Do you need the axiom of choice if the non-empty sets in question are defined recursively?

Suppose I pick (using a single choice) an element $q_1$ from a nonempty set $U$. I then pick $q_2$ from the set $U/\{q_1\}$, $q_3$ from the set $U/\{q_1, q_2\}$ and so on. At each stage, the set in question is guaranteed to be non-empty. Thus, I have constructed a sequence $(q_n)_{n\in\mathbb{N}}$ using a single choice each time. Thus, I can safely assume that no (countably infinite) axiom of choice was used in the construction of this sequence, right?


$r$ and $R$ difference with Schwarzschild metric

Why did Schwarzschild in his article : $$R=(r^3+\alpha^3)^{1/3}$$     Whereas, nowadays the variable used is just the radius $r$? Doesn't that change the meaning of the equations?


AJAX select returns 'illegal choice detected'

Create a settings form for a module in Drupal 8 - when a user selects a View from a list, the drop down under it should populate with the displays in that view.  While the form updates the option list for the user, it also throws an error message on the screen "Illegal choice has been detected".  Here is the code (it doesn't paste very well):    getViewDisplays is the ajax callback that is populating the options.  Some people who have posted about this around the internet say to set #validated on the select field to TRUE, though, that doesn't necessarily feel right. I still want to validate the submission to do some checks.


I have a datetime I want to convert to a formatted date and time. The format is 109(9). I have always used:  CONVERT(char(26), c1.DateTime, 109)   Which works successfully, but at least on SQL Server 2014 the Cardinality Estimator is throwing a warning:     Type conversion in expression (CONVERT(char(26),c1.DateTime,109)) may affect "CardinalityEstimate" in query plan choice.   I would like to correct this if possible at all, but maybe this is the improved cardinality estimator I am not sure.  The full query in this contrived example is from a temp table populated from an real table which is what I am trying to correct.   CREATE TABLE #Vic (     DateStamp   datetime    not null,     TIN int not null ); GO INSERT INTO #Vic VALUES ( N'1985-09-06T00:00:00', 123456789 ),  ( N'2003-01-14T20:55:00.983', 123456789 ),  ( N'1997-08-07T00:00:00', 123456789 ),  ( N'2016-11-15T09:31:28.15', 123456789 ),  ( N'2003-01-14T20:45:29.247', 123456789 ); GO  SELECT TOP (10) CONVERT(char(26), v.DateStamp, 109) ,     CONVERT(varchar(26), v.DateStamp, 9) ,     CONVERT(nvarchar(26), v.DateStamp, 9),     CONVERT(nvarchar(30), v.DateStamp, 9),     CONVERT(varchar(9), v.TIN) FROM    #Vic AS v;   This gives a warning on every column listed.   This may be related to , but I am not sure the context is the same based on the query this Connect item provides.


Is there a way to get Statistic info in Blender? Or heads up display? Like when I select a group of vertices, I need a way to know how many vertices are selected and How many polygons "or triangles my scene has.


How to make Google Chrome reopen my tabs after closing it?

Let's say I have 4 tabs open, then I close the browser to shutdown my computer.   I'd like that next time I turn it back on and open the browser, the 4 tabs to be there. If they got saved onto some cache or they just reload again, I don't care.  I want it to always reopen all the tabs I have open at the time of closure, much like Notepad++. And much like a smartphone's browser, now that I think of it.  I am aware of Ctrl+Shift+T to reopen the last closed tab. It's not what I am looking for.  If that is not possible with Google Chrome, then: is there any other browser capable of that?


To show that Egoroff's Theorem continues to hold if the convergence is point-wise a.e. and  $f$ is finite a.e. on  $E$.  And Egoroff's Theorem states that if $E$ is a set of finite measure and $\{f_n\}$ is a sequence of measurable functions that converges pointwise on $E$ to the real valued function $f$, then there exists a closed set $F$ that is roughly the same size as $E$ on which $\{f_n\}$ converges uniformly.


How can I reinstall GRUB to the EFI partition?

I want to reinstall GRUB 2 and I found these instructions: . In my case, the boot loader is installed in the EFI partition. If I use the commands provided in this guide, will GRUB be reinstalled to the EFI partition automatically, or will it be installed into the root partition where Ubuntu is installed ? Obviously, I do not want this to happen.


limit of product of $(a_1a_2.\dots a_n)^{\frac{1}{n}}$

How to calculate the following limit  $$ \lim_{n\rightarrow \infty} \left[ \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)\cdots \left(1+\frac{n}{n}\right) \right]^\frac{1}{n} .$$  I was trying this by taking the $\log $ of the product and then limit but I am not getting the answer could anybody please help me. And, also is there any general rule for calculating the limit for  $$ (a_1a_2.\dots a_n)^{\frac{1}{n}}.$$  Thanks.


How to \show the code of the command \autoref?

Edit: I think this is a duplicate of  .  I wanted to see the code for the hyperref \autoref command, so created this simple document:  \documentclass{article} \usepackage{hyperref} \begin{document} \show\autoref \end{document}   However, in the log output, instead of the code, I see:  > \autoref=macro: ->\protect \autoref  . l.4 \show\autoref   Changing line 4 to \show\section shows the code for \section, as expected:  > \section=\long macro: ->\@startsection {section}{1}{\z@ }{-3.5ex \@plus -1ex \@minus -.2ex}{2.3ex \@plus .2ex}{\normalfont \Large \bfseries }. l.4 \show\section   How can I get the actual code for \autoref?


What are the benefits of Stack Overflow Careers invitations and why are only a limited number issued?

After I received some invitations, I didn't know what to do with them. I asked  and I got the answer that as a developer I might know some good developers. But still something is missing:   If the invitations are to attract good developers why do we get a limited number of invitations? I have got 5 invitations, why shouldn't I be able to invite more than 5 developers? I was member of Stack Overflow Careers for more than a year but I got the invitations somehow like a reward for completing my profile. If invitations are just for attracting good developers they shouldn't be limited. Secondly imagine that I invited some developers, does the quality of invited developers have effect on me and my careers account? If yes then I should just keep these invitations for some special people as I just have limited number of them.


How to find $\lim\limits_{n\to\infty} \dfrac{1!+2!+...+n!}{n!}$

I saw this limit in my high school math textbook (senior year) and couldn't find it. $$\lim\limits_{n\to\infty} \dfrac{1!+2!+...+n!}{n!}$$


I'm currently thinking about my portfolio design and I would like some advices from experts. For a personal and professional portfolio, is it better to have a contact form or a mailto? This is my choice bellow:   Build Simple contact form with great design. Under my biography/about me a section, have a button showing "Contact me" and when you hover on, it show my contact email and if you click on it you have the mailto in action. The only thing is that I'm not sure you can copy/paste text appearing on hover, so it will not work with people without mail client. Just my contact email and when you click on it you have mailto bellow about me section, at the bottom of the page or in the footer.   I know that many people created the same topic before, but maybe it changed since then.  Thanks


Hello, is there a specific logical way to determine if there is an integer in a String?

I would wondering if using a for loop to determine if an integer is inside of a string would be the best option, but I am not so sure.  Please help thank you!!  This is for Java btw.


MacBook Pro Internal speaker has just stopped to sound (but startup chime sounds)

The internal speaker of my MacBook Pro suddenly stopped sounding. I just tried PRAM reset, but it doesn't work.   The audio works when I plug in earphones and goes when plug out.  I don't think, it's a hardware problem, because, the startup chime sounds when I start the computer. (correct me if I am wrong in this point).  Anyone have any idea why this may happen and how to fix it?  Image : It also disappeared from the output list:      Not a hardware problem: Some people are referring this as a duplicate of a post, which has a hardware issue, I already mentioned above, the sound works for me while startup (startup chime). So it's not a hardware issue. (Pls explain in comment, if I am wrong in this point, other than marking as duplicate without any will to help).


It is posible to have a function $f$ with the following property?

I am considering the function $f$ defined as  $$f:\emptyset\to\emptyset$$  My thought is that a function maps elements from a set to another one, but the empty set has no elements to map, so I think there cannot exist a function $f$ that has this property, but I don't know how to prove it and I'd like some light on this.  There is a function $I$ though which can map the empty set to the empty set if its domain and codomain are the set containing the empty set. But it is not the same question.


I have a Child and parent case. I have the following fields:   Reopen Flag (Checkbox field) Case Reopened By (Drop down field)   The vales in Reopened By fields are Customer and Internal  Total Reopen Count Customer Reopen Count Internal Reopen Count   Details by Steps:   Select Reopen Flag in Child Case Select Case Reopened By (Value: Customer) in Child Case Customer Reopen Count Field gets incremented by 1. in Child Case Total Reopen Count gets Incremented by 1. in Child Case Parent Case also gets updated.   Repeat the steps but it does not gets updated in Parent Case.  Change the Value in Case Reopened By - "Internal" in child Case then the values will get updated in Parent Case.  How to update Parent Case from child case every time Total Reopen Count and Customer Reopen Count/Internal Reopen Count gets updated.  trigger Update_Parent_Case on Case (after update) {      map<string,case> case_map = new map<String,Case>();      for(case cs : trigger.new){          if(trigger.oldMap.get(cs.id).Total_Reopen_Count__c != cs.Total_Reopen_Count__c){                         case_map.put(string.valueof(cs.ParentId),cs);         }     }       list<case> to_update = new List<case>();     if(case_map.size() > 0){         for(case cc : [Select id,Case_Re_opened_By__c,Re_open_Flag__c, Customer_Re_open_Count__c,Internal_Re_open_Count__c from case where id in: case_map.keySet()]){             case c = case_map.get(cc.id);               cc.Case_Re_opened_By__c = c.Case_Re_opened_By__c;              cc.Re_open_Flag__c = true;             cc.Total_Reopen_Count__c = c.Total_Reopen_Count__c;             cc.Customer_Re_open_Count__c = c.Customer_Re_open_Count__c;                cc.Internal_Re_open_Count__c = Internal_Re_open_Count__c;               to_update.add(cc);         }         update to_update;         case_map.clear();     }  }


It is some time since I used Latex, but am now up-and- running again and using pdflatex. I want to insert a Russian symbol (in particular the symbol sh, as in sh(x), to indicate a row of delta functions) into an equation that is contained in an eqnarray and I don't want to be forced to have a space on either side of the symbol. I can manage to type Russian symbols in straight-forward text, but so far not in an array. Can anyone help?  Answers:  Just found some excellent answers to my question. These were posted some years ago, they seemed to pop-up when I browsed around my question. Not exactly sure how I found them, but one was submitted by a lady name of Barbara. It involves the fuction \Sha.  Many thanks


