What exactly happens when you 'index' a MongoDB database?

So I understand that indexes are crucial because they allow you to make queries without having to look at the entire collection, but what exactly is an index? What really happens to the data when you call .createIndex()? Thanks!


Occasionally, when I ask a question on some Stack Exchange site, I'll see a page  wanting to verify whether or not I'm human.   I'm trying to figure out what I am doing that looks suspiciously non-human. How is this page triggered?  (Ironically, when I posted this question, it asked me to do the CAPTCHA.)


how do I get a function from another script and insert it into a button, I did this is giving this error  "Object reference not set to an instance of an object"  public Button Mybutton;      void Indice(){         if (index <= 0)     {         index = 0;     }      if (index >= 2)     {         index = 2;     }          if (index == 0)     {         Mybutton.GetComponent<Button>().GetComponent<MyScript>().MyFunction();     }     else if (index == 1)     {         Mybutton.GetComponent<Button>().GetComponent<MyScript>().MyFunction2();     }     else if (index == 2)     {         Mybutton.GetComponent<Button>().GetComponent<MyScript>().MyFunction3();     }


What's the rhetorical term for when a historical quote is repurposed?

I'm writing a point about how Donne changes the words of the Lord's Prayer to alter the meaning. Is there a rhetorical term for this, when we borrow from a historical quote to lend our point gravitas? I would say parody, but crucially in this instance it would be to add gravitas rather than to poke fun at something? ALthough I'm not sure if I'm missing the point!


Is Gandalf the Gray's power actually limited or did he merely promise to not use it?

We know that the Maiar sent to Middle-earth as Istari are not using their full Maiar power. Gandalf the Gray is more than a human power wise, but not nearly equal to his full real power.  Is it known (from canon) whether there is something explicitly restricting Olorin's power when he's Gandalf the Gray, or is he merely prohibited from using it but still has it at his disposal?  Question arose from  comment. Daniel was using Saruman having greater powers once he turned "bad" as his reasoning.


Testing for normality in SPSS: Procedure for two or more independent variables WITHOUT levels/groups

In order to do a linear regression, I need to test my data set for normality. I have one dependent variable plus three independent variables. The independent variables are all scale variables, i.e. without any groups/levels (e.g. male/female). How do I test for normality in SPSS? Unfortunately, I can only find procedures that describe what to do if the independent variables have different groups/levels. In such a case, it seems you have to establish normality for all separate combinations of the groups/levels of the independent variables by splitting the file and organizing the output by the different groups/levels. See this instruction video on youtube: . But what if my variables don't have any groups/levels?


i try to download games on my tablet and it keeps saying no space on device

I try to download games and it always say insufficient space on device what should I do. Google play or play store


Catenary problem adaption with additional point mass

Consider a wire of length $L$ hanging between two poles of the same height that are located a distance $d$ from one another, such that the mass density of the wire is constant, and at a fixed length (meaning, length along the wire) $l$ from the left hanging point, there is a point mass $M$. This is an adaption of the classical catenary problem in classical mechanics (and calculus of variations) which I find interesting. How would you write down the Lagrangian, end conditions and constraints for this problem? And how would you try to solve it? The action should be the total potential energy for the wire. Does this mean that the Lagrangian should have a delta function term where the point mass is located? How would you parametrize this in a way which will 'fit' well with the constraint for the total length of the wire? I'm quite new to this so I'd be happy to hear as many details as possible (or if there is a good source which addresses the problem, that would also be good).


Proving Geometric Hahn-Banach Implies Analytic Hahn-Banach

I've come across a proof online of the H.B theorem using the goemetric version.   There is a step in the proof which im not sure why is true and it is as follows:   Let $X$ be a linear space and $M \subset X \times \Bbb R$ be a maximal subspace.  Then $M = G(F)$ for $F :X \to \Bbb R$ linear.   Someone can show me why this is true?   Maybe I misunderstood the proof, its the last paragraph of Matrin's answer here -.   Thanks a lot for helping!


"An active device or component is something which can provide an infinite energy or non-zero power for an infinite interval"   I learned this definition for an active device in a book, which is valid for capacitor, inductor and batteries (I have evaluated). I was wondering what is a "PN junction", "junctions of a transistor", "OPAMP", "JFET", "MOSFET"? I mean what are the above mentioned devices inside the quotation marks? Are they active devices or passive? If either one then please provide explanation for my understanding.


Where does the offset go in Poisson/negative binomial regression?

(First of all, just to confirm, an offset variable functions basically the same way in Poisson and negative binomial regression, right?)  Reading about the use of an offset variable, it seems to me that most sources recommend including that variable as an option in statistical packages (exp() in Stata or offset() in R). Is that functionally the same as converting your outcome variable to a proportion if you're modeling count data and there is a finite number that the count could have happened? My example is looking at employee dismissal, and I believe the offset here would simply be log(number of employees).  And as an added question, I am having trouble conceptualizing what the difference is between these first two options (including exposure as an option in the software and converting the DV to a proportion) and including the exposure on the RHS as a control. Any help here would be appreciated.


How to use a special character as a normal one in Unix shells?

Many questions like 'How to type the double-quote char (")?' are being asked, and we don't want to clutter our community with the same answer (Type it as \" if not enclosed in 's, " if enclosed in 's.) So, the question is here.   You can't type special chars into a terminal like normal ones, e.g. this command will fail:  echo Updates (11)   So, how to type in these chars in the terminal as if they were normal ones?  !#$^&*?[](){}<>~;'"\|<space><tab><newline>


Can not install software from ubuntu software center

Whenever I try to install software from the ubuntu software center, it gives me the following error after I enter my password:  Package operation failed The installation or removal of a software package failed OK   and if I try to install it a lot more times, a  ▶Details   thing apears. When I click that, it gives me this:  dpkg: error: parsing file '/var/lib/dpkg/updates/0174' near line 0:   Also something that might be helpful is that I am running ubuntu through virtualbox and when my computer crashed (not the virtual one, but my mac one), I was running ubuntu in virtualbox, and ever since then I have had this problem. Anyone know why? Thanks.  EDIT: I've tried again, and when I click details, the message changed:  dpkg: error: parsing file '/var/lib/dpkg/updates/0174' near line 0:   EOF after field name `'


How big is a gemstone in the DMG gemstone table?

Context  The  (DMG p134) describe six categories of gemstone: 10gp, 50gp, 100gp, 500gp, 1000gp, and 5000gp.  What does this mean? An agate can be worth anywhere between 10gp and 5000gp depending on how big it is, not to mention other factors.  Therefor, I believe we are forced to assume a standard gemstone size for this table.  For the table to be of any use as a resource, a 10gp agate must be roughly the same size as a 5000gp black sapphire.  The statements “an amethyst is worth 100gp” and “a topax is worth 500gp” simply do not mean anything without a size reference.        I understand that gemstone value is not entirely, or even mostly dependent on size: color, clarity, and cut are also important.  But this is not any help, and only makes the existence of a table ranking of gemstone value even more baffling unless we can also assume a standard level of quality, and indeed this assumption is supported by the fact that the table already lists different grades of certain gems.  Sapphires and rubies, for example, appear in different categories of value depending on their color and clarity.  However there is some slight evidence to suggest that there is no standard size.  The 5,000gp gemstone list includes both a diamond and a ruby, which are often not the same value, so perhaps the ruby on this list is larger than the diamond?  Even if this were the case, as I have argued above the table does not make sense without at least some reference to size, so the size variation must be slight, or within a range.  Alternatively, there is a standard gemstone size and either (A) rubies and diamonds are worth the same in this world or (B) the listed diamond is lower grade or the ruby is higher grade (and indeed, there are lower grade rubies listed elsewhere in the table).   My Question  Is there indeed a standard gemstone size in the DMG's treasure tables, and if yes, what is it?   Parameters  I do not require a strictly RAW answer to this question.  There does not seem to be guidance on this issue within the official rules, but I can think of three possible ways of answering this question, in order of authority:    Inference from official adventure modules that contain a description of a gemstone’s size and value.  To get at the pure value of the gemstone as a material, such a reference should not be to gemstones that are part of an art object Inference from real world gemstone value, applied to the RAW.   SE answer to a similar question has some helpful guidance. If nothing else, a secondary source with more usable gemstone tables would be helpful.  This includes previous editions, thoughtfully written homebrews, and third party publications.   All I want is a number that is plausible, based on either real life or existing D&D materials.


Installing ClipBucket but installation cannot find ffmpeg

I am running the installation of ClipBucket and I have installed ffmpeg. I rerun the installation to refresh the requirements and it continues to show:  Unable to find ffmpeg   If I do a find of ffmpeg, I find it though:  :~$ sudo find / -type f -name "ffmpeg" /opt/ffmpeg/bin/ffmpeg   I am using Ubuntu 14.04.4 LTS with Plesk. Do I need to do something with Plesk for this to be seen by the web page?  I am not a pro when it comes to Ubuntu so I'm not sure where to look not or what to do.


How can I validate a 10 digit phone number (digits and spaces only) in CakePHP?

I wish to validate a 10 digit phone number, and allow for up to four spaces in between each numeric segment, in CakePHP. How might I do this?  Examples of valid input:   04 123 123 34  0266 234 234  0266123123 02 66 55 12 12


Is regular charge cycling important to maintain battery health?

I read about a full charge cycle at least once per month - how is this done? Just purchased this wonderful machine, brand new, want to keep it as perfect as possible, and am not sure how to do a full charge cycle of the battery.


Client-Server: Data Model and Protocol, best practice and examples?

I want to write (for the sake of learning) how to write a client-server app using C++. I have actually done it in the past and found many excellent tutorials on the web, including this good post on stack overflow:    What I would like to learn this time (and better understand) is how to actually write a protocol to communicate "meaningful" data between the client and server. Most examples just pass strings such as "Hello world". Great but not very practical.  What I would like to do is pass for example commands to the server that would modify some data (a document that the server would for example be responsible of keeping a copy of). I have been inspired after watching  in which they explain how the clients send commands like [insert, 10, "caterpillar"] to the server, which has for effect for example, to insert the chain of character "caterpillar" at index 10 in a string maintained by the server.  How would you send such commands typically in professional applications (how do you define them in the code, how do you pass them on, how to read them on the other end?)?   Bonus question;-): the video speaks a lot about data model. How does it relate to the protocol (the commands exchanged between the client and server and that allow them to understand each other)?  EDIT:  Actually found this question on Stackoverflow with some helpful answers:      The solution seems to be called serialisation.


Two different expansions of $\frac{z}{1-z}$

This is exercise 21 of Chapter 1 from Stein and Shakarchi's Complex Analysis.  Show that for $|z|<1$ one has $$\frac{z}{1-z^2}+\frac{z^2}{1-z^4}+\cdots +\frac{z^{2^n}}{1-z^{2^{n+1}}}+\cdots =\frac{z}{1-z}$$and   $$\frac{z}{1+z}+\frac{2z^2}{1+z^2}+\cdots \frac{2^k z^{2^k}}{1+z^{2^k}}+\cdots =\frac{z}{1-z}.$$  Justify any change in the order of summation.   [Hint: Use the dyadic expansion of an integer and the fact that $2^{k+1}-1=1+2+2^2+\cdots +2^k$.]  I don't really know how to work this through. I know that $\frac{z}{1-z}=\sum_{n=1}^\infty z^n$ and each $n$ can be represented as a dyadic expansion, but I don't know how to progress from here. Any hints solutions or suggestions would be appreciated.


