Disagreement between the p-value and the confidence interval in a binomial test

This is a question regarding the binomial test in R.  What happens if I get a p-value < 0.05, which would generally cause me to reject the null hypothesis that the population value is equal to a certain proportion (in this case 0.75), but the hypothesised proportion to be tested (i.e. the null hypothesis) still lies within the 95% confidence interval?  Do I still reject the hypothesis of equal proportions?  Here is an example R code:  x <- 31  n <- 50 binom.test(x, n, p=0.75)  # p-value = 0.04812 # 95 percent confidence interval: # 0.4717492 0.7534989


Is a horizontal line considered periodic?

Given the following definition of a periodic function:  $$\exists P, P > 0, f(x + P) = f(x)$$  It is possible to argue that $f(x)=k$ ($k$ being a constant) is a periodic function, since you can define $P$ to be any given constant within the real numbers and the definition would be valid. ($f(x + P) = f(x)$ will always be true if $P\in \mathbb R$).  So my question is, can a horizontal line be considered periodic, even when its period is ambiguous?


I want to add two more loopback interfaces.  I used the following command:  ifconfig lo: 127.0.0.2 netmask 255.0.0.0 up   and type in ifconfig, i can see the loopback address was added.  But if i want to add one more interface... (for example 127.0.0.3) the previous interface (127.0.0.2) was overwritten.  Also when i look in /etc/network/interfaces i see no entry.  How can i add multiple loopback interfaces permanently?


How to select lenses for outdoor sports photography?

I would like to get into sports photography, and would probably want a better telephoto lens so I can get better close up shots.  What other factors should I keep in mind as I make my choice? Does IS (or VR) matter?  What is a good focal length?  I'll probably be shooting mostly little league baseball/softball, church softball leagues, and kids soccer.


Why is it impossible to override a getter-only property and add a setter?

Why is the following C# code not allowed:  public abstract class BaseClass {     public abstract int Bar { get;} }  public class ConcreteClass : BaseClass {     public override int Bar     {         get { return 0; }         set {}     } }      CS0546 'ConcreteClass.Bar.set': cannot override because 'BaseClass.Bar' does not have an overridable set accessor


Is it valid to conduct t-tests with just 20 students?

article I think I found a bug:  Seams to me that 20 is a very small number of samples in this article assuming 20 students are taken random and the order of students is not important. I  and it looks to me this question is super important but not treated with great care since it can be a reference to basically any sampling question.


I can't find an answer to the following "simple" question:  If I order elements of a list and put the whole thing into a new list, like   var newList = new List<IMyElement>(myElements.OrderBy(x => x.AnyProperty));   Can I be sure, the elements in newList are still ordered by AnyProperty at access time?  Thanks so far!


Winforms issue - Error creating window handle

We are seeing this error in a Winform application.  Can anyone help on why you would see this error, and more importantly how to fix it or avoid it from happening.   System.ComponentModel.Win32Exception: Error creating window handle.    at System.Windows.Forms.NativeWindow.CreateHandle(CreateParams cp)    at System.Windows.Forms.Control.CreateHandle()    at System.Windows.Forms.Control.CreateControl(Boolean fIgnoreVisible)    at System.Windows.Forms.Control.CreateControl()    at System.Windows.Forms.Control.OnVisibleChanged(EventArgs e)    at System.Windows.Forms.ButtonBase.OnVisibleChanged(EventArgs e)


I have someone asking for an integration of $\int \sin^n x$. I have little to no knowledge of integration, so can someone help?  To be clear, I need a solution understandable for a sophomore or thereabout who knows integration.


How to get HDRI Environmental Maps to light a scene?

I'm using HDRI's in Blender 2.8 (cycles) and I don't understand how these are supposed to work to create realistic environmental light. The BLUE in the "Sky" shots is casting so much BLUE that my entire world looks ridiculous.   Is there a way to use JUST the sunlight within the HDRI to create more realistic sunlight?  UPDATE: I think the trick is to ensure that the trees or mid-point of the HDRI is exposed as to cut down on the sheer amount of blue influencing the rendering. This version looks acceptable to me.


All I made up in my mind about light beeing a wave  traveling at vertain speed, made me thing of it like something we could store in tehory.  So I would assume if I had a box where the inside is made up completly with mirrors, when sending light in and closing the box, this light would keep traveling inside the box, beeing reflected by the mirrors untill we release it again.  But afaik this isn't the way it is. So how does it come? Why isn't light working this way?


what i want to do is make a function that will get a list as an input and a number and will delete the node of that list that equals to that particular number. So if i have a linked list lets say:  struct num // list 1 {         char *val;         struct num *next; };   and i have added 4 items to that list, i want to be able to delete the third item and get back the new list with now 3 items. Everything i have tried till now though wont work, i think because i am not linking the remaining items correctly after i delete one of them.  Since you insist here is what i have till now   struct num1 *temp;     temp = head;  struct num1* deletend(int del){     for ( int i = 0; i < listSize; i++)     {                if (i == del){                 free(temp);             }             temp = temp->next;     }     return temp; }


How do I show the labels of theorems, definitions, etc

I'm using the package showlabels which has the effect that when I label something with \label{thing1} the thing1 gets typeset in the margin of my document next to where I put the label. This works fine for equations in align and proof environments, and things like that.  The problem is that it does not work when I label a theorem, which I do like this:  \begin{theorem}\label{fact1} Important math statement. \end{theorem}   I can still refer to said theorem via \ref{fact1} but I cannot get the label to typeset in the margin next to the theorem.  EDIT: I originally failed to include a compilable example of the problem. @DavidCarlisle posted an example of the problem not occurring, but with showlabels replaced with showkeys, upon which I noticed that showkeys did not produce the problem.  Looking more closely at my preamble, the problem had to do with the hyperref package. The following does not result in the label on the theorem being displayed.  \documentclass{article}  \usepackage{showlabels} \usepackage{hyperref} \usepackage[english]{babel}  \newtheorem{theorem}{Theorem}[section]  \begin{document}  \begin{theorem}\label{a theorem}     Important math statement. \end{theorem}  \end{document}   On the other hand, if one moves the hyperref package so it is implemented before showlabels, as follows, it works.  \documentclass{article}  \usepackage{hyperref} \usepackage{showlabels} \usepackage[english]{babel}  \newtheorem{theorem}{Theorem}[section]  \begin{document}  \begin{theorem}\label{a theorem}     Important math statement. \end{theorem}  \end{document}


Learning development with Force platform. Any good books?