Not able to write the message into excel file in console showing java.lang.NullPointerException

public void write(int row1, int cell1, String message, String sheet1) throws Throwable {      String path = ".\\resources\\APItestdata.xlsx";     FileInputStream fis = new FileInputStream(path);     //File fis=new File(path);     Workbook wb = WorkbookFactory.create(fis);     Sheet sh = wb.getSheet(sheet1);     Row r = sh.getRow(row1);     Cell c = r.createCell(cell1);     c.setCellValue(message);     FileOutputStream fos = new FileOutputStream(path);     wb.write(fos);     wb.close(); }


PHP does not write out hungarian characters from MySQL database

So, I made a searching system test (This code searches items out of the "diakok" named database) and there is a problem with it. When I type in my name (Géró Kristóf) it says there are no names in the database like this, but when I write it as Gero Kristof, it finds that right (but it doesn't write out the name, because of these special letters), while there are é and ó instead of e and o in the database. I tried changing the encoding types also in the database and the code, but nothing works right. (With names which don't have special characters, it works just fine)  <?php   $keresesi_tipus = 'felhasznalonev';   $keresesi_kifejezes = trim($_POST['keresesi_kifejezes']); header("Content-type: text/html; charset=utf-8");   if (!$keresesi_kifejezes) {     echo "Nem adott meg keresni való nevet. (1-es hibakód)";     exit;   }    if (!get_magic_quotes_gpc()) {     $keresesi_tipus = addslashes($keresesi_tipus);   }   @ $adatbazis = new mysqli('localhost', 'root', '', 'diakok');   if (mysqli_connect_errno()) {     echo "Hiba! Nem sikerült csatlakozni az adatbázishoz. (2-es hibakód)";     exit;   }    $lekerdezes = "SELECT * FROM diakok WHERE ".$keresesi_tipus                 ." LIKE '%".$keresesi_kifejezes."%'";   $talalat = $adatbazis->query($lekerdezes);   $talalatok_szama = $talalat->num_rows;    echo "
A keresésnek megfelelő diákok száma: ".$talalatok_szama."
";    for ($i = 0; $i < $talalatok_szama; $i++) {     $sor = $talalat->fetch_assoc();     echo "
".($i+1).". Teljes neve: ";     echo htmlspecialchars(stripslashes($sor['teljes_nev']));     echo "
 Felhasználóneve: ";     echo stripslashes($sor['felhasznalonev']);     echo "
 Kategóriája: ";     echo stripslashes($sor['kategoria']);     echo "
";     echo "
";   }   $talalat->free();   $adatbazis->close(); ?>   Here is a pic about the database:


I am looking at a flight from Ecuador to Singapore which stops in JFK.    Do I need a transit visa if I am not leaving the airport?    The layover is four hours, the same on my return. Also stops in Toyota. I have an Ecuador passport.


Something is wrong with this community wiki author username

I recently noticed . The 'author box' shows this:    However, clicking on the username takes me to  - with 'not Pekka' as a username. Also, the correct username is shown in the post's revision history.  It's almost like an old version of the username is being somehow cached - but I'm pretty sure that that doesn't happen. What's different about this instance?


Should I consider buying a velomobile as my daily commute vehicle instead of a bike?

What are the advantages/disadvantages between a (possibly electric) velomobile and a regular bike when in daily use?


Hamilton's equations for Dirac Hamiltonian

The Dirac Lagrangian $$\mathcal{L} = i\bar{\psi}\gamma^{\mu}\partial_\mu \psi - m \bar{\psi}\psi$$ gives a Hamiltonian $$\mathcal{H}(\Pi,\bar{\Pi},\psi,\bar{\psi})=\Pi \dot{\psi}-\mathcal{L}=-\bar{\psi}\gamma^{i}\partial_i \psi + m \bar{\psi}\psi,$$ $$\text{where}\quad  \Pi=i\bar{\psi}\gamma^0.$$ So the Hamiltonian is actually independent of $\Pi,\bar{\Pi}$. Suppose I wanted to start from this Hamiltonian and tried to find the equations of motion via Hamilton's equations $\dot{\psi} = \partial\mathcal{H}/\partial \Pi$ and $\dot{\Pi} = -\partial\mathcal{H}/\partial \psi$, plus equivalent ones for conjugate field.  Clearly something is wrong as the first of Hamilton's equations gives $\dot{\psi}=0$, while the second gives $\dot{\Pi}=i \partial_i\bar{\psi}\gamma^i +m\bar{\psi}$ and I don't see the Dirac equation popping out...


Event handler and null-conditional operator

For example, implement INotifyPropertyChanged interface:  public event PropertyChangedEventHandler PropertyChanged;  private void OnPropertyChanged([CallerMemberName] string propertyName = null) {     var handler = PropertyChanged;     if (handler != null)         handler.Invoke(this, new PropertyChangedEventArgs(propertyName)); }   Two things:   Copy event to local variable to prevent errors with multithreading ( are some examples). Resharper gives notification, if you don't copy to local variable:         Check it for null, to prevent NullReferenceException   But now, we can use ?. operator for null-checking. And if I use it, Resharper is idle:   So, question is: should I copy event ProperyChanged to local variable, if I use null-conditional operator?


I have a question related to modeling short time-series. It is not a question , but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq 20$)? By "best" I mean here the most robust one, that is the least prone to errors due the fact of limited numbers of observations. With short series single observations could influence the forecast, so the method should provide a cautious estimate of errors and possible variability connected to the forecast. I am generally interested in univariate time-series but it would be also interesting to know about other methods.


How to make sure that my lecture notes do not infringe on copyrights?

I'm trying to change the numbers in problems I write for examples I use in my class as well as assignments. However the problems are still inspired by the textbook. Are the problems sufficiently different from the textbook problems to not have copyright issues? There is also an issue of theorems and definitions. Authors of the calculus textbook certainly did not come up with these things. Is it OK to just copy them down in my lecture notes?  By the way I do share my lecture notes on Piazza and the course I'm teaching is multivariable calculus.


Assume $A$ is a nontrival submodule of a free $R $-module, where $R $ is a ring.   Is it true that $A $ is also free?


Can't extend partition to use free space

On my Windows 10 drive I have the following partitions    How can I extend the C partition so that it uses the (Extended) "Free space" partition?  The extend option is greyed out when right clicking the C partition    Deleting the free partition gives the following error     There is not enough space available on the disk(s) to complete this operation


How can I modify an item while it is inside the player's inventory?

I'm wondering about whether it is possible to change part of an NBT or add NBT to an item that a player is holding. My goal is to make custom enchants. For example when a player uses an item to enchant a sword they get the score "EnchantMight" 5, which would cause the next weapon they hold to get "Might V". This, in reality, would just be +5 additive damage in the NBT. I know /replaceitem would be an option, but that only works if the new item is predetermined. I hoped /data modify entity @p {SelectedItem:[{AttributeModifiers:[{AttributeName:"generic.attack_damage",Amount:5,Operation:0,UUID:[I;-120919,1237,151734,-2474],Name:"generic.attack_damage"}]}]} insert/append/merge  would work, but obviously it didn't. If anyone even just has an idea I can try out, it'd be of help. If you give a datapack related answer, please explain clearly as I don't know a lot about it.


Closing a div by clicking outside and clicking a button

i am trying to setup a dropdown menu, that can be closed by clicking outside (the opened div) and by clicking the button/img (that opens the div).  Image with onclick funtion:     Dropdown list that should be opened and closed, class declares dropdown as display:none:

...

   This is my solution so far:  function hide() {     var x = document.getElementById("dropdown");      if (x.style.display === "none") {         x.style.display = "block";     } else {         x.style.display = "none";     } }   When i am trying to add a function that closes the dropdown when the user clicks outside the dropdown:  window.addEventListener('mouseup',function(event){         var dropd = document.getElementById('dropdown');          if(event.target != dropd && event.target.parentNode != dropd){             dropd.style.display = 'none';         } });   Then i end up with a opened dropdown because the onclick-function starts.  Can someone help me to combine those functions? Thank you!


Is it okay to use symbolic links in my web server?

I have the following directory setup:  /var/www/html   and  /home/tim/Website/files_here   The folder html is actually a link to /home/tim/Website. This means all my Website files are in my home area (they get included in the backup etc).  Is there anything wrong with this method? Is there a better way to get the homepage to be in /home/tim/Website?  Are symbolic links on a web server ever incompatible with users not on linux?


Some of you may recognize this as Project Euler's problem number 11. The one with the grid.  I'm trying to replicate the grid in a large multidimensional array, But it's giving me a syntax error and i'm not sure why  grid = [  [ 08, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 08 ], [ 49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 04, 56, 62, 00 ], [ 81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 03, 49, 13, 36, 65 ], ...   And I get this error:     File "D:\development\Python\ProjectEuler\p11.py", line 3     [ 08, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91 , 08 ],        ^ SyntaxError: invalid token   Why is it throwing an error before the comma?


I need a keyboard manipulation to switch input language.  I know how to switch by clicking on the desktop.   On Windows, we have Alt+Shift.  What is the equivalent?


How do I "align" numerator and denominator?

\documentclass{amsart} \begin{document} $\frac{(n+1)!}{(n+1)^{n+1}}$ \end{document}   The problem is that I want to make (n+1) on the same line. How do I achieve this?


I try to create a regex for nr. of decimal of a number and the number of decimal will be pass from variable.  (Ex:  123.4545)-> 4decimals  const regex = 4; const decimalValidation = helpers.regex('decimalValidation',/^\d*(\.\d{1,4})?$/);  //Insted of 4 ,I have to replace with regex const.


Prove that there no $k$ such that : $3n^{2}+3n+7=k^{3}$

Problem :   Let $n,k$ be natural numbers   Prove that there no $k$ such that :      $$3n^{2}+3n+7=k^{3}$$    I see this short solution from a book :   We use $\pmod{9}$   $k^{3}\equiv 0,1,8\pmod{9}$   And $3n^{2}+3n+7\equiv 4,7\pmod{9}$   $\implies $ no solution ?   But I don't understand why he chose mod $9$ and how we know that $k^{3}\equiv 0,1,8\pmod{9}$ ?   And how he know $3n^{2}+3n+7\equiv 4,7\pmod{9}$ ? Can someone explain to me or give me another solution !


Is it correct to use "their" instead of "his or her"?

Is this sentence grammatically correct?  Anyone who loves the English language should have a copy of this book in their bookcase.  or should it be:  Anyone who loves the English language should have a copy of this book in his or her bookcase.


How to remove border and legend of 1:50 000 rasterfile in QGIS?

How does one remove the border and legend of a 1:50 000 map? Want to combine several maps to form one.


