Calculating the stiefel whitney class of Tangent Bundle of projective space

I was reading the proof of the fact that whitney sum of the tangent bundle of $RP^n$ with the trivial bundle is isomorphic to whitney sum of $n+1$ tautological line bundles on $RP^n$ from Hatcher's Vector Bundles and K theory.  However I am confused at this particular point in which he says  In the normal bundle $NS^n $ the identification $(x, v) ∼ (−x, −v)$ can be written as $(x, tx) ∼ (−x, t(−x)) $. This identification yields the product bundle $RP^n × R$ since the section $x \to (−x, −x)$ is well-defined in the quotient. Now let us consider the identification $(x, v) ∼ (−x, −v)$ in $S^n × R^{n+1}$ . This identification respects the co- ordinate factors of $R^{n+1}$ , so the quotient is the direct sum of $n + 1$ copies of the line bundle $E$ over $RP^n$ obtained by making the identifications $(x, t) ∼ (−x, −t)$ in $S^n × R$ . The claim is that E is just the canonical line bundle over $RP^n $. To see this, let us identify $S^n × R $ with $NS^n$by the isomorphism $(x, t)\to(x, tx)$ ,hence $(−x, −t)\to ((−x, (−t)(−x)) = (−x, tx)$ . Thus we have the identification$ (x, tx) ∼ (−x, tx) $in $NS^n$ . The quotient is the canonical line bundle over $RP^n$ since the identifications $x ∼ −x$ in the first coordinate give lines through the origin in $R^{n+1}$ , and in the second coordinate there are no identifications so we have well-defined vectors $tx$ in these lines.  So it seems like he is proving that $(x,v) \sim (-x,-v)$ is trivial in the first three lines and later he seems to be proving that it is the tautological line bundle which is non trivial. Also I could not find this same proof anywhere else(all had the proof from the book characteristic classes by Milnor-Stasheff).  If anyone can point out where I am going wrong or give some other reference it would be great. Thanks


<input type="text" id="message" param="1" placeholder="chat here.." />   This is  element inside the div which is working fine outside the javascript  here is the case after appended element  $('.chat-wrapper').append('
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 ujwal (online)

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 <input type="text"  id="message" placeholder="chat here.." />

');   now when i do       $('#message').keypress(function(event){  alert('WORKING'); });   alert('working') only works when i type any key in the 1st element after the append is made on some click and if i type something inside that appended input box i get nothing but why?


Help installing Linux on Samsung Chromebook Plus

I'm new to installing Linux, but I do know that my chromebook has an Armv8 processor. I was following this  and everything was fine  but when I run  sudo startxfce4   I get an error   euid != 0 directory /tmp/.x11   and more stuff and then it tells me   server terminated with error (1). closing log file unable to connect to x server: connection refused.   What should I do?


Hiding specific objects from rendering in one camera while showing on others

How can I dynamically hide an object from one camera view while allowing it to show on another camera view?


Put update-like notification bubble on multiple CPTs menus for pending items

Much like how the Plugins or Comments menu items have these number notifications in a bubble for updates and unmoderated comments respectively, I'd like to use that bubble to display the number of CPTs which have a "Pending review" status. How to go about doing that?  I have found , but not quite sure where to go from there.  That would be neat to have; as I need this feature on a site that uses user-generated content (custom post types). Whenever users submit a new CPT, its status is set to "Pending review", and I want the site admins to quickly glance at the menu to see how many items need their attention.  EDIT: I now have this code:  // buuble notifications for custom posts with status pending add_action( 'admin_menu', 'add_pending_bubble' );  function add_pending_bubble() {     global $menu;      $custom_post_count = wp_count_posts('custom-post-name');     $custom_post_pending_count = $custom_post_count->pending;      if ( $custom_post_pending_count ) {         foreach ( $menu as $key => $value ) {             if ( $menu[$key][2] == 'edit.php?post_type=custom-post-name' ) {                 $menu[$key][0] .= ' ' . $custom_post_pending_count . '';                 return;             }         }     } }   ...which does work, albeit a bit inconsistent. Sometimes displaying, sometimes not. Also, if I have multiple CPTs, how do I apply this code for each and every menu item of those CPTs? The above code will work with only one CPT.


We will have a lot of skills, but certainly, we also have limitations.   I don't know whether it's right or wrong to place "but" and "certainly" together. Since "but" is conjunction, while "certainly" is adverb here. Should i change it into:     We will have a lot of skills, but, certainly, we also have limitations.   Can you give me some help?


I asked a question regarding the design choices made in the Haskell language and got slammed.  Is there a Stack Exchange community for the philosophy of computer science?


Policing gender expressions and pronouns

The  says the following:     8. What if someone wants to be referred to as "the Great and Mighty One" or by an obscenity or something?      If something is obviously unreasonable and seems to be requested unkindly, please feel free to flag for moderator attention. Pronouns are a fairly well defined thing in language and styles/nouns/titles (“Your Majesty”) are generally poor substitutes for them. Note that “it sounds silly to me” is not sufficient grounds to think something is obviously unreasonable. If you and they can't agree, ask a moderator (or, if a moderator is one of the parties to the dispute, the Community Team) as you would in other cases of dispute. The Community Team is also available to help guide moderators upon request. Offensive/trolling “pronouns” (e.g.“attack helicopter”) should be flagged.   , this means:     whether someone's requested pronouns are legitimate is now something that moderators are supposed to determine.   If these moderators and staff have not had diversity training, but are now supposed to police gender (i.e., determine whether someone's gender expression is appropriate or not). This is highly problematic.    describes the experience of a user (whose pronouns happen to be similar to mine). The pronouns were a derivative of the user name.   To summarize the post, pronouns were removed from this user's profile and an about me from one Stack Exchange site was copied over to all Stack Exchange sites, including those sites where the user had an anonymized profile.  A moderator  explaining that a staff member had done this, speculating that it was because the pronouns were not considered legitimate. I can see why a person who is not familiar with nonnormative gender expression could think this. It happens to be a manner of gender expression that is used by others (though this is a highly problematic standard, equating a valid gender expression with one that conforms to norms). It is also similar to my gender expression on this site (though, again, I hate to have to use myself as a norm against which other gender expressions should be measured). Regardless, it does not use offensive content. It was believed to be inappropriate merely because it was unique. That is the wrong standard.  I do not know this user personally, but by post history, the user does not appear to be a troll at all. In fact, this user appears to be an ally who, by identifying with nonstandard pronouns, is expressing a de facto non-binary gender identity and being punished and mocked for this.   Why not just report this as a CoC violation?  I have written this as a post rather than using the Contact Me mechanism because I believe, now that we have seen a clear example of CoC enforcement being used to restrict nonnormative gender expression, the issue of unfamiliar moderators policing gender needs to be discussed by the community and addressed in that context. For that matter, I empathize with the moderator and staff member in question. I believe they are trying their best and should not have been asked to do this.   Is this question a duplicate?  This is not a duplicate of the suggested post. It is relevant to discuss the manner in which current actual enforcement is being used to punish and mock non-normative gender expression, which is counter to the intention of the CoC changes.     We've had several posts discussing concerns about a hypothetical troll, offering statistics about how normal or abnormal individual neopronouns might be. This post is about the actual effect of requiring untrained and unfamiliar people to use their judgement to determine whether a user’s gender expression is appropriate. It is in the context of actual, not hypothetical, actions taken by staff and moderators, and whether we should reconsider the methods this site now uses to regulate the gender expression of its users.  In conclusion  How can we avoid the problems created by policing users' gender expression?


Would it be possible to edit character models of a PS1 game, to be played on an emulator?

There are some abandoned PS1 oldies out there that I would love to see revamped with improved assets. I have some skills with some some modelling programs, so I was wondering if it would be possible to rip some models with or without their textures so that I could try to update them, and experience them on an emulator. Is this possible?  Even if the edited copies cannot be reinserted into the game, would it still be possible to rip the models out so that I could edit them?


How should I structure an extensible asset loading system?

For a hobby game engine in Java, I want to code a simple but flexible asset/resource manager. Assets are sounds, images, animation, models, textures, et cetera. After a few hours of browsing and some code experiments I'm still not sure how to design this thing.  Specifically, I'm looking for how I can design the manager in a way so that it abstracts away how specific asset types are loaded and where assets are being loaded from. I would like to be able to support both file system and RDBMS storage without the rest of the program needing to know about it. Similarly, I would like to add an animation description asset (FPS, frames to render, reference to the sprite image, et cetera) that's XML. I should be able to write a class for this with the functionality to find and read an XML file and create and return an AnimationAsset class with that information. I'm looking for a data-driven design.  I can find a lot of information on what an asset manager should do, but not on how to do it. The generics involved seem to result in some form of cascading of classes, or some form of helper classes. However I haven't seen a clear example that didn't look like a personal hack, or a point of consensus.


Brian Aldiss short story about caveats of advanced military technology

I'm trying to remember a short story I read many years ago about the negative side of developing and deploying advanced weapons technology in an SF setting. It was about some intergalactic power that was trying to crush an adversary by using multiple new military technologies and how each one in turn caused this power so much grief it was defeated by the adversary. I think it was also required reading for military strategists at some schools here in the US, at least at the time I read it. I think the story was written by Brian Aldiss.


How are these modern physics figures made?

I am curious to know how the figures in popular introductory physics/Engineering textbooks are made. As examples of what I mean, see the posted figures and my comments, all from various editions of the Physics book by Serway and Jewett book (I think).  Look at all of these color gradients throughout the metals, and the imitations of lighting on the spheres. Notice the relatively realistic nature of the force scale and pullies.  Notice here that we have proper, LaTeX-like font on the mathematical symbols.  (source: ) Wow. So many complex shapes, good water drawings, and the ability to annotate the drawing freely.  Lastly, we see more extremely complicated, realistic objects, like the ship and the mountain. But this isn't just pictures, it's clear that the software used has a very precise coordinate system in it, as evidenced by the kinematics drawings overlaid. I am aware of other posts on Physics SE recommending drawing softwares such as PowerPoint, TiKZ, aymptote,  mathematica, etc. But I highly doubt these figures were produced in any of these. My suspicion is that the publishers have some specialized software for this task. So what is that software? Does anyone know? The Physics SE did not have the answer... It is important to realize the stipulation that one must be able to type properly formatted mathematics (using some manifestation LaTeX) into the figures. I say this because I intend to use such figures in a book, and the fonts must match.


What happens when C# reached its limit to generate Guid.NewGuid() ? How to handle it?

I have a scenario where i need to generate a unique key for which i am using Guid.NewGuid() in C#, and sending this key to the user via an email when user request for it and for next 48Hrs that user will be identified by this unique key. There is no limit for the user to request for this key but only the latest one will be a valid key to identify the user. My question is when C# reached the limit to generate new key what happens then?. Do i really need to worry about it?