Proper way to subscribe to events raised in another thread Winforms C#

I have a WCF client class that I would like to run in another thread - the thing is there are events occurring in the client that I would like to handle. Specifically How to Subscribe to them. - the Event itself and invoke of the UI - I have a great InvokeEx example that came form stack..  So for example some quick pseudo code :  class WinFormExample : Form {    public WinFormExample() {    Task.Run(client => client.Start() , TaskOption.LongRunning);  // How Do I subscribe to the events that are occurring in the client // Would I need to create an Instance of InstanceContext in winforms and pass that to the client.Start(instanceContext) method ?  // would it be this way. InstanceContext myInstanceContext = new MyCallbackInstanceContext();    Task.Run(client => client.Start(myInstanceContext ) , TaskOption.LongRunning); myInstanceContext.SomeEvent += MySomeEventHandler(); }   }  class WCFDuplexClient  {  public DuplexClient MyClient  = new DuplexClient(MyinstanceContext, binding, endpoint);  public Start() {  MyinstanceContext.SomeEvent();  }  OR   public Start(InstanceContext myContext, binding, endpoint) {  MyClient  = new DuplexClient(MyinstanceContext, binding, endpoint);   } }   EDIT 11-23-2015  I am not asking about invoking controls on the UI thread; ie How to marshall a subscribed event using Invoke to ensure the UI gets updated.  I am asking about SUBSCRIBING to events that occur in a context that is passed into a Client Class that is running on a different thread. Maybe I just do not understand well enough that my question is not appropriately formed - or I am asking because of my ignorance of a concept here: please I don't know it all I am learning - hence my question. I would like to know the answer before I go about converting my code completely to do this.  I have a WCF Duplex CLIENT class it is continually running receiving data from a process via myContext which is the callback channel. myContext has events. one such is SomeEvent - do I subscribe to that event the same way as subscribing to events that are on the same thread. For example with a Button_Click event it is on the form - I simply Subscribe  Button.Click += myButtonClickHandler;   With a Class running in a different thread my InstanceContext - myContext is a callback channel the client is in another thread executing the instance context is passed into that thread when it is started.  Do I subscribe to it the same way as I subscribed to the button  like this:   myContext.SomeEvent += myContextSomeEventHandler;    or must I perform another manner of capturing the data that the callback myContext receives? - I know some things use a async progress report , some use a backgroundworker - I simply want to capture the data through an event and subscribe to the events.  END of EDIT 11-23-2015


CSS Styling both img and paragraph child elements

I'm having issues with my 2 child elements both being affected from styles applied to each other. I'm just trying to line up the one with the other better vertically. I pretty much just went to move the img down a few pixels to line up with the  content. Any css thing I'm missing here?

TestingFileName.pdf

        .fileIcon {     text-align: center;     overflow: auto;   }    .iconImg {     display: inline-block;     z-index: 1;     width: 22px;     height: 22px;     padding: 0px 5px;   }      #fileName {     display: inline-block;     z-index: 1;     color: #999;     font-size: 1.1em;     margin: 0;   }


Punctuation with complete or incomplete list of items

Here's a situation:     John, Anne, Jake, Pete...they are all from the same class.   Is there any way to punctuate this sentence without using the ellipsis? Is an "and" necessary before the last item (here, Pete) in this kind of a list? What would be the best way to punctuate this sentence in formal writing, e.g. a book manuscript?


Why is it car exhaust fumes and not car's exhaust fumes? & What type of nouns are they?

I would like to know what type of nouns car exhaust fumes, car accident, school day, air quality... are because, many times, I write such nouns with apostrophes, like car's exhaust fumes, air's quality, and car's engine, then find out they are not written this way.  For example:     (bedroom, football, sunglasses...) = Compound nouns      (high-spirited, long-lasting, never-ending...) = compound adjectives       (car exhaust fumes, car accident, school day, air quality...) = ?   I know my question might sound silly but please bear with me.


I have encountered a strange issue with calling my @AuraEnabled method from Lightning.  The second parameter (which is a method overload) is consistently null when called from Lightning - but is never null when called via executeAnonymous()  Here is the first method definition:  @AuraEnabled public static ReportSummary getReportSummary(String reportName) {   Id userId = UserInfo.getUserId();   return getReportSummary(reportName,userId); }   Here is the second definition (overload):  @AuraEnabled public static ReportSummary getReportSummary(String reportName, Id userId){   System.debug(LoggingLevel.DEBUG, 'USER ID: ' + userId);   ReportSummary summary = new ReportSummary(userId, '');   //ect ect...   //the above system.debug prints out 'USER ID: null'   I call first (single parameter) method from Lightning.  If anyone can shed some light on this, it would be appreciated.


Suppose that $x \equiv 1 \pmod n$ and $x \equiv 1\pmod m$. Prove that $x \equiv 1 \pmod{ mn}$.

I know the Chinese Remainder Theorem implies that there exists a unique solution modulo $mn$, but I can't spot how to show directly that you can deduce that $ x \equiv 1 \pmod {mn}$.  Thanks in advance!


Is any article needed before the word "interpreter" in the following sentence?

I have asked this question on Grammarly.com too, but didn't get any answers.  English is not my first language and I'm trying to get better at it therefore I can't give much input or put my "research" here. Here is the sentence:     Max had an opportunity to play the role of interpreter in an international film festival organised here.   Please explain if any article is needed or not.


What is the difference between running a script file like this:  sh myfile.sh   Or this:  ./myfile.sh   I thought they are the same thing, but noticed sometimes they are not, as seen below example:  root@kali:~/Documents# sh sweep-ips.sh ips range: ping: 10.11.1.{0..24}: Name or service not known  root@kali:~/Documents# ./sweep-ips.sh  ips range: 64 bytes from 10.11.1.5: icmp_seq=1 ttl=128 time=242 ms 64 bytes from 10.11.1.8: icmp_seq=1 ttl=64 time=249 ms 64 bytes from 10.11.1.22: icmp_seq=1 ttl=255 time=249 ms 64 bytes from 10.11.1.24: icmp_seq=1 ttl=64 time=241 ms   script:  #!/bin/bash echo "ips range"  for ip in 10.11.1.{0..24}  do    ping -c 1 ${ip} | grep "time="   done


Hillbilly-type family with supernatural powers

I am trying to find titles and author of 1950s era short stories about a family of hillbillies with supernatural powers. One family member was called Cousin Lemuel. This is categorically NOT Ray Bradbury's Elliot Family.    These stories appeared in sci-fi pulp collections, possibly Amazing Stories, in the late 1950s and early 1960s. Any help greatly appreciated.


Redshift due to a static gravitational field and the conservation of energy

I am standing on the surface of some planet. Gravity is described via General Relativity with some static metric (e.g. the Schwarzschild metric, so static means no time dependence, but the metric may vary from place to place). I send a blue photon up to my friend, who is x meters above me in some tower (we are both at rest relative to each other). He measures the photon and finds out it is red. We both conclude that a gravitational redshift occured. However, where did the energy go? In GR there is no gravitational energy so the photon did not trade "light energy" with potential energy.  I found several threads about this, but often they viewed this topic from a cosmological point of view where the metric does depend on time and thus Noether does not work to argue for a conservation of energy. Arguments without cosmology used the explanation via potential energy (which is not a thing in GR, as far as I know). So, since the metric is still time independent the energy should be conserved according to Noether.  What is going on?  Edit: On the Einstein thought-experiment in the linked question:  This does not explain why energy is not conserved from a mathematical or physical point of view. This could also be viewed as a reason why you can not turn photons into matter (and vice versa) without losing energy.


How do I see the exact position of my website in google SERP?

Whenever I search with keyword in my computer, it shows my website in first page and in reality(other computers) it is not showing what I see in my computer, I understand that this is because of I visited the website so many times, but I want to see only the reality position, what should I do to see the reality ? and Is there any option for webmasters to avoid this ?


My Enchanted Bow Command Doesn't Work. MC 1.8.8

/give @p bow 1 0 {ench:[{id:21,lvl:100},{id:48,lvl:2000},{id:49,lvl:2000},{id:50,lvl:2000},{id:51,lvl:2000,{id:34,lvl:2000}],display:{Name:"Dead Man Crack",Lore:["This Bow Is Only Effective When Shot At The Butt"]}}     This is my command and is it's always saying "unbalanced square brackets".  Does anyone have a answer, a clue or even a hint?


Can I still travel by air even if I applied for indian visa travelling by road?

I have applied for an Indian tourist visa not knowing I clicked travel by road via Haridashpur. Am I still able to travel by air?


Make clickable cell in dynamic table with JQuery

I would like to add a detailed link in specific cells in a dynamic table in JQuery.  This code works fine when adding a cell/row :  $('<td class="ploegen-details-naam" onclick="link_naar_info_speler(this.parentNode.childNodes[0].textContent)">    </td>').text(speler_naam).appendTo(details_rows);   But if I want to add dynamically detailed id's to the cell, this does not link anymore:  for (var x = 0; x < len; x ++) {    $('<td>', {id:"naam_thuis" + x}, {class:"ploegen-details-naam"},   {onclick:"link_naar_info_speler(this.parentNode.childNodes[0].textContent)"}).text(speler_naam).appendTo(details_rows); }    This function is exactly the same for the 2 examples :  function link_naar_info_speler(speler_id)  {     location.href="/ADL/Info/Spelers/Spelers.html?" + speler_id; }   The part that doesn't work in the second example is the onclick with the link. I only posted the relevant code, since the rest of the code is the same in the 2 cases.


Google isn't surfacing Events rich snippets in SERP when JSON-LD Structured Data is valid

Google confirms our site has thousands of valid MusicEvent structured data objects presented using JSON-LD, as indicated in the Structured Data section of Webmaster Tools. However, rich snippets for the events do not show up in any search result pages. The Rich Cards tab in Webmaster Tools says:     We did not find any structured data for rich cards on your website.   The structured data is valid with no errors in the Structured Data Testing Tool. We do generate some warnings occasionally for missing endDate and price fields. Comparing our code to a survey of other sites whose rich snippets do appear, we are not doing anything unique in terms of our markup.  The data has been there for months, in fact over the months we've tried also using Microdata format. The Structured Data section indicates that many pages were crawled this week.  Besides SDTT validation, what else can I check to troubleshoot this issue?


How to Launch Applications as root by default without using terminal

Trying to find a  way to launch apps from GUI as root by default without using terminal or command. I have gone through several sites and all says to launch by using "sudo %app name%". But what i am looking for is to launch apps automatically as root by clicking on the graphical icon without having to use terminal each time. Thanks in advance.


Is there a tree data type in windows libraries?

Working in C#. I need a simple tree data type to store some objects.  Is there a native windows libraries tree data type?  I've looked in System.Collections.Generic but couldn't find anything.   Tried Googling it, all I see is custom built trees.


DEM - calculate shortest/easiest path over mountain range

In QGIS, I have a mountain range with a valley on either side (DEM raster file). Is there software or a plugin that allows me to calculate the easiest pathway over the mountain? The answers at  are from 3 years ago and involves skills I've not yet acquired. Has nothing been developed in 3 years for us novices? Does QGIS3 not yet offer anything?


What is the name / author of the book where the protagonist lives on a planet where it is a forest and rains all the time?

I know this is a little vague, but it's been a long time since I read the book. If I remember correctly, the guys world is a forest and it rains all of the time. It's science fiction and the main character is a young guy. I read it in English in the early 80s. By today's standards it was a short novel, probably less then 130 pages.  On further reflection, I seem to recall the author may have written about Saturn - anybody remember any stories about rainforests on Saturn?


What is a synonym for "relatively unknown"?

I am trying to describe a place that is not often publicized in tourist guides and is not frequently visited. I currently have "visit the relatively unknown", but I am not particularly happy with the phrase because it sounds vaguely snobby to me. I am also not sure "unknown" should be qualified by degree. Does anyone have any suggestions?


Proof that $\rho = \pm1$ implies linear combination

I need to prove that $$\rho(X,Y) = \pm 1 \implies Y = aX+b,$$ for some constants $a, b$.  With the help of  and  here's what I've got so far:  Let $X, Y$ be random variables and $a$ some constant. $aX + Y$ is also a random variable whose variance by definition is non-negative $$V(aX+Y) \ge 0.$$ From variance properties: $$a^2 V(X)+2a\text{Cov}{X,Y}+V(Y)\ge 0$$ This is a quadratic as a function of $a$, which has a maximum of 1 root. It has a root only for $a$ that satisfies $$a^2 V(X)+2a\text{Cov}{X,Y}+V(Y)=0$$ let it be $a_0$. That means that $$V(a_0X+Y)=0$$  How can I continue from here?  Thank you.


Calculate the limit of two interrelated sequences?

I'm given two sequences:  $$a_{n+1}=\frac{1+a_n+a_nb_n}{b_n},b_{n+1}=\frac{1+b_n+a_nb_n}{a_n}$$  as well as an initial condition $a_1=1$, $b_1=2$, and am told to find: $\displaystyle \lim_{n\to\infty}{a_n}$.  Given that I'm not even sure how to approach this problem, I tried anyway. I substituted $b_{n-1}$ for $b_n$ to begin the search for a pattern. This eventually reduced to:  $$a_{n+1}=\frac{a_{n-1}(a_n+1)+a_n(1+b_{n-1}+a_{n-1}b_{n-1})}{1+b_{n-1}+a_{n-1}b_{n-1}}$$  Seeing no pattern, I did the same once more:  $$a_{n+1}=\frac{a_{n-2}a_{n-1}(a_n+1)+a_n\left(a_{n-2}+(a_{n-1}+1)(1+b_{n-2}+a_{n-2}b_{n-2})\right)}{a_{n-2}+(a_{n-1}+1)(1+b_{n-2}+a_{n-2}b_{n-2})}$$  While this equation is atrocious, it actually reveals somewhat of a pattern. I can sort of see one emerging - though I'm unsure how I would actually express that. My goal here is generally to find a closed form for the $a_n$ equation, then take the limit of it.  How should I approach this problem? I'm totally lost as is. Any pointers would be very much appreciated!  Edit:  While there is a way to prove that $\displaystyle\lim_{n\to\infty}{a_n}=5$ using $\displaystyle f(x)=\frac{1}{x-1}$, I'm still looking for a way to find the absolute form of the limit, $\displaystyle\frac{1+2a+ab}{b-a}$.


Linker error on forward declaring template function

I am trying to forward declare a bunch of template functions, which are present in the header file SelectionSort.h trying to learn about the working of function pointers. I tried reading this  still not sure how it fits my problem Here are the files - SelectionSort.h #ifndef SELECTIONSORT_H #define SELECTIONSORT_H  template<typename T, size_t N> void selection_sort(T (&arr)[N], bool (*comparer_func)(T, T));  template<typename T> bool ascending_comparer(T, T);  template<typename T> bool descending_comparer(T, T);  template<typename T, size_t N> void print_array(const T (&arr)[N]); #endif  SelectionSort.cpp #include <algorithm> #include <iostream> #include "SelectionSort.h"  template<typename T> bool ascending_comparer(T x, T y) {     return x > y; }  template<typename T> bool descending_comparer(T x, T y) {     return x < y; }  template<typename T, size_t N> void selection_sort(T (&arr)[N], bool (*comparer_func)(T, T)) {     for (size_t i = 0; i < N - 1; i++)     {         size_t smallest = i;         for (size_t j = i + 1; j < N; j++)         {             if (comparer_func(arr[smallest], arr[j]))             {                 smallest = j;             }         }          if (smallest != i)         {             std::swap<T>(arr[i], arr[smallest]);         }     } }  template<typename T, size_t N> void print_array(const T (&arr)[N]) {     for (const auto& item : arr)     {         std::cout << item << " ";     }     std::cout << std::endl; }  main.cpp #include <iostream> #include <iterator> #include "SelectionSort.h"  int main(int argc, char** argv) {     int arr[] = { 5, 4, 3, 2, 1, 0, -1 };     constexpr size_t len = std::size(arr);      selection_sort<int, len>(arr, ascending_comparer);     print_array<int, len>(arr);      return 0; }  So I am getting the linker error LNK2019 only when I try to forward reference them via a header file but it compiles successfully without any error too, not sure what is wrong here - 1>FunctionPointers.obj : error LNK2019: unresolved external symbol "void __cdecl selection_sort<int,7>(int (&)[7],bool (__cdecl*)(int,int))" (??$selection_sort@H$06@@YAXAAY06HP6A_NHH@Z@Z) referenced in function _main 1>FunctionPointers.obj : error LNK2019: unresolved external symbol "bool __cdecl ascending_comparer<int>(int,int)" (??$ascending_comparer@H@@YA_NHH@Z) referenced in function _main 1>FunctionPointers.obj : error LNK2019: unresolved external symbol "void __cdecl print_array<int,7>(int const (&)[7])" (??$print_array@H$06@@YAXAAY06$$CBH@Z) referenced in function _main  The above solution works if I straightaway copy the contents of SelectionSort.cpp into main.cpp. Any ideas for obvious mistakes I am making?


"Recheck Cond:" line in query plans with a bitmap index scan

This is a spin-off from comments to the previous question:      Using PostgreSQL 9.4, there always seems to be a Recheck Cond: line after bitmap index scans in query plans output by EXPLAIN.  Like in the EXPLAIN output of the referenced question:   ->  Bitmap Heap Scan on table_three  (cost=2446.92..19686.74 rows=8159 width=7)       Recheck Cond: (("timestamp" > (now() - '30 days'::interval)) AND (client_id > 0))       ->  BitmapAnd  (cost=2446.92..2446.92 rows=8159 width=0)             ->  Bitmap Index Scan on table_one_timestamp_idx  (cost=0.00..1040.00 rows=79941 width=0)                   Index Cond: ("timestamp" > (now() - '30 days'::interval))             ->  Bitmap Index Scan on fki_table_three_client_id  (cost=0.00..1406.05 rows=107978 width=0)                   Index Cond: (client_id > 0)    Or in the output of EXPLAIN ANALYZE for a simple, huge table (with very little work_mem):  EXPLAIN ANALYZE SELECT * FROM aa WHERE a BETWEEN 100000 AND 200000;    Bitmap Heap Scan on aa  (cost=107.68..4818.05 rows=5000 width=4) (actual time=27.629..213.606 rows=100001 loops=1)   Recheck Cond: ((a >= 100000) AND (a <= 200000))   Rows Removed by Index Recheck: 758222   Heap Blocks: exact=693 lossy=3732   ->  Bitmap Index Scan on aai  (cost=0.00..106.43 rows=5000 width=0) (actual time=27.265..27.265 rows=100001 loops=1)         Index Cond: ((a >= 100000) AND (a <= 200000))    Does that mean index conditions have to be checked a second time after a bitmap index scan? What else can we learn from the EXPLAIN output?


How to call inherited method of superclass from the overridden subclass method?

I have a class shape that has a toString() method. I have another class circle that extends shape. This circle class overrides the inherited toString() method. What I want to do is call the superclass - shape's toString() method from inside the circle's toString() method. The following is what I have done as of now. I thought calling toString() in the toString() of the circle might invoke the inherited toString() but that just goes into an infinite loop.    Shape class:  class shape{ String color; boolean filled; shape() {     color = "green";     filled = true; } shape(String color, boolean fill) {     this.color = color;     this.filled = fill; } public String toString() {     String str = "A Shape with color = " + color + " and filled = " + filled + " .";     return str; } }   Circle class:   class circle extends shape { double radius; circle() {     this.radius = 1.0; } public String toString() {     String str = "A circle with radius " + radius + " and which is a subclass of " + toString();     return str; }   Please Help!


If $x+y+z=\pi$ how to prove that $\sin x+\sin y+\sin z=4\cos\frac{x}{2}\cos\frac{y}{2}\cos\frac{z}{2}$?  I got that $\sin x+\sin y+\sin z=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}+\sin x\cos y+\sin y\cos x$ and I don't know what to do next.   Can somebody help me, please?


I have a black and white image which serves as a template for my game. Non selected country borders are white, and selected country borders should be outlined by solid black lines.  Each country border is represented by a mesh which I position over a country.  Meshes are created in Blender using BezierCurves and convert to mesh option.  Is it possible to create a material in a simple manner, which would make my 2d mesh render as solid black lines, to achieve select/deselect effect?  I'm quite new at Blender and didn't manage to achieve it via FreeStyle component for mesh outlining.  QUESTION UPDATE  Managed to render solid lines in Blender render view.    When you export your mesh from Blender, is your material exported also?  Because when I imported the mesh into Unity, the mesh was not rendered.  Meshes without faces aren't visible in Unity, so I expected my material to make the mesh visible.  Every advice will be appreciated :)  CONCLUSION  The outline effect can be achieved in Blender relatively easily, but you cannot export it in my case.  The mesh must be shaded with a Unity compatible shader and materials used must be built  inside Unity in most cases.  Sadly, free version of Unity doesn't allow writing shaders in OpenGL, Unity shader syntax must be used.  Thx, everyone!


I am working on a diplomatic edition of a 15th century book and it numbers its folios using the standard roman numerals of the time.  I've been using the following to get the page/folio in my header:  \newcommand{\rectoverso}[1]{\ifthenelse{\isodd{#1}}{r}{v}} \newcommand{\folio}[1]{\the\numexpr (#1+1)/2\relax} \uppercase\expandafter{\romannumeral \value{\folio{\thepage}}}\rectoverso{\thepage}   This works great, but the problem is that the roman numeral sequence is off of what I need.  Instead of I, II, III, IIII, V, VI, VII, VIII, IX, X, I get the subtractive IV (somewhat understandably, given it's the far more common one in modern usage).  My source text only (and always) uses the additive 4 in the one's position: 24 is XXIIII, 34 is XXXIIII but 44 is XLIIII.  9 is universally rendered subtractively as IX or XC.  Is there a package that allows for some control over which numbers are done additively and which are subtractively, or would my best option be to write my own custom definition to account for the specific style used in my book?


I am confused by this question for a long time. Let's say the initial states are R=1,S=0,Q=1,Q'=0, and both NOR gates are ideal (no propagation delay). Then both gates should change their states simultaneously, and we get R=1,S=0,Q=0,Q'=0.    But as the figure below shows, it contains two steps change, firstly R=1,Q'=0 and we get Q=0. Then S=0,Q=0 and we get Q'=1. This is the result in all contexts. I don't understand why it is two steps change.    Thanks


How to remove old device from Safari iCloud Tabs?

I returned a MacBook to Apple Store, however apparently I forgot to sign out of iCloud and the latest tabs I was browsing still appear in Safari iCloud Tabs of my new MacBook and existing iPad.  I removed the device from icloud.com -> Find My iPhone but it didn't work. Tabs list from my old computer is still there and I am trying to remove it from my devices list. I appreciate any ideas.


How to decide if Central Limit Theorem is applicable on a sum of Poisson variables?

I'm confused about the behaviour to expect from a large sum of independent and identically distributed Poisson variables.   We know that a sum of $n$ Poisson variables of identical mean $\lambda$ is a Poisson variable of mean $n\lambda$. We also know from the Central Limit Theorem that if $n$ is large, this sum should be approximately normal of mean $n\lambda$ and variance $n\lambda$ as well.   Now, what if we set $n\lambda = 1$ for instance?  Does it mean that the $\lambda$ mean parameter cannot anymore be considered as finite when $n$ is large, so we cannot apply the CLT anymore? Because obviously, a $\mathcal{P}oisson(1)$ is different from a $\mathcal{N}(1,1)$...    Context: the concrete situation is from a model of evolution of DNA sequences:  we take a sequence of $n$ sites, and at each site, the number of mutations in a given time follows a Poisson distribution, but we know that over the whole sequence (e.g 200-1000 sites), the mean will be like 5 mutations in 1 million years. I feel like I can't apply the CLT, although in , the normality assumption is used to deduce confidence intervals.


How to find WPS Spreadsheet exe, located in wine (lubuntu 16.04)?

I have installed wine-staging from  in my lubuntu 16.04 box , and also installed WPS 2016 (setup.exe) in wine.  So after installing WPS successfully ,i am trying to run WPS spreadsheet from wine using command line but i am not able to find its executable file i,e .exe for spreadsheet.  For example i have also install MS office 2007 in wine & executable for MS office(2007) Excel file is located at   /home/wineuser/.wineprefix/drive_c/Program Files/Microsoft Office/Office12/EXCEL.EXE   And it can run using below command from terminal :  WINEPREFIX=~/.testadmin WINE=/opt/wine-staging/bin/wine /opt/wine-staging/bin/wine ~/.testadmin/drive_c/Program\ Files/Microsoft\ Office/Office12/EXCEL.EXE   So my question is how can i run WPS spreadsheet under wine in lubuntu box 16.04 , where its executable actually located ?


I don't understand what is the verb "do" doing in this sentence

"Only in Queensland do people brag about the weather as if they built it themselves."     Wouldn't it sound better or make more sense by simply omitting it?     "Only in Queensland people brag about the weather as if they built it themselves."   Or is it doing something like:     "Only in Queensland is where people brag about the weather as if they built it themselves."   Can someone, please, explain? Is it adding some sort of different emphasis?


str_replace characters with 2 other characters

I am trying to replace , with . and ' with `  I can do it like this  $bodyweight = str_replace("'", "`", $form->data['bodyweight']); $bodyweight = str_replace(',', '.', $bodyweight);   Is the a way to do it in one str_replace?


For changing the view's background color, I've used the following code:  self.view.layer?.backgroundColor = NSColor.mainColor().cgColor   But I would also love to change the color's of the application bar, which I suppose is the bar right above the window which has the three buttons (red, orange and green).


XTerm only display part of some unicodes and Urxvt displays nothing

In my case, (U)XTerm does display some unicodes, but only partially. For exmaple: for letters are: 𝒫φϕ𝒟. Here is a screenshot of UXTerm and Urxvt respectively   It seems that the problem is related to the letter space or letter length. By the way, everything is fine with gnome-terminal.  My current .Xresources file is: Xft.dpi:       120 Xft.antialias: true Xft.hinting:   true Xft.rgba:      rgb Xft.autohint:  false Xft.hintstyle: hintslight Xft.lcdfilter: lcddefault  XTerm*faceName:          Fixed XTerm*faceSize:          14 XTerm*reverseVideo:      false XTerm*selectToClipboard: true  UXTerm.vt100*faceName:          Fixed UXTerm.vt100*faceSize:          14 UXTerm.vt100*reverseVideo:      false UXTerm*selectToClipboard: true  URxvt.font:            xft:Fixed:pixelsize=18  URxvt.depth:                      32 URxvt.background:                 #222D31 URxvt*scrollBar:                  false URxvt*mouseWheelScrollPage:       false URxvt*cursorBlink:                true URxvt*background:                 black URxvt*foreground:                 grey URxvt*saveLines:                  5000  How to make XTerm and Urxvt to display those characters correctly? Is it possible?


I have heard much about the numerous appearances of the ratio found in nature: 1.6180339887.  Are there any actual mathematical uses that have been found of this number? What are its advantages? Just curiosity, really.


How does one get a smoked flavor in their beer?

For those who have tried it, Im thinking like the smokey flavor in Stone's 'Matts Burning Rosids'.


How does a moving charge produce a magnetic field? In AC, charges are accelerating but they are possessing magnetic field also

I am unable to understand that how the moving charge produces magnetic field around itself. Some one has answered that any moving charge is without acceleration due to which it produce electric and magnetic field. I am confused that electric field is possessed by charge when it is in rest as well. Why does it  not posses magnetic field?


How do I make Firefox start always maximized?

I am setting up Ubuntu with gnome for my grandma. How can I make firefox start ALWAYS maximized.


Prove or disprove: If $\sum{a_n}$ with $a_n>0$ is convergent then $\sum{a_n^2}$ is always convergent.

So that's the question. But I am unable to find a counter example if it's false. Or how should I proceed to prove if it is true? I am confused please help. Many thanks.


Looking for a hint on the class of a particular equation

I've to solve the following nonlinear matrix equation, and I was wondering if there is any bigger class where to fit such an equation so that I can either:   Obtain a closed-form solution (ideal) Use appropriate algorithms to solve it numerically.   Assume that $V\in\mathbb{R}^{1\times k}$, $B_i\in\mathbb{R}^{k\times 1}$, $T_i\in\mathbb{R}^{k \times k}$ with $i=1,\dots,k$, and finally $L\in\mathbb{R}^{1\times k}$. The equation reads:  $$V - \sum_{i=1}^{k} VB_iVT_i = L$$  And it has to be solved for $V$ (all the other matrices are assumed to be known). Any help or suggestion will be extremely appreciated! Thanks!!!


Line between points in projective space?

I am trying to find the line through the points $(0 : 1 : 0)$ and $(1 : 1 : 1)$ in $\mathbb P^2$ and $(0 :1 : 0: 1)$ and $(1: 1: 1: 0)$ in $\mathbb P^3.$  Would the first line be the set of points $\{(b, a+b, b)\}$ for all $a,b \in \mathbb P^1$  and the second, $\{(d, c+d, d,c)\}$ for all $c, d \in \mathbb P^1$?  Thanks


What happens when you conquer a city where a spaceship is under construction? Can the conquered civilization continue construction in its new capital? Does the conquered civilization retain its already-constructed modules? Do you get to capture the already-constructed modules as your own?    Note : I am talking about modules that have already been added to the spaceship, not ones who are still walking around as units.


Why did this file not convert to UTF-8 when using iconv?

Versions: Linux 2.6; Bash 4.1.2; iconv 2.12  The ISO conversion returned no errors, yet the converted file still shows as US-ASCII.  Question How can I transcode foobar.txt to UTF-8?  $> file -bi foobar.txt    text/plain; charset=us-ascii  $> iconv -f US-ASCII -t UTF-8 foobar.txt >  foobar_utf8.txt iconv: illegal input sequence at position 573167  $>iconv -f ISO-8859-1 -t UTF-8 foobar.txt >  foobar_utf8.txt $> $> file foobar_utf8.txt    foobar_utf8.txt: ASCII text


What are the rules for taking electronics and other expensive gifts from the USA to the EU?

I am an American with residence in Belgium.  I came here to the USA for the holidays and brought my old, iPhone, iPad and my MacBook. Now, here, I want to buy a new iPad and also a surface pad, among some other stuff.   Assuming I leave the boxes at home, and boot these devices up, maybe downloading some stuff on them, before leaving to the airport, will it be safe to bring them without risk of paying tax?  I can't find any info on the limit of goods I can bring over. I suppose if they are not in their boxes, it's clear that I am not selling them (in fact they are Xmas gifts).  Is there some regulation about this?


All sites except Meta.SE have wrong icons in inbox, achievements, and site switcher

This happened within the last hour or so on Mi Yodeya:      The achievements drop-down is similarly affected.  This happens on every site I've tried (responsive or old design, with or without an account) except for Meta.SE, which has the correct icons.  I see that some (but not all) HNQ icons in the right column are also affected, but haven't looked for a pattern there.  I know that "meta is different", but this isn't the kind of "different" we usually see.


How can I get the equivalent of C++'s "const" in C#?

In C++, if I want an object to be initialized at compile time and never change thereafter, I simply add the prefix const.   In C#, I write       // file extensions of interest     private const List<string> _ExtensionsOfInterest = new List<string>()     {         ".doc", ".docx", ".pdf", ".png", ".jpg"     };   and get the error     A const field of a reference type other than string can only be   initialized with null   Then I research the error on Stack Overflow and the proposed "solution" is to use ReadOnlyCollection<T>.   But that doesn't really give me the behavior I want, because       // file extensions of interest     private static ReadOnlyCollection<string> _ExtensionsOfInterest = new ReadOnlyCollection<string>()     {         ".doc", ".docx", ".pdf", ".png", ".jpg"     };   can still be reassigned.  So how do I do what I'm trying to do?   (It's amazing how C# has every language feature imgaginable, except the ones I want)


$A_n$ is the only subgroup of $S_n$ of index $2$.

How to prove that the only subgroup of the symmetric group $S_n$ of order $n!/2$ is $A_n$?  Why isn't there other possibility?  Thanks :)


How to call a space in which every G$_\kappa$-set is open

Recall that in a topological space $X$, we say that a subset $A\subset X$ is a G$_\delta$-set if $A$ is the intersection of countably many open sets of $X$. Also, we say that $X$ is a  if G$_\delta$-sets are open.  Now, call as G$_\kappa$-set the intersection of $\kappa$ many open sets, where $\kappa\geq\aleph_0$ is a cardinal. I would like to know if there is some standard name for those spaces in which G$_\kappa$-sets are open, for a fixed cardinal $\kappa\geq \aleph_0.$  Motivation: this kind of space arose in my PhD thesis, but I do not know any references in which they appear. I'm temporary calling them as $P_\kappa$-spaces.


I want to plot a function x^3/(x^2-1) but it doesn't work.  \documentclass{article}     \usepackage{tikz}  \begin{document}    \begin{tikzpicture}[domain=-5:5,smooth]     \draw[->] (-5,0) -- (5,0) node[right] {$x$};      \draw[->] (0,-5) -- (0,5) node[above] {$y$};     \draw [color=blue, thick] plot ({\x},{pow(\x,3)/(pow(\x,2)-1)});   \end{tikzpicture}  \end{document}   It does something like this. It should be non-continuous function, not this.    How to fix it? Thanks.


There is a system B with the following open servers: I have a web server listening on port 80 and a ssh server listening on 22. However, only port 22 is publicly available. Now, I would like to create some kind of tunnel, so that I can access B:80 from A. However, my client computer A that would like to connect to the system B is not publicly open, either.  So, all I have is a client computer A from where I would like to access the server B and, there, an open port 22. On A, no port is open or can be opened.  What (I think) I would need is to open locally (on A) some port that connects in some way through port 22 of B to port 80 on B.  Is this possibly without using any man-in-the-middle open servers with multiple ports?


Ubuntu 14.04 installation on Lenovo Ideapad 100-15IBD

I'm trying to install ubuntu version 14.04 on my Lenovo ideapad 100-15IBD but every time it gets unsuccessful. I need to install ubuntu alongside windows 8.1 pro via USB. I'm using YUMI multiboot USB creator. After choosing option "Install ubuntu", the screen gets blackened. Help me with this problem.


Saying for using an overly powerful tool to fix a minor problem

I found "A sledgehammer to crack a nut" as one example. What are some others?


Matcap materials as a material for render?

Is it possible to use Matcap materials as an actual material for a model so that I can render with it? There are certain parts that I want to apply specific Matcaps textures to but I want to actually use them to render and not just for sculpting purposes.  Is this at all do-able?


Is $\log (1 + {x^2})$ uniformly continuous on $[0,\infty)$?

Is  $\log (1 + {x^2})$ uniformly continuous?  Here is my attempt: Let $\forall\left| {x - y} \right| < \delta$:  $\left| {\log (1 + {x^2}) - \log (1 + {y^2})} \right| = \left| {\log (\frac{{1 + {x^2}}}{{1 + {y^2}}})} \right| < \varepsilon $  because $\log (1) = 0$ it's sufficent to prove:    $\left| {\frac{{1 + {x^2}}}{{1 + {y^2}}} - 1} \right| < \varepsilon $  This is where I got stuck. What do you suggest?   EDIT: I'd like to prove it without involving derivative. Namely, by the definition of uniform continuity.


I have an arduino, beaglebone black, and an arndale octa board and they all work 5V DC (albeit different amp rates).  Most of my electrical sensors seem to operate around the 5V range.  Why is this the case?  How is it I can power a linux computer with 10 watts yet my light bulbs need 60?


Why says readlink that there is no such file or directory

I am creating a bash function that should return true/false if a specified symlink refers to specified target. I based myself on   However, I am having trouble getting readlink to work as I want:  is_symlink_to () { # $1 = symlink / $2 = symlink target     echo "arg1: $1 and arg2: $2"     echo readlink arg 1 is: $(readlink -v $1 )   # -v for troubleshooting     if  [ "$(readlink -- $1)" = $2 ]; then         echo "$1 is a symlink to $2"         return 0;     else         return 1;    fi }  ...  if is_symlink_to "~/$file" "$dir/$file" ; then     echo "is already symlinked" else    ... fi   Question: Why does readlink -v return No such file or directory?  arg1: ~/.bash_profile and arg2: /home/me/dotfiles/.bash_profile readlink: '~/.bash_profile': No such file or directory readlink arg 1 is:   If I run readlink from a bash shell, it works fine:  me@mango:~/dotfiles$ readlink -v ~/.bash_profile /home/me/dotfiles/.bash_profile


I've got a Postfix mail server setup for hosting multiple virtual domains (say xxx.com and yyy.com).  Users configure their outgoing mail server as mail.xxx.com and mail.yyy.com. All mail servers refer to the same physical Postfix server (same IP, single instance of Postfix running on this Linux server).  Which SSL certificate do I need for Postfix smtpd_tls_cert_file configuration option?  Or do I have to use a single certificate for mail.xxx.com and tell users of yyy.com to use mail.xxx.com as their outgoing server? This would break the illusion of separate virtual servers.  [Note: the domains are completely separate. These are not multiple subdomains sharing a common root].


Copy every nth line from one sheet to another

I have an Excel spreadsheet with 1 column, 700 rows. I care about every seventh line. I don't want to have to go in and delete the 6 rows between each row I care about. So my solution was to create another sheet and specify a reference to each cell I want.  =sheet1!a1 =sheet1!a8 =sheet1!a15   But I don't want to type in each of these formulas ... `100 times.I thought if I selected the three and dragged the box around, it would understand what I was trying to do, but no luck.  Any ideas on how to do this elegantly/efficiently?


How to retrieve Custom Profiles' objectpermissions using SFDX or MDAPI

Problem  The <objectPermissions> tags are missing from my custom profiles when I pull from a scratch-org using SFDX or MDAPI.   Steps to reproduce   Create a new Scrach-org. Create a custom profile, say "Support".  Add some Standard Object Permissions to the profiles. Looks like this:       Use SFDX pull or MDAPI Retrieve.   The Support.profile-meta.xml contains all the settings I added to the profile, except for <objectPermissions>. The missing tag should look like this:       <objectPermissions>         <allowCreate>true</allowCreate>         <allowDelete>true</allowDelete>         <allowEdit>true</allowEdit>         <allowRead>true</allowRead>         <modifyAllRecords>true</modifyAllRecords>         <object>Account</object>         <viewAllRecords>true</viewAllRecords>     </objectPermissions>   If I now push the profile to a new scratch org, then the profile will be missing some permissions such as View All and Modify All since the tags are missing. Looking like this:     Questions  How can I use SFDX or MDAPI to retrieve the missing tags? Or, do some workaround exist?


I know that this question may be a bit trivial but just curious about it. I know that according to grammar, “six-week course” is the right form. But when I replace “six” with the number 6, I read that both “6 week course” and “6-week course” are pretty common, so a bit confused about which is grammarly correct and which may be better. Thanks!


How do I fix a syntax error in .bash_profile

I was installing ruby on rails along with homebrew the other day and was following a step by step list of what to do. I now have this bash syntax error every time I enter the terminal:  -bash: /Users/briggsmcknight/.bash_profile: line 6: syntax error near unexpected token `source' -bash: /Users/briggsmcknight/.bash_profile: line 6: `if which rbenv > /dev/null; then eval "$(rbenv init -)"; fi source /Users/briggsmcknight/.bash_profile'   Could I get a small step by step breakdown of what I should do to fix this? I believe the syntax error is by "fi" or "source", but do I just retype it again or what?


How I update the Managed Metadata Field in Document Library for only .Zip Files using PowerShell

<Code For Termset> [System.Reflection.Assembly]::LoadWithPartialName("Microsoft.SharePoint.Taxonomy") $site = Get-SPSite http://invi28apps9c $session = New-Object Microsoft.SharePoint.Taxonomy.TaxonomySession($site) $termStore = $session.TermStores["Managed Metadata Service"] $group = $termStore.Groups["KB"] $termSet = $group.TermSets["IPS Document type"]      $terms = $termSet.GetTerms(100) $term = $terms | ?{$_.Name -eq "Docset"}     $web = Get-SPWeb http://invi28apps9c/DemoTeamSite $list = $web.Lists["KBDocument"]  $query = New-Object Microsoft.SharePoint.SPQuery  $query.ViewAttributes = "Scope='Recursive'"; $query.RowLimit = 2000  $caml = "<Where>    <Eq>      <FieldRef Name='DocIcon'/>      <Value Type='Computed'>.zip</Value>    </Eq>     </Where>"  $query.Query = $caml     do     { $listItems = $list.GetItems($query) $spQuery.ListItemCollectionPosition = $listItems.ListItemCollectionPosition  foreach($item in $listItems) {      $spItem = [Microsoft.SharePoint.SPListItem]$item;       $taxField =     [Microsoft.SharePoint.Taxonomy.TaxonomyField]$spItem.Fields["Document Type"]      $taxField.SetFieldValue($spItem,$term)     $spItem.Update() }    }   while ($spQuery.ListItemCollectionPosition -ne $null)   This code override the all old value with new value i need a code to append the new value with oldone.


One systemctl command to both start and enable

Using one command to both start and enable systemctl managed software would be useful to spare a few lines in a few scripts, making them a bit more aesthetic (not really a problem but a nice thing to have).  Is there one systemctl command to both start and enable a program controlled by systemctl?


The power delivered by a force is given by the relation $$P=\frac{\alpha}{\beta}e^{-\beta t},$$ where $t$ is time. Find the dimensional formula for $\alpha$.   So, $-\beta t$ doesn't make sense for the dimensional formula of $P$. But then we have two unknowns and one equation since we do not know if $\beta$'s dimensions. But then if I put $\beta t$ as dimensionless, it fits just right with the answer $([ML^2 T^{-4}])$ . But does this happen exactly. Why is  $\beta t$ dimensionless, because we are just using it's numerical value. Please help. I don't understand it.


If $ab=ba$, Prove $a^2$ commutes with $b^2$

From Dr. Pinter's "A Book of Abstract Algebra":     Given $a$ and $b$ are in $G$ and $ab=ba$, we say that $a$ and $b$ commute.         Prove $a^2$ commutes with $b^2$      I tried:  $$ ab=ba $$ $$ a^{2}b^{2}=b^{2}a^{2} \text{ // to prove that $a^2$ commutes with $b^2$} $$ $$ aabb=bbaa $$  Then, knowing that $$a=b^{-1}ab,$$ I substituted that '$a$' into '$aabb=bbaa$'.  But that simplified to '$aabb=bbaa$', i.e. I got nowhere with it.  How can I prove that $$aabb=bbaa$$ per this problem?


Sugar daddy wants money returned to bitcoin for his son

I have been talking to a gentleman who says he’s a sugar daddy and would love to spoil me for a personal online connection because he is lonely. He has my banking information and is sending me a check for 10K and told me to keep 1K to myself and send the rest to his “son” through bitcoin because his son wants to invest in that. I asked him why I had to be the one to send the money to his son when his “account officer” is sending me the money. Am I being scammed? If I don’t return the money to him, will he be able to do me harm? I also should put it out there that the only reason I met him was because he messaged me on Pornhub. I just need some help.


Suppose that $\underset{x\rightarrow0}{\lim}\frac{f\left(x\right)}{\left|x\right|}=1$ , may $f$ be differentiable at $0$?

Prove or disprove: Let $f$ be a function that is defined on a neighbourhood of $0$. Suppose that $\underset{x\rightarrow0}{\lim}\frac{f\left(x\right)}{\left|x\right|}=1$ , then $f$ is not differentiable at $0$ I somehow think its false but couldn't find a counter example. So I tried proving it and this is my prove of it being true: let us assume by contradiction, that $f$ is differentiable at $0$. thus: $\underset{x\rightarrow0}{\lim}\frac{f\left(x\right)-f\left(0\right)}{x}=f'\left(0\right)$ Which implies: $f'\left(0\right)=\underset{x\rightarrow0^+}{\lim}\frac{f\left(x\right)-f\left(0\right)}{x}=\underset{x\rightarrow0^+}{\lim}\underbrace{\left[\frac{f\left(x\right)}{\left|x\right|}-\frac{f\left(0\right)}{\left|x\right|}\right]}$ and: $f'\left(0\right)=\underset{x\rightarrow0^-}{\lim}\frac{f\left(x\right)-f\left(0\right)}{x}=\underset{x\rightarrow0^-}{\lim}{\left[\frac{f\left(x\right)}{-\left|x\right|}-\frac{f\left(0\right)}{-\left|x\right|}\right]}=\underset{x\rightarrow0^-}{\lim}-\left[\frac{f\left(x\right)}{\left|x\right|}-\frac{f\left(0\right)}{\left|x\right|}\right]=\underbrace{-\underset{x\rightarrow0^+}{\lim}{\left[\frac{f\left(x\right)}{\left|x\right|}-\frac{f\left(0\right)}{\left|x\right|}\right]}}$ They must be equal, thus: $\underset{x\rightarrow0}{\lim}{\left[\frac{f\left(x\right)}{\left|x\right|}-\frac{f\left(0\right)}{\left|x\right|}\right]}=0$ As we know $\underset{x\rightarrow0}{\lim}\frac{f\left(x\right)}{\left|x\right|}=1$, then: $\underset{x\rightarrow0}{\lim}\frac{f\left(0\right)}{\left|x\right|}=1$ which cant be, because if $f(0)=0$, then the limit is $0$, and if $f(0)\ne0$, the the lim is $\pm\infty$ Which in both cases, doesn't equal $1$, Contradiction. . . Was there a problem separating to $0\pm$ and change $x$ to $|x|$ without modifying $f(x)$? Or was there any other problem ? First post, be gentle. Thank you!


How can I create a bootable USB disk from a CD image?

I have a bootable CD image that I would like to transfer to a USB stick, so that I can boot from it. The Startup-Disk creator doesn't support it. How can I make a bootable USB disk from it? The ISO is quite old so that might be a problem.


Only hot questions in feed from sites I have an account for

In the android app, it would be great if you could choose if you wanted to see only hot questions from the sites you are registered on in your Feed, or (as it is the case now) to see all hot questions from all networks. I'm mainly active on StackOverflow and honestly I don't currently care that much about for example The Great Outdoors or Academia, so I think this feature would be quite welcome.


How I can allow two html tags <sup> and <sub> in node title of all content types.  Or may be is there some module for BB tags which allow using BB-codes in title?  Or my ba is there some hook for preprocess all titles?


If you can't see it coming, how do you get a dex save?

So, I was thinking simply fog cloud.. to obscure vision then fireball.  Input?


Is there a way to format a diff patch block?

I'm trying to inline a few snippets of diff patches, and manually formatting them is a droll - is there a way to do it automatically?  In general I want it to look like the following example, but obviously the finer details of font and colour are less important (as long as they're internally consistent)


Has anyone done any research about the upwind vehicle ?  I think it is impossible but get a surprising number of disputes from some pretty educated people. It seems to me that if it were possible for a wind powered vehicle to go into the wind at greater than the speed of the wind X, then it would follow that on a windless day, a Ford F-150 towing the same vehicle at speed X (equaling the relative wind), would allow the vehicle to accelerate and pass the Ford, which is absurd, especially considering that the towed vehicle only needs to overcome the rolling coefficient of friction while the self starting vehicle must overcome the static coefficient of friction.    Am I overlooking something?


I am measuring the tcp and udp throughput by iperf3. I run iperf3 in virtual machines, one as server and the other as client. The VMs are connecting via 10 Gbps link. The results show that tcp get much higher throughput than udp. However, as we know TCP runs more algorithms and computation and it has three-way handshaking also, so why udp throughtput is less that tcp?is it something related to the buffer size of tcp and udp?  below are result of tcp and udp measurements. It is apparent that iperf sends more data for tcp rather than udp in a specific time, but why?  TCP: 8.88 Gbps  [ ID] Interval           Transfer     Bandwidth       Retr  Cwnd [  4]   0.00-1.00   sec   922 MBytes  7.73 Gbits/sec    1   3.04 MBytes        [  4]   1.00-2.00   sec  1.04 GBytes  8.92 Gbits/sec    0   3.04 MBytes        [  4]   2.00-3.00   sec  1.07 GBytes  9.15 Gbits/sec    0   3.04 MBytes        [  4]   3.00-4.00   sec  1.05 GBytes  8.99 Gbits/sec    0   3.04 MBytes        [  4]   4.00-5.00   sec  1.04 GBytes  8.91 Gbits/sec   80   2.17 MBytes        [  4]   5.00-6.00   sec  1.04 GBytes  8.91 Gbits/sec    0   2.35 MBytes        [  4]   6.00-7.00   sec  1.04 GBytes  8.98 Gbits/sec    0   2.54 MBytes        [  4]   7.00-8.00   sec  1.01 GBytes  8.69 Gbits/sec  176   1.88 MBytes        [  4]   8.00-9.00   sec  1.04 GBytes  8.97 Gbits/sec  208   1.42 MBytes        [  4]   9.00-10.00  sec  1.02 GBytes  8.80 Gbits/sec    0   1.48 MBytes        - - - - - - - - - - - - - - - - - - - - - - - - - [ ID] Interval           Transfer     Bandwidth       Retr [  4]   0.00-10.00  sec  10.3 GBytes  8.80 Gbits/sec  465             sender [  4]   UDP: 3.26 Gbps, packet length is default 8Kbytes  iperf3 -c "server address" -u -b 0   [  4] local 145.100.132.197 port 58375 connected to 145.100.132.34 port 5201 [ ID] Interval           Transfer     Bandwidth       Total Datagrams [  4]   0.00-1.00   sec   375 MBytes  3.15 Gbits/sec  48035   [  4]   1.00-2.00   sec   394 MBytes  3.31 Gbits/sec  50457   [  4]   2.00-3.00   sec   352 MBytes  2.94 Gbits/sec  45114   [  4]   3.00-4.00   sec   391 MBytes  3.30 Gbits/sec  50092   [  4]   4.00-5.00   sec   403 MBytes  3.38 Gbits/sec  51566   [  4]   5.00-6.00   sec   403 MBytes  3.38 Gbits/sec  51599   [  4]   6.00-7.00   sec   418 MBytes  3.51 Gbits/sec  53493   [  4]   7.00-8.00   sec   372 MBytes  3.12 Gbits/sec  47651   [  4]   8.00-9.00   sec   444 MBytes  3.73 Gbits/sec  56892   [  4]   9.00-10.00  sec   399 MBytes  3.34 Gbits/sec  51033   - - - - - - - - - - - - - - - - - - - - - - - - - [ ID] Interval           Transfer     Bandwidth       Jitter    Lost/Total Datagrams [  4]   0.00-10.00  sec  3.86 GBytes  3.32 Gbits/sec  0.020 ms  354384/505931 (70%)    according to the packet length the throughput in udp is calculated based on the packets which are sent, regardless of the recieved ones!


How to keep an application on top of all others on windows xp?

Is there a way to put any application I want on top of all others? I'm on a windows XP machine.


I have HP-2000-Notebook Pavilion series with windows on it. More my notebook doesn't support visualization technology.   I want to develop and iOS app in objective c. Is there any alternative that work for me? rather than buying apple notebook.


Is it okay to cross-post my own posts on multiple separate WordPress.org sites? Is it good or bad for SEO?

I write blog posts for multiple WordPress.org blogs and where content overlaps, I wonder if I should post it separately on multiple blogs or not. Often this happens with posts I write to my personal blog which are pertinent for groups I volunteer for who share my interests. Will this kind of cross-posting hurt or help search engine optimization for the sites, and is there anything other than SEO to consider related to this? If anything, I imagine linking a post between multiple websites improves SEO for either/both since both become linked to by at least one additional node of the internet.  If it is OK to cross-post to different, separately hosted Wordpress.org blogs on independent URLs, are there better and worse ways to do it? Is copy and pasting the content between sites any better or worse than using a plugin to do it aside from work involved either way?


Is there any way to generate perpendicular faces while deforming geometry?

Weird question probably, but this is the part where I elaborate!  Lets say I have a plane and subdivide it with 4 so that the plane is now a grid of 5x5 faces.  Is there some magical script or perhaps built-in way to have it so that when I move the central face, perpendicular faces are generated to prevent surrounding faces from deforming? Pic attached. Left portion is normal behavior, right portion is desired behavior. Which would occur regardless of what face is extruded.   So basically when any given face is moved, rather than the adjacent faces being deformed, perpendicular ones are generated.


how are the math node operations in cycles calculated?

How does the math node do calculations with a specific operation:    the usual operations of add,subtract, multiply and divide are quite understandable and are(empirically) very similar to some of the operations in MixRGB node. But, how do the operations such as Sine, Power, Logarithm, Minimum, Maximum, Modulo, Round, etc,.. interpret with the values. How can we visualize this in realtime?


Bibtex and abbrv.bst: List as "A. van Surname", sort under "S" in bibliography?

Using the abbrv.bst, is it possible to get a bibtex entry like  @article{Surname,  author = {Surname, Author van},  title = {Title},      journal = {Journal},  year = {2016}  }   typeset as A. van Surname. Title. Journal. 2016., but sorted under the first letter of the surname, rather than "V" for "van"?


I am running Ubuntu 17.04 on a 2015 Macbook Pro. On the keyboard the Tilde~/Backtick</kbd> key is mapped to<and>`. I have found a few fixes for this, but have found no way to make it permanent.  I have found that the command   echo 0 > sys/module/hid_apple/parameters/iso_layout   corrects the issue, as does  setxkbmap -option apple:badmap   My issue is getting either of these commands to run inside of a script at startup/login so that I am not having to manually run it every time I want it fixed. I have tried using /etc/rc.local but in Ubuntu 17.04 when trying to enable it with systemctl I get no results. I will take anything that will work. Thanks guys!


This is a really simple question, but even after reading about wildcards/regex, I can't seem to grasp entirely what the differences between these commands are:  grep . test.txt   this one will look for lines containing any character in test.txt  grep \. test.txt   this one also apparently does the exact same thing, even though I assumed it shouldn't, since it would be escaped and return only those lines containing an actual '.'  grep ? test.txt   since ? is a special character, I guess it would be interpreted as a wildcard, but since grep doesn't deal with wildcards, it's not going to output anything; however  grep \? test.txt   does find the lines which contain an '?' in them, but also those that contain an '\?' in them. Why is this?


I am migrating to a new reseller hosting plan.  By default, they expect me to create a new cPanel account for every domain I add but this would be hugely inconvenient.  So I setup my addon domains in the following fashion:  /public_html/mydomain1.com/www/ /public_html/mydomain2.com/www/   The problem is, my Default domain in the account points to /public_html/ and cannot be changed by conventional methods.  I created a .htaccess file with the following data:  Rewrite Engine On Rewrite Rule ^$ /mydefaultdomain.com/www/ [R=301,L]   The only problem is that it redirects to:  mydefaultdomain.com/mydefaultdomain.com/www/   How can I force it to use the subfolder but not show it in the finished URL?


How to prove that $\sum\ln(n\sin\frac{1}{n})$ converges rigorously?  The idea is to expand $\sin(t)$ and $\ln(1+t)$. But I'm not sure how to do it rigorously. We have $n\sin(1/n)=n(1/n+O(1/n^3))=1+nO(1/n^3)$ as $n\to \infty$. Then I need to substitute it into $\ln (1+t)=t-t^2/2+O(t^3)$. (Or should I use the little o in one of both cases?) This involves taking powers of $nO(1/n^3)$ (or of the little o) and multiplying it by functions, and I'm not very familiar how the o's behave under such operations (and not aware of any source to find that out). So how to do the prove in a rigorous way?


Deleting two rows that have a same Value in a Parameter - SQL

I have a table that contain similar Values in the Column  "Name" in different  rows, I would like to delete the duplicate ones and keep one, I tried the while loop but it didn't work, any simple methods to do that?


Is it possible that my laptop shut down because my mobile is too close?

If I put my phone on my notebook's left corner, it shuts down. Can anybody give me reliable explanation as to why this is happening??


Sometimes I get upvote surges, and I want to know which website referred to the question page in question.  Could be done by adding a page filter at:  , although I'd rather also have a date filter for referrals.


On my server (Synology DS212) some files and folders have nobody nobody users and groups. What are the characteristics of this user and group? Who can write of read this file?    How can I change it ? For which user and group?


Admiral Gonzeles told his men to search for a gun. A soldier asked if the admiral had any further instructions.  Should the second time admiral is used be capitalized or not?  Thanks  Frank


How to check outstanding fines in the US as a tourist

A year ago I rented a car in Miami, and I might have gone though a red light, in front of a red light camera.  After checking, I saw that the car rental company entered the wrong address of my home country.  In a few months I’m going to NY, and I want to be sure I didn’t get a fine. Is there a way to check if there are any open warrants for non-US residents?   If not, what is likely to happen at the immigrations?


How to compress jpeg images for Google Page Speed Insights?

I hope this question fits here. I would have asked on Stackoverflow, but there is a similar question there that was closed with the suggestion to ask at Server Fault, and Server Fault closed my question with the suggestion to ask here (which is extremly frustrating):    I need to automatically compress images (uploaded by users) so  doesn't complain about the image size anymore. Using the Google Page Speed Mod for Apache/Nginx is not an option.  I looked at the official image compression FAQ here: .  They suggest jpegtran and jpegoptim for jpeg images. I tried both with various different settings, but they didn't compress the images any further, and sometimes the images actually got bigger.  Then I tried Guetzli, a new jpeg encoder from Google itself: .  This did compress the images much better than before, but Page Speed Insights still complains that the images are to big.  So how can I compress (hundreds of) Jpegs automatically (on a linux machine) so Google Page Speed Insights doesn't complain anymore?    Edit: To clarify: Google Insights allows you to download optimized images, and they really are much smaller than anything I am able to produce. How can I compress the images (slight quality loss is okay) so they are as small as the images I can download from Google Insights? Since there are hundreds of images on the site using Google Insight to compress them all isn't really practical.  Are there any command line tools for linux that will compress as well as Google Insight?  (There is a protected question on stackoverflow from 2011 but none of the answers work anymore: )


The following simple claim is used without proof in Proposition 2.9 of Atiyah and MacDonald (p.23). Although I believe I can prove it with a fairly involved argument, the claim is treated by the authors as a triviality so I feel like there should be a simple argument. Is there such an argument?      Let $M, N$ be $A$-modules. Let $v\colon M \to N$ be a homomorphism. Suppose that for all $A$-modules $P$, the dual maps $v^*\colon\operatorname{Hom}(N,P) \to \operatorname{Hom}(M,P)$ are injective. Then $v$ is surjective.   (Note that the claim is trivial for free modules, but I am looking for a general proof).


Question: Let $V$ be an inner product space finitely generated over $\Bbb C$ and let $\alpha$ be an endomorphism of $V$ satisfying $\alpha \alpha^* = \alpha^2$. Show that $\alpha$ is selfadjoint.  **Edited after more thought:  I know that in order to be selfadjoint $\alpha^*=\alpha$. Becuase this inner product space is over $\Bbb C$ does it change the proof?   Or, can I show selfadjoint for $\Bbb R$ and then state the proposition that for an inner product space over $\Bbb C$ and an End$(V)$, If $\langle{\alpha(v), v}\rangle \in \Bbb R$ for all $v \in V$, then $\alpha$ is selfadjoint.


Unresolved getSupportFragmentManager() in fragments

In the navigation drawer Im trying to open a new fragment on pop up menu item click in adapter. But getting the error as: Attempt to invoke virtual method 'androidx.fragment.app.FragmentManager androidx.appcompat.app.AppCompatActivity.getSupportFragmentManager()' on a null object reference. Unable to resolve. Below is the code PopupMenu popup = new PopupMenu(mCtx, holder.buttonViewOption);             //inflating menu from xml resource             popup.inflate(R.menu.options_menu);             //adding click listener             popup.setOnMenuItemClickListener(new PopupMenu.OnMenuItemClickListener() {                 @Override                 public boolean onMenuItemClick(MenuItem item) {                     switch (item.getItemId()) {                         case R.id.menu_map:                             //handle menu1 click                           //  Intent i = new Intent(mCtx, IntroActivity.class);                             //mCtx.startActivity(i);                              Fragment mFragment = null;                             mFragment = new PasswordFragment();                             FragmentManager fragmentManager = ((AppCompatActivity)context).getSupportFragmentManager();                             fragmentManager.beginTransaction()                                     .replace(R.id.container_view1, mFragment).commit();                             break;                         case R.id.menu_document:                             //handle menu2 click                             break;                     }


:Duplicate: How to prove that $\cos (\pi * z) = \prod_{n \in \mathbb{Z}_{\text{odd}}} (1-\frac{2 z}{n})e^{2z/n}$

Duplicate  The question was also answered here:   I found this formula on Wikipedia under ,  $\cos (\pi z) = \underset{n \in \mathbb{Z}_{\text{odd}}}{\prod} (1-\frac{2 z}{n})e^{2z/n}$  However, I am not able to prove it from   $\sin (\pi z) = \pi z \underset{n \neq 0}{\prod} (1-\frac{z}{n})e^{z/n}$  The derivation of $\sin (\pi z)$ on page 175 of "Functions of One Complex Variable I" by Conway may be helpful.  Would someone please help me prove it? Thanks!  Edit: I would like to derive $\cos (\pi z)$ from $\sin (\pi z)$. Sorry for the confusion


Does the Dirac delta function derivative potential have a solution in one dimension?


How to reset Security Token of API Only User?

How to reset Security Token of API Only User ? I created a new user in salesforce exclusively for integration purpose. Got the welcome email,Verified Account and changed password. Prior to this, I created a Profile 'API Only' and assigned this User to the Profile. 'API Only User'  and 'API Enabled' is checked. I need the security token for this user. However when I go to the User record, and Login as this user, under personal settings, I do not see the option to 'Reset Security Token'


Getting an error when trying to use a one line if statement in Unity

I am getting an error when trying to use an one line if statement in Unity. I can't figure out what is wrong with it. Here is the line: MyImage.color == Color.white ? MyImage.color = Color.green : MyImage.color = Color.white;  I have it in the Update function. It's all that is in the update function. It says only assignment, call, increment, decrement, await, and new object expressions can be used as a statement. I am assigning a color to an image so I'm not sure what is wrong. This is unity 2018.3.0f3 if that matters.


How to use "with" construction in javascript?

I have this code:  var home = {} home.table={} home.table.width = 100 home.table.length = 200 home.table.weight = 20 home.table.material = "wood" home.table.color = "brown"   How can I use structure with (object) {code} right to get something like this?  var home = {} with (home) { table = {} table.width = 100 table.length = 200 table.weight = 20 table.material = "wood" table.color = "brown" }


Switching to English keyboard with Alt + Shift

Is it possible to configure Mac, so I will be able to switch to English keyboard with Alt+Shift?


This about the famous article   Zermelo, E., Beweis, daß jede Menge wohlgeordnet werden kann, Math. Ann. 59 (4), 514–516 (1904),   available . Edit:  (OCR'ed, may be behind a paywall)  An English translation can be found in the  Collected Works/Gesammelte Werke by Ernst Zermelo. Alternative source: the  From Frege to Gödel: a source book in mathematical logic, 1879-1931, by Jean Van Heijenoort.  [See also this interesting  by Dan Grayson.]  I don't understand the paragraph on the last page whose English translation is     Accordingly, to every covering $\gamma$ there corresponds a definite well-ordering of the set $M$, even if the well-orderings that correspond to two distinct coverings are not always themselves distinct. There must at any rate exist at least one such well-ordering, and every set for which the totality of subsets, and so on, is meaningful may be regarded as well-ordered and its cardinality as an "aleph". It therefore follows that, for every transfinite cardinality,    $$\mathfrak m=2\mathfrak m=\aleph_0\,\mathfrak m=\mathfrak m^2,\mbox{and so forth;}$$   and any two sets are "comparable"; that is, one of them can always be mapped one-to-one onto the other or one of its parts.   It seems to me Zermelo says that the fact that any set can be well-ordered immediately implies that any infinite cardinal equals its square. Is this interpretation correct? If it is, what is the argument?  Side question: What is, in a nutshell, the history of the statement that any infinite cardinal equals its square? Where was it stated for the first time? Where was it proved for the first time? (In a similar vein: where was the comparability of any two cardinal numbers proved for the first time?)    Edit: German original of the passage in question:     Somit entspricht jeder Belegung $\gamma$ eine ganz bestimmte Wohlordnung der Menge $M$, wenn auch nicht zwei verschiedenen Belegungen immer verschiedene. Jedenfalls muß es mindestens eine solche Wohlordnung geben, und jede Menge, für welche die Gesamtheit der Teilmengen usw. einen Sinn hat, darf als eine wohlgeordnete, ihre Mächtigkeit als ein „Alef“ betrachtet werden. So folgt also für jede transfinite Mächtigkeit   $$\mathfrak m=2\mathfrak m=\aleph_0\,\mathfrak m=\mathfrak m^2\text{ usw.,}$$   und je zwei Mengen sind miteinander „vergleichbar“, d. h. es ist immer die eine ein-eindeutig abbildbar auf die andere oder einen ihrer Teile.


How does the electron jump across "gaps" in its orbital?

I saw on perhaps COSMOS, and have heard mention from other professors, that electrons sort of "teleport" or something, in their orbital and the quantum level. So looking at the orbitals for a lone hydrogen atom...  (source: ) ...some of those orbitals have 2 or more "blobs" that are separated from each other by some gap; there's some discontinuity. Take for example that (3,2,2) orbital in that image, where there are two blobs and a gap in between. How does the electron jump from place to another? How do you describe what's happening here?


I wanted to know is ui and ux design is all about designing a website and app on how it looks? Like how should a particular box should appear whether it should be small or big? Should it have shadow or how will it aling? Is this how ui and ux design is all about?


What is the difference between correlation and sufficient causation?

I have been told that X is a sufficient cause of Y if every time X happens, Y happens, too. However, isn't it the same as 'correlation'? For instance, if I say that global temperature is correlated with human average height, is it valid to say that a rise in global temperature is a sufficient cause of an increase in human average height?


I have been confused for so long about the plural and singular forms of "people". I want to put an end to this confusion.  What is the difference between these following expressions, and is it correct to use these expressions in both their singular and plural forms?    "The German people are not warlike" "The German people is not warlike"     (As in "The German people is no warlike nation. It is a soldierly one, which means it does not want a war but does not fear it....")    "People are funny" "People is funny"    Here I suppose that "people is" referring to a population/community: "the German people is not warlike" = "the German population is not warlike" and "People is funny" = "population is funny".  Is this correct? If it is correct, then what does "people are" mean?


Calculate circle's offset given distorted ellipse, when projected onto a sphere

I have a circle moving on a spherical surface. If the camera angle is fixed, is there a way to calculate the original circle's offset from the centre given the distorted ellipse formed when the circle moves to the edge of the sphere(as seen from the camera)?  I've looked into Listing's plane and the Tissot directrix(because I'm working with eyeball rotation), but neither seems to provide a clear solution to this. I've also looked papers regarding eyeball roation but they seem to focus on the physiological aspects rather than the math of the movement.    In other words: In the picture above, given one of the outer nine images as well as the middle one, I want to calculate how much the circle(i.e. iris) has moved/rotated from its position in the middle picture. I assume it has to do with comparing the distorted ellipse with the circle, but I can't seem to find out how. Is there some formula for this?


what about using "this" with methods in Java? Is it optional or there are situations when one needs to use it obligatory?  The only situation I have encountered is when in the class you invoke a method within a method. But it is optional. Here is a silly example just to show what I mean:  public class Test {      String s;      private String hey() {         return s;     }      public String getS(){         String sm = this.hey();         // here I could just write hey(); without this         return sm;     } }


Recover the source code from the pdf file

Recently, I lost most of my drive content, and now I've succeed to retrieve my Curriculum_Vitae.pdf. I have a little problem if I want to modify this file, because I don't have the source code anymore. Is there exists a way to recover or to reload that source code from the pdf file?  Thanks for your help!


Today i was working on a problem on a ring with goes as follows. Let A be a ring, prove that any element of A has either $0,1$ or an infinity of left inverses. I think i found a proof of this statement, but the official solution looks nothing like mine. It is said that i should show that if any element has two distinct left inverses then there's an infinity of them (which i did) by considering the kernel of $f:x\rightarrow ax$. My try goes as follow: let $x,y$ be such inverses then for all $p,q\in\mathbb Z$ satisfying $p+q=1$, $px+qy$ is another left inverse, because : $(px+qy)a=p+q=1$. And for all $p\in\mathbb Z$ we have : $px-(p-1)y=(p-1)x-(p-2)y$ that implies $x=y$. Hence there are infinitely many distinct elements of the form $px+qy$. Is my proof flawed ?


How many numbers of 6 digits, that can be formed with digits 2,3,9. And also divided by 3?  $$$$ I was trying to to add 2^6 (when there is no 2)+ C(6,2)2^2 (when 2 can be in two places)+C(6,3)2^3 (when 2 can be in three places)...


I used Linux 10 years ago for a couple of years and decided to use it again as my main OS this year. Initially, I installed Linux resizing my main Windows 10 partition. After a couple of weeks I decided to get more space from my Windows partition (/dev/sda3) to my Linux partition (/dev/sda7). That is when the problems started. My Linux partition did not recognize the free space within the partition, so I decided to reinstall the system. Currently, I do not know what happened, but System Monitor shows I have the root and home partitions separated as it shows on the images below:   (Click images to enlarge)


Why use an anonymous function as a variable?

Im trying to wrap my head around some basic MVC OOP coding concepts.  Consider the following.  private $notfound public function __construct(){         $this->notFound = function($url){             echo "404 - $url was not found!";         };     }    $this->notfound = function($url) So the way Ive been taught is that a function should start with the reserved keyword function name(params) In the statment $this->notfound = function($url)obviously there is no name after function...Im pretty sure I get the gist of the code but for readability sake would like to understand it a bit deeper. Why use a function after $this->notFound...? Why cant it be something like $this->notFound = $var[$url] Usually the closing parenthesis of If, Functions etc does not require a semicolon ; Why do I get an error when I omit the ; for the closing parenthesis for the statment $this->notFound = function{};`   Thanks


Interlining: How is responsibility distributed in case of a missed connection?

Suppose I have an itinerary A - C with 1 stop at B, booked under a single ticket number on the website of airline X, where the leg A - B is operated by airline Y and B - C is operated by X.   If the flight A - B is delayed to a point where I miss my connection, whose responsibility is it to see that I'm fed, watered, and eventually delivered to destination C? Is it Y or X?   Apart from an academic interest in the answer, I'm going to be travelling on such an itinerary soon, and would like to known with whom I should be having a polite but firm conversation in case things go wrong. In my particular scenario, the leg B - C is only operated a few times a week, not daily, so a missed connection would be quite inconvenient.


A Putnam Integral $\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$

This is a Putnam Problem that I have been trying to solve (on and off) for two years, but I have failed. I am in Calculus BC. This problem comes from the book "Calculus Eighth Edition by Larson, Hostetler, and Edwards". This problem is at the end of the first section of the chapter 8 exercises. Here's the problem:  Evaluate $$\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$$  Please. Any help is very much appreciated. So are solutions. Thank you!  Edit: I like the solution given, but I was interested to see if there is any other way of doing the problem? I'm excited to see the results.


Ask a question again, or there is a different way to get an answer?

I wanted to ask a question similar to , but it is from 2012 and does not have any answers or comments or anything.  So what's the suitable action in this case according to SE community? Asking it again?


python regex weird length issue with unicode flag

I am facing a weird regex issue. This is a simple regex to replace a-z with a space. But it only replaces up to a certain fixed length.  import re  s = 'aaaaaaaaaaaaabbbbbbbbbbbbbbbbbccccccccccccccccccdddddddddddddddddd' s = unicode(s, 'utf-8') s = re.sub(r'[a-z]', ' ', s, re.UNICODE) print s   On running this code, the output is                                  ccccccccccccccccdddddddddddddddddd   If I remove the re.UNICODE flag, then it works fine. Can someone please explain why is this happening.


I'm having troubles while using the url command in my bibliography.  I mean:  1) \bibitem{[8]} {\url{http://projects.webappsec.org/w/page/13246989/Web20Application20Security20Statistics\#Tableofcontent}}  2) \bibitem{[5]} Justin~Clarke ``SQL Injection Attacks and Defense'', Syngress Publishing, Inc.2009   Unfortunately font 1) is different from 2).  What should I do in oder to get the same font for both items?   I'd like the font used in 1)  to be identical to the one displayed in 2)


How to fill this type of gradient in circle in photoshop?

How can I fill this type of gradient in a circle?  This is my sample:


Converting Unix script to Windows batch for FFmpeg resizing

I want to reduce video dimension to 720:480 & keep original aspect ration when input video width > 720 else, keep original dimension and aspect ratio.  I am trying to reproduce this script in a Windows batch file and it fails:    set $width=720 set $height=480 ffmpeg -i file8.3gp -vcodec libx264 -preset slow -crf 20 -filter:v "scale=iw*min($width/iw,$height/ih):ih*min($width/iw,$height/ih), pad=$width:$height:($width-iw*min($width/iw,$height/ih))/2:($height-ih*min($width/iw,$height/ih))/2" -threads 0 -acodec libvo_aacenc -b:a 128k out.mp4   The errors I'm getting:  ffmpeg -i file8.3gp -vcodec libx264 -preset slow -crf 20 -filter:v "scale=iw*min($width/iw,$height/ih):ih*min($width/iw,$height/i h), pad=$width:$height:($width-iw*min($width/iw,$height/ih))/2:($height-ih*min($ width/iw,$height/ih))/2" -threads 0 -acodec libvo_aacenc -b:a 128k out.mp4 ffmpeg version N-54691-g7f4a1fd Copyright (c) 2000-2013 the FFmpeg developers   built on Jul 12 2013 16:31:48 with gcc 4.7.3 (GCC)   configuration: --enable-gpl --enable-version3 --disable-w32threads --enable-av isynth --enable-bzlib --enable-fontconfig --enable-frei0r --enable-gnutls --enab le-iconv --enable-libass --enable-libbluray --enable-libcaca --enable-libfreetyp e --enable-libgsm --enable-libilbc --enable-libmodplug --enable-libmp3lame --ena ble-libopencore-amrnb --enable-libopencore-amrwb --enable-libopenjpeg --enable-l ibopus --enable-librtmp --enable-libschroedinger --enable-libsoxr --enable-libsp eex --enable-libtheora --enable-libtwolame --enable-libvo-aacenc --enable-libvo- amrwbenc --enable-libvorbis --enable-libvpx --enable-libx264 --enable-libxavs -- enable-libxvid --enable-zlib   libavutil      52. 39.100 / 52. 39.100   libavcodec     55. 18.102 / 55. 18.102   libavformat    55. 12.102 / 55. 12.102   libavdevice    55.  3.100 / 55.  3.100   libavfilter     3. 80.101 /  3. 80.101   libswscale      2.  3.100 /  2.  3.100   libswresample   0. 17.102 /  0. 17.102   libpostproc    52.  3.100 / 52.  3.100 Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'file8.3gp':   Metadata:     major_brand     : 3gp5     minor_version   : 256     compatible_brands: 3gp53gp4     creation_time   : 2005-10-28 17:36:40   Duration: 00:00:04.93, start: 0.000000, bitrate: 46 kb/s     Stream #0:0(eng): Audio: amr_nb (samr / 0x726D6173), 8000 Hz, mono, flt, 8 k b/s     Metadata:       creation_time   : 2005-10-28 17:36:40       handler_name    : Apple Sound Media Handler     Stream #0:1(eng): Video: mpeg4 (Simple Profile) (mp4v / 0x7634706D), yuv420p , 176x144 [SAR 1:1 DAR 11:9], 35 kb/s, 15 fps, 15 tbr, 600 tbn, 1k tbc     Metadata:       creation_time   : 2005-10-28 17:36:40       handler_name    : Apple Video Media Handler File 'out.mp4' already exists. Overwrite ? [y/N] y [Parsed_scale_0 @ 0000000000318640] Invalid size 'iw*min($width/iw' [AVFilterGraph @ 00000000024c0540] Error initializing filter 'scale' with args ' iw*min($width/iw:flags=0x4' Error opening filters!


I downloaded a file from the internet (I can link to it here, but in the interests of not annoying other users, I won't post the link), and I can't delete the file with the message:   You need permission to perform this action  You require permission from the computer's administrator to make changes to this file   Trouble is, I am the administrator and UAC is completely off.  If I go into the Properties/Security tab, I get the message   You do not have permission to view or edit this object's permission settings   Clicking "Advanced"/Owner, it says:   Current owner: Unable to display current owner.   If i try to change the owner, I get the same message:   Unable to set new owner on file  Access is denied.


How to get the saved password of a RDP connection?

2 Years before one my client given the password for a remote server available in USA, I have directly typed the password in the screen and saved the credential. Now I need to forward the same credential to another person. So is there any way I can know the saved password for that machine.


Determine which app connects to a specific host and port?

As the title says, I need to know which app establishes a connection to a host on a specific port (in my case within LAN).  In case the answer depends on the platform: The device is a Moto G (xt1045) with the stock Android 5.1 which is not rooted (and not rootable).  I think the question is meaningful as is, so it should not be necessary to read the following to answer it. As it will probably be asked anyway and should help establish context, here is my broader problem: I have a homeserver that also acts as home entertainment system using Kodi. Kodi starts when any packet is received on port 8080, which is the case when remote apps like Kore or Yatse are used on android. With my old phone (older android version) it worked fine. With my new phone Kodi starts whenever my phone is in the LAN. Logging on the homeserver confirms the received signals originate on my phone. However I have removed the remote app from the "app switcher view" and it is not listed under running apps. So I want to know which app actually establishes this connection (the remote app shouldn't be running and other apps shouldn't connect to that specific port, so I can't figure it out in any other way).


What do I put for my affiliation on a paper when I have none

I have been asked by a journal to provide my affiliated university. The assumption is that I am a professor or researcher. I work in industry and spend my non-working hours doing research. What is a common way to handle this problem?