Ubuntu 18.04.03 installer tries to mount a drive, fails, drops into initramfs

I've been trying to dual boot Windows 10 and Ubuntu 18.04. I know my Windows 10 is in Legacy mode. For some reason, Ubuntu decided to install in UEFI mode, which caused me a lot of problems when trying to dual boot (aka unable to do so).  I want to reinstall Ubuntu in Legacy mode. Whenever I boot into the installer (now that I have Ubuntu installed and want to reinstall it), for some reason it tries to mount my drives (it really shouldn't). This of course fails and bumps me to the initramfs prompt.  I cannot simply remove the drive since that's where I want to install Ubuntu, but I don't even get that far. The installer is trying to mount /dev/sdc2 to /cow, but that is entirely unrelated to the install process. Same thing happens when trying to go into Live Ubuntu instead.  Edit: As it turns out, a persistent partition was created on my USB live installer. It was trying to load this and failing. Removing the persistent storage solved the issue. Additionally, when booting in UEFI mode, my USB drive is /dev/sdd, and when booting in Legacy mode, it is /dev/sdc, hence the confusion.


Can't log in after installing CUDA toolkit

I have latest version of Ubuntu 16.04 and I installed latest version of Cuda Toolkit 8.0. After install Cuda Toolkit, I am stucked on login screen and I can't login into Ubuntu with my password. Is there posibility to get into system? Or do you have any manual, how to corectly install Cuda toolkit? I need Cuda toolkit on Ubuntu. (Sorry for my English)   There is my procedure, how I installed Cuda (officialy from Nvidia)  sudo dpkg -i cuda-repo-ubuntu1604-8-0-local_8.0.44-1_amd64.deb sudo apt-get update sudo apt-get install cuda


If $A$ is a connected set and $\{A_i : i \in I\}$, $I$ an arbitrary set (can be countable or not) of connected sets.  How to show that if $A \cap A_i \neq \emptyset$ for all $i \in I$ then $A \cup (\cup_{i\in I} A_i)$ is connected?  I am trying to show that if $A \cap A_u \neq \emptyset~~ \forall i \in I$ then for all $i, j \in I$ $A_i\cap A_j \neq \emptyset.$ This enought to conclude the result. But I stuck here.  What I tried: Suppose that there are $i,j\in I$ such that $A_i \cap A_j  = \emptyset.$  Then since $A\cap A_i \neq \emptyset$ and $A\cap A_j \neq \emptyset$ it somehow induces me to think that is possible to obtain a split for $A$. I don't know how to proceed.  Thanks


I am trying to do a new environment or command (i tried both) where i can put in the name, description and code of a Method in c++ and it gives me a new section with the MethodName, the code listed and the description below. But i am not able to use the listings environment in a new command or new environment.. Consider my MWE   \documentclass[a4paper,11pt]{article} \usepackage{listings}  \newcommand{\method}[3] { \section{#1}\label{#1} \begin{lstlisting} #2 \end{lstlisting} #3 }   \begin{document}  \method{MethodName}{Method Void MethodName()}{Description of the Method blablabla}  \end{document}   How can I fix this?   I would prefer to do it using a macro since I don't need an ending.


Look at this if block:  #!/bin/bash  str="m.m" if [[ "${str}" =~ "m\.m" ]]; then     echo "matched" else     echo "not matched"     exit 1 fi  exit 0   This should print "matched", but it doesn't. Where am I going wrong?


Why do loadings of princomp in R report identical proportion of variance for all principal components?

I'm trying to run a few tests using princomp in R.  In princomp there is a value called loadings, which is supposed to show many things.  One of those things is the proportion of variance explained by each principal component.    For some reason, the principal components using this tool in R always come out such that the proportion of variance is the same for all components!!  For example, try this on the iris dataset:  data = iris[c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width")] iris_fit <- princomp(data, cor=TRUE)   then, when I print out the loadings, I see this:  iris_fit$loadings  Loadings:              Comp.1 Comp.2 Comp.3 Comp.4 Sepal.Length  0.361 -0.657 -0.582  0.315 Sepal.Width         -0.730  0.598 -0.320 Petal.Length  0.857  0.173        -0.480 Petal.Width   0.358         0.546  0.754                 Comp.1 Comp.2 Comp.3 Comp.4 SS loadings      1.00   1.00   1.00   1.00 Proportion Var   0.25   0.25   0.25   0.25 Cumulative Var   0.25   0.50   0.75   1.00   All of the Proportion Var row is 0.25, meaning that the variance is split evenly across the components.    So, I tried a few other datasets with, for example 2 or 3 features.  And, every time, the Proportion Var is 1 divided by the number of features!  Why is this?  I want to be able to use this for feature selection, and it makes it difficult to select components/features when they are all the same.   Why is this?


How to dynamic cast different (UnderGraduate, PostGraduate)) type from list of (Student) type in C++?

Uni lab tutorial asks us to create an abstract class Student and extend that class into 2 more classes UnderGraduate and PostGraduate. After that create another class called Conference that stores a list of students. The issue is we then need to use functions specific to the UnderGraduate & PostGraduate classes as well as inherited functions from the virtual functions in class Student. Instead of that, it uses the virtual functions (returns 0 instead of other definitions of it), and it gives an error when trying to dynamically cast in order to use the specifically needed functions.     int countUnderGraduate(int years){     int total = 0;     list <Student> :: iterator i;          for(i = students.begin(); i != students.end(); i++){         if(i->getYears() < years){             total++;         }     }          return total; }  int countPostGraduate(int projects){     int total = 0;     list <Student> :: iterator i;          for(i = students.begin(); i != students.end(); i++){         PostGraduate *pg = dynamic_cast<PostGraduate*>(*i);         if(pg){             if(pg->getProjects() > projects){                 total++;             }         }     }          return total; }  gives 2 errors:  In the countUnderGraduate function: error: ‘class Student’ has no member named ‘getYears'. In the latter function (tried dynamic cast): cannot dynamic_cast ‘i.std::_List_iterator<  >::operator*()’ (of type ‘class Student’) to type ‘class PostGraduate*’ (source is not a pointer)  Both functions work with this list:     Conference(list <Student> students){     list <Student> :: iterator i;          for(i = students.begin(); i != students.end(); i++){         this->students.push_back(*i);     } }  Are there any workarounds?


How do I get email notifications of new replies to my question?

Is there is a way I could get email notifications of new replies to my questions posted on Stack Exchange?  I have searched about this question already and can't find the options mentioned in other answers.


Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly

While reading David Williams's "", the following statement caught my fancy:     Every subset of $\mathbb{R}$ which we meet in everyday use is an element of Borel $\sigma$-algebra $\mathcal{B}$; and indeed it is difficult (but possible!) to find a subset of $\mathbb{R}$ constructed explicitly (without the Axiom of Choice) which is not in $\mathcal{B}$.   I am curious to see an example of such a subset.


How to reduce dc 5 volt to below 1.5v by add extra load

I have an USB charger with 5V DC output.  I want to use this charger to power a 1.2V DC motor.  I think about adding an extra load, like a DC bulb, to this circuit, maybe it could reduce the voltage to my requirements.  Could you help me?


When I render it I got a fully black image

I am trying to make a 360degree photo. I just do such i saw in some you tube tutorials. I change blender render to cyclic render and change camera to panoramic .But when I render it I got a fully black image. How i can solve this.(hopping you can understand. Because my English is very bad)  This is my blender file:   Can you just render it to image and show me it  Because I think it may be problem of my system.   My project  Camera view  Rendering window


Hello. I'm a beginner.  In the model shown, when I select all of the top vertices and then scale them to the center, the center of scaling is not the center of the 3d-model.   How do I move the center of scaling? How do I move the manipulator widget where I want it after selecting?


Prove for $ \forall n \in \mathbb{N}, \exists x,y,z$ ( $0 \leq x < y < z$ ) such that $ n = \binom{x}{1} + \binom{y}{2} + \binom{z}{3}$

I'm trying to solve a problem from the combinatorics book. Prove or disprove for $ \forall n \in \mathbb{N}, \exists x,y,z \in \mathbb{N} $ ($0 \leq x < y < z$) such that $$ n = \binom{x}{1} + \binom{y}{2} + \binom{z}{3}$$  I was trying to substitute binomial coefficients with:  $$ n = \binom{x}{1} + \binom{y}{2} + \binom{z}{3} = x + \frac{y*(y-1)}{2} + \frac{z*(z-1)*(z-2)}{3}$$  However, I've stucked after that. I know that any binomial coefficient is integer-valued. So, it's likely equation hold.


How can I use Regular Expression to match Chinese characters like ，。‘；’

I'm using javascript to convert string to what I want!! Can I use Regular Expression and use what  Regular Expression?? Is there anyone that can help me?


Using end-of-line delimiter in plain Tex macro

How is it possible to use the end-of-line character as a macro parameter ? I would like something along the lines of :  \def\mymacro#1\endlinechar{Content:#1} \mymacro First content \mymacro Second content   Giving the following output :  Content: First content Content: Second content   I have tried \endlinechar and \^^M but it does not work that easily.


Reproducing P. Aluffi's Definition/Theorem style

Currently reading  and I really like the way theorems, definitions, etc. are emphasized by a lower right corner symbol (). For reference        I have tried recreating this formatting by manually inserting \hfill$\rlcorner$ in the following way  \documentclass[a4paper, 10pt]{article} \usepackage{amsmath, amssymb, amsthm} \usepackage[singlespacing]{setspace}  \theoremstyle{definition} \newtheorem{exam}{Example} \newtheorem{definition}{Definition}  \DeclareMathOperator{\im}{im}  \begin{document}  \begin{exam} A complex $$\cdots\longrightarrow M\overset\beta\longrightarrow N\longrightarrow0\longrightarrow\cdots$$ is exact at $N$ if and only if $\beta$ is an epimorphism.\par Indeed, the complex is exact at $N$ if and only if $\im\beta=$ kernel of the trivial homomorphism $N\to0$, that is, $\im\beta=N$.\hfill$\lrcorner$ \end{exam} \begin{definition} A {\it short exact sequence} is an exact complex of the form $$0\longrightarrow M\overset\alpha\longrightarrow N\overset\beta\longrightarrow0.$$\hfill$\lrcorner$ \end{definition}  \end{document}         Anyway, I am not happy with this solution as, on the one hand, it does not seem efficient and, one the otehr hand, I am not able to adjust the height of the second \rlcorner to match the excerpt (writing $$[Diagramm].\hfill\rlcorner$$ does not work).     Could someone help me out? I would prefer to declare this style within the preamble for all kinds of theorem enviroments at once.   Thanks in advance!


Could we declare a pointer of the class's type in the class declaration?

I know that is possible for a struct:  struct A{     A* p; };   But could we do that to a class:  class B{     B*p; }   I tried to google it, but end not found it. Thank you very much!


Proving the series $s_n=1+\frac{1}{\sqrt2}+\cdots +\frac{1}{\sqrt n}$ is not bounded

Let $s_n=1+\frac{1}{\sqrt2}+\cdots +\frac{1}{\sqrt n}$. This sequence is definitely increasing, and I tried to show that it is not bounded above, by induction. However if $s_n\leq2$, then $s_{n+1}\leq2+\frac{1}{\sqrt n}\nleq2$. So I thought this is not bounded above.  Now, the second sequence is $s_n=\frac{1}{1^2}+\frac{1}{2^2}+\cdots+\frac{1}{n^2}$. The problem requires to prove that this one is bounded above by $2$.  I tried to apply the same method as before: if $s_n\leq2$, then $s_{n+1}\leq2+\frac{1}{(n+1)^2}\nleq2$. But, this is bounded above by $2$.  What is wrong with my logic?