I'm a bit familiar with Java and SQL, any good books to get on coding in Apex for salesforce?


minimum value of $\frac{x}{2-x}+\frac{y}{2-y}+\frac{z}{2-z}$ is

If $x,y,z>0$ and $x+y+z=1.$ Then minimum value of $\displaystyle \frac{x}{2-x}+\frac{y}{2-y}+\frac{z}{2-z}$ is  What i try From Titu lema $$\frac{x^2}{2x-x^2}+\frac{y^2}{2y-y^2}+\frac{z^2}{2z-z^2}\geq \frac{(x+y+z)^2}{2(x+y+z)-(x^2+y^2+z^2)}=\frac{1}{2-(-1-2(\sum xy))}$$ How do i solve it help me please


Battery drained out while i was working in Ubuntu and now i am unable to access to it

I use hp laptop with preinstalled windows 10 when I brought it, I dual installed ubuntu 20.04 in it after a couple of months while i was working in ubuntu the battery drained out and became 0 and it shut down automatically,after i charged it i was back in windows 10 and i even tried to access bios setup to see if i can do something like in the way this person has done  but i cant find advanced options in the BIOS setup what to do?


What exactly is the difference in meaning between the questions     Do you want to join us?   and     Did you want to join us?   in the context of a group of people asking asking another person who happens to be in the same place (for example, friends having dinner in a restaurant and bumping into another friend).  I would use the first variant, because to me "did" implies that the person who is asked had made up his/her mind before the question was asked.


Uniform integrability of a backward submartingale

Let $\{\mathcal{F}_n\}_n$ be a decreasing sequence of sub-$\sigma$-fields of $\mathcal{F}$($\mathcal{F}_{n+1}\subset\mathcal{F}_n$) and let $\{X_n\}_n$ be a backward submartingale($E[|X_n|]<\infty$, $X_n$ is $\mathcal{F}_n$ measurable and $E[X_n|\mathcal{F}_{n+1}]\geq X_{n+1}$).  If we know $l=\lim_{n\rightarrow\infty}E[X_n]>-\infty$, how to prove that $\{X_n\}_n$ is uniformly integrable? Many thanks!  I have an idea, it is enough to show:    $\sup_nE[|X_n|]<\infty$;  $\forall\epsilon>0$, $\exists\delta>0$ s.t. $\forall A\in\mathcal{F}$ such that $\mathbb{P}(A)<\delta$, we have $\sup_nE[1_{A}|X_n|]<\epsilon$.    For $|X_n|=2X_n^+-X_n$, we have  $$E[|X_n|]=2E[X_n^+]-E[X_n]\leq 2E[X_0^+]-l\leq 2E[|X_0|]-l$$  which implies $\sup_nE[|X_n|]<\infty$.  Secondly, $\forall A\in\mathcal{F}$, we can suppose without loss of generality that $A\in\mathcal{F}_0$.  $$E[1_{A}|X_n|]=2E[[1_{A}X_n^+]-E[[1_{A}X_n]$$  Does someone have an idea for this term? Thanks a lot.....


Example of a finitely generated faithful torsion module over a commutative ring

Can a finitely generated module $M$ over a commutative ring have $\operatorname{Ann}(x) \neq 0$ for all $x \in M$ while $\operatorname{Ann}(M) = 0$?  It's not difficult to show that there is no such module if the ring is a integral domain. For general, I guess the answer is yes. But I failed to find a desired example.


I would like to calculate $ 2^{5^{77}}\bmod 113 $. I solved similar problems but with smaller exponent e.g. $ 2^{185}\bmod 113 $ with successive squaring method. Is there any way to use this method to solve it?


How Planck's quantum theory of energy solved the ultraviolet catastrophe?

Hello I am a high school student and I am stucked at a concept in chemistry  . I have studied  black body radiation and Planck's quantum theory which is written in very short description but I have to understand it clearly so that I can understand further concepts in detail.  I know Planck's theory of quantisation which was given to account for blackbody radiation that energy from radiation is produced in discrete quantities in the form of packets .But I can't figure out how it was able to solve the ultraviolet catastrophe problem.This is not given in detail in my textbook and I am stuck at that.I have read other books but it is too much difficult for me to understand at this level . So please help me by giving an easy explanation.


Interesting Questions for all MY Stack Exchange sites in one place

At the moment, I actively participate in Stack Overflow. I would like to be able to participate in others (Project Management for instance). I can do this but I have to watch two "Interesting" lists. Imagine wanting to participate actively in 10 sites. How would you manage?  I think it would be great if, alongside tags, I could also select sites to include questions for.


How do i prove that any subgroup of $A_5$ has order at most 12?

I know this question has been answered   But i have difficulty in understanding that proof.The book says we can assume that $A_5$ has no normal subgroup.How to find the proof using this property ?  EDIT- (I solved the previous question ( $A_5$ has no normal subgroup ) but i am not able to solve this problem ).  I have already mentioned that my question similar to   so please don't mark it as duplicate.  The book which i am talking about is  - Topics In Algerbra by Herstein. (2.10.15)  I am thankful if some can explain the same proof ( provided in link ).I have difficulty in understanding the homomorphic part of that answer.


How to render a equirectangular non distorted panorama in Blender cycles?

Hi I would like to render my scene as 360x20 degrees (or 360x30) panorama, but without the fisheye effect.  I'm looking for a way to render it so it'd look like that:   I've been trying with panorama - equirectangular, but It seems like I can't get the parameters right.  How would I go about doing this?.


I understand what signed and unsigned int means.But a  signed char doesn't make any sense to me. Also why both signed and unsigned int occupies the same amount of space. Signed int should occupy more space since it can contain both negative and positive numbers. Thanks in advance.


Deduction from past form of " have (got) to "

I'd like to ask if there is any form of " have (got) to "  in order to make a deduction  from the past   equivalent to " must have + past participle" ?  For example:     They hadn’t eaten all day. They must have been hungry.   Is there any structures as follows:     They hadn’t eaten all day. They have to have been hungry.   or     They hadn’t eaten all day. They had to have been hungry.


I have an Ethernet cable with no printed markings - how can I determine what Category it is?

Whilst upgrading a switch and re-cabling to suit I discovered on of my ethernet cables has no printed markings on it.  Is there a non-invasive way for me to tell if it's Cat5, 5e or 6?


I'm trying to clear parents of some mirrored and seperated objects and even if I clear parent while keeping transform, the scale and rotation of the objects still change and warp the objects which destroys all the work. I don't quite understand how to get this to work.


Lines on map when I change projection on QGIS

I changed the projection of my base to WGS 84 PDC but I get these lines on top. This also happens to a few other projections. I am trying to make the Pacific the center of the map.


"Speaking Downtown" without the preposition at

Reading  there is a line say,  “So if you want to hear about $15 an hour and health care, Senator Sanders will be speaking downtown,” Clark added. “But if you would like to make at least $15 an hour and have good health care, Amazon is hiring.”  So I assume this CEO of the world wide division of Amazon is saying Sanders will speak about the lowest wage and the health care, at downtown, which is defined by Merriam  1: of, relating to, or located in the lower part or business center of a city or town  Why isn't there the preposition "at"? Googling by "speak downtown meaning" didn't produce anything so I think this is not an idiom. Thank you for your time in advance(m_m).


