For two continuous functions $f(x)$ and $g(y)$ let their integrals be given by:  $$I_1 = \int f(x)\,\mathrm{d}x$$  $$I_2 = \int g(y)\,\mathrm{d}y$$  Then under which conditions is it true that  $$\int \int f(x)\cdot g(y)\,\mathrm{d}y\,\mathrm{d}x = I_1 \cdot I_2$$  That is to say that the integral of their product is equal to the product of their integrals?

I'm self-studying and was doing the following integral:  $$I = \int \frac{e^{\frac{1}{x}+\tan^{-1}x}}{x^2+x^4} dx $$  I solved it fine by letting $ u = \frac{1}{x} + \tan^{-1}x$.   My question is about an alternative method I saw in which it seems the product rule was not applied:  $$ I = \int \left(\frac { e^{\frac{1}{x}}} {x^2}\right) \left( \frac{e^{\tan^{-1}x}}{x^2+1}\right) dx $$  $$ = \int \frac {e^{\frac{1}{x}}}{x^2} dx \cdot \int \frac{e^{\tan^{-1}x}}{x^2+1}dx$$  Completing the work following this step leads to the same solution as I originally found.   It is this step that has confused me. I have  and the two statements are equivalent but I do not understand why.  Why are we able to write the integral of products as the product of integrals here, and not apply the product rule?  Thanks in advance.


According to latest modern theory on subatomic particles, electrons and protons are further divided into quarks, having fractional charges.  My question is, why can't they exist independently?  and why don't they show up Millikan's experiment?

I simply know that a single free quark does not exist. What is the reason that we can not get a free quark?  If we can't get a free quark then what is single-top-quark?


I finished the mission and watched the shaman get taken by the tentacle. I went ahead and jumped into the big swirly thing and got stuck after that. Apparently there is some NPC supposed to be there when you finished the mission? Also apparently there is an NPC who gives you a quest to go back to Orgrimmar. I didn't find either of those and am really stuck.   What am I supposed to do after the "Defending the rift" quest?

What do I do after the Defending the Rift quest in Abyssal Depths? Legionnaire Nazgrim jumped into the vortex and I am left alone on the ledge.


#include<stdio.h> main() {   char s[]="man";   int i=0;   printf("%c%c\n",s[i],i[s]); }   o/p: m m   *Both s[i] and i[s] prints 'm' and 'm'. *However s[i]=m, that is acceptable,but how i[s]=m ?? *Can any one explain me about this please.

As Joel points out in , in  (aka: K & R), there is mention of this property of arrays in C: a[5] == 5[a]  Joel says that it's because of pointer arithmetic but I still don't understand. Why does a[5] == 5[a]?


I have an ASA5505 firewall and I need to block an external IP address which is talking to my server.  Basically, the ASA firewall shows that my server is "attacking" this Destination Address. So the Source IP is i.e. 192.168.100.100 which is internal, attacking 188.247.70.93 on port 80 thru the inside interface. which is outside.  I have blocked the IP from my server firewall but I need to know how to block it from the ASA Firewall via asdm as I am not too familiar with CLI  I mean, I did create an ACL with all the entries and applied it to the Inside interface, but then I have to create another rule to allow any to any for outgoing otherwise the firewall blocks all outgoing.  The problem with creating any to any is that as soon as I create that I saw 350+ hits on that rule. So how do I go about doing this block without compromising my system?  Thank you

I want to block my server talking to an external IP address continously.  The IP address in question is I think is being hijacked or spoofed. When Used who.is it resolves to Netherlands. But if you use any other tools it resolves to Jordan.  Any step by step configuration is highly appreciated.  Thank you Kind Regards N


When I do an ls in the /proc/PID directory a number of @ symbols show up next to the file names.  Normally I would consider this to mean extended attributes but when I do the long form of ls they do not show up in the place I would expect and the output looks different than usual.  I tried googling but only found the extended attributes description.  What is going on?  root@hashcat:/proc/29286/ns# l ipc@  mnt@  net@  pid@  user@  uts@ root@hashcat:/proc/29286/ns# root@hashcat:/proc/29286/ns# ls -l total 0 lrwxrwxrwx 1 dylan dylan 0 Mar 21 21:09 ipc -> ipc:[4026531839] lrwxrwxrwx 1 dylan dylan 0 Mar 21 21:09 mnt -> mnt:[4026531840] lrwxrwxrwx 1 dylan dylan 0 Mar 21 21:09 net -> net:[4026531956] lrwxrwxrwx 1 dylan dylan 0 Mar 21 21:09 pid -> pid:[4026531836] lrwxrwxrwx 1 dylan dylan 0 Mar 21 21:09 user -> user:[4026531837] lrwxrwxrwx 1 dylan dylan 0 Mar 21 21:09 uts -> uts:[4026531838]

For command ls     -F, --classify           append indicator (one of */=>@|) to entries   Wikipedia says * represents executable and / dir.  Regular files are not followed by any of the above symbols.  But * follows text file and pdf file too. Are they executables?  Do the -F indicators always mean same as the first field in -rwxrwx---?  It seems like there is no difference between hardlinks and the files  in either the -F indicators or the first field in -rwxrwx---. How do you distinguish them?  Thanks.


So, I was watching a youtube video in order to understand quantum entanglement- you know, as a non-physicist- and at one point the speaker says that it doesn't understand how the energy of one photon can be divided to several different atoms and how it can interact at the same time with each (as this photon is entangled). What I don't understand- and please excuse my lack of knowledge in the field- why are scientists so awed at the fact that a photon- which is energy- is divided? it's not as if it's a definite hard object, it's energy. Plus, isn't matter made up of energy? I've been thinking about it for a while and would really appreciate it if someone could explain what all the fuss is about.

Bearing in mind I am a layman - with no background in physics - please could someone explain what the "big deal" is with quantum entanglement?  I used to think I understood it - that 2 particles, say a light-year apart spatially, could affect each other physically, instantly.  Here I would understand the "big deal".  On further reading I've come to understand (maybe incorrectly) that the spatially separated particles may not affect each other, but in knowing one's properties you can infer the other's.  If that it the case, I don't see what the big deal is... 2 things have some properties set in correlation to each other at the point of entanglement, they are separated, measured, and found to have these properties...?  What am I missing? Is it that the particles properties are in an "un-set" state, and only when measured do they get set?  (i.e. the wave-function collapses).  If this is true - why do we think this instead of the more intuitive thought that the properties were set at an earlier time?


I've looked at an introduction to simple ANNs for time series analysis . In the tutorial, the train dataset r2 score is 0.897 and the test dataset r2 score is 0.789. They end up with some pretty neat predictions (see graph below, also from the same tutorial). Now my question is, for real world time series data, is there a consensus on what r2 scores make for an acceptable model?

I've fitted my model and am trying to understand whether it's any good. I've calculated the recommended metrics to assess it ($R^2$/ AUC / accuracy / prediction error / etc) but do not know how to interpret them. In short, how do I tell if my model is any good based on the metric? Is an $R^2$ of 0.6 (for example) sufficient to let me proceed to draw inferences or base scientific/business decisions?     This question is intentionally broad, to cover a wide variety of situations that members frequently encounter; such questions could be closed as duplicates of this one. Edits to broaden the scope beyond the metrics mentioned here are welcome, as are additional answers - particularly those that offer insight about other classes of metrics.


I have a multi-language website and according to the , I should keep the two or more versions of my website in two different subfolders, like:   www.example.com/en www.example.com/it   So far so good. This way the crawler will properly index the two versions of the website and it will present search results based on the user local language.  But what should I do with the root of the website? I mean, what index.html should I put straight into   www.example.com   Is it required to have an index.html? Should I put a small PHP script that redirects users to the appropriate localized website? (e.g. user goes to www.example.com and gets redirected to www.example.com/en). It looks like most websites implement this automatic redirect.

My question is not technical (how to do it using X technology), it's about choosing proper approach that is good for SEO.  Description  Let's say I have a website example.com. It's a multilingual site, but there is no default language at root level. Instead of that I'd like to redirect to proper subdirectory based on http_accept_language (or any other condition, whatever) to keep things consistent. Condition is unimportant right now, but let's make it easier with example:  example.com     # redirects to … example.com/es  # … /es if spanish is accepted language example.com/da  # … /es if danish is accepted language example.com/en  # … /en otherwise   They're actually the same websites, with translated content so if example.com/en/items/1 exists, also /es/items/1 and /da/items/1 exist. Of course all pages have alternate hreflang links etc.  Question  Is it good design? Can you tell me why if not? And how should it be done?


Im trying to copy a players inventory to a chest upon death but noticed that it only copies the hotbar and the first two rows of the inventory. Command: /data modify block ~ ~ ~ Items set from entity @p Inventory So now my plan is to copy certain parts of the inventory into two separate storage containers. This has led to the problem where i am unable to select certain sections or specific items out if the player inventory and copy them into a chest. I tried: /data modify block ~ ~ ~ Items set from entity @p Inventory[{Slot:0b}] /data modify block ~ ~ ~ Items set from entity @p Inventory.0 /data modify block ~ ~ ~ Items set from entity @p Inventory[0] Let me know if there is something wrong with my code, or if I need to try a different approach.

I am on a multiplayer Minecraft realm in 1.16 and I was wondering if there was any way to set a chest's Items to a player's entire Inventory including the offhand and armor slots. Using data modify <chest coordinates> Items set from entity <player> Inventory, I was only able to copy over the hotbar and the top two rows of a player's inventory. I honestly don't care if it takes 50 command blocks, any response is gladly appreciated.


Suppose a map $f:A\to B$ is continuous and invertible. Will the inverse map $f^{-1}:B\to A$ be always continuous also?

What are some examples of functions which are continuous, but whose inverse is not continuous?  nb: I changed the question after a few comments, so some of the below no longer make sense. Sorry.


It is a well-know fact that an inner product induces some norm.   How about the converse? I think it's false but I can't think of an example.   I'm thinking some properties like the parallelogram law will not hold with any norm...

I realize that every inner product defined on a vector space can give rise to a norm on that space.  The converse, apparently is not true.  I'd like an example of a norm which no inner product can generate.