How to send Alt+Ctrl+Del key sequence in a VirtualBox VM guest

I have a   VM guest, which I run in vboxHeadless mode. The host is Linux 64-bit. The VirtualBox version is 4.2.12r84980.  The VM loads fine, and I am presented with the "windows server" greeting screen. That is, I have to press Alt + Ctrl + Del to log on.  I have tried numerous ways to send Alt + Ctrl + Del:   Remote desktop to the VM from the port that is assigned by VirtualBox headless. That is, <VirtualBox host IP address>: VMguestPort. A-C-D doesn't work as the key sequence gets intercepted by the client PC at which I'm sitting and trying to log on to the VM guest. Remote desktop directly to the VM <Windows Server 2008 VM guest IP address>:3389 doesn't work for the same reason.  gives an a button to send A-C-D to a VM guest. This doesn't work either. I read that from a command line I could use the command  VBoxManage controlvm win2k8_64 keyboardputscancode 1d 38 53  VBoxManage controlvm win2k8_64 keyboardputscancode 9D B8 D3    for key press and then key release sequence. This doesn't work either.  Why do these work? Especially with a Windows Server 2008 as a VM guest?    The suggested previous answer does not work (pressing Alt + Ctrl + End does not work either) and also, as I am running a headless server, there isn't any change for me to see the VirtualBox GUI. The best I can get is the phpVirtualBox web interface and in VirtualBox there isn't any "right Ctrl" capture key.


What's the difference between the various printer connections?

I'm installing a new printer and I'm given 4 connection options.   AppSocket/JetDirect network printer via DNS-SD LPD network printer via DNS-SD IPP network printer via DNS-SD AppSocket/HP JetDirect   Which one should I choose?  It's a Samsung CLP-320 if it makes a difference.


Why the derivatives and gradient are used interchangeably?

I am not good at mathematics and have been learning ML from Udacity. In its tutorial video, the tutor mentioned derivatives at time 4:24  and gradient across the whole video e.g. at time 3:03  So this makes me thinking derivatives and gradient are interchangeable. Am I correct? If not, what are the differences between Gradient and Derivative in laymen's language?(yes, I did searched the differences, but they are too mathematic. My hopeless not-math-capable brain cannot understand it but my curiosity keeps driving me to get it understood.... >_<) and when to use gradient and when to use derivative?


Why do du/df and by System Monitor show used space in home differently?

$ sudo du -h -d 0 home/ 309G    home/  $ df -h Filesystem      Size  Used Avail Use% Mounted on ... /dev/sda4       550G  309G  214G  60% /home ...   System Monitor on Ubuntu shows the used space on /home  is 331.1 GB    Do the different ways measure the same thing?   How differently do they make the measurements?  Thanks.


Question pertaining to the relationship between the GCD and LCM of 3 numbers.

I am a high school student self-studying Number Theory and came across this question in the book Challenge and Thrill of Pre-College Mathematics (For reference, $(m,n)$ means $\gcd(m,n)$ and $[m,n]$ means $\text{LCM}(m,n)$):  If $m$, $n$, and $k$ are any three positive integers, prove that  $$(m,n)(m,k)(n,k)[m,n,k]^2=[m,n][m,k][n,k](m,n,k)^2$$  I was able to derive this identity by trial and error and then prove it mathematically:  $$\frac{(m,n)(m,k)(n,k)[m,n,k]}{(m,n,k)}=mnk$$  And I suspect that this may be true as well:  $$\frac{[m,n][m,k][n,k](m,n,k)}{[m,n,k]}=mnk$$  Which would prove the proposition. However, I am unable to prove this statement and am unsure of its truth.  Please offer a hint to how I would go about proving the second part, or in case if my assumption is incorrect than the correct method of proof.


gcc doesn't do anything when trying to compile a code

I'm new using Ubuntu OS, I've Ubuntu 12.04 and I'm trying to run a simple Hello world C program  #include <stdio.h> int main(){ printf("Hello world!"); return 0; }   When using gcc --version command at cmd, it returns 4.6.3 (I think that is the version), the problem is that when I try to use the command gcc helloworld.c in the address where the helloworld.c file is, it doesn't prompt anything, not the hello world! printing nor an error, the cmd just change line like if the enter key was pressed, but it appears that an a.out file were create by the command.  I've been working with python in the same way by using python file.py command and have no problem, what am I doing wrong?  Thanks for reading!


What is the difference between "have" and "have got"?

I am confused between the following sentences:  I have a pen. and I have got a pen.  What is the difference between them?


This is likely ground that has been covered but I have yet to find an explanation that I am able to understand. It is likely that I will soon feel embarrassed.  For instance, I am trying to find the order of magnitude using Big-O notation of the following:  count = 0; for (i = 1; i <= N; i++)     count++;   Where do I begin to find what defines the magnitude? I'm relatively bad at mathematics and, even though I've tried a few resources, have yet to find something that can explain the way a piece of code is translated to an algebraic equation. Frankly, I can't even surmise a guess as to what the Big-O efficiency is regarding this loop.


I was running a Python script that malfunctioned and used sudo to create a file named >.  How can I get rid of this file?  Of course, when I try sudo rm >, I get the error bash: syntax error near unexpected token 'newline', because it thinks I'm trying to redirect the output of rm.  Its permissions are -rw-r--r--.


Can I read Rhythm of War, before the rest of The Stormlight Archive or will I be lost

I want to know if I can listen to the Rhythm of War Audiobook, because it's up on Brandon Sanderson's youtube, before I read the rest of The Stormlight Archive. I know there's alot of books in the Cosmere, and I want to get into it, but I don't know if I have to read it in order to understand it all. P.S. my dad has the Mistborn books already, so if not I can get into those first.


Can the limit of a sequence of functions in $L_p$ and the limit in almost everywhere convergence be different?

I'm sure this is an easy question, but I am somewhat confused. I'm considering here a measure space $(X, \mathcal{A}, \mu)$, and the functions are real valued. Given a sequence of functions $(f_n) \in L_p$ that converges almost everywhere to a function $f$ and converges in $L_p$ to a function $g$, is it true that $f=g$ almost everywhere?


How do I disable "modern login items" (shared helper applications) which don't show up in system login items?

Spotify auto-launches even if I tell it not to from within its own preferences. It does not seem to be started through any of the "classic" means of auto starting a program - i.e. Login Items or user or global launch agents. Is there any way to turn off this sort of 'modern login items' in general? (official name: shared helper applications) Extra points for preventing auto-launching of any apps, especially after MacOS crashed.


Is it possible to define what the last hidden layer represents in a neural net?

I am trying to determine how to set up a neural net to use in a recommendation engine I am building to recommend a cheese to the user. I have a clear understanding of what the output layer represents (the probability of whether it should recommend cheese 1, 2, 3, etc) but it would be very useful to me if I could also define what the layer before it represents as the weights of each of the features of each cheese (feature 1: creaminess (scale of 0 to 1), feature 2:  saltiness (scale of 0 to 1), etc). Being able to extract this layer and have the values signify what I want them to would help me build another part of my project I'm working on. I should mention that the input to the neural net comes from a dataset of what cheeses the user has previously rated and what rating out of 5 they gave it. I understand that you can define how many layers make up the hidden layers and how many nodes are in each layer, but if I have 20 cheese features and I set the last hidden layer to have 20 nodes, I assume that definitely does not guarantee that each node represents a feature. Any help would be much appreciated. Thanks


What is the best directory to install a Bash Script?

I have developed my own Bash Script (to undo the last APT commands), and now I'm looking for the best directory to install it.  Is the /usr/bin always the best choice?  Just for information this is my script:    and this is a little demo:


Should "Catalyst" prequel novel be read before or after watching "Rogue One: A Star Wars Story" film?

"Rogue One: A Star Wars Story" film has a companion canon prequel novel, "Catalyst" by James Luceno.  Should "Catalyst" be read before or after watching the film and why?  (the question assumes that the story will be read, one way or another)


Is the text of a closed question indexed by Google's spider?

Some time ago, we had a problem with -type questions on Earth Science Stack Exchange. After some users , we closed and deleted 500 questions with some effort and we made them off-topic. We stopped coming up as the first entry for searches for "help identify my rock" on Google, and the flood of questions ended. However, we still receive some questions. We close them, but I realized that +2k users were not deleting them, so I made . I asked for help from a mod but they don't want to delete them unilaterally. My question is if we are at risk of appearing again at the top of Google searches if we don't delete them, because I am a bit tired of asking users to delete the questions. Apparently the problem is that delete votes don't put posts into a review queue and we don't have many +2k users using meta frequently. Does Google index closed questions? Should I continue battling for the deletion of these unwanted questions for this reason?


I registered my site a month ago, and appeared in google search result of focused keyword. The ranking is not so bad, my site placed in 4th~5th page when google results have 9~10 pages. But after 1 day the ranking falled 4~5 pages. So, my page appeared in 9th page. In some computers, there is no my page in SERP. Of course, I didn't take any Black-hat SEO. Is my site penalized by google? Can my site increase ranking again?


Methods to see if a polynomial is irreducible

Given a polynomial over a field, what are the methods to see it is irreducible? Only two comes to my mind now. First is Eisenstein criterion. Another is that if a polynomial is irreducible mod p then it is irreducible. Are there any others?


Can I use a correlation matrix and variances to find the covariance matrix?

I want to calculate error propagation of the non-linear $A\times B$ function, where $A=a+\sigma_A$ and $B=b+\sigma_B$ are two correlated random variables, using toy MC. I am lost as to how one finds the desired covariance matrix, assuming that $A$ and $B$ are 100% correlated, to provide it to e.g. numpy's numpy.random.multivariate_normal(mean=[An, Bn], cov=[...], size=1)  in order to sample a pair of values, and calculate a value for a product, and repeating to get the standard variation of the sample of the product values. Is this line of thinking correct, and also is it the same as sampling from two independent Gaussians and then using the covariance matrix to correlate a pair of sampled numbers?


Schengen visa from UK for Indian citizen

I am an Indian citizen holding a regular passport, can I apply for a Schengen visa from within the UK?


Are Excel formulas and Google Spreadsheet formulas the same?

I want to be sure all my Google Spreadsheet work can be converted OK to Excel. How many of the Excel formulas match the formulas of Google spreadsheets?


I have searched the web a lot and could not find an answer that fits my situation. Here are two links that are quite contradictory:       My situation:  I've visited Portugal in December 2012 for 29 days on a Schengen visa valid from December 1st, 2012 to February 1st, 2013 for research purposes (I am a Ph.D. student). I want to visit Sweden from February 10th, 2013 to May 10th, 2013 (89 days). I have applied for a Schengen visa again (for research). How will the 90/180 rule work in my situation?