I'm wondering if there is any possibility to make a clickable logo like in html  code, it would be like this   \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{hyperref}  \begin{document} \href{link_adress}{\includegraphics[scale=0.5]{logo}}    \end{document}    Is it possible to do something like that but which works?


Is it possible to vary material colour depending upon thickness of the underlying mesh?

Is there are way to create a material that will colour according to the thickness of the mesh it covers, based, perhaps, on length of edges at right angles to the mesh surface?  For example, white for a zero thickness plane, through a spectrum, to black at an arbitrary thickness beneath, that will change automatically if the mesh is manipulated.


How to apply the ! (not) operator in simple terminal commands

It seems to be a really simple thing to do. I have done it in my Bash scripts, but I wonder how to do the same in the terminal.  For example, suppose I want to ls all files that are not js. Probably I would do:  ls ! *.js   But I get errors for my ! operator.  How can I execute mv, rm, and any other operations with the not (!) operator?  Note that my shell is Bash.


Deducing Galois group of $t^6 + 3$ over the rationals

I am asked to deduce, in the following order, 3 facts about $G = Gal(f(t) = t^6+3)$ over the rationals:   $G$ is order 6 The elements have orders $1,2,3$  $G \cong S_3$   I have figured these out but in the wrong order so I wanted to write down a different train of thought that I am less sure of to see if there is anything wrong with it.   By Eisenstein $f(t)$ is irreducible, and is thus the minimal polynomial of a root $\beta$ of $f$ over $\mathbb Q$, so if $L$ is the splitting field of $f$ over $\mathbb Q$ then as the degree of $f$ is $6$, then the degree of the extension $\mathbb Q\leq L$ is also $6$. Letting $\xi$ be a primitive $6$-th root of unity, then we see that over $\mathbb Q(\xi) = \mathbb Q(i\sqrt 3), \; f$ factorises as $f(t) = (t^3 + i\sqrt 3)(t^3 - i\sqrt 3)$ . This means that all permutations $\sigma \in Gal(L/\mathbb Q(\xi))$ permute the roots of each cubic factor amongst themselves. i.e. $\sigma$ is a $3$-cycle, and there are three of them. Also we note that complex conjugation preserves $\mathbb Q$ in $L$, so $G$ contains an order $2$ permutation. The identity is order $1$. I am not quite sure how to conclude that there is no element of order $6$, but with that we have that the elements are of orders $1,2,3$ Finally, we notice that composing complex conjugation with one of the $3$-cycles gives us the inverse of the original $3$-cycle. This gives a dihedral relation and hence $G$ is the dihedral group of order $6$, i.e. $G \cong S_3$   I would like to clarify why it is exactly that we can conclude that there is no element of order $6$ in $G$. I can feel that it is a very simple thing that I have overlooked, but I can't figure out what it is and would appreciate a little help or a hint. Additionally I would really appreciate it if anyone could let me know if there's anything flawed with my logic here at all. Thank you.


Derivation of the moment generating function of the geometric distribution - why is this wrong?

Let $P(k,X)=p(1-p)^{k-1}$.  When deriving the moment generating function I start off as follows:  $E[e^{kt}X]=\sum\limits_{k=1}^{\infty}e^{kt}p(1-p)^{k-1}$.  How I end up rearranging this is as follows:  $\frac{p}{1-p}\sum\limits_{k=1}^{\infty}e^{kt}(1-p)^k=\frac{p}{1-p}\sum\limits_{k=1}^{\infty}(e^{t}(1-p))^k=\frac{p}{1-p}\frac{1}{1-e^t(1-p)}$  I'm obviously not arriving at the correct answer, but I want to know why this derivation is wrong.


how can i add special charcter like breckets[ ], single quote ' double quote" in mysql database

I can insert the special characters fine when using PHPmyAdmin, but it just doesn't work when inserting them via PHP. Could it be that PHP is changing the special characters into something else? If so, is there a way to make them insert properly?  $name = mysqli_real_escape_string($name); this is not work...


Getting text of HTML elements to an array

I have the following html code.  <!DOCTYPE html>

My First Heading

My first paragraph.

Paragraph First

alice

bob

foo

grow

coding

fun

Paragraph Second

           I want to get the text of all the elements to an array(pre order transverse preffered). So for the following example array consists of,  [My First Heading, first paragraph, Paragraph First, alice, bob, foo, grow, coding, fun]   I can use jQuery if it needsHow. can I achieve this ?  My own non-working attempt  var root = document.documentElement;  recursivePreorder(root); // Recusively find and handle all text nodes  function recursivePreorder(node) {      // If node is a text node      if (node.type == 3) {     //add to the array      }   // else recurse for each child node      else {          for(var i=0; i<node.childNodes.length; i++)              recursivePreorder(node.childNodes[i]);      } }    UPDATE  when my tag is
boblink textalice
 it gives me as [bob, link text, alice] . But I want the output as [boblink textalice] means links are working correctly. This is my current solution,  var arr=$('body').find('*').contents().filter(function () { return this.nodeType === 3&&this.textContent.trim()!=""; });    how to solve this problem ?


I can't restart my iPad mini by holding the power button and even in the powwr button in AssistiveTouch.Furthermore,I can't use any app that needed wifi.Lastly, my battery life is staying at 96% even after a couple hour.Please tell me how to fix it .tq


Is there a difference in meaning and/or connotation between "can not" and "cannot"?  I have read and seen both used interchangeably, but I know people who argue for a slight difference in meaning. That is, cannot indicates that there is an incapability whereas can not indicates the possibility of absence. Is this a real difference?


Why is Stack Exchange allowing Google ads though they have their own profitable revenue model via https://stackoverflow.com/jobs?

Why is Stack Exchange allowing Google ads though they have their own profitable revenue model via ?  I mean, I just recently saw Google ads here. Don't you think it adds extra noise to the site? I mean I don't want to see ads; please don't show it.


Why doesn't Stack Overflow use Highlight.js instead of Google-Code-Prettify?

You heard me. From what I see , and unless I am looking at a completely wrong place, Google Code Prettify hasn't been updated in almost an year now. Has it been abandoned? I have  about Highlight.js, and it looks promising, up-to-date, and moreover its functionality is similar to that of Google Code Prettify (automatic syntax highlighting for 41 languages). Is there a reason why Stack Overflow is sticking with Google Code Prettify? PS: I am only asking, not suggesting, like some have (mis-)understood.


