the paths that some circular objects would follow if before and after colliding with the box.  How can I calculate this?


I have a LINQ select query which fetches a list of books:  var books = from b in _context.Books             where b.Available && b.BookType == bookType             orderby b.Title             select new BookViewModel             {                 Title = b.Title,                 Description = b.Description,                 Id = b.Id,                 SortOrder = ?             };   BookViewModel has a SortOrder property which I want to set in the query. The first book in the list would have SortOrder = 1, the second book would have 2, etc. It's essentially just the index of the book in the returned list.  Is there a way to set this within the query? I understand I could do another linq query once I have the list, but this seems inefficient. I don't properly understand the innards of a linq select, but given it's sorted by the orderby I don't see why there wouldn't exist some way to set the index of the element.

Is there some rare language construct I haven't encountered (like the few I've learned recently, some on Stack Overflow) in C# to get a value representing the current iteration of a foreach loop?  For instance, I currently do something like this depending on the circumstances:  int i = 0; foreach (Object o in collection) {     // ...     i++; }


I read that in large utility systems more and more generators are added to provide extra power. I'm lacking some basic knowledge here. So, what happens when we connect two generators in parallel? Is it like connecting 2 voltage sources in parallel with a resistor R? I'm trying to think it as a circuit but it doesn't help. Does the current in the load increase? And if so, how?

My question is the following: We have two 220V 20A generators connected in parallel to total power 8.8 kw 220 v 40 A load  is 5.5 ohms I'm interested how each generator sees this load since every generator gives half the power. I put this question because one generator can not see this load like 5.5 ohms because it gives half power to not the full power I would like to have somebody explain it a little bit better because it makes me confused .     simplified question   my question is that since every generator in the parallel circuit gives half power in the ideal case it would mean that the generator 1 that gives 220v 20A that is half the power can not "see" the resistance of 5.5 ohms because if "seen" this resistance he had to give complete current in that case we have two problem generator 1 burned because it is not made for such a current problem two if generator 2 gives the same current then the law on energy conservation is not worth what is absolutely not possible  thanks    The last attempt to explain what I asked is very simple  we have two 220v 20A generators and a load of 5.5 ohms if we connect this resistance to just one generator it exceeds its power because it is 220v and 20 A 4.4 kw and the current at that resistor is 40A which would mean that it exceeds the maximum power of one generator ok if we add another generator then together have enough power to supply load it if we know that every generator gives half power ie 220v and 20A  it is impossible to "see "a resistance of 5.5 ohms


I think this has happen by some natural disasters like storms, droughts, fires, encroaching, and the seas taking over our land.

So the stories of the Hunger Games are set in , a post-apocalyptic society situated in North America. Is there anything to explain what caused the Apocalypse? Whether from the main books, any extra material or interviews? (No fanfic please.)  As well as the cause, is there any indication of when the apocalypse happened? And how long after the apocalypse are the events of the Hunger Games?


How can I connect to a remote host using SSH and create one Bash script to copy all files and folder from my old server to my new server for backup every day?

I want to be able to login to a remote via ssh without having to enter the password all the time.   How do I set it up? Is a different command required to execute a password-less session?


A question was asked a number of times on this forum, mostly in 2011-2013, of the theoretical reasons for exactly 3 generations of elementary particles. The answers mentioned that certain observed processes could not happen with less than 3 generations, but at that time almost all sources (except ) agreed that the specific reasons for exactly 3 generations were unknown.  My question is if there have been any theoretical developments lately suggesting a theoretical reason fo the number of generations being exactly 3.  The question is about potential recent developments, please do not mark it as a "duplicate" of questions asked years ago.

In the  of particle physics, there are three generations of quarks (up/down, strange/charm, and top/bottom), along with three generations of leptons (electron, muon, and tau).  All of these particles have been observed experimentally, and we don't seem to have seen anything new along these lines.  A priori, this doesn't eliminate the possibility of a fourth generation, but the physicists I've spoken to do not think additional generations are likely.     Question: What sort of theoretical or experimental reasons do we have for this limitation?   One reason I heard from my officemate is that we haven't seen new neutrinos.  Neutrinos seem to be light enough that if another generation's neutrino is too heavy to be detected, then the corresponding quarks would be massive enough that new physics might interfere with their existence.  This suggests the question: is there a general rule relating neutrino masses to quark masses, or would an exceptionally heavy neutrino just look bizarre but otherwise be okay with our current state of knowledge?  Another reason I've heard involves the Yukawa coupling between quarks and the Higgs field.  Apparently, if quark masses get much beyond the top quark mass, the coupling gets strong enough that QCD fails to accurately describe the resulting theory.  My wild guess is that this really means perturbative expansions in Feynman diagrams don't even pretend to converge, but that it may not necessarily eliminate alternative techniques like lattice QCD (about which I know nothing).  Additional reasons would be greatly appreciated, and any words or references (the more mathy the better) that would help to illuminate the previous paragraphs would be nice.


I'm wondering if I should be woried about these SMART values on my new harddrive (Seagate 2048 GB ST2000LM015). Just look at screenshoots, id 01 and id 07 seems bad or not? Should I return hdd to the seller? Error scan (full) -> no errors.

I've just had an issue pop up related to my drives.  First things first, I was working in my case when I clumsily shifted the foot of the case off of my desk. Case shifted and hit the desk somewhat hard, but only fell an inch or two. It had been properly shut down so this may not have anything to do with the issue.  After booting up, I noticed that when playing a video from my F: Drive (Seagate), it produced a whine, almost a chirping sound coming from the hard drive bay. I think I may have heard this before the drop, but quieter.  Fearing impending failure I downloaded GSmartControl and inspected the drive information. The Seagate drive displayed a high Raw Read Error Rate, as well as a high Seek Error Rate.  I've read some of these values can be high on Seagate drives from the start. This drive is about 6 months old and the producer of the noise.  I also checked my Toshiba drive, which came with a refurbished prebuilt I bought about a year ago. It showed more normal SMART data, but displayed some concerning statistics (2 "Mechanical Start Failures" and 2 "Reported Uncorrectable Errors").  Both of the drives passed the basic SMART test, but the noise was quite alarming. It would stop as soon as a paused the video and start right up again as soon as I resumed playing.  Here is an album with 3 photos of the SMART data, the Seagate did not display statistics.  Could I please have help interpreting the SMART data, and whether this may indicate an impending failure?   Thank you for your time.   Here are images of the SMART data.


I'm studying password encryption algorythms. I know the existence of bcrypt, scrypt, and varients, but I want to chanllenge myself on this question and that's why I came up with this algorythm in PHP:  $secret = md5( uniqid( mt_rand(), true ) ); // Length is 32 $passwd = 'qwert123'; $hash = $secret . hash( 'sha256', $secret + $passwd );   Since secret is randomly determined and added at the front of the password hash, I could verify the password input like this:  $secret = substr( $hash_from_db, 0, 32 ); $hash_from_db === $secret . hash( 'sha256', $secret + $input_from_user );   What do you think about this implementation? I would do like to receive some feedback about it. Thank you.

It is currently said that MD5 is partially unsafe. Taking this into consideration, I'd like to know which mechanism to use for password protection.  This question,   suggests that hashing multiple times may be a good idea, whereas  suggests using salt.  I'm using PHP. I want a safe and fast password encryption system. Hashing a password a million times may be safer, but also slower. How to achieve a good balance between speed and safety? Also, I'd prefer the result to have a constant number of characters.   The hashing mechanism must be available in PHP It must be safe It can use salt (in this case, are all salts equally good? Is there any way to generate good salts?)   Also, should I store two fields in the database (one using MD5 and another one using SHA, for example)? Would it make it safer or unsafer?  In case I wasn't clear enough, I want to know which hashing function(s) to use and how to pick a good salt in order to have a safe and fast password protection mechanism.  Related questions that don't quite cover my question:


I want to set my login screen (greeting screen or GUI) to the default setting, which asks for password befor let me login, I dont know how did I messed it out, now running saucy, it just can show me the list of desktop environments, but after I chose the environment I want, I just click and login directly, then after I login to the descktop another message pop out asking me to type my keyring password.     I wounder if me inserted (PGP) key from previous system did that!, any how, I just want the normal default login back, any help please? step by step for a newbie  I tried System Settings --> User Accounts GUI tool, or use the passwd command  sudo passwd username   pressing "Unlock" but is not responding as all other "Unlock"s in this laptop right now nor the terminal commands change anything, they change the password in terminal but still the same exat above mentioned drama

I just installed Ubuntu 12.10 and afterwards, I accidentally set the administrator account password to empty/null. This gave me problems when trying to do administrative tasks in the GUI, so after reading up on askubuntu I used the passwd command to set the password for the account anew.  However, at the login screen when clicking on the account, I'm not asked to enter the password; but, instead, I log in directly as if there is no password set for the account.  When doing administrative tasks in the GUI, I will be asked for a password.  What do I do to be asked for the password at login time?  I did already try, several times, in the User Account settings window to set a new password for the account. That is, in the settings window it does not say "login without a password" for my account and it shows that there is a password set for the account.


Is it possible to change the "user2612587" display name and also change the picture for the Stack Exchange Network profile, like on all the other sites on the network? Or is the Stack Exchange account a generic one that can't be changed?  There are a few questions and answers about changing the display name but I don't think it addresses this particular question. Because the answers to those questions are usually about the synchronization mechanism.  For example, I saw :     Did you change all of the display names manually, without using the   synchronization mechanism? If so, try this:         Go to your account page   Click the "Accounts" tab   Scroll to the very bottom   Click the "Copy [site] profile to all Stack Exchange sites"      I have tried this, but in my case that option isn't showing up.