I am working on a media project that contains little clips from movies and I wonder if there any way to avoid downloading all of the data instead only the specified parts of the movies?


About cases you don't use the article "the" and "a" | Would anybody be able to tell me why there is no article in this case?

I read an article of the link below:    My question is why the subject "Hong Kong protester" in the title has no article "a" and similarly the specific word "China's Communist Party" has no article "the" in front of them, even though those articles are put in front of each word in the body.  Would anybody be able to tell me why in this case?


How to display inches in the Print Composer margin guide

I can't figure out how to change the margin guides in Print Composer to inches rather than metric.   In the "Composition" tab, under "Page size" I have ANSI A (8.5 x 11 in) selected.   However, the "Units" box below that is greyed out. The "Guides and Grid" section below that only gives options in terms of "mm".   This was indicated as fixed at    However, as was noted there,  "I am having the same issue as above, and have not been able to reproduce your answer. In my installation, choosing a paper size in inches only changes the presets box. The width, height and units are all still in 'mm', and the units are locked and grayed out. – Get Spatial Oct 28 '15 at 23:13"  I am having the same experience as "Get Spatial". Does anyone have any idea why we continue to have this problem, although it seems to have been fixed for some?


If you leave something outside, its colors seem to inevitably fade or bleach due to exposure. Is this due to UV absorption? What sort of mechanism causes this - is it that man-made dyes  deform on a molecular level? Are there notable materials that are exceptions?  To turn this string of questions into a focused query, let me refer back to the title:   Why does sunlight cause colors to fade?


How do I take pictures of a mat from the top?

My mats are 6x9 feet and I want to take pictures at a perpendicular angle from the top so that it is even. As of now I am taking  pictures from the side.  Here is how I am looking to take the picture:    Here is what I'm currently doing, which I don't want:


Why does redirecting a file into itself clear its content?

I expected the last command to return "test", but it does not.  foo@bar:~/docs$ echo "test" > test foo@bar:~/docs$ cat test test foo@bar:~/docs$ cat test > test foo@bar:~/docs$ cat test foo@bar:~/docs$


Minecraft LAN not showing up after multiple attempts to fix it

I'm trying to play with my sister. I have tried the same version, same WiFi and Ethernet cable, firewall changes, nothing works. I hope someone has an answer.


Is it good for SEO to have domain alias that describes company service?

I have bought a domian that is like service.city.example Where service is eg. "haircut".  Is it good to have this kind of domains as aliases to main domain company.example?  What would be best for SEO, serving the main domain content on this alias or redirect 301 from alias to main domain?


Did someone succeeded in getting to my server?

I have a server running ubuntu 14.04. On it i have latest wordpress version on nginx. I was going trough my logs and noticed this.  198.204.224.122 - - [05/Dec/2017:13:06:10 +0200] "GET / HTTP/1.1" 200 826 "-" "}__test|O:21:\x22JDatabaseDriverMysqli\x22:3:{s:4:\x22\x5C0\x5C0\x5C0a\x22;O:17:\x22JSimplepieFactory\x22:0:{}s:21:\x22\x5C0\x5C0\x5C0disconnectHandlers\x22;a:1:{i:0;a:2:{i:0;O:9:\x22SimplePie\x22:5:{s:8:\x22sanitize\x22;O:20:\x22JDatabaseDriverMysql\x22:0:{}s:5:\x22cache\x22;b:1;s:19:\x22cache_name_function\x22;s:6:\x22assert\x22;s:10:\x22javascript\x22;i:9999;s:8:\x22feed_url\x22;s:54:\x22eval(base64_decode($_POST[111]));JFactory::get();exit;\x22;}i:1;s:4:\x22init\x22;}}s:13:\x22\x5C0\x5C0\x5C0connection\x22;i:1;}\xF0\x9D\x8C\x86"   I looked around the internet and i found that it use to be joomla problem but im still worried because i see that that request was handled with status code 200. Later on i noticed this happening in my logs     162.158.92.173 0.058 - [05/Dec/2017:13:35:13 +0200]   "GET /wp-admin/users.php HTTP/1.1" 200 10389 " /wp-admin/update-core.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.002 - [05/Dec/2017:13:35:13 +0200]   "GET /wp-admin/load-scripts.php?c=1&load%5B%5D=hoverIntent,common,admin-bar,svg-painter,heartbeat,wp-auth-check&ver=4.9.1 HTTP/1.1" 200 12580 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.035 - [05/Dec/2017:13:36:14 +0200]   "POST /wp-admin/admin-ajax.php HTTP/1.1" 200 78 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.033 - [05/Dec/2017:13:37:15 +0200]   "POST /wp-admin/admin-ajax.php HTTP/1.1" 200 78 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.030 - [05/Dec/2017:13:39:16 +0200]   "POST /wp-admin/admin-ajax.php HTTP/1.1" 200 78 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.028 - [05/Dec/2017:13:41:17 +0200]   "POST /wp-admin/admin-ajax.php HTTP/1.1" 200 78 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.033 - [05/Dec/2017:13:43:18 +0200]   "POST /wp-admin/admin-ajax.php HTTP/1.1" 200 78 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.031 - [05/Dec/2017:13:45:19 +0200]   "POST /wp-admin/admin-ajax.php HTTP/1.1" 200 78 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.030 - [05/Dec/2017:13:47:28 +0200]   "POST /wp-admin/admin-ajax.php HTTP/1.1" 200 78 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.060 - [05/Dec/2017:13:47:29 +0200]   "GET /wp-admin/users.php HTTP/1.1" 200 10389 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   162.158.92.173 0.029 - [05/Dec/2017:13:48:30 +0200]   "POST /wp-admin/admin-ajax.php HTTP/1.1" 200 78 " /wp-admin/users.php" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/62.0.3202.89 Safari/537.36 OPR/49.0.2725.47"   Should i be worried ? By the way i am running fail2ban however i have cloudflare aswell which makes it harder for me to ban the ips.


Random question du jour, inspired by the thoroughly depressing airport Holiday Inn I'm writing this in due to a missed flight connection:  Why don't American hotels have ceiling lights?  Every chain hotel I've ever stayed at has instead had a motley assortment of bedside, table and floor lamps.  What's more, instead of a single master light switch, there are individual switches/knobs to turn them on and off located next to the bulb, on the cable on the floor, on a switch on the side, etc, so you get to fumble around when turning them on and once more when turning them off.  And yes, I'm sure there are exceptions, but no, that doesn't make "you're wrong, I stayed at Motel Z in Bent Arm Pit, Wyoming once and they had a ceiling light!" an answer.  I'm curious about the reason why: Lower ceilings so cheaper to build?  Easier/cheaper to maintain?  Fire code?  Something else?


How can I properly display German characters in HTML?

My pages contain German characters and I have typed the text in between the  HTML tag, but the browser views some characters differently. Do I need to include anything in HTML to properly display German characters?  <label> ausgefüllt </label>


Story about relearning basic/advanced math/physics after (possibly apocalyptical) event

There is some event which leads to a general loss of knowledge, and the story involves (or at least includes) a person or a group relearning such knowledge, mostly math and physics. I heard about it in the 90's but it's probably much older than that (though surely 20th century). Edit: sorry about the lack of details (although I think Michael got it right; I'll mark it as the correct answer). It's a written, most likely short story, which a teacher described to me a couple of decades ago. I realize it was very little to go by but this had been nagging me for years.


Keyboard and mouse unresponsive after suspend

I have a Toshiba Satellite S55-A5154 with 14.04 installed.  Every time it resumes from being suspended, neither the keyboard nor mouse work.   What can I do to fix this or provide you with more info?


How to reduce the gaps between words in a reference entry

I am using the Easy Thesis template to write my thesis. I find one of my reference entry contain huge gaps between the words. .   I am using natbib bibliography style. How I can reduce or condense the empty gap between words?


I'm working on the following problem:     Prove that $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic as groups.   Here is my attempt at a solution:  If $\mathbb{Z} \cong \mathbb{Q}$, then there must exist a bijective homomorphism $\varphi: \mathbb{Z} \to \mathbb{Q}$. Consider $\varphi(x) = x$. Clearly, this is a homomorphism as it is the identity map. Moreover, it is also clearly injective. However, it fails to be surjective since there exist elements of $\mathbb{Q}$ that are not mapped to by $\varphi$ (like $3/2$ or $1/4$). Hence, since $\varphi$ is an injective homomorphism, but not surjective, we see that there cannot exist a bijection between $\mathbb{Z}$ and $\mathbb{Q}$. Thus, $\mathbb{Z} \not \cong \mathbb{Q}$.  Could anyone critique this solution? Am I on the right path?


How can I brighten up blue directories in ls --color?

I see one other   with the same problem:  Instead of two kinds of blue (normal and bright/bold) I have only one, very hard-to-read so-called "bold blue". Normal blue is even worse, almost invisible.   I don't want to change LS_COLORS. I do want directories in blue, but in a brighter one. I don't want them in magenta or green.  In dircolors' output I see dozens of extensions (tar, tgz, mp3) coding for bright red or magenta. And something as fundamental as a directory gets completely lost in it's midnight blue!    It is already set to bright:  `DIR 01;34 # directory`   or with dircolors -b:    LS_COLORS='...di=01;34...'   In XTerm I can set *VT100*color12: SkyBlue2 in the app-defaults/ file. But for the console? The kernel only gives me 16 predefined ANSI colors!  Do I have to recompile the kernel to change these RGB definitions for the console? This navy blue must be coded somewhere!     /* added after 1st answer */  I tried echo -en "\e]PCrrggbb" as proposed: this works! This is really special - the bracket is the other way round. And "should be OSC" in the man page...thank you!   The link in dirkt's answer also has setvtrgb as a second solution. Number salad, but no escape codes.    Do these two methods amount to the same?


Downloaded Ubuntu, no dual boot, can't access Windows

I installed Ubuntu following the partition tutorial and everything seems fine except I seemed to have lost Windows. I can still see it in GParted, but there is no dual boot menu + I can't seem to get to it in any way.   I tried boot repair but no improvement. .  My System: HP Envy Spectre 14, 4GB i5, 128SSD, F9 Boot Manager, F10 Bios   Partition, File System, Mount, Label, Size, Used, Flags   /dev/sda1, ntfs, system reserved, 100MiB, 26.10MiB, Boot /dev/sda2, ntfs, 95.37GiB, 47.53GiB /dev/sda4, extended..20.99GiB.. /dev/sda5, ext4, /, 18.99GiB, 4.61GiB /dev/sda6, linux-swap, 2.00GiB, 4.00KiB, diag unallocated, unallocated, 2.01GiB


Is it safe charging a Galaxy Nexus through a USB 2A port?

This is a newbie question. While travelling, I need to recharge my Galaxy Nexus and my digital camera, both of which are meant to be charged through a micro-USB port, ie. 0,5A.  To reduce charging time, I have an 1A AC adaptor but it only has a single USB port.  Google shows a number of two-port AC adaptors:   one port is 1A, the other is 2,1A (it looks like Apple devices expect 2,1A)  delivers 2A when using a single port, but 1A when using both ports   In case I only need to charge a single device, is it safe to have it fed 2 or 2,1A? I read that a device only uses the intensity it needs, but will it fry if it's fed too much intensity?  Thank you.


Passing option constants as arguments to a class

I have a Python class that takes an arguments to set the state of an object. This argument must be one option in a list of available options; for example, a traffic light can either be red, green or orange.   I have two approaches to handle this problem. I can use a string to set the state, but then I'll have to do additional error checking and it is unclear without looking at the code what states are available. Alternatively I can create a class that acts as an enum.   Which of these methods (or what other method) should I use?  Example with strings:  class Light(object):      def __init__(self, color):         self.color = color      def turn_on(self):         if self.color == 'red':             self.turn_on_red_light()         if self.color == 'green':             self.turn_on_green_light()         if self.color == 'orange':             self.turn_on_orange_light()      def turn_on_red_light():         # do stuff         return      def turn_on_green_light():         # do stuff         return      def turn_on_orange_light():         # do stuff         return  light = Light('red') light.turn_on()   Alternative using simple "enum":  class Colors(object):     red, green, orange = range(3)  class Light(object):     def __init__(self, color):         self.color = color      def turn_on(self):         if self.color == Colors.red:             self.turn_on_red_light()  # as above         if self.color == Colors.green:             self.turn_on_green_light()  # as above         if self.color == Colors.orange:             self.turn_on_orange_light()  # as above  light = Light(Colors.red) light.turn_on()   Maybe this is not the best example as you can just call light.turn_on_red_light(), but then that logic to decide what function to call must sit somewhere else. Let's pretend that is not an option.  I come across this situation often. Frequently I use it to define 'settings' within the class. I'd be interested to know what is the preferred method in Python or any other ways it can be improved?


Find two elements that don't have a gcd in a subring of Gaussian integers

Find two elements in the domain $R := \{ x + 2y \sqrt {-1} \mid x,y \in \mathbb{Z} \}$ that do not have a gcd.     I have no idea how to start. But I know if we consider $R^\prime = \{ x + y \sqrt {-1} \mid x,y \in \mathbb{Z} \}$ then every two elements have a gcd. So there must be something wrong with the 2 here.  Any help is appreciated.


Canon 5d mk iv - Problems setting the speed to faster than 1/200th when I have my speedlite attached

5d mk iv - Problems setting the speed to faster than 1/200th using both Manual or TV when I have my speedlite attached. Totally confused as I can't figure out why I'd be limited to that or how to change it. I've looked at the manual and it's says High speed sync is possible but doesn't say how????  I was shooting a fashion show today indoors and really needed a faster speed for bits of it??   Any help would be appreciated :)


Why does half of my question not show in the preview?

When I post, half of my question isn't shown. Why is this?


I'm using drupal 6, I wanted to give feed back on a simple quiz (that is answered during user registration - to be a profile field).  I made a template for the profile page: user-profile.tpl.php  And the code (at the bottom of the page) works fine, but it doesn't work when I try the same code in the template(for the specific block I want): block-block-10.tpl.php  I added this function to template.php, to (TRY) make $account avaialble to block-10  function blockaccess() { // access globals   global $account; global $node;  }   What do I need to change?  the code in block-block-10.tpl.php:
     <?php      blockaccess();     dsm($node);     dsm($block);     dsm($account);   $correct_ans = "3) I'm from Spain.";   $quiz_ans = $account->profile_quizoffer_ans;   print $quiz_ans;   print "--------------------------------------------
";   print '
チラシの裏のクイズ:

Q: Where are you from?	Result
';    if ($quiz_ans == $correct_ans) {     print '

';     print $quiz_ans;      print '

CORRECT

You passed the quiz!
';    }   else {     print '

';     print $account->profile_quizoffer_ans;      print '
INCORRECT

You didn'."'".'t pass the quiz!

The correct answer was:	';     print $correct_ans;     print "
"  ;    };   print "
"; ?>


Can SQL Server's Page Life Expectancy be too high?

I've read several articles about SQL Server's Page Life Expectancy and what it means and what kind of information you can glean from it. In most of these articles that I've read, a common, healthy PLE value is somewhere around 1000-2000 seconds. I've read that getting down to around 300 seconds can mean you're likely low on RAM.  I recently just upgraded our hardware to have 64GB of RAM, up from 14GB. On the 14GB my PLE was around 300 seconds, and I was having a lot of 5-6 memory grants pending per second. So, that was bad and I increased the RAM. Now, my PLE is much, much higher around 5000 seconds, and no more pending memory grants. I've seen it 7000 seconds, if I recall. This is much higher than anything I've read.  Can a high PLE be a bad thing? Or is it the higher the better?  EDIT: I'm sorry, my PLE wasn't 7000 seconds, it was 70,000 seconds! Although, at the moment it is down to around 7000.     The database size is around 160GB. A few tables have 5+ million rows. max_server_memory is set to 2147483647.


I want to remove a few steps in the approval process. You may refer to the images that I attached here. The actual process, once user click return shipment approval/reject button from page 1, page 2 will come out, user can click either yes or no. Then user will go to page 3, then after click on Approve/Reject Record, page 4 will come out. What I want to do is, once user click on page return shipment approval/reject button from page 1, the user will go to page 4 directly without go to page 2 or 3. Is there any idea on how to do that?


As a retention incentive, I was granted stock (about $60,000) in my employers privately owned company.  The stock grant went through payroll in December and had FICA taken out but no income tax. I anticipate a huge tax bill when I file ($20,000+).  Is the IRS going to clobber me for this? Will I have penalties for not paying quarterly taxes or be forced to pay quarterly taxes this year even though this was a one-time thing? Should I do anything now or handle it all when I file?


Is there a possibility to assign existing nodes as translation of a node?  Cause i migrated a lot of content from a D6 instance. On D6 and D7, it was easy to assign the translation nodes but in D8 it seems not to have that possibility. I also didn't found any modules which helps.  Any advice?


I need shapefiles of Indian states that of 2011 which has almost 671 districts of India. Can anyone please help me?


Create hotspot using CLI only - ubuntu 14.04

I saw many howto's for creating a hotspot in Ubuntu 14.04 (in AP mode) using system settings. They are perfect.   How do I create a hotspot using only command line however?   I tried messing around with eth0 and eth1 but I did not get anything at all.   (The same question has been asked some months ago, but it was not answered).


Why don't wizards adopt or copy Muggle technology generally?

asked why wizards couldn't use firearms to defeat Death Eaters. There are a variety of answers, but the lurking question there, I think, is why the wizarding world doesn't adopt certain everyday Muggle technologies (or make a magic-based equivalent) that would make their life easier. Some examples that come to mind are:   Pretty much anybody who needs to write anything uses a quill, an inkwell, and parchment, despite the fact that this is inconvenient compared to a ballpoint pen and regular printer paper. When wizards go shopping, they have to carry a satchel with coins minted out of precious metals, instead of using a more convenient fiat currency (banknotes, small coins minted out of inexpensive metal). Perhaps wizards have decided that they really want their currency backed by a physical commodity, but then, it would be easier to create the magical equivalent of a debit/credit card, which would magically transfer an agreed amount of gold from the buyer's vault to the seller's without having to physically carry the gold into the shop. Certain basic safety features on magical equipment. For example, a child-lock on wands, so that kids don't go out casting spells they are not qualified to use (remember that Harry Potter nearly killed Draco Malfoy because he used a spell he didn't understand), or the equivalent of an "are you sure?" dialog box on the floo network, to ensure that you don't send yourself to the wrong destination. The magical equivalent of an e-book reader: a single piece of parchment that displays pages of whatever books you have "downloaded" into it. Again, it sounds more convenient for students than having to lug large books around.   What strikes me is that wizards are actually quite adept at creating magical equivalents of muggle technology when the plot demands it. There are various occasions where two people on separate locations talk to each other through fireplaces, which is clearly the magical counterpart of Skype. The coins that Dumbledore's Army uses to communicate are effectively equivalent to having push notifications from a newsgroup into your smartphone.


Do we need email for bounties that can't be awarded?

I got me an email for a bounty that was going to expire in 23 hours, so I went to see if I could award it.  It turns out  has only been answered by myself, so I can't award a bounty.  Which means the email was essentially spam.  (Or if you prefer, one more worthless automated reminder of the type that I train my spam filter to hide from my inbox.) It's bad enough that my bounty will expire worthless—does the system really need to get my hopes up that an answer arrived only to dash them when I actually follow the link in the email?  Could the system add one more check to see if a bounty could be awarded before encouraging users to go out and award it?  For reference, here is the text of the email minus emphatic formatting:  Reminder: Your Bounty Is Ending Soon! Your bounty on the question … Option to disable “share a link to this question” popup? … ends in 23 hours. Don't forget to review the answers and award your bounty by clicking the bounty icon to the left of each answer. If you don't award your bounty, the highest scored answer (with a minimum of 2 score) provided after your bounty started may be automatically awarded half the bounty amount! For more information, refer to the bounty faq. Questions? Comments? Let us know on our feedback site. If you no longer want to receive mail from Meta Stack Overflow, unsubscribe from all Meta Stack Overflow emails with a single click. Stack Exchange Inc. 55 Broadway, 26th Floor, NY NY 10006 <3


Find index position of characters in string

I am trawling through a storage area and the paths look a lot like this:  storagearea/storage1/ABC/ABCDEF1/raw/2013/05/ABCFGM1   I wont always know what year is it. I need to find the starting index position of the year   Therefor I am looking for where I find the following in the file name (2010, 2011, 2012, 2013, 2014 etc...)   I have set up a list as follows:  list_ = ['2010', '2011','2012','2013','2014', '2015', '2016']   and I can find if it is in the file name  if any(word in file for word in list_):      print 'Yahooo'   But how do I find the character index of the year in the absolute path?


How can I monitor all and any Internet traffic from my home PC?

I would like to monitor all and any Internet traffic from my home PC to see what programs installed on my home machine are accessing the Internet.  I thought I could use  for this, but I noticed Firefox traffic doesn't show up by default; you need .  What options do I have to monitor all traffic?


Android My Sites edit screen rendering incorrectly

It appears that the edit my sites screen has some problems. I am able to add and remove sites, but I can't move them up or down, and only one is visible at a time.      App Version: 1.0.85 Device Manufacturer: motorola Device Model: MotoG3   OS Version: 6.0 (28)


How soon can I re-enter the USA having stayed for 90 days under the Visa Waiver Program?

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


If an object with more mass experiences a greater gravitational force, why don't more massive objects fall faster?

According to Sir Isaac Newton, the gravity equation runs like this:  $$ F = \frac{Gm_1m_2}{r^2} $$  where $F$ is the gravitational force, $G$ the gravitational constant, $m_1$ and $m_2$ are the respective masses of two bodies being pulled together by said force, and $r$ is the distance between them.  Now Galileo asserted that regardless of the difference in mass of two objects falling onto Earth, their acceleration rate will always be the same, i.e. 9.8 meters per second squared.  Question:  Is this actually true?  It is clear from the above equation that the larger the object's mass (either of the $m$'s), the greater the force ($F$).   In other words, should we leave the distance ($r$) the same but increase the mass of either object, the force ($F$) would increase proportionately, resulting in a greater acceleration rate. Which was what Aristotle and everyone else after him thought until Galileo decided Aristotle was wrong and proved it by throwing two different objects from the tower of Pisa. They hit the ground at the same time: yes. So far as the naked eye could judge, anyway.   To clarify:    Compared to the Earth's mass, the masses of the two objects would have been so small that any difference in their respective acceleration rates would have been too tiny to detect, i.e. NEGLIGIBLE.  In other words, to all, or most, PRACTICAL (i.e. earth-based) purposes, Galileo was right.  But was he TECHNICALLY right?  Einstein's theory states that gravity and inertia are the same exact force. This strikes me as perfectly reasonable. However, it is asserted that this somehow confirms Galileo's conclusion. I don't see how.   Please explain.


I recently bought the nikon 50mm 1.8 af-s lens. I bought a uv filter for it. It was a "multi-coated" filter, but when I put it on, the first thing I noticed was that it causes reflections. I returned it. Now I'm wondering what is a good UV filter for this lens?


Some images shown outside of preview rectange before uploading, eg:


Verbose details shown during boot of Ubuntu 18.04

I'm using Ubuntu 18.04 LTS.  My system boots properly and works fine, but during boot, I can see the verbose details about what is happening during the boot process:     Is this supposed to happen?  Can it be changed?


What was the origin of the meme where Batman slaps Robin?

I have seen the meme of Batman slapping Robin so many times. I really want to know the origin of it. When did it occur in the comics, and why did he even slap him?  Note: Spoilers are welcome.


Difference between the new Salesforce Platform Developer 1 certificate and the old Developer certification DEV-401

I'm a little bit confused about the new Salesforce Platform Developer I certificate. Is it a replacement of the old developer certificate (DEV-401)? If so, does DEV-401 certified developers need to pass the new one to be recognized as Salesforce developers?  The same applies to the new Platform Developer II. Does it replace DEV-501?  Thanks!


Which is the correct heading? What StackOverflow does. or  What StackOverflow do.


Unable to install android studio ubuntu 17.10

From terminal unable to locate package error. I have already added repository.


To get an arrow white inside and black border

I need your support to draw an arrow like this in Tikz. White inside, black border. I’d like to insert it between two nodes and change the length, width and head extend. Accordingly with the distance. I got this once \draw[-{Triangle[width=8pt,length=5pt]}, line width=3pt] (bloco2.east) -- (bloco3.west); but I can’t fill it in white. I would be grateful for easy solutions. Thanks!


There should probably be an Ant keeping Stack Exchange, as we would probably get more traffic, because there are many Ant keeping forums out there, but they all seem to be outdated, while Stack Exchange stays alive. I'm sure there are a lot of ant keepers out there who could be helped by other ant keepers and ant experts, and the Stack Exchange community in general.   If this request is denied, could anyone please link me to a good Ant keeping forum where I could post my questions?


My Ubuntu has been running pretty slow, but I don't know why. I have the latest updates and all. I installed Ubuntu i368 on a AMD processor does that effect the speed?  Thank you.


What's the difference between [[False] * 26] * 26] and [[False] * 26 for _ in range(0, 26)]?

What's the difference between [[False] * 26] * 26] and [[False] * 26 for _ in range(0, 26)] in Python ?


$a, b,c $ are positive real numbers such that $a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$  Any ideas ?


What is the difference between test set and validation set?

I found this confusing when I use the neural network toolbox in Matlab. It divided the raw data set into three parts:   training set validation set test set   I notice in many training or learning algorithm, the data is often divided into 2 parts, the training set and the test set.  My questions are:   what is the difference between validation set and test set?  Is the validation set really specific to neural network? Or it is optional. To go further, is there a difference between validation and testing in context of machine learning?


Why is average velocity the midpoint of initial and final velocity under constant acceleration?

Since average velocity is defined as$^1$ $$\vec{\mathbf v}_\mathrm{av}=\frac{\vec{\mathbf x}-\vec{\mathbf x}_0}{t-t_0},$$ where $\vec{\mathbf x}$ denotes position, why is this quantity equal to $$\frac{\vec{\mathbf v}+\vec{\mathbf v}_0}{2},$$ where $\vec{\mathbf v}=\frac{d\vec{\mathbf x}}{dt}$ and $\vec{\mathbf v}_0=\left.\frac{d\vec{\mathbf x}}{dt}\right|_{t=t_0}$, when acceleration is constant?  What in particular about constant acceleration allows average velocity to be equal to the midpoint of velocity?  $^1$: Resnick, Halliday, Krane, Physics (5th ed.), equation 2-7.


openssl installation - `/bin/` directory missing

I was following     It worked when I tried it on a VM (running ubuntu). But while executing on my actual machine, I noticed, my /bin/ folder is missing.  root@akki-X555LAB:/usr/local/ssl# ls certs  misc  openssl.cnf  openssl.cnf.dist  private     The command I was trying to execute was:  ln -s /usr/local/ssl/bin/openssl /usr/bin/openssl   I was simply following the commands in that link and don't understand what went wrong! For reference:  root@akki-X555LAB:/usr/local/ssl# openssl version openssl: error while loading shared libraries: libssl.so.1.1: cannot open shared object file: No such file or directory


A friend of mine just asked me how to prove that if $a=b$ then $a+c=b+c$, where $a,b$ and $c$ are real numbers, I'm not sure what I should answer. I have a book called introduction to logic and to the theory of the deductive sciences by Alfred Tarski, which is about propositional logic, and I remember reading that two things $a$ and $b$ are equal if any proposition that is true about $a$ is also true about $b$ and vice-versa. However I think this isn't very formal.  I haven't taken any set theory course, I think that another way to justify it is to say that sum is a function and since the ordered pairs $(a,c)$ and $(b,c)$ are equal then $+(a,c)=+(b,c)$. But I'm not too convinced.  If we use the standard axioms how would we justify $a+c=b+c$ using the mainstream axioms of today. I think there is something Zermelo-Frankl with choice. Would these be enough, what properties of the real numbers do we need? Can we prove it using the usual construction of the real numbers and Zermelo-Frankl?   As you can probably see I am not very knowledgeable about these topics, so I would like a delicate explanation.  Many thanks and regards.


If $f:[a,b] \rightarrow R$ be continuous , let $f(x) =0$ when $x$ is rational. Prove $f(x) =0$ for all $x$ that is an element of $[a,b]$.   Thanks for the help I can't seem to find the f[a,b] notation in my notes and it is throwing me off.


How to unfocus a file using keyboard on Windows?

This is my folder:    This is how it looks like when I press the menu key on my keyboard just after opening the folder:    As you can see above, it is the same menu that we get when we right click the mouse on any empty (white) place in the folder.  This is how it looks like when I press my cursor keys after opening the folder:    This is how it looks like when I press the menu key on my keyboard in this state:    Now my question is, is there any way to go to the state at the 1st picture from the state at the 3rd picture by only using the keyboard? Alternatively, going from picture 3 to this is also acceptable:


Check what package provides a debian dependency

There are some such packages that are not actually available from the repository, but are instead "Provides" provided by other packages.  For example, packages may depend on libc-dev, but (at least in my case) libc-dev is provided by libc6-dev.  Is there way to check which package provides some other package/dependency?


E:Type 'sudo' is not known on line 53 in source list

I have done some looking around for a solution. However, I have come to the conclusion that the solution to my problem is just not on the internet. I am unable to update Ubuntu and download apps from the Software Center due to an error on line 53. Here is what is on line 53.   sudo apt-key adv --keyserver pool.sks-keyservers.net --recv-key   Is this line scripted correctly? If not, what should be on this line?


I was reading this answer by @dessert:  about how to delete old backup folders from directory using cron in Ubuntu. The command given was:  find /BACKUPDIR/ -mindepth 1 -maxdepth 1 -type d -print0 | sort -z | head -zn-6 | xargs -0 echo rm -rf  However, CentOs 7 doesn't like the z flag in his call to head:  head: invalid option -- 'z'  Is there a work-around for CentOs7?  I took a look at:  I don't think this explanation is applicable to my question. I don't see how I would change my command if I want to delete backups older than n.


Will database replication increase the size of the replicated database?

We have a SQL Server database that was assigned to be replicated. the original size of the database was 5 GB for the datafile, not the log file. Now after the replication the data file is 4 times bigger around 19 GB. Any pointers to see what could happened will be appreciated. I know SQL as developer and some little management but nothing about replication. The performance of the database has been damaged very bad so I am trying to see what need to be done to improve it.


How can I find out what happened to my Debian box?

I have an old PC lying around which I've installed Debian 6.0 on.  Last night I was trying to SSH in and it wouldn't respond so I pressed the reset button.  How can I find out what happened to it?  It seems fine now.


Is it possible to get the information for a device tree using /sys of a running kernel?

Commonly for arm systems, device trees supply hardware information to the kernel (Linux). These device trees exist as dts (device tree source) files that are compiled and loaded to the kernel. Problem is that I do not have access to such a dts file, not even to a dtb file.   I have access to /sys and /proc on the machine and I wanted to ask if that would allow me to "guess the correct values" to be used in a dts?  Also potential answer could highlight additionally the aspect if the answer to this question also depends on whether the device tree interface was used in the first place (i.e. a dtb was created and provided to the kernel) instead of some more hacking "we simply divert from vanilla and patch the kernel so as to solve the device information problem for our kernel only"-solution?


Specific newcolumntype (for 'R') not working?

Could someone kindly explain why the following works:  \documentclass{article} \usepackage{tabular} \newcolumntype{C}[1]{>{\centering}m{#1}} \newcolumntype{L}[1]{>{\centering}m{#1}} \begin{document} \begin{center}   \begin{tabular}{ | L{3cm} | C{3cm} | r | }     \hline     A & B & C \\ \hline     1 & 1 & 16384 \\     \hline   \end{tabular} \end{center} \end{document}   But if I try to include the following, it fails(?):  \newcolumntype{R}[1]{>{\centering}m{#1}}   Many thanks


Switching between Devanagari script and italicized Roman script

I am making a document in which I would like have text in Devanagari script and italicized Roman script interspersed amongst one another.  If my Devanagari font had an italicized Roman font, I would use that, but it doesn't have one.  So, outside of finding a Devanagari font that includes italicized Roman script, which I haven't been able to do, I will have to switch every few words between fonts, which isn't very practical.  Is there an easier way to switch between a Devanagari script and another Roman font whose italicized script I can use?


Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction

I recently proved that  $$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k \right)^2$$  using mathematical induction.  I'm interested if there's an intuitive explanation, or even a combinatorial interpretation of this property. I would also like to see any other proofs.


Allow disabling all the annoying popovers on SE sites

Today I tried to look up a question on Stack Overflow. I had two popovers on the page, one inviting me to take a short survey (which didn't even load!) and one inviting me to learn how the review queue works. In addition, the GDPR cookie consent dialog doesn't seem to remember its settings, and reappears periodically. Perhaps it's using the old "only remember the setting properly if it was 'Accept All'" dark pattern? This visual clutter makes the site less usable. Please don't keep going down the road of "every other site spams people with popovers so it's OK for us to do it". It's not. There should be an easy way to turn off all this intrusive rubbish and just show the question, the answers, the answer box, and the linked/related/hot network questions — and this method should be configurable even when logged out (if I'm linked to an SE site I don't normally participate in, I shouldn't have to log in just to have a usable experience). Ideally, every site would be a subdomain of stackexchange.com so people could set one set of overrides in a custom stylesheet, or configure their adblockers once, and the work needed at the SE end would be to continue not using randomly-generated class names and IDs in the CSS. But I don't suppose there's much appetite for moving SO to stackoverflow.stackexchange.com :)


Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time?   PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass make space-time always curve concavely?


Accidentally unchecked Unity in system settings - blank desktop?

Accidentally unchecked "unity" in system settings. Now my Ubuntu 11 boots into a "desktop background only" screen. no panels, no icons. Although I was able somehow to invoke Nautilus.  any way I can launch the system settings process and change that? or am I doomed to format my machine and re-install everything?


How are file types known if not from file suffix?

I would like to know how file types are known if filenames don't have suffixes.  For example, a file named myfile could be binary or text to start with, how does the system know if the file is binary or text?


For Hamiltonian Monte Carlo, why does negating the momentum variables result in a symmetric proposal?

I have been going through Radford Neal's . However, there is one detail that I'm really obsessing with now, and I'm not sure if I'm thinking about it right. When describing the Metropolis step for HMC, which is needed for computer implementation, he says:     The negation of the momentum variables at the end of the trajectory makes the Metropolis proposal symmetrical, as needed for the acceptance probability above to be valid   However, I cannot figure out why negating momentum variables means the proposal is symmetric. To be clear, here's my understanding of things:   Define a proposal $f(s_2|s_1)$ which indicates the density of starting at state $s_1$ and then getting $s_2$ as the proposal, which we then check for acceptance using MH. In many cases, we want the proposal to be symmetric so the MH test reduces to the Metropolis test. One way to do this is with a Gaussian proposal, so define $f(s_2|s_1)$ as sampling from a Gaussian with fixed variance, centered at $s_1$. Then since Gaussians are symmetric, $f(s_2|s_1) = f(s_1|s_2)$. With HMC, we have the following steps when starting from $(q,p)$: (1) sampling momentum variables, typically Gaussians, (2) run $L$ leapfrog steps to update both variables, (3) negate the momentum variables at the end to get our final proposed state $(q^*,p^*)$. Here, I'm using Radford Neal's notation about the state of the system, with $q$ as position and $p$ as momentum.   OK, so now I need to know why the proposal is symmetric. I suppose I need to understand these points:   I think the leapfrog steps are "deterministic" after the sampled momentum variables (unless we're injecting stochasticity in computing the derivatives). Does this mean that the probability of starting at a given state and then simply applying leapfrog steps (assume no sampling of momentum variables) until we land at a later state, is one? So it's a delta distribution, really. But then what happens when we sample those Gaussian momentum variables. Don't they impact the proposal probabilities? I do not know how to analyze this when you include the leapfrog steps. Neal also discuss reversibility, conservation of Hamiltonian, and volume preservation of Hamiltonian Dynamics. I think I need to better understand how reversibility and volume preservation mean we can claim the proposal is symmetric. (Conservation of the Hamiltonian I think is used to show that in theory, $H$ should have the same value, but in computer implementation it doesn't.) Unfortunately I seem to have a roadblock here.   Thanks for your time!


How can I drive 12v LEDs from my Arduino Nano?

Background I am building a scale RC helicopter and ordered a bunch of 3mm LEDs to give it some nice navigation and strobe lights which I plan to drive with an Arduino Nano. Problem is that I goofed and didn't notice that the LEDs are 12v until they arrived.  I know that the Arduino Nano can accept 12V on pin 30, but I think the voltage output on any of the "D" or "A" pins is always 5v (correct??). Question If the voltage output of the Arduino pins is 5v, then how can I drive the 12v LEDs using the Arduino, or is it impossible?


Why is the word 'number' abbreviated to 'No.' in UK English and '#' in American English?

Why the disparity? And why use 'No.'? Is it from the French?  And the hash or pound sign seems a weird choice too, is there a history or any reason involved?


Setting Visualforce Page url parameters within standard page layouts

What is the best (or preferred method) of setting a url parameter on a visualforce page embedded on a standard layout page?    This is easy to do when creating a custom link or a button, but I don't get how to do this on page load via the Apex Controller for the page.   When using a custom button you can do something like /apex/MyPageName?parameter=value  Can I use something like this?   ApexPages.currentPage.getParameters().put('Id',myId)


How to find the value this sum converges to?$\sum_{n=0}^{\infty}n·\frac{3^{n-1}}{4^{3n+1}} $

How to find the value this sum converges to?$$\sum_{n=0}^{\infty}n·\frac{3^{n-1}}{4^{3n+1}} $$ I've no clue how to simplify $ \frac{3^{n-1}}{4^{3n+1}} $ so if you could help me with that I could do the rest by myself so any hint would be appreciated.


Can't retrieve data from database spring boot

I have a mysql database and I added two entries in the table TvSeries. But I can't retrieve the the entries. Below are my Model Class, my Repository Class, my Service Class and the main method where I've tried to retrieve the information.  import javax.persistence.*; import javax.validation.constraints.NotEmpty; import javax.validation.constraints.NotNull; import java.util.ArrayList; import java.util.List; import java.util.Set;  @Entity public class TvSeries {     @Id     @GeneratedValue(strategy= GenerationType.IDENTITY)     private Integer id;      public Integer getId() {         return id;     }      @NotNull     @NotEmpty     private String title = "";      private String description = "";      @NotNull     @NotEmpty     private int noOfSeasons;      public String getTitle() {         return title;     }      public String getDescription() {         return description;     }      public int getNoOfSeasons() {         return noOfSeasons;     }      @ManyToMany(mappedBy = "watchedSeries")     Set<User> watches;      @OneToMany(mappedBy = "tvSeries")     List<Episode> episodes = new ArrayList<>();      @Override     public String toString() {         return "TvSeries{" +                 "id=" + id +                 ", title='" + title + '\'' +                 ", description='" + description + '\'' +                 ", noOfSeasons=" + noOfSeasons +                 '}';     } }   import com.example.tvseriestrackingwebapp.backend.models.TvSeries; import org.springframework.data.jpa.repository.JpaRepository; import org.springframework.stereotype.Repository;  @Repository public interface TvSeriesRepository extends JpaRepository<TvSeries, Integer> { }   import com.example.tvseriestrackingwebapp.backend.models.TvSeries; import com.example.tvseriestrackingwebapp.backend.models.User; import com.example.tvseriestrackingwebapp.backend.repositories.TvSeriesRepository; import org.springframework.stereotype.Service;  import java.util.List;  @Service public class TVSeriesService {     private TvSeriesRepository tvSeriesRepository;      public List<TvSeries> findAll() {         return tvSeriesRepository.findAll();     }  }    public class TvSeriesTrackingWebApplication {      public static void main(String[] args) {          SpringApplication.run(TvSeriesTrackingWebApplication.class, args);         TVSeriesService tvSeriesService = new TVSeriesService();         Iterator itr = tvSeriesService.findAll().iterator();         while (itr.hasNext()) {             TvSeries tvSeries = (TvSeries) itr.next();             System.out.println(tvSeries);         }     }  }   Also, I'm getting the java.lang.NullPointerException error and I think it's because there aren't any elements in the table.


How do I figure out the right size font / text for a given read distance?

To avoid printing single letters at varying sizes and measuring how far away I can see it from a distance is there a formula for determining what size font for a particular read distance? Is it better to take the midpoint between the ascender line and x-height or to go purely off of the x-height (since going purely off the ascender line could leave lowercase letters difficult to read)? How does vertical height play into this? Would I need to then figure the hypotenuse distance instead of a straight distance?  For example if I'm shooting for a 20' read distance but the sign is to be placed about 30' up should I use a distance of  35' instead of 20'?  I'm shooting for a 20' read distance for the headline and then possibly a 10' read distance for additional content depending on how it all fits on the active area.


The expected value of log Gamma function

Suppose $X$ is exponentially distributed with the rate parameter $\lambda$. If we have the expected value of $\log X$ as \begin{equation} \langle \log X\rangle=-\gamma-\log\lambda \end{equation} where $\gamma$ is the Euler–Mascheroni constant. Now I am wondering how I can compute a lower bound for $X\log X-\log \Gamma(X)$ since this is a concave function? I originally wanted to compute the following integral \begin{equation} \langle \log \Gamma(X)\rangle=-\exp(-\lambda X)\log\Gamma(X)+\int \psi(X)\exp(-\lambda X)\mathrm{d}X \end{equation} where $\psi(X)= \frac{\mathrm{d}}{\mathrm{d}X}\log \Gamma(X)$. I came across  which they are tackling more and less the same problem as mine and they suggested this bound: \begin{equation}\label{eq:lb} \begin{split}     x\log x-\log\Gamma(x)&\ge x^*\log x^*-x^*-\log x^*-\log\Gamma(x^*)\\     &+\Big(\log x^*-\frac{1}{x^*}-\psi(x^*)\Big)(x-x^*)+\log x+x \end{split} \end{equation} It seems it works just for small $x^*$. I wonder whether there is a tighter bound or not? Any suggestion would be appreciate?


Are all magical staves and wands spellcasting foci?

Are magical items such as:  Staff of Frost DMG page 202 Staff of Power DMG page 202 Wand of Fireballs DMG page 210 Wand of the War Mage +1 DMG page 212  Considered to be foci usable for spellcasting, such as:  Staff PHB, page 151 Wand PHB, page 151


How can I draw annotated braces over and under math expressions?

What LaTeX markup would one have to write to produce a result similar to the image below?    Please excuse my Paint-and-mouse drawing skills. :-)