How to correctly store a newline character in a (POSIX) shell variable?

update attempt to clarify more, using an example, does the following shell commands:  SHELLVARIABLE="1st line, 2nd line, 3rd line, "  printf '%s' "$SHELLVARIABLE"   generate this output:   1st line,<newline>2nd line,<newline>3rd line,<newline>   <newline> being the character 0x0a / \n?  Original question formulation  What is the correct (POSIX-confirm) way to store a newline character 0x0a (aka known by its commen c style escap \n) into a shell variable.  I want to make sure that doing the following:  SHELLVARIABLE=" "   is, not merely working by chance but instead is indeed the correct way.  Since POSIX's  is perfectly capable of producing a newline character (i.e. printf '\n', or printf '%b' '\0012') I first attempted a more explicit (? or correct?) form:  SHELLVARIABLE="$(printf '\n')"   though a tempting approach, does not work. As the according to , command substitution (i.e. via $() and ` `) shall remove     sequences of one or more newlines at the end of the substitution.   Note: Asking to store a single trailing newline into a shell variable is only to abstract the more general use case (i indeed seek answer to) that is how to store a string into POSIX shell variable which ends with the newline character.


Apps are running into another apps like a new instance

What I notice is that one App (let say Slack), has a link in a message, when I click on it, it opens Firefox, but in way that this Firefox is linked to Slack. It doesn't even show the dot under Firefox icon, but add one dot at Slack. The problem I notice is that Alt+Tab loses performance since Slack and Firefox are under Slack, and in the first time firefox opened as a pretty fresh one, without my account and user settings (I had to do all of this twice) so it's as if I have two firefox, one 'free' and one 'bound to'... it happens for all kinds of situations that one app opens another one.... VSCode to firefox / Slack to Zoom / Zoom to firefox... Is there any way to make apps open in their own place?


Is this a safe way to operate an H-bridge with SPDT relays?

I am trying to create a circuit to drive a hand drill motor as seen in this drawing with just relays. The current formation to make it go forward, switching 2 and 3 at the same time to make it go backwards, and switching 1 to make it stop. I expect it to be ~18V at ~20A when running. Do I need flyback diodes for this to work correctly and if so how would I go making that calculation and selecting that part? When switching 2 and 3 at the same time is there anything I should be concerned about?


I'm new to java and I'm trying to do a log in with a list, but the validation method does not work.  I've tried accessing the value of the list with the counter and the tried assigning it to a variable, in the debug mode the value i'm getting is correct but the condition still does not work (user: test, password test)  This is my user class with the methods to set and get the password.  public class user {     String user;     String pass;       public user(String u, String p) {         user = u;         pass = p;      }      public String getUsername() {         return user;     }      public String getPassword() {          return pass;      }      public void setUsername(String username) {         this.user = username;     }      public void setPassword(String password) {         this.user = password;     } }   This is the log in class  import java.util.ArrayList; import java.util.Scanner;  public class LogIn {     public void Welcome() {          System.out.println("Welcome, please enter your username");         Scanner input = new Scanner(System.in);          String username = input.next();         System.out.println("Enter your password");          String password = input.next();          this.validate(username);      }      private void validate(String username){         int attemps = 0;         ArrayList<user> users = new ArrayList<user>();         user User = new user("test", "test"); //Here I add the new user with the fixed value of test for password and user         users.add(User);         for(int i=0; i<=users.size()-1;i++){             while (attemps<=3){                  System.out.println(users.get(i).getUsername());                  String test = users.get(i).getUsername();  //This condition here is the one not working and with the user already added to the list and getting the correct value in the variable it still does not work                 if(username == test){                     System.out.println("Here");                     attemps = 3;                  }else{                     System.out.println("invalid credentials");                     attemps++;                 }}                 System.out.println("You have exceed the number of attempts");              }         }     }   Using the credentials test for the user and test on the password it doesn't work


I always have been passionate about the beautiful country Bhutan, but after searching for some infomation, I found out that Bhutan restricts the travellers there. So how can I gain a visa to this country? What is the requirement to get a Bhutan visa and where do have it? Thank you.


Lat $x < y < z$. Suppose $f : (x, z) \rightarrow \mathbb{R}$ is continuous and differentiable at every point of $(x, z)$ \ ${y}$, and that $f'$ has a limit at $y$. Prove that $f$ is differentiable at $y$ and that $f'(y) = \lim_{x \to y} f'(x)$.  How will we go about showing differentiability and the limit in this case? Firstly, I'm unsure what is meant by the fact that "$f'$ has a limit at $y$" and how is that relevant? Moreover, am I allow to use the mean-value theorem or does that require differentiability at y?


Software to backup data and files on a Windows computer

I have data and files on my system, running Windows, and want to make sure that I don't lose all the data or information when it gets toasted, either by a power surge or corrupted medium.  I've heard that I should look into some kind of archive tool.  What should I be looking into here in a backup program?


As you can see on the picture, there are some aliased edges (I mean the little circles and the black circles edges)even though this was made in Illustrator. How can I fix this.   Please help. Thank you so much.


How to say something like "A is x times as much likely ..."?

How to accurately, unambiguously and concisely say something in the following cases:  Case 1. The predictor is significant, with 1.5615 times as much likely to get higher scores when it is true. Case 2. Subjects with A are 1.5615 times as much likely to get higher scores as those without A.  Maybe can I use "chance" instead of "likely" to form the sentence better?


How do I make more block for Bootstrap theme?

My bootstrap theme block region look doesn't have much block section.  How do I make this like the second image? How do I make more block.


I am not sure about what is right:     I can start my career at an international company.   or     I can start my career in an international company.   For me at sounds appropriate?


When I open Ubuntu Software, and check the installed software, I found that there are 2 different versions of GNOME runtime (3.26 and 3.28).   How to check which one of them is running? Is it OK to uninstall one of them (the one that is not used)?  INFO:  I am using Ubuntu 18.04 gnome-shell --version gives: GNOME Shell 3.28.4


Having the input and layout side by side

I have just installed latex on my mac. I opened the texwork and I can type in latex script there, whenever I compile it, I will get an output.   But is it possible to have the output instantly standing side by side, so that when I type, I can see the change immediately?   Do I have to get any other plugin?


Different behavior with map, select, etc. when using do...end blocks

I noticed following difference in behavior when I use map, select, and other  methods.  Let's assume we have a hash like below:  h = {a: 1}   Below code prints the output of select as expected.  p h.select { |k, v| true } #=> {:a=>1}   However, below code shows that output is an Enumerator, even when a block has been provided.  p h.select do |k, v|    true  end #=> #<Enumerator: {:a=>1}:select>   Any idea why this difference of behavior?  I run into this issue often as I keep using inspect p while working, and this behavior derails my thought process quite often.


/desktop/gnome/peripherals/keyboard/general/disable_indicator in gconf is set to yes Additionally I restarted, but it's still there. Maybe there is some setting buried in CCSM?  here is screenshot of what I'm talking about if it's not clear:  I want to remove it if possible


How can we show that the dyadic rationals are dense in $\mathbb R$?

Numbers of the form $ \dfrac{m}{2^{n}} $, where $ m $ is an integer and $ n $ is a non-negative integer, are called dyadic rational numbers.  How can one show that the dyadic rationals are dense in $ \mathbb{R} $?