I was able to change my name on all Stack Exchange sites, but not on the main profile at  itself.  Is there a ways to do the change on  as well?


in late Feb I'll be travelling to the USA on the visa waiver program, after my 3 months is up I wish to spend 2 weeks in South America, then return to the States, am I able to do this? Or do I need to return my home country?   Do I also need to book my flight from the US to South America beforehand? At the moment I wish to book a flight to the USA with a return flight 6 months and 2 weeks later, bookng my (visa run) flight while there.  I know getting a B2 visa sounds more simple, however being in northwest Australia I live more then 1000 km away from a US consulate, therefore it is cheaper and less time-consuming to book a 2 week stay in South America.

I am currently visiting the USA from the UK (I am a UK citizen) and am intending on staying here for the full 90 days under the Visa Waiver Program.     How long would I have to stay out of the US at the end of this period before returning again?    Would I have to return to the UK, or could I stay with friends in another country (such as Canada) for a while?


Recently I drove on a road not yet mapped on . As soon as I get back, I will add it. It made me wonder if every piece of land is already mapped, or if you could still have a bit of adventure, doing some real exploring.

To be clear, yes, we can see everything from Google Earth or other satellite imagery, but that doesn't mean we can explore it.  GE can't see into forests, canyons and caves.  Has every mountain been scaled? Has every ocean depth been mapped? Has every jungle been navigated?  Basically, the question is, is there any part of our planet left to explore? To put your foot on a rock and shove a flag in the ground and name it whatever you please.  What are the main areas left for exploration that someone might want to try and do.  Clearly not every square foot of the Sahara has been navigated, but that's a bit harder than say, a North American forest.


How do I figure out which file system a given file/directory is located on?  (For example, I would like to know if the file/directory is a temporary file in RAM, or if it's stored on disk. And what mount point it corresponds to, if any. Etc.)

If I do  # cd / # ln -s /home test # cd test # mount --bind $PWD /mnt   the entry in /proc/mounts is  /dev/sda2 /mnt ext4 rw,noatime,data=ordered 0 0   which is the device that is mounted to /home and is not easily deducible from $PWD which is /test. How can I determine which device (i.e., /dev/sda2) is going to show up in /proc/mounts in general given that the bind mount may be to a directory/file that is potentially "obscured" by symlinks, other bind mounts, etc?


I am little confused as I thought HashMap and Hashtable should behaves same way when it comes to hashCode and equals method. in this example below my key class has overridden equals method to always return false.  does any one have any idea that can explain in this difference in behavior because it seem like output is different for both  value null  value null  value Value 1  value Value 2  import java.util.Hashtable; import java.util.HashMap;  public class HashTest {      public static void main(String[] args) {          Hashtable ht = new Hashtable();         HashMap hm = new HashMap();         KeyClass k1 = new KeyClass("k1");         KeyClass k2 = new KeyClass("k2");          ht.put(k1, "Value 1");         ht.put(k2, "Value 2");         hm.put(k1, "Value 1");         hm.put(k2, "Value 2");          System.out.println("value " + ht.get(k1));         System.out.println("value " + ht.get(k2));          System.out.println("value " + hm.get(k1));         System.out.println("value " + hm.get(k2));     } }  class KeyClass {     String key;      public KeyClass(String str) {         key = str;     }      @Override     public int hashCode() {         return 2;     }      @Override     public boolean equals(Object obj) {         return false;     } }

What issues / pitfalls must be considered when overriding equals and hashCode?


Im trying to automate export chrome history to a file. Ive learned google keep changing the mechanism for keeping history, while they used SQLLite i see in the version of chrome im using (88.X...) i cannot open the History file in that way, all of my searches for this issue are not updated to this time, does anyone have information about this?

In Google Chrome, is there a built-in method to make an HTML file I can save to my local machine, like the file for bookmarks?  If not, is there an extension that does the same?


I'm getting 'cars' array using xmlhttprequest and dynamically creating the anchor tags for each value in the array.   Now im not able to access the innerhtml of newly created anchor tags.  //script for getting array and creating anchor tags dynamically  var xmlhttp = new XMLHttpRequest(); xmlhttp.onreadystatechange = function() { if (this.readyState == 4 && this.status == 200) {       var cars = JSON.parse(xmlhttp.responseText); for (i = 0; i < cars.length; i++) { var mydiv = document.getElementById("myDiv"); var aTag = document.createElement('a'); aTag.setAttribute('href','#'); aTag.setAttribute('class','cl'); aTag.innerHTML = cars[i] + "<br>"; mydiv.appendChild(aTag); }  } };  xmlhttp.open("POST", "http://localhost:3000/welcomepage", true); xmlhttp.setRequestHeader("Content-type", "application/json"); xmlhttp.send();   //script for accessing innerhtml of the above created anchor tags.  $('.cl').click(function(e) { e.preventDefault(); var t = $(this).text(); alert(t); }

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


Simplify   $$\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt{5}-\sqrt[4]{125}}}$$   Found in a book with tag "Moscow 1982", the stated answer is $1+\sqrt[4]{5}$. Used all tricks that I know but without success. The answer appears to be correct, checked in Wolfram Alpha.   Hints and answers welcomed. Sorry if this is a duplicate.

Question:     show that: the beautiful ${\tt sqrt}$-identity:      $$ \left({2 \over \sqrt{\vphantom{\Large A}\, 4\ -\ 3\,\sqrt[4]{\,5\,}\ +\ 2\,\sqrt[4]{\,25\,}\ - \,\sqrt[4]{\,125\,}\,}\,}\ -\ 1\right)^{4} =5 $$   Can you someone have methods to prove this by hand? (Maybe this problem have many methods?because this result is integer. It's a surprise to me.) Thank you   Because I found this $$4\ -\ 3\sqrt[4]{\,5\,}\ +\ 2\sqrt[4]{\,25\,}\ -\ \sqrt[4]{\,125\,}$$ is not square numbers.


Can I write the integral as $f(x)=\int_0^{x} |t-x|t\,dt + \int_{x}^1  |t-x|t\,dt$  so that $f(x)=\frac{2x^3-x}{2}+\frac{1-2x^3}{3}$  But here I'm restricting $x$ to the interval $(0,1)$ and I need $x$ to be any real number.   So what should be the correct approach here to find the minimum value of $f$?

Let $f(x)=\int_0^1|t-x|t~dt$ for all real $x$. Sketch the graph of $f(x)$, what is the minimum value of $f(x)$    I could not in any way understand how to approach this problem. I think I will be able to plot the graph if I know how the function looks like, so one can wish to avoid that part.   To find the minimum value I thought of differentiating the function. But, there is $x$ on one side and $t$ along with $x$ on the other side. I got really confuse how should I do that. Please help.


Yesterday, I saw serial upvotes to my Questions and Answers. Today all those upvotes were reversed, as per the rules.    But, today I see that I am being serial-downvoted.    Now, I don't know if these serial downvotes get rollbacked or not tomorrow.    What I am thinking is, there should be a time difference between two votes, say 30 seconds. So it can reduce serial voting.

I just noticed that I lost a bunch of points from my reputation score, and I used the "reputation" tab on my user profile page to try and track down the cause.  During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question title, it says "voting corrected".     What does this mean, and what caused it?  Did I do something wrong? Why did I lose all of that reputation? Is the system punishing me for leaving too many good answers?  Is there any way to earn it back?


Can anyone tell me the most proper commands with all steps to change my desktop environment to GNOME 3?  I am using Ubuntu 14.04.

I followed the instructions for compiling GNOME Shell and it did compile with a few errors here and there but it didn't run. I installed GNOME Shell using sudo apt-get install gnome-shell but I got version 2.31.x, while the latest is 2.91.5 or something. So is there a way for me to install the latest build?   Is there some repository available for the latest build?


Edit: This is not a duplicate question. The vivid folders in  are simply not there.  I understand that this is not directly supported, but I want to upgrade first to wily then to xenial.  I ran:  $ sudo sed -i -re 's/([a-z]{2}\.)?archive.ubuntu.com|security.ubuntu.com/old-releases.ubuntu.com/g' /etc/apt/sources.list   In order to be able to upgrade to wily, but there seems not to be a vivid folder in old-releases.ubuntu.com/ubuntu/dists/ though wily is there.  How do I upgrade to wily? Will vivid appear in old-releases with time?

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


I have problems with layerproperties in Qgis. I load a shapefile, edit textsize and color and do labeling some points with text. After i saved the layer as shapefile again and open it......all changes as edited color and textlabeling are gone. Do someone know what exactly the problem could be?  Regards Prospekteur

I'd like to create a Categorized style in QGIS, classify with it data in a shapefile and then save the shapefile with the new categorized style. Is it possible?