SQL Server restore database with active connections

I am trying to run this SQL script on a SQL Server instance to restore a test database to a newer copy of the live database.  RESTORE FILELISTONLY    FROM disk = '\\staging_server\path\to\db_backup.bak'     -- Restore the files for  RESTORE DATABASE Test_DB    FROM disk = '\\staging_server\path\to\db_backup.bak'    WITH replace,    MOVE 'Test_DB' TO 'D:\R2_BIN\Test_DB.mdf',     MOVE 'Test_DB_log' TO 'D:\R2_BIN\Test_DB_log.ldf',     stats = 5 GO   However, on running the script I receive the following error.     Msg 3101, Level 16, State 1, Line 5   Exclusive access could not be obtained because the database is in use.   Msg 3013, Level 16, State 1, Line 5   RESTORE DATABASE is terminating abnormally.   Is there some way I can force this operation to go through, and kill any connections it needs to to get it done? I tried to close down any applications that may connections to the DB, but some of the connections I simply cannot identify. There are several from my username and yet I only have one instance of SQL Server Management Studio open.  Anyway, is there some way to kill all connections to a specific database? There are quite a few databases running on this instance, so I don't want to just shutdown and restart the instance all together if I can help it.


How do I stop orca from starting up on login?

Orca keeps starting up after system starting, and I'm not able to find it in "Startup Applications".  How to stop it?


Explicitly approximating $\sqrt{2}$ with rationals from left and from right

After it is shown in a book "Principles of mathematical analysis - W. Rudin" that $\sqrt{2}$ is not rational number then it is shown that if $A$ is set of all positive rationals $r$ such that $r^2<2$ and if $B$ is set of all positive rationals $r$ such that $r^2>2$ then $A$ does not contain the largest and $B$ does not contain the smallest element.  That is done by defining for positive rational $r$ the number $s=r- \dfrac{r^2-2}{r+2}$.  Then it is shown that $s^2-2=\dfrac{2(r^2-2)}{(r+2)^2}$ so if $r$ is in $A$ then $s>r$ and $s$ is in $A$ and if $r$ is in $B$ then $s<r$ and $s$ is in $B$.  Is algebraic expression $\dfrac{r^2-2}{r+2}$ somehow special in this context or even some other algebraic expressions can be subtracted from $r$ "to satisfy the needs" of this construction?


A term for words that change pronunciation with part of speech

I'm talking about words like:   construct: CON-struct(n.), cun-STRUCT(v.) present: PRE-sent(n.), pre-SENT(v.) record: RE-cord(n.), ri-CORD(v.)   They are pronounced differently based on whether they are a noun or a verb.  Here are the terms I DON'T think would apply:   Homograph: same spelling, different meanings: for example, bark (the sound of a dog) and bark (the skin of a tree). Homophone: same pronunciation, different meaning: for example, to and two Homonym: same pronunciation and spelling, different meanings: for example: bank (river bank or savings bank) Heteronym: same spelling,  different pronunciations and meanings: for example bow (the front of a ship) and bow (a ranged weapon)   Bow is particularly interesting. It is a heteronym based on the two nouns I described. But in the sense of the body movement, the noun and the verb are pronounced alike (rhyming with wow), thus, not belonging to the category I've explained.  In fact none of the terms explained  satisfy my requirement.  I'm looking for the term for words that have same (or related at best, NOT different) meanings, same spelling and different pronunciation.  Specifically, different pronunciation depending on the part of speech. As against the words which have the same pronunciation in different parts of speech like bill, turn, case (or bigger ones like manoeuvre)  TL;DR:  Fill in the blank:     The noun and verb forms of construct are pronounced differently   because the word construct is a _____   or      The noun and verb forms of construct are pronounced differently   because they are _____s.


English as a second language - Is it acceptable to edit spelling and grammar?

This question refers specifically to questions posed by individuals that are clearly using English as a second language. It does not refer to people who are making minor mistakes in their native language.  I don't want to seem pedantic, but I see some good questions that are written in English as a second language, with some detracting grammar and spelling mistakes.


Virtual photons, what makes them virtual?

The wikipedia page "" says:     The electromagnetic force can be described by the exchange of virtual photons.   The virtual photon thing baffles me a little. I get that  are supposed to be short lived, but as photons live for zero units of proper time I can't see how their lifetime can be used to distinguish between virtual and non-virtual.  Another idea I had was that virtual photons are only those associated with the electromagnetic field, non-virtual ones are not. But in this case, I could not see what was wrong with this: If I have a photon detecting instrument it is just detecting the force carrying particles of the electromagnetic interactions between it and the thing I am using it to observe? (even if that thing is a long way away)  Are virtual photons just photons that you don't observe? Or, is there some kind of photon that is not connected with the electromagnetic field? Or something else? Or perhaps there is no concrete distinction to be made?


Pointer to template method of template class within a template function

Is there a way to make the commented definition of b working?  template <typename t0> struct comp_impl {         t0 g;          template <typename t1>         t0 h(t1 x)         {                 return g;         }; };  template <typename t0, typename t1> void foo() { //      WORKS         int (comp_impl<int>::*a)(int) = &comp_impl<int>::h<int>; //      FAILS //      t0 (comp_impl<t0>::*b)(t1) = &comp_impl<t0>::h<t1>; }  void bar() {         foo<int, int>(); }   The error is:  comp-3.cpp: In function ‘void foo()’: comp-3.cpp:19:51: error: expected primary-expression before ‘>’ token   t0 (comp_impl<t0>::*b)(t1) = &comp_impl<t0>::h<t1>;                                                    ^ comp-3.cpp:19:52: error: expected primary-expression before ‘;’ token   t0 (comp_impl<t0>::*b)(t1) = &comp_impl<t0>::h<t1>;


I am beginner in Java. I am trying to make a gui game and I want to add key adapter but I dont know where should i get as parameter start- where is Jframe extended Slides-where is new Layout set (panels buttons etc) Casual - where is setText change I use many seperate class like Colors and Fonts but I think that I dont have to include that. Here is a two fragments that throws Null Pointer Exception. I must add I tried all classes above as parameter to constructor but it didnt worked .After all here is code : Casual.java (fragment)             public void firstDay(){             pv.movingHandlerON=true;             start.addKeyListener(new MovingChoiceHandler(slides)); // naprawic !             music.setMusic(pv.musicDay);             music.loopMusic(99);             music.startMusic();              slides.textPanel.setText("You had the accident in forrest.\nYou take all u got and go              into adventure.\n\nWhere do You want to go?\n\n[Q] Go forest Pathway  [Z] Go Muddy               road");             }  MovingChoiceHandler .java (full code without import and package)           public class MovingChoiceHandler extends KeyAdapter {         PlayerVariables pv=new PlayerVariables();         Start start;         Slides slides;         Casual casual;                   MovingChoiceHandler(Slides slides){     this.start=slides.start;                   }               // tutaj przez strzałki bedziemy zmieniac slajdy         public void keyPressed(KeyEvent e){           //  if(pv.movingHandlerON==true) {                 switch (e.getKeyCode()) {                          case KeyEvent.VK_Q:                         System.out.println("Sprawdzanie gory check");                         break;                               case KeyEvent.VK_W:                         System.out.println("Sprawdzanie dolu check");                         break;                           }             //}         }               }  If You interested more here it is full code if You dont see here any problem. As I say i tried start, casual,and  slides but it still throw this exception.I tried even like this.slides=slides; this.start=slides.start; Full code : Start.java :  StartButtonHandler (start->slides) : Slides.java :  (Casual is added without handler into Slides) Casual.java : MovingChoiceHandler.java:  (added in first method in casual to change next "slides"


Photographic techniques to avoid chromatic aberration?

I've read   here on Photo SE, as well as the  on CA.  I understand that it is inevitable that some amount of chromatic aberration shows up for a particular lens, especially on the extreme cases: high contrast of colors/luminosity, etc.  But I'd like to know if there is any technique one can do to -minimize- this when some photo opportunity arises;    eg: if i'm visiting some place and want a picture of a building, for example. i can't go "meh, too contrasty, results won't be good."     Would stop down the aperture help? I haven't tested it, but according to the causes of CA, it could help (bigger DoF, more things in focus, less specific color in different focus).   Other than that, nothing comes to mind..   I already got a prime lens for the extra oomph of image quality, but i want more :)  please no "buy better gear" of "fix it in post" answers.. Obviously, i can fix stuff in post, AND I DO. But i'd like to make the most of my gear, and spend maybe a bit more time taking a picture, and less on lightroom.


Existence of two disjoint closed sets with zero infimal distance

Are there two closed sets $A,B\subset\mathbb{R}^2$ with the following properties?   $A\cap B=\emptyset$ $\forall \epsilon>0$ there exist $a \in A$ and $b\in B$ such that $\|a-b\| < \epsilon$


How can you make an armor that has infinite protection armor?

When I was using the new attribute command, I saw an attribute called "armor." I don't know what it actually does, but I think it has to do with protection. I was wondering if I could make an armor that has infinite protection so I tried to make a command: give @s netherite_helmet{AttributeModifiers:[{AttributeName:"generic.armor",Name:"generic.armor",Amount:1.79769313486232E+308d,Operation:0,UUID:[I;439,684,724,99]},Slot:"head"}]}  I thought it would give me infinite protection, but it only gives me a helmet with the empty "protection" attribute. It works fine on older versions, but not on the 1.17 snapshots.


java collection to retain order and should be unique

Set<String> stringSet = new HashSet<String>();   will not retain order obviously   Set<String> linkedHastSet = new LinkedHashSet<String>();   while reading elements from the above set it should retain order but in some times it does not ? am I wrong in my observation or I am missing something ?


Moving parameters position in toolbox and combining parameters into one row

I've been working with ArcGis for a while now and was wondering if there was a way to change positions of parameters inside the toolbox for the user. The only time I have seen this done in arc toolbox is with the Raster clip tool with the Rectangle parameter where the 4 parameters are aligned in a circle in the toolbox.     I don't know if what I want is possible since I haven't seen anyone else do it.


Why doesn't the solar wind disrupt the planets?

The sun creates this heliosphere by sending a constant flow of particles and a magnetic field out into space at over 670,000 miles per hour, which is also known as solar wind. If the speed of the wind is that great, why doesn't it disrupt the planets in our solar system? Does it just prevent foreign particles from interstellar space entering the heliosphere?


Pascal casing or Camel Casing for C# code?

I've been arguing with my coworkers about Pascal casing (upper camel case) vs. lower . They are used to lower camel casing for everything from table names in SQL databases to property naming in C# code but I like Pascal casing better, lower camel casing for variables and Pascal casing for properties:  string firstName; public string FirstName { ... }   But they are used to this:  string _firstname; public string firstName { ... }   I try to keep up with their "standard" so the code looks the same but I just don't like it.  I've seen that at least the .NET framework uses this convention and that is how I try to keep my code, e.g.:  System.Console.WriteLine("string")   What do you use/prefer and why? I'm sorry if somebody else asked this question but I searched and did not find anything.  Update: I've given a method example and not a property but it's the same. As I stated in the first paragraph my colleagues use the Pascal convention for everything (variables, methods, table names, etc.)


Is it calculated on the fly every time a reputation score needs to be displayed, or is every user's reputation stored as an integer in the database and updated as necessary?


A logo that will be printed on a T-Shirt

I want to make this logo print-ready on a T-shirt, but I have a few questions:  1) I have an overlap in my logo, I tried to merge the whole artwork but I get conflation artefacts, I also tried the shape builder but the same occurs. I don't want the conflation artefacts and I also know I should't have any overlaps in the logo that will be printed on a T-Shirt. what should I do?  2) I have 5 colors in the logo (white, 2 blacks, 2 grays), I knew from the videos on youtube that I must convert them to spot colors to make a color separation. After that, I check them in the separations preview. I also know that white is not counted as a spot color, is that right? so now I will have  only 4 colors as spot.  3) should the black be 0,0,0,100 as a spot color for T-shirt print? what about the other colors should they have a specific values or as soon as I change them to spot it's okay?  4) I will save the file as High quality print PDF and leave the rest as default, is that correct?  5) If the client didn't mention which method he will use for printing the T-Shirt, should I still use spot colors, or I should make other file with Pantone colors so I cover all his needs?  6)if the client will use the sublimation method, is there any difference in saving method or colors?


I updated from 20.04 to 20.10, and during the installing updates phase, the system crashed. Is there a way to just update the Ubuntu files, without editing /home? I have a backup from a bit ago but its slightly outdated so wouldn't want to use it. The system thinks it's 20.10


I want to create a select option in Razor pages from Enum object Description This is my code: <div class="dropdown-box">     <select id="type-select">         @foreach (var item in Enums.OrderStatus)         {             <option>@item</option>         }     </select> </div>  and the enum: public enum OrderStatus {     [Description("در انتظار تایید")]     PendingForAccept = 0,      [Description("تمام شده")]     Finished = 1,      [Description("لغو شده")]     Canceled = 2,      [Description("رد شده")]     Rejected = 3,      [Description("تایید شده")]     Accepted = 4 }  How can I extract items descriptions of this enum to string


How to Cite Hardware in Scientific Articles?

I am writing a scientific article. In the "materials and methods" section I must specify the hardware I used, namely an HP Pavilion dv6 Notebook PC (I also specified the details of its features).  Now my doubt:  Should I use bibliographic citations (such as when mentioning a software, book, or scientific article) when I mention the hardware?  What is standard (if any) for such cases?  Thanks in advance for any help and/or suggestion.  P.S. I use APA standards for bibliographic references, although the question is independent of that subject.


Render multiple images simultaneously in blender from multple cameras

If I have 2 cameras in my scene, and I want to render images from both the cameras simultaneously and not one after the other, is that possible ?   One alternate option I was thinking of doing was open two blend files and render image from one camera in each blend file simultaneously. But my doubt is can it be done in the same blend file?


Taylor Series Expansion for $\frac1{(1+z^2)}$

Given $f(z) = \frac{1}{1+z^2}$, I want to find the Taylor series of $f(z)$ about $z_0 = 0$.  Intuitively, and based on the formation of a standard power series I have $f(z) = \sum (-1)^n(z^2)^n$.  What I need now is to find the power series for $(\frac{1}{1+z^2})^2$ and $(\frac{1}{1+z^2})^3$.  I assume I'll need to use partial fractions here but I'm a little stuck at the start. Tips would be appreciated.


My teacher said it is impossible to use Past Simple with Present Perfect. What about this example:  I went shopping [today/yesterday] to improve my mood but instead I ... sad.  Should I use became or have become? I want to emphasize I am still sad.  or is it better to say:  I went shopping and I am sad.


My teacher said that after switch is shifted (after very long time), $\phi_i = \phi_f$ $\implies i_oL  = i3L \implies i = \dfrac{i_o}{3} $ where $i_o$ is $\dfrac{\varepsilon}{R}$  So the initial current in the circuit after switch is shifted is $\dfrac{i_o}{3}$  But, I really didn't understand why the flux should be conserved in this case i.e. why  $\phi_i = \phi_f$. I would like to know about this concept and the reasons involved.   $\phi_i$ and $\phi_f$ are the total flux in both inductors immediately before and immediately after the switch is shifted?


Remove square brackets from bibliography list

I have seen that  provides an answer to how to remove square brackets in this example. However, I do not know from that answer where those adjustments can be made because I do not have any of the commands this post cites.  I wish to remove the square brackets and the numbers from the bibliography list as seen in the picture. Moreover, I wish to remove the indentation that comes through this numbering.  I have tried as kindly suggested to use \makeatletter \renewcommand(...) as seen in the comment section but that did not change anything. Perhaps, it needs addressing where to put the individual command.    I am using as bibliography style the file ecta.bst which is available here:  .  I am using the natbib package which is required for the ecta.bst bibliography style.  Here is a test document that is standalone save the .bib file which I am also providing in an abbreviated version.  I am trying to achieve the following:  I wish to remove the square-bracketed numbering from the bibliography altogether, which, as I was kindly told includes removing the indentation as well. So I just wish to have the last names in an alphabetically ordered list.  Thank you so much!  See for .tex file below and below that the content of the bibo.bib file.  \documentclass[aps,superscriptaddress,nofootinbib]{revtex4}  \usepackage[latin9]{inputenc}  \setcounter{secnumdepth}{3}  \usepackage{mathtools}  \usepackage{natbib}  \makeatletter  \special{papersize=\the\paperwidth,\the\paperheight}  %% Because html converters don't know tabularnewline \providecommand{\tabularnewline}{\\}  \newcommand\mycite[1]{% with Numbers  \citeauthor{#1}~(\citeyear{#1})\@ } %%%%%Here is the command to be tried out. \renewcommand\@biblabel[1]{} %%%%%%%%%%%%End of Jerome's custom area \makeatother  \begin{document}  \vspace{0.6cm}  \title{Test Document}  \author{Me}  % \date{2 December, 2014} %  \maketitle  \section{Testing Citations}  As he said, \mycite{ECTA:ECTA438}, we need to be clear on testing. Also, \mycite{RefWorks:14} will play a role. When we now add \mycite{RefWorks:12}.  \section{Introduction}  Hello Intro.  \bibliographystyle{ecta}  \bibliography{bibo}{}  \end{document}   WITH BIBLIOGRAPHY FILE:  @article{RefWorks:12,     Abstract = {Abstract.},     Author = {Sophocles Mavroeidis and Mikkel Plagborg-M{\o}ller and James H. Stock},     Date-Modified = {2015-01-14 22:54:50 +0000},     Journal = {Journal of Economic Literature},     Number = {1},     Pages = {124-188},     Title = {Empirical evidence on inflation expectations in the New Keynesian Phillips Curve},     Volume = {52},     Year = {2014} } @article{RefWorks:14,     Abstract = {Abstract.},     Author = {Kang Yong Tan and David Vines},     Date-Modified = {2015-01-15 13:45:29 +0000},     Journal = {Available at SSRN 1026339},     Title = {Woodford goes to Africa},     Year = {2007}} @article{ECTA:ECTA438,     Abstract = {Abstract},     Author = {Moreira, Marcelo J.},     Date-Added = {2015-01-14 22:57:58 +0000},     Date-Modified = {2015-01-14 22:57:58 +0000},     Doi = {10.1111/1468-0262.00438},     Issn = {1468-0262},     Journal = {Econometrica},     Keywords = {Instruments, similar tests, Wald test, score test, likelihood ratio test, confidence regions, 2SLS estimator, LIML estimator},     Number = {4},     Pages = {1027--1048},     Publisher = {Blackwell Publishing Ltd},     Title = {A Conditional Likelihood Ratio Test for Structural Models},     Url = {http://dx.doi.org/10.1111/1468-0262.00438},     Volume = {71},     Year = {2003}}


Cutting videos at exact frames with ffmpeg select filter

Instead of using -ss and -to seeking parameters, which seem not very accurate, can I cut videos for given frame numbers? For example; ffmpeg -i video.webm -startingframe 80 -endingframe 560 output.webm  [80th frame and 560th frame included. So, as total it makes (560 - 80 +1) frames] After the answers and a bit search, I have tried some commands. But so far I couldn't find an acceptable way. If someone wants to cut video stream between 250th and 750th frames, this is the way to go. It will give 501 frames as output: Note: movie.mp4 has 25 fps, and its audio sample rate 48k ffmpeg -i movie.mp4 -an -vf "select=between(n\,250\,750),setpts=PTS-STARTPTS" v_stream.webm  As expected, the output is 20 seconds long, exactly. Using the same method for audio: ffmpeg -i movie.mp4 -vn -af "aselect=between(n\,480\,1440),setpts=PTS-STARTPTS" a_stream.webm  Unexpectedly, this one has very poor accuracy. It should have given me 960001 (960k+1) samples which equal 20 seconds audio. But instead, the output was 20.505 seconds long and has 984240 samples. Also, if I increase the duration, error increases as well. Then I tried to use -ss -to parameters for cutting audio stream: ffmpeg -i movie.mp4 -vn -ss 10.000 -to 30.000 a_stream.webm  The old classic way works much better. Output was 20.003 seconds long and has 960144 samples. Plus, increasing duration does not increase the error, the error is constant, there is always 144 samples surplus with that input file. Summing up: select filter works well most of the time but aselect is not. The classic -ss parameters work better for audio but not sample-accurate. Also, it is not possible to use -vf select and -ss parameters together, because -ss will affect both audio and video streams while we want it only affect audio. So, to precisely cut a media file I have to do these 3 steps: ffmpeg -i movie.mp4 -an -vf "select=between(n\,250\,750),setpts=PTS-STARTPTS" v_stream.webm  ffmpeg -i movie.mp4 -vn -ss 10.000 -to 30.000 a_stream.webm  ffmpeg -i v_stream.webm -i a_stream.webm -c:v copy -c:a copy  movie-between_10th_and 20th_seconds.webm  This gives the most accurate results. Video is 20.000 seconds long and frame-acurate Audio is 20.003 seconds long and has 960144 sample. Not exactly matches with the video stream, but it is OK. There is only 144 samples surplus. The biggest downside is, whenever I want to cut a file, I have to send 3 commands for a simple job and it creates two unnecessary files: a_stream.webm and v_stream.webm. And the select filter is not working on some input files I have tried. It does the job successfully (?) but never stops the encoding process, so I have to close command prompt every time.


What is the difference between these two Breusch-Pagan Tests?

Using R on some data and trying to see whether or not my data is heteroscedastic, I've found two implementations of the Breusch-Pagan test,  (package lmtest) and  (package car). However, these produce different results. What is the difference between the two? When should you choose to use one or the other?  > model <- lm(y ~ x) > bp <- bptest(model) > bp studentized Breusch-Pagan test  data:  model  BP = 3.3596, df = 1, p-value = 0.06681  > ncvTest(model) Non-constant Variance Score Test  Variance formula: ~ fitted.values  Chisquare = 3.858704    Df = 1     p = 0.04948855    These example shows that according to the tests, my data is in one case heteroscedastic and in the other case homoscedastic. I did find  so bptest might be studentized and ncvTest might not be, however, what does this mean then?


Creating generic tool with ModelBuilder in ArcGIS Desktop?

We are working on the creation of a tool with ModelBuilder in ArcGIS Desktop 10.1. We want to build a generic tool that can be launched from any computer. In order to do so, we have set the input files as parameters in the model. When launched from the Toolbox, the paths on our computer come up in the parameter boxes. The user can change them, but we would like to have blank boxes instead.  To do so, we delete all relative path of the parameters in the model. When we test the model in ArcMap, we get the following message “Error Warning 000873” which says that our workspace does not exist. Also we have a second kind of error: “ERROR 001000” which means that some value of zone field does not exist.  Is there anyone who has executed this operation with success and could explain us the right way of process?


Where & how do i change the Ubuntu sound theme in Ubuntu 16.04?

I have looked all over the settings for a way to change the sound theme, but I can't find one. There is one spot in the settings where you can choose an alert sound, but that doesn't look like it would be what I want and it only gives the option of default. I have the Unity Tweak Tool,but there are no sound options present there. I downloaded a theme and placed the theme folder in /usr/share/sounds, but I don't know where to choose the theme.  This is for Ubuntu 16.04 and not a duplicate but its very similar.


Allow us to filter Suggested Edits and Review section by tag

I've had the ability to review suggested edits for a while now, however I don't often do so because the list is usually full of questions about languages and technologies I'm not familiar with or not interested in, and can sometimes be hundreds of questions long.  I would like to help out more, but most of my rep has been gained by questions within a specific technology, so I only feel comfortable reviewing edits within that tag.   Can you allow us to filter suggested edits by tag?  Edit:   Actually, can you let us filter the entire Review section by tag, and not just Suggested Edits?  I would find it much more interesting to review questions in tags I'm familiar with and can  understand the question content of, and it would give me a bit of pride to help maintain "my" section of SO.


What is the difference between residual and null deviance?

I applied poisson regresson on count data. In the model summary I got NULL deviance and residual deviance. I understood that residual deviance is the part which accounts for what is not explained by the model. But I am still not sure of significance of NULL deviance.


Is It Okay To Use Real Designs In My 2D Game? [Cars and Weapons]

I am making a 2D mobile game that includes cars and weapons (like GTA let's say). I am using real car and weapons designs to make 2D images, however, I use made-up names for the both cars and the weapons. Is it still copyrighted?  For example; Traffic Racer and Traffic Rider. In the games, the car models are exactly the same as the real ones, but there is no logo nor name in Traffic Racer. In Traffic Rider, you can clearly see BMW in the game (both the design and the logo). Because of these examples, I think, my situation should be okay since the game is not even 3D.


How do I apt-get gddrescue and testdisk?

Gddrescue and testdisk are not on the 12.04 ISO that I downloaded and burned to a CD that I'm currently using to boot my system.  Where do I point apt-get to install those packages?  I have Internet access but got this results:  root@ubuntu:/# sudo apt-get install testdisk Reading package lists... Done Building dependency tree Reading state information... Done  E: Unable to locate package testdisk root@ubuntu:/#


Hashset and List :Which one is efficient way to store list of objects

Which one of the folowing is efficient way to store list of objects?   Hashset<object> listOfObjects = new HashSet<object>();   or  List<object>listOfObjects = new List<object>();


Can you extend your own life with the death note?

How to Use: LVIII    By manipulating the death of a human that has influence over another human’s life, that human’s original life span can sometimes be lengthened.    which means you can use the note to extend your lifespan in the example i gave:  have some one get the shinigami eyes by giving them your death note and have them write down your life span then give back owner ship of the death note to you again (use the note to manipulate them into doing so) for example lets say you die 1st arpril 2009 at 1pm  next find some one who will out live you, you could use the person who you manipulated into finding your life span we'll call this person mr.X  write down your own name and have the cause stabbed by mr.X after calling him fat at 1st april 2009 at 1pm  next write down mr.X's name in the death note and the cause of death is a heart attack just before stabbing some one on the streert who called him fat on 1st april 2009 at 12:58pm  now if this would work you should get his remaining life span. Would this work?


What, if anything should one do if a user's "about me" profile section contains extremely inflammatory terms (racist, etc.)

I don't think anyone wants to be the thought police, and I'm particularly wary of censorship on a part of the site that is a user's personal self-statement, and is a little off the beaten path.  On the other hand, I'm also concerned that we may not want a site where clicking on a user to see their other posts would expose folks to racist or other bigoted terms that almost everyone would agree are inappropriate for civil discourse.    Don't forget the "be nice" rule".  Note that I don't want a "flag user" rule, which I know has been beaten to death already, and further think that swears and semi-inflammatory opinions, etc. should generally just be ignored - I'm only asking about terms that provoke serious emotions around racial, religious, ethnic, or sexual orientation issues.  What, if anything, is the appropriate response in such cases?


What statistical tool do i use to determine the assocation between a nominal variables with three options and a continuous variable ?)

My topic is on: Relationship between  age of teachers and academic performance of students in Mathematics.


Testing the difference in AIC of two non-nested models

The whole point of AIC or any other information criterion is that less is better. So if I have two models M1: y = a0 + XA + e and M2: y = b0 + ZB + u, and if the AIC of the first (A1) is less than that of the second (A2), then M1 has a better fit from the information theory standpoint. But is there any cutoff benchmark for the difference A1-A2? How much less is actually less? In other words, is there a test for (A1-A2) other than just eyeballing?  Edit: Peter/Dmitrij... Thanks for responding. Actually, this is a case where my substantive expertise is conflicting with my statistical expertise. Essentially, the problem is NOT choosing between two models, but in checking if two variables which I know to be largely equivalent  add equivalent amounts of information (Actually, one variable in the first model and a vector in the second. Think about the case of a bunch of variables as against an index of them.). As Dmitrij pointed out, the best bet seems to be the Cox Test. But is there a way of actually testing the difference between the information contents of the two models?


How to localize ASP.NET MVC application?

What would be best practice to localize your ASP.NET MVC application?  I would like to cover two situations:   one application deployment in IIS which would handle multiple languages one language/application deployment.   In first situation should you go with some kind of view based thing like, ~/View/EN, ~/View/FI, ~/View/SWE or something different?  What about second case, just application based config via Web.config and point these different languages to different URLs?


What book describes consuming vials of vampire blood to pseudo-Rage?

I know I've ran across this in one of my 3.5 books recently and I cant remember the book or much about it, and am having trouble re-locating this. There was an entry towards the front of the book for a vial of vampiric blood. It gave similar stats as a barbarians rage but you were also considered under the control of the vampire while its effects lasted.   About the book: If i recall correctly, the book was focused more on monsters; but not the monster manual. I believe the passage where it talked about the vials was also talking about how a vampire could make a human its servant without changing it to a spawn or charming it. I really cant recall much about the book itself...  i believe it was in one of the thinner books ( <250 pages) but i cant be sure as I've spent three days going through these books now and cant locate it.  If it helps my 3.5 collection consists of : Exalted Deeds, Vile darkness and VD more archfiends, Complete adventurer, complete arcane, complete divine, complete warrior, draconomicon, DMG, PHB, Monster Manual, Expanded Psionics, Ghostwalk, and Unearthed Arcana.  And i also have other books, incase I'm wrong about it being a 3.5 thing...  Monster Manual 2, tome and blood, sword and fist, song and silence, oriental adventures, Masters of the wild druids grove and MotW barbariands druids and rangers, manual of the planes, fiend folio, Defenders of the faith, arms and equipment, and... uh..  the book of erotic fantasy.  =)   I know that its a long shot for someone to pin-point this as I'm having issues finding it with my books in front of me or with google...  but I appreciate any information or help on finding this ruling.


The value of derivative at zero for holomorphic function on unit disk

Let $\mathbb{D}$ be the unit disk of complex plain. Let $f:\mathbb{D}\rightarrow\mathbb{C}$ be a holomorphic function on $\mathbb{D}$. Note the by Cauchy's formula, for $0<r<1$, $$2\pi if'(0)=\int_{|\zeta|=r}\frac{f(\zeta)}{\zeta^2}d\zeta$$ On the other hand, change $\zeta$ into $-\zeta$, we have $$2\pi if'(0)=\int_{|\zeta|=r}\frac{-f(-\zeta)}{\zeta^2}d\zeta$$ Summing up, $$2f'(0)=\frac{1}{2\pi i}\int_{|\zeta|=r}\frac{f(\zeta)-f(-\zeta)}{\zeta^2}d\zeta$$ Let $d=sup\{|f(z)-f(w)|:z, w\in\mathbb{D} \}$, then the above integral formula yields $$2|f'(0)|\le \frac{d}{r}$$ Taking $r\rightarrow 1$, we have  $$2|f'(0)|\le d$$  The main problem is to find the condition that equality holds. It says that the equality holds iff $f(z)=a_0+a_1z$ where $a_0, a_1$ are constants. I wanna show the only if direction and I tried to set $$f(z)=a_0+a_1z+a_2z^2+...,\quad h(z)=\frac{f(z)-f(-z)}{z}$$ and using maximum principle ($h(0)=2f'(0)=d$, $|h(z)|\le d/r$ on $|z|=r\quad\forall 0<r<1$) to get $h$ is a constant function so that a_3=a_5=a_7=...=0  But I cannot find similar things for a_2, a_4, a_6.. Can you help me?


I have the following code:  \documentclass[10pt]{beamer}  \usefonttheme{serif} \usetheme{Warsaw}  \usepackage{tikz} \usetikzlibrary{arrows}  \title{Newton's Approximation of $\pi$}  \author{Daniel Rui}    \begin{document}    \begin{frame}  \titlepage  \end{frame}    % \section{Part 1}    % \begin{frame}  % \frametitle{Outline}  % \tableofcontents  % \end{frame}    \begin{frame}  \frametitle{Approximation}  \begin{columns} \column{0.6\textwidth} Newton begins with a circle centered at $\frac 12$, as shown. He draws a vertical line at $\frac 14$, and uses two different methods to find the area of the shaded region. \column{0.4\textwidth} \begin{center}  \begin{tikzpicture} [ circ/.style={circle, draw, solid, fill=white, inner sep=0.75pt,              label=#1,              node contents={}              }, every label/.append style = {inner sep=2pt, font=\footnotesize}                     ] % shaded area \fill[gray!30]  (0,0) arc (180:120:1.5cm) |- cycle; % axis \draw[->]   (-0.5,0) -- + (4.0,0) node[below left] {$x$}; \draw[->]   (0,-0.5) -- + (0,3.0) node[below left] {$y$}; % rest of image \draw (0,0) node[circ=above left:$B$] arc (180:0:1.5) node[circ={}]; % \draw[densely dashed]   (60:1.5) -- (0:1.5) node[circ=below:$\frac{1}{2}$]; \draw                   (60:1.5) node[circ=$A$] -- (0:0.75) node[circ=below:$D$]; \end{tikzpicture} \end{center}  \end{columns} \end{frame}    \end{document}   Using my compiler (it’s an app called TeX), it gives me the following error:  Illegal parameter number in definition of \test     On another compiler, it seems to work, but on this one, it is very consistently telling me that there is an error. Is this a compiler problem, or is there actually a problem in the   label=#1   that seems to cause a lot of trouble? I tinkered with that particular line a lot, and I believe it is the heart of the problem. Thank you for your help.


For A,B subsets of a Normed Vector Space, A closed, B Compact, Show A - B Is Closed

Statement of the problem:  Let $E$ be a Normed Vector Space over the real numbers. Let $A, B$ be subsets of $E$ such that:  $A$ and $B$ are non-empty, $A \cap B = \emptyset $. Assume $A$ is closed and $B$ is compact. Define the set $C := A - B = \cup_{b \in B} (A - b)$. Here, $A - b = \{ a - b : a \in A \}$. i.e. a translation of the set $A$ in the direction of $-b$.  Prove that C is closed.  I am sure that $B$ being compact is key here, and suspect I should consider finite covers in some way, but I cannot figure out why $A - S$ should be closed for any potentially infinite set $S$... Could someone please offer me a hint? Thank you.


When to use Conservation of Energy vs Conservation of Momentum

I am confused as to when each should be used to solve problems.I am not looking for the answer to this question, but I will include it here so you have all the information about what I am asking about.      A 15.0 kg block is attached to a very light horizontal spring of force   constant 400.0 N/m and is resting on a frictionless horizontal table.   (See (Figure 1) .) Suddenly it is struck by a 3.00 kg stone traveling   horizontally at 8.00 m/s to the right, whereupon the stone rebounds at   2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.   I see that the idea suggested  is to use conservation of momentum to solve this problem. But I wanted to solve using conservation of energy in the following way:   $K.E =\frac{mv^2}{2}$  $Spring-P.E=\frac{kx^2}{2}$  $KE_i = KE_f + PE_f$  $KE_i - KE_f = PE_f$  Solving the equations, you get  $x = 0.670m$  The correct answer given is 0.387m.


Is there a real word to replace "examplary"? (note: not exemplary)

"Examplary" doesn't appear to be a real English word, and I'm not searching for exemplary because I'm just interested in practical, instructive examples, not necessarily anything especially good nor a particularly desirable model. What I'm looking for would be used in some form of the following awkward but examplary sentence:  The speaker mentioned several occurrences in an examplary way, showing how each was a helpful example of the class of events. They found that immediately after a definition and explanation this example-providing process was important in order for the students to grasp the underlying concept.  Is there a real English word that would work the way I'm trying to use the fake word examplary?


What if I'm wiped out battling against the legendary Pokémon?

My brother failed to save before battling the legendary (Groudon), and saved afterwards when his team had been wiped out by Groudon. Upon returning to the Cave of Origin, to the same spot that Groudon first spawned, he is not there. What can be done to make him respawn so he can be battled again, in order to advance in the story?


Which animation method to use in blender for later use in Unity?

I'm trying to understand which animations on blender will be able to be animated in unity.  I have tried animating a net in such a way that when the ball hits it I will activate the animation to look realistic- I built a net, added a lattice modifier and animated with this lattice, but then I saw the posts about Unity not able to run them.  So figured I'll try Cloth animations but then I saw posts says Unity wont accept those animations also.  So, beside manually moving each individual vertex on my net, how can I animate that?


A Binomial distribution of which the number of trials is a Poisson distribuion

It is known that X is a random variable which follows Poisson distribution Po(λ), Y is a random variable which follows Binomial distribution Binomial(X,p). The problem I encountered is: Proof that Y~Po(pλ). I tried two approaches but none of them is satisfying. Method 1: Since the mean and variance of X are both λ, each trial of X has the same success rate p, so the mean and variance of Y are both λp. Hence, Y~Po(λp). But I have made an assumption here is that a distribution of which the mean and the variance are the same is a Poisson distribution, but this clearly not a fact. Method 2: I used the Poisson limit theorem to proof, i.e. Po(λ) = lim(n->inf) Binomial(n,λ/n) But the maths becomes complicated uncontrollably. So, are there any rigorous proofs for this problem?


I'm fairly new to programming and web dev and up until now I haven't worked on any projects that I felt were large enough to warrant using proper version control. However, I am now working on a project that is getting bigger and bigger (very exciting!). I think it would be prudent to use some kind of version control. At the moment I work alone, but if this project gets where I want it to then I expect at some point I am going to need (and want!) some other people to come on board.  My problem is because I've never used version control, I don't really know what it is, how it works etc etc.  I hope this question isn't classed as subjective. I'm not asking for people to tell me which version control they think is best, I'm quite happy to spend some time looking around and trying them out for myself.  I'm really wanting some people to either give me a quick run down of how a standard version control system works (I know they'll all be different, but I'm talking basics here) and if possible, in a non-subjective way, to explain the differences between some of the major players. ie what is the difference between mercurial and git, not which is better - I'll decide that for myself thank you!


I was using Apex Sharing and it was working fine, but then I noticed that for some objects when I use CustomObject__Share it says 'Entity is not org-accessible'. I tried to google it, but wasn't able to find any info on why I can't access Apex Sharing Objects.


Given that $\frac{2^n +1}{n^2}$ is a integer.Find $n$

Determine all set of integers $n\gt 1$ such that  $$\frac{2^n+1}{n^2}\;\;\text{  is a integer. }$$  I found that $n$ is an odd.   Please help by providing me with a hint.


When a recipe calls for brown sugar, could I use white sugar instead?

I don't really use brown sugar that often and I would like to know, if I am baking a recipe that calls for a cup of brown sugar, could I use white sugar instead? If not, why? Do they not "bake" the same?   Thank you!


I have a tif file of 7378 X 6923(widthXheight) resolution. I resized it to 1200 X 1200 pixels using Image class in python.   img = Image.open('path to tif file')  img = img.resize((1200,1200))   But after resizing, the pixel values show unusual values. Before resizing, a certain pixel's value was 125.28. Now, after resizing, that pixel's value has turned to 1123715645. I am reading the pixel value with:   with rasterio.open('path to tif file') as dataset:     band = dataset.read(1)     print(type(band))     value_of_interest = band[row_of_interest, column_of_interest]     print(value_of_interest)   Why does this happen?  How can I preserve the height values in same pixel position?


Can Bigby's Hand move creatures that are Grappled into the air?

can grapple via Grasping Hand. This allows:     The hand attempts to grapple a Huge or smaller creature within 5 feet of it. You use the hand's Strength score to resolve the grapple. If the target is Medium or smaller, you have advantage on the check. While the hand is grappling the target, you can use a bonus action to have the hand crush it. When you do so, the target takes bludgeoning damage equal to 2d6 + your spellcasting ability modifier.   With a strength of 26, can it move creatures? Not only do you get the action, but you can:     When you cast the spell and as a bonus action on your subsequent turns, you can move the hand up to 60 feet and then cause one of the following effects with it.   So, after a grapple, could I move it 60' in the air? Then next turn move it another 60' and cause the crushing damage? At some point while it's way up in the air, release the grappled creature for falling damage?


I can't seem to find a way to change this equation into its irreducible form to solve it: $$x^{3}-x-2=0.$$   It should have 1 real root and 2 complex roots.


A square matrix $A$ is idempotent if $A^2 = A.$  Prove that if $A$ is an $n\times n$ matrix that is idempotent and invertible, then $A$ is the identity.  How do i prove this?


Covariance between estimates of slope and intercept

I wonder why the covariance between estimates of slope ($\hat{\alpha}$) and intercept ($\hat{\beta}$) is $-\bar{X}\times Var(\hat{\beta})$. How can I derive this solution by not using matrix?  I add a new picture of my solving steps. I tried to use the rule of variance - which is $Var(x+y)=var(x)+var(y)+cov(x,y)$ - to derive covariance of $\hat{\alpha}$ and $\hat{\beta}$. But as you can see, the final solution I got is something wrong. I can't understand why '$-\sigma^2/2n$' adds to $-\bar{X}\times Var(\hat{\beta})$.  Can you plz help me find the stage in which I made mistake...?


Vector space of infinite sequences in $\Bbb R$

How do you show that the set of infinite sequences with entries in $\Bbb R$ is uncountably infinite-dimensional as a vector space over $\Bbb R$.


What purpose to use "!!" inside the if statement

I saw the code below recently: std::error_code ec;  // --- some code  if (!!ec) { //error reaction }  For what purpose the !! is used? The only idea is to force bool operator, but for what? May it have sense for some implementations of boost error types?


Generating a number between 1 and 2 java Math.random()

I'm working on creating a range of numbers between 1 and 2 using the imported math.random() class.  Here's how I got it working so far, however I can't see how it would work:  int tmp = (int)(Math.random()*1)+1;   Anyonould?e know if that actually works to get the range? if not.. then what  EDIT: Looking for either the number 1 or 2.


How does a photon 'perceive' the 2-D plane in which it perceives itself?

In a recent thread discussing  it is mentioned that from the photon's perspective, the universe is two-dimensioned. I take it that these two dimensions are both perpendicular to the direction of travel, as the photon travels at the speed of light and thus is everywhere on its path at once.  However, if I'm not mistaken, a photon can . Thus, the 2-D plane perpendicular to the direction of the photon also changes. How is this fact perceived by the photon?  Of course I am aware that a photon has neither sentience nor time, so what does this perception even mean for a photon? If it has no meaning, then what is the meaning of 2-D space for the photon, seeing how it can never interact with, be affected by, affect, or travel to any other location on that 2-D plane?


The Commitment form on Area 51 requires your full name to be provided. Is this publicly viewable? Why not just use the existing usernames?


I want to be able to make callouts to JotForm, but they do not support OAuth and username/password is insufficient for their API. ; for reference, here are the 3 auth options:        Authenticate with Query Parameters   Authenticate with HTTP Headers   Authenticate with Javascript SDK      Basically, they provide an API Key and want me to include an apikey parameter in the header. I don't want to hard code it, I don't want to store it as plain text in custom settings/metadata, and this isn't a managed package. Is there any way to securely store/authenticate from Salesforce, ideally using a Named Credential?  I'd love to be able to just have a Named Credential that is just a securely stored, obscured API Key...


Vertically align text within Objects in Illustrator

I am using Adobe Illustrator CC (latest version) and although I have been working with Illustrator for many years, I only do small vector related things in it, so by no means an expert.  I would like to align a bit of text inside a rectangle object, so I select both, then I tell it to align relative to rectangle, and press the Vertically Align Center option, but this is what I get:    As you can see, it is NOT vertically centered, what am I doing wrong?  This seems to behave this way with text only! I'm sure if I changed the text to paths and did the alignment, I'd get the result I'm after, but must I do this? Is there no easier way?  UPDATE:  Following solution provided by duplication link still doesn't work for me! Am I missing something? I applied the Effect > Path > Outline Object  Here is what I get:    Thank You.


How do I add a BCC field to a WP_MAIL function on Wordpress

I need some help from someone. I managed to get this below code working on sending emails to a certain user role. However, when the emails sends it sends to all 200 people and they can all see each others emails in the To fields. How can I add all their emails as BCC so they can't see each other?  $args = array( 'role'    => 'freelancers', 'orderby' => 'user_nicename', 'order'   => 'ASC' );  $users = get_users( $args );  $emails      = array ();   foreach ( $users as $user ) {  $emails[] = $user->user_email;  /*$body = sprintf( 'Hello.');*/   $body = 'Hello,
  Kind Regards
';    }     wp_mail( $emails, 'New jobs posted', $body );


Proving that $\overline{S \cap U} = \overline U$ if $U$ open and $S$ dense

In my general topology textbook there is the following exercise:  Let $S$ be a dense subset of a topological space $(X,\tau)$. Prove that for every open subset $U$ of $X$: $$\overline{S \cap U} = \overline U$$   My approach: My idea is to prove that $\overline{S \cap U} \subseteq \overline U$ and $\overline{S \cap U} \supseteq \overline U$, thus proving that $\overline{S \cap U} = \overline U$. I had no trouble proving that $\overline{S \cap U} \subseteq \overline U$, but I'm having some trouble proving the opposite. I'm doing the following: My proof: Let $x \in \overline U$. We have that $\overline U = U \cup U'$, where $U'$ is the set of all limit points of $U$. So we have that $x \in U \cup U'$. This means that $x \in U \vee x \in U'$ First case: If $x \in U$: There are two possible scenarios:  $x$ is also a member of $S$, this is $x \in S$ $x$ is not a member of $S$, this is $x \notin S$  1: We have that $x \in U \wedge x \in S$,  so $x \in S \cap u$. Because $\overline{S \cap U}= (S \cap U) \cup (S \cap U)'$, then $x \in \overline{S \cap U}$. 2: $S$ is dense in $X$. This means that $\overline S = S \cup S' = X$. So, if $x \notin S$, this implies that $x \in S'$. Therefore, we know directly from the definition of limit point that: $\forall A \in \tau$ such that $x \in A, \exists p \in S: p \in A \wedge p \neq x$ we have that $U \in \tau$, so $\exists p \in S: p \in U \wedge p \neq x$  This is the conclusion that I arrived, but I'm now sure how to proceed from now on. we know that $x \notin S \cap U$, because in situation 2 we have that $x \notin S$, so this leaves us with $x \in (S \cap U)'$. In other words I have to prove that: $\forall A \in \tau$ such that $x \in A$, $\exists p \in S \cap U: p \in A \wedge p \neq x$. How can I arrive at this conclusion?


If you compute the 95% CI for a population mean from a given sample, apparently it is taboo to say something like "there is a probability of 0.95 that the true mean lies in this specific CI".  Yet when you look at what "confidence" means, it is a statement about all the possible CI (computed using the same sample size), which says that 95% of these CI will contain the true mean.  When we know that if 1% of the tickets in a lottery have the predetermined winning number, we have no problem saying (after we draw a ticket) the probability we drew a winning ticket is 1%.   Why do we have such a problem making a similar probability statement for a given CI?


Physical interpretation of complex numbers

Complex numbers are used widely in quantum mechanics and the waveform, is there a physical interpretation of what this means about the structure of the universe? Why is it not used in macro physics?   Do physicists really think that calling imaginary numbers a 90 degree rotation is a good enough answer? It seems to be used in many areas to mean similar things.  Is there an explanation to do with dimensions as I have tried in this conversation a better way to understand them?


Synaptic installation problem Ubuntu 12.10?

I'm not able to install Synaptic, please help me.  jhon@jhon-Inspiron-N5010:~$ sudo apt-get install synaptic [sudo] password for jhon:  Reading package lists... Done Building dependency tree        Reading state information... Done Package synaptic is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'synaptic' has no installation candidate


My code looks like this  $to = "mymailid@gmail.com"; $subject = "sample subject"; $body = "<div> hi hi .. </div>"; $headers = "Reply-To: The Sender <mymailid@gmail.com>\r\n";  $headers .= "Return-Path: The Sender <mymailid@gmail.com>\r\n"; $headers .= "From: The Sender <mymailid@gmail.com>\r\n";  $headers .='X-Mailer: PHP/' . phpversion(); $headers .= "MIME-Version: 1.0\r\n"; $headers .= "Content-type: text/html; charset=iso-8859-1\r\n";   mail($to, $subject, $body,$headers)   I have sent the suitalbe header in my mail function. Everytime when i run this code, my mail will go to the spam folder in my gmail account.. How do i avoid my mail going to spam folder?


YA book about paper mâché dragons coming to life

i remember reading a young adult book about a teen in modern times (1980-1990) who makes a bunch of paper mâché dragons as a hobby and they end up coming to life and attacking him in his home.   I have no idea the title or author  but I recollect the cover drawn as the main protagonist in a chair as the dragons come find the stairs behind him.  Any help!?   I have scoured the Internet for l the last 5 years on and off with no luck.


$\Delta U = n C_v \Delta T $ non-constant volume

In the formula $\Delta U = C_v\Delta T$, we get the constant volume heat capacity by assuming constant volume conditions. However, I've understood that a constant volume is not required when using the formula.  I tried understanding the solution through several other posts but it still doesn't make sense to me. Unless my base knowledge is wrong (I have a hard time understanding thermodynamics), why are we allowed to use $\Delta U = C_v\Delta T$ when volume changes?


How to read Exchange e-mails on Android?

Is there any Outlook for Android? If not, should I use an IMAP or POP3 client for Android instead? Which one do you recommend?


Why MOSFET source is indicated with arrow ?

I know that , a basic MOSFET contains source and drain , and either it's a NMOS or PMOS ; it is indicated by an arrow at source . But let's look at a fabricated NMOS.   Here we can easily see that either a pin is source or drain is totally depended on the connection. Without connections , this device is symmetrical . But look at the conventional MOSFET symbols .   all these symbols marking a pin as source and other one as drain. Why is that ? Why this symbols are not symmetrical as the device is?   When I work on Cadence , schematics symbols all have this types of symbols where sources are marked .But when it will be used for fabrication , source and drain will be determined by the connection , not by the symbol.


I was looking at the Community user's profile, and I noticed that there was about 15 sites missing in the "accounts" tab. There's a little over 120 sites on SE, and, there's about 15 sites missing from this count. Why is this happening?    Additionally, clicking on view more just shows one account, on Area51:


I ran into a phrase that does not make sense to me. It reads: We are always pleased to have new subscribers, and I am certain you will be delighted with the upcoming season. Please find enclosed the tickets for the five plays for this season.  By Googling, I discovered such phrase is commonly used in business emails, albeit one that is frowned upon by grammarians. But "find enclosed the tickets" sounds odd and ridiculous to me. I believe the sentence would be better as "find the enclosed tickets."  Could someone explain the reasoning behind the seemingly odd structure of the phrase?  Thank you.


How could the following integral be solved in a good manner?  $$\int \frac{\sin(x)}{x}\;\mathrm{d}x$$  Regards:


Multiples of an irrational number forming a dense subset

Say you picked your favorite irrational number $q$ and looking at $S = \{nq: n\in \mathbb{Z} \}$ in $\mathbb{R}$, you chopped off everything but the decimal of $nq$, leaving you with a number in $[0,1]$.  Is this new set dense in $[0,1]$? If so, why? (Basically looking at the $\mathbb{Z}$-orbit of a fixed irrational number in $\mathbb{R}/\mathbb{Z}$ where we mean the quotient by the group action of $\mathbb{Z}$.)  Thanks!


How to switch between tty from a shell on a graphic session

I would like to know if it's possible to create an alias (on my .zsh_aliases) to launch a command from the graphical session to a tty (does not matter 1 or 6 ...) ? I tried with for example cmatrix:     alias matrix='sudo chvt 1 && cmatrix -B'  and it will open the tty 1 but launch cmatrix on the current shell (on the Xsession). (I have a zsh shell on Debian 10)


Relationship between complex number and vectors

What is the relation  between complex numbers and vectors?  I have read in some places "a complex number a 2-dimensional vector".  One can easily observe that $i\cdot i=-1$ in complex multiplication like the cross product of vectors.    Is  vector only the generalisation of complex number to n dimensions?   Is there any fundamental difference between those two?


What is the fastest lens available for a DSLR?

I've seen references to f1.2 lenses. I was wondering, are there any faster lenses available for a DSLR mount?


I want to use gdal_retile. I have gdal installed after installing it from OSGeo4W by my bin folder is missing gdal_retile. How can I install it? I am working on a Windows machine. Is it expected not to be part of GDAL from OSGeo4W? Edit: I can see my question has been closed due to duplication. What I am confused about is how I am suppose to install and use gdal_retile. I found an OLD installation from OSGeo4W which include bat files so I can run it as a command line tool. But that does not seem to be the case anymore? gdal_retile itself is a python script? But then I must run it using python not a command line tool? I am completely stumped in what direction I should go to get it running. If I want to use gdal_retile I assume it is not enough to install just gdal? You can install GDAL in numerous ways  Using the OSGeo4W installer Or binaries from  I am not a computer scientist and there are too many options for me to understand the differences between them and the requirements to get going. I can post a new question if that make more sense.


Using Operators and Decision Constructs: reference and local variables

N.B. What I don't understand about the answer to the Enthuware.com answer below is that sb.append(str) seems to result in a change to sb of main but sb = null does not.  What will be the output of the following class?       public class TestClass{   public void testRefs(String str, StringBuilder sb){     str = str + sb.toString();     sb.append(str);     str = null;     sb = null;   }   public static void main(String[] args){     String s = "aaa";     StringBuilder sb = new StringBuilder("bbb");     new TestClass().testRefs(s, sb);     System.out.println("s="+s+" sb="+sb);   } }   s=aaa sb=bbb  s=null sb=null  s=aaa sb=null  s=null sb=bbbaaa  ANSWER is:  s=aaa sb=bbbaaabbb   Always remember that Strings are immutable, you cannot change them. In this case, s refers to "aaa", and no matter what testRefs() method does, the variable s of main() will keep pointing to the same string "aaa".  StringBuilder on the other hand, is mutable. So, initially sb is pointing to a StringBuilder object containing "bbb". Its reference is passed to the testRefs() method. In that method, we change the local variable str to point to a new string "aaa"+"bbb" = "aaabbb". Then we append this to sb. Therefore sb now contains "bbbaaabbb". Setting the local reference str and sb (in method testRefs()) to null, does not affect the variables s and sb of the main() method.


scp between two remote hosts from my (third) pc

I have two remote hosts. host1-> 10.3.0.1 host2-> 10.3.0.2 Both run an ssh server.  The ssh server listens on port 22 in host1 and on port 6969 in host2. Now, using my local machine, I need to copy something from host1 to host2 without logging into either host1 or host2 via ssh. Something like,  scp user@10.3.0.1:/path/to/file user@10.3.0.2/path/to/file   How can I do this, please note that the two hosts use different ports for ssh.


Mac excel opening files as read-only but has full access

I have a user who is trying to open an .xlsx file and modify its contents. However, the user is constantly faced with the message saying that someone else is in it. I have checked the Open Files on the server and no is in the file, also the person who is apparently locking it has left the company and the account has been deleted.  When looking at the permissions of the file the user has read-write access as well as the file not having a locked status on the Get Info window.  The version of Mac Excel that is being used is 12.3.6, and has not have any other issues opening other Excel sheets.


Limits of Poisson's ratio in isotropic solid

For an isotropic solid, Poisson's ratio can be expressed in terms of stiffness constants as:  $$\sigma = \frac{c_{11} - 2c_{44}}{2c_{11} - 2c_{44}}$$  Alternatively we may express Poisson's ratio in terms of the Lamé constants $\lambda$, $\mu$ where $\lambda = c_{12}$ and $\mu = c_{44}$.  For an isotropic solid, we have $c_{12} = c_{11} - 2c_{44}$.  When we solve this algebraically we get:  $$\sigma = \frac{\lambda}{2(\lambda + \mu)}$$   I am supposed to show that $\sigma$ must lie between $-1$ and $+\frac{1}{2}$.  I figure that by setting $\mu=0$, it follows from the last expression of $\sigma$ that we get the value $\frac{1}{2}$.  However, I can't see how to show that the lower bound must be $-1$.  I've tried fidgeting around with the expressions and letting them go towards $0$ or $\infty$, but I still don't get the $-1$ value.  If anyone can help me out here, I would greatly appreciate it!


If $P$ is a prime ideal of $R$ and $X\subseteq P$ then there's a minimal ideal

Let a ring $R$ and let $X\subseteq P\subset R$ such that $P$ is a prime ideal of $R$. Prove that there's a minimal prime ideal $M$ of $R$ such that $X\subseteq M\subseteq P$.  I think of using Zorn's lemma but the last one deal with a maximal subgroup and not a minimal one. Thanks.


I messed up my /.bash_profile and Bash will not recognize most commands

I was trying to add paths to my ~/.bash_profile and accidentally screwed up the final one right when I closed it. Now, I cannot use a majority of the basic shell commands, like ls, touch, etc. I can still use echo and cd. When I echo my path, I get: “/Users/Forthman/Desktop/paml/bin:??. If I try other commands, I get: -bash: touch: command not found.  My ~/.bash_profile is invisible, and so I cannot directly open it in TextWrangler or TextEdit. How can I fix this?


How do I use locate to find hidden files in Terminal?

I am trying to find a hidden file that I know the name, but no the location of. The name is "message", and I have tried sudo locate *message*, but I have not found it. I have too much output, plus I do not think locate is showing the hidden files. Any ideas?


I'm trying to select a variable column name in my table, but this doesn't seem to work:  $reponse = $bdd->prepare('SELECT :day AS day FROM TABLE WHERE id= :id');                $reponse->execute(array('day' => 'monday', 'id' => '5'));  $day = $reponse->fetch();   Even by setting 'day', to a sure known element in my table (monday), it doesn't work. Same for id.  Does someone know how to fix that?  I have no php error output, only a mysql query error (that doesn't show). By replacing ':day' by monday, I have an output.


How to check "Is Valid Image File" in C#

I'm trying not using try-catch to achieve this goal  here's my code  using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Drawing;  namespace ConsoleApplication3 {     class Program     {         static void Main(string[] args)         {             Bitmap imagePattern = new Bitmap(@"test.jpg");             Console.Read();         }     } }   But if test.jpg is damage then C# will show error, so my question: is there a function like IsValidImage() in C#?  THX!


How to calculate weighted averages in Google Sheets?

I have a Google Sheets where products are listed as rows and attributes as columns. Each product's attribute is rated on a scale of 1-10. My last column is an average of these values (i.e. =Average(B2:D2)). This works fine if each attribute has the same weight.  +--------+-------+-------+-------+---------+ |        | Attr1 | Attr2 | Attr3 | Overall | +--------+-------+-------+-------+---------+ | Prod 1 | 10    | 8     | 9     | 9       | | Prod 2 | 2     | 10    | 7     | 6.33    | | Prod 3 | 4     | 6     | 6     | 5.33    | +--------+-------+-------+-------+---------+   The problem is that I want each attribute to have a different weight. For example, Attr1 might not be important and should only be worth 50%, while Attr3 is very important and should be worth 300%.  +--------+-------------+-------+--------------+---------+ |        | Attr1 (50%) | Attr2 | Attr3 (300%) | Overall | +--------+-------------+-------+--------------+---------+ | Prod 1 | 10          | 8     | 9            | 8.89    | | Prod 2 | 2           | 10    | 7            | 7.11    | | Prod 3 | 4           | 6     | 6            | 5.78    | +--------+-------------+-------+--------------+---------+   The value for the first row would be:  (10*0.5 + 8*1 + 9*3) / (0.5+1+3) = 8.89   which could be calculated by using:  (   B2*(IFERROR(REGEXEXTRACT(B1, "\d+"), 100)/100)    + C2*(IFERROR(REGEXEXTRACT(C1, "\d+"), 100)/100)   + D2*(IFERROR(REGEXEXTRACT(D1, "\d+"), 100)/100)  ) / (   IFERROR(REGEXEXTRACT(B1, "\d+"), 100)/100   + IFERROR(REGEXEXTRACT(C1, "\d+"), 100)/100   + IFERROR(REGEXEXTRACT(D1, "\d+"), 100)/100 )   which, as you can see, can become very difficult to manage as more attributes are added. Ideally, I'm looking for a solution that doesn't require creating temporary cells to help with the calculations.  Is there any built in function or a common convention that can help me calculate these weighted averages?


I just installed Ubuntu 16.04 LTS, and because I want to use my Chromecast I think I'll need Chrome or Chromium.  The the software-center ("store") doesn't launch.  So I pasted the line sudo apt-get install chromium in the terminal and entered my password.  chromium-bsu:i386 chromium-bsu   I obtained the following text:  Reading package lists... Done Building dependency tree        Reading state information... Done Package chromium is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it:   chromium-bsu:i386 chromium-bsu  Reading package lists... Done Building dependency tree        Reading state information... Done Package chromium is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it:   chromium-bsu:i386 chromium-bsu E: Package 'chromium' has no installation candidate   So I pasted chromium-bsu:i386 chromium-bsu  but got this answer:  chromium-bsu:i386: command not found   What now?  I also downloaded the installation file of Chrome,  google-chrome-42-0-2311-90-32-bit-multi-ubu.deb   but nothing happens when I double-click it   I was a Windows user, so I don't know what to do.


Why do all my folders have ! or ? or a bomb sign on them after I installed rabbitvcs?

I recently installed rabbitvcs on an Ubuntu 17.10 machine.   After installing I am trying to clone one of my folders, but all my folders have an ! exclamation mark or ? question mark or a bomb sign after installing rabbitvcs. I have tried tortoise git in Windows but it didn't happen like this there.  I tried reinstalling rabbitvcs but the problem remains the same. And also the all the folders have those signs outside the folder which I am trying to clone.  Is rabbitvcs is the best alternative for tortoise git in Ubuntu for the latest Ubuntu version?    What is the fix for this problem? Is there any good documentation for rabbitvcs?


Is there a way to programmatically determine which document class is in effect?  I'd like to be able to write conditional macros that behave differently depending on which document class is currently being used.


Interval of convergence of $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(2x)^n$

I want to find the interval of convergence of $$\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(2x)^n$$ By the root test, $\sqrt[n]{|(\frac{n}{n+1})^{n^2}(2x)^n|}=|(\frac{n}{n+1})^{n}(2x)|$  And $(\frac{n}{n+1})^n=(1-\frac{1}{n+1})^n\to\frac1e$ as $n\to\infty$  So I've got an open interval(of convergence) s.t. $|\frac1e 2x|<1\implies |x|<\frac e2$.  Now I need to figure out whether the series is convergent or not at the end points, $x=\frac e2, -\frac e2$.  So there are two series I need to deal with, namely, $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}e^n$ and $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(-1)^ne^n$.  Suppose $(\frac{n}{n+1})^{n^2}$ is increasing. Then $$(\frac{n}{n+1})^{n^2}<(\frac{n+1}{n+2})^{(n+1)^2}\iff 1<(\frac{n+1}{n+2})^{(n+1)^2}(\frac{n+1}{n})^{n^2}$$ $$\iff 1<(1-\frac{1}{n+2})^{2n+1}(1+\frac{1}{n^2+2n})^{n^2}$$  But $(1-\frac{1}{n+2})^{2n+1}\to\frac{1}{e^2}$ and $(1+\frac{1}{n^2+2n})^{n^2}<(1+\frac{1}{n^2})^{n^2}\to e$  So I have $1<\frac1e<1$, which is a contradiction. Hence $(\frac{n}{n+1})^{n^2}$ is not increasing. But I don't know if it's decreasing. (is it true that $(1+\frac{1}{n^2+2n})^{n^2}\to e$?)  If $(1+\frac{1}{n^2+2n})^{n^2}\to e$ is true, then $(\frac{n}{n+1})^{n^2}e^n$ converges to some positive number, so $\sum(\frac{n}{n+1})^{n^2}e^n$ diverges. But I don't know if it's decreasing: can't apply the alternating series convergence test(Leibniz's criterion).  So, can you help me with the two end points?


Proof limit of the sequence $\lim_{n\to\infty} [\frac{1}{n+1}+\frac{1}{n+2}+...+ \frac{1}{2n}]=\log 2$

Proof the limit of the sequence $\lim_{n\to\infty} [\frac{1}{n+1}+\frac{1}{n+2}+...+ \frac{1}{2n}]=\log 2$ ...  I think that each term of the sequences is of the type $ {\frac {1}{n}}$, then why the result is $ \log 2$?


What to do with users having access to moderator tools?

Have a look at these Stack Overflow questions,  and . Doesn't it fall under the following flag category?     Questions asking for code must demonstrate a minimal understanding of the problem being solved. Include attempted solutions, why they didn't work, and the expected results.   And yet a user having access to moderator tools is answering the question instead of putting it on hold or raising a flag.  So, is it the time to rethink about how moderation privileges should be granted? Or some kind of flagging mechanism should be introduced for users belonging to 10K+ reputation category?  Have a look at . What's wrong with it?   Reading all the answers and comments, Stack Overflow seems to be following double standards. Rules are there, but not for everyone. It's totally on luck that either your not-so-good question will be accepted by the community or not.   for example.


Finding a suitable distribution for data in R?

I have a set of data with summary as below:    The data are non-normal and transformations did not obtain normality.  Given the data are continuous I have narrowed the range of distribution down to 'Cauchy','Weibull','Gamma','f','Laplace'.  Below is the density plot for the data:    How do I determine the right distribution for the data?


Integrating by splitting up trig functions

The problem is $$\int \cos^3 (x)  \sin^5 (x) dx.$$  The method we've gone over in class involes splitting up the trig functions so that we can set one to U, then take du so that du matches a part of the function. But I'm struggling to find these. Any explanation is helpful.


Suppose I have a string:  string = "VNYTQAKENGSD"   And I need to find the positions where this expression holds.  N{P}[ST]{P} (Meaning 4 letters, [N,¬P,S or T, ¬P]  The output would be  2 9   because at position 2 you have NYTQ and at 9 NGSD  How to write this in regular expressions?   consider regex as the regular expressiom   for(i in 1:nchar(string)){   # If regex is equal to the substring of REGEX, get index.    if(regex == substr(string, 1, nchar(regex))){    vector = c(vector,i)    }    #Reduce String  string = substring(string,2)  }     Please help


I need help for this Volley requestQue, always crashes in actual device

the error is pointing to this requestQueue.add(stringRequest). Everytime i run this app in actual device, it crashes. i declared my Volley requestQue right after service declaration.  public class SmsService extends Service {          public RequestQueue requestQueue;         public StringRequest stringRequest;   stringRequest = new StringRequest(Request.Method.POST, smsurl, new Response.Listener<String>() {                 @Override                 public void onResponse(String response) {                     Log.e("Debug", response);                  }             }, new Response.ErrorListener() {                 @Override                 public void onErrorResponse(VolleyError error) {                     Log.e("Debug", "No Internet Connection!!");                  }             }){                 @Override                 protected Map<String, String> getParams() throws AuthFailureError {                     HashMap<String, String> hashMap = new HashMap<String, String>();                     hashMap.put("email",email);                     hashMap.put("targetname",targetname);                     hashMap.put("smstype",smstype);                     hashMap.put("phone",phone);                     hashMap.put("contactname",contactname);                     hashMap.put("body",body);                     hashMap.put("date",date);                      return hashMap;                 }             };             requestQueue.add(stringRequest);


Can a LINQ filter alter the ordering of the original list?

Imagine I have a IEnumerable<string> ordered alphabetically. If I filter it like myStrings.where(s=> s.StartsWith(filter));, will the resulting enumerator still be in alphabetic order or not necessarily?  EG: is it there any guarantee that the original order will be maintained?  Edit 1: there is a answer from 2008 about this question. I read it yes, but because it's 12 years old, and a lot changed since then, specially regarding .Net Core and TPL, I would like a fresh, authoritative answer on the matter, to subside further developments. .Where changing the order of a IEnumerable is the kind of problem that is VERY hard to pinpoint and troubleshoot  Edit 2: by "IEnumerable" I don't only mean List<T>, I also mean Dictionaries<T,T>, Array<T>[] and the whole Concurrent versions of it such as ConcurrentBag<T>, ConcurrentDictionary<T,T> and others


Why does the derivative of sine only work for radians?

I'm still struggling to understand why the derivative of sine only works for radians. I had always thought that radians and degrees were both arbitrary units of measurement, and just now I'm discovering that I've been wrong all along! I'm guessing that when you differentiate sine, the step that only works for radians is when you replace $\sin(dx)$ with just $dx$, because as $dx$ approaches $0$ then $\sin(dx)$ equals $dx$ because $\sin(\theta)$ equals $\theta$. But isn't the same true for degrees? As $dx$ approaches $\theta$ degrees then $\sin(dx \,\text{degrees})$ still approaches $0$. But I've come to the understanding that $\sin(dx \,\text{degrees})$ approaches $0$ almost $60$ times slower, so if $\sin(dx \,\text{radians})$ can be replaced with $dx$ then $\sin(dx \,\text{degrees})$ would have to be replaced with $(\pi/180)$ times $dx$ degrees.  But the question remains of why it works perfectly for radians. How do we know that we can replace $\sin(dx)$ with just $dx$ without any kind of conversion applied like we need for degrees? It's not good enough to just say that we can see that $\sin(dx)$ approaches $dx$ as $dx$ gets very small.  Mathematically we can see that $\sin(.00001)$ is pretty darn close to $0.00001$ when we're using radians. But let's say we had a unit of measurement "sixths" where there are $6$ of them in a full circle, pretty close to radians. It would also look like $\sin(dx \,\text{sixths})$ approaches $dx$ when it gets very small, but we know we'd have to replace $\sin(dx \,\text{sixths})$  with $(\pi/3) \,dx$ sixths when differentiating. So how do we know that radians work out so magically, and why do they?  I've read the answers to  and followed the links, and no, they don't answer my question.


How do I change grass blocks within a set region to magma blocks?

I'm wanting to change grass to magma on my Bedrock Edition, Nintendo Switch world to make a Skyblock challenge sort of thing but so far every command I've tried just says "invalid command". Does anyone here know what I should be doing differently?   PS The range is from x256 z256 to x-256 z-256 if that changes anything.


Why is String "==" operator working with android?

The below java(android) source works on debug build, release(signed) build, and allatori obsfucation build(signed).  SomeActivity.java  //Sends event to an async event processing class public void emitEvent(){      EventHandlerClass.emit("myEvent");  }  .... //Recieves callback from EventHandlerClass public void handleEvent(Event event){//Event object has a String field named eventField;      if(event.eventField == "myEvent"){       }else if (event.eventField == "myEvent2"){               .......      } }   EventHandlerClass.java  public void emit(String eventName){   ...//process async event      eventSource.handleEvent(new Event(eventName));  }   As you can see, the callback gets a string and compares it with the  "=="  operator. Somehow, this works, but I really don't know why this should work. As far as I know, the "==" should be a reference comparison.   This means that the 'event.eventField' has the same reference as the hardcoded String "myEvent". Is there a special rule on java for storing hardcoded Strings?


There is one cup, one plate, and one spoon in the drawer   or     There are one cup, one plate, and one spoon in the drawer   Which one should i use?   There's sounds more natural, but I feel like I'm talking about multiple items, so I should use There're.


What are the advantages of booking through a booking site instead of booking directly with the hotel?

Should I use booking.com, Airbnb or any site like that?  Why should I?  Are there any advantages?


How do I calculate the duration my solar battery will last when fully charged?

How can I calculate the duration my solar battery will last after charging to full? I want to know how to calculate the battery back up time.


Why i have different historical prices of AAPL between Quandl and Yahoo Finance? How should I behave in cases like this?

I'm a programmer and recently I'm approaching to the world of trading. Now I'm attempting to obtain historical data of AAPL. This is code for obtaining historical data from Quandl: import datetime import numpy as np import pandas as pd import seaborn as sns import matplotlib.pyplot as plt %matplotlib inline  pd.options.display.max_rows = 99999  import quandl quandl.ApiConfig.api_key = "PersonalCode"  dataset_quandl = quandl.get('AAPL', start_date="2018-01-01", end_date="2018-12-31") dataset_quandl = dataset_quandl.iloc[:,:4] dataset_quandl.columns = ["open","high","low","close"] dataset_quandl.head(10)  And i will obtain the following DataFrame:  If i try to download the same data from Yahoo Finance, i will read totally different prices: import ffn  dataset_ffn = ffn.get('aapl:Open,aapl:High,aapl:Low,aapl:Close', start='2018-01-01', end='2018-12-31') dataset_ffn.columns = ["open","high","low","close"] dataset_ffn = dataset_ffn.apply(lambda x: round(x,2)) dataset_ffn.head(10)   I would like to know what is the reason for this difference. How I should behave in these cases?


I am working on oAuth integration with Drupal. I'd like to programmatically assign users to groups upon logged in. Does the Group module have an API to accomplish something like this?


How do I allow long URLs to have line breaks at any point. This is in the bibliography not the main text. I am trying to save space so don't want extra spaces to be added to make it only break at slashes, for example, as it does by default.  I am using biblatex+biber.


Binary sequences and ${2}^{\mathbb{N}}$ have the same cardinality

I recently got the book "selected problems in real analysis", and I'm stuck solving the very first problem  $(u_n)$ is a binary sequence iff it only contains $0$ and $1$ in the sequence  Let $A$ be the set of all binary sequences  I have to prove that $A$ and ${2}^{\mathbb{N}}$ have the same cardinality, that is to say there exists a 1-1 function from one set to another  I've thought about maybe considering integers as base-2 numbers  Thanks for your help


I would like to pass event types such as TNotifyEvent or TKeyPressEvent.  How do I declare method param to accept these types ?  procedure RegisterEventType(AEventType: ???)   so that these compile:  RegisterEventType(TNotifyEvent) RegisterEventType(TKeyPressEvent)   Point being that TKeyPressEvent and TNotifyEvent are obviously different:  TNotifyEvent = procedure(Sender: TObject) of object; TKeyPressEvent = procedure(Sender: TObject; var Key: Char) of object;   So it's not an instance of event that I want to pass, it's the type.  To give some context this is the implementation:  procedure RegisterEventType(AEventType: ???; AFactory: TRedirectFactory) var   vTypeInfo: PTypeInfo; begin   vTypeInfo := TypeInfo(AEventType);   Assert(vTypeInfo.Kind = tkMethod);   vTypeInfo.Name <------ contains string 'TNotifyEvent'    SetLength(fFactories, Length(fFactories)+1);   fFactories[High(fFactories)].EventType := vTypeInfo.Name;   fFactories[High(fFactories)].Factory := AFactory; end;   context: TRedirectFactory creates an instance of IEventRedirect which implements TNotifyEvent and is used for redirecting event handlers on forms. There is one implementation for every supported event type (TNotifyEvent, TKeyPressEvent...). This allows centralised logging and measuring of forms that have lots of code in event handlers.  So the intent is to not pass a string 'TNotifyEvent' but actual type TNotifyEvent.


Prove that for $1\leq p\leq 2$ and $0<b<a$, $(a+b)^p+(a-b)^p\geq 2a^p+p(p-1)a^{p-2}b^2$.

To start this one, my idea is dividing both side by $a^p$, then the question will become $(1+x)^p+(1-x)^p\geq 2+p(p-1)x^2$. So we need to check $f(x)=(1+x)^p+(1-x)^p- 2-p(p-1)x^2\geq 0$ on $x\in(0,1)$ for all $p\in[1,2]$. It's clear that it's true as $p=1,2$. And for $p\in(0,1)$, I try to take first and second derivative, but the case becomes very complicate.


With a custom built PC that hasn't gone through the BIOS setup could I get Ubuntu?

So I just built a PC with 8 cores (4.0Ghz) and a GTX750. So since I don't have a OS on it yet could I download Ubuntu on a USB and install it as my OS on the BIOS setup? I don't know much about how to install a OS so... Any replies will be greatly appreciated!