$\sin\alpha + \sin\beta + \sin\gamma = 4\cos{\frac{\alpha}{2}}\cos{\frac{\beta}{2}}\cos{\frac{\gamma}{2}}$ when $\alpha + \beta + \gamma = \pi$

Assume: $\alpha + \beta + \gamma = \pi$ (Say, angles of a triangle)  Prove: $\sin\alpha + \sin\beta + \sin\gamma = 4\cos{\frac{\alpha}{2}}\cos{\frac{\beta}{2}}\cos{\frac{\gamma}{2}}$    , however I want to avoid using the sum-to-product identity because technically the book I go by hasn't covered it yet.  So, is there a way to prove it with identities only as advanced as $\sin\frac{\alpha}{2}$?    Edit: Just giving a hint will probably be adequate (i.e. what identity I should manipulate).


How to create a clickable link in a command

I'm trying to get a command block to open up Netflix when i activate it. If the link is "", then what should the command be? P.S. I want the text to be red and not underlined.


For what values does $x^{x^{x^{x^{.^{.^{.}}}}}}$ make sense

For which values of $x\ge 1$ does the expression $x^{x^{x^{x^{.^{.^{.}}}}}}$ make sense? To tackle this, define  $f_1(x)=x$ and $f_{n+1}(x)=x^{f_n(x)}$ for $x \ge 1$ and $n\ge1$.    a) Show that $f_{n+1}(x) \ge f_n(x)$ for all $n\ge1$.    b) When $L(x) = \lim_{n\to\infty} f_n(x)$ exists, find an equation for $L(x)$. Use it to find an upper bound for $x$.  c) For these values of $x$, show by induction that $f_n(x)$ is bounded above by $e$ for all $n\ge1$. What can you conclude?  d) What happens for larger $x$?    I'm having trouble showing it is increasing for a).  I solved b) with the fact that $\lim_{n\to\infty}f_n(x)=L(x)=x^{L(x)}\implies x=L(x)^{\frac{1}{L(x)}}$  Maximizing on $L>0$: $$\frac{d}{dL}L^{1/L}=\frac{d}{dL}e^\frac{\ln(L)}{L}=\frac{d}{dL}\left(\frac{\ln(L)}{L}\right)e^\frac{\ln(L)}{L}$$ $$=\frac{1-\ln(L)}{L^2}L^{\frac{1}{L}}=L^{\frac{1}{L}-2}(1-\ln(L))$$ $$=-L^{\frac{1}{L}-2}(\ln(L)-1)=0\iff\ln(L)-1=0 \text{ so } L=e$$  Therefore $\max\{L^{1/L}\}$ happens when $L=e$ so $x\le e^{1/e}$ and I now have bounds for $x$  It then follows for c):  Since $f_n$ is increasing on $[1,e^{1/e}], \max\{f_n(x)\}=f_n(e^{1/e})$  Base case: $f_1(x)=x\le e^{1/e}<e$.  Assume $f_n(x)<e$, consider $x^{f_n(x)}\le x^e$ $\implies f_{n+1}(x)\le f_{n+1}(e^{1/e})<x^e<(e^{1/e})^e=e$ therefore by principle of mathematical induction, $f_n(x)<e$ for $x\in[1,e^{1/e}]$


Interpreting the significance in multiple regression

Why in regression analysis does the inclusion of a new variable make  statistically insignificant coefficients that previously were not? In model 3 length of contraception becomes insignificant when controlling for age. How to interpret this


Is there a way to store my password when ssh'ing on a server? I tried to change the variables BatchMode and PasswordAuthentication in my file /etc/ssh/ssh_config, but to no avail. Could someone indicate me how to proceed?


How to prove that if $x$ and $y$ are real numbers greater than $0$, then $\sqrt{x}+\sqrt{y}>\sqrt{x+y}$?

How to prove that if $x$ and $y$ are real numbers greater than $0$, then $\sqrt{x}+ \sqrt{y}>\sqrt{x+y}$?  Here is my attempt: To show that $A>B$, we need to show that $A-B>0$. This implies that we need to show that $$\sqrt{x}+\sqrt{y}-\sqrt{x+y}>0.$$ I'm now stuck in this portion.


But latex is very difficult to use without shortcuts. I also tried to use the solutions mentioned in the last post by someone about the same problem, but still it doesn't.


UK student visa refusal for not being a genuine student

I am an Indian citizen and applied for my MSc in UK for the first time. However my visa got rejected on the basis of not being a genuine student, though all my documents are genuine. The rejection was based on the visa interview. I am planning to apply again for the same country and the same university for the January intake.    Will my rejection will haunt me and I what are the chances of getting the visa this time?


$\chi_A(\lambda)=\lambda^n -Tr(A)\lambda^{n-1}+...+(-1)^ndet(A) \implies \chi_{A^{-1}}? $

Let $A \in GL_n(\mathbb{F})$ and $\chi_A$ denote the characteristic polynomial of $A$. I want to calculate $\chi_{A^{-1}}$. I know that the characteristic polynomial of $A$ is of the form $$\chi_A(\lambda)=\lambda^n -Tr(A)\lambda^{n-1}+...+(-1)^ndet(A).$$ Using the form of $\chi_A$ how can i calculate $\chi_{A^{-1}}$?


Let $a$ and $b$ be nonzero integers. Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$.   Since this is a iff statement, I need to prove it both ways:  $\Rightarrow$ If $a=\pm b$, then  $a$ divides $b$ and $b$ divides $a$;  and  $\Leftarrow$ If $a$ divides $b$ and $b$ divides $a$, then $a=\pm b$.  I tried to prove it but I don't know how to manage the $\pm$ sign, can anyone give me a hit or suggestion to start this proof?  Thanks


Most efficient way to integrate $\int_0^\pi \sqrt{4\sin^2 x - 4\sin x + 1}\,dx$?

$$\int_0^\pi \sqrt{4\sin^2 x - 4\sin x + 1}\,dx$$  Please help with this. I cannot do this problem in a definite way.


Search for files inside multiple subdirectories and zip directories

I need to extract more than 2k files from 1000 folders..the problem is, each folder has a zipped folder inside and inside this folder, there is another folder called "fileholder" which contains some temp.processed filetype that I need to get. Is there any way to search for all these files and copy them to another location? or do I have to extract all of the zip files?   I have ran:   find -type f -iname \*.PROCESSED   but that does not search inside the zipped files. Can someone point me to the right direction?


Why does the exit command not exit from nested while loop?

I have the following script. It prints all of first characters to console from passwd, but my expectation was to get only one character and for the program to then terminate.  #!/bin/sh   cat /etc/passwd | while read -r line do     echo ${line} |         grep -o . |         while read char         do             echo ${char}                exit 1                done done   Actual output:  r b d a (etc)   Expected output:  r


In "" the bug that left review flags visible in the top-bar counter was supposedly fixed, but it's never actually been fixed for me. This is what I'm looking at today:    My review queues are all empty though. Six is abnormally high, normally it sits (every day, all day) at 3. This is on , where we get lots of flags but we have enough reviewers that the queues are usually dealt with super-quickly. The only time the flag count drops to zero-and-invisible is when I get to the queues first and clear them out myself. I don't know why it should make a difference whether it's me or someone else clearing them, but if I don't, it's that [ 3 ] shouting at me all day.  The review flag count has been useless for long enough that I just don't click it much. This is really counterproductive, especially for one of the top users of the site.  Why is the review count unrelated to the content of the review queues?  Update: This appears to be a symptom of using the skip button in a review queue. It seems like the number/flag doesn't clear when a review item is skipped, even though that dismisses the item and removes it from my queue.  If that's the case, skipping should either not remove it from the queue interface and the count/flag left working how it does now, or skipping should clear that item's count/flag and the queue left working how it does now.


I bought myself a new laptop with 1 TB hard-disk.While installing Ubuntu i made that Windows 10 stays in a 200 GB partition.I thought i could create a partition  for Ubuntu while installing but i couldn't.So now i have 200 GB for Windows and 800GB for Ubuntu. I would like to leave 100 GB for Ubuntu and have 700 GB common storage to access from both storage.So any idea how i can do it? I kinda new to Ubuntu and I would like to have your help? Thanks!**


Using the Terminal in Ubuntu to change directory

I have a question about using the terminal in ubuntu 11.04.I have installed wine and steam and civ III thru steam.According to instructions on wine forum in order to play civ some font files need to be moved within the wine folder which i have done but it also informs to do the following:   then open a console and browse to: .wine/dosdevices/c:/Program Files/Steam/steamapps/common/sid meier's civilization iii complete/Conquests/  and type the following command: sudo chown root LSANS.*   when I open the terminal I am able to change directory to .wine/dosdevices/c but when I try to change to the next "program files" I get message in terminal not found. I type in ls command and does list "program files"  why am I NOT able to change to directory "program files"  below is actual steps in terminal i have done  mike@ubuntu:~$ cd .wine mike@ubuntu:~/.wine$ cd dosdevices mike@ubuntu:~/.wine/dosdevices$ cd c: mike@ubuntu:~/.wine/dosdevices/c:$ ls Program Files  users  windows mike@ubuntu:~/.wine/dosdevices/c:$ cd program files bash: cd: program: No such file or directory mike@ubuntu:~/.wine/dosdevices/c:$   I also tried capitalize


Solving the Quasilinear PDE $u_{t} - u^2 u_{x} = 0$ with piecewise initial condition.

Solving the quaslinear PDE by the method of characteristics is a bit tricky for me.  I was trying to obtain the solution $u$ for the PDE   $$u_{t} - u^2 u_{x} = 0$$  The initial condition is given by:  $$u(x,0) = g(x) = \begin{cases} -0.5, & x \leq 0 \\ 1, & 0<x<1 \\ 0.5, & x \geq 1 \end{cases}$$  Using the method of characteristics I have tried to write the characteristic equation as  $$\frac{dt}{1} = \frac{dx}{-u^2}$$  Trying to obtain an expression for $u$ from the above equation seems tricky as there is no $u$ term.


$R$ semisimple artinian ring $\Rightarrow\varphi(R)$ is such

Let $R$ be a semisimple artinian ring, i.e. a right artinian ring with no nonzero nilpotents right ideals.  We know that:   $R\simeq M_{n_1}(D_1)\times\dots\times M_{n_t}(D_t)$ for suitable$t,n_1,\dots,n_t\in\Bbb Z_{\ge1}$, $D_j$'s division rings (Wedderburn Artin theorem). The right ideals of $R$ are exactly of the form $I_1\times\dots\times I_t$ where $I_j$ is a right ideal of $M_{n_j}(D_j)$.   I want to prove that homomorphic images of $R$ remains semisimple artinian rings.  So, let's consider a ring $S$ and a ring homomorphism $\varphi:R\to S$. We must check that $\varphi(R)$ is a semisimple artinian ring.  I have proved that $\varphi(R)$ is right artinian ring, showing that an arbitrary decreasing sequence of right ideals, becomes necessarely stationary.  My problem is to show that $\varphi(R)$ has no nonzero nilpotents right ideals! Here is my try: let's by contradiction consider $0\neq J\leq_{\mbox{r}}\varphi(R)$ be a nonzero nilpotent right ideal. Then $J=\varphi(I)$ for some $0\neq I\leq_{\mbox{r}}R$ (it's easy but not immediate).  Then $J^N=0,\;\exists N\ge1.$ Thus $0=J^N=\varphi(I^N)$, from which $I^N\le\ker\varphi$.  So I considered the descending chain $$ \ker\varphi\ge I^N\ge I^{N+1}\ge\cdots $$ in $R$ which is right artinian by hypotesis: thus there must exists $\overline N\ge1$ s.t. $I^{N+j}=I^{N+\overline N}\;\;\;\;\forall j\ge\overline N$. But $J\neq0\Rightarrow I\neq0$ so being $R$ semisimple artinian ring $I^{N+\overline N}\neq0$.  Here I stuck, I can't reach any contradiction.  Can someone help me? Many thanks!


Equation that outputs digit in 1's 10's 100's slot

I need an equation that outputs the digit in the slot of my choosing  EX1: I want the 10's slot in 1837  EX2: I want the 10's slot in 123456789  EX3: I want the 1000's slot in 93037352  I also need it to be super simple, preferably only using +,-,/,x


What would happen if a charge could travel at $c$?

We know that an electron can move at sublight speed, but can we figure out what would happen if a charge moved at $c$, surfing the wave of the electric field it has produced? There does not seem to be anything that prohibits charged particles from moving at light speed. (If it sounds better, consider a Weyl fermion)  It would be pushed forward, repelled by its own field, but there are 2 possible scenarios depending on whether the speed of propagation of the wave can be exceeded or not.


What is the ammount of current when using no resistors

Ohm's law states that V=IR, thus if we have a 9V battery and one would use no resistance (R=0) then I= 9/0 which can't be done. Then what happens to the current? Does this mean there is an infinite amount of current? Or does a battery have a max amount of current it can provide (if so, what is this max amount of current)? Or do wires have a little resistance for example: R = 1 * 10^-6. This leads to an insane amount of current.


Why does the ring finger not move independently?

Why is it that we need to move little finger in order to move ring finger with it? For example, put your palm on a table and fold your middle finger inside. You won't be able to move your ring finger unless you move your little finger along with it. Why?  and  and various other guitarists are the only people that I'm aware of that use the ring finger and looks independent. Is it possible to have surgery to make the fingers independent or is it not functional to do that?


Best choice for Microsoft Paint for Mac?

Are there any Mac apps that are very similar to Microsoft Paint besides Paintbrush and Paint.net? I've tried those apps but found a lot of quirkiness and am looking for something more polished and user friendly.