I have an application that passes data to an sql variable called @inputvar. The application passes the data as a string. The stored procedure declares the variable @inputvar as varchar. The problem is, the data is of the format '12,13,15'. because of a where clause in the stored procedure, i am getting an error saying that conversion failed when converting the varchar value to datatype int  The where cause is:  select *  from table  where ID in (@inputvar)   I have tried stripping the quotes: replace(@inputvar,'''','') and I have tried converting the variable to an int: cast(@inputvar as int), but both attempts failed

Is there a graceful way to handle passing a list of ids as a parameter to a stored procedure?   For instance, I want departments 1, 2, 5, 7, 20 returned by my stored procedure. In the past, I have passed in a comma delimited list of ids, like the below code, but feel really dirty doing it.   SQL Server 2005 is my only applicable limitation I think.  create procedure getDepartments   @DepartmentIds varchar(max) as   declare @Sql varchar(max)        select @Sql = 'select [Name] from Department where DepartmentId in (' + @DepartmentIds + ')'   exec(@Sql)


In my algebra course (taught from Artin), a principal ideal domain is defined as an integral domain such that all ideals are principal. This got me wondering:      Are there rings for which every ideal is principal, but the ring is not an integral domain?

In the usual definition, a principal ideal domain $R$ is also assumed to be an integral domain. However, the property that every ideal is generated by a single element does not seem to immediately imply that the ring is integral. Is this correct and if so:  Do there exist rings where every ideal is generated by a single element and has zero divisors?  I am most interested in the case where $R$ is commutative with unity, but don't mind examples where these properties don't hold. Also, assuming there are examples, is there any reason why we make this assumption?


Given a differentiable function ${\rm f}:\left(1,+\infty\right) \to \mathbb{R},\quad$ and $\quad\left\vert\,{\rm f}'\left(x\right)\,\right\vert \leq \frac1x\,,\ \forall\ x>1$.  $$ \mbox{Prove that}\quad \lim_{x \to +\infty}\left[\vphantom{\Large A}% {\rm f}\left(x + \sqrt{x\,}\,\right) - {\rm f}\left(x\right) \right]=0 $$

Given a differentiable function $f:(1,+\infty) \to \mathbb{R}$, and $|f'(x)| \le 1/x$ for every $x>1$. Prove that:  $$\lim_{x\to +\infty} \left(f(x+\sqrt{x})-f(x) \right)=0.$$


I am wondering if package listings has a feature that can skip a few lines and substitute them with some dots, to produce something like the following  1 | error_temp = error - ((numpy.linalg.norm(b, 'fro')) ** 2.0) ... | ... 5 | error -= (numpy.linalg.norm(b[j, :])) ** 2.0  I would like to be able to specify a few lines and ask listings to substitute them with dots and also print a few dots as its line number to indicate that it is skipping a few lines here. Also, when the skipping is over, resume to the actual line number as if the skipped lines were not skipped. Here is my minimal working example, which might not help though \documentclass{article} \usepackage{listings} \lstset{breaklines = true, frame = trBL, tabsize = 4, basicstyle = \small \ttfamily, keywordstyle = \color{blue}, stringstyle = \color{red}, rulecolor = \color{black}, numbers = left, numberstyle = \tiny}  \begin{document}  \begin{lstlisting}[language = Python, escapeinside = {(*@}{@*)}] error_temp = error - ((numpy.linalg.norm(b, 'fro')) ** 2.0) (*@ \cdots @*) error -= (numpy.linalg.norm(b[j, :])) ** 2.0 \end{lstlisting}  \end{document}  The problem with the code is, it would not skip line numbers and it can not print dots as line number for skipped lines. Please let me know if it is not clear of what I am trying to do, thanks in advance!

Is it possible to add non-number characters on the left of a code block?  Specifically, I want to add ... to correspond with some source code (see image).    I am currently using commands to stop / start the line numbers. Here is the code:  \documentclass[12pt]{article}  \usepackage[a4paper, margin = 20mm, top = 30mm, bottom = 25mm]{geometry} \usepackage{xcolor, soul} \usepackage{listings}  \definecolor{codebackground}{rgb}{0.95, 0.95, 0.92}  \lstset {     frame            = tb, % hrule above and below     keepspaces       = true,     columns          = flexible,     basicstyle       = {\normalsize\ttfamily},     escapeinside     = {(*@}{@*)}, % for escaping     backgroundcolor  = \color{codebackground},     showstringspaces = false,     language         = C,     keywordstyle     = \color{blue},     stringstyle      = \color{red},     commentstyle     = \color{teal},     numbers          = left, % {none, left, right}     firstnumber      = 1,     numberstyle      = \scriptsize\color{black},     numbersep        = 5pt }  \let\origthelstnumber\thelstnumber \makeatletter % for stopping line numbers \newcommand*\stopnumber {     \lst@AddToHook{OnNewLine}     {         \let\thelstnumber\relax         \advance\c@lstnumber-\@ne\relax     } } % for starting line numbers \newcommand*\startnumber[1] {     \setcounter{lstnumber}{\numexpr#1-1\relax}     \lst@AddToHook{OnNewLine}     {         \let\thelstnumber\origthelstnumber         \refstepcounter{lstnumber}     } } \makeatother  \begin{document} \begin{lstlisting}[firstnumber = 456] int third_function(const int c) {     /* error checking */     if(c < 0)     {         return;     } (*@ \stopnumber @*)      ...     (*@ \startnumber{512} @*)     /* other stuff */     int d = 4;     char* word = "third function"; (*@ \stopnumber @*)      ...     (*@ \startnumber{678} @*)     return (c * d); } \end{lstlisting} \end{document}


I was taking a look for questions, and I started to read  thread.  One of the answers says to use the command cat /etc/passwd|grep '/bin/bash', to test if there's other users in the computer. For security purposes, I tested that and I got this:  root:x:0:0:root:/root:/bin/bash nori:x:1000:1000:Nori,,,:/home/nori:/bin/bash   Now, I would like to know, why there is a root user? I thought I only created 1 user.  Also, please note that after installing Ubuntu, my friends (who also use Linux, but not Ubuntu) told me to create a root password (which is different from the user password).  EDIT: To add the root password, I used the sudo -i, and then I used the passwd to create a new password.  Thank you for the help, and sorry if this question have already been answered.

If you use sudo su - or sudo -s you will get the full root certification  "likewise a root user ".  Is this user an official user or is it from canonical?  ~$ sudo su - [sudo] password for username:  root@lp:~# id uid=0(root) gid=0(root) groups=0(root) root@lp:~# pwd /root root@lp:~#


Let $R$ be a ring and $x \in R$.  Prove that if $x$ is nilpotent then $1-x \in R$ is unit.  May I use the fact that $$ \frac{1}{1-x} = 1 + x + x^2 + \ldots $$ and then say that since $x$ is nilpotent, there exist $n$ such that $x^n=0$, and of course $x^{n+1}=0$, and therefore this sum is finite and $1/(1-x)$ is a well defined element.  will that prove compile ?

Let $(A, +, \cdot)$ be a ring with $1$.  An element $a\in A$ is nilpotent if there exists $n\in \mathbb{N}$ so that $a^n=0$.      Show that if $a$ is nilpotent then $1+a$ and $1-a$ are invertible.


I am running into some strange problem in PostgreSQL  $ sudo -u postgres psql Blogging psql (10.10 (Ubuntu 10.10-0ubuntu0.18.04.1)) Type "help" for help.  Blogging=# \dt                List of relations  Schema |         Name          | Type  | Owner  --------+-----------------------+-------+-------  public | Blogs                 | table | e  public | Posts                 | table | e  public | __EFMigrationsHistory | table | e (3 rows)  Blogging=# select * from Blogs Blogging-# ; ERROR:  relation "blogs" does not exist LINE 1: select * from Blogs                       ^   The same problem occurs when I log in as the owner of the tables:  $ psql -U e Blogging psql (10.10 (Ubuntu 10.10-0ubuntu0.18.04.1)) Type "help" for help.  Blogging=# \dt                List of relations  Schema |         Name          | Type  | Owner  --------+-----------------------+-------+-------  public | Blogs                 | table | e  public | Posts                 | table | e  public | __EFMigrationsHistory | table | e (3 rows)  Blogging=# select * from Blogs;  ERROR:  relation "blogs" does not exist   I created the database when running my application which uses Entity Framework, following . But I had  not sure if they are related to my question here.

I used pg_restore to load my postgres db with a dump file. I connected to my db with my user :  sudo -u arajguru psql dump  select current_user;  current_user  --------------  arajguru   Now I was able to see all the newly created tables:  dump=> \dt                List of relations  Schema |       Name        | Type  |  Owner    --------+-------------------+-------+----------  public | Approvals         | table | arajguru  public | Approvers         | table | arajguru  public | Conditions        | table | arajguru  public | Entities          | table | arajguru  public | EntityDefinitions | table | arajguru  public | Projects          | table | arajguru  public | Rules             | table | arajguru  public | run_history       | table | arajguru (8 rows)   But when I try to fire a select * query, it gave me this error:  dump=> select * from Approvals; ERROR:  relation "approvals" does not exist LINE 1: select * from Approvals;   What can be the reason for this error? Please help.


I understand the appeal of not actually deleting questions and answers, but what can we do when we accidentally post confidential information?  For example, passwords or company names. Sometimes we forget to edit those out before posting a code snippet, and if we don't notice within the 5 minute grace period, it becomes permanent.  Is there anything we can do about this?

I've observed several incidents where users inadvertently posted detailed, sensitive information. For example, a Server Fault user who posted a question with working login credentials to his actual production server, or the Stack Overflow user who posted actual medical records as example data for his question.   What should be the procedure for handling such cases?


I would like to automate the following steps that I am currently performing manually.  In a terminal, I perform these steps:   start tmux split into 10 panes tile the panes navigate to each pane and ssh into a server, repeat 10 times synchronize the panes   Is there a way to script all this, including the 10 different ssh login commands?

Is it possible to make a bash script that starts tmux and split the screen horizontally and runs watch -n1 tail -n5 file_n in each ? Basically I'm starting a script multiple times and write its progress into different files that I'd like to monitor. Would be nice if I could run that from one script as opposed to manually open 10 files by myself. I never used tmux btw that's why I'm asking this.


The  says:  Regarding: $*     When the expansion occurs within double quotes, it expands to a single word with the value of each parameter separated by the first character of the IFS special variable. That is, "$*"is equivalent to "$1c$2c...", where c is the first character of the value of the IFS variable.   Regarding: $@     When the expansion occurs within double quotes, each parameter expands to a separate word. That is, "$@" is equivalent to "$1" "$2" ....    Provided the first character of the value of the IFS variable is in fact a single space, I can't seem to come up with an example where these two special parameters would produce different behavior. Can anyone provide me with an example (again, without changing IFS) where they would produce different behavior?  My own test, which still baffles me a bit, is as follows:  #!/usr/bin/env bash # File: test.sh # set foo and bar in the global environment to $@ and $*  test_expansion () {   foo="$@"   bar="$*" }   Now testing:  . test.sh test_expansion a b c d # foo is $@ # bar is $*  for e in "$foo"; do   echo "$e" done # a b c d  for e in "$bar"; do   echo "$e" done # a b c d

Consider the following code:  foo () {     echo $* }  bar () {     echo $@ }  foo 1 2 3 4 bar 1 2 3 4   It outputs:     1 2 3 4       1 2 3 4   I am using Ksh88, but I am interested in other common shells as well. If you happen to know any particularity for specific shells, please do mention them.  I found the follwing in the Ksh man page on Solaris:     The meaning of $* and  $@  is   identical  when  not  quoted  or  when  used  as a parameter   assignment value or as a file name. However, when used as  a   command argument, $* is equivalent to ``$1d$2d...'', where d   is the first character of the IFS variable,  whereas  $@  is   equivalent  to  $1 $2 ....   I tried modifying the IFS variable, but it doesn't modify the output. Maybe I'm doing something wrong?


I'm trying to do something like this:   public void <String,int> getItem  {     return <"Jen",23>;  }   I know I can use a custom class, but how I would I return two results in one function call.  1 - Is the above template function possible in java, and how would by caller get part 1 of it and part 2 later.  2 - Can I do it using an associative array like in actionscript?  3 - Can I do it using a hashmap of some sort?  4 - What are other possible ways are there   I attempted all three ways, but one way or another syntax is hitting me. So if anyone can give clear examples

I want to return two objects from a Java method and was wondering what could be a good way of doing so?  The possible ways I can think of are: return a HashMap (since the two Objects are related) or return an ArrayList of Object objects.  To be more precise, the two objects I want to return are (a) List of objects and (b) comma separated names of the same.  I want to return these two Objects from one method because I dont want to iterate through the list of objects to get the comma separated names (which I can do in the same loop in this method).  Somehow, returning a HashMap does not look a very elegant way of doing so.


Hello guys I just want to ask if there's a formula to activate hyperlinks in excel. Let's say I have 10,000 rows in column D all the rows consists of URL. I know how to activate it using F2 command but I have 10,000 rows. How can I do that? Thanks.  This is the example link I have

How do I turn a column of urls into hyperlinks, so that users can click on the url in a cell and have it open in a browser?  I pasted 100 urls and each went into its own cell. When I double-click in the cell and then leave it, Excel turns the text blue and makes a link out of it. I don't want to double-click a hundred times, but still want to format all the cells into links.


I know I can take square root on both sides so I get z and $\sqrt{\sqrt3+3i}$ but is there a way of simplifying $\sqrt{\sqrt3+3i}$ ?  EDIT: Seems like taking the square root may not be the best thing to do (as answer suggests).

I was reading an example, where it is calculating the square roots of $\sqrt 3 +3i$.  $w=\sqrt 3 +3i=2\sqrt 3\left(\frac{1}{2}+\frac{1}{2}\sqrt3i\right)\\=2\sqrt 3(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3})$  Let $z^2=w \Rightarrow r^2(\cos(2\theta)+i\sin(2\theta))=2\sqrt 3(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3})$.  But how did they get from $\sqrt 3 +3i=2\sqrt 3\left(\frac{1}{2}+\frac{1}{2}\sqrt3i\right)=2\sqrt 3(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3})$?  And can one just 'let $z^2=w$' as above?  Edit: $w=2\sqrt 3(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3})=z^2\\ \Rightarrow z=\sqrt{2\sqrt 3}(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6})\\ \Rightarrow \sqrt{2\sqrt 3}\frac{\sqrt 3}{2} +i \sqrt{2\sqrt 3} \frac{1}{2}$


Is there a more efficient way to write a series of equations?  \begin{equation*}     B'(x)=0 \end{equation*} \begin{equation*}     -\frac{1}{x^2} + \frac{1}{(1-x)^2}=0 \end{equation*} \begin{equation*}     \frac{-(1-x)^2 +x^2}{x^2(1-x)^2}=0 \end{equation*} \begin{equation*}     -x^2+2x-1+x^2=0 \qquad \text{Con $x\neq 0 \wedge x\neq 1$} \end{equation*} \begin{equation*}     2x-1=0 \end{equation*} \begin{equation*}     x=\frac{1}{2} \end{equation*}

I am trying to align a multiline equation using array within the equation but it turns out it doesn't do very well. The code I am using is as follows:  \begin{equation}    \begin{array}{lcl} \mathcal{L}^{-1}\left\{f(d)\right\} &= \mathcal{L}^{-1}\left\{f_1(\delta).f_2(\delta)\right\} \\ & = exp(mt) \star \left\{\frac{l}{2\sqrt{\pi t^3}} exp(-l^2/{4t})\right\} \\ & = F_1 * F_2 \end{array} \end{equation}   Can anyone suggest better way to deal with it ?


Writing the code  The weight decay was set to $1 \times {10^{−4}}$ for Model 8 and $5\times 10^{−4}$.   the negative sign is missing.    And these are the packages I'm using  \usepackage{jmlr2e} \usepackage{indentfirst} % Definitions of handy macros can go here \usepackage{float} \usepackage{underscore} \restylefloat{table} \newcommand{\dataset}{{\cal D}} \newcommand{\fracpartial}[2]{\frac{\partial #1}{\partial  #2}}

My beamer presentation presents this problem Package inputenc Error: Unicode char − (U+2212)(inputenc) not set up for use with LaTeX. \end{frame}. I tried remove some elements and I see that problem appear when I use - in equation. I'd like one hint about this problem.   \documentclass[pt]{beamer} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage[utf8]{inputenc} \usepackage[brazil]{babel} \usepackage{upgreek} \usepackage{mathtools} \usetheme{Berlin}  \begin{document} \begin{frame}{Convergência - Prova}     %\justifying     Sem perda de generalidade a demonstração foi focada numa partícula unidimensional. Reescrevendo a Equação, tem-se que     \begin{equation}     x_i(t + 1) + \alpha_1 x_i(t) + \alpha_2 x_i(t − 1) = \alpha_3     \end{equation}     onde     \begin{equation}     \begin{aligned}     \alpha_1 &= (1 + \omega) + u(r_1 - r'_1)c_1 + u(r_2 -r'_2)c_2 + c_1r{'}_1 + c_2r'_2 \\     \alpha_2 &= \omega \\     \alpha_3 &= u(r_1 - r'_1)c_1p + uc_2(r_2g - r'_2n) + c_1r'_1p + c_2r'_2n                         \end{aligned}     \end{equation} \end{frame} \end{document}   Sorry by english


I have a database with MongoDB 2.4.14 and I want to migrate the database to MongoDB 3.6.  Note: the file is original from the db path. Not from mongodump.  This process is messy as it requires doing so on many of our clients.  Any advice will be welcomed as I'm a bit lost in this process.

I have a database file from MongoDB 2.4 and we want use this on mongodb 3.6.  note: the file is original from the db path. Not from mongodump. This process is messy as it requires doing so on many of our clients.  Any advice will be welcomed as I'm a bit lost in this process.  Thanks


Imagine that I'm exactly in the middle of two identical masses. So that each of them exerts an identical acceleration on me and in the exact opposite direction. My question is Will these opposite accelerations cancel, or will they split me in half?

What if a person is put between two identical dense spherical bodies (well, not as dense as black holes, but definitely 100 times more than earth) with mass $M_1=M_2=10^{30}kg$, exactly in the middle between them ( vertical axis parallel with "human height vector" and the line connecting two spheres' centres passes exactly trough person's  centre of mass). Let's say $M_1$ and $M_2$ are mounted onto some very strong poles and they are not approaching each other, but are stationary at $1$ meter.   I am aware that the forces would cancel out at exactly the middle, but human body is not symmetrical and it's mass is not equally distributed across it's volume. Would the human in question be torn apart or would it just deform? What would happen if the human body was completely symmetrical and with equal mass distribution, and could withstand such forces without being deformed? Would the person maybe spin?  I am not sure if this will affect the overall outcome, but let's  say the mass of the person in question is $m=80~kg$.


Show that every subgroup of $ ( \Bbb{R} ,+)$ is cyclic or dense.  (Note that we say $A \subset  \Bbb{R} $ is dense if $\overline{A} =\Bbb{R}$.)  For example $\Bbb{Q}$ is a subgroup that is dense but not cyclic and $\Bbb{Z}$ is cyclic but not dense.  I think no subgroup of the real numbers can be both cyclic and dense.

Possible Duplicate:          Let $(\mathbb{R},+)$ be the group of Real Numbers under addition. Let $H$ be a proper subgroup of $\mathbb{R}$. Prove that either $H$ is dense in $\mathbb{R}$ or there is an $a \in \mathbb{R}$ such that $H=\{ na : n=0, \pm{1},\pm{2},\dots\}$.  I am not able to proceed.


I am trying to find out how to make a cannon or gun that works with the physics simulation. but I have two problems.   I'm not sure how to suddenly apply force behind an object,then remove it. I can't stop the projectile from wedging into the barrel and bouncing around trying to escape.(the alternative is to make is smaller, but it still "bleeds" through the mesh)   how can I use the ridged physics engine to create a ballistic simulation( mortar, gun,etc)?

I'm trying to create a bowling animation and I want the ball to hit the pins. I already added the Rigid Body physics to the objects but can't get the ball to move.  Obviously I could just add keyframes but   that seems to interfere with the Rigid Body physics it doesn't look too realistic.   Is there a way to add some kind of motion to the ball?


I am trying to create a custom map where colored terracotta can only be placed on other terracotta blocks of the same color, but I don't know the command.

I'm currently in the process of making a custom map and I want to add blocks that can only be placed on a certain colour clay.  This is the command I tried using.  /give @p cobblestone 1 0 {CanPlaceOn:["hardened_stained_clay"],Damage:3}   However, even with this command the cobblestone can be placed on any colour of stained clay. What command can I use for placing only on a certain block?


What I want to do is quite self explanatory. Just like the title states. I want to code something that will generate a grid which contains is filled of Tetris pieces. However some conditions must be met :   Having no empty holes for the final grid (all sections of the grid filled) Having no blocks sticking out (e.g. a long tetris block sticking out of the square grid)   I have tried to approach the problem using my way since the methods used online are too complicated for me. The first idea I had was to use a 2D array which each row will be gone through to have some generation algorithm. The next row will depend on the previous row. Such as making a 2x2 block. It will check if the current row position is empty, if it is then it will check if the previous row is empty. If it is then it will make keep note that this point is being used. But if the previous block is already been used. It will check what kind of block it is and depending on what information is on that position. It will either be a connecting piece of just a blank piece.  The second idea i have in mind is similar to the first idea. That is, it will also go through each row but this way is dependent on maths. Lets say we have a 10x10 grid. We can say each row is made of 10 blocks. And from that we can say each tetris shape is made of miniblocks. E.g the 2x2 block is made of 2x2 small blocks. So from this we can, go through the first row and for the first 2 blocks of the 10 keep note in the array that we want to generate the a 2x2 tetris block. And we can go to the next row and we know that the previous row there was a 2x2 tetris block that is need to be finished creating in the second row. And so we repeat this to try and get a filled grid of tetris blocks.  Sorry I am not good at explaining/implementating/reading code. Sorry for the inconvenience. I have been suggested by some people to look at Tetris AI. And maybe use the AI to solve my problem. But I'm not good with reading other people's code. Plus it isn't in the language i understand. And i dont have anyone to go through the code with me.  So i prefer to use my own idea since i know what is going on. But i don't know how to implement the code.  If there is anyone who could help me in any way it would be my honor. Thank you in advance.

I'm thinking of making a puzzle game where the objective is to fill a grid with shaped puzzle pieces (for example, the classic Tetris shapes).  How can I go about generating a set of pieces that can be guaranteed to be used to fill the grid, leaving no gaps? How could I adapt this algorithm to scale the difficulty of the resulting puzzle?


$$A,B,C$$ are real numbers such that ,$${ A }^{ 2 }+{ B }^{ 2 }+{ C }^{ 2 } = 1 $$ and $$A+B+C = 0 $$   find the maximum value of ${ (ABC) }^{ 2 }$   I don't know how can I start to solve this question . I hope you can help me in solving it or even giving me hints .

If a,b,c are real numbers satisfying $a+b+c =0; a^2+b^2+c^2=1$.  Prove that $a^2 b^2 c^2 \le \frac{1}{54}$.


I have a mysql production database, with multiple tables. Tables are related with foreign key constraints. I want to make a small test database, by collecting/exporting only a small subset of data from the whole database (i.e. from all tables), so that foreign key constraints are preserved in the data subset.  How can I do that?

Is it possible to back up a PostgreSQL database with only a fraction of the data (1000 Rows from each table)?  I am able to back up that database using pg_dump. In some case I need db with minimum data.  pg_dump --host=localhost --port=5432 --username=postgres --password          --column-inserts --schema=test  testdb > test_backup.sql   How can I modify the above command to take the back up with 1000 number of  data??


I desperately want to avoid asking "do we need tag tags".  Many of the SE sites have tag pages inundated with titles; most notably  and to a lesser extent ,  and .  I am of the opinion that having titles for tags on these sites is 100% necessary and relevant and allows proper categorization of related questions.  Unfortunately, as evidenced by the tag pages of these sites, having titles obfuscates more general tags of other relevance, such as utility tags (using Movies & TV as an example: , , , , etc.), title tags (again, M&TV: , , etc.), and possibly site-specific categorized tags (M&TV; category would be "genre": , , etc.).  Even tag aliases could be categorized as such, if they aren't already.  Every SE Meta already does this to some extent with the "required" tags.    While the expected practice is for the tag pages of these sites to sort themselves based on usage (in Movies & TV, a lot of the common utilities have bubbled to the top as expected over the lesser titles, but then-again, it's still in Beta), there are other sites (notably, Arqade) where applicable tags are drowned in titles and therefore will never be found in order to be used enough to sort in the expected fashion.  Yes, I do understand it is up to each community's participants to manage their tags, but even general clean-up is somewhat daunting and might not prove to be effective.  Why do I think we need this?  Without foreknowledge or expertise, or knowing what to type out during a question, it is very tough to locate a tag you might want to use in these sites.  Tag categorization could help a user properly tag a question by suggesting categories of tags to choose from, then relevant tags.  Is tag categorization needed, and if so, how should categorization be applied; via a new built-in SE utility, an adopted practice, or other enhancement?

Possible Duplicate:          Since so many thousands of tags and topics exist, it would be really useful to visually browse through tags by organizing them into a , or hierarchical map. This drill-down map would make it easier to find the tag/subtopic you want or just generally browse within the topics you're interested in.  So we could nest all "visual-studio-2008" and "visual-studio-2003" tags into "visual-studio", which would be under "dev-tools". Something like how Wikipedia's categories have sub-categories.


I have two layers: a 30m x 30m grid and a layer of polygons indicating landuse. I already know how many landuse polygons are in each cell. For example cell 105 has 4 different classes of landuse. However, I also want to know which landuse classes are in this cell. Is there are way to use "Join attributes by location (summary)" or another function to get a summary of the landuse classes for each cell? For example: cell 105 contains residential, industrial, allotment and park.

I have a woodland scheme advice layer that has a polygon for each area of advice (brown layer in the picture). I also have a polygon layer of UK local authorities (red boundary layer in the picture). I would like to perform a spatial query which returns the local authority name for each woodland advice scheme. This would work fine if each woodland advice scheme was found in just one local authority boundary. However many are found across a boundary of two different authorities. For instance, one scheme sits across the boundaries of the authorities of Fife and Angus. The scheme is the yellow selected polygon in the picture and the red line is the authority boundary. How do I get the spatial join to return a value of Fife; Angus (or something similar to identify two values) instead of just Fife or Angus.


I am following . It says that     Unpack the downloaded Hadoop distribution. In the distribution, edit the file etc/hadoop/hadoop-env.sh to define some parameters as follows:   but when I open etc directory, I right-click to create a new directory inside. But "Create New Folder" option is disabled in context-menu. How can I create it?

I'm new to linux and the terminal. As I learn how to use the terminal to navigate through directories, I like to use the gui file explorer to mirror my terminal navigation. The icons and file extension info in the gui file explorer help me figure out what everything is. However, I can't access the root folder via the gui, I can only access it via the terminal. Is there a way to enable access to the root folder outside of the terminal?


I have a secondary internal hard drive to store files. However, Snap programs in Ubuntu do not have the permissions to open the files on the secondary hard drive. To open files with certain Snap apps, I have to copy them first to the primary Ubuntu drive to access them. Desired solution: How do I enable Snap access to contents on my secondary internal HDD as if it was my main hard drive with full permissions.

I have Ubuntu 18.04 LTS installed. I inserted USB-flash to my laptop. It was automounted to /media/username/DISKLABEL and opened in Nautilus. I can read and write objects to it. How can I access it from the application, which is installed as Snap? I tried snaps of the following applications such as gedit, arduino-mhall119, organize-my-files. All them show me errors if I navigate to /media folder:    Could not read the contents of Media Error opening the directory of '/media': permission denied  Output of active Snap  is below: $ snap interfaces  | grep -v ".*-$" Slot                             Plug :browser-support                 organize-my-files :core-support                    core:core-support-plug :cups-control                    gedit :desktop                         gedit,organize-my-files :desktop-legacy                  gedit,organize-my-files :gsettings                       gedit,organize-my-files :home                            arduino-mhall119,gedit,organize-my-files :network                         arduino-mhall119,gedit,organize-my-files,pulsemixer :opengl                          organize-my-files :pulseaudio                      organize-my-files,pulsemixer :unity7                          arduino-mhall119,gedit,organize-my-files :wayland                         gedit :x11                             arduino-mhall119,organize-my-files,pulsemixer gnome-3-26-1604:gnome-3-26-1604  gedit gtk-common-themes:gtk3-themes    gedit gtk-common-themes:icon-themes    gedit gtk-common-themes:sound-themes   gedit -                                arduino-mhall119:serial-port -                                gedit:avahi-observe -                                gedit:mount-observe  Updates:  connecting mount-observe to Gedit with snap connect gedit:mount-observe does not help. it seems that we need special Snap with support of  interface.


Assuming I get a good model after the training and testing phases, then I am using it to predict on some new input data. Just wondering if I should use the mean and std which I get from the training set to standardize the input data? Or should I just do the independent standardization based on the new input data themselves?  Many thanks in advance!

I am supposed to standardize a training and a validation set "so that the training set has zero mean and unit $l_2$-norm". In order to do so I use the data.normalization function from R's ClusterSim package,       normalizedtrainingset <- data.Normalization(trainingdata,type="n12",normalization="column")   which does do the trick for the training set. Now I am a bit confused about how to proceed with the validation set. I surely cannot use the same function because it would use the validation set's mean and sd and not the mean/sd from the training data. Thus, I proceeded like this:      validation.standardized <- (validation-mean(training))/sd(training)   This takes into account the mean and sd of the training set. However, the values in the validation set are still quite a bit larger than those of the training data because it has not been normalized. My question now is: do I divide the validationset by its own $l_2$-norm, do I divide it by the $l_2$-norm of the training set or do I not divide it at all and the values in the validation set have to remain larger than those in the training data (the latter seems unlikely).


I'm looking for a relatively easy way for doing custom keyboard shortcuts on Ubuntu. Coming from OS X, there was an amazing tool called Karabiner that allowed me to easily remap keys to predefined shortcuts, and even add custom ones. I was wondering if there is a similar tool for Ubuntu.

I'm searching for a way to remap certain keys in ubuntu.  i.e.   I'd like to change PgUp to Home or PgDown to End.  Does a built-in command or a tool exist reassign keys in Ubuntu/GNOME?


I don't want 3D printing to show up in 'my websites'. I am using the Android app. How can I remove that site?

Is there any way to remove individual SE accounts for particular SE sites?  So in other words, say I want to keep my current Stack Overflow account just like it is.  But say I want to delete my account on Server Fault so that it no longer exists and doesn't show up in my SE/SO profile.  Is there any way to do that?  Recap: Keep current login (and certain Stack Exchange sites) but remove particular SE sites' membership for my particular login.  Does that make sense?  Current Accounts Me - StackOverflow Me - SuperUser Me - ServerFault  Desired End Result Accounts Me - StackOverflow Me - SuperUser  Where the desired end result accounts will be the same user (Me) with the persistent questions/answers/reputation/etc.


What is the total no. of permutations of the letters of the word MISSISSIPPI in which no four "I"s come together?   My try-:  $7!/4!\times 2! \times 8!/4!$  But not getting the right answer.  Please help

In how many ways can the letters of the word $MISSISSIPPI$ be rearranged ?   I am confused on whether it is  $\dfrac{11!}{4!4!2!}$ or $\dfrac{11!}{4!4!2!}-1$  since it is given rearranged and not arranged.


Zenodo and ResearchGate can assign a DOI to an article. After publishing an article on Zenodo or ResearchGate with a DOI, if the article is good, will the article still be accepted for publication by peer-reviewed journals?  Assume that the journal in question allows green open access (i.e., posting of a preprint on a public site).

On ResearchGate, if you upload something like a thesis, and then it says publish resources, does this mean the thesis becomes properly published in the sense of the usual requirements of journals that there be no prior publication of the submitted work?   I ask because I’m drafting thesis chapters into journal articles and did not choose to publish the thesis as a whole work in order to do so, so I want to make sure that by clicking publish resources I am not actually publishing the copy I’ve uploaded, I’m just making it publicly available? Does this mean it becomes published despite it not technically being a published work? (If so, I’ll just remove the copy I uploaded).


The Financial Times, like many other newspapers, has a strip under its title on the front page, split into several items (three in today’s paper — see illustration) promoting articles on internal pages. I was wanting to refer to one of these in a letter but realized I had no idea what the technical/journalistic term for it is. There must be one, because people working on the newspaper have to refer to it, but it’s something that is quite difficult to formulate an internet search for. Does anyone know what it is?    Addendum  Apologies, but it didn’t occur to me that US journalistic usage may possibly be different from British usage, which is my practical concern in this case. I’ve addressed that myself.

Often newspapers have a header on the front page where they feature headlines, as well as the page number, for feature articles in later pages of the newspaper.   Here "'Power granny' to the royals" refers to a page on B5 to read the article.   What do you call these?


I have two internet connection, each with 4mbps bandwidth. I want to join/merge both of them to get 8mbps speed, both routers have WLAN and LAN capability.    How to Double my speed using two routers? Can I bond two connections in Windows and double my internet connection speed? Any download manager that accepts two internet connection to download?

We have a broadband line coming into our building which delivers around 8-10Mbps, which is okay but not great. Fiber is available in our area (30-100Mbps) but it's not available where we are just yet.   Is there some way we could connect two lines (which we would take from two different providers so we would have redundancy if one failed) and merge them into one signal which we could distribute?  Is there some sort of setup that can do this?  Of course we have the option of a leased line but for 12Mbps symmetrical upload/download we'd be looking at around £500 per month compared to £15 per month for normal or fiber broadband.  I made a small pseudo flow chat of the setup below:


When you use find-all and find-in-files in Notepad++ a search-result window appears below the screen. On my system this window have been hidden (possible I have dragged it to minimize) and it cannot be unhide.  I have tried to drag all bars in notepad++ window; but nothing was able to unhide it. The window is still there - somewhere in dark - and if I press F7 and enter, the first search result will be open. but the search-result window is still hidden.

When I do a find (not a find all, which closes the dialog) or replace in Notepad++, the focus will remain on the find/replace dialog. If I want to focus on the main window with the text in it, I either have to click or clumsily alt-tab + alt-shift-tab, or to close it I have to click. Is there a keyboard shortcut for closing the find/replace dialog?  I have read  question, but it relates to the opposite situation - his version of Notepad++ was focusing on the main window after a find or replace and he was wanting to revert focus back to the dialog.  I'm on 64-bit Win7 if that makes any difference.


x=(100+1.0/3)-100 y=1.0/3 z=1+1.0/3-1   x, y, z clearly have the same values mathematically, but   print(x==y) print(x==z) print(y==z)   generate False values for all.   Is there any way to make them equal to each other in python? I'm not quite sure why they're not considered same. I'm aware that rounding off would be the cause of it, but I'm not sure why that happens in different ways for x, y, z.

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


First time using generics.  I've successfully created an ArrayList of generic objects, and I would like to convert it to a regular array T[].  Normally, this is something like  String[] x = (String[])myStrings.toArray(new String[0])   However, in this case, replacing String with T does not work. i.e.  return (T[]) ret.toArray(T[0]);   Here is complete code for my method, tho not sure it is relevant:

Due to the implementation of Java generics, you can't have code like this:   public class GenSet<E> {     private E a[];      public GenSet() {         a = new E[INITIAL_ARRAY_LENGTH]; // error: generic array creation     } }   How can I implement this while maintaining type safety?  I saw a solution on the Java forums that goes like this:  import java.lang.reflect.Array;  class Stack<T> {     public Stack(Class<T> clazz, int capacity) {         array = (T[])Array.newInstance(clazz, capacity);     }      private final T[] array; }   But I really don't get what's going on.


I read this manga maybe 2/3 years ago. He is given targets (usually women), which he at first thinks he can do anything with them (i.e. sexual assault). However, the system tasks him with actually figuring out a dark secret with each of his targets. He has the ability to 'scan' people, revealing some information about them. However, he cannot fully scan higher profile targets. He can buy extra items to assist him and will also be resurrected if he dies.

Can someone tell me the manga in which the protagonist is teleported to an alternative world where he needs to make the girls fall in love with him, then he gains some skills like an invisible sword. Then, when he finishes these "quests", he will be able to bring one of them to the real world. He has the ability to save and load like checkpoints of games.


Here's my code thats throwing an error saying Cannot convert type "int" to Cards.Suits and Cannot convert type "int" to Cards.Rank  private Card[] cards; public Deck() {     cards = new Card[52];     for (int suitVal = 0; suitVal < 4; suitVal++)     {         for (int rankVal = 0; rankVal < 14; rankVal++)         {             cards[suitVal * 13 + rankVal - 1] = new Card((Suits)suitVal, (Rank)rankVal);         }      } }   the cards constructor is   public readonly Suits suit; public readonly Rank rank; public Card(Suits newSuit, Rank newRank) {     suit = newSuit;     rank = newRank; }   Now the Suits enum and Rank enum are as a regular deck of cards starting at ACE = 1 so on and suits are DIAMONDS, CLUBS, HEARTS, SPADES.  Can anyone tell me why im getting the above error. The following code was taking from a book.  Thanks!  *EDIT      public enum ranks     {         ACE = 1,         TWO,         THREE,         FOUR,         FIVE,         SIX,         SEVEN,         EIGHT,         NINE,         TEN,         JACK,         QUEEN,         KING,     }      public enum Suit     {         DIAMOND,         CLUB,         HEART,         SPADE,     }

How can an int be cast to an enum in C#?


I'm trying to achieve the following:  So I'd like to have in-line lists, that our flush with the left margin and vertically aligned with each letter. I achieved the result above by manually spacing, which is not ideal. I can't seem to find an environment that covers each of the above conditions.  Using the following answers:  I can achieve the following:  \usepackage{tasks} \begin{tasks}[counter-format={(tsk[a])}, label-align=left, label-offset={0mm}, label-width={5mm}, item-indent={5mm}, label-format={\bfseries}, column-sep=-30mm, after-item-skip=-1mm, after-skip={3mm}](2) \task $f(5)$ \task $f(x+h)$ \task $f(x+h) - f(x)$ \task $\dfrac{f(x+h)-f(x)}{h} \quad h\neq 0$ \end{tasks}     I don't know how to put a space between the letter and the expression. For example: (a)[INSERT SPACE HERE] f(5). Adjusting the parameters listed in the code above seems to adjust other things. Using ":/" in math mode works, but it's not an ideal solution.

This might seem like a very simple question, but what is the easiest way to turn a normal vertical list into a horizontal one?


I am facing a problem with on(). Here is my code:  add this stuff   $(".add").on('click', function() {     $.post("/toto.com/add.php", { trainning: this.id }, function() {});     $(this).html("Remove this stuff");     $(this).removeClass("add").addClass("remove");     //alert($(this).attr("class"));-->give the good class });  $(".remove").on('click', function() {     //doesn't work     $.post("/toto.com/remove.php", { trainning: this.id }, function() {});     $(this).html("add this stuff");     $(this).removeClass("remove").addClass("add"); });   The selector for the class remove doesn't recognize it whereas when I click on the button with the add class, the class is changing. Do you know what the problem is?  Thank you for your help!

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


Where is the loop hole in my code..  trigger updateSumOfTotal on contact (after insert, after update) {     set<Id> toUpdate = new set<Id>();     List <Account> toUpdateDML = new List<Account>();     Map<Account,List<contact>> accToOpp = new map <Account,List<contact>>();     public Decimal annualrevenue;     for(contact o : trigger.new) {         toUpdate.add(o.AccountId);     }     for(Account a : [SELECT Id,LightiningName__Sum_of_Total__c,(SELECT ID,LightiningName__Amount__c FROM contacts) from Account WHERE Id IN : toUpdate]) {         accToOpp.put (a, a.contacts);         annualrevenue=0;         for(contact ooo : accToOpp.get(a)) {             if(ooo.LightiningName__Amount__c!=null){                 annualrevenue +=ooo.LightiningName__Amount__c;             }         }         a.LightiningName__Sum_of_Total__c = annualrevenue;         toUpdateDML.add(a);     }            if(toUpdateDML.size()>0){          update toUpdateDML;      } }

i have created a trigger which creates an opprtunity when the accounte is created and i have a custom field No of contact on account which displays the count of related contact for a particular account whenever it is updated.  I have tested seperated that the opportnity is created but for the second part ,it displays a big error when i try to save a record.  I am not getting any error while saving a record.Can someone help      trigger insertOpp on Account(After insert,after update,before update) { List<Opportunity> opplist=new List<Opportunity>(); for(Account acc:Trigger.new){  Opportunity op=new Opportunity(); op.Name='Cook'; op.accountid=acc.id; op.CloseDate=System.today(); op.StageName='Qualification'; opplist.add(op); }  insert opplist;     if(trigger.isupdate) {         Integer no_of_contact;         String accID;      for(Account c:Trigger.new )     {         accid = c.id;      }      account acclist = new account();     acclist = [select No_of_Contacts__c from account where id = :accid ];     no_of_contact = [SELECT count() FROM Contact WHERE AccountId = :accid];     acclist.No_of_Contacts__c = no_of_contact;     //update acclist;  }  }   ERROR:       Review all error messages below to correct your data. Apex trigger   insertOpp caused an unexpected exception, contact your administrator:   insertOpp: execution of AfterUpdate caused by: System.DmlException:   Update failed. First exception on row 0 with id 00128000002r8gKAAQ;   first error: CANNOT_INSERT_UPDATE_ACTIVATE_ENTITY, insertOpp: maximum   trigger depth exceeded Account trigger event AfterUpdate for   [00128000002r8gK] Account trigger event AfterUpdate for   [00128000002r8gK]


Devanagari fonts appear broken like this:     It should appear this way    I have the same problem in browsers and office applications.  Is there any way to fix it?

I'm using Hindi (Bolnagri) layout to type in Hindi. I'm typing in Hindi for first time.  My problem is, I want to type स्वाद. How do I type that half स?    EDIT 1:  How to type औ with this layout?    EDIT 2:  How to type र्श as in आदर्श?


I think this 'to' is some kind of connecting word. I think it connects a verb and what the verb intends. I think in this usage, the originally transitive verb becomes an intransitive verb needing a complement. I think some Americans could consider the to-infinitive as a adverbial complement that describe what the before verb intends, and 'to' as a connecting word. Do Americans or some Americans not regard it as a noun phrase, but as what I think of?

I'm a passionate Korean English-learner, and I would like to ask you a question about grammar.   It was 3 years ago when I first started to study the to-infinitive as studying grammar with Grammar In Use series and English Grammar series by Longman, having been exposed to English for 3 years. There wasn't any mention of the author saying that the usage of the to-infinitive is as an (direct) object. And for me also, the times I have encountered sentences in which the usage of the to-infinitive, so to speak, as direct objects were used, I've read them as some kind of obligatory adverbial that shows what the verbs are about, not as objects, which means they are noun phases! 100% of Korean textbooks say the usage is as a direct object, but I doubt it. I think it's some kind of obligatory adverbial that shows what the verbs are about.    I thought it was better for me to ask Americans themselves. Do you read this usage of to-infinitive as a noun phrase or an adverbial?


I must be missing something simple but could not find  \right| and was wondering how to duplicate a matching vertical bar after a formula.  Edit  My mistake! I forgot \left. . But I guess one can ask the question for \right!. Not sure if it is of much use though.

Given an arbitrary thin vertical symbol, can I create a new math delimiter from it (and if so, how)?   Edit: Ideally, I would like to be able to create an extensible symbol, either built out an existing normal symbol, or even made from scratch.  Edit 2: I am pretty sure that what I am after is an explanation of how to create a .tfm file for an extensible symbol (which Werner's answer describes the general structure of, but not how to make one).    For example, let's say I wanted to use the \dagger () or \wr () symbol as a delimiter, and write expressions like    \[\left\ldagger \sum_{n=1}^\infty a_n \right\rdagger\]   where the symbol scaled appropriately. Would there be any distinction between declaring a symmetric delimiter (like \vert), as opposed to one that has inherently different "left" and "right" versions like [ and ]?  Now, even being unaware of the inner workings of TeX, I imagine that there has to be lots of information in the fonts for how a delimiter is to be scaled in different situations, and if I try to make my own delimiter, this information won't be present. Would I need to get deep into FontForge or equivalent to achieve my custom delimiters, or is there an easier way?


For example, $\mathbb{Z}_7$ has at least two units, since $2\cdot 4 = 4\cdot 2=1$.   But $\mathbb{Z}_6$ has no units (since nothing multiplies to $7$).   But $\mathbb{Z}_8$ has a unit: $3\cdot 3=1$  So it seems that for $\mathbb{Z}_m$ $($ where $m\in \mathbb{Z})$, if $m+1$ is not prime then $\mathbb{Z}_m$ has units, and if $m+1$ is prime then $\mathbb{Z}_m$ does not have units.  Is this a correct characterization (does it always hold)?

I was thinking of this question and when I googled I couldn't find any MSE results, but I found one from Reddit. I just wanted to ask the question here and post the answer as community wiki just so MSE could have some discussion. If you want this taken down, you can comment and I'll take it down.  The  from u/matqkks:      I need to introduce Euler's totient function but I don't want to start with the definition. What applications and impact does this function have? I need something which will can be used to hook students into why Euler's totient function is important.   If you have other ideas for good ways to teach this function, please add your answer!  Edit: another good tactic is if someone knows of some problem (that's natural enough to formulate) where we do stumble across the totient function early on, but in fact the problem is so "deep" that even though its "purpose" is to introduce the totient function (in terms of why/how a mathematician would come up with such a definition), it's also a good springboard into harder number theory questions, kind of like in this thread: .


Since on Mathematics stackexchange I didn't get an answer, I'll try it here, since people here are more familiar with this topic (general relativity related).  I am reading a dissertation of Porfyriadis "Boundary Conditions, Effective Action, and Virasoro Algebra for $AdS_3$", and I am trying to solve a system of DE to get the appropriate diffeomorfism (page 31 onward).  I am trying to solve a system of ODE, such that each DE is equal to some degree of term that I'm expanding to. For instance, one DE is this:  $\xi^r\partial_r g_{rr}+2g_{tt}\partial_t\xi^t=\mathcal{O}(r)$  which you get by taking a Lie derivative of background metric and setting it equal to certain $\mathcal{O}(r^n)$ terms.  $g_{ij}$ are given, from metric ofc. I need to assume that the solution (since I'm looking for components of $\xi^\mu$( which is a vector with components $\xi^t, \xi^r, \xi^\phi$) is given with power series of the form:  $\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$,  and this is to be seen as expansion around 1/r (expansion around $r=\infty$).  Now when I plug this in the ODE I get this  $\frac{2}{l^2}\sum_n\xi^r_nr^{n+1}+2\sum_n\xi^t_{n,t} r^n+\frac{2}{l^2}\sum_n\xi^t_{n,t}r^{n+2}=\mathcal{O}(r)$, where  $\xi^\mu_{n,i}$  is the derivative with the respect to i-th component.  What troubles me is, how to expand this? Do I set n=0,-1,-2,... until my O(r) terms cancel each other out? Or?  I'm kinda stuck, at this seemingly easy point.  In the thesis he gets 6 equations with coefficients, first one should be:  $\xi^r_{n-1}+l^2\xi^t_{n,t}+\xi^t_{n-2,t}=0,\ n\ge 2$,  But I am not getting this. What am I doing wrong?    EDIT: For further clarity: The metric is that of $AdS_3$ given with line element:  $ds^2=-\left(1+\frac{r^2}{l^2}\right)dt^2+\left(1+\frac{r^2}{l^2}\right)^{-1}dr^2+r^2 d\phi^2$,  and the differential equations in question are given by solving $\mathcal{L}_\xi g_{\mu\nu}=\mathcal{O}(r^n)$, where $\mathcal{O}(r^n)$ are the fall off conditions. In the dissertation, he took the deviation of nonzero components of the metric to be subleading, that is:  $\mathcal{L}_\xi g_{tt}=\mathcal{O}(r)$ $\mathcal{L}_\xi g_{rr}=\mathcal{O}(r^{-3})$ $\mathcal{L}_\xi g_{\phi\phi}=\mathcal{O}(r)$, while others are $\mathcal{O}(1)$.  Solving Lie derivative gives me 6 equations, which I should solve by plugging in the above ansatz ($\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$), but this is the part I get stuck.  ADDENDUM:  I was looking at other components, and have noticed that I have $g_{rr}$ factor with some of them. That term in metric is:  $g_{rr}=\left(1+\frac{r^2}{l^2}\right)^{-1}$  Now, is it legitimate thing to expand this around $r=\infty$ so that I can put $r$ terms inside the sums (assumed solution)?

I am solving a series of ODE, such that each DE is equal to some degree of term that I'm expanding to. For instance, one DE is this:  $\xi^r\partial_r g_{rr}+2g_{tt}\partial_t\xi^t=\mathcal{O}(r)$  $g_{ii}$ are given, from metric, but that's not important. I need to assume that the solution (since I'm looking for components of $\xi^\mu$, which is a vector with components $\xi^t,\xi^r,\xi^\phi$) is given with power series of the form:  $\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$, and this is to be seen as expansion around $1/r$ (expansion around $r=\infty$).  Now when I plug this in the ODE I get this  $\frac{2}{l^2}\sum_n\xi^r_nr^{n+1}+2\sum_n\xi^t_{n,t} r^n+\frac{2}{l^2}\sum_n\xi^t_{n,t}r^{n+2}=\mathcal{O}(r)$, where   $\xi^\mu_{n,i}$   is the derivative with the respect to i-th component.   What troubles me is, how to expand this? Do I set n=0,-1,-2,... until my $\mathcal{O}(r)$ terms cancel each other out? Or?  I'm kinda stuck :\


I'm asking specifically for the schrodinger equation.  Is there a unique correspondence between the energy eigenfunctions $\phi_i(x)$ and the potential term $U(x) = V(x)\phi(x)$? Furthermore, is this still true for a more general potential term that is a functional of $\phi(x)$ such as: $U(x) \equiv F(\phi(x))$?  If not, I'm interested in what statements can be made.

A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential.    Is there a one to one correspondence between the potential and its spectrum?  If the answer to the previous question is yes, then given the spectrum, is there a systematic way to calculate the corresponding potential?


I read this Phys.SE thread which is similar   but I did not want to necro that thread. It seems that most discussions of a three body problem are presented in two dimensions. I am thinking about the set of points where two cones intersect. One cone with the vertex at the sun and described by the angle sub tended by L4-sun-L5. The other cone defined by L4-earth-L5. The intersection of these two cones is a circle that includes L4 and L5. This circle is the set of locations where the gravity of the sun and earth cancel out. This circle is perpendicular to a line connecting the earth and sun.   if we are considering L4 and L5 as stable points, why are we excluding all the other points on this circle?

According to , there are 5 equilibrium, or  of the Earth-Moon system and only 2 of them are said to represent stable equilibrium points.     This made me think if there is an equation that describes this system, and from which Physics Laws was it derived?


Consider the contour $C_{\epsilon,R} = \Gamma_R \cup \gamma_{\epsilon} \cup [-R,-\epsilon] \cup [\epsilon, R]$ and $f(z)=\frac{1-e^{2iz}}{z^2}$. By Cauchy's Theorem we have $$\int_{C_{\epsilon,R}}f(z)dz=0$$ It is easy to see that $\int_{\Gamma_R}f(z)dz \rightarrow \infty $ as $R \rightarrow \infty$.  Therefore $\int_{-\infty}^\infty \frac{1-e^{2ix}}{x^2}dx=\int_{\gamma_\epsilon} f(z)dz = \frac{1}{2}2\pi i \operatorname{Res}(f,0) =2\pi$. My question here is why the integral on $\gamma_\epsilon$ is exactly half of the residue of $f$ at $0$. I can't see why the integral of $f$ on the upper semi-circle and the lower semi-circle are the same. I know there is an alternative way to compute $\int_{\gamma_\epsilon} f(z)dz$ but I want to know why $\int_{\gamma_\epsilon} f(z)dz = \frac{1}{2}2\pi i \operatorname{Res}(f,0)$ holds.

I am looking for a short proof that $$\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$$ What do you think?  It is kind of amazing that $$\int_0^\infty \frac{\sin x}{x} \mathrm dx$$ is also $\frac{\pi}{2}.$ Many proofs of this latter one are already in this .


In the iOS Mail app, there are 5 emails in the "All Inboxes" section. Those 4 emails are NOT in any other inboxes.  So I tried deleting them and ... they keep coming back!  Even stranger, the 4 emails ONLY appear in "All Inboxes", they don't appear in any of the sub-account inboxes.  So, I disabled "Mail" in my outlook account. They're still here! I no longer have a "outlook" sub-account, but those 4 emails are still in All Inboxes. I tried to quit the app a few times, restart the phone. Still here...  When I tap on one of those messages, I get a black screen (dark mode) Or gray empty screen, no errors.  I completely deleted the account in settings but they are still there!! Any tips?

In the iOS Mail app, there are 4 emails in the "All Inboxes" section. Those 4 emails are NOT in the actual inbox on Gmail.  I thought, oh well I don't mind deleting them entirely since they're just newsletters. I deleted them directly on gmail, but they still appeared in iOS. So I tried deleting them via iOS and ... they keep coming back!  Even stranger, the 4 emails ONLY appear in "All Inboxes", they don't appear in any of the sub-account inboxes.  So, I disabled "Mail" in my gmail account. They're still here! I no longer have a "gmail" sub-account, but those 4 emails are still in All Inboxes. I tried to quit the app a few times, restart the phone. Still here...  When I tap on one of those messages, I get a black screen (dark mode), no errors.


I've came across this problem which seems to be a classic mean inequality problem, but I can't get it right.     Let $x$, $y$ and $z$ be pozitive real numbers with $xyz=1$. Prove that   $$\frac{x}{1+x^4} + \frac{y}{1+y^4} + \frac{z}{1+z^4} \leq \frac{3}{2}$$   My first try was $$\sqrt{1 * x^2} \leq \sqrt{\frac{1+x^4}{2}}$$ $$2x^2 \leq 1+x^4$$ $$\frac{x}{1+x^4} \leq \frac{x}{2x^2} = \frac{1}{2x}$$ then, using geometric mean and arithmetic mean, we obtain the inequality inside out.  A hint would be really apreciated.

Given that $xyz=1$, prove that $$\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le\frac{3}{2}.$$  I proved this with , but: is there a better/more elegant way?


I am trying to use a constructor to declare the strings a1,b1 and also declaring two other strings a2,b2. Upon checking if they are equal, I am getting different responses.  public class Practice {     public static void main(String args[]){          String a1= new String("Check");         String b1= new String("Check");         String a2="Check1";         String b2="Check1";         System.out.println(a1==b1);         System.out.println(a2==b2);     } }  Output: false true

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


I inherited a lot of USB flash drives and would like to find out what USB version they are (i.e. 2.0, 3.0 or maybe even older). How can I do that on Ubuntu?

I have a bunch of thumb drives, and many of them don't have any writing on them to indicate that they are USB 3.0.  In Ubuntu; how can I ascertain if they are USB 3.0 when I plug them in?


I  have a computer with no access to internet, however, lubuntu 18.04 (also tried with lubuntu 20.04) does not produce sound. It keeps saying "no dummy output". While on a computer with internet access I downloaded "Cube-Get" and downloaded the DKMS package , which included all of the dependencies. I moved the dependencies for the dkms package on to a USB and transferred it to my computer with no internet. While installing , it halted because of broken dependencies. The reason im installing dkms package is because I need the snd-hda-intel driver. Does anyone have any ideas on how I can navigate this problem?

I have a friend who has got a computer that is not connected to the Internet. Is there any way to install software offline easily?


Is there any way to use OFFSET without LIMIT in mysql?  I tried many ways and many times.  I also searched a lot.

I would like to construct a query that displays all the results in a table, but is offset by 5 from the start of the table. As far as I can tell, MySQL's LIMIT requires a limit as well as an offset. Is there any way to do this?