Definition:     dilemma      a situation in which a difficult choice has to be made between two or   more alternatives, especially ones that are equally undesirable.      a difficult situation or problem.   Source: .  Example sentence:     The dilemma of modern life: trying to find an outlet outside of your   house.   I guess this sentence fits the second definition. So is it correct? (Or should I use another word instead?)

I was surprised to discover my dictionary had this entry for dilemma:     a situation in which a difficult choice has to be made between two or more alternatives, esp. equally undesirable ones   The notion of dilemma meaning two or more flies against what I was taught about the word. The very idea of a  is specifically based on the number two.  Has my dictionary merely updated its definition to encapsulate the many people who use dilemma for more than two equal choices? Or was someone in my youth being unnecessarily pedantic?


Given the file with numbers from 1 to 100 (seq 1 100 > dataset.txt),  and the pattern file with numbers from 1 to 20 (seq 1 20 > patterns.txt),  I would like to to print all exact matches from the dataset file given the list of patterns.  Here is my command using BSD grep:  $ \grep --version grep (BSD grep) 2.5.1-FreeBSD  $ \grep -w -F -f patterns.txt dataset.txt 1 2 3 4 5 6 7 8 9   but the output is missing the numbers from 10 to 20.  However all patterns are printed when running the same command in GNU grep, e.g.  $ \ggrep --version ggrep (GNU grep) 3.1 Packaged by Homebrew  $ \ggrep -w -F -f patterns.txt dataset.txt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20   When tested with , all are returned as well.  Why is that? Is there any different approach to make them both return the same result?

I am removing stop words from a text, roughly using this   I have the following  $ cat file file types extensions  $ cat stopwords i file types   grep -vwFf stopwords file  I am expecting the result: extensions  but I get the ( I think incorrect)  file extensions   It is as if the word file has been skipped in the stopwords file. Now here's the cool bit: if I modify the stopwords file, by changing the single word/letter i on the first line, to any other ascii letter apart from f, i, l, e, then the same grep command gives me a different and correct result of extensions.  What is going on here and how do I fix it?  I'm using grep (BSD grep) 2.5.1-FreeBSD on a Mac OSX GNU bash, version 4.4.12(1)


I want to get all keys from a collection, is there a standard way to do this? std::unordered_map<std::string, size_t> map; auto keys = map.get_keys();

This is one of the possible ways I come out:  struct RetrieveKey {     template <typename T>     typename T::first_type operator()(T keyValuePair) const     {         return keyValuePair.first;     } };  map<int, int> m; vector<int> keys;  // Retrieve all keys transform(m.begin(), m.end(), back_inserter(keys), RetrieveKey());  // Dump all keys copy(keys.begin(), keys.end(), ostream_iterator<int>(cout, "\n"));   Of course, we can also retrieve all values from the map by defining another functor RetrieveValues.  Is there any other way to achieve this easily? (I'm always wondering why std::map does not include a member function for us to do so.)


I was able to create sand, however am unable to draw lines on it.I want to animate a tiller working on sand leaving lines on sand. Plse help with video

When any object is dropped onto the material like sand in real life it changes it's surface like it's shown in the photo.    How can I do it in Blender having the object and a subdivided plane that are shown below using physics?   Thanks for help !


In my school days, I had been taught that we cannot move a vehicle by applying any force from inside. That is we cannot push the vehicle from inside. But when I was sitting in a scrolling chair, I was able to move it without touching anything other than the chair. Can anyone explain the reason for this?

I did a weird activity and now I am trying to figure out the physics behind it:  While sitting on a chair I kept my feet above the ground and tried to move the chair forward. I was able to. Initially, I thought that perhaps the center of mass won't be changing as I was pushed backwards. But I moved the chair for a while and saw that it had moved a considerable distance and I was still sitting on the chair. Hence the center of mass did change for sure. According to Newton's second law, there must be an external force acting on the system(me and the chair). But I am not able to figure out what force is it. I have a feeling that it is somewhere related to the fact that the system is not completely isolated but I am not sure how.     Note: I am not in contact with the ground or any other object close to me. I have lifted my feet and have my hands on my lap.


I have read some grammar points about definite/indefinite articles, but I still have problems recognizing the right choice in questions requiring them. I know sometimes I can omit articles but I don't know exactly when.(Maybe this is the most confusing point for me!)  For example:     It would be difficult to imagine---life without---telephone.   Answer:(zero article/the)   Why not?(zero article/zero article)    Why "the" is needed here?      ---government is now insisting that --- math is taught with traditional methods.   Answer:(The/zero article)   Why not?(zero article/zero article)    Why "the" is needed here?      ---company needs to make sure that it is earning --- profit.   Answer:(A/a)    Why not(zero article/a)? Isn't company a general thing? Or maybe any special company?(using "the") We don't have any context here to understand what it really means.   Same things here:   I don't mind---airport;it's---flying that I hate.(the/the) or (the/zero article)   During---spring semester,---chemistry will not be offered.(the/zero article) or (zero article/zero article)      ---Microscope was invented by him.(the/zero article)   Can someone please provide information or resources to get better answers?

I can’t for the life of me figure out where to use a and where to use the — and where there is no article at all. Is there a simple rule of thumb to memorize?   The standard rule you always hear:     “If a person knows which item you are talking about then use "the"   . . . doesn’t clear things up for me, as I have no idea whether or not they know.


Most Makefile users use the commandline. Thus they have no need of evoking it in the GUI. But Makefile can be used as an administration tool for the users too.  In my case, a clerk is tasked to maintain a document which changes daily, and as soon as she saves the file, the "source" is changed. I want her to convert it to PDF, stamp the PDF with a given template, encrypt it, merge it with a few other files, and produce three variations for different departments with different stamps.  I have a Makefile for that purpose, already written. Is there a way to let her evoke the Makefile without putting me to the mire of doing additional commandline training? She can save the document, evoke Makefile, and be done.  P.S. This is not about how to execute a shell script or an .EXE file because there is no shell scripts or .EXE files or any executable files in the question at all.

How can I make a bash script executable by double clicking just like .exe files in Windows? I tried , but there are two consequences:   the terminal twinkles, disappears, and nothing is done. you must specify to run in terminal in order to work.   I have a script that installs tomcat on an offline PC, including all dependencies of tomcat in the script. I need to make the script work on double clicking like windows since most who use the script will not be familiar with Ubuntu.  Forget the above explanation. I want to make a script that can be run by double-clicking on it, without using the terminal. Anybody knows how?


Is it cheaper to prebook a taxi from Heathrow to get to King's Cross station, or better to find a taxi waiting at the airport? We're flying in from New Zealand.

My wife and I will be arriving in London via Heathrow Airport (LHR) and are staying at a hotel near King's Cross station. So, we were wondering what the best (which means fastest but also easiest when carrying two large pieces of luggage and two carry-ons) way to get from LHR to King's Cross?  I gather that, with only one changeover, we can take the Tube. However, in the interest of other passengers, we thought it would be best to take a taxi, or maybe a bus?  Thoughts?


If $A$ is an $R$-module, I am having difficulty proving that $A$ is also a well-defined $R/ann(A)$-module with $(r+ann(A))a=ra$.

Let $I$ be an ideal of $R$ and let $M$ be an $R$-module. Prove that the formula $(r + I) \cdot m = r \cdot m$ for $r + I \in R/I$, and $m \in M$ makes $M$ into an $R/I$-module if and only if $i \cdot m = 0$ for all $i \in I, m \in M$.   I don't quite understand why we must have $i \cdot m = 0$ instead of $I \cdot m \in M$. This is for proving the only if part.


I have a website with blog articles. I added it's sitemap to google search console and it say that the sitemap has been processed. However, half of my articles (the important pages) have not been indexed. I am not sure why some of them are indexed and some not?   They are all built from the same php-file using url slugs. They are also all linked from the index page so it is not as if they can not be found. They are all in my sitemap.xml file that Google Search console says it has processed. They are counted for in "pages submitted by me" section in the search console. They do not come up when I do a search for site: mysite.com (50% of my articles do, not all). They are not blocked in a robots.txt file or .htaccess file. They have been online several days before Google search console said it had processed my sitemap. There are no bad content, just simple articles about whitelisted subjects. There are no crawl errors or error response codes. This is why I ask this question because I have read all the other posts about this subject and I do not deem it a duplicate unless you can point out something I missed.  There might be one thing I did get wrong: I submitted my sitemap.xml, it said "pending" then some time later it said "processed". Does this not mean that google updated my site and added the pages in the sitemap to it's index? Is it just processed and waiting to crawl or something like that?  Can anyone please give some insight into this because I am at a total loss what to do. Only thing I got so far is to maybe split the sitemap into two files: one with site structure (categories/tags etc) and one with only articles, would this be a good option?

This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it?


Looking for a story I read many years ago, long before the Harry Potter books. Probably a short story in an anthology, but maybe a short novel?? I'm guessing I read it in the 90s or earlier.   A young boy is growing up "normally" in his world that includes magic of all sorts, but especially being able to fly (I think on broomsticks). His whole society includes magic as the norm, similar to the HP universe. He has never known a non-magical world.   The magical world is encircled by a massive wall so high that no broom can fly high enough to get over.   The drama in the story begins when he finds a way to make his broom go over the wall. On the other side, he is stuck in our non-magical world where the wall is invisible, magic doesn't exist and his world is considered fantasy.   I don't remember the rest and would like to reread it some day.

Reading another question today reminded me of a short story I read in the early 90s (probably written in 60s or 70s though). A society is blocked off by a really high wall; the story follows a girl who tries to get over the wall. I think she manages it with a hot air balloon. When she reaches the other side she meets an older man who had managed to scale the wall in his youth - his solution had been to use a flock of birds to carry him.  UPDATE  I seem to recall that it splits off an elite group of people - getting over the wall is like a rite of passage. Most people don't even bother to get over it (or even be concerned by its existence at all), but a few try. There might be some magic involved (on the other / better side), or they might just be more advanced technologically.  FINAL UPDATE  As pointed out in the answer, and confirmed by me re-reading the story, I was mistaken in a few details. The main protagonist is not a girl, it's a boy called Porgie. He doesn't use a balloon, it's a glider he made, assisted with a broom. Magic is involved, but it's on the inside, with technology on the outside.