What is a shortcut to doing this kind of problem?  I know that 7 and 107 are both prime number; thus, I assume that has something to do with the appropriate approach/solution.  But beyond that I am not sure. Any ideas?


Today I downvoted an answer so it went from 0 to -1  But I realised it was by mistake so I upvoted the same answer again but this time the value went up to +1.  I was expecting this to be zero.  I have attached the image.    EDIT  When I refreshed the page it came back to 0 again.


Story about plagiarism by means of time machine

I can't remember the name of the story, and couldn't find anything on Google searches either.  The story is about a science fiction writer whose story gets rejected by the publisher because it's word-by-word identical to another story published years ago. The writer then writes another story only to find out that the same author also published this story around the same time as the other one.  Our writer then writes a story about a man who uses a time machine to read other people's work in the future and then publishes it in his time. Only to find out that this story was also published by the same guy years ago.  The story I'm trying to find out was in the form of letter correspondence between the writer and the publisher.  So, does anyone know its title?


Statistical test to assess the strength of the assertion "time series' values stayed the same"

The title somewhat gave my question away, but here goes...  I have a time series of values covering a certain time span...  If I chart it, I can visually conclude values roughly stayed the same. That is, if I draw a regression line, the slope is very near 0. But, if that slope is slightly above or below 0, I could just as well conclude the data shows a small uptrend or downtrend.  So, my question is: Is there any statistical test I could use to feel confident that the values of the time series were not significantly increasing or decreasing over the observed period of time?  One idea I had was the following: If some values in the last quarter of the time series fall above the 3rd quartile of all values AND some values in the last quarter of the time series fall below the 1st quartile of all values, then it is unlikely the time series exhibit a significant uptrend or downtrend.  I think a concrete example would make this easier to understand:  Imagine a machine that burns a fuel to generate power. As time passes, if the components of the machine do not have adequate heat dissipation, producing the same amount of power requires increased amounts of fuel.  Testing the machine and its ability to dissipate heat involves letting it run for a rather long period of time at a constant power output, while monitoring the amount of fuel it consumes over that period of time.  So, you end up with a time series of fuel consumption and the goal is to have a test to decide whether a steady state was achieved.


Is there ways to download youtube video?

is my 3nd favorite web after  and , everyday i always watch new video from Youtube, but I do not like about YouTube is video buffering,  so annoying to wait it. Now my question is there ways/program to install YouTube Videos quickly and user friendly ?  UPDATE  I know there's many ways to download YouTube videos using terminal, add-ons and other but any is there anyone here who can explain it in detail and use simple words ?


Finding an angle in a $80^\circ$-$80^\circ$-$20^\circ$ triangle (variant involving $70^\circ$ and $60^\circ$)

Let CAB be a 20-80-80 triangle, what is the value of DEA? (EAB = 70, DBA = 60)  I tried creating a parallel of BC passing through D but I didn't get anything. I also tried creating an equilateral triangle with AD as its side but it also did not work.


Strange colors in Ubuntu (green tint, 14.04 LTS)

I have a Dell Inspiron 17R 5737 with an Intel Haswell Core i5 4200U, and an AMD Radeon HD8870 graphics card (switchable).  When installing Ubuntu (after checking disk for errors) and choosing "Try without installing", there's a green tint on the whole screen (where it's supposed to be pink/purple). I thought it might just be an issue that wouldn't show up after installing it onto the hard drive, and so I went on with the installation without any problems. My computer rebooted and I booted Ubuntu for some tweaking.   But the green tint was still there. I tried plugging in my LG HDTV via HDMI and on that screen there was no tint, but it was still there on my laptop.  What I'm wondering is why this happens and if there's any way to fix it, because I would really like to be able to use Ubuntu.


Does Devil's Sight enable one to see into Hunger of Hadar?

The  spell (PHB, p. 251) creates a black void of darkness, which cannot be penetrated by light. This means that no one can see in, and those inside cannot see at all, which is a handy way to damage and control enemies since they don't know which way is out. This also means that characters cannot easily attack those inside. The Devil's Sight , however, enables a warlock to see normally in magical and non-magical darkness. Does this enable the warlock to see into the area of blackness created by hunger of Hadar and attack creatures inside? Are there any other sight mechanics that allow someone to see in or out of the spell?


Shall I use have forgotten or forget in this sentence?

First, thank you userr2684291 for reminding me of the web site's name.  Here is the situation: I couldn't remember the name of LXXX-8 web site, so I went to the chatroom to get some help. (I don't know whether advertisement is allowed here or not, so I put XXX in the web site's name)     Could you remind me the web site's name please?   It is a web site that you can write some sentences, and some other users will come to help   you check your grammar.   ColleenV once told me the web site's name, but   I have forgotten   I felt like using simple present tense in the last sentence, but my hands was typing the sentence in present perfect tense.   I think simple present tense is also correct, but I don't know how to explain it to myself that which one is the better.      ColleenV once told me the web site's name, but I forget it now   I am sorry, moderators. I have read the suggested answer in the given link, but I do not understand how it can help me solve my question. I would like to know which of the tenses is the better in the given situation.  I need help. And which one sounds more natural to your native ears?     "I have forgotten" or "I forget it now"


Underfull \hbox (badness 10000) in paragraph in a EUSFLAT2019_template.tex

I have downloaded on my local machine eusflat 2019 template for paper  and using it in miktex following section in EUSFLAT2019_template.tex   \section{How Microsoft detects anomaly in azure} Microsoft uses a technology called security center \cite{microsf41} in its cloud environments.To detect threats and reduce false positives Security Center  collects data from Azure resources and network and then applies a lot of  machine learning and big data algorithms to detect threat.These techniques as more advance than normal signature based anomaly detection techniques.It is impossible to  manually identify the attack and predict the attack when it might happen.So the Microsoft \\ Security Centre uses following technologies     \newline   shows output in log as   Underfull \hbox (badness 10000) in paragraph   so I want to know why is this giving me message for badness in the template.


Find all elements with same class but exclude the clicked element?

I have this html:

   At the event of a click I need to fire some actions. Problem is that I need to exclude the clicked element. Let's say that I click at the first .child then actions just be applied ONLY to the second and third .child elements.    $('.child').on("click", function() {     $(".parent").find(".child").DO_SOMETHING();   });


I have a , and the SD card is automatically mounted when the UI is visible. The problem is when I log in to the TX2 without GUI (Graphic User Interface), via SSH it doesn't read SD cards.  I watched /dev/ path, and I can't see the SD card device. So I think for some reason the SD card is not read when I disable the GUI. I tried using lsblkand fdisk -l but the device is not shown.


Point in polygon does not appear in my QGIS 2.18.0 (Windows 10).   The tutorials indicate I should find it in Vector -> Analisis Tools -> Point in Polygons, but it is not there.   How should I install it?


Unable to save emoji/emoticon in MySQL from PHP using PDO, but can insert them from cmd/phpmyadmin

after some research I converted the field and table collation to utf8mb4_bin.  If I paste an emoji in the field directly through phpmyadmin, or if I write the query in the command line, it works fine.  The problem is doing it from the website.  Here is my PDO configuration:  $driver_options = [     PDO::MYSQL_ATTR_INIT_COMMAND    => "SET NAMES utf8",     PDO::ATTR_ERRMODE               => PDO::ERRMODE_EXCEPTION,     PDO::ATTR_DEFAULT_FETCH_MODE    => PDO::FETCH_OBJ,     PDO::MYSQL_ATTR_FOUND_ROWS      => true ];  $db = new PDO('mysql:host='.$host.';dbname='.$database.';charset=utf8mb4;collation=utf8mb4_unicode_ci', $username, $password, $driver_options);   Doing it from my website, the emoticons/emojis are saved as ????.  What else do I need to do to be able to save them correctly?  Thank you  EDIT  Solved it. If you use SET NAMES utf8 in the options, it will overwrite the charset=utf8mb4 in the DSN, so in my case it was ultimately utf8 and not utf8mb4


Is there any evidence in The Force Awakens towards or against Jar-Jar being Snoke?

There was a popular fan theory  that Jar Jar Binks was really Supreme Leader Snoke. Was there anything in Star Wars: The Force Awakens or any of its novelizations that would lead evidence towards either supporting or disproving this theory?  To be clear, I'm looking for evidence from the film itself, not Word-of-God answers. I don't care about specific comments from producers regarding the validity of the theory. Those can already be found . I'm just looking for what evidence can be found from the film itself.


prove that $[F(\alpha):F]=p$ where $\alpha$ is a root of $x^p-a$

This is the problem 1.1 from the book, A Gentle Course in Local Class Field Theory.  Let $p$ be a prime, let $F$ be a field of characteristic $\neq p$, and let $a \in F^{\times} \backslash F^{\times p}$. We make no assumption on the presence of roots of unity in $F$, and we wish to prove that $[F(\alpha):F]=p$, where $\alpha$ is a root of $X^p-a$. For this, we assume $[F(\alpha):F] \neq p$, and work toward a contradiction:   Consider the composite field $F(\mu_p, \alpha)$, and show that $F(\alpha) \subset F(\mu_p)$.   2. Deduce that $F(\alpha)/F$ is Galois, and then that $F(\alpha)=F(\mu_p)$   From the fact that $[F(\alpha):F]$ does not depend on the choice of root $\alpha$, conclude.   Note that $\mu_p$ stands for a pth primitive root of unity in the algebraic closure of $F$, aka $F^{alg}$. Also, $F^{\times p} = \{f^n|f  \in F\}$.  I've had a hard time proving that $F(\alpha) \subset F(\mu_p)$ and $F(\alpha)/F$ is Galois, and didn't get how the assumption for absurdness would fit in the proof. Could anyone please give some help on this?   I have been aware that the problem is kind of equivalent to the proposition that $x^p-a$ is irreducible iff $x$ has no root in $F$ (there is an answer regrading this). However, I am trying to understand the way from the book.


I have this weird issue with chrome. When I launch it in desktop mode, everything is blurry. However when I go to its settings and relaunch in windows 8 mode, everything is super clear and crisp.  I have a QHD+ screen and firefox is so far the only browser which works out of the box, but I want to use chrome. However I don't want to use it in windows 8 mode (metro crap). I've scoured the internet for answers but the registry hack doesn't seem to work anymore.   Why is it that I have to launch chrome in windows 8 mode to get hidpi support?  Note: the chrome://flags page says that high dpi is not available on my platform.. what?


$K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal

Consider $K$ field and consider the ring $R=K[X^2,X^3]\subset K[X]$. It is clear that $R$ is not a Dedekind domain, since with the element $X$ one immediately see that it is not integrally closed. But $R$ is a Noetherian domain and every non trivial prime ideal is maximal. I have a proof for the last two part, but it is a bit heavy and maybe someone can help me finding a better proof! Thanks in advance!


Random variable $X$ has uniform distribution on ($0,1$). The question is to find the distribution of $U=|X-1/3|$. So, by using the definition of continuous variables, I got to the equation $Fx(u+1/3)-Fx(-u+1/3)$, and that is correct. Now, I don't understand how to subtract these two functions, since one is non-zero on the interval $(-1/3,2/3)$ and the other on the interval $(-2/3,1/3)$. The answer in the book is $2u$ on ($0,1/3$), $u+1/3$ on ($1/3,2/3$), and $1$ after that.


How do you breed horses in Minecraft?  Do you just spawn one in creative mode right on top of another one or something like that?


Delete all but the most recent n file for each group of files that share the same prefix in a directory

My question is a bit different from some older questions simply asking for "deleting all but the most recent n files in a directory".  I have a directory that contains different 'groups' of files where each group of files share some arbitrary prefix and each group has at least one file. I do not know these prefixes in advance and I do not know how many groups there are.  EDIT: actually, I know something about the file names, that is they all follow the pattern prefix-some_digits-some_digits.tar.bz2. The only thing matters here is the prefix part, and we can assume that within each prefix there is no digit or dash.  I want to do the following in a bash script:   Go through the given directory, identify all existing 'groups', and for each group of files, delete all but the most recent n files of the group only. If there are less than n files for a group, do nothing for that group, i.e. do not delete any file for that group.   What is a robust and safe way of doing the above in bash? Could you please explain the commands step-by-step?


I found out an OLD pc with the following specification: Intel core Duo CPU 1.8 GHz RAM 2.00 GB Can I install Ubuntu on it? if not what is the best distro?


How to set up the matrix in data generation in R?

I am trying to generate two continuous predictors and one continuous outcome from mvrnorm. This is my R code. n.tr=10 mu = c(3, 3, 3) Sigma = cbind(c(0.91,0,0.3),               c(0 0.91,0.3),               c(0.3,0.3,0.91) dat =  as.data.frame(mvrnorm(n=n.tr, mu=mu, Sigma=Sigma,                       empirical=TRUE)) colnames(dat) = c('z', 'w','y')  I want both of the standardized slopes to be 0.3, and 0 correlation between z and w. I also want the variance of y to be 1, so the residual variance of y is 0.91. If i want the diagonal of the matrix to be residual variance, how can I set up the matrix?


Missing something obvious with tick label styles in pgfplots

Why does this not produce y tick labels in fixed number format? (pgfplots version 1.9 produces y tick labels in scientific format)  \documentclass[12pt]{article}   \usepackage{pgfplots}  \begin{document}   \begin{tikzpicture}  \begin{axis}[y tick label style={/pgf/number format/fixed}]  \addplot{cos(x)/12.0};  \end{axis} \end{tikzpicture} \end{document}


Will Mass Effect 2 bought in US work in UK?

I have an unