I have a Sql Server logging table, that continuously is being inserted into, I want to revise the design of this table.  Currently, we are using a GUID as the PK,  because the software can generate this and we just insert it, and hopefully, multiple inserts won't block each other. However, UniqueId is not a very efficient PK for a table and our indexes are very large and fragmented.  If I change this column to a long with auto-increment enabled.  Will this become a concurrent insert bottleneck?  I do not need my primary key to be in any sort of order, Just a unique id for that row?

Our company would like to understand the effects:   If we have single table with Primary Key Identity column, int primary key IDENTITY(1,1),  and the Application is conducting multi-threading parallel processing, trying to conducts 1000s of simultaneous inserts on one table.   Would the identity primary key column fail, with a primary key violation in any way, for example: processors are trying to input the same identity number?  Or was SQL designed to be successful even in multithreading parallel insert?  Note: IDENTITY_INSERT is OFF


I am beginning to learn Java,so please pardon if the question seems silly, I was going through some online examples.  I found a String question, should not the output be true ?  As I am comparing two strings which are equal.  public class HelloWorld{       public static void main(String []args)      {       String morning2 = new String("Morning");       System.out.println("Morning" == morning2);      } }   Similarly for this program, should not this print True  public class HelloWorld{       public static void main(String []args)      {         String str1 = new String("Paul");         String str2 = new String("Paul");         System.out.println(str1 == str2);      } }   But for this program, it prints true.  public class HelloWorld{       public static void main(String []args)      {         String str3 = "Harry";         String str4 = "Harry";         System.out.println(str3 == str4);      } }   Can anyone explain why is there difference in output ?  I have seen this question and answer  but It does not really fit the explanation.

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


I got this refusal letter: 1- It seems to me the ECO has not understood my blocking account status that is 8740 Euros.  2- I am a student in Germany, I have obtained the money in both my blocked account and my personal current account in Iraq where I worked for 5 years.  3- I am fully sponsored by my fiancee, but he has ignored this and the evidences with it. What shall I do? It is really important to me to visit her for these three weeks, because here in Germany I live in a shared flat. It is not possible for her to come and live with me here. if I reapply explaining my financial situation, do I have a chance of getting it?   I appreciate your kind responses.

Many of the UK visa refusals we see here share a common pattern and the prevailing reasons refer to V 4.2 (a) and (c).    I do understand that, while the applicants may describe very different individual circumstances, there's a consistent pattern and, broadly, fall into specific categories:    Credibility (lifestyle, lack of ties, visit history, lies & omissions) Funding (insufficient funds, provenance of funds, funds parking) Sponsorship (family, friends, employer)   Question: What most commonly triggers a UK visa refusal where V 4.2 (a) and (c) are given as the grounds?  Secondarily: Given that there is a clear pattern, to what extent are these refusals predictable? Does sponsorship make a difference? Is there a set of personal circumstances, however abstract, where a refusal is all but guaranteed? For example, why do those we see here on TSE who sought entry for the PLAB or British Army appear to be refused with a common theme? Is there a uniform shortcoming or is it just discrimination?   PLAB: What is about applications for a visa, for the purpose of sitting the Professional and Linguistic Assessments Board (PLAB) exam, that seem to invite refusals. After all, the test is given so that international medical graduates can show that they qualify to practise medicine in the UK. The first part, PLAB 1, can be taken in centres outside of the UK. However, PLAB 2 can be taken only in the UK. Why can't you can't get a visa just to sit the exam, promising that you'll leave immediately after?    British Army: Since Commonwealth citizens are eligible to apply online to join, even those who don't reside in the UK, why is it so difficult to get a visa just to attend an interview to see whether you are suitable? Even with an invitation from the Army, such visa applications seem to be unsuccessful. Isn't a career in the British Army a valid reason?     Lastly:  After such a refusal, what approaches would increase the chance of a successful application?


I am using the simple code for Sqlite database saving and retrieval. My problem is my code takes always the else part even the strings are same.           Toast.makeText(getApplicationContext(), "No UName: "+utext+","+str+"; Pswd: "+ptext+","+str1, Toast.LENGTH_LONG).show();  instead of,     Toast.makeText(getApplicationContext(), "Yes UName: "+utext+","+str+"; Pswd: "+ptext+","+str1, Toast.LENGTH_LONG).show();  I checked the output with toast and with debug mode. The value of utext is equal to str and the value of ptext is equal to str1. Is anything I made mistake here? I don't find anything.    public void onClick(View v) {             utext=t1.getText().toString();             ptext=t2.getText().toString();              Cursor c = db.rawQuery("SELECT * FROM " + tbl_name+" WHERE USERNAME= '"+utext+"' AND PASSWORD= '"+ptext+"'", null);               if(c.moveToLast() ) {                       str=c.getString(c.getColumnIndex("USERNAME"));                       str1=c.getString(c.getColumnIndex("PASSWORD"));                       Toast.makeText(getApplicationContext(), "True : "+str+", "+str1, Toast.LENGTH_LONG).show();               }               else                   Toast.makeText(getApplicationContext(), "FALSE", Toast.LENGTH_LONG).show();               if(str==utext || str1==ptext)                   Toast.makeText(getApplicationContext(), "Yes UName: "+utext+","+str+"; Pswd: "+ptext+","+str1, Toast.LENGTH_LONG).show();               else                   Toast.makeText(getApplicationContext(), "No UName: "+utext+","+str+"; Pswd: "+ptext+","+str1, Toast.LENGTH_LONG).show();          }


If I do graphic design and I want to include on my resume a list of digital skills that indicate my proficiency level, how would I put this, e.g.: is it better to write:  1) a list of softwares and/or programming languages, such as the following: -  "Photoshop - Illustrator - Inkscape..."   2) a list of "areas of application", like in the following: "Typography - Brochure - Social Media..."  Which (generic) skills and digital skills, related to graphic design, should be included in a resume?

I was looking at the resume in  question, and I noticed the skills bar chart. I've seen this on several designers' resumes and was wondering if it is a new fad, if it's something that I should consider adding to my resume/website, etc.    Wouldn't this get you less clients if you forget or didn't have the room to add every single piece of software that you know and your skill level of said software? I can understand adding fundamental software like Photoshop and Illustrator, but what about all the little programs that I don't use very often, but I still know how to use? If I were to list all those, the resume would be like 3 pages long.  Is this a useful graphic to add?


I have seen this sentence in an article on bbc, which is about how people lived thousands of years ago. "When this Neolithic home was built, it would have had a cosy roof of turf.." When I read it, I got confused. Because the fact seems as a simple past situation or guessing/assumption about something in the past. it simply gives information about a past event, eg "when I was a child, I had a blue toy car. I have been making a lot of research on whether or not this structure "would+have+past participle" could be used instead of the simple past or "must+have+past participle", but I could not find any satisfying explanation. Almost all grammer contents cover this structure is used when we imagine the opposite of what actually happened in the past eg. "referring to a missed opportunity" (eg. "if you had come to the party, you would have seen Tom."), But, in this case of this sentence, "type 3 conditional" is irrelevant. It is not an if sentence,  It simply gives information about how this house was like or was probably like when it was built long ago. Just like it would be If and old lady would want to tell about "how she was like when she was a child years ago. she would simply say "when I was a child, I had long curly hair.**. So "when I was a child, I would have had long curly hair." would be wrong. So, my question is: 1-Does this structure "would+have+past participle" completely replace simple past sentences? or can be it be used instead of simple past? 2- If this structure was simply used because the author was not %100 sure about the fact as it was a long long time ago -so he wanted to make a guess or assumption, why did he not simply use "must+have+past participle" or "it was likely that blah blah" which must be used for guessing or assumptions about past happenings. Would it not have made more sense if it was like: "When this Neolithic home was built, it must have had a cosy roof of turf.

I have noted that in books/articles dealing with history, "would have" is often used. E.g.:     Many of the tools used by Woodland people would have been familiar to   their Archaic ancestors.      Such spears (made of yew or spruce) would have been thrusting weapons   not javelins, due to their poor piercing power as a projectile so   would have required the hunters to ambush their prey.   Is this usage related to likelihood/uncertainty? Would it change the meaning if I rephrase the first sentence and used "by Woodland people were likely familiar.."?  Or what if I use simply "past simple" tense in the other example?


I was clicking around Meta Stack Overflow earlier and suddenly ran into a page with a big red error message at the top, "Meta Stack Overflow requires external JavaScript from another domain, which is blocked or failed to load.":    Looking at the error log, I saw Undefined ReferenceError: $ is not defined.    So it looks like  failed to load. Being at work when this happened, I got distracted by something work-related and by the time I came back to continue my investigation of this, I realized I had accidentally closed the browser tab, so I didn't get a chance to look at the developer tools "Network" tab and confirm my suspicion that the Google  failed to serve jQuery. But it still seems likely. Especially considering the error is coming from "stub", which is included right after jQuery:    So, since you're not using an asynchronous script loader here, it would be easy to implement a piece of code that falls back to a local copy of JavaScript code in the case where Google's CDN fails. Something like this:  <script type="text/javascript" src="//ajax.googleapis.com/ajax/libs/jquery/1.7.1/jquery.min.js"></script> <script type="text/javascript">window.jQuery || document.write('<script src="/content/js/query.min.js"><\/script>')   Is it a good idea?

Google's CDN is nice, but it's not 100% reliable for all users. It occasionally fails to load for me. Other users , and some .  It's one more possible point of failure. It would be preferable if Stack Exchange didn't depend on it.  If you don't want to stop using it, consider adding a fallback if it fails to load. Something like this:  <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.1/jquery.min.js"></script> <script>   if (!window.jQuery) {     document.write('<script src="https://cdn.sstatic.net/stackoverflow/content/js/jquery-1.7.1.min.js"><\/script>');   } </script>


I have an issue with installing Teamviewer on fresh install of Ubuntu 20.04 LTS.  Does anyone knows what I've done wrong?

There are now errors when updating and I cannot install most software due to a corrupted  /etc/apt/sources.list   file. Is there a copy I can download to replace it?  The file would be for Ubuntu 12.04 (Final Beta) in the United States.


I know that 5e magic items are supposed to be very rare and not for sale, yet both the DMG and XGtE list magic item prices based on rarity. We're going to be doing a series of one-shots with the same characters and have been put on a very low initial budget for items (no items from background or class), but are allowed to buy magic items with this money.  Magic item cost in both the DMG and XGtE only references the rarity of a magic item. Unless I'm missing a rule somewhere, this has the strange consequence that a commonly enchanted plate armor (100 gp) is (a lot) cheaper than a non-enchanted plate armor (1500 gp).   Am I missing something? If I'm not missing something: is this a design oversight or has there been an official comment on this?

The table on page 129 of the DMG lists the costs to craft an item.  Taking as an example a Common magic items, such as a level 1 spell scroll, the cost is listed as 100 gp.  The crafter can only make 25 gp worth of progress per day, so this takes 4 days worth of effort, at 8 hours per day.  The crafter must use a spell slot to cast the spell once on each of those days.    Meanwhile, the guidelines on page 139 for the costs of magic items states that a common magic item is worth 50-100gp with consumables, such as a spell scroll, costing half.  So a first level spell scroll "should" cost at most 50 gp.    Looking at the tables for other rarities of items, again the creation cost is listed as the maximum of the suggested values for items of that rarity, and that doesn't even take into account the value of the crafter's time to work for many, many days to craft it.  Am I missing something here?  Can someone explain how this makes sense?   (Obviously, this assumes a campaign where at least common magic items are available for purchase)  I understand that the prices listed in the DMG are suggested starting points only, but why are the suggested starting points for item values inconsistent with the suggested starting points for item creation?


once again I am repeating my question, Reliance ISP--> connected with ADSL Modem-->connected with TPLINK Router (First Router)--->connected with second Router), Straight cable connected first router lan port is not recognizing to my lapotp as it has 49 meter long,   same thing is working brilliant when connected via Patch cord- 2mtr,   router setting is fine, as it works via patch cord

FIrst router(TPLINK) is connceted with ADSL Modem, and second router is connected via 49 meter cat-6 cable with straight connection, it is not working, but connection between two routers using patch cord (up to 3 mtrs) is very fine, what is the solutions


My wife and I are thinking about selling our home and are very upset about the prospect of losing 6%+ of our home value on commission. We live in Texas.  We both have careers that are unrelated to real estate but we love and understand a little bit of the real estate market. From what I understand, in the USA it is not mandatory to use a realtor for selling your home, but obviously we would be super cautious about it.  With that in mind, and considering we want to do real estate in the long term, is it possible, does it make sense, and what are the potential risks of either getting a realtor license or simply watching all the real estate school courses (without getting a license) in order to save on that commission in the long run and deal with all the businesses ourselves?

There have been numerous "for sale by owner" signs appearing recently.  This seems like a convenient way to reduce the commission charged by Real Estate agents but I have heard that this is still a "closed" market unless one already has a buyer lined up (like a friend or family member).  What are the advantages and disadvantages?


public double hypotenuse() {            //return Math.hypot(leg, leg); //returns 7.0710678118654755     //return 0.1 * Math.floor(Math.hypot(leg, leg) * 10); //returns 7.0     //return 0.1 * Math.ceil(Math.hypot(leg, leg) * 10); //returns 7.1000000000000005     return 0.1 * Math.round(Math.hypot(leg, leg) * 10); //returns 7.1000000000000005 }   I am trying to round to the nearest 10th place, so this number should round up to 7.1.  Why does this method work with Math.floor but not with Math.round?   Does anyone have any insight?    Thanks,   Sky

What I would like is a method to convert a double to a string which rounds using the half-up method - i.e. if the decimal to be rounded is 5, it always rounds up to the next number. This is the standard method of rounding most people expect in most situations.  I also would like only significant digits to be displayed - i.e. there should not be any trailing zeroes.  I know one method of doing this is to use the String.format method:  String.format("%.5g%n", 0.912385);   returns:  0.91239   which is great, however it always displays numbers with 5 decimal places even if they are not significant:   String.format("%.5g%n", 0.912300);   returns:  0.91230   Another method is to use the DecimalFormatter:  DecimalFormat df = new DecimalFormat("#.#####"); df.format(0.912385);   returns:  0.91238   However as you can see this uses half-even rounding. That is it will round down if the previous digit is even. What I'd like is this:  0.912385 -> 0.91239 0.912300 -> 0.9123   What is the best way to achieve this in Java?


Here's what I tried (Python):  import time  def wait(seconds):     start_time = time.time()     while start_time + seconds <= time.time():         pass   But this just quits instantly.

I would like to know how to put a time delay in a Python script.


I have an entry in cron.d:  31 17 * * * root /home/some_user/.bash_profile; /home/some_user/bin/some_script   The profile sets a specific path, and I echo the current path in the profile to ensure its correct. But, when the script executes, a command in it fails because it's not in PATH and, when I display the current PATH within the script - it's not what was set in the profile.  Why doesn't the PATH set in the profile survive into the script's execution?

This is a  about using cron & crontab.   You have been directed here because the community is fairly sure that the answer to your question can be found below. If your question is not answered below then the answers will help you gather information that will help the community help you. This information should be edited into your original question.  The answer for 'Why is my crontab not working, and how can I troubleshoot it?' can be seen below.  This addresses the cron system with the crontab highlighted.


I am using this shortcode to load a list of links to post per user profile or author:  /* * * Shortcode to display Post as links on Profile Pages *  */  function imwz_golfs_list_function( $atts ) {     if ( is_user_logged_in() ):      global $current_user;     wp_get_current_user();     $author_query = array('posts_per_page' => '-1','author' => $current_user->ID);     $author_posts = new WP_Query($author_query);     while($author_posts->have_posts()) : $author_posts->the_post();     ?>
<a href="<?php the_permalink(); ?>" title="<?php the_title_attribute(); ?>"><?php the_title(); ?>
     <?php                endwhile;      else :      echo "not logged in";      endif;     }  add_shortcode( 'golfslist', 'imwz_golfs_list_function' );   Now it does work on Twenty Seventeen except for its position. However on the Total theme it is loaded just after the body tag as well on top of the positioning issue. So on both themes it is loaded before the main content and not as positioned in the post or page after the content using [golfslist] in the WYSIWYG editor.  Any ideas how I can load the list where I want in the post by placing it in the editor? Any idea how it could be loaded in the post content and also just below the body tag?

The shortcode produced by this function - a list of all sites in a multisite - outputs above the content in the loop, no matter where it is placed in the editor.  I've looked at the other related questions and answers on WPSE and realize that it has to do with the function using echo instead of return, but it's not as easy as replacing the instances of echo with return in the function below. Or adding echo=0 with a WP function like wp_list_pages()  Any ideas? Where is the function that needs to be returned instead of echoed?  // Output a single menu item function projects_menu_entry($id, $title, $link_self) {     global $blog_id;     if ($link_self || $id != $blog_id) {         echo '
';         if ($id == $blog_id) {             echo '';         }         $url = get_home_url($id);         if (substr($url, -1) != '/') {             // Note: I added a "/" to the end of the URL because WordPress             // wasn't doing that automatically in v3.0.4             $url .= '/';         }         echo '' . $title . '';         if ($id == $blog_id) {             echo '';         }         echo '
';     } }  // Output the whole menu // If $link_self is false, skip the current site - used to display the menu on the homepage function projects_menu($link_self = true) {     global $wpdb;      echo '
';      projects_menu_entry(1, 'Home', $link_self);      $blogs = $wpdb->get_results("         SELECT blog_id         FROM {$wpdb->blogs}         WHERE site_id = '{$wpdb->siteid}'         AND spam = '0'         AND deleted = '0'         AND archived = '0'         AND blog_id != 1     ");      $sites = array();     foreach ($blogs as $blog) {         $sites[$blog->blog_id] = get_blog_option($blog->blog_id, 'blogname');     }      natsort($sites);     foreach ($sites as $blog_id => $blog_title) {         projects_menu_entry($blog_id, $blog_title, $link_self);     }     echo '
'; }  // Adds a [bloglist] shortcode  function bloglist_shortcode($atts) {     projects_menu(false); }  add_shortcode('bloglist', 'bloglist_shortcode');


I created an object but i would like to put a wood texture on it, how apply with blender 2.9?

I am creating a model of a glass and I would like to put a drawing on it (a png picture).  I know how to do it using Blender Render, but not with Cycles Render. Help :)


Apologize for repeating question. I have already tried the solution given, doesn't work in my case. For disconnection i have already handled socket exception , 0 bytes received for handling disconnection. This works perfectly in case of server shutdown , lan disconnection. But when internet disconnects, socket does not disconnects immediately. After internet disconnection when i sent some data on socket, that time socket  get disconnected. How do i immediately detect socket disconnection in case of internet disconnection. I have tried Socket.Poll().This doesn't works. My code is written in c# .net

How can I detect that a client has disconnected from my server?  I have the following code in my AcceptCallBack method  static Socket handler = null; public static void AcceptCallback(IAsyncResult ar) {   //Accept incoming connection   Socket listener = (Socket)ar.AsyncState;   handler = listener.EndAccept(ar); }   I need to find a way to discover as soon as possible that the client has disconnected from the handler Socket.  I've tried:   handler.Available; handler.Send(new byte[1], 0, SocketFlags.None); handler.Receive(new byte[1], 0, SocketFlags.None);   The above approaches work when you are connecting to a server and want to detect when the server disconnects but they do not work when you are the server and want to detect client disconnection.  Any help will be appreciated.


I'm building a home studio to record Math classes: I have a blackboard (1,90m width by 1,20m height) and the distance from the camera to the blackboard would be around 1,80m (on a tripod, 1,70m from the ground).  How can I calculate the lens I should buy to record the full width and height of the blackboard?  I'm planning on buying a Canon 70D for the studio.  Thank you.

I am thinking about buying a new lens specifically to take photos of distant targets (birds, bears, etc). I currently own the Canon 70-300 IS USM, which is a nice lens, but I find that if I want to take a photo of anything further away than about 10 meters, the target does not fill a large amount of the frame (meaning I have to significantly crop in post production).  I am currently looking at the Canon prime 400mm, however I would like to determine at what distance an object will fill a reasonable proportion of the frame.  Is there a formula or rule of thumb I can apply that will help me in this situation? I realise the size of the target I am shooting will play a role here, so if we need to make an assumption about the size of the target please let me know.


Let $y(x)$ be a continuous solution of the IVP:  $$\left\{\begin{eqnarray}y'+2y &=& f(x)\\y(0) &=& 0\end{eqnarray}\right.$$  Find $y(\dfrac{3}{2})$.  $$f(x) = \begin{cases} 1 &\text{$0\leq x\leq 1$} \\ 0 &\text{$x>1$} \end{cases}$$  My try :  I solved it in two cases:  Case 1:$x\in [0,1]$ taking $y^{'}+2y=1$ and using $y(0)=0$ on solving I get $y=\dfrac{1-e^{-2x}}{2}$  case 2:$x>1$ taking $y^{'}+2y=0$; I get $\ln y=-2x+c$ where $c$ is a constant.  what should I do now?

Let , $y(x)$ be a continuous solution of the initial value problem $y'+2y=f(x)$  , $y(0)=0$ , where, $$f(x)=\begin{cases}1 & \text{ if } 0\le x\le 1\\0 & \text{ if } x>1\end{cases}$$Then, $y(3/2)$ equals to (A) $\frac{\sinh(1)}{e^3}$ (B) $\frac{\cosh(1)}{e^3}$ (C) $\frac{\sinh(1)}{e^2}$ (D) $\frac{\cosh(1)}{e^2}$  Integrating both sides we get , $$\int_0^xd(y(x))+2\int_0^xy(x)\,dx=\int_0^xf(x)\,dx$$ $$\implies y(x)+2\int_0^xy(x)\,dx=\int_0^xf(x)\,dx=1$$ $$\implies y(x)=1-2C$$where , $$C=\int_0^xy(x)\,dx=(1-2C)x\implies C =\frac{x}{1+2x}$$ Then , $y(x)=\frac{1}{1+2x}$ and so, $y(3/2)=1/4$.  But no option match..Please help..


My Canon camera realize videos with the characteristics described in the picture.    The problem is that those files are huge (1Gb for 2 minutes). Is there any application which allow me to compress or resize the films already made?

I have a raw video that has the following properties:   25 FPS  UYVY Codec 876 MBit/s AVI Container   I want to convert this raw file to another container using ffmpeg. Right now the problem is that the output video is being compressed. Any idea how to do this without compressing the output file. I have tried:  ffmpeg -i video.avi -r out.avi  and it did not help.


How did Kirito bring back Yui when she was deleted by Cardinal SAO? I honestly don't understand this.

We know that Yui was saved in Kirito's NervGear's local memory in the first season of Sword Art Online but in in the second season when Kirito is in Gun Gale Online, when everyone is watching Battle of Bullets Yui is there with everyone else watching it in ALO. she also talks to Asuna on her phone when she heads off to the hospital and in Agil's bar when Kirito sets up the cameras for her.  in all of these cases Kirito isn't using his NervGear and i would suspect it is turned off. so where is Yui now stored? and how is she able to go from this place to ALO, Asuna's Mobile and the cameras in Agil's bar?


My question is different from  since my question asks to clarify the proof, while the other question asks to check if the proof is correct.   Let $z_1, z_2, z_3\in\mathbb{C}_\infty$ be distinct points. Then $\alpha(z):=[z; w_1, w_2, w_3]=[\mu(z); \mu(w_1), \mu(w_2), \mu(w_3)]=\frac{(z-z_1)(z_2-z_3)}{(z-z_3)(z_2-z_1)}$ for all $z\in\mathbb{C}_\infty$ (where $\mu$ is a Möbius map). This means that Möbius maps preserve cross-ratios.  Here's the proof I have in the notes:     $\mu^{-1}$ is a Möbius map, and:      $$\alpha\circ \mu^{-1}(\mu(w_1))=\alpha(w_1)=0 $$   $$\alpha\circ \mu^{-1}(\mu(w_2))=\alpha(w_2)=1 $$   $$\alpha\circ \mu^{-1}(\mu(w_3))=\alpha(w_1)=\infty $$      Thus $\alpha \circ \mu^{-1}(z)=[z;\mu(w_1), \mu(w_2), \mu(w_3)], \forall z\in \mathbb{C}_\infty$.   What I don't understand is how this proves that Möbius maps preserve cross-ratios. I would assume that we would have to take $\alpha(\mu(w))$ to show the preservation.  Moreover, if we show that some map is equal to $\alpha$ at just three points, how does this prove that two cross-ratios are equal? Perhaps I don't understand something about the meaning of cross-ratios.

Problem statement:  Given $z_1,z_2,z_3,z_4$ different points of $\overline {\mathbb C}$, we define the cross ratio $(z_1,z_2,z_3,z_4)$ as $(z_1,z_2,z_3,z_4)=\dfrac{z_1-z_2}{z_1-z_4}\dfrac{z_3-z_4}{z_3-z_2}$.  Note that $(z_1,z_2,z_3,z_4)$ is the image of $z_1$ under the Möbius transformation $T$ such that $T(z_2)=0$, $T(z_3)=1$, $T(z_4)=\infty$.  a) Prove that if $T \in \mathcal H$ then $(T(z_1),T(z_2),T(z_3),T(z_4))=(z_1,z_2,z_3,z_4)$.  b) Show that $z_1,z_2,z_3,z_4$ lie in a line or circle if and only if $(z_1,z_2,z_3,z_4) \in \mathbb R$  My attempt at a solution:  For a), using the "hint" they give, if $T \in \mathcal H$, I did the following:  If I call $H=(z,,z_2,z_3,z_4)$, I can consider $H \circ T^{-1} (z)$. Note that $H \circ T^{-1}(T(z_2))=0$, $H \circ T^{-1} (T(z_3))=1$ and $H \circ T^{-1} (T(z_4))=\infty$. This means that $(z_1,z_2,z_3,z_4)=H \circ T^{-1}(T(z_1))=(T(z_1),T(z_2),T(z_3),T(z_4))$.   I don't know if my answer is correct, I would like to check it, and if anyone has a better or different answer, he/she is very welcome to post it.  For b) I am lost, for the forward implication, I've tried to show that $(z_1,z_2,z_3,z_4)=\overline {(z_1,z_2,z_3,z_4)}$ or that $arg((z_1,z_2,z_3,z_4))$ is a multiple of $\pi$ but I couldn't conclude anything. I would appreciate some help with this point.


First post here, just can't seem to wrap this one up, was hoping someone could point me in the right direction. I have a custom post type and taxonomy structure that creates permalinks as "custom post type / taxonomy / term" and displays the taxonomy based on the term in the permalink. The below code works as designed for projects/%projectscategory%. I would like to add another custom taxonomy to the cpt such as projects/%projectstype%. Note I am not trying to change the structure of the permalink just add another taxonomy, "type" in this example. Am getting stuck because of how the filter rewrites the link I think, also wonder the best way to add the additional taxonomy, ie in this block or outside. Hope this is clear.  Thank you        functions file:  <?php add_action('init', 'projects_cpt'); function projects_cpt() {  $args = array(     'hierarchical' => true,     'rewrite' => array('slug' => 'projects'),     'show_in_nav_menus' => true,     'labels' => $labels );  register_taxonomy('projectscategory', 'projects', $args);  unset($labels); unset($args);    $labels = array(     'name' => 'Projects',     'singular_name' => 'Project',     'add_new' => 'Add New',     'add_new_item' => 'Add New Project',     'edit_item' => 'Edit Project',     'new_item' => 'New Project',     'all_items' => 'All Projects',     'view_item' => 'View Project',     'search_items' => 'Search Projects',     'not_found' => 'No projects found',     'not_found_in_trash' => 'No projects found in Trash',     'parent_item_colon' => '',     'menu_name' => 'Projects' ); $args = array(     'labels' => $labels,     'public' => true,     'publicly_queryable' => true,     'show_ui' => true,     'show_in_menu' => true,     'query_var' => true,     'taxonomies' => array('projectstype' ),     'rewrite' => array('slug' => 'projects/%projectscategory%', 'with_front' => false),      //Adding custom rewrite tag     'capability_type' => 'post',     'has_archive' => 'projectsarchives',     'hierarchical' => false,     'menu_position' => null,     'supports' => array('title', 'editor', 'author', 'thumbnail', 'excerpt'), ); register_post_type('projects', $args);  $labels = array(     'name' => 'Projects Categories',     'singular_name' => 'Projects',     'search_items' => 'Search Projects Categories',     'all_items' => 'All Projects Categories',     'parent_item' => 'Parent Project Category',     'parent_item_colon' => 'Parent Project Category:',     'edit_item' => 'Edit Project Category',     'update_item' => 'Update Project Category',     'add_new_item' => 'Add New Project Category',     'new_item_name' => 'New Project Category', );   }  ?>  <?php add_filter('post_type_link', 'projectcategory_permalink_structure', 10, 4); function projectcategory_permalink_structure($post_link, $post, $leavename,  $sample) { if (false !== strpos($post_link, '%projectscategory%')) {     $projectscategory_type_term = get_the_terms($post->ID, 'projectscategory');     if (!empty($projectscategory_type_term))         $post_link = str_replace('%projectscategory%', array_pop($projectscategory_type_term)->         slug, $post_link);     else         $post_link = str_replace('%projectscategory%', 'uncategorized', $post_link); } return $post_link; }  ?>

I've been combing this site and google for the answer and I've come up completely empty.  Basically I want to do exactly what  asks, but I need a hierarchical taxonomy.  The answer given in that post works great, but only with a single level taxonomy.  Is it possible to do what I want?  I've tried a million things, but none work, at best I can get the right permalinks but they come up 404.  To visually illustrate what I want:  /basename/ - ideally a page, but I think this will cause a permalink collision     /basename/top-cat/ - top parent custom taxonomy archive     /basename/top-cat/child-cat/ - child cat custom taxonomy archive      /basename/top-cat/child-cat/grandchild-cat/ - grandchild cat custom taxonomy archive     /basename/top-cat/child-cat/grandchild-cat/post-name/ - my custom post type post   You can do this fine with the built in posts and categories, how do you do it with custom taxonomies and custom post types?  I know that you need to use 'rewrite' => array( 'slug' => 'tax-name', 'with_front' => true, 'hierarchical' => true ), to get hierarchical slugs, which works fine on the archive pages, but the custom post type posts come up 404.  If I remove the 'hierarchical' => true part then the posts work, but I lose the hierarchical urls (only /basename/grandchild-cat/post-name/ works).  So, any solutions?  Thank you so much, this has been driving me nuts for about 3 weeks now.


How can I fix a Macbook Pro when the Touch Bar doesn't work? I have 13 inch 2019 MacBook Pro, and after updating to macOs 10.15.6, the Touch Bar went black. I visit keyboard preferences and saw this  no option for control strip I tried almost all methods even I erased everything and reinstall the macOS; now I am at Mojaive 10.14.6 METHODS I TRIED i. commands in terminal    sudo pkill TouchBarServer;       sudo killall “ControlStrip”;  But after second command an error shows up      No matching processes were found  ii. Erase everything and reInstall macOS from recovery mode Still the entire TOUCHBAR is black

I'm on a new 2019 MacBook pro 13”. The TouchID fingerprint sensor is working. But my touch bar has gone completely blank. I tried restarting my MacBook Pro but it did not help.    I've also done a factory reset, SMC, NVRAM/PRAM and an Apple diagnostics, hoping to fix the problem but it did not work.  After re-install macOs, I was able to see touch bar configuration on System Preferences -> Keyboard menu:    I am not able to see touch bar option and it is completely dark black.  I tried resetting the touchbar through the terminal by using the below syntax:   sudo pkill “TouchBarServer” sudo pkill "Touch Bar Agent" sudo pkill ControlStripAgent   I have tried to verify whether they are running by using below command and could not find any process running.   ps -A | grep -i "touch bar agent" ps -A | grep -i "controlstrip”   I can see the control strip and touch bar server is running in activity monitor:      I could see this is a common issues across mac book pro and customer don’t have any proper fix for it.


After some research, I find that the relationship between $R^2$ and the F distribution is as follows:  $$ R^2 = 1 - (1 + F \cdot \frac{p-1}{n-p})^{-1} $$  But I am not sure what the $p$ and $n$ values should be. Suppose my $R^2$ is calculated from 10 values of $x$ and $y$, what would $p$ and $n$ be?  Thanks!  EDIT: don't think it's a duplicate because my question is more basic, i.e. what $p$ and $n$ values are.

I was wondering if there is a relationship between $R^2$ and a F-Test.  Usually $$R^2=\frac {\sum (\hat Y_t - \bar Y)^2 / T-1} {\sum( Y_t - \bar Y)^2 / T-1}$$ and it measures the strength of the linear relationship in the regression.  An F-Test just proves a hypothesis.  Is there a relationship between $R^2$ and a F-Test?


Prove or disprove that $$\int_0^\infty \left|\frac{\sin{x}}{x}\right|dx < \infty.$$  I tried by Wolframalpha and this integral seems to satisfy the Cauchy property, but I do not know how to prove it.  Thank you very much.

In  wikipedia article for improper integrals,  $$ \int_0^{\infty}\frac{\sin x}{x}dx $$ is given as an example for the integrals that have an improper Riemann integral but do not have a (proper) Lebesgue integral. Here are my questions:   Why does this one have an improper Riemann integral? (I don't see why $\int_0^a\frac{\sin x}{x}dx$ and $\int_a^{\infty}\frac{\sin x}{x}dx$ converge.) Why doesn't this integral have a Lebesgue integral? Is it because that $\frac{\sin x}{x}$ is unbounded on $(0,\infty)$ and Lebesgue integral doesn't deal with unbounded functions?


I installed Virtualbox on Ubuntu 20LTS, I have some questions you may help me solve. I am trying to run a Ubuntu VM from an USB as a disk About Users & Groups: which groups needs the user to have permission to? After a research I made up this list: vboxusers fuse sudo disk dip adm plugdev netdev virtualbox-ext-pack & MOK Do I need to install the virtualbox-ext-pack?? when I install this package it requires me to go through a process of rebooting and adding some passwords. Is this process really need it in order to run a VM from an USB as a disk?? Thanks!!

The question is simple and straight forward:  How to boot from an USB drive in VirtualBox?  EDIT:  I have attached usb to VirtualBox as shown in the screenshot.    But it is not possible to boot from an USB drive even when attached  .  So I would like to know if there is any other possiblity to boot from an USB drive?


An OBJ sequence is necessary for making complex animations using other 3D programs. I want to use blender and realflow together.  Realflow particle simulations and meshed realflow simulations are in *.bin format.  These images suggest this was at some point in development:     How can I import an OBJ sequence?

I have an obj sequence of a fluid simulation from Realflow. I've found a few tools that can import an obj sequence into blender, but most are outdated and don't work. Are there any scripts or plug-ins that can do that?


In the opening credits of a TV show, I have seen that sometimes on the last actor/actress, they will get an "and" before their name. An example that comes to mind is on It's Always Sunny In Philadelphia, Frank is credited with "and Danny DeVito". Why do they do that, what is the purpose of it? What determines if a cast member is worthy of the "and"? I know there is  question about "with"; do the same rules apply for "and"?

I've always been curious what decides if a credit is in the opening or closing credits.  It seems loosely that cast (in order of today's "big name" significance), directors and financiers get the front spots, and everything else appears later.  But lately I've been developing some specific curiosities about how cast members are credited on TV shows.  Opening credits seem to follow this rough outline:  Part of "opening credits" video segment   (optional) Major Actors Show Title Core Cast Actors Directors Producers (optional) Episode Title Episode Writers   Subtitles over beginning of show, after opening video   (Episode Title and Writers may appear here, instead) Special Guest Actors   I've probably missed a few things, and mis-ordered a few things.  But, as I said, my main curiosity is about actor credits.  Typically, there is little indication of which characters the core cast actors play.  Sometimes their name is edited to appear along with an image of the character as an indictator, but sometimes there is no indication.  As I've never seen anyone credited in both the opening and closing credits, that leaves the potential for core actors to never be directly associated with their character.  This seems potentially problematic; is there a reason for this?  Are viewers expected to know who's who?  Guest actors sometimes are simply credited by name (and not being part of the opening video, this means they will never be associated with their character in credits).  But often they are credited as "special guest as character name".  This is quite helpful.  The thing I find really confusing is, sometimes the last few regular cast actors will get the guest actor treatment.  I've seen opening video with "and actor as character" paired with an image of that character for an entire season.  Why does this actor get special treatment?  Finally, sometimes guest actors will be credited at the front following the opening video, sometimes they'll be credited in the closing credits.  Are there rules for deciding who get's credited early or late?  I've sometimes wondered if shows deliberately play with actor's name position to obfuscate plot arcs ("you won't think we're killing of this character if their actor is still in the opening credits", or "you won't expect this recurring guest if we place their name in the closing credits") and I've also wondered if there are thresholds for "people appearing in XX number or YY percentage of episodes get placed here."  But it's difficult to build a good sampling base for this.  And season 7 of Stargate SG-1 kinda took a shotgun to my guesses so far.  So...  Are there rules?


I'm upgrading a VM from Fedora 29 to Fedora 30.  I triggered the update from inside GNOME Software.  It downloaded the upgrade, and asked to reboot.  It started installing...  atop shows the qemu process using about 15% of one CPU core.  And my one hard drive at about 15% utilization.  What other resource(s) could the VM possibly be waiting for, the other ~ 70% of the time?  Is it just ??  Is there some other way to explain or find this out?  The upgrade showed the normal progress indicator, and completed without errors.  The VM is in libvirt (virt-manager), using the default KVM backend on x86-64.  I configured the VM disk using cache mode "none".  There's a 2x2 matrix of caching options; "none" means O_DIRECT, but not O_SYNC.  (My intent was to avoid ; at least it seems to have left the host system so much more responsive than the last time I tried this).  "IO Mode" is set to "Hypervisor default".  The virtual disk controller is using VirtIO.  libvirt is from Fedora 29; it is version 4.7.0 and qemu is version 3.0.0.

sudo dd if=/dev/sda of=/dev/null bs=1M iflag=direct atopsar -d 5    # in a second terminal top             # in a third terminal  Results from atopsar : 19:18:32  disk           busy read/s KB/read  writ/s KB/writ avque avserv _dsk_ ... 19:16:50  sda             18%  156.5  1024.0     0.0     0.0   5.0   1.15 ms 19:16:55  sda             18%  156.3  1024.0     0.0     0.0   4.9   1.15 ms ...  Why is disk utilization ("busy") reported as much less than 100% ? According to top, the dd process only uses 3% of a CPU or less.  top also provides an overall report of hardware and software interrupt (hi and si) usage of the system's CPU's, which shows as less than 1%.  I have four CPUs (2 cores with 2 threads each). /dev/sda is a SATA HDD.  It is not an SSD, it is not even a hybrid SSHD drive.  It cannot read faster than about 150 megabytes per second :-).  So that part of the results makes sense: 156 read/s * 1024 KB/read = 156 MB/s The kernel version is 5.0.9-200.fc29.x86_64 (Fedora Workstation 29).  The IO scheduler is mq-deadline.  Since kernel version 5.0, Fedora uses the multi-queue block layer.  Because the single queue block layer has been removed :-). I believe the disk utilization figure in atopsar -d and atop is calculated from one of the .  The linked doc mentions "field 10 -- # of milliseconds spent doing I/Os".  There is a more detailed definition as well, although I am not sure that the functions it mentions still exist in the multi-queue block layer.  As far as I can tell, both atopsar -d and atop use  to read this field 10.  (I believe this field is also used by sar -d / iostat -x / mxiostat.py) Additional tests Variant 2: Changing to bs=512k, but keeping iflag=direct. dd if=/dev/sda of=/dev/null bs=512k iflag=direct 19:18:32  disk           busy read/s KB/read  writ/s KB/writ avque avserv _dsk_ ... 19:18:00  sda             35%  314.0   512.0     0.0     0.0   2.1   1.12 ms 19:18:05  sda             35%  313.6   512.0     0.2     4.0   2.1   1.11 ms  Variant 3: Using bs=1M, but removing iflag=direct . dd uses about 10% CPU, and 35% disk. dd if=/dev/sda of=/dev/null bs=1M 19:18:32  disk           busy read/s KB/read  writ/s KB/writ avque avserv _dsk_ ... 19:21:47  sda             35%  242.3   660.2     0.0     0.0   5.4   1.44 ms 19:21:52  sda             31%  232.3   667.8     0.0     0.0   9.5   1.33 ms  How to reproduce these results - essential details Beware of the last test, i.e. running dd without iflag=direct It is a bit of a hog.  I saw it freeze the system (mouse cursor) for ten seconds or longer.  Even when I had swap disabled.  (The test fills your RAM with .  It is filling the inactive LRU list.  I think the turnover evicts inactive cache pages relatively quickly.  At the same time, the disk is busy with sequential reads, so it takes longer when you need to page something in.  How bad this gets probably depends on whether the kernel ends up also turning over the active LRU list, or shrinking it too much.  I.e. how well the current  is working in your case). The exact results of the first test are difficult to reproduce. Sometimes, KB/read shows as 512 instead of 1024.  In this case, the other results look more like the results from bs=512k.  Including that it shows a disk utilization around 35%, instead of around 20%.  My question stands in either case. If you would like to understand this behaviour, it is described here:


Hello, I want to make the kettlebell shiny but without those reflections of other objects. Is there a way to make certain objects not visible in the reflection in Eevee?

I am trying to work out how to have a fake mirror in my scene. Character A walks by a mirror on the wall, which should reflect the room and everything in it, except Character A. Instead of Character A, it reflects Character B. So, basically, I want a simple reflective surface, but:  Character A should not be visible in what the surface reflects. Reflections should be rendered as if Character A is not in the scene Character B will be in the scene, but only visible in the reflective surface, not in the world itself.  Here, crude graphic to show what I mean :D  Less crude graphic here:  Is this possible with Blender? I'm familiar with all of the most general functionality, but I can't think of anything that would achieve this. Are there data properties I can tweak? Is there a modifier that'll achieve it? Reflection probe trickery? I intend to use Eevee for the rendering, but if Cycles achieves this better, I can switch. EDIT: I can of course elect to not using a reflective but a transmissive surface and just model the contents of the mirror behind the surface. So instead of having any reflection at all, I'll just copy and mirror the geometry and do everything manually, but 1) that's a lot of work, 2) not really an answer to the technical question I'm asking.


If I try to compile this example document \documentclass{beamer} \begin{document}  \begin{frame}{Test}   Test \end{frame}  \end{document}  with htlatex temp.tex I get the output: l.34951 --- TeX4ht warning --- \Configure{frametitle}? ---  ! LaTeX Error: Missing \begin{document} in `'.  See the LaTeX manual or LaTeX Companion for explanation. Type  H <return>  for immediate help.  ...                                                                                l.34952 ...i \EndP \HCode{
}                                                   \bgroup ?  ! Emergency stop.  ...                                                                                l.34952 ...i \EndP \HCode{
}                                                   \bgroup No pages of output.  Full log can be found

\documentclass{beamer} \usetheme{Madrid} \begin{document} \begin{frame} aaa \end{frame} \begin{frame} bbb \end{frame} \end{document}   The above tex file is to be converted into html. I am using the following command   make4ht filename.tex   However it throws error. The basic question is "Is it possible to convert beamer presentation to html using make4ht?"


We recently had  which showed that "Mik" had cast a close-vote on one of the questions however his profile wasn't linked. It became clear later on in the answers and comments that Mik's profile is now deleted and hence his name is not linked to his profile.  Another example for same user:    But then, why isn't the name of the user obfuscated like it gets done for posts/comments once the user gets deleted?

When an account is deleted, the username in the user's posts and comments is changed to a generic user<userID>. But the username stays the same on close and delete notifications on posts the user had voted to close / delete1. I think it shouldn't, especially for users who used their real name as their username, if they chose to distance themselves from the site and remove their accounts, it makes sense that they wouldn't really want their name plastered on close and delete notifications.   A perhaps easy way to avoid the actual username remaining visible would be to change it to the generic user<userID> (or anything generic enough, like "anonymous") prior to deletion, and wait a bit for the generic username to propagate all over the site. If I'm not horribly misreading , this was part of the process in the old days.   This could be automated or added as a suggestion to the .  Glaring example can be seen , where the deleted user also posted a comment where their name is properly anonymized:        1 I've seen it on close notifications and self deleted answers. I'm not sure it happens on deleted questions, or deleted answers that aren't self deletions, and I don't have a way to verify it - other than stumbling on them accidentally


eg. 1 I have to be sharp and clever lest I go hungry? (infinitive)  eg. 2 John and his friends feared lest the inquiry promised into the extent of the hated forest areas would be carried out too rigorously? (past tense?).  Are both examples acceptable? I've read somewhere that the clause after 'lest' is usually in subjunctive mood and therefore the tense should be an infinitive? Are there other possibilities?  Thank you very much!

I remember my grandfather giving examples of "lest" like      ...lest you should fail.   Is "lest" always followed by "should" because I see "lest" all the times without being followed by "should" in some articles and novels, but I am not sure if they are grammatically correct.   Please provide examples of such exceptions.


Can someone help me to clarify this. Is the word Jesus' feet pronounced as "Jesuses feet" or simply "Jesus feet"?  I read up some articles and most of them said both versions are correct.  However, when I was in London recently, I heard St. James' Park pronounced as "St. Jameses Park."  I am not sure whether it was spelt as St. James' Park or St. James's Park.  Should it then be Jesus's feet?  Much appreciated!  Petra

What is the possessive of a noun ending in ‑s?  Are these both right, or is the second one wrong?   the boys' books the boss' car


I've to prove that 𝓢n is generated by the two permutations (1 2), (1 2 3 ... n). I've already proved that the symmetric group can generated by the following transpositions (1 2) (2 3) (3 4), ..., (n − 1 n) in a previous exercise. So I think I've to prove that those two elements are able to generate all elements of the form (m,m+1) with $m = 1, \ldots n-1$

I have a homework question that asks     Find necessary and sufficient conditions on $1 \leq i < j \leq n$ so that $(i \, j)$ and $(1 \, 2 \, \dotsc \, n)$ generate $S_n$.   Here is what I have done so far.  Call $c = (1 \, 2 \, \dotsc \, n)$.  I made the observation that $$ \overbrace{c c \dotsb c}^{n - j + 1} (i \, j) \overbrace{c^{-1} c^{-1} \dotsb c^{-1}}^{n - j + 1} = (1 + i - j + n \, 1). $$ Thus, $\langle (i \, j), c \rangle = \langle (1 \, i - j + n + 1), c \rangle$, so it suffices to look at $\langle (1 \, k), c \rangle$ for positive integers $2 \leq k \leq n$.  I've checked that, for the value $k=2$, $\langle (1 \, 2), c \rangle = S_n$.  This immediately implies $\langle (1 \, n), c \rangle = S_n$.  I suspect that no other values of $k$ will work, but am not sure how to prove it.


I read Ben Franklin had it wrong by stating "current is the flow of positive charge". Right from the start Ben Franklin could have easily decided to say that current is the flow of negative charge.   So why is it that when J.J Thompson discovered the electron the physics community decided the correct elementary particle that moves is negative?  Why could they not have said it was just positive and be consistant with what Ben Franklin said?  Today we compensate by having the positive move in reverse so the negative turns out to be moving in the "forward" direction. Is there something really fundamental about the electron that it must be called negative instead of positive perhaps?

I recently came to know about the Conventional Current vs. Electron Flow issue. Doing some search I found that the reason for this is that Benjamin Franklin made a mistake when naming positive and negative charges. There is even this little comic about that   My question is, how can a naming convention be wrong? Perhaps I don't understand what is the actual mistake here, I don't know. But I don't see how a naming convention could be wrong or right. There is no right and wrong about that. It could've been any other name, like charge A and charge B.  I'll appreciate anyone can help me understand what is wrong in all this.


I'm a college student and pursuing (in part, at least) a statistics and data science track. Much of my coursework beyond the introductory statistics sequence has involved topics like multiple regression, logistic regression (and probit and tobit), discriminant analysis, clustering techniques, etc. However, the issue with these courses is that they tend to introduce the motivation behind each topic and then move straight into implementation and interpretation. The last time I actually understood the mathematics behind a methodology was linear least squares, and I want to be able to derive the equations for the coefficients for logistic regression or for discriminant analysis.  Where can I learn to do this? Is there a good statistics manual or "encyclopedia" of sorts that collects reference material on all sorts of statistical methods? Ideally, I'd also envision some source that I can look to years down the road, when I'm rusty and need a refresher on how a certain estimator is derived or can quickly look at what the assumptions for a model are without having to sift through paragraphs of explanation.  I've looked through Introduction to Statistical Learning, but it's fairly surface-level (and also pretty focused on how to use R, and not even a very modern approach to R); I'm working through Elements of Statistical Learning and it seems to be closer to what I want, but it still doesn't seem to have the treatment I want of certain topics (mostly topics that fall under the realm of traditional statistics, such as MANOVA, rather than modern data mining/machine learning).  For specificity purposes, let's say that right now, I want to learn the underlying theory behind logistic and probit regression. What's the best place for me to do that?

Before I ask my question, let me give you a bit of background about what I know about statistics so that you have a better sense of the types of resources that I'm looking for.  I'm a graduate student in psychology, and as such, I use statistics almost every day.  By now I'm familiar with a pretty broad array of techniques, mostly as they are implemented in the general structural equation modeling framework.  However, my training has been in the use of these techniques and the interpretation of results -- I don't have much knowledge of the formal mathematical foundations of these techniques.  However, increasingly, I've had to read papers from statistics proper.  I've found that these papers often assume a working knowledge of mathematical concepts that I don't know much about, such as linear algebra.  I have therefore become convinced that if I wish to do more than blindly use the tools that I have been taught, it would be useful for me to learn some of the mathematical basis of statistics.  So, I have two related questions:   What mathematical techniques would be useful for me to know if I want to brush up on the mathematical foundation of statistics?  I've encountered linear algebra pretty often, and I'm sure that learning about probability theory would be useful, but are there any other areas of math that would be useful for me to learn about? What resources (online or in book form) can you recommend to me as someone who wants to know more about the mathematical foundations of statistics?


How do I completely factor $a^3 + b^3 + c^3 - 3abc$ over the complex numbers? The first thing I did is factor this into $(a + b + c)(a^2 + b^2 + c^2 - ab - bc - ac)$. But I am not sure how to factor $a^2 + b^2 + c^2 - ab - bc - ac$ over the complex numbers. Can anyone help me?

I found this amazingly beautiful identity . How to prove that $A^3+B^3+C^3 - 3ABC = (A+B+C)(A+B\omega+C\omega^2)(A+B\omega^2+C\omega)$ without directly multiplying the factors? (I've already verified it that way). Moreover, how could someone possibly find such a factorization using complex numbers? Is it possible to find such a factorization because $A^3+B^3+C^3 - 3ABC$ is a symmetric polynomial in $A,B,C$?


Spoilers for The Last Jedi:   An explosion caused General Leia to be flung into space. We then see her hand move and the  plays, implying some sort of Force use.  That much is clear. What is not very clear is   what exactly she is using the Force to do.  I assumed she was simply guiding herself towards safety. People don't actually immediately explode/implode/freeze/etc. when in space so to me it makes sense that all she would need to do is use the Force to nudge her body in the right direction and the inertia would carry her to the intended destination (because there's no friction in space).  However I've seen others claim she was creating a force bubble of air or something, while still others say she pulled the rebel ship to her, and so on. So my question is do we know for sure what Leia used the Force to do?   I prefer official sources that shed new light on the subject (like scripts/novelizations/interviews/etc.) rather than answers that just say "well I watched that scene and to me it looked like she was doing ___" (but I guess I'd accept either kind if the argument is compelling enough).   I'd argue that my question is different from the 'dupe' one. That one basically asks "How did she do it? Was that the force?" and its answer is essentially "Yes, it was the Force".  My question is "What did she do? Did she Force pull? Force push? Force-not-need-to-breathe? Force cocoon/shell/shield-filled with air? See what I'm saying? I think that makes my question sufficiently different. :D

In the Last Jedi movie, there is a scene where      her spaceship is taken down, Princess Leia is thrown into outer space, and seen floating there, frozen.    However, she manages to survive this, while any ordinary human being couldn't.   How did she manage this? Is this done by using the Force?


When coding with Collections:  Why use:   List<String> mList= new ArrayList<String>();   Why not:   ArrayList<String> mList=new ArrayList<String>();   When I ask the answer is : "It is JAVA convention".  I need a comprehensive, logical and expressive answer on this.

I have seen this mentioned a few times and I am not clear on what it means. When and why would you do this?   I know what interfaces do, but the fact I am not clear on this makes me think I am missing out on using them correctly.   Is it just so if you were to do:  IInterface classRef = new ObjectWhatever()   You could use any class that implements IInterface? When would you need to do that? The only thing I can think of is if you have a method and you are unsure of what object will be passed except for it implementing IInterface. I cannot think how often you would need to do that.   Also, how could you write a method that takes in an object that implements an interface? Is that possible?


Whenever there's a hurr durr chat flag in one of a given network site's chatrooms, every 10k+ user across the network can see and action it.  This is not always ideal, particularly if the offending chat has active mods or 10k users of its own who are present, and who can see context; local users should have first crack at dealing with chat flags.  I propose something like this:  A 30 second window where a flagged message is only visible to those on the current site's chat, possibly even only users in the current room.  If the flag is actioned by local users, it's dealt with and other network users don't even have to see it.  If after 30 seconds the flag hasn't been actioned, then it pushes out to the rest of the network users, who can action it as they see fit.  Good idea?  Bad idea?

The offensive/spam flags in chat are shown to every moderator from a parent site (on chat.stackexchange.com that is every SE 2.0 moderator, more than 200 right now) and 10k chat users as well. This is potentially far more users than a flag on an SE site itself is shown to.   I don't think it is necessary to show the flag to so many users at once. This can lead to the impressive sight of an entire horde of moderators descending onto one chat room when some flagging is going on, but it often notifies far more people than necessary to act.  Another huge disadvantage of notifying so many users at once is that only the fastest users to act decide on the fate of the flag. If you read up on the context of the flagged message, odds are that by the time you're finished with that someone already validated or dismissed the flag. This leads to hasty decisions on those flags because the users that take their time won't get to decide on the flag.   I propose that the chat flags are first shown only to mods and users in the same chat room, if there are enough users present that the flag could be acted on (so either one moderator or six 10k+ users). If they don't act after a short while or not enough privileged users are present in the room, the flag should be escalated to the mods and users of the parent site. If those users don't act on the flag, it be shown to all moderators and users on Chat.SE.  The exact delay should be just long enough to allow present and active users to handle the flag. Given the high speed that flags are currently handled in many cases, 30-60 seconds might be enough. Though looking at some hard data on flag handling times might be a better way to come up with a useful length.   It might also be useful to increase the number of users that see the flag incrementally even at the stage where all 10k users and moderators are notified. You don't need all of them, and the wide exposure .  The advantages would be:   Not bothering users that are not needed to come to a quick decision Allows local differences in chat culture to be policed more consistently Higher chance of showing the flag to users that already know the context   But there is also a danger to this, if flags are handled locally and nobody outside the room can see them, the potential for abuse is much higher. This could allow a chat room to develop a very hostile culture, and just flag away anyone that complains, or just dismiss valid flags.   There should be an obvious way for a user to involve moderators from outside the chat room. This could be the "flag for a moderator" option, they would remain global by default and ignore the escalation system. That would also need some UI work as this option is currently rather well hidden and I suspect that many chat users don't even know that there are two types of flags. I've posted my ideas about this


New user trying to update software but don't know the authentication pass word

Just got a new netbook running Ubuntu.  When I turn it on it auto-logs-in to the desktop automatically, but when I try to connect to the wireless network it wants my Keyring password to store the password.  Problem is it isn't in the documentation (yes, I read the documentation.)  I see a lot of people asking about "Enter password to unlock your login keyring" and the cause usually centers around either they forgot the password, or the keyring password is different than the login password. So the advice is either how to change the keyring password to match the login, or deleting the keyring and creating a new one with a password they remember.  While I could delete and recreate the keyring, I still wouldn't know the login password. Without the login password I cannot run sudo either.   I tried blank for the keyring password and that didn't work either.  Also, I know that the root password is blank, and the account is disabled.  So I am not asking about that.  Question comes down to this: Is there a way to discover the password for the account that was auto-logged in? If not can I change it?  I'm up for reinstalling if I have to, but would rather not.  Besides, it is a netbook and does not have a optical drive.


I have a table that I want to insert on a page, but at least one (perhaps both) of the following conditions are met:   The table is too wide to fit within the text block or page. That is, I'm exceeding some horizontal restriction. The table is too tall to fit within the text block or page. That is, I'm exceeding some vertical restriction.   What are my options to make this table fit? If it doesn't fit, regardless of my attempts, what other options exist?


I'm preparing some labels for sending some suitcases.  How can I change the line spacing according to the font size?  \documentclass{article} \usepackage{eurosym} \begin{document} \bfseries\pagenumbering{gobble}\centering\vfill \begin{minipage}{.75\linewidth} Mittente:  \begin{LARGE} Sender Name\newline Sender Address\newline 12345 City (XX)\newline tel.\ 123456789 \end{LARGE}  Destinatario:  \begin{Huge} Receiver Name\newline Receiver Address\newline  67890 Town (YY)\newline tel.\ 01234567 \end{Huge}  \begin{LARGE} Price \euro\ 11,11\newline  Booking n. 12345 \end{LARGE} \end{minipage}\vfill \end{document}

I was working on a Beamer presentation, and noticed that, if I open a group scope and use a \tiny, the font size will bet set, but there will be a large space between lines. However, if I issue a \par at the end of the paragraph, it works as intended:  \documentclass[t]{beamer} \newcommand{\shortlipsum} {Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue euneque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Mauris ut leo. Cras viverra}  \begin{document} \begin{frame} \shortlipsum  {\tiny \shortlipsum\par   % <--- removing this \par will break line spacing } \end{frame} \end{document}   Here's a comparison between not using and using \par:    Am I doing it the right way? Why is \par the right way?


I try to create the list of object with some attributes like this. info.py  import numpy as np class MapInfo(object):     """docstring forInfomation."""     def __init__(self, arg):         super(MapInfo,self).__init__()         self.arg = arg     cost = np.array([[0,12,11,7,10,10,9,8,6,12],             [12,0,8,5,9,12,14,16,17,22],             [11,8,0,9,15,17,8,18,14,22],             [7,5,9,0,7,9,11,12,12,17],             [10,9,15,7,0,3,17,7,15,18],             [10,12,17,9,3,0,18,6,15,15],             [9,14,8,11,17,18,0,16,8,16],             [8,16,18,12,7,6,16,0,11,11],             [6,17,14,12,15,15,8,11,0,10],             [12,22,22,17,18,15,16,11,10,0]])     luggage = np.array([0, 10, 15, 18, 17, 3, 5, 9, 4, 6])     capacitor = 40 class depot(object):     """docstring for depot."""     def __init__(self):         super(depot, self).__init__()         next_pt = np.zeros((1,10))   I am trying to add data for next_pt of 10 "depot" objects like this. main.py  from info import MapInfo as inf from info import depot as dp import numpy as np  def init():     for i in range(0,10):         depot.append(dp)  """-------__init__method----------------""" def ArrangeNextDes():     temp = np.zeros((1,10))     pos = np.zeros((1,10))     for i in range(0,10):#for depot object         for j in range(0,10):                 temp[0,j] = inf.cost[i,j]                 pos[0,j] = j         for pt in range(0,9):# for next_pt object             for jpt in range(pt+1,10):                 if (temp[0,jpt] < temp[0,pt]):                     t = temp[0,pt]                     temp[0,pt] = temp[0,jpt]                     temp[0,jpt] = t                     p = pos[0,pt]                     pos[0,pt] = pos[0,jpt]                     pos[0,jpt] = p         depot[i].next_pt = pos         print(depot[i].next_pt) """-------------------------------------"""  """------main program-----------""" start_pt = 0 map_status = np.zeros((10,10)) map_status[0,0]=1 depot = [] init() ArrangeNextDes() for i in range(0,10):     print("depot[%d] = "%i,depot[i].next_pt)   And the result like this:  [[0. 8. 3. 7. 6. 5. 4. 2. 1. 9.]] [[1. 3. 2. 4. 0. 5. 6. 7. 8. 9.]] [[2. 1. 6. 3. 0. 8. 4. 5. 7. 9.]] [[3. 1. 0. 4. 2. 5. 6. 7. 8. 9.]] [[4. 5. 3. 7. 1. 0. 2. 8. 6. 9.]] [[5. 4. 7. 3. 0. 1. 8. 9. 2. 6.]] [[6. 2. 8. 0. 3. 1. 7. 9. 4. 5.]] [[7. 5. 4. 0. 8. 9. 3. 6. 1. 2.]] [[8. 0. 6. 9. 7. 3. 2. 4. 5. 1.]] [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[0] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[1] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[2] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[3] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[4] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[5] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[6] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[7] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[8] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] depot[9] =  [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]]   The problem is that after the loop finishes, all the object of the list is the last result of the loop [[9. 8. 7. 0. 5. 6. 3. 4. 2. 1.]] when they must be equal to each results in the loop orderly (the first ten lines).  The question is what is going wrong here. Thanks

When you pass a collection like list, array to another function in python, does it make a copy of it, or is it just a pointer?


Is there a method to get the number of replacements using .Replace("a", "A"); ?  Example:  String string_1 = "a a a"; String string_2 = string_1.Replace("a", "A");    In this case, the output should be 3, because a was replaced with A 3 times.

I am doing something where I realised I wanted to count how many /s I could find in a string, and then it struck me, that there were several ways to do it, but couldn't decide on what the best (or easiest) was.  At the moment I'm going with something like:  string source = "/once/upon/a/time/"; int count = source.Length - source.Replace("/", "").Length;   But I don't like it at all, any takers?  I don't really want to dig out RegEx for this, do I?  I know my string is going to have the term I'm searching for, so you can assume that...  Of course for strings where length > 1,  string haystack = "/once/upon/a/time"; string needle = "/"; int needleCount = ( haystack.Length - haystack.Replace(needle,"").Length ) / needle.Length;


Here I am again, asking the same question I asked a few months ago. But no, I don't believe this is a duplicate, because there are so many contradicting answers on this that I find it difficult to determine the correct one.  seroundtable.com says,     H1 tags should be used for what they were originally created for: organizing your documents to stress the key points.   That being said, it would be illogical for search engines to not think that a h2 is of lesser importance than a h1.  ehow.com says this,     it is recommended that a page should always have an H1 element, but only one. The H1 tag should include the main keywords targeted within the page.   So that right there contradicts an answer provided to me on S/O a few months ago. The answer that was provided went along the lines of, 'You can have as many h1 tags as you like' (I was asking a question about how to use them when I need more than 6).  So now I am confused.  I believe that by using many h1's sends a less-than-clear message to the viewer and search engines. But I also feel dirty making a p tag 28px;  What should I do? The issue here is, this is a unique design, and all 5 main navigation links are spread horizontally and are all the same size. I want to use a h1 for them all, I do not want to use h1, h2, h3, because all links - in this case - are of equal value. What I mean is, you wouldn't dare try to pass one page off as less important than the other.

I have a webpage that I use h1 tags multiple times within various DIVs and I style h1 for each div to be the appropriate size.  For example...  #content h1 {   font-size:22px; }  #left-nav h1 {   font-size:14px; }  #content .recent-news h1 {   font-size:16px; }   Is this alright? I am worried about SEO.  What is the best way to go about this? Or am I worrying about nothing?


How to stop my 5 year old from sucking her finger more often , accompanied by playing with her nipples or her hand down her pants ( no idea what she's doing ).

My 4-years-old daughter still sucks her thumb while sleeping.  How can help her stopping this habit?  I have tried to give her a pacifier, but she refuses it. She does not have this habit during the day and is also upset in the morning when she sees her nails are flaky and her thumb hurts.


I am working on level sensor which give output of 4-20 mA. I have to feed output of level sensor to an ADC of a micro-controller, to do so I have to convert it from current to voltage.Voltage range needed is 0-1.8 Volts.  So I have gone through some circuits below:      I want to know which would be much more suitable to be used with ADC of micro-controller.

Looking for a simple design to convert from 4-20mA signals to 0-3V3, I'm thinkin about configuration shown at picture attached.   And I would like to discuss its suitability.  It is based on: - A follower configuration for a Rail-to-Rail OpAmp, powered  at 3V3. - A 165Ohm resistor to get, 3V3 at 20mA, and 0V66 at 4mA.  What do you think about?  It is any improvement I can do? Or it would be better to work with another more precise configuration?   It is thought for a low power applications (<5V), but it would like to know if it could work with 4-20mA transmitters powered at 24V too.


How to implement with the package titlesec in the preamble to maintain the same vertical alignment and numbering?

So far, I've been trying code from various examples, and landed with:  \usepackage(titlesec) \titleformat{\section}[block]{\bfseries}{\thesection.}{1em}{}  \titleformat{\subsection}[block]{\hspace{2em}{\thesubsection}{1em}{} \titleformat{\subsubsection}[block]{\hspace{3em}}{\thesubsubsection}{1em}{}   to indent the headers and their numbering. But I don't know how to get the content within each section/subsection/subsubsection to have an indented margin. In other words, I'd like to have the section/subsection/subsubsection content to be in line with it's indented header.  Is titlesec able to do this? I've been battling with the documentation, but I think they assume some more tex knowledge than I have as everything I try doesn't seem to work.  I'd like to use titlesec because, according to my understanding, I won't have to make any further adjustments while writing the document. I'm using pandoc to generate that part from markdown, so I can't have inline formatting on my sections.  Added the following as per comment requests:  Here is what I have:    And, here is what I would like:    Or, I would like something like this:


I am running 2 OS flavors on my 2010 Macpro, 10.6.8 Snow Leopard on one startup drive and the latest Yosemite on another.   The Snow Leo drive contains a folder "private" that looked like it was 25GB but once opened and listing subfolders, dropped to under 2GB. What is the purpose of this folder? It doesn't seem to exist on the Yosemite drive at all. The drive is an SSD and anything I can do to keep it smaller would be great. This is the view of the whole drive -    The folder is named private but it's visible, and at the top level of the drive folder system.

Why is /tmp a symlink to /private/tmp on Mac OS X? In other words, why isn't /tmp just a regular directory, like on Linux or BSD? I understand how it works and I don't mind it, I'm just interested in the (historical?) reasoning behind it.


I was having a discussion with someone about what sites we should add to google search console. I argued that we would only need our canonical site i.e.   https://www.example.com   Where as he argued that we should have all variants:   http://example.com https://example.com  http://www.example.com https://www.example.com   Annoyingly, he couldn't provide any reasons as to why we should add them all ' it's just something you do' he said. I'd be grateful if someone could shed some light on why you would want all the sites listed?   Note: We do server 301 redirects from the three non-canonical sites to the canonical one, so there is actually no way anyone could get to any URL other than https://www.example.com

In researching the best practice for adding sites to the Search Console, I've often seen it suggested to add separate properties for different versions of the same website. Even in  it states:     "Similarly, if your site has http:// and https:// versions, you should   add each as a separate site."   I've seen the same suggested for www/non-www. So if a site is accessible at all the variations of http/s and www/non-www we should have four properties.  But what if the site is only accessible at one variant? i.e. https and www are forced via htaccess, so only  can ever be accessed - should we still add all the variants?   In essence, the problem is that I don't know why Google wants us to do this, so I can't work out if it'll be ok just to have one instance.


I faced a strange problem today. I can't open my serial port and it says permission denied!! It's strange because I checked and I member of the dialout group! I'm using arduino.

I'm using the Arduino IDE in Ubuntu, and am having issues with the serial port. It has worked in the past, but for reasons that may be unnecesary, I felt the need to change the ownership of some of the files from root ownership to my users ownership.  This made the IDE work correctly, but I lost the ability to use the correct serial port.  In the dev folder, the port I need is listed as permission 166. Someone (who is no longer in the area to help me) swapped the permissions to 666, which made it all work gloriously.  However, it reverted back as soon as I restarted my computer, and if I now try to use the command:  sudo chmod 666 ttyACM0   nothing happens. No error messages, but no permission change either.    How can I change it, and how can I get it to change permanently.  I apologize if this question is overly simplistic or unclear, I'm an ubuntu noob, and I wouldn't begrudge feedback!


I'm aware that the t-test needs 'normally distributed data'.   But take the variable y. When it is plotted without being split by group, it isn't normally distributed:  set.seed(1) y <- c(rnorm(1000, 1), rnorm(1000, 5)) group <- c(rep("A", 1000), rep("B", 1000)) df <- data.frame(y=y, group=group) library(ggplot2) ggplot(df, aes(y)) + geom_histogram()     But when y is split by group, it is normally distributed:  ggplot(df, aes(y)) + geom_histogram() + facet_grid(~group)     Can anyone clarify if a variable only needs to be normally distributed after being split by group?

An addition to the common confusion about normality testing in inferential statistics for general linear models:  I understand the assumption of normality refers to the residuals in ANOVA and regression models, but what about t-tests?  Calculation of the t-statistic uses standard deviation as a measure of dispersion, rather than sums of squares for the F-statistic in ANOVA and regression. If I understand correctly, it is because of this that there is an assumption that the samples are normally distributed (i.e. the sample standard deviation provides an accurate estimate of the population standard deviation). Is this right?  What do you do if the statistical population of the dependent variable is not distributed normally (thus samples are unlikely to be normally distributed)? Is this where transformations fit in?


Every night, we run a batch that sends data from a point of sale service that sends data to Google Sheets, with the hope that we can trigger a Mailchimp automation or add subscribers (the POS software doesn't have an integration :().  The data is sent as an array value, which outputs like this...   The data is sent in single cells, nightly. This day in particular, 82 records were added as a single row, with commas separating the values.  What we need is to take those 82 values, and have them as separate rows in a different sheet automatically. Once that's done, we can use Zapier to send each new row to Mailchimp as a subscriber.  Pic below for desired effect...    Hope this makes sense!

I'm compiling a database of business address info, including key staff for each business. The Google spreadsheet I've inherited for this project includes a column for 'key staff' (in column B), with multiple key staff names listed in the same cell, separated by line breaks (ie CHAR(10) ). There is one business per row. The number of lines in the 'key staff' cell varies row-by-row.  My initial sheet looks like this:    I need to do the following to optimize this sheet:   split each multi-line ‘key staff’ cell so each key staff name appears on its own row. This requires that new row/s be inserted beneath the original row. duplicate the data from all other cells on the original row (i.e. from columns A & C:E), so that each new row contains the full data for each business I need an automated process - I'll have about 1000 businesses to process so can't do this with any manual steps   The sheet should then look like this:    Using =TRANSPOSE(SPLIT(B1,CHAR(10))) obviously only goes part of the way - it doesn’t insert new rows and doesn’t duplicate the surrounding column entries. All help gratefully accepted!


i'm trying to make a simple code and this point in the code generates an error in the script saying String can't be used as boolean even though i'm not using it as boolean  String wc = Mt.input("asks for input") /*i have a class called Mt that basically just makes writing lines and asking for input easier*/  if (wc = "a possible input for wc") {//error occurs here     Mt.s("words");     Mt.input("");     System.exit(0); }   the error is  Exception in thread "main" java.lang.Error: Unresolved compilation problem:      Type mismatch: cannot convert from String to boolean      at Main.main(Main.java:20)//line of if statement in full code

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


I have a year old ideapad laptop, I was running 14.04 for a few months without issues, it's only recently that I started encountering a lot of freezes, I would generally be browsing the internet maybe edit a file via vim or some simple tasks like that. very annoying

All operating systems freeze sometimes, and Ubuntu is no exception. What should I do to regain control when...   just one program stops responding? nothing at all responds to mouse clicks or key presses? the mouse stops moving entirely? I have an    In what order should I try various solutions before deciding to pull the power plug?  What should I do when starting up Ubuntu fails?  Is there a diagnostic procedure I can follow?


It's now been almost four years since Stargate Universe flopped, and as far as I'm aware there's been no word of anything else in that universe since then. I can understand this being the case with the TV series'; but I'm wondering if there are other media, especially novels. I can think of several things that are begging for it such as Universe's continuation and the Stargate going public. Does anyone know if there's any new novels set after Universe, or any other plans in place?  I'm aware that  basically asks the same, but since it was answered shortly after that happened the question was still somewhat up in the air. I'm hoping things have changed since then.

The Stargate storyline begins in the , and then continues in , then , and finally in .  Are there any films, novels, or TV series that take place in this universe after Stargate: Universe?  If there are none presently, are there any announcements of works in development?  (For example, the Stargate: SG1 series was extended through two films,  and , and both SG1 and Atlantis have several tie-in novels).


Why is the definition $\text{Work}= \text{Force}\cdot\text{Displacement}$ useful to describe the physical world?  Edit: Added another question as suggested by probably_someone, I think that this topic must also be covered to fully understand work

So the formula for work is$$ \left[\text{work}\right] ~=~ \left[\text{force}\right]  \, \times \, \left[\text{distance}\right] \,. $$  I'm trying to get an understanding of how this represents energy.  If I'm in a vacuum, and I push a block with a force of $1 \, \mathrm{N},$ it will move forwards infinitely. So as long as I wait long enough, the distance will keep increasing. This seems to imply that the longer I wait, the more work (energy) has been applied to the block.  I must be missing something, but I can't really pinpoint what it is.  It only really seems to make sense when I think of the opposite scenario: when slowing down a block that is (initially) going at a constant speed.


I live in Tunisia, exactly in Gafsa .. and there's a weird effect is happening, i really tried to ask people but no one had a clue, also i have seen that in other places on the internet. If you put a car on a road, it ll twist towards the low place, which is obviously against gravity laws .. i don't know if there's a magnetic field which affects the car, but i should of tried another metal to be sure .. well anyways, it really interested me for years and i'm looking for an answer . The video of someone recording this in my city :

(Sorry: above links in Slovak.)   Can someone explain this to me? Is it a hoax?  (In case of link rot try  or  Youtube search.)


So I have an Intel 5500 as integrated GPU and AMD R5 M430 as Dedicated (Discrete) GPU, I installed Oibaf's Drivers and vga_switcheroo and I want to switch to the Dedicated GPU, forever.  Here's the output for sudo cat /sys/kernel/debug/vgaswitcheroo/switch 0:IGD:+:Pwr:0000:00:02.0 1:DIS: :DynOff:0000:0d:00.0  And when I do sudo echo OFF > /sys/kernel/debug/vgaswitcheroo/switch which is connecting to the Dedicated GPU, I get this error bash: /sys/kernel/debug/vgaswitcheroo/switch: Permission denied  How can I connect to the Dedicated (AMD) GPU, and do I need to connect everytime I reboot my laptop?

I have a Dell 5110 laptop that has hybrid graphics. I have tried using vgaswitcheroo to some limited success, but I have still not been able to select my discrete ATI 6470 card. I use the following commands with the following outputs:  root@mikelaptop:~# cat /sys/kernel/debug/vgaswitcheroo/switch 0:DIS: :Off:0000:01:00.0   1:IGD:+:Pwr:0000:00:02.0  root@mikelaptop:~# echo ON > /sys/kernel/debug/vgaswitcheroo/switch  root@mikelaptop:~# cat /sys/kernel/debug/vgaswitcheroo/switch 0:DIS: :Pwr:0000:01:00.0   1:IGD:+:Pwr:0000:00:02.0  root@mikelaptop:~# echo DIS > /sys/kernel/debug/vgaswitcheroo/switch  root@mikelaptop:~# cat /sys/kernel/debug/vgaswitcheroo/switch 0:DIS: :Pwr:0000:01:00.0   1:IGD:+:Pwr:0000:00:02.0  root@mikelaptop:~# echo IGD > /sys/kernel/debug/vgaswitcheroo/switch  root@mikelaptop:~# cat /sys/kernel/debug/vgaswitcheroo/switch 0:DIS: :Pwr:0000:01:00.0   1:IGD:+:Pwr:0000:00:02.0  root@mikelaptop:~# echo OFF > /sys/kernel/debug/vgaswitcheroo/switch  root@mikelaptop:~# cat /sys/kernel/debug/vgaswitcheroo/switch 0:DIS: :Off:0000:01:00.0   1:IGD:+:Pwr:0000:00:02.0   As you can see here, vgaswitcheroo turns power on and off to my discrete card, but for some reason will not select my discrete card. When I tried using echo DDIS > /sys/kernel/debug/vgaswitcheroo/switch, then logged out, my system froze. Can anyone help me?  Thanks!


I am looking for a word...     Red is a color       Blue is a color       Color is a ____ of blue and red   What word goes in the blank?

Bats and rats are mammals. 1 and 2 are positive integers. Oaks and maples are trees. Carrots and cake are food.   I seek a word to describe this, the process of finding a concept that encompasses several given concepts. Is there such a word?


produces nice looking plots, that have consistent look and feel. But sometimes you have a good reason to change that look, and I found it tricky to change style of an specific line, circle, etc.  I am using R to process my data, and I need to create a  and use it with LaTeX. Using tikz/pgfplots to draw boxplot, I can produce the boxplot using data generated by R, but I want boxplots that have thick line in the mean value. Using keyword thick causes all lines of the boxplot to be drawn thick.  This is an  that I use:  \documentclass{article}  \usepackage{pgfplots} \usepgfplotslibrary[statistics] \pgfplotsset{compat=1.12}  \begin{document}  \begin{tikzpicture} \begin{axis}[boxplot/draw direction=y] \addplot+[ boxplot prepared={     lower whisker=5,     lower quartile=7,     median=8.5,     upper quartile=9.5,     upper whisker=10, }, ] table[row sep=\\,y index=0] { data\\ 1\\ 3\\ }; \end{axis} \end{tikzpicture}  \end{document}   My desired plot should look like this:    which is created with R, and it should optionally have a dashed vertical line, and smaller min and max limits.

I have been trying to add boxplots to my barcharts and I've finally got some where. After many hours of tearing through these forums and their examples and exhausting the PGFPLOTS 1.10 Manual I got nowhere very slowly. Many of the StackExchange examples were coded for previous versions of PGFPLOTS, not version 1.10 and the native boxplot. What I would like to know is: How do I change the box width (horizonal box height), the line thickness, the whisker height, the line color, box fill color, etc. ? I don't see much listed in section 5.11.1 Boxplots in the manual dated 2/28/14. Might someone be kind enough to post some examples of a truely customized boxplot. I should also post I'm using boxplot with sample data from a file (small number). Also, what libraries should be used as  there seems to be several statistics libraries.  Any help here is greatly appreciated. Regards, Dave


I have seen a proof that every relation which is symmetric and transitive is also reflexive.  if $A=\{1,2,3\}$ Then if $R=\{(1,2)(2,1)(1,1)\color{blue}{(2,2)}\}$  here $R$ is symmetric and transitive on $A$ but not reflexive right?  Can anyone clear up this confusion for me?

Definition: Given a set $X$, a relation $R$ on $X$ is any subset of $X\times X$.  A relation $R$ on $X$ is said to be  reflexive if $(x,x) \in R$ for all $x \in X$, irreflexive if $(x,x) \not\in R$ for all $x \in X$, transitive if $(x,y) \in R$ and $(y,z) \in R$ implies that $(x,z)\in R$, intransitive (or antitransitive) if $(x,y) \in R$ and $(y,z) \in R$ implies that $(x,z)\not\in R$, symmetric if $(x,y) \in R$ implies that $(y,x) \in R$, antisymmetric if $(x,y) \in R$ and $(y,x) \in R$ implies that $x=y$.   Given any combination of the properties listed above, is there a nontrivial (i.e. nonempty) relation which satisfies that combination of properties?


I have an extra Android device (a mobile phone, Samsung Galaxy Y Duos, S6102B, Android 2.3.6 - rooted), that I call D1 here, and would like to use it as my "car brain", like a low-cost multimedia central, to do a lot of things.  On this question, I would like to know:   If I have another Android device, called here D2; How to play every sound from D2 on D1 using bluetooth connection.   Example:   I'm on a call on D2. When I enter the car and turn D1 on, when D1 and D2 become bluetooth-paired, I can drive and continue talking via D1 (like a handsfree device), with D2 on my pocket; I'm hearing music on D2 with my headphones. When I enter the car and turn D1 on, when D1 and D2 become bluetooth-paired, I can hear the music from D2.

Is there a way to make an Android phone (HTC Desire HD) act as Bluetooth speakers or headset?  I'd like to use the phone as wireless headphones whilst watching a movie on a computer (running Ubuntu).


I have an under-armed vault. That is, I only have 3 or 4 weapons in a vault with almost 30 dwellers. When there's an invasion, I often have to quickly scramble a defense squad but I cannot tell who's got the big guns.  How can I quickly tell who's got which weapon?  Does the game provide an interface that let's you find that out quickly? If not, what would be a useful way for me to keep track of who's carrying which gun?

I keep all my dwellers un-armed, and arm them when it's needed. This way all my best weapons are available at any moment. After an incident, then I need to un-arm all the dwellers I previously armed. I can't find a good way to do this; is there some way to see an overview of dwellers and their weapons? Or some way to ensure that all dwellers are dis-armed?


If $a+b$ is even, then $24|ab(a^2-b^2)$. Since $a+b$ is even, then $a+b=2n$ for some integer $n$. This also implies that both $a$ and $b$ are either even or odd. So there are two cases to consider. Case $1$: Both $a$ and $b$ are even, then $a=2p$ and $b=2q$ for integers $p$ and $q$. Also $24=2^33$. So $$ab(a^2-b^2)=2^32q(p-1q)(p-0q)(p+1q).$$ If $(p-1q)(p-0q)(p+1q)$ is divisible by $3$, then case $1$ is done. I know that one of three consecutive integers is always divisible by $3$ and what I have found with this problem is the same thing, but where the consecutive aspect was replaced by shifting each $p$ term $q$ units. I'm trying to see how to incorporate this and know with certainty that I'm right and then do this for case $2$ where both $a$ and $b$ are odd. I'm also certain that there is an easier way to do this problem because what I'm doing is unlike anything in the textbook I'm using, where the problem came from. Any hints or solutions are greatly appreciated. I feel like I'm using a tank to kill a roach.

Let $p> 3$ a prime number and $a, b \in \mathbb{Z}$ arbitrary.  Prove that $6p \mid (ab^{p} - ba^{p})$.