Say that we have a bunch of random-values $x_1, x_2, ..., x_n$  Let $\bar{X}$ be the mean of these random-values. The variance of this sample-set is given by:  $$\sum(x_i-\bar{X})^2$$  Apparently, the above sum is smaller than if $\bar{X}$ were any other value besides the average of the $n$ observations.  I've seen a Calculus-based explanation...are there other ways to show this? Perhaps geometrically or algebraically?   Thanks.

I am trying to understand the sentence  the mean minimizes the mean squared error.   from wikipedia .  From a previous post  I can see a formal proof which according to the authors prove that the mean minimaze. But my objection on that prove is that is you substitute m with median all the reasoning still stands.  Therefore, I restricted myself to one dimension and built the following example :   MSE = 1/n[SUM(Y_hat_i - Y_i)**2]   Given the following distribution Y = [5,3,2,7,4], minimizing MSE I intended as in the following: I should find a function Y_hat such that when it is applied to the MSE formula (more specifically to each element of the Y distribution), we are sure that we obtain the minimum value. For simplicity, I could consider the Y_hat as any measure or function for the central tendency, including, mean, median, mode, etc.  Lets suppose, Y_hat = mean (=4.2 for our distribution), therefore, I did all the calculations such as:  1/5 [(4.2-5)**2 + (4.2-3)**2+ (4.2-2)**2 + (4.2-7)**2  + (4.2-4)**2 ] = 2.96   Let's suppose, Y_hat = median (=4 for our distribution), therefore, I did all the calculations such as:  1/5 [(4-5)**2 + (4-3)**2+ (4-2)**2 + (4-7)**2  + (4-4)**2 ] = 2.8   If I did all the calculation correctly, the result shows that for this case, the median is minimizing better than the mean.  I am sure, I am doing something wrong and missing important aspects of the overall reasoning.  Please, could you provide any clarification on the above topic? I would really appreciate it.  Many Thanks in advance, Best Regards, Carlo


Recently, a collaborator of mine received a paper to referee from a journal, and he proposed me that we review the paper together. When he submitted the report, he indicated to the journal that he reviewed the manuscript with me. Am I allowed to write in my CV that I am a reviewer for this journal?

My professor sometimes asks me to referee papers for him.  Should I list the corresponding journals in the professionals activity section of my CV?


I am doing practice problems for an upcoming exam and am wondering what approach I might take to solve $53^{1069}$ mod 54. 1069 is a prime number, which means I can't factor the exponent.   Some other similar problems that I solved used Fermat's theorem (if N is prime, then $a^{N-1} \equiv$ 1 mod N), but 54 is not prime so I'm not sure if that is correct.

I've read about Fermat's little theorem and generally how congruence works. But I can't figure out how to work out these two:   $13^{100} \bmod 7$ $7^{100} \bmod 13$   I've also heard of this formula:  $$a \equiv b\pmod n \Rightarrow a^k \equiv b^k \pmod n $$  But I don't see how exactly to use that here, because from $13^1 \bmod 7$ I get 6, and $13^2 \bmod 7$ is 1. I'm unclear as to which one to raise to the kth power here (I'm assuming k = 100?)  Any hints or pointers in the right direction would be great.


So I have been watching some "thenewboston" on youtube and I just started learning java like an hour ago and I seem to not be able to find what my problem is. (There is no error message)  package rockPaperScissors;  import java.util.Scanner; import java.util.Random;  public class RockPaperScissors {     public static void main(String args[]){     String playerChose;     String computerChose;     String winner;     while(true){         System.out.println("Welcome to rock paper scissors!");         System.out.println("Please enter \"rock\", \"paper\", or \"scissors\"");         Scanner playerChoice = new Scanner (System.in);         playerChose = playerChoice.nextLine();         Random computerChoice = new Random();         int computer = computerChoice.nextInt(3) + 1;         switch(computer){             case 1:                 computerChose = "rock";                 System.out.println("Computer chose rock!");                 break;             case 2:                 computerChose = "paper";                 System.out.println("Computer chose paper!");                 break;             case 3:                 computerChose = "scissors";                 System.out.println("Computer chose scissors!");         }          computerChose = new String();         winner = new String();          if(playerChose=="rock" && computerChose=="scissors" || playerChose=="paper" && computerChose=="rock" || playerChose=="scissors" && computerChose=="paper"){             winner="player";         }          if(playerChose==computerChose){             winner="NoWinner";         }          if(computerChose=="rock" && playerChose=="scissors" || computerChose=="paper" && playerChose=="rock" || computerChose=="scissors" && playerChose=="paper"){             winner="computer";         }          if(winner!="NoWinner"){             System.out.println(winner+" won!");         }else{             System.out.println("Game tied!");         }     } } }   Yes, I am new to this java stuff and I have no idea why this code is not working because I thought for sure it would work. I'm sure it's just something stupid that I need to learn. Since I come from Python this is a lot more complex because there are a lot of rules to java that don't exist in Python.

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 have replication set up between two servers.  This morning I came in and it was failing.  I was getting these errors:     Error messages:         The process could not execute 'sp_replcmds' on 'PSQL3'. (Source: MSSQL_REPL, Error number: MSSQL_REPL20011) Get help:   Cannot execute as the database principal because the principal "dbo" does not exist, this type of principal cannot be impersonated,   or you do not have permission. (Source: MSSQLServer, Error number:   15517)    The process could not execute 'sp_replcmds' on 'PSQL3'. (Source: MSSQL_REPL, Error number: MSSQL_REPL22037)

I am having a problem running the CDC change capture job against some of my test databases.  The error message I'm getting is the following:     Executed as user: NT AUTHORITY\NETWORK SERVICE. Cannot execute as the database principal because the principal "dbo" does not exist, this type of principal cannot be impersonated, or you do not have permission. [SQLSTATE 42000] (Error 15517).   How can I fix this?


If I got two independent random variables $A \sim R(0,1)$ and $B \sim R(0,1)$ and I have to calculate $E(max(A, B))$ wouldn't that then just be to pick one of them since they are equal in size? So it would be the same $E(A)$?  What would E(max{A,B}) be?

If I have two variables $X$ and $Y$ which randomly take on values uniformly from the range $[a,b]$ (all values equally probable), what is the expected value for $\max(X,Y)$?


I have a question about the steps in the book "An Introduction To Quantum Field Theory" By Peskin & Schroeder. In page 213, i don't understand why the $e^{iPx}$ before the $<\Omega|$ in equation 7.4 disappear in the second line. Please help me^^.

Let $\langle\Omega|$ be the ground state of an interacting theory, just as Peskin & Schroeder(PS) describes on page 82 and page 213. On page 213 PS do the following   $$\tag{1}\langle\Omega|\phi(x)|\lambda_{\vec{p}}\rangle = \langle\Omega|\exp(+\mathrm{i}Px)\phi(0)\exp(-\mathrm{i}Px)|\lambda_{\vec{p}}\rangle \\ =\langle\Omega|\phi(0)|\lambda_{0}\rangle\exp(-\mathrm{i}px)\bigg|_{p^0=E_{\vec{p}}} $$  In the above $|\lambda_0\rangle$ is an eigenstate of the full interacting hamiltonian $H$. The ket $|\lambda_{\vec{p}}\rangle$ is the boost of $|\lambda_0\rangle$ with momentum $\vec{p}.$ Furthermore $E_{\vec{p}} = \sqrt{p^2+m_\lambda^2}$ and $\vec{P}|\lambda_0\rangle = 0.$  I assume PS used $$\tag{2}\langle\Omega|\mathrm{e}^{\mathrm{i}Px}=\langle\Omega|\mathrm{e}^{\mathrm{i}0x}$$ in $(1)$.   Is $(2)$ true?   I thought $\langle0|\mathrm{e}^{\mathrm{i}Px}=\langle0|\mathrm{e}^{\mathrm{i}0x}$ where $\langle0|$ is the ground state of the free theory.   I hope I have provided enough info for the question to make sense.


I'm looking for an alternative to expressions of the form "X and I's Y", where X is a person/group and Y is a noun. Examples include:   My partner and I's project was well-received. My family and I's trip went well.   I'm not even sure if the above two sentences are gramatically correct, but even if they are, they sound awful. What's a better way to say these sentences?

I just stumbled upon a :     My wife and I's seafood collaboration dinner. How does it look?   Sure enough, the top comment immediately points out that it should be "my wife's and my". However, a cross-post to the Grammar subreddit produced :     It's fine as it is written. "my wife and I" is a noun phrase, functioning as a subjective pronoun in the singular and made possessive with the apostrophe. It is exactly the same as "our".      It seems weird because you would never use "I's" on its own but it is not on its own here - it is part of a noun phrase.   That's a rather intriguing argument. Does it hold any water?


I am wondering if there is any way to add a curve to this ōdachi I made without having to go into the mesh and add it manually, since it'll be very painstakingly difficult to do it manually.  Thank you in advance!

I'd like to curve my object, but I'm considering two options.  The first one is to make the object up with lots of vertices, like a sphere can be. The second is to apply some kind of modifier curve to a straight mesh, as I've understood there is such a possibility.  Here's an awesome pen drawing of what I'd like to achieve:    and here's my current even more awesome result:    Rather non-awesomely, they don't quite match. So if someone would kindly point me to the correct method to achieving a nice-looking solution with relatively low polygons, I'd be much enlightened


I've been doing some WordPress development for the past few years and never really used the User Meta API within WordPress.   Now with one of my projects requiring to store data unique to a user, I needed to look into it.   One thing I've noticed when I looked at the database is that add_user_meta just creates duplicates when there is already an existing one.   My question is, why does this not override any existing key? And we should check first if the Meta Key already exists and then use update_user_meta? Therefore creating an extra custom function if you would like to overwrite this by default.

I'm looking at the docs for add_user_meta() vs update_user_meta().    If the current meta_key does not exist for a user, will update_user_meta() automatically add the meta_key for that user or do you have to define the meta_key with add_user_meta() first?


What do you call a person who starts projects, doesn't ever finish, then starts another project?

I have googled but didn't find. "A person who gets interested in anything very quickly and loses interest in it sooner." What is such a person called?


A form of cross validation takes multiple subsets of a data and trains the model on them, then tests on the remaining subsets. Eventually, all subsets will be trained on.   Although I know that training once on the whole dataset will more likely result in overfitting than using cross validation, the end result is both methods result in the whole dataset being trained on. Why is cross validation better?

How would you describe  to someone without a data analysis background?


I often get the comment on my answers that "this should be a comment." They are right, it should be, but I can't because I need 50 rep to comment on questions. I think it should be possible to comment without rep because many people out there are asking themselves questions to clarify other questions. For example...  User a asks: How can I set a dyndns on my router? User b responds: Have you looked at the firewall settings on your router?  It's not really an answer, but it's good enough that it could lead him to find an answer himself. It's pedagogically better because now he knows the solution, and got the "I did it myself" feeling. My problem now is that I can't help them help themselves the correct way, because I can only answer, not comment!

is a great example of people coming from Google and using answers as comments.  I understand the reputation threshold is there to prevent spam, but Answers are just as prone to spam as comments and you can post them at reputation 1. Furthermore there are already flags in place as a preventive measure for both.  Essentially the reputation threshold of comments is forcing people to use the site in ways the designers did not intend. Removal of the reputation cap would also make the site more new user friendly as newbies that use the site in this manner are commonly given a unfriendly welcome in the form of downvotes from people who forget you need 50 rep to post comments.


when i am trying to install required plug-ins to play music,the following notice is coming:  Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/libd/libdvdread/libdvdread4_4.2.0+20121016-1ubuntu1.1_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/libd/libdvdnav/libdvdnav4_4.2.0+20130225-1ubuntu0.1_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/libm/libmad/libmad0_0.15.1b-7ubuntu2_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/l/lame/libmp3lame0_3.99.5+repack1-3_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/m/mpeg2dec/libmpeg2-4_0.5.1-5_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/o/opencore-amr/libopencore-amrnb0_0.1.3-2_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/o/opencore-amr/libopencore-amrwb0_0.1.3-2_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/x/x264/libx264-123_0.123.2189+git35cf912-1_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/a/a52dec/liba52-0.7.4_0.7.4-16build1_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/libs/libsidplay/libsidplay1_1.36.59-5_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/t/twolame/libtwolame0_0.3.13-1build1_i386.deb 403  Forbidden Failed to fetch http:/bd.archive.ubuntu.com/ubuntu/pool/universe/g/gst-plugins-ugly1.0/gstreamer1.0-plugins-ugly_1.0.6-1_i386.deb 403  Forbidden    what should I do now?....and is there any better Music Player than Rhythmbox? (i had to cut off one '/' after every http,cause i am not allowed to post more than 2 links.

I've start a new job today and I am trying to set up my machine to run through their Windows server.  I've managed to get a internet connection through the server now but now I can't run apt-get update as I get a "403 Forbidden" error.  This is for every repo under my source list, apart from translations(?).  I do have a proxy in apt.conf, if I don't have it I get a 407 Permission Denied error.  Here's my apt.conf file (I have omitted my username and password)  Acquire::http::proxy "http://username:password@192.168.0.2:8080/";   Here's my sources.list  #deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ dists/precise/main/binary-i386/  #deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ dists/precise/restricted/binary-i386/ #deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ precise main restricted  # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to # newer versions of the distribution. deb http://gb.archive.ubuntu.com/ubuntu/ precise main restricted deb-src http://gb.archive.ubuntu.com/ubuntu/ precise main restricted  ## Major bug fix updates produced after the final release of the ## distribution. deb http://gb.archive.ubuntu.com/ubuntu/ precise-updates main restricted deb-src http://gb.archive.ubuntu.com/ubuntu/ precise-updates main restricted  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu ## team. Also, please note that software in universe WILL NOT receive any ## review or updates from the Ubuntu security team. deb http://gb.archive.ubuntu.com/ubuntu/ precise universe deb-src http://gb.archive.ubuntu.com/ubuntu/ precise universe deb http://gb.archive.ubuntu.com/ubuntu/ precise-updates universe deb-src http://gb.archive.ubuntu.com/ubuntu/ precise-updates universe  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu  ## team, and may not be under a free licence. Please satisfy yourself as to  ## your rights to use the software. Also, please note that software in  ## multiverse WILL NOT receive any review or updates from the Ubuntu ## security team. deb http://gb.archive.ubuntu.com/ubuntu/ precise multiverse deb-src http://gb.archive.ubuntu.com/ubuntu/ precise multiverse deb http://gb.archive.ubuntu.com/ubuntu/ precise-updates multiverse deb-src http://gb.archive.ubuntu.com/ubuntu/ precise-updates multiverse  ## N.B. software from this repository may not have been tested as ## extensively as that contained in the main release, although it includes ## newer versions of some applications which may provide useful features. ## Also, please note that software in backports WILL NOT receive any review ## or updates from the Ubuntu security team. deb http://gb.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse deb-src http://gb.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse  deb http://security.ubuntu.com/ubuntu precise-security main restricted deb-src http://security.ubuntu.com/ubuntu precise-security main restricted deb http://security.ubuntu.com/ubuntu precise-security universe deb-src http://security.ubuntu.com/ubuntu precise-security universe deb http://security.ubuntu.com/ubuntu precise-security multiverse deb-src http://security.ubuntu.com/ubuntu precise-security multiverse  ## Uncomment the following two lines to add software from Canonical's ## 'partner' repository. ## This software is not part of Ubuntu, but is offered by Canonical and the ## respective vendors as a service to Ubuntu users. # deb http://archive.canonical.com/ubuntu precise partner # deb-src http://archive.canonical.com/ubuntu precise partner  ## This software is not part of Ubuntu, but is offered by third-party ## developers who want to ship their latest software. deb http://extras.ubuntu.com/ubuntu precise main deb-src http://extras.ubuntu.com/ubuntu precise main   I can sort-of fix this by changing all the http in sources.list to ftp but I still have issues with ppas


I'm new on Lubuntu and so I downloaded a editor like LightTable and it runs only with this command from command line     ./LightTable   So HOW CAN I ADD THIS SOFTWARE ON MY MENU ?

The GNOME on-board documentation covers only the things anyone can easily guess. I have an application for that I can only start from the command line. Not that I mind using a terminal but ...  Anyway, how do I add the command (and preferably a nice logo) to GNOME WM?


Maybe I'm just clueless, but in looking through the documentation for TinyMCE 4.0 I can't seem to find information how how to specify which editor buttons to display. The theme_advanced_buttons[n] argument that works fine in TinyMCE 3 doesn't appear to be supported in version 4, and I can't find information on the replacement argument. Can anyone point me in the right direction?

With WordPress 3.9 coming soon it's bringing along TinyMCE 4.0. I'm running my plugins and functions through some testing and found that one of my functions seems broken / not working with the new TinyMCE function myformatTinyMCE( $in ) {     $in['theme_advanced_buttons1'] = 'bold';     $in['theme_advanced_buttons2'] = 'formatselect';     $in['wordpress_adv_hidden'] = false;     return $in;  } add_filter( 'tiny_mce_before_init', 'myformatTinyMCE' );  The above function used to limit the buttons in the tinyMCE to specific buttons, I've simplified it a bit to make it easier for testing. If I print out $in it shows the correct values in the correct spots, but when I actually load up a page it just defaults to the normal buttons. I've also tried to use the example in the  which also didn't seem to have any effect. I'm using the  Plugin and I do have  installed but disabled. With the new TinyMCE how can I continue using / customizing, and are there any 'Gotchas' that have changed from the previous TinyMCE Version? EDIT Looks like $in['wordpress_adv_hidden'] = false; is not longer being used - No idea how to unhide the Kitchen Sink.


Let $G$ be a finite set and $*$ an associative binary operation such that $x*y=x*z \implies y=z$ and $y*x=z*x\implies y=z$, $\forall x, y, z \in G$. Prove that $(G, *) $  is a group. I only need to prove that $(G, *) $ is a monoid because if a finite monoid has the cancellation property then it is a group. However, I can't prove this.

Suppose $G$ is a semigroup and it holds both left and right cancellation. Also for each $a,b\in G$, $xa=b$ has solution in $G$. Prove G is a group.   I know this question looks very "old" style. First I think it's easy for me too since I already practice probelems like "semigroup, $xa=b$ and $ax=b$ have solution , then group" Or "finite semigroup, both left and right cancellation hold, then group ". But I still get stuck... My try:  First of course, for $xa=a$ , there exists $e_a$ such that $e_aa=a$. Now we need to proof $e_a$ is left identity for all elements. Then left inverse exists hence $G$ is a group. But the key is to proof $e_ab=b$ for all $b\in G$.


I have a URL to a PDF document which I uploaded to the public_html/docs folder. How do I get search engines to index this link and PDF document?  When I submit the URL to the search console it does not index it, instead provides a message saying there was a problem.  Related info.: I have Cloudflare, do I need to make changes to it? Do I add something to robots.txt or sitemap?  I also noticed that the URL does not redirect to one format example:  and without www i.e.  open individually and as for my main domain no matter how you enter the URL it will always go to the . version. So, could this be a sign of the issue?  @StephenOstermiller I have a link as mentioned in the question, what does indexability have to do with the quality of the content? Quality of the content affects the rankings and not the indexability factor. You can have an image of a penguin on your website and get the URL crawled and indexed by Google. Lastly, you say this question has been answered, can you tell me where? I have ripped all related questions and all of them point to deindex the pdf and not get it indexed so this question is unique

This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it?


I'm using VirtualBox-4.3.6-91406-Win on Windows 7 x64 with an AMD 64-bit processor. The virtualbox installation is also a 64-bit install. I've been able to install Win Server 2008. When I try to install ubuntu-13.10-desktop-amd64.iso in Virtualbox, I get this msg:  This kernel requires an x86-64 CPU, nut only detected an i686 CPU. Unable to boot - please use a kernel appropriate for your CPU.   I'm using an AMD Phenom II X2 555 processor. It sounds like the .iso file may be corrupt? Any ideas/thoughts would be greatly appreciated.  Thanks

I was trying to install Ubuntu 12.04 in VirtualBox 4.2.12r84980. I see    this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot   But I am using a 64 bit Windows 8, and trying same .iso for trying Ubuntu. Then what is the problem?


I'm simulating the travel times of trucks moving between two points. The time it takes them to reach their destination is dependent on a few variable so it never the same. I need to compare the simulated travel times to historical data to show the simulation accurately portrays the real world system.   My question now is how many times do i need to repeat my simulation before I'm able to confidently say my simulation is able to represent the real world system?

