first question so I apologize in advance if my formatting is rough. I'm currently working on a project with a professor I'll be starting a MSc in statistics with soon. One curious thing I've been asked to do when making residual plots is to have our predictor variables on the x axis instead of the fitted values from the model. Heres an example using the iris dataset library(tidyverse) library(broom)  fit <- lm(Sepal.Length ~ Petal.Length, data = iris)  d <- fit %>%    augment()  ##Residuals vs fitted ggplot(data = d, aes(x = .fitted, y = .resid)) +   geom_point() +    geom_smooth(se = FALSE, col = "red") + #Adds the line of fit   geom_hline(yintercept = 0, linetype = 2) + #Adds the horizontal dashed line   labs(x ="Fitted Values", y ="Residuals", title = "Residual vs Fitted") +   theme_bw()  ##Residuals vs Petal.Length (what my prof wants) ggplot(data = d, aes(x = Petal.Length, y = .resid)) +   geom_point() +    geom_smooth(se = FALSE, col = "red") + #Adds the line of fit   geom_hline(yintercept = 0, linetype = 2) + #Adds the horizontal dashed line   labs(x ="Petal.Length Values", y ="Residuals", title = "Residual vs Petal.Length") +   theme_bw()  Which lead to these (mostly) identical graphs   While I understand that theoretically that fitted values and observed values should be equivalent, and we can clearly see this example is the same, everything i've been taught, seen, or read plots residuals against fitted values. Is there any benefit or statistical reason to do otherwise?

I am fitting a linear model to a problem, and a little confused by what is going on. Without the details here are the two plots confusing me:  Residuals vs Fitted    Residuals vs Y    Now the residuals vs fitted looks good to me. Fairly evenly dispersed, no clear pattern. However, the $y$ vs fitted do not look good. I would have expected there to also not be a clear trend in this relationship.   This seems basic, but I'm rather lost. I don't want to fit a model that allows large positive errors at high values of $Y$ to make up for large negative errors at low values of $Y$.  Is this just an indication of a poorly fitting model? Or is something else going on here?  EDIT: Asked for fitted vs y (changed to have labels)    EDIT2: Just want to point out that this question has already been asked and answered (albeit in a more abstract sense)  .


I read tutorials about int* and int&. first, I type   int a = 3    and then,  int* x = &a;    means x is a pointer to the address of a which means the VALUE of x is something that POINTS to the address of a. Correct?   but if I do   int& x = a;    that means the ADDRESS of x is pointing to the VALUE of a right? or does it mean something different? what EXACLTY does it mean?

I know references are syntactic sugar, so code is easier to read and write. But what is the difference between a pointer variable and a reference variable?


How can I take an animated gif or mp4 screen capture of work I'm doing, as is seen in the gif below?  I need the capture to span more than a single window. I prefer not to pay for software to do this, but I'm open to installing open-source with . Bonus points if the tool is written in golang, like  (but I'd rather have a nice capture UI instead of manually defining capture coordinates in golang source as screenshot does) I have a MacBook running Catalina.

I'm looking for a screen capture tool working on MacOSX that will export the capture to animated gif.


I'm new to Blender and just following . I wanted to put a bit of my own stamp on it and got this grid set up at the top to give it an 80s vibe:  But its making a mess of my ocean. I want to have the pink grid object in the top to be hidden from being reflected in the ocean modifier plane below. I tried searching and looking for how to hide an object, turn off the shadows, etc. I thought maybe I could add a plane in between that would work as a one way mask - you can see the orange plane outlined which has a holdout material shader applied to it and backface culling on so I can see through this side, but it didn't stop the ocean still getting a peek. Can anyone point me in the right direction? Is it possible? (Update, I've been using Eevee to render this)

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


Why aren't hats shown in the iOS App?        There does seem to be hats in the App as seen in the About page:        As seen, I'm using the iOS App version 1.6.2.1, the TestFlight version.

I'm seeing some weird hat behavior on the iOS app.  On some answers, I'm wearing the trophy hat.        On other answers, I'm not wearing any hat at all.        And on the web, I'm wearing the taco hat.        What's going on?   App Version: 1.6.2.5 Device: iPhone 6 OS Version: Version 9.3.4 (Build 13G35)


To be honest, I'm new to Ubuntu and 've heard that this OS more advanced rather than Windows. But why the installation of the simple browser became so complicated is out of my mind. So I downloaded google-chrome-stable_current_amd64.deb. After running sudo apt-get install google-chrome-stable_current_amd64.deb and after running sudo apt-get install google-chrome-stable_current_amd64 and after running sudo apt-get install google-chrome-stable in the terminal nothing happens, but the message Couldn't find any package by glob and Couldn't find any package by regex. Trying to install it normally through UI brings Ubuntu Software window to a frozen state. Has anything might be done to install the browser on the Ubuntu? Tried to navigate to Downloads folder where my google-chrome-stable_current_amd64.deb is located and run sudo apt install command - didn't work. Terminal shows Unable to locate package google-chrome-stable_current_amd64.deb Thanks.

How do you install Google Chrome on Ubuntu?


This question has been posted earlier.  I could not understand the solution. Can anyone please help me to understand the solution?  let $C_c(\mathbb{R})$ = { f : $\mathbb{R} \rightarrow \mathbb{R}$ | f is continuous  and there  exist  a  compact  set $K$ such that  $f(x) = 0$ for all $x \in K ^c$} . let $g(x) = e^{-x^2}$  for all $x \in$ $\mathbb{R}.$  which of the  following satemnet is true?  1.There  exist a sequence {$f_n$} in $C_c(\mathbb{R})$ such that $f_n \rightarrow g$ uniformly  2.There exist a sequemce  {$f_n$} in $C_c (\mathbb{R})$ such that $f_n \rightarrow g$ pointwise    If  a sequence in $C_c (\mathbb{R})$ converge pointwise to g then it must converge uniformly to $g$.   4.There doesnot  exists any sequence $C_c (\mathbb{R})$ converging pointwise to $g$  I can not understand the solution of 3. Can anyone please make me understand?   False. Start from $f_n$ but add a function $\psi_n\in C_c^{\infty}(\mathbb{R})$ with $\operatorname{supp}\psi_n\subset [n+1,n+2]$, and such that $\psi_n(\xi)=-1$ for some $\xi\in (n+1,n+2)$. Then $g_n:=f_n+\psi_n\in C_c^{\infty}(\mathbb{R})$ and $g_n(x)\to e^{-x^2}$ for all $x\in \mathbb{R}$, but $g_n$ does not converge uniformly to $e^{-x^2}$ because  $$\sup_{x\in \mathbb{R}}|g_n(x)-e^{-x^2}|\geq |g_n(\xi)-e^{-\xi^2}|\geq 1  $$

let $C_c(\mathbb{R})$ = { f : $\mathbb{R} \rightarrow \mathbb{R}$ | f is continious  and there  exist  a  compact  set $K$ such that  $f(x) = 0$ for all $x \in K ^c$} . let $g(x) = e^{-x^2}$  for all $x \in$ $\mathbb{R}.$  which of the  following satemnet is true?  1.There  exist a sequence {$f_n$} in $C_c(\mathbb{R})$ such that $f_n \rightarrow g$ uniformly  2.There exist a sequemce  {$f_n$} in $C_c (\mathbb{R})$ such that $f_n \rightarrow g$ pointwise    If  a sequence in $C_c (\mathbb{R})$ converge pointwise to g then it must converge uniformly to $g$.   4.There doesnot  exists any sequence $C_c (\mathbb{R})$ converging pointwise to $g$  My attempts :  I thinks  option 1 and option 3  Trues...I don't  know  how to Prove  But  in my  mind i was thinking  that  uniform convergence implies  Pointwise convergence,,,,  Any solution/Hints  will be  appreciated  Thanks in advance,,i would be thanksful


When jobs is run in a shell, does it mean that all other jobs must be either background or stopped? Is there no foreground jobs?  Does jobs list only background and stopped jobs?

A job can be running or stopped (suspended).  When we are talking about foreground jobs and background jobs, are we only talking about running jobs?  Are background jobs and foreground jobs always in running state?  Does it make sense to say whether a stopped job is foreground or background?


The question is as follows:  Let $G$ be a finite and abelian group that satisfies $$\#\{g\in G\,\vert\, g^p=e\}\leq p$$ for all $p\in\mathbb{N}$, where $e$ is the identity element in $G$. Prove that $G$ is a cyclic group.  It doesn't seem difficult, but I have hit a wall and I don't know where to start. Any help or hit would be highly appreciated!

Let $G$ be a finite group. For each positive integer $m$, if $x^{m}=e$ has at most $m$ solutions in $G$, $G$ is cyclic.   What I have thought is that $n=\sum_{d\mid n}\phi(d)$ can be used to solve this and showing that $|G|$ order element in $G$ exists is enough.


In the last episode of The Matrix trilogy, when Neo becomes blind, he sees a yellow/orange Matrix (as opposed to “regular” Matrix, the green one) in what is supposed to be the real world. He has powers he used to only have in the Matrix.  Are there clear explanations of this? I have two hypotheses:   What is said to be the “real world” is another matrix (yellow/orange), which contains the other one (the green one). Neo has root access to this matrix, hence the control over machines. He has some sort of wireless connection to the machines system, therefore he can control them outside the Matrix.    I find the second one more convincing. I prefer the first one. It means we never see the real world in any of the movies.  Edit: the question was marked as duplicate to a complementary, but different question: how can Neo control the machine while he is not connected to The Matrix. This is not my question, this one of the facts that leads me to my question.  The discussion with the Oracle and the Architect mentions the source. This suggests the yellow/orange things which appears when Neo is in the “real world” is the source, as opposed to the Matrix (green). However looking at our world (the real real, outside the fiction) you have programs, their source, both on a computer, which is part of the world. Both sources and programs are “virtual”.  The wireless hypothesis means Neo's plug has something special that makes it possible for him to communicate with the machines' system in some way. So he can be both in the “real world” and the “meta Matrix” which contains both the source and the running programs. But if he can connect wirelessly, why does he have to protecting the core part of the Matrix?  What puzzles me, and makes me think about the other hypothesis is the mention to these several reboots of the systems, and previous occurrences of Neo facing the Architect (as depicted on the screens). How can this be the same person in the physical world? Is he a clone? Why did it have to be a clone? What makes his physical body critical for it, as opposed to his counterpart (program) in the Matrix? With the first hypothesis, Neo is a meta program of the yellow/orange matrix, hence he is just patched between reboots. This quote of the Oracle can be interpreted as a mention to another Matrix including the Matrix.     Oracle: The power of the One extends beyond this world. It reaches   from here all the way back to where it came from.   What are the actual facts leading to the wireless hypothesis?

In The Matrix Revolutions, when Neo and Trinity are trying to get to the Machine City, when the Machines launch weapons against them, Neo is able to destroy some of the incoming weapons. This is in the real world at this point, not in the Matrix.  How does Neo have any powers against the machines outside of the Matrix? Addendum: I'm looking for in universe answers only.  I would think that would be obvious, but I'm adding this after an answer that is essentially, "It's a movie..."


I have a multi-card reader that connects to my motherboard via USB 9/10 pin port, the problem is that I have none available, however I have a free 19/20 pin USB 3 port. I have been looking everywhere for an adapter to convert the 9 pin to 19 but I cannot find it anywhere... The only one I found is the other way around, 19 to 9.  Am I missing something? Like it's not possible to do the conversion or something?  Thanks!  EDIT: I don't want to just jam the 9 pin into the 19... I was looking more for an adapter/converter

I've been working on my new PC build with the  motherboard. This board comes with a wifi/bluetooth card that goes into a PCIe x1 slot... but the card also wants to be connected to the motherboard through an internal USB cable:  to a motherboard USB2 header. This would be fine and dandy but this motherboard only has two USB2 headers and they're already occupied by my case front panel USB pin blocks. However, there are at least two USB3.0 headers free on the motherboard; can I just connect this internal cable to a USB3 header?  Pictured: USB3.0 header (middle, light blue), USB2 header (right, blue) (not my motherboard) Looking at pinouts and discussions online, it seems like it could work if I connect the USB2 pin block to the first 9 pins of the USB3.0 header, though I'm afraid of frying the wireless card, motherboard, or both. Some sites even say that the USB3.0 motherboard header isn't standard, and can vary in pinout depending on manufacturer! Can anyone shed some light on this? P.S. If I can't do this, then is there a way to 'split' my existing USB2 motherboad headers?


I want to parametrize the lemniscate in polar coordinates.  By definition the lemniscate is the locus of all points z in complex plane, so that the product of  distances from z to $\pm 1 $ is $1$.  I found something like that: $$x^2-y^2-(x^2+y^2)^2=0$$  How can I get to that? From there it is easy to make the step  to polar coordinates.

All over the net, it is stated that the parametrization of the lemniscate with Cartesian equation $(x^2 + y^2)^2 = 2a^2 (x^2 - y^2)$ is: $$\varphi: t \mapsto \left(\frac{a\sqrt{2}\cos(t)}{1+\sin^2(t)}, \frac{a\sqrt{2}\cos(t)\sin(t)}{1+\sin^2(t)}\right)$$  I don't understand how to get there…  My method is as follows:  I transform the Cartesian equation to polar coördinates, and I find: $$r=a\sqrt{2\cos(2\vartheta)}$$  Then replacing $r$ in $(r\cos(\vartheta), r\sin(\vartheta))$ gives: $$\psi: t \mapsto \left(a\sqrt{2\cos(2t)}\cos(t),a\sqrt{2\cos(2t)}\sin(t) \right)$$  Are these equivalent? (I guess theory says that there must be a certain function which maps $\psi$ into $\varphi$; I can't seem to find which function…)


Now this may be utterly weird layman-physics-question, but anyways...  I have read recently following:  "The fundamental universe laws are everywhere the same. It's just that the manifestation (!) of (these) laws is different (!) on a specific "scale"."  Which brings me to the question:  Could it be that GR and QM are one and the same thing on a "different scale"?  If yes (LOL), that would "explain" why it is not possible to "merge" GR and QM.  Was question like this ever considered?

It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them?  E.g. relativity theory uses a space-time continuum, while quantum theory uses discrete states.  I am not merely looking for a solution or rebuttal of such opposites, more for a survey of the field out of interest.


We have two vf page and two controllers. What is the best way to allow these classes to share data between each other.  Example:   public class A {     public static DateTime dt{get;set;}     public  CSC_CommuncationController() {         dt = system.now();                 }     }  public class B{     public static DateTime dt{get;set;}     public B() {     system.debug('**'+A.dt);     } }   debug returns the blank value. can any one help on this. Note: We cant merge into single class as per requirement.

I have a Visualforce page with two controller extensions. Is there any way to get a reference to one of the extensions in the other one?


In a question tagged , this answer:     {- inside a comment,      {- inside another comment, -} still commented! -}    The nested comments aren't highlighted the right way. Is this by-design or is this a bug?

I noticed that sometimes my code gets highlighted in different colors when rendered.   What is syntax highlighting? How does it work? Why isn't my code being highlighted correctly? How do I report a bug or request a new language? How do I use syntax highlighting? What languages are currently available on Stack Exchange?


I've got a grid layout. I want to add a 5px margin all around it but doing so adds a scrollbar. Is it possible to set a margin without having a scrollbar added?   function toggle() {   document.querySelector(".container").classList.toggle("withMargin"); } html, body, .container {   height: 100%;   margin: 0; }  .container {   display: grid;   grid-template-rows: 50px 1fr 1fr;   grid-template-columns: 300px 1fr 1fr;   gap: 5px 5px;   grid-auto-flow: row;   grid-template-areas: "logo header header" "nav-one main main" "nav-two main main";   background-color: black; }  .main {   grid-area: main;   background-color: lightcoral; }  .logo {   grid-area: logo;   background-color: lightcyan; }  .header {   grid-area: header;   background-color: lightgoldenrodyellow; }  .nav-one {   grid-area: nav-one;   background-color: lightgray; }  .nav-two {   grid-area: nav-two;   background-color: lightgreen; }  .container.withMargin {   margin: 5px; } <!DOCTYPE html>

<button onclick="toggle()">toggle .container margin</button>

logo

header

nav one

nav two

With HTML/CSS, how can I make an element that has a width and/or height that is 100% of it's parent element and still has proper padding or margins?  By "proper" I mean that if my parent element is 200px tall and I specify height = 100% with padding = 5px I would expect that I should get a 190px high element with border = 5px on all sides, nicely centered in the parent element.  Now, I know that that's not how the standard box model specifies it should work (although I'd like to know why, exactly...), so the obvious answer doesn't work:  #myDiv {     width: 100%     height: 100%;     padding: 5px; }   But it would seem to me that there must be SOME way of reliably producing this effect for a parent of arbitrary size. Does anyone know of a way of accomplishing this (seemingly simple) task?  Oh, and for the record I'm not terribly interested in IE compatibility so that should (hopefully) make things a bit easier.   EDIT: Since an example was asked for, here's the simplest one I can think of:

         The challenge is then to get the black box to show up with a 25 pixel padding on all edges without the page growing big enough to require scrollbars.


I have a long filtered list of numbers next to names. I am trying to count the zeros as I change the filter. Unfortunately COUNTIF includes cells that have been excluded by my filter.  How can I count the zeros in my Numbers column only when they are not excluded by the filter?

I have a sheet in which I first apply a filter to a certain column to show "Unique records only". Now I have a column which contains, for e.g., values like:  Applepie Applesauce Crabapple Banana Mango   What I need is the count of all visible cells containing the word "Apple". Note that this should exclude the hidden (filtered out) cells. Now I have found out a formula:  `=SUMPRODUCT(SUBTOTAL(3,OFFSET(Sheet1!A:A,ROW(Sheet1!A:A)-MIN(ROW(Sheet1!A:A)),,1))*(Sheet1!A:A="<Text to search>"))`   However the problem with this one is this formula searches for the entire text. NOT just a part of it. How do I modify this formula to return count of cells containing "Apple" i.e. for this example it should return 3 as the result.


I would like to paraphrase a sentence:     "This is how the costs of each course should be."   So my idea was:     "This is how the price/prices per course should be."    What are the differences between singular + per vs. plural + per?  Or  If you have better paraphrases, you're very welcome to share them.  Thank you :)

I would like to paraphrase a sentence:     "This is how the costs of each course should be."   So my idea was:     "This is how the price/prices per course should be."    What are the differences between singular + per vs. plural + per?  Or  If you have better paraphrases, you're very welcome to share them.  Thank you very much :)


Correct duplicate:     Regarding the claimed duplicate (consecutive lists): that question was closed since it apparently follows Markdown spec in the Markdown => HTML conversion. This question is about CSS styling, not the HTML structure. Also, unlike the possible duplicate, this issue is not reproducible in other Markdown/CommonMark parsers.  It's also about a different issue: not enough space before the first unindented paragraph after nested unordered lists. The 'duplicate' is talking about issues with extra space between list items even without nesting, and only when an extra line break is added to the Markdown source (more line breaks do not affect this particular bug).    Paragraph breaks result in double line spacing everywhere except immediately after a nested bullet point. Top-level bullet points are fine, it's just the nested ones that exhibit this behaviour.  This is inconsistent. And it looks bad. It's a bit harder to tell that the line immediately after the list is supposed to be a new paragraph.  I cannot reproduce this behaviour with MarkdownPad 2 using the GitHub Flavored Markdown, Classic or CommonMark renderers with the GitHub, Markdown and None CSS options.  This behaviour also does not occur on the mobile version of SE sites, lending more credence to my theory that it's a CSS bug and not something actually intentional.  This appears to be because of an intentional ul ul { margin-bottom: 0px; } rule. Not entirely sure why that exists.  Example:     Lorem ipsum dolor sit amet, consectetur adipiscing elit. Maecenas vestibulum orci quis felis feugiat, quis sagittis ante fermentum.   Curabitur sed nisl sagittis, fringilla neque quis, tristique mauris. Mauris fringilla elementum commodo.   Sed pretium vulputate vehicula. Nullam vestibulum eleifend risus, id luctus lacus fringilla id. Maecenas tortor nibh, mollis sed eros vel, maximus interdum risus.   Maecenas rutrum nisl in venenatis sodales.    Phasellus eleifend sit amet dolor tempor porta. Phasellus tempus iaculis orci eu eleifend.    *  Lorem ipsum dolor sit amet, consectetur adipiscing elit. Maecenas vestibulum orci quis felis feugiat, quis sagittis ante fermentum.       Curabitur sed nisl sagittis, fringilla neque quis, tristique mauris. Mauris fringilla elementum commodo.      * Sed pretium vulputate vehicula. Nullam vestibulum eleifend risus, id luctus lacus fringilla id. Maecenas tortor nibh, mollis sed eros vel, maximus interdum risus.      Maecenas rutrum nisl in venenatis sodales.   Phasellus eleifend sit amet dolor tempor porta. Phasellus tempus iaculis orci eu eleifend.     More:

I have post  2. > Why is no support for a optional spec-version in Maven?   Maven has options for disabling Specifications and Implementations, so both are optional    * `addDefaultSpecificationEntries`    * `addDefaultImplementationEntries`       Read about   The problem is space between addDefaultImplementationEntries and Read about.   This is rendered as:    Post is visible here:


I try to build registration form, I have problem when I get the errors back from the PHP to the javascript.  I got the right data but i got it like a string and I need it like a javascript object because it can contain some errors in the same time..  Here is the data that I got back form the server side:  {"success":false,"errors":{"name":"Name is required.","superheroAlias":"Superhero alias is required."}}   This data is a string, when i do data[0] i get "{"  i need to get that data back as javascript object. I guess i supose to create function Json2Javascript or somthing like that but i dont know how its need to look, can you help me please create the function that will that?  If you write function please show me how to call the vars to, for example if i need to get the error on the name i want to get it like:   var a = data.errors.name;   Please help i tryed to find this function like hours =\ * I know how to create object in php and convert it to json and then to javascript object but i do that only with strings vars not on objects..

Given a string of JSON data, how can I safely turn that string into a JavaScript object?  Obviously I can do this unsafely with something like:  var obj = eval("(" + json + ')');   but that leaves me vulnerable to the JSON string containing other code, which it seems very dangerous to simply eval.


Imagine a person sitting on a very high chair. To be more specific, on a chair that has the same height as a satellite with a person aboard and which orbits the earth in a circular path. Let's say the (arbitrary) height is 400 kilometer.  The person in the chair feels an upward e.m. force, while the person in the satellite feels no force at all. Is there a difference between the pace of time which the person on the chair experiences and the one which the person in the satellite experiences? Of course, the person on the chair has taken proper precautions. Let's not consider centrifugal forces.  This is not the same as asking for the pace of time in a satellite orbiting the earth in a circular orbit. The satellite is in free fall and tries to maximize the time passed, just like any other object in free fall (this is an approximation for low velocities; at high velocities, the curvature of space also comes into play). As the satellite is moving in an orbit of which every point has the same pace of time (faster as on the surface of the earth), the time moves at the same pace as the time at the height at which the satellite moves.   The extra thing I ask is if the pace of time for the man in the chair is different from the pace of time in the satellite. Since the man stays put at the height of the orbiting satellite, he is finding himself in a point in space where the time has the same pace as in all the points through which the satellite travels, so one is tempted to think there is no difference in the pace of time for both persons.  Is the slowing of time for the person in the free falling satellite due to its speed (if no gravity were present it would travel in a straight line with the same velocity as in the circular orbit) so it would in that case be a special relativistic effect, while the slower pace in time for the man on the chair would be a general relativistic effect? In other words, can you use the special relativistic time dilation formula for a person (in a satellite) traveling in flat space with the same speed as the circular orbiting satellite (for low velocities)?

In the Wikipedia article on  I see two formulae for the gravitational time dilation. One contains $\sqrt{1 - r_0/r}$ but the other $\sqrt{1 - 1.5 r_0/r}$. What formula should I use to calculate the time dilation due to gravity inside a satellite? The speed induced time dilation is of course just special relativity.  With the first of these two formulas I can perfectly reproduce the graphs on time dilation as a function of $r$,  I find that the two contributions to time dilation cancel at 1.5 Earth radii, all numbers are OK... But why not the second formula?


I mistakenly disabled my administrator account in Ubuntu 12. Now all my documents are locked. I have tried entering the password but it's responding with "invalid password". I'm only able to login using the guest account.  How can I re-enable my administrator account?

I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution?


I expect this has been asked and answered elsewhere, but I couldn't find an exact duplicate.  The multi-leg return fare:  CWL > AMS > PDX > AMS > CWL    is significantly cheaper than:   AMS > PDX > AMS   KLM's booking office couldn't explain to me exactly why, other than to say it's how the fare structure works.  I assume the airlines have good economic reasons for this, though I can't imagine what they are.  And I also assume that the fare system and its terms and conditions have been carefully engineered, for whatever reason, to make a cheaper fare for the single leg unavailable.

It seems like one-way tickets are always more expensive than buying round-trip. But what if I have two destinations? For example I would like to go on the following itinerary this March:  London --> Austin --> Rio de Janeiro --> London  At the moment the cheapest way to do this seems to be:  London --> Austin --> Rio de Janeiro --> Austin --> London  but that seems a bit ridiculous. Is there not a way to just buy a series of one way tickets that would follow the first itinerary? Please keep in mind, my main concern is price.


There is a statement in my physics textbook in gravitation chapter - The force of attraction due to hollow spherical shell of uniform density on a point mass situated inside it is zero Is it valid for solid sphere? What happens in solid sphere? Please explain this statement.

It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero.   What exactly is the reason behind this? Except for, of course, the mathematics behind it. Is there any logic why the field intensity should be zero within a sphere? For example, it is logical to say that the field intensity would be zero at the center, as all the intensities cancel out. However, this cannot be the case for any point within the sphere.


If a character with the shillelagh spell and polearm master feat can they use a d8 for their second attack with a quarterstaff?  Shillelagh For the duration thereafter, you can use your spellcasting ability modifier instead of Strength for the weapon, and its damage die becomes a d8.    Polearm Master When you take the Attack action and attack with only a glaive, halberd, quarterstaff or spear, [...] the weapon's damage die for this attack is a d4, and the attack deals bludgeoning damage.  One could argue that the feat makes it clear that your extra attack with Polearm master says that it deals a d4, period. But one could also say that the d4 is one of the quarterstaff's damage dice, and therefore becomes a d8 because you are making a second attack with the weapon.

Shillelagh imbues a quarterstaff with magic for a minute. This allows a caster to attack with the quarterstaff using his casting ability.  Polearm Master allows a player who attacks with a quarterstaff to get a second attack with the haft as bonus action.   Can I use my casting ability for the quarterstaff haft bonus attack?  I think so, but I am not sure. A good answer should include rule text and discussion to show why this is possible or why not.


For example, if I had a dark blue or black background choosing white text will make it stand-out and more readable.   If I had a white or off-white background, black text will stand-out and be readable.  What do I do if the background color is neither dark enough for white to show well nor light enough for black to show well?

I've come here seeking for a bit of design help or advice on how I could possibly improve the following:  Like the title says, I'm having a website banner with multiple text displayed on different images as backgrounds. Now, since most of the images are dark, I've set the font color as white. But even then, some of the text is not very readable on a couple of images like:    Since I'm working with CSS, I've tried different options such as:  Adding Text Shadows:    CSS:  text-shadow: 3px 3px 0px #000;  Also tried, creating a semi-transparent box around the text:      I feel the box one looks out of place.  I've created a  for anyone who knows CSS. If not, please feel free to advice me based on your imagination alone.  PS: You could also advice on using a different font if that would help it stand out better.


I'd like to insert a huge infographics image into a post. The problem I'm facing with is that WordPress provides smaller versions of the image even though I choose "large" thus the image won't go full width of its container and smaller texts in the image are not readable. In the image details, the full size option isn't the original full size, but smaller. I'd need an option for 960px width.  These are the physical files created by WP:  srcset: Infographic2-min-46x300.jpg 46w, Infographic2-min-157x1024.jpg 157w, Infographic2-min-768x4998.jpg 768w, Infographic2-min-236x1536.jpg 236w, Infographic2-min-315x2048.jpg 315w, Infographic2-min-scaled.jpg 393w  sizes: (max-width: 393px) 100vw, 393px  I noticed that WP uses srcset & sizes to make images responsive. Is it possible to override/customise it? Or how should these kind of large images be displayed?

I'd like to insert a large infographics image into a post. The problem is that WordPress scales the image and applies a limit of 393px in my case. When I try to manually increase it, a red exclamation mark shows up, and won't use the value given by me:  How to remove that limit?


The OpenJDK implementation of AbstractSet throws a NullPointerException when you pass a null value to removeAll.        public boolean removeAll(Collection<?> c) {     Objects.requireNonNull(c);   e.g.      Set<String> parent = new HashSet<String>();     Set<String> children = null;     parent.removeAll(children);   Results in  Exception in thread "main" java.lang.NullPointerException     at java.util.AbstractSet.removeAll(AbstractSet.java:152)   What is the architectural logic behind this?  Why wouldn't it do a null check and return modified = false instead of throwing a NullPointerException?  What is the benefit in this case between differentiating between null and an empty set?  EDIT:   I know the interface specifies it. You can ask the same question about the interface. The point of the question is that removing nothing from something leaves you with the original. There doesn't seem to be a logical reason for throwing a NullPointerException.  For those that say any null should be fixed, that isn't a logical reason for throwing a NullPointerException in this case.  It isn't a duplicate question of   because I am asking about the architectural design of a specific method and not asking what a NPE is.

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


So I wanted to use the WiFi somewhere with a captive portal today. No problem, right? I'll just open my browser, type in www.google.com, and see the login page for the WiFi.  Wrong! My browser wants to connect to Google by HTTPS, and that prevents the captive portal from intercepting my traffic to Google. I try some other sites that I can think of. They also all use HTTPS to connect. Finally, I try http://www.intel.com/, a site that I can think of but never visit. It works. I get the captive portal. Then at some point, I disconnect from the WiFi network and have to try again. This time, it turns out that www.intel.com has sent an  header has telling my browser that in the future, it should only use HTTPS to connect to www.intel.com.  If most or all websites want me to connect via HTTPS these days, how am I supposed to reach the captive portal's login page?

Captive WIFI portals suck.  So often when I open in a browser (Desktop Chrome or Mobile Chrome) a HTTP site, I get the captive portal, but with auto-completion and so quickly I connect again to WIFI.  The problem is that after the captive portal redirects, I'll have also a HTTPS redirect and Chrome remember the certificate and to use only HTTPS.  So I cannot use the same site twice (in a session).  A well-known public HTTP only site will resolve this.  Well-known sites usually work, causing some less debugging of the WIFI connection.


What do the following numbers represent?

When I entered the -al attribute with the  command, I got the following:  anupam@JAZZ:~/blog$ ls -al total 76 drwxrwxr-x 13 anupam anupam 4096 Aug 28 21:45 . drwxr-xr-x 34 anupam anupam 4096 Aug 28 20:52 .. drwxrwxr-x  8 anupam anupam 4096 Aug 28 12:19 app drwxr-xr-x  2 anupam anupam 4096 Aug 28 12:19 bin drwxrwxr-x  5 anupam anupam 4096 Aug 28 12:19 config -rw-rw-r--  1 anupam anupam  154 Aug 28 12:19 config.ru drwxrwxr-x  3 anupam anupam 4096 Aug 28 12:37 db -rw-rw-r--  1 anupam anupam 1339 Aug 28 12:19 Gemfile -rw-rw-r--  1 anupam anupam 2871 Aug 28 12:19 Gemfile.lock drwxrwxr-x  7 anupam anupam 4096 Aug 28 21:45 .git -rw-rw-r--  1 anupam anupam  466 Aug 28 12:19 .gitignore drwxrwxr-x  4 anupam anupam 4096 Aug 28 12:19 lib drwxrwxr-x  2 anupam anupam 4096 Aug 28 12:29 log drwxrwxr-x  2 anupam anupam 4096 Aug 28 12:19 public -rw-rw-r--  1 anupam anupam  249 Aug 28 12:19 Rakefile -rw-rw-r--  1 anupam anupam  478 Aug 28 12:19 README.rdoc drwxrwxr-x  8 anupam anupam 4096 Aug 28 12:19 test drwxrwxr-x  6 anupam anupam 4096 Aug 28 12:33 tmp drwxrwxr-x  3 anupam anupam 4096 Aug 28 12:19 vendor   What does each column mean, and what does the total 76 signify here?


All I know about the constraint is it's name, but I want to see the columns it is using.

All I know about the constraint is it's name (SYS_C003415), but I want to see it's definition.


I've checked around here and have been unable to find anything that solves my problem. There are several other questions that ask similar things, but the solutions do not give a global way to apply the change.  I've been using \left[\begin{array}{rrr}...\end{array}\right] for the longest time when typesetting matrices, but recently found \bmatrix to be much quicker to accomplish (almost) the same goal. The problem is that I don't like the fact that the entries are centered in their columns instead of flush right. Is there a way I can alter this behavior globally, or maybe \renewenvironment{bmatrix} so that I can mimic the behavior with an array, but use only \begin{bmatrix}...\end{bmatrix}?  For example, I'd like the following two environments to look as close to the same as possible:  \left[\begin{array}{rrr}   x-y & 2 & 3n\\   2 & 4 & 2\\   a & x^2 & 2x^2-3 \end{array}\right]  \begin{bmatrix}   x-y & 2 & 3n\\   2 & 4 & 2\\   a & x^2 & 2x^2-3 \end{bmatrix}

I'd like to left align the -1 entry in the following matrix so that the 1s line up. Is there a way to get matrices to ignore signs in that way?  \begin{matrix}     1 & 1  \\     1 & -1 \\ \end{matrix}   Using \flushright{-1} doesn't seem to work.


Is it possible to disable the internal Keyboard on my Laptop? I poured Tea over it and now the "M"-key is stuck.   I tried a lot and it is far too expensive to replace the keyboard on this old laptop.  I would rather just connect a USB Keyboard and disable the internal one.  I tried uninstalling it in the Manager, but it reinstalls immediately.  I also tried autohotkey to fix this:  ; This script disables the broken "m" key and replaces the caps lock key with an m key Capslock::m m::return   But this copletely disables the  key also on the Capsloc key

I frequently plug a USB keyboard into my laptop to use instead of the laptop keyboard.  However, when I do this, the OS (Windows Vista) then accepts input from both the laptop keyboard and the USB keyboard.  I want to place the USB keyboard on top of the laptop keyboard and that might result in accidental keypresses if the laptop keyboard is still enabled.  So, is there any way to disable the laptop's built-in keyboard when a USB keyboard is plugged in?  My laptop is a Dell Inspiron.


I'm trying to root my android using adb from a linux distro. When I run   fastboot flash recovery recovery-clockwork-5.0.2.0-blade.img I get  > sending 'recovery' (3768 KB)... OKAY [  0.142s] writing 'recovery'... FAILED (remote: partition 'recovery' not support flash ) finished. total time: 0.155s  I'm following this site   I have looked the solution since a while but there are not specifics about my android, I guess adb is not working correctly. What can I do?

My mobile is Lenovo S920 running official Android OS 4.4.2.  I am trying to install cwm recovery through fastboot.  I tried executing the command   fastboot flash recovery recovery.img   But I am getting the error as partition 'recovery' not support flash. Please any one help me to fix this. Whether I need to change anything on the recovery partition?


I am pretty new to linux and LAMP setup. I want to setup a LAMP environment with AP on one linux server and M on a different linux server. I have a hard time finding a relevant document with such a configuration.  I have done the following steps so far:  server1:  yum install -y httpd /sbin/service httpd restart yum install -y php php-mysql sed -i "s/Listen 80/#Listen 80/g" /etc/httpd/conf/httpd.conf yum install -y mod_ssl openssl /sbin/service httpd restart service iptables stop   I changed the ServerName in /etc/httpd/conf/httpd.conf from  #ServerName www.example.com:80   to  ServerName 172.32.35.14 (ip address of server1) /sbin/service httpd restart   server2:  yum install -y mysql-libs yum install -y mysql yum install -y perl-DBI yum install -y perl-DBD-MySQL yum install -y mysql-server /sbin/chkconfig mysqld on /sbin/service mysqld start mysql -u root  -e "CREATE USER 'mysqluser' IDENTIFIED by 'password'"  mysql -u root  -e "CREATE USER 'mysqluser'@'localhost' IDENTIFIED by 'password'" mysql -u root  -e "GRANT ALL PRIVILEGES ON *.* TO 'mysqluser'@'localhost' WITH GRANT OPTION" mysql -u root  -e "GRANT ALL PRIVILEGES ON *.* TO 'mysqluser'@'%' WITH GRANT OPTION" mysql -u mysqluser -p password -e "CREATE DATABASE mysqldb"  mysql -u mysqluser -p password mysqldb < /tmp/mysqlinstaller/world.sql service iptables stop   Then I had these post configuration steps:  On server 2, where my mysql is installed, I did the following in /etc/my.cnf under the tag [mysqld]  bind-address = 172.32.35.14 (ip of server 1 where apache/php are installed) service mysqld restart  service mysqld start MySQL Daemon failed to start. Starting mysqld:                                           [FAILED]   I am facing these issues...    When I run the url  on my browser to check the apache installation, I am not able to get the default apache homepage. Instead it says Problem loading page. When I run - service mysqld restart - on the server where mysql is installed, I get the following error:   service mysqld start MySQL Daemon failed to start. Starting mysqld:                                           [FAILED]   Can you point out what I am missing and guide me please

I am pretty new to linux and LAMP setup. I want to setup a LAMP environment with AP on one linux server and M on a different linux server. I have a hard time finding a relevant document with such a configuration.  I have done the following steps so far:  server1:  yum install -y httpd /sbin/service httpd restart yum install -y php php-mysql sed -i "s/Listen 80/#Listen 80/g" /etc/httpd/conf/httpd.conf yum install -y mod_ssl openssl /sbin/service httpd restart service iptables stop   I changed the ServerName in /etc/httpd/conf/httpd.conf from  #ServerName www.example.com:80   to  ServerName 172.32.35.14 (ip address of server1) /sbin/service httpd restart   server2:  yum install -y mysql-libs yum install -y mysql yum install -y perl-DBI yum install -y perl-DBD-MySQL yum install -y mysql-server /sbin/chkconfig mysqld on /sbin/service mysqld start mysql -u root  -e "CREATE USER 'mysqluser' IDENTIFIED by 'password'"  mysql -u root  -e "CREATE USER 'mysqluser'@'localhost' IDENTIFIED by 'password'" mysql -u root  -e "GRANT ALL PRIVILEGES ON *.* TO 'mysqluser'@'localhost' WITH GRANT OPTION" mysql -u root  -e "GRANT ALL PRIVILEGES ON *.* TO 'mysqluser'@'%' WITH GRANT OPTION" mysql -u mysqluser -p password -e "CREATE DATABASE mysqldb"  mysql -u mysqluser -p password mysqldb < /tmp/mysqlinstaller/world.sql service iptables stop   Then I had these post configuration steps:  On server 2, where my mysql is installed, I did the following:  bind-address = 172.32.35.14 (ip of server 1 where apache/php are installed) service mysql restart   But I am not able to establish a connection. Can you point out what I am missing and guide me please.


I was trying to make more room on my Windows 10 partition, so I used Gparted Live to reduce partition size by 6GB of the Ubuntu boot. The Ubuntu will still boot, but the Windows partition boots with a blue, sad face screen. I get the windows error of 0xc0000225 when starting up. I did not move the left side of the Windows partition, only expanded it, and the partition had at least 60Gb of free space in it. There were no errors while partitioning the boots with Gparted Live.  Gparted Live cannot access the partition, although I can access Windows through Ubuntu and all files are accounted for.  I have tried to download a Windows 10 recovery disk onto my USB, though couldn't figure how to run it.  [EDIT] For further information, the grub for dual-boot does open up. Everything works fine, I can see the Windows partition, though when I open it, it crashes. On further note, I am going to also post this on Windows forum ().  [EDIT] Just so you guys know. This is NOT a duplicate. The post you linked as a duplicate is indeed different. The boot works just fine and this is not UEFI. Nonetheless, I think this is more a windows problem then Ubuntu.  [EDIT] This question was solved on the linked page. For summary: The recovery disk was very difficult to download and install for some reason, but in the end it was indeed the answer. Just popped in and "repaired" startup. It didn't appear to have worked at first, but normal Windows startup repaired it further into function. Thankyou all for attempting to help.  As a clarification, this was indeed a Windows problem. However, Downloading and installing the recovery iso onto a usb was an Ubuntu problem (which took me half a week to figure out).

I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this?


I am trying to meal prep for the work week. I have come up with recipes that meet my calorie goals, and I am trying to make them in advance. I have tried this in the past, but what I noticed is that I got bored after about the 3rd day or the meat did not taste good after approximately 3 days (especially chicken and fish).   I tried making meals for only 3 days in advance vs 5 days, but the problem is that I have very little to no time to cook during the weekdays. I tried yesterday, and it took me over 2 hours and I still was not able to complete the meals.   My meals are as follows: brown rice with veggies and some meat, wholewheat pasta with some meat, wholewheat tortilla tacos with some meat, and a lean veggie soup base (veggies with broth). Each of the meals may be supplemented by some extra roasted potatoes. All of the meals also include some veggies (onion, bell pepper, spinach, etc)  I have time on sunday to cook but I want the meals that I am going to eat on Thursday/Friday to last if I cook them on Sunday. I am trying to figure out the best way of doing this.   I usually make the meals individually. So for example I'll make specifically 114g of pasta for a single meal and cook that separately from the rest of pasta meals I will cook, since I don't know how much 114g of raw pasta weighs when it is wet. The meats are usually done in batch. I'll cook the chicken around the same time as I cook my flank steak, shrimp, and chicken sausage. Here are my questions:  1) If I make the individual meals on Sunday, and the meals contain brown rice/wholewheat pasta with some meat like chicken/shrimp/flank steak and veggies, can i immediately freeze the meals in the tupperware? Will this taste good if I thaw them 4 days later and reheat them?  2) Let's say I don't freeze anything. Then can cooked pasta/brown rice last for 5-6 days? I read online that chicken/meats in general only last about 3 days before they spoil/taste bad. But it would save me a lot of time if I cooked the pasta/rice in advance and just cooked the meats/veggies on wednesdays.  3) how long can cooked veggies last in the fridge? I make veggie soup as part of my meals, so can that last for 5 days if needed?  Sorry for the long list of questions. Mainly I am trying to figure out what is the best way of prepping this stuff. An ideal solution for me would be cooking all 10 meals (5 days x 2 meals for lunch and dinner) in one day and then preserving the taste of the meals that will be eaten on thursday/friday.

How do I know if a given food or ingredient I have is still good, or if I should discard it?  How can I best preserve a food or ingredient?     This broad question is intended as a "general reference" question to quickly answer many how long will food keep for? questions. Please feel free to edit this question to expand and clarify as needed.


I recently updated ubuntu to 15.10. After the update I couldn't see any text in Skype! I tried reinstalling it     sudo apt-get purge skype   Deleted the /home/username/.Skype folder  and reinstalled Skype but that didn't solve the problem.   As you can see from the image screenshot above, I can't event start it now as it is stuck on the Terms of Use window  I managed to login after restarting ubuntu but then it failed again

Skype app in my Ubuntu system work perfectly. But today when I run the app, I see this:    How Can I fix this?


Find all the possible functions $f:\mathbb{Q}\to\mathbb{Q}$ such that $$f(1)=2$$ and $$f(xy)=f(x)f(y)-f(x+y)+1\text.$$  I managed to find the function for the set of natural number, by putting $x=1$ and $y=n$. From it, I have that $$f(n+1)=f(n)+1\text,$$ which means that $f(n)$ is an arithmetic progression of natural numbers. I am stuck with generalizing this into the set of rational number, any hit will be appreciated.

I'm working on this problem already, the domain and co-domain are the set of Rational Numbers. we see that setting $x = 1$ and $y = n$, we obtain $f(n + 1) = f(n) + 1$  But I'm trying to prove that $f(n) = n + 1$ for all $n$, the case when $n = 1, 2$ is obviously true, how do I approach this via induction?


Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$  How would you do the inductive step for this proof? I have the base case done.

I am trying to prove that $\dfrac{(2n)!}{2^n}$  is integer. So I have tried it by induction, I have took  $n=1$, for which we would have $2/2=1$ is integer. So for $n=k$ it is true, so now comes time to proof it for $k+1$, $(2(n+1))!=(2n+2)!$, which is equal to $$1 \times 2 \times 3 \times \cdots \times (2n) \times (2n+1) \times (2n+2),$$ second term would be $$2^{n+1}=2 \times 2^n$$ Finally if we divide $(1 \times 2 \times 3 \times \cdots \times (2n) \times (2n+1) \times (2n+2)$ by $2^{n+1}=2 \times 2^n$,and consider that,$(2n)!/(2^n)$  is integer, we get $(2n+1) \times (2n+2)/2=(2n+1) \times 2 \times (n+1)/2$, we can cancel out $2$, we get $(2n+1)(n+1)$ which is definitely integer. I am curious this so simple? Does it means that I have proved correctly?


I would like to move a folder from Downloads into Program Files. It used to work in older Windows versions (e.g. 7), but I can't do it in Windows 10 (Version 1607).  I tried the following, it always fails silently:   Drag and drop from one Explorer window to another Copy (or cut), and then paste Using the "Move to" button in the ribbon   The image below shows what I used to get, but no longer see. Any way to get it back? I'm not sure if this was a change in Windows 10, or if there is a problem on my side.

When I'm trying to copy or move files to a system directory (like C:\Program Files or C:\ProgramData\Microsoft\Windows\Start Menu) nothing happens instead of being prompted for access rights with the usual UAC dialog. The files are not copied/moved and there is no error message.  Here's the story behind it: I got a new PC with Windows 10 installed. There was already a user account "user" created, but I wanted my own account "Florian" with my own name. So I created my account in Administrative Tools and added it to the Administrators group. I switched to my new account and deleted the old "user" account.    Since then I started to setup my PC and install my programs. I tried to copy some portable programs to C:\Program Files when I noticed that I could not simply copy a directory into C:\Program Files. I expected a UAC prompt, but I only got the wait cursor for the fraction of a second and nothing happened. I cannot even delete directories from installed programs.  My user account has no permissions except "special permissions" for C:\Program Files, but as I am in the Administrators group I should be able to modify files there. I checked this with another Windows 10 installation and the permissions are the same.    I get the regular UAC prompt when modifying system settings running programs "as Administrator".  Any ideas why I am not prompted for permission when copying to system folders?


I applied for normal family visit visa for my mother and brother to visit me in UK from Pakistan. I am myself British citizen.  Their visa was rejected based on ECO's remarks about not being satisfied with my brother's financial situation.  I want to apply for their Visa again, but this time I want to use Sponsorship Undertaking SU07 form which means that I will be legally responsible for the travel arrangements. My question is can I send them Sponsorship Declaration form SU07 even though it is general family visit visa .I am not calling them on dependent Visa.  My second question is if I use this Declaration form, will they still have to  prove that they have means to support their travel even though when I am submitting the declaration form.

Someone (a relative) from the UK (already a naturalized British Citizen) will be financing my trip, as well as taking care of my accommodation. What are the documents I need to submit aside from bank statements? Does the sponsor need to fill-out the Sponsorship Undertaking Form? ()  something to consider from my question: -my relative is a naturalized citizen in the UK. Is proof of naturalization needed?


I've just made a test few minutes ago, the scenario is the following:  There was a question with 7-8 answers (all of them were correct because the question was very easy), someone downvoted all of the answers and leaves no comment (I suppose it was the question author because his question was downvoted). This situation has bothered me since I think it is not very professional and also I've loose 2 rep points for a whim. So I tried to delete my answer and repost it as-was. The trick worked: I've my 2 points back and the answer has now 0 votes.  I think that this trick should be avoided in some ways, obviously it can't be a simple text-check between the 2 answers because it will be easilly bypassed, I think that a good way can be that: if you repost an answer after an answer deletion, the rep points don't turn back.

I haven't seen this behavior out in the wild much, but it happened again recently and I was wondering if a flag could be automatically raised when this happens:   User posts answer Answer is down voted User deletes answer User posts exact same text as a new answer User effectively ditched down votes   Got down voted again? Wash, rinse and repeat. Profit (perhaps after modifying the post, which is what you should have done to begin with)    I feel that this should raise a duplicate content flag, with slightly stronger wording. Would this be possible to implement? Or, perhaps, don't let users post new answers if they have a deleted answer to a question. Rather, force them to edit and restore the deleted answer instead, unless locked by a moderator.  I do have a link, but I don't want a lot of people to descend on it and create an even bigger disruption. It happened exactly as I described.


Before I updated to Catalina, I was able to add MP3 files to iTunes, then select get info -> options, and change media type to podcast. I was then able to listen to MP3s (which were mostly lectures) as podcasts on my phone, giving me the ability to rewind 15 seconds .  Now Catalina has disturbed my universe and removed podcasts from iTunes and isolated it as its own app. This no longer allows me to categorize songs as podcasts and I am therefore becoming stupider as the days go by.    How can I add MP3s to the podcast app on my MacBook Pro (Catalina 10.15)?

I'm on macOS Catalina (10.15 Beta (19A471t)), and I'm trying to add manually downloaded podcasts that I copied from an iTunes library to the new Podcasts.app.    I tried to simply drag the files into the ~/Library/GroupContainers/243LU875E5.groups.com.apple.podcasts folder (- location of all the downloaded podcasts), but after that, the files still aren't appearing in the app.    I can see that the downloaded files in the mentioned podcasts folder have special file names (e.g. 7BE50452-8412-4232-B384-D9E1B94813ED.mp3).  Downloading again the files within the Podcasts.app, is not always a solution, As @Dillon pointed out in the comments.  Is there any solution for this issue?


I am not able to understand logic behind coming up with this formula for covariance. We know that the sample covariance formula is:    $${\rm Cov}(x,y)=\frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{n-1}$$  I am not able to understand the logic behind the numerator. Why are we multiplying the terms? I mean, I know we need to find the change in x is appearing along with change in y (if they co-vary), so this formula will give direction of that change in terms of sign of the number that you get after substituting the values in the formula. And also we will be able to make some comparisons, e.g., having a covariance of 50 is more evidence of x and y moving together than having it as 30. So their ordering will make sense. But if you just think of a single value of covariance without having to compare it with anything else, does it have any real intuitive meaning (just the number in itself)? For example, in case of variance or standard deviation one can easily see that it is average number of 'deviation from the mean' per data point in the sample. But here in case of covariance, I am not able to come up with any such intuitive understanding.     As I was adding tags for this question just now—I saw this as the tag description for the covariance the tag:      Covariance is a quantity used to measure the strength and direction of the linear relationship between two variables. The covariance is unscaled, & thus often difficult to interpret   So probably my difficult to understand covariance can be attributed to this.

...assuming that I'm able to augment their knowledge about variance in an intuitive fashion (  ) or by saying: It's the average distance of the data values from the 'mean' - and since variance is in square units, we take the square root to keep the units same and that is called standard deviation.  Let's assume this much is articulated and (hopefully) understood by the 'receiver'. Now what is covariance and how would one explain it in simple English without the use of any mathematical terms/formulae? (I.e., intuitive explanation. ;)  Please note: I do know the formulae and the math behind the concept. I want to be able to 'explain' the same in an easy to understand fashion, without including the math; i.e., what does 'covariance' even mean?


$$\sum_{n=1}^{\infty}n^210^{-n} = \frac{110}{3^6}$$  I noticed this while playing around on my calculator. Is it true and how come?

The question I've been given is this:  Using both sides of this equation:  $$\frac{1}{1-x} = \sum_{n=0}^{\infty}x^n$$  Find an expression for $$\sum_{n=0}^{\infty} n^2x^n$$ Then use that to find an expression for $$\sum_{n=0}^{\infty}\frac{n^2}{2^n}$$  This is as close as I've gotten:  \begin{align*} \frac{1}{1-x} & = \sum_{n=0}^{\infty} x^n \\ \frac{-2}{(x-1)^3} & = \frac{d^2}{dx^2} \sum_{n=0}^{\infty} x^n \\ \frac{-2}{(x-1)^3} & = \sum_{n=2}^{\infty} n(n-1)x^{n-2} \\ \frac{-2x(x+1)}{(x-1)^3} & = \sum_{n=0}^{\infty} n(n-1)\frac{x^n}{x}(x+1) \\ \frac{-2x(x+1)}{(x-1)^3} & = \sum_{n=0}^{\infty} (n^2x + n^2 - nx - n)\frac{x^n}{x} \\ \frac{-2x(x+1)}{(x-1)^3} & = \sum_{n=0}^{\infty} n^2x^n + n^2\frac{x^n}{x} - nx^n - n\frac{x^n}{x} \\ \end{align*}  Any help is appreciated, thanks :)


A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio $4:3$.   What is the probability that the three sticks that are left CANNOT form a triangle?   My approach is let be the larger part be $x$ and so the smaller part be $(1-x)$, now the two other sides be $\frac{4x}{7}$ and $\frac{3x}{7}$, now I know a triangle has a property its two sides sum is larger than the third side, but how to apply that in this question, I am confused. The answer given is $1/4$.

A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio 4:3. What is the probability that the three sticks that are left CANNOT form a triangle? in this problem i am not getting how to proceed like  what is  sample space?it is quiet confusing to me. Please give any simple view for this problem.


The body of the function set_bit(uint64_tx, int pos, bool value) which returns the modified value of the input x, where the bit at the pos position is replaced with the value value.  Remember that in the C language (this is defined in stdbool.h), true is the integer 1 while false is the integer 0.  Code  uint8_t a=0b00000000; uint8_t b=0b00001000; uint8_t c=0b11111101; uint8_t d=0b11011011;  // l'opération  ~( a ) renvoi 0b11111111 // l'opération (c & a) renvoi 0b00000000 // l'opération (c & b) renvoi 0b00001000 // l'opération (a | b) renvoi 0b00001000 // l'opération (d & c) renvoi 0b11011001    #include <stdint.h> #include <stdbool.h>  /* * @pre 0<= pos < 64 */  uint64_t set_bit(uint64_t x, int pos, bool value) {     // à compléter }

How do you set, clear, and toggle a bit?


I am a beginner in Python. I have written a code in which the name of the contestants and their scores will be stored in a dictionary. Let me call the dictionary as results. However I have left it empty while writing the code. The keys and values are going to be added to the dictionary when the program is being run.  results={}      name=raw_input()     #some lines of code to get the score# results[name]=score     #code# name=raw_input()     #some lines of code to get the score# results[name]=score   After the execution of the program, let us say results == {"john":22, "max":20}  I want to compare the scores of John and Max, and declare the person with highest score as a winner. But I wont be knowing the names of the contestants at the beginning of the program. So how can I compare the scores, and declare one of them as the winner.

I have a dictionary: keys are strings, values are integers.  Example:   stats = {'a':1000, 'b':3000, 'c': 100}   I'd like to get 'b' as an answer, since it's the key with a higher value.  I did the following, using an intermediate list with reversed key-value tuples:  inverse = [(value, key) for key, value in stats.items()] print max(inverse)[1]   Is that one the better (or even more elegant) approach?


I uninstalled my Clash of Clans and now my data is being lost.  I have tried everything to recover it.  How can I recover my save data?

I unintentionally and stupidly wiped my Clash of Clans game data. I went to Application Manager on my Android and clicked 'Clear data'. (I used this for fixes before and it never started a new game.)   Now, my level 60 or so base has been wiped as if was to start a new game. Have I doomed myself to starting again or is there a way in which I can retrieve my old game save? Maybe by contacting Supercell? I have a snapshot of my base.


We can assume all the assumptions of the classical setting of linear regression with unknown variance of the residual.   What would be the multivariate distribution of the vector $\hat{\beta}$?  The result should be consistent with the fact that the marginal distribution of each element of $\hat{\beta}$ is a t-distribution.   We should also be able to compute the distribution of any linear combination of $\hat{\beta}$.

I have a simple linear OLS regression $Y_i = \alpha+ \beta_1 X_{1i} + \beta_2 X_{2i} + e_i$ where $e_i \sim N(0,\sigma)$. I have estimated the regression from the data and obtained estimates for my coefficients as well as the corresponding covariance matrix. Assume my dataset is large (>500)  Now I would like to construct the 95% confidence interval for $Z = a_1 \beta_1 + a_2 \beta_2$. My first thought was that I could assume that Z follows a normal distribution because my regression coefficients are approximately normal and a linear combination of normal variables is also a normal variable. I do find some sources where they treat $Z$ as a normal random variable.  But now I am in doubt because I found that a linear combination of normal random variables is only normal if they are independent. So is it still save to assume $Z$ is random?


How to solve :$$\lim_{x\to0}\Big(\frac 1{x^2} - \frac 1{\sin^2x}\Big)$$ My approach : as $\lim_{x\to0}{\frac {\sin x}x}=1$. Therefore when $x\to0$ , $\sin x=x$. So when $x\to0$ , $\frac 1{X^2}=\frac 1{\sin^2x}$. So the answer to the problem is $0$. But in the book answer is given $\frac 13$ . How?

Evaluate   $$\lim \limits_{x \rightarrow  0}\left(\frac{1}{x^2}-\frac{1}{\sin^2(x)}\right)$$   I tried to combine the fractions $$\frac{1}{x^2}-\frac{1}{\sin^2(x)} = \frac{\sin^2(x)-x^2}{x^2\sin^2(x)}$$ and apply L'Hopitals which only made a mess.  I feel like there is a simpler way of doing this but I'm not quite sure what to do


Sometimes when i am working in a shell i suddenly find out that standard error has been linked to /dev/null. If i open a new shell it is back to normal.  I am using zsh with oh-my-zsh and prezto. I have looked over the rc files but i cannot find any reason why this should happen seemingly at random.

Running some shell functions and ctrl-c-ing them leads to my stderr being suppressed, such that echo hi >&2 and echo hi > /dev/stderr print nothing. I want to debug this, but I have no idea how to start. How can I check where stderr is redirected to? Doing a exec zsh doesn't solve this problem in an affected shell, which indicates the problem is indeed with a rogue redirection.  I'm on macOS.  I tried:  ll /dev/fd crw--w---- 0,11 evar 12 May 18:32 0 crw--w---- 0,11 evar 12 May 18:32 1 crw-rw-rw-  0,2 root 12 May 18:32 2   Perhaps the issue is that /dev/fd/2 is somehow owned by root?  Update:  lsof -p $$ COMMAND   PID USER   FD   TYPE DEVICE  SIZE/OFF                NODE NAME zsh     69568 evar  cwd    DIR    1,6      1472          8624004142 /Users/evar/Base/Lectures zsh     69568 evar  txt    REG    1,6    618652          8678375637 /usr/local/Cellar/zsh/5.8/bin/zsh zsh     69568 evar  txt    REG    1,6    452676          8677805768 /usr/local/Cellar/pcre/8.44/lib/libpcre.1.dylib zsh     69568 evar  txt    REG    1,6    312924          8678370072 /usr/local/Cellar/ncurses/6.2/lib/libncursesw.6.dylib zsh     69568 evar  txt    REG    1,6    251160          8678375669 /usr/local/Cellar/zsh/5.8/lib/zsh/zle.bundle zsh     69568 evar  txt    REG    1,6    123012          8678375645 /usr/local/Cellar/zsh/5.8/lib/zsh/complete.bundle zsh     69568 evar  txt    REG    1,6     65188          8678375676 /usr/local/Cellar/zsh/5.8/lib/zsh/compctl.bundle zsh     69568 evar  txt    REG    1,6     18220          8678375661 /usr/local/Cellar/zsh/5.8/lib/zsh/terminfo.bundle zsh     69568 evar  txt    REG    1,6     27888          8678375680 /usr/local/Cellar/zsh/5.8/lib/zsh/system.bundle zsh     69568 evar  txt    REG    1,6     17240          8678375681 /usr/local/Cellar/zsh/5.8/lib/zsh/langinfo.bundle zsh     69568 evar  txt    REG    1,6     38064          8678375656 /usr/local/Cellar/zsh/5.8/lib/zsh/parameter.bundle zsh     69568 evar  txt    REG    1,6     22864          8678375674 /usr/local/Cellar/zsh/5.8/lib/zsh/pcre.bundle zsh     69568 evar  txt    REG    1,6     37588          8678375667 /usr/local/Cellar/zsh/5.8/lib/zsh/zutil.bundle zsh     69568 evar  txt    REG    1,6     62316          8678375647 /usr/local/Cellar/zsh/5.8/lib/zsh/complist.bundle zsh     69568 evar  txt    REG    1,6     22620          8678375675 /usr/local/Cellar/zsh/5.8/lib/zsh/stat.bundle zsh     69568 evar  txt    REG    1,6     29076          8678375649 /usr/local/Cellar/zsh/5.8/lib/zsh/zpty.bundle zsh     69568 evar  txt    REG    1,6     18736          8678375668 /usr/local/Cellar/zsh/5.8/lib/zsh/datetime.bundle zsh     69568 evar  txt    REG    1,6     17628          8678375660 /usr/local/Cellar/zsh/5.8/lib/zsh/zleparameter.bundle zsh     69568 evar  txt    REG    1,6     18208          8678375654 /usr/local/Cellar/zsh/5.8/lib/zsh/termcap.bundle zsh     69568 evar  txt    REG    1,6     63728          8678375662 /usr/local/Cellar/zsh/5.8/lib/zsh/computil.bundle zsh     69568 evar  txt    REG    1,6     22440          8678375673 /usr/local/Cellar/zsh/5.8/lib/zsh/sched.bundle zsh     69568 evar  txt    REG    1,6   1534352 1152921500311885154 /usr/lib/dyld zsh     69568 evar    0u   CHR  16,11   0t56261                3469 /dev/ttys011 zsh     69568 evar    1u   CHR  16,11   0t56261                3469 /dev/ttys011 zsh     69568 evar    2w   CHR    3,2 0t1314232                 314 /dev/null zsh     69568 evar   10u   CHR  16,11   0t21049                3469 /dev/ttys011 zsh     69568 evar   11u   CHR   15,9    0t9086                 583 /dev/ptmx


This is an exercise in "Elements of set theory by Enderton". I can construct a function from the rational unit interval into rationals easily. So, If I can find a $1-1$ correspondence from real unit interval into reals that transform irrationals into irrationals, I can construct the required function easily.   Now I assume that I can find a function $g$ mapping rationals into rationals.   Now For irrationals: I can transform irrationals of $\mathbb{R}-(0,1)$ into $(0.1,1)$ as follows, suppose $a_ma_{m-1}..a_1.b_1b_2...$ is an irrational real number whose integer part is $a_ma_{m-1}..a_1$. Now consider $0.a_ma_{m-1}a_{m-2}...a_2a_1b_1b_2......$ as its image under the transformation. It seems that this is another irrational which lies between $0.1 $and $1$, notice that $a_m\ne 0$, So we still have $(0.0.1)$ to be used. Now for $x\in (0,1)$, we can  embed them into $(0,0.1)$. Suppose $0.c_1c_2c_3...$ is an irrational between zero and $1$. its image is $0.0c_1c_2c_3...$. So we can transform all irrationals of reals into irrationals of the open unit interval. we call this transformation $h$.  Now consider $f:(0,1)\rightarrow \mathbb{R}$ where $f(x)=h(x)$ if $x$ is irrational, $f(x)=g(x)$ otherwise.  My main question: Is my construction valid? If not, why?   Also, If my construction works well, Is there any better constructions?

While reading about cardinality, I've seen a few examples of bijections from the open unit interval $(0,1)$ to $\mathbb{R}$, one example being the function defined by $f(x)=\tan\pi(2x-1)/2$. Another geometric example is found by bending the unit interval into a semicircle with center $P$, and mapping a point to its projection from $P$ onto the real line.  My question is, is there a bijection between the open unit interval $(0,1)$ and $\mathbb{R}$ such that rationals are mapped to rationals and irrationals are mapped to irrationals?  I played around with mappings similar to $x\mapsto 1/x$, but found that this never really had the right range, and using google didn't yield any examples, at least none which I could find. Any examples would be most appreciated, thanks!


How can I post questions to know the community opinion about a theme, in 'A or B' style, without get 'off-toppic'?

Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com.


As the title describes, I'm looking for a word or phrase that describes the phenomenon that a bug/error/etc. disappears when you want to show it to someone.  Example: Your Internet connection does not work properly. You try everything to fix it, but it won't work. You call an expert but then when you want to show the issue to them, your Internet connection seems to be fine. Obviously, once your expert left, your Internet connection is broken again. Bad luck.  So, what would you call it?

I am an IT professional. More specifically in automation. I am looking for a term or phrase that describes the event when either:  a. you are watching something closely and the issue doesn't occur  or  b. you are not watching something at all and the issue does occur


So I have this question, but it's good for more than just 1 website. Is it allowed / good to post the question on the websites where I feel it should be on? My question for example:   It is a C# question but also a gis question. So it should belong on and could be usefull for either  and  .  So should I post it on both?

It is possible to migrate a question from one Stack Exchange site to another by closing, but if I have a question that I think is on-topic for multiple Stack Exchange sites, is it OK to post it on both (multipost)?   For example, I have a question that's earned me the tumbleweed badge on SO and I'm not sure what the best thing to do with it is. It's about a web server so it might be answerable on Server Fault but it's really more of a programming thing, hence the posting the question on Stack Overflow.    Is there any way to make the question visible on multiple sites (crosspost) and then accept the answer wherever it came from?


We had a server called DC01 set as a domain controller. Then we got another server and added it to the domain as a backup domain controller DC02. Months after adding DC02 to the domain DC01 had a catastrophic failure and was unplugged/taken off the network. But DC02 still things DC01 exists and I get errors like     The specified domain controller could not be contacted. This affects the following domain in the console.       Domain: domain.com   The error was: The specified domain either does not exist or could not be contacted.   Please choose from the following options:   [ ] Choose a different domain controller   [ ] Retry   [ ] Remove this domain from the console   Choosing a different domain controller leads me to the following:     Current domain controller: (blank)   Look in this domain:   domain.com   Change to:   [x] The domain controller with the Operations Master token for the PDC emulator   [ ] Any available domain controller   [ ] Any available domain controller running Windows Server 2003 or later   [ ] This domain controller:   dc01.domain.com   dc02.domain.com   I select This domain controller and choose dc02.domain.com and the pop up goes away.  How do I get rid of the references to the old primary domain controller, dc01? And what must I do to dc02 to make it the new primary domain controller?

I have 2 domain controllers on a non-Internet connected network running Windows Server 2008 R2. They running RAID 5 on a 8 Hard Drive server. Sometime last week the Boot Sector became corrupt on DC1 and I was unable to recover the server. I am not going to have to rebuild the server. I have been reading about the changes from Server 2003 to Server 2008. DC1 was the main domain controller and now that it won't but it is all falling to DC2. I know that in previous versions of Windows Server you had to make on the primary and one the secondary. Since DC2 does not see DC1 anymore is there anything I need to do to DC2 as it is now the one in control? I am thinking some kind of meta data clean up but I can't find any hard information on what procedure to do. I understand as of Server 2008 domain controllers are on an equal footing and provide replication to each other so they should be the same correct?


I've been told that stock/share value is 100% controller by supply/demand -- nothing more/less.  Financial history of the company is supposedly zilch -- so is any profitability/etc.  Basically, companies trading at sky-rocketed prices can have dirt-poor financial caps -- and super-profitable companies can trade for pennies on the mark. It's supply/demand based on a myriad of reasons -- not all of which are related to company performance but investor expectancy.  Given such, past or future projecting of company performance is not a guarantee for a high value stock. What determines price is only the equilibrium between buyers and sellers outstanding. If someone is buying more than selling, the difference is reflected in higher shares -- and vice-versa.  The true way to get your shares to go up would be to assure people buy at alarmingly higher rates than they sell -- not about whether a company does good because that's just one factor. Correct?  Given such, one would need to worry about more investors buying the shares they are holding -- not about how well the company does (unless they are sure this will lead to more buying).  In this figure, one can never know what can drive buys/sells in every case. I could tell you that some guy bought shares in "Golden Goose Drunkards" because he thought their logo was cool -- that's it; or maybe he liked the name. If other people follow along, the shares are worth more.  Given such, how can we reliably predict or help assure ourselves higher demand of our shares?

So a company decides to raise money by selling shares of its stock. The stock is offered at an initial price of their determination. The stock is then traded in a market where forces of supply and demand, as well as speculation, affect its price.  When a company performs well (or makes decisions that will likely increase the company's earnings in the future), more people want to buy that stock than do people wanting to sell it. This creates demand for that stock which causes its sell/bid prices rise. When a company performs poorly, the opposite occurs; more people want to sell the stock than want to buy. This creates a surplus that causes sell/bid prices to fall.  Understanding this, people speculate over company performance to determine the future behavior of a stock, and attempt to "buy low, sell high" or "borrow high, return low" in order to make a profit.  But my question is regarding the first part of that process. What is it about company performance that causes the perceived value of its stock to rise? This is especially perplexing since I would guess that most people don't exercise their voting rights, and many stocks don't pay dividends.  It's not like a shareholder has any direct financial gains from increased company earnings (speculative stock pricing notwithstanding).  What is the intrinsic value of the stock?  It seems to me that all participants in a stock market tacitly agree that stock price will have a direct correlation with company performance. So another way of asking the question is, would an opposite agreement hold? What financially (this isn't a question about logistics, communication, or feasibility) stops all participants in a market from agreeing to value a particular company's stock inversely with respect to the company's performance?  Since I feel like I can't quite nail down my question, another form of it would be, why is stock market behavior driven by company performance?


If a ribosome is made of protein, yet is used in protein sysnthesis, what created the first ribosome?  What created the ribosomal RNA?

Proteins are synthesized on ribosomes from mRNA copies of regions of the DNA. But ribosomes themselves are made up of proteins (and RNA). So how could the first ribosomes have arisen? Was there previously some other way of making proteins other than by ribosomes and mRNA?


guys! I'm pretty sure this will be a piece of cake for y`all, but I'm trying to add pagination to my loop. I've tried some codes that were available around, and got to paginate it, but pages 2, 3, etc had the same content from page 1. What's the best solution for what I have at the moment?  <?php     $recentPosts = new WP_Query();     $recentPosts->query('showposts=5'); ?> <?php while ($recentPosts->have_posts()) : $recentPosts->the_post(); ?>     <article>     </article> <?php endwhile; ?>   Thanks in advance.

I have added a custom/secondary query to a template file/custom page template; how can I make WordPress use my custom query for pagination, instead of using the main query loop's pagination?  Addendum  I have modified the main loop query via . Why isn't pagination working, and how do I fix it?


My UK visit visa has been refused. If I reapply through Super Priority visa service, it says:      If your application is not straightforward, it may not be possible to meet this timescale.    If so, within how many days would I get a decision?

Last Saturday, I got a refusal from BHC due to lack of funds and my reasons to come back to India. I am planning to visit my family who are settled in the UK. I am married and planning to visit my family along with my husband. My father is sponsoring our whole trip. But we got a refusal as we didn't show much funds in our account. We thought that if my father is sponsoring, we should show his documents only. But now I have applied again with a fast track service. Will BHC will consider it under the fast track process? This time I have cleared all their doubts which they mentioned in the refusal letter.


I am looking for some help with the following question. How do I prove that the series  $\displaystyle  \sum_{n=1}^{\infty} \frac{n}{(n+1)!}$ converges, and then how would I find its sum?    I see that this series $a_n$ converges if the sequence of partial sums $s_n$ converges.  So $s_n = \frac{1}{2} + \frac{1}{3} + \frac{1}{8} + \frac{1}{30}+... + \frac{n}{(n+1)!}$  I see that $\lim\limits_{n\to\infty}\frac{n}{(n+1)!}= 0 $ as $(n+1)!$ approaches infinity faster than $n$

Can someone give an explanation using the definition of convergence in partial sum to show how the above infinite sum converges to 1?  Thanks


Let $X$ be a compact Hausdorff space, $C(X)$ denote the set of all complex-valued continuous functions from $X$. Show that the smallest closed convex set containing the extreme points of the unit ball of $C(X)$ is the unit ball. The problem is from Douglas's book Banach Algebra Techniques in Operator Theory, problem 1.8. For the case $X=[0,1]$, I have shown that the set of all extreme functions are those that have modulus value $1$, but still have no clue how to proceed, even for the case $X=[0,1]$.   Please help.

Let $X$ be compact Hausdorff, and $C(X)$ the space of continuous functions over $X$. Denote the closed unit ball in $C(X)$ by $(C(X))_1$, then it can be shown $f$ is an extreme point of $(C(X))_1$ if and only if $|f(x)|=1$ for all $x\in X$.  In , we are asked to show that the convex hull of extreme points of $(C(X))_1$ is dense in $(C(X))_1$. By using a theorem of Fejer we can show this is true when $X=[0,1]$. But I do not know how to do it for general $X$.   Since it is only the 7th problem in the first chapter, I am guessing the solution should be elementary.   Thanks!


What is a word to describe an individual who acts like an expert in a subject area, constantly stating facts and correcting people, but who actually has very little knowledge on the subject?

Is there an idiom in English to describe someone who thinks he/she is smarter/wiser than everyone else?  In Polish, we have an idiom, which literally translated, would sound like:     He/she has eaten all minds


I have my HP all-in-one PC which previously had Windows 7 and just installed Ubuntu 20. To do this, I chose to format my drive and install Linux. The thing is that I forgot to backup some files.   I know there are file-recovery software solutions around but all seems to recover files after reinstalling the same OS and in my case I changed from Windows to Linux.  Any ideas?

About two weeks ago I had a problem with my PC that my brother wrote a question about at .  I still haven't solved the problem, so my PC is unusable now.  Now I think that it would be simpler to re-install both Win7 & Ubuntu than repair them, but there're some data on their partitions. I want to recover this data.  These partitions are not mountable for some reason. I don't know why.  sudo fdisk -l about the problematic partitions:     Device    Boot      Start         End      Blocks   Id  System /dev/sda1            2048     147912703    73955328   83 Linux /dev/sdb2            206848   174079999    86936576    7  HPFS/NTFS/exFAT   And in GParted:      And the error of the mount command:  Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   And the exact same message for /dev/sda1  How can I recover my data from those HDDs?  EDIT     I have tried to specify the type of the drive:  $ sudo mount -t ext4 /dev/sda1 /olddisk mount: wrong fs type, bad option, bad superblock on /dev/sda1,        missing codepage or helper program, or other error        In some cases useful info is found in syslog - try        dmesg | tail  or so $ sudo mount -t ntfs /dev/sdb2 /olddisk NTFS signature is missing. Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   EDIT     sudo ntfsfix /dev/sdb2 returns:  Mounting volume... NTFS signature is missing. FAILED Attempting to correct errors... NTFS signature is missing. FAILED Failed to startup volume: Invalid argument NTFS signature is missing. Trying the alternate boot sector Unrecoverable error Volume is corrupt. You should run chkdsk.


I spilled water on my laptop (HP 745 G5) and I switch it off after 30min and next day it won't come on but it has sound and it's not charging I need help what should I do

I'd love some advice in repairing a water-damaged laptop.  My girlfriend spilled a glass of water on her Sony Vaio and now it doesn't turn on...at all...dead! What steps should I go through to work out where the problem is and which part(s) I'll need to replace?  I can't seem to find out what has happened by just looking at the circuit boards. I'm new to electronics but could buy relevant volt-meters etc. I'm just looking for a decent trouble-shooting guide.


I understand this my concern has been expressed previously ,` and  but the responses cannot still solve my problem.  I included an image in my Latex code, which was running normally until today. All attempts only show undefined control sequence.\includegraphics{IDP}. I have checked for errors, retyped the code without any luck. It seems there is something I am not doing right.  I would very much appreciate any assistance on how to correct my code.  Here is the code I am using  \documentclass[12pt,a4paper]{memoir} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[american]{babel} \usepackage[strict]{csquotes} \usepackage{apacite} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{makeidx} \usepackage{graphicx} \graphicspath{ {./images/} } \begin{document}  \begin{figure}[htp] \includegraphics{IDP} \caption*{Source:~\citeA{dunning1996investment}} \caption{Patterns of Investment Development} \label{figIDP} \end{figure}   \end{document}

After updating MiKTeX graphics package on 10/5/19 to version 1.3b (packaged on 10/4/2019 8:11:27 PM), I am unable to compile LaTex files that contain \includegraphics{}.  My system: Windows 10  with MiKTeX 2.9.7200  A minimum working example:  \documentclass{article} \usepackage{graphics}  \begin{document}  \begin{figure}    \includegraphics{MC_Antenna_Gain} \end{figure}  \end{document}   The error report   This is pdfTeX, Version 3.14159265-2.6-1.40.20 (MiKTeX 2.9.7200) entering extended mode (C:/Users/nicrog/Dropbox/T_P_2/Scholar/Grants/Written/EWU_20/Test.tex LaTeX2e <2018-12-01> ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/base\article.cls" Document Class: article 2019/08/27 v1.4j Standard LaTeX document class ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/base\size10.clo")) ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics\graphics.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics\trig.sty") ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics-cfg\graphics.cfg") ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics-def\pdftex.def")) No file Test.aux. ("C:\Program Files (x86)\MiKTeX 2.9\tex/context/base/mkii\supp-pdf.mkii" [Loading MPS to PDF converter (version 2006.09.02).] ) ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/oberdiek\epstopdf-base.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\infwarerr.sty") ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/oberdiek\grfext.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\kvdefinekeys.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\ltxcmds.sty"))) ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/oberdiek\kvoptions.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics\keyval.sty") ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\kvsetkeys.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\etexcmds.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\ifluatex.sty")))) ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\pdftexcmds.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\ifpdf.sty"))) ! Undefined control sequence. \Ginclude@graphics ...\Ginput@path \set@curr@file                                                    {#1}\edef \uq@curr@file {\... l.8    \includegraphics{MC_Antenna_Gain}  ?    I will report this potential bug to  as well.


Computing the limit: $$ \lim\limits_{n\to +\infty}\left(\dfrac{1}{\sqrt{n^2 + 1}} + \dfrac{1}{\sqrt{n^2 + 2}} + \cdots + \dfrac{1}{\sqrt{n^2 + n}}\right).$$  I've tried taking:  We have $\lim\limits_{n\to +\infty}\left(\dfrac{1}{\sqrt{n^2 + 1}}\right)  = \lim\limits_{n\to +\infty}\left(\dfrac{1}{\sqrt{n^2 + 2}}\right) = \ldots = \lim\limits_{n\to +\infty}\left(\dfrac{1}{\sqrt{n^2 + n}}\right) = 0.$   Then, we obtain $$ \lim\limits_{n\to +\infty}\left(\dfrac{1}{\sqrt{n^2 + 1}} + \dfrac{1}{\sqrt{n^2 + 2}} + \cdots + \dfrac{1}{\sqrt{n^2 + n}}\right)\\ = \lim\limits_{n\to +\infty}\left(\dfrac{1}{\sqrt{n^2 + 1}}\right)  + \lim\limits_{n\to +\infty}\left(\dfrac{1}{\sqrt{n^2 + 2}}\right) + \cdots + \lim\limits_{n\to +\infty}\left(\dfrac{1}{\sqrt{n^2 + n}}\right)  = 0.$$  Any other approach to this is welcome. Thanks!

I have to compute the limit of this sequence ${\textstyle\sum_{k=1}^n}\frac1{\sqrt{n^2+k}}$ as $n\rightarrow\infty$. First I was thinking about some Riemann sum and and forced the $n^{2}$ outside the square root but the function was not so pleasant.


Can we incorporate member functions inside a structure in C++? As we do in classes can we put functions inside structures.  If yes then what is the fun on keeping both Structures and Classes in C++?

This question was .  Now I'd like to learn the differences between a struct and a class in C++. Please discuss the technical differences as well as reasons for choosing one or the other in OO design.  I'll start with an obvious difference:   If you don't specify public: or private:, members of a struct are public by default; members of a class are private by default.   I'm sure there are other differences to be found in the obscure corners of the C++ specification.


I get normal beamer pdf file without any option, \documentclass[]{beamer}, but I add handout option to get different file \documentclass[handout]{beamer}. I modify the beamer source and compile twice to get these two normal and handout beamer files, but I want to automatize it.   How can I do it? How can I have one beamer source that has a different option from a command line?

I am writing a journal paper which is roughly 15 pages long. Out of this journal paper, I would also like to make a conference version which should be 5 pages long.   My question is: Is it possible to only work with one latex file and produce two pdf of different length?   For example, can I select a text and specify that it goes to the long version only?


I am writing my bachelor dissertation and several times Microsoft Word has corrected me from "to have" to "having". One of the sentences, for instance, goes like this:      The author recommends to have ‘(...)'. Bugeja further recommends having a student blog where prospective...   Can anyone enlighten me?

Some verbs are followed by ing, e.g. I enjoy swimming. We can't say I enjoy to swim. Likewise, some verbs are followed by to, e.g. I decided to make a plan.   Which particular verbs are followed by ing and to? Can you please provide a list for that?  Moreover, which verbs can be followed by both without having the meaning changed?


When I tried  $ inxi -Fxz   There was an entry about the graphics card as shown below  Card-2: Advanced Micro Devices [AMD/ATI] Whistler [Radeon HD 6630M/6650M/6750M/7670M/7690M] bus-ID: 01:00.0   There is no mention of 1GB graphics card in About this computer in the core, nor in tools like Stacer or Additional Drivers  Does this mean that graphics card is not working?

I have 14.04.5/16.04 or newer and an AMD GPU. I'm not getting the performance I want, and some programs say they need things like OpenCL.  I've heard about fglrx, but if I try to install it on my machine, it breaks and I have no GUI.  Is there anything I can do to get my AMD card working to its full potential?


I am planning on installing Ubuntu on an external hard drive.  My question is where does data get saved when I use this OS?  For instance, if I create a folder on the desktop of Ubuntu where is that information being saved?  Ideally, I want all data related to my Ubuntu OS stored on the external drive… Is this possible?

OS: Windows 7. I want install Linux Ubuntu on portable external Hard Drive USB 2.0. I read a variety of methods, but I'm confused by contradictory advices and methods. Actually, installing Ubuntu on anything other than clean PC looks much more complicated than installing Windows. I need to have Ubuntu package + Python 2.7 + C compiler installed. My external hard drive is partially filled, I need to keep all files.   Will Ubuntu run entirely on external hardrive, without writing anythinhg to Windows system folders and to registry?  Can anyone post detailed guide how install Ubuntu on external hard drive?


If a have a sentence: "A depends on B", then I can describe A as a "dependent" (adj.). How can I describe B with one adjective?

I can't think of the word to fill this blank:     More importantly, now we've got ourselves an "organic" roadmap—that is, one that follows the natural order of our concerns, rather than a logical order such as ____.   Though unrelated to my context, an example of such an ordering would be:   a bride and groom a wedding a wedding cake   A wedding cake wouldn't exist without a wedding, which in turn wouldn't exist without its bride and groom. (I'm sorry, the real example is technical and complex, and I can't think of a better example at 3 in the morning.)  I want to say predecession but that's not a real word. Does anyone know the word I'm looking for?


While checking SO data dump I have noticed that SO stores tags as an array inside Post table. And at the same time there is a mapping table with TagId and PostId. I assume this is used for tag counting and search by tag functionality. What I want to know is how does SO inserts data into mapping table.  Here is the scenario : let us assume that I have created a post/question with 5 tags. Obviously a record will be added into Posts table. What I want to know how records will be added to mapping table. Is there a trigger which will run 5 inserts into mapping table ? Is there a background process which will take care of this ?   UPDATE: This is not a duplicate of , if you will check the question and the answer to it will become obvious. There is nowhere decried how SO stores the post and tags into tables.

We have a home-grown learning management system (LMS - highly abused term, but I'll be damned if I can find a more succinct way of putting it) that includes a list of classroom classes (filed under various categories) and a list of online educational modules (filed under various categories) - and there have been some (justified) complaints about it being difficult to find things.  I've read a couple of articles on creating a tagging system, and have seen a number of implementations. I was curious as to how the S[O|F|U] implementation was set up as it seems to be much better than most of what I've found.  Please don't hear what I'm not saying: I don't want the code handed to me on a silver platter. I'm just curious as to the general DB/Infrastructure used for the tags here as I like the system much better than what I've found elsewhere.