Background  I am designing a Monte Carlo simulation that combines the outputs of series of models, and I want to be sure that the simulation will allow me to make reasonable claims about the probability of the simulated outcome and the precision of that probability estimate.  The simulation will find the probability that a jury drawn from a specified community will convict a certain defendant. These are the steps of the simulation:   Using existing data, generate a logistic probability model (M) by regressing “juror first ballot vote” on demographic predictors. Use Monte Carlo methods to simulate 1,000 versions of M (i.e., 1000 versions of the coefficients for the model parameters). Select one of the 1,000 versions of the model (Mi). Empanel 1,000 juries by randomly selecting 1,000 sets of 12 “jurors” from a “community” (C) of individuals with specified demographic characteristic distributions. Deterministically calculate the probability of a first ballot guilty vote for each juror using Mi. Render each "juror’s" probable vote into a determinate vote (based on whether it is greater or less than randomly selected value between 0-1). Determine each "jury’s" “final vote” by using a model (derived from empirical data) of the probability a jury will convict, conditional on the proportion of jurors voting for conviction on the first ballot. Store the proportion of guilty verdicts for the 1000 juries (PGi). Repeat steps 3-8 for each of the 1,000 simulated versions of M. Calculate the mean value of PG and report that as the point estimate of the probability of conviction in C. Identify the 2.5 & 97.5 percentile values for PG and report that as 0.95 confidence interval.   I am currently using 1,000 jurors and 1,000 juries on the theory that 1,000 random draws from a probability distribution—demographic characteristics of C or versions of M—will fill out that distribution.   Questions  Will this allow me to accurately determine the precision of my estimate? If so, how many juries do I need to empanel for each PGi calculation to cover C's probability distribution (so I avoid selection bias); may I use fewer than 1,000?  Thank you so much for any help!


I am working on a Web Project. I want to create "Forget my password" system and send a mail to user when it needed but when i try this, it gives errors like SmtpException : Failure Sending Message, SocketException: Party did not properly respond or connection failed because connected host failed to respond and fails to send mail. I tried 2525, 25 and 587 ports. I also checked if i can connect smtp.gmail.com by mxtoolbox:  This is SMTP Email Server Test    This is SMTP DNS Test     and here is my code:   protected void lblForPass_Click(object sender, EventArgs e)  {      SmtpClient client = new SmtpClient();      client.DeliveryMethod = SmtpDeliveryMethod.Network;      client.EnableSsl = true;      client.Host = "smtp.gmail.com";      client.UseDefaultCredentials = false;      client.Port = 25;      client.Timeout = 300000;      System.Net.NetworkCredential credentials = new System.Net.NetworkCredential("mytestmail@gmail.com", "1122334455");      client.Credentials = credentials;       MailMessage msg = new MailMessage();      msg.From = new MailAddress("mytestmail@gmail.com");      msg.To.Add(new MailAddress("mytestmail2@gmail.com"));       msg.Subject = "Subject Test";      msg.IsBodyHtml = true;      msg.Body = string.Format("Body Test");         try       {           client.Send(msg);           ScriptManager.RegisterClientScriptBlock(this, GetType(), "Mail Status", "alert('Sended Successfuly')", true);       }        catch(Exception ex)       {           Exception ex2 = ex;           string errorMessage = string.Empty;           while (ex2 != null)           {               errorMessage += ex2.ToString();               ex2 = ex2.InnerException;            }           string err = ex.Message;           ScriptManager.RegisterClientScriptBlock(this, GetType(), "Mail Error", "alert('" +err+"')", true);         }       }     Is there anything that i missed at this code block or do i need to check anything else? Thank you.

Instead of relying on my host to send an email, I was thinking of sending the email messages using my Gmail account. The emails are personalized emails to the bands I play on my show.   Is it possible to do it?


I'm guessing there has to be a reasonable way to solve my issue but I'm trying to get some advice on a best practice to implement.  I have recently moved to a Web Design company and we need to be able to spoof DNS entries for websites we're working on. However we want to only override certain A records, but keep the others so the site seems to work.  i.e:  We want to make "support.abcd.com" resolve locally, but everything else go to the real site. This would allow us to design/demo a fully functioning site with only the work in progress locally.  We have an internal BIND DNS server (9.9.5.dfsg-3).   What should my zone file look for "abcd.com" based on the example above?  Edit: Would this work?            IN ns1 abcd.com. IN NS ns1 support.abcd.com. IN A 192.168.1.1 faq.abcd.com.     IN A 192.168.1.1 *.abcd.com.       IN NS abcd.com     <- External?

I have an internal network with a DNS server running BIND, connected to the internet through a single gateway. My domain "example.com" is managed by an external DNS provider. Some of the entries in that domain, say "host1.example.com" and "host2.example.com", as well as the top-level entry "example.com", point to the public IP address of the gateway.  I would like hosts located on the internal network to resolve "host1.example.com", "host2.example.com" and "example.com" to internal IP addresses instead of that of the gateway. Other hosts like "otherhost.example.com" should still be resolved by the external DNS provider.  I have succeeded in doing that for the host1 and host2 entries, by defining two single-entry zones in BIND for "host1.example.com" and "host2.example.com". However, if I add a zone for "example.com", all queries for that domain are resolved by my local DNS server, and e.g. querying "otherhost.example.com" results in an error.  Is it possible to configure BIND to override only some entries of a domain, and to resolve the rest recursively?


Sorry if this is a dupe (did a search, couldn't find anything).  In single variable calculus, if the following limit exists:  $$\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h},$$  then this expression itself is the derivative of $f$ at $x$. This is nicely motivated geometrically and otherwise. This definition gives of $f'(x)$ which gives the best linear approximation $\tilde{f}$ to $f$ at $x$ by  $$\tilde{f}(t) = f'(x)t + f(x).$$  For functions of several variables, most of the time I see the derivative defined in terms of the best linear approximation to the function explicitly. Specifically, the derivative of a multivariable function $g$ at $\mathbf{y}$ is some linear operator $L(\mathbf{y})$. Concretely, if the following expression is satisfied:  $$\lim_{\mathbf{h} \rightarrow 0}\frac{\|g(\mathbf{y} + \mathbf{h}) - g(\mathbf{y}) + L(\mathbf{y})\|}{\|\mathbf{h}\|} = 0,$$  then $L(\mathbf{y})$ is the derivative of $g$ at $\mathbf{y}$. We can show that $L(\mathbf{y})$ is unique in this case.  My question is why is this generalization necessary? What is the problem with simply defining is analogously to the single variable case as  $$L(\mathbf{y}) = \lim_{\mathbf{h} \rightarrow 0}\frac{g(\mathbf{y} + \mathbf{h}) - g(\mathbf{y})}{\|\mathbf{h}\|}?$$

I've leart in Calculus 1 that the derivetive of $f(x)$ is:  $$\lim_{h\to0} \frac{f(x+h) - f(x)}{h}$$.  suppose $f(x,y)$ is a function with 2 variables,  does $$f'(x,y) = \lim_{h\to0} \frac{f(x+h, y+h) - f(x,y)}{h}$$ ?  If not , what is the derivetive of function with 2 variables?


The uncertainty principle of Heisenberg says that the uncertainty in the position of a particle multiplied by the uncertainty of the momentum of a particle is always more than or equal to $\frac{\hbar}{2}$: $$\Delta x \Delta p \ge \frac{\hbar}{2}$$ Rearranging, you get this: $$\Delta p \ge \frac{\hbar}{2\Delta x},$$ which means that the uncertainty in momentum will never be $0$ unless the uncertainty in position is $\infty$. But that can never happen... I mean at maximum the uncertainty in position can't be more than a certain value because the universe doesn't have infinite space, right? Besides, if you think about electrons around an atom, that’s finite space. That would mean that there will always be an uncertainty in momentum... Meaning that momentum is not conserved... This question has been bothering me lately. It would be great if someone could give me an explanation.

The law of the conservation of momentum has been established for hundred of years. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. Can this theorem still be violated?  If yes, what requirements must have a momentum-non-conserving theory? Is Heisenberg's uncertainity principle $\Delta x \Delta p \geq \frac{\hbar}{2}$ the possible answer? (when one considers physical Systems in which $\Delta x$ is very small)?


There are $10$ types of ice creams available. We want to buy $3$ for each of $20$ students. In how many ways can this be done?  Since there is no restriction on the number of times an ice cream can be taken, one can choose all three different ice creams, or even all same ice creams. This is where my confusion begins.   There are $10^3$ ways to choose $3$ ice creams with repetition, but in this way, I'll be over counting in the sense that $ABC, CAB, BCA$ and so on correspond to the same set of ice creams, which have been counted separately.  If I consider the cases where a student takes all same ice creams, two same and one different ice cream, all different ice creams separately, I would also have to consider the number of students taking them.  Please give me some hint.  Thanks!

The I Scream Shop specializes in triple scoop sundaes. How many different triple scoop sundaes could be made using these flavors: vanilla, chocolate, strawberry, cherry, lime, and lemon?  I attempted to solve this problem by breaking it down into three cases: The first case involves the same flavor 3 times in a row. The second is 2 of a kind and then another flavor. The third is for ice cream containing three different flavors.  EDIT: The order of the scoops does not matter for each ice cream served.  The main problem I have is that I feel my work is not only incorrect, but also for the cases that I did manage to find an answer, I wish to find a more concrete answer instead of counting.  Case $1$: For three different ice creams, we have $\binom63= 20$  Case $2$: This case we can choose two different flavors. There are $\binom62$ ways of doing this. Now we must consider which one of these flavors doubles. At this point, I had a gut feeling that it is twice as much, but I'm not to sure how to do this for $n$ scoops.  Anyways, the total here is $\binom62\times{2}= 30$  Case $3$: We choose one flavor, so there is $\binom61= 6$ ways.  Therefore, there is a total of $20+30+6=56$ possible ice cream scoops. Again, my main concern is if there is a more concrete and general way to do the second case, or in the general, the cases between the two extremes- choosing one and choosing all different.


I accidentally set the scaling settings at 4, and couldn't reset them. Is there any way to reset these settings back to default? I'm running a Microsoft Surface Pro (10.6", 1920x1080), and I cannot see the slider. I have tried all the ways people posted and this hasn't worked. Using Pre-Ubuntu 14.04 Final Beta (Beta 1). So i am editing this post and hopes a moderator will unlock it because none of the answers work for me.

I scaled the UI from the display menu. Now it is way too big and I can't get to the slider to reset it.  Any ideas how I can change the scaling in Unity back to default without accessing the settings menu??  I tried   dconf reset -f /org/unity    with no luck.


Let's say  and my ten other black creatures are wiped out with "Wrath of God". Do then 10 white 1/1 Spirits appear on the battlefield even though Teysa has just been destroyed?  Sounds pretty strong to me. Am I right?  Thanks a lot.

has the following ability:     Whenever a creature you control with a +1/+1 counter on it dies, return that card to the battlefield under your control at the beginning of the next end step.   I had a number of creatures on the battlefield, including Marchesa herself, with one or more +1/+1 counters on them when  was played, destroying each creature on the board.  When Marchesa and several other creatures would be killed simultaneously,   Does Marchesa's ability trigger for herself? Does Marchesa's ability trigger for the other creatures under my control with +1/+1 counters?   In attempting to resolve the issue, we tried to look things up, leading to , which cites Rule 603.6d as proving that Marchesa's ability should trigger both for herself and for each other creature with +1/+1 counters.  Unfortunately, none of us could actually understand Rule 603.6d, aside from this example:     Two creatures are on the battlefield along with an artifact that has the ability Whenever a creature dies, you gain 1 life. Someone plays a spell that destroys all artifacts, creatures, and enchantments. The artifacts ability triggers twice, even though the artifact goes to its owners graveyard at the same time as the creatures.   The example certainly seems analogous to me, but without understanding the actual rule, rather than just the example, we weren't too sure.  A complete answer has to not only answer the question, but back up that answer with citation and explanation of the official rules on the matter.


I want to use epigrafica font as "sans serif" in sections and chapters but I don't have any idea how to do it. I found here a solution in pdftex. Is there a chance to do something similar using pdflatex?

I'd like to use epigrafica specifically for chapters and sections, but like to use times font for main texts.  \usepackage{epigrafica}          % for chapter/section \usepackage{newtxtext,newtxmath} % for main text   Is there any way to do this? I can only use pdftex.


My DNA match on Ancestry was thought to be my half sister. After my test came back, 713 cMs across 20 segments, 10% shared DNA, longest segment 136, that says my Grandfather would be her father, but my father makes more sense. I have read that females carry more DNA from their fathers than Males do. If my full sister gets tested, is there a possibility that hers may come up higher into the half sibling? Is there any possible way with my numbers I could be her half sibling? Also, what about getting my daughter tested? She and my sister are the only females in the family on my fathers side.

Given two tests that share some cM of autosomal DNA, how can I easily find the predicted relationships that such shared cM would suggest? For example, a 2,200 cM match suggests it could be either: grandparent, half-sibling, or grandchild.


What's the difference between substitution and permutation in DES? From my understanding substitution is replacing the data with new data and permutation is just rearranging the data?

I've noticed confusing definitions about permutation and substitution, preventing me from understanding the difference.  A permutation changes the order of distinct elements of a set, but this can be written as a function changing one element by another, exactly as a substitution.  So, how exactly can we distinguish between these two notions?  This question is interesting since we have these two notions in block ciphers, in which S-boxes perform substitution. The problem is that this table is used to replace one element by another, exactly like a permutation.


The standard for ethernet says you should use a transformer for isolation.  It seems like a cap-based solution would be smaller, more versatile, and a better fit for my application.  Is there any reason why a (capacitor-based) highpass filter couldn't be used instead?  EDIT: This question is different from others because it references a specific alternative, rather than asking the generic purpose of ethernet magnetics.

How / can you connect Ethernet devices together without magnetics? How do you wire it up? What sorts of practical limitations are there on doing this?  To clarify, I'm not trying to connect two computers here. I'm thinking specifically of creating a small network of microcontrollers on a single board. Lets say the total length of a network segment is no longer than 6 inches. This would be for 10BaseT or at most 100BaseT.


Prove that if $H$ is a normal subgroup of a group $G$ and has index $n$, then for any $g\in G$ we have $g^n\in H$.  Give an example for if $H$ is not normal, the mentioned statement is not correct. (Please give an example, except the symmetric group :D )

I need some help in relation to this exercise    "Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$."  I'm not allowed to use quotient groups in the proof, because the exercise is in the chapter before.   I tried by induction on $n$. The case $n=1,n=2$ are obvious, but even  the case $n=3$ is giving me trouble so I give up studying the general case of the inductive step.  My other approach was studying left or right coset of $G$. But I only proved that if $g \in aH$ then $g^2 \notin aH$ if $a \notin H$, and I can't find a way to demonstrate that $g^n \in H$. (my starting idea was to prove that every power of $g$ is in a different coset but then I realize that in this way I don't handle several case, for example $g$ has period strictly lesser than $n$ and in conclusion it doesn't prove the exercise)  Maybe I'm missing something about indexes, and this is why I asked here for some help,  (I can't use quotient groups because they are introduced later than this exercise, forgot to add this info in the beginning) Thanks in advance :)


I've just asked something here:   In the meantime I figured it out myself, so I don't know what is the proper process at times like this?

Often you have a question, you can't find the answer on Stack Overflow so you search for it (or think a bit more). Having found the answer you'd like to keep a record so you can find it again later.  Before Stack Overflow I would write a blog post so I could search for it later. Jeff and Joel, I think, specifically said SO is a good place to replace these blog posts. So what is the best etiquette for adding your answer?   Just ask the question, then post your answer immediately and let voting sort the answers out. This is okay, but it looks like you are just trying to generate reputation, and other people often don't vote or answer, and a lot of the SO information is lost. Provide the answer in the question and ask the question phrased as "is there a better answer". This allows others to gain reputation, and doesn't look so greedy but makes your answer harder to vote on. Post your question, let others answer it. If no-one puts the answer you already found, then add it an hour or so later. If someone else gets it then accept their answer (or the best one). This is more selfless with reputation, but makes other people do work you have already done which feels a bit lazy and a waste of everyone's time.   Or maybe there is another way?


I know that the reason I couldn't lift myself up(without the help of any items or a pulley system)was due to that my force was internal and there is a reaction force. However, assuming that somebody attempts to lift me up, wouldn't there also be a reaction force that prevents him from doing so?

Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction?


There are currently no employees assigned to this work center.  or  There are no employees currently assigned to this work center.

He is arguably the best actor of his generation   In the above sentence the adverb is placed just after "be" Can we use adverb after "be"? If we can use then please explain properly because I have studied that adverb can be used before adjective and adverb .


Given a collection $\mathcal A$ of sets and a large set $X$. What are  $\bigcup_{S\in\mathcal A}S$ and $\bigcap_{S\in\mathcal A}S$ ?  The problem is  if $\mathcal A$ is empty, what  do  $\bigcup_{S\in\mathcal A}S$ and $\bigcap_{S\in\mathcal A}S$  mean  ?   Muknres's "topology" page 12,  if $\mathcal A$ is empty, then  $\bigcup_{S\in\mathcal A} S=\emptyset$ and $\bigcap_{S\in\mathcal A}S=X$.  I 'm puzzled about this. Can someone tell me why? Thanks a lot!

Let $\mathbb S = \varnothing$.      Then from the definition: $ \bigcap \mathbb S = \left\{{x: \forall X \in \mathbb S: x \in X}\right\}$      Consider any $x \in \mathbb U$.      Then as $\mathbb S = \varnothing$, it follows that: $\forall X \in \mathbb S: x \in X$ from the definition of vacuous truth.      It follows directly that: $\bigcap \mathbb S = \left\{{x: x \in \mathbb U}\right\}$      That is: $\bigcap \mathbb S = \mathbb U$. ()   Proofwiki uses the above "proof" to "prove" that intersection of the empty set is the whole universe.   My question is, is the use of vacuous truth really allowed in axiomatic set theory, like ZFC? I don't see how the use of vacuous truth is justified.   The next problem I can think of is that we cannot really "define" the elements of empty set (to my knowledge, there is no element in empty set) so how can we then prove as the above proof did? This seems to contradict the use of vacuous truth.  And of course, there is issue of using the whole universe as a set, and I don't think this is allowed.... (Maybe proof above is using a different axiomatic set theory, as I am using ZF-minded thoughts...)


Following is the code to generate a table with input fields and buttons.

         <input type="text" class="text1">	         <input type="text" class="text2">	         <input type="text" class="text3">	         <button type="button" class="append_up">Up</button>	         <button type="button" class="append_down">Down</button>

         <input type="text" class="text1">	         <input type="text" class="text2">	         <input type="text" class="text3">	         <button type="button" class="append_up">Up</button>	         <button type="button" class="append_down">Down</button>

         <input type="text" class="text1">	         <input type="text" class="text2">	         <input type="text" class="text3">	         <button type="button" class="append_up">Up</button>	         <button type="button" class="append_down">Down</button>

   I want to be able to append a similar row anywhere in the table using JavaScript. If I click the Up button I want a similar row to be appended just above that row, and if clicked down, just below that row. And finally I want to be able to get all the data from the table in the order as created by clicking the buttons. Please help.  After receiving few answers this is what i did.  $(document).ready(function(){           var html = '
<input type="text" class="text1">	<input type="text" class="text2">	<input type="text" class="text3">	<button type="button" class="append_up">Up</button>	<button type="button" class="append_down">Down</button>
';            $('.append_up').click(function(e) {               e.preventDefault();               $(this).closest('tr').before(html);           });            $('.append_down').click(function(e) {               e.preventDefault();               $(this).closest('tr').after(html);           });        });    I was able to append rows but clicking on the button from the new row does nothing.

What is the best method in jQuery to add an additional row to a table as the last row?  Is this acceptable?  $('#myTable').append('
my data	more data
');   Are there limitations to what you can add to a table like this (such as inputs, selects, number of rows)?


Hey guys im working on an ulam's spiral problem and I want to search through the 2D array I have created and find the number entered by the user (numb). I don't get why the if statement (marked with a comment) is always returning false  Edit: Here is the partial code, I have run my genUlam function through the debugger and it DOES in fact return the number, unfortunately this is an assignment so i cannot post the entire code.   public static void main(String[] args)    {     //create scanner object     Scanner input = new Scanner(System.in);      //get input for dimensions     //System.out.print("Enter dimension: ");     int dimension = 3;      //check if dimensions are odd     if (isOdd(dimension) == false)     {        //if input for dimensions is even, get the next odd dimension        dimension += 1;     }      //get input for number in center    // System.out.println("Enter number in spiral: ");     int numb = 2;       //check that number in center is in range of 1 to dim^2     if (numb > Math.pow(dimension,2) && numb < 1)     {         System.out.println("Number not in range");         System.exit(0);     }      //create 2D array using my function     String[][] ulam = {{"1", "2", "3"},{"4","5","6"},{"7","8","9"}};    //check to see if the number user entered does exist, then print array    for(int r = 0; r < dimension - 1; r++)   {      for(int c = 0; c < dimension - 1; c++)      {      //String current = ulam[r][c];      /*the line below should be returning true when match is found, but it is returning false no matter what*/      if(ulam[r][c].equals(Integer.toString(numb)))        {        printArray(ulam, r, dimension);        }        else         {         System.out.println("match not found");        }      }   }   }     public static void printArray(String[][] array, int row, int dimension)   {      for (int i = 0; i < dimension - 1; i++)      {         System.out.println(array[row][i] + " ");      }   }     }

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 have an "if" formula that I need to duplicate for many columns, preferably without typing each if statement.  Formula is =if(k5>j5,0,j5-k5)  I have columns j through cy to include in the formula string.

I have a bunch of formulas in a column that I wish to duplicate exactly into another column, where I will go through and tweak them so that a different function is run on the same parameters.  When I do a copy/paste, the cell addresses are all altered to be one higher, which is not desired.  The only way that I have found is to move the cells using cut/paste, but then I destroy the source cells, leaving me without the duplicate cells.  If you want more detail, I have a column full of CORREL() calculations, and I want to duplicate them to another column where I will do SLOPE() calculations.


In proving Jordan's lemma, the inequality $$1 \geq \frac{\sin(\theta)}{\theta} \geq \frac{2}{\pi}$$ is used, for $\theta \in [0,\frac{\pi}{2}]$.  I got as far as establishing $1 \geq \sin(\theta) \geq 0$ and $\theta^{-1} \in [\frac{2}{\pi}, \infty)$.  I'm looking for a modest hint.

There is an exercise on $\sin x$. How could I see that for any $0<x< \frac \pi 2$, $\frac 2 \pi x \le \sin x\le x$?  Thanks for your help.


Is it possible for two or more photons to collide simultaneously with one electron, resulting in the emission of that electron from the metal surface? I searched for two photon absorption and found that an atom or molecule can absorb two photons if the sum of their energies is greater than the work function, but I want to know whether it is possible for two or more photons to interact with a single electron and cause its emission?

I understand that assuming light is quantized implies that if a lower energy interacts with  metal, it is possible that that quanta will not have enough energy to eject the electron. What prevents two quanta from interacting with the electron at the same time, though, and summing to have enough energy to release the particle. Indeed, what if two separate light rays of the same frequency impact the electron, why can't that free it?


In the  page, there are some mismatches between the display in the main page and the period-wise report page.  For example in the Stack Overflow League, the top user for the month is unutbu and the top user for the quarter is Ciro Santilli, but clicking on the  and  pages, the top user is listed as Gordon Linoff.         Likewise, in the Meta Stack Exchange League the top user for the quarter is displayed as Glorfindel, but clicking on the  page the top user is listed as Sterling Archer:        Is this a bug or known functonality?

We can see who earned the most reputation in the current week, current month, current quarter, current year or all time. There is this  for that. Also see the below screenshot.    What struck me as odd was the different users for the Mathematics site. So I clicked on the picture that is listed as top user for the current year, which led me . Also see the below screenshot:    Here a different user is shown as the top user for 2019 when compared to the overall overview. I suspect the week or month listing to be somewhat volatile, but the difference between both users in this case is so big I can hardly blame caching.


The domain rspb.org.uk has the nameservers   ns1.namecity.com.   ['62.128.193.35'] (NO GLUE)   [TTL=172800]  ns2.namecity.com.   ['84.22.161.171'] (NO GLUE)   [TTL=172800]  And on the website intoDNS, there is this warning:  The parent nameserver ns1.nic.uk is not sending out GLUE for every nameservers listed, meaning he is sending out your nameservers host names without sending the A records of those nameservers. It's ok but you have to know that this will require an extra A lookup that can delay a little the connections to your site.  In the registrar's settings, I can change these nameservers, but it only allows names, not ip addresses.   My question is, how does the DNS server know the ip address of the nameservers?   I did read somewhere that all nameservers must first be registered in the registry so perhaps an IP address is required during this step. The intoDNS warning mentions "an extra A lookup". Where is the DNS looking?

I register a new domain, mynewdomain.com, at a hosting company.   In the advanced DNS settings there is an A record which maps mynewdomain.com to a ip address.  In my webhost control panel, it shows me the nameservers for the domain: ns1.mywebhost.net & ns2.mywebhost.net  When I type in mynewdomain.com into a browser and hit enter I believe the following happens.   ISP resolver searches "." nameserver ISP resolver then told to search ".com" nameserver instead. ISP resolver finds mynewdomain.com, and searches the zone file to get the A record.     So my question is, where does my webhost's nameservers come into play? I believe the flaw in my logic comes from the fact that my zone file (in which the A record is kept) is stored on ns1.mywebhost.net). But if that is the case, how does my ISP resolver know to look here? (because I didn't type this into my address bar)


I am trying to use Linq to convert a list to Dictionary. I have been able to get proper results with anonymous types as keys, but not with concrete types. Please see code snipped below:          // Works. Produces 329 entries in dictionary, as expected.          var groupByMonth =             from e in list             group e by new { e.chk.Month, e.chk.Year } into g             select new { month = g.Key, rates = g.ToList() };         var monnthlyRates = groupByMonth.ToList();         var monnthlyRatesDict = groupByMonth.ToDictionary(t => t.month, t => t.rates);          // IS NOT WORKING. Produces 30K entries in dictionary; same num as in the list.         // i.e. the grouping does not happen         var groupByMonth2 =             from e in list             group e by new MonthYear { Month = e.chk.Month, Year = e.chk.Year } into g             select new MonthYearRates { MonthYear = g.Key, Rates = g.ToList()};         var monnthlyRatesDict2 = groupByMonth2.ToDictionary(t => t.MonthYear, t => t.Rates);          // Works. Dictionary has 329 entries         var groupByMonth3 =             from e in list             group e by new DateTime(e.chk.Year, e.chk.Month, 1) into g             select new MonthYearRates2 { MonthYear = g.Key, Rates = g.ToList() };         var monnthlyRatesDict3 = groupByMonth3.ToDictionary(t => t.MonthYear, t => t.Rates);   I tried to fix the problem by implementing IComparer and/or IComparable in the concrete type; to no avail  class MonthYear : IComparer // class MonthYear : IComparable, IComparer {     public MonthYear()     {     }     public MonthYear(int month, int year)     {         Month = month;         Year = year;     }     int IComparer.Compare(Object x, Object y)     {         MonthYear xo = (MonthYear)x;         MonthYear yo = (MonthYear)y;          if (yo.Year > xo.Year)             return 1;         else if (yo.Year < xo.Year)             return -1;         else         {             if (yo.Month > xo.Month)                 return 1;             else if (yo.Month < xo.Month)                 return -1;             else                 return 0;         }     }      //int IComparable.CompareTo(object obj)     //{     //    MonthYear o = (MonthYear)obj;      //    if (Year > o.Year)     //        return 1;     //    else if (Year < o.Year)     //        return -1;     //    else     //    {     //        if (Month > o.Month)     //            return 1;     //        else if (Month < o.Month)     //            return -1;     //        else     //            return 0;     //    }     //}     public int Month;     public int Year; }   I understand that Lookup might be a better fit that dictionary; I will lookup Lookup once I am done with anyonymous types.

If I want to use objects as the keys for a Dictionary, what methods will I need to override to make them compare in a specific way?  Say I have a a class which has properties:  class Foo {     public string Name { get; set; }     public int FooID { get; set; }      // elided }    And I want to create a:  Dictionary<Foo, List<Stuff>>   I want Foo objects with the same FooID to be considered the same group.  Which methods will I need to override in the Foo class?  To summarize: I want to categorize Stuff objects into lists, grouped by Foo objects. Stuff objects will have a FooID to link them to their category.


around the eyes it just goes dark and i do not know how to fix it

While rendering a mesh with smooth shading on, I get a dark region/shadow on certain faces. The effect is more evident when smooth shading is applied to a mesh containing ngons, with the ngons turning black when rendered.   The blackening effect is visible in the viewport too.  How can I solve this problem?


She is the one whom I love the most.   During an English lesson, this sentence came up and my answer was whom. My teacher told me that it is not the best answer (that is who), it is kind of awkward and she would not use it should she say something like this.  Could anybody comment on the use of whom in Modern English and how acceptable it is?  Is there any case when whom cannot be replaced with who, either stylistically or grammatically?

Many times, I've been asked the difference between "who" and "whom". I myself know the difference, but it is hard to explain to others. What is the easiest way to explain it to those with a basic understanding of English? A mnemonic (if possible) would help.


I am designing my Wordpress website directories and url structure, my website is a listing of doctors.  I have a review section for collecting user reviews as a single post that can indexed by google, doctor's profile and medical procedures landing pages (I will show reviews for each procedure inside its landing page) Which of these path are the best structure for my website:    Home > reviews > rhinoplasty reviews > review title Home> procedures > rhinoplasty > reviews

Let’s take an example of a movie site. So a well structured set of URLs for this site can be:     Movie page - example.com/movies/the-matrix Review for movie - example.com/movies/the-matrix/reviews Trailers for movie - example.com/movies/the-matrix/trailers Specific trailer for movie - example.com/movies/the-matrix/trailers/trailer1   where it’s possible to navigate the resource even by directly deleting/appending resource name seamlessly.  For SEO purpose I read somewhere that for two given pages, Google will prefer the page which have search query up in the URL hierarchy among other things. So for the given 2 URLs and the query "the matrix trailer"    example.com/movies/the-matrix/trailers example.org/trailers/the-matrix/    `     Google might prefer the second URL as it has the keyword "trailer" at first level comparing to first URL which has "trailer" at 3rd level (a resource deeper in URL hierarchy may be less important).    If it is correct, one may be tempted to create URL hierarchy somewhat like      Movie page - example.com/movies/the-matrix Review for movie - example.com/reviews/the-matrix/ Trailers for movie - example.com/trailers/the-matrix/ Specific trailer for movie - example.com/trailers/the-matrix/trailer1     which will break the seamless hierarchy.    My questions are:   Is it true that resource deeper in URL hierarchy is tend to be less important when comparing to URLs of other site?   Is sacrificing meaningful, seamless hierarchy worth for this SEO optimization?


I booked a plane ticket to Argentina with my name as it is on my Tunisian passport. Recently I changed my first name on my french passport so the first name doesn't match the one for the plane ticket/Tunisian passport. So my question is can I travel to Argentina using my Tunisian passport as document of identification and my french passport as a visa/proof of right of entry ? Or the airline may refuse it. Is there any other solution than applying for Argentinian visa with my Tunisian passport ?

I am a citizen of two different countries, and have two passports.  How should I use my passports when traveling?


Blender split the 3d view into 4 parts,I don't want this,I want the default blender 3d view,How do I go back?  Here is a screenshot:

I would like to close some view windows that I opened accidentally.  See the image below:    Edit: another note: I tried searching for the solution, but only found things like "Join Area", which don't seem to work in this situation.


I've just seen Interstellar and I have two questions:   How did the information from the black hole save humanity? What was that information about? I would rather not hear that "it's about the answer" I'd like to hear THE answer.

In Interstellar, what do Murph and NASA do to save humanity after solving Brand's equation? Do they get the entire human race on giant space ships and transport them to a habitable planet? (How exactly do they do  this?)  If yes, is this habitable planet Edmunds' (the one that Amelia lands on)?


What is the strategy to solve for:  $$(1+\tan1^\circ)(1+\tan2^\circ)(1+\tan3^\circ)\cdots(1+\tan45^\circ)$$  I don't know where to start. Thanks.

Which  is the fastest paper-pencil approach to compute the product $$ \prod  \limits_{i=1}^{45}(1+\tan i^\circ) $$


this regex give string between two string "(?<='v')(.*)(?='d')",  but i have some problem sometime with regex,  like this ex "   'v'string1d'd'string2'd'  ",  if use this regex he give me this result : string1d'd'string2  i want only get the string1  there any way to fix it

I have this gigantic ugly string: J0000000: Transaction A0001401 started on 8/22/2008 9:49:29 AM J0000010: Project name: E:\foo.pf J0000011: Job name: MBiek Direct Mail Test J0000020: Document 1 - Completed successfully  I'm trying to extract pieces from it using regex. In this case, I want to grab everything after Project Name up to the part where it says J0000011: (the 11 is going to be a different number every time). Here's the regex I've been playing with: Project name:\s+(.*)\s+J[0-9]{7}:  The problem is that it doesn't stop until it hits the J0000020: at the end. How do I make the regex stop at the first occurrence of J[0-9]{7}?


I have some browser bookmarks to a few filtered-tag queries. These now all show no matches ("No questions found."), but if I put the tag(s) in the search bar and query there are plenty of hits.  This is the case for Google Chrome as well as IE8, at least. For instance, this filter: .  I stumbled on this workaround: I start to create a new filter, defining it the same way as one of my existing filters, and I hit Preview.  Then I can go back to choosing the previously defined filter, and it works. But I apparently need to use that workaround separately for each filter that I have. It is not enough to do it for one filter, in order to fix things for all of the filters. Am I missing something? Thx.

SE is really acting up today, sometimes it doesn't show any questions in the questions tab in the sites.  I first noticed the problems when I opened my questions tab, and this shows up:        All I did was change the name of the question, and now meta stackoverflow thinks it's two questions.  Well the thing is, MSO actually created it as a new question!  Why?


I want to proof that $$\tag{*}(x\in y\land y\in x)\to\bot$$ in First-Order Logic.   Being $x\in y\land y\in x$ cyclic, it is an infinitely-descending $\in$-chain. Such a thing is excluded in ZFC by the axiom of foundation/regularity (see ).  Here the mentioned axiom: $$\forall x \left[\exists y(y\in x)\to \exists y\left(y\in x\land \neg\exists z\left( z\in x\land z\in y\right)\right)\right],$$ or $$\forall x\,(x\neq \varnothing \rightarrow \exists y\in x\,(y\cap x=\varnothing )).\tag{**}$$  The example $x=\{y\}$ and $y=\{x\}$ satisfies (**), doesn't it?  EDIT  I would like my question to be reopened because, although the question   is similar in content, I would like a formal proof as is mentioned in the title (or I thought to mention by specifying FOL). It is not about understanding (the answer to the other question is perfect, actually the comment to this question was enough to understand), but about the formal proof. Thank you.

A quick preface to the below question: this is my first post on math.se! I am excited to begin participating in such a wonderful community. Any feedback as to how I can improve this or subsequent posts is certainly feedback from which I could benefit.      (Exercise 3.2.2 of Tao's Analysis I) Use the  (and the singleton set axiom, which guarantees the existence of the singleton set) to show that if $A$ is a set, then $A\notin A{. \kern 0.05em}^\text{1}$ Furthermore, show that if $A$ and $B$ are sets, then $A\notin B$ or $B\notin A$.    Thoughts: Consider some set $A$ and the singleton $\{A\}$. By the axiom of regularity, the only element of $\{A\}$, namely $A$, is not a set or disjoint from $\{A\}$. Clearly, $\{A\}\cap A=\emptyset$ and thus, $A\notin A$.   Moreover, suppose $B$ is some other set such that $\neg(A\notin B \lor B\notin A)$, i.e. $A\in B\land B\in A$. This implies, in very vauge notation, that $A=\{\{A,\dots\},\dots\}$ and $B=\{\{B,\dots\},\dots\}$. Can I get a contradiction out of this? In the case of $A$, we get that $x\in\{A,\dots\}\lor x\in \{a\}$ for some $x\in A$ and all other objects $a\in A$. How can I prove that there exists no element of $A$ (and $B$) that is not a set unless it is disjoint from $A$. I would greatly appreciate any hints as to how I can complete my argument.     1 This first problem has been discussed on this site times before (see  and ). I include a solution only because the context demands it, but to avoid a duplicate question, I ask that it not be discussed here.


On , in the side bar is a list of the "Top Network Askers", having just found this I thought it would be showing off the most prolific and highest rep earning users ever to ask questions on Stack Exchange but this does not seem to be the case.  The first user I clicked on was a new account, from today, with a single question, hardly a "Top Network Asker" by anyone's definition of the phrase.  Further investigation shows a whole mess of users with all kinds of different statistics based on their questions, some are higher rep, with many questions, others like the one I previously mentioned and everything in-between, so now I am confused about what actually makes a "Top Network Asker".  What is the criteria for someone to appear on this list?  If it doesn't actually show the top askers on the network, shouldn't the title be changed to reflect what the list actually shows?

I was browsing the main Stack Exchange  and came across the "Hot posts" tab. It is a fun thing to see the diversity of the entire network. Then I noticed that there is a list with "Top network askers" right beside it, which is simply a list of the authors of the questions that are listed on the left half of the page.  I suspect that there was some sort of use for this feature, or it was adapted from something similar, but in its current state I don't see any use for it.   Should we:    adapt it to include a more relevant ranking?  consider changing the name of the list to reflect what is actually listed? consider omitting it at all?


Prove that every prime number greater than 3 is either one more or one less than a multiple of $6$. (Hint: Consider the contrapositive by cases.) I tried  this problem using contrapositive but It is not sure, As I'm new to this subject!! Here what I tried, Firstly I divide this as $P\rightarrow Q$ here, if $\forall p$ such that $p>3$ is prime then $p+1$ or $p-1$ multiple of 6 contrapositive of this statement is $\lnot Q\rightarrow \lnot P$, if $p+1$ is not multiple of 6 and $p-1$ is not multiple of 6 then there is no prime number $p>3$. So I assume $p+1$ is not multiple of 6 and $p-1$ is not multiple of 6 it implies $ p+1=3(mod6)$ and $ p-1=1(mod6)$ $\rightarrow p=2(mod6)$ $ p+1=4(mod6)$ and $ p-1=2(mod6)$ $\rightarrow p=3(mod6)$ $ p+1=5(mod6)$ and $ p-1=3(mod6)$ $\rightarrow p=4(mod6)$ from these three I said there is no prime number $p>3$ Can anyone please tell me is this correct If wrong give me hint to prove!!

Is that true that all the prime numbers are of the form $6m \pm 1$ ?  If so, can you please provide an example?  Thanks in advance.


I am using windows 7 64 bit, whenever I open new tab in my browser I got open some porn site as pop up window (just like we got adds as pop up window).This happens on almost every minute. All it started after connecting my laptop with my office network. So please tell me the solution for this.

What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.


Investigating a problem. I found out that I had so many calls to wp-login, but from many different ip's. Any idea on how to handle it?

I already used Limit Login Attempts wordpress plugin. Are there other ways to prevent brute force attacks?  I'm worried because I saw a lot of locked out.


What's the way to write or to read power (math) it in words?  Does "powered by" is correct?   For example:  "2 powered by 5 divided by 2 powered by 3." works?   Also "What 4 powered by 3 does equal to?" is correct?

I have this value    How to read that in English? translating from my native language, I would say     Ten base of nine.   but is that really correct?


Which STL container should i use if:   Data is inserted and removed regularly. Data is accessed regularly at random.   E.g : dataset(4,10,15) if i want to find the closest number to 9, then it should return me 10.   I am only storing an integer. It needs to be sorted Can go to 100k datasets   I thought of using vector, but vector insertion and removing is expensive.     vector<int>   If i were to use list, i would have to access O(n) elements before reaching the data.     list<int>   I was thinking of using set as it will be good if it is sorted, but im not very sure about the efficiencies for using SET  So i hope someone can give a good solution!

I've been reading up on STL containers in my book on C++, specifically the section on the STL and its containers. Now I do understand each and every one of them have their own specific properties, and I'm close to memorizing all of them... But what I do not yet grasp is in which scenario each of them is used.  What is the explanation? Example code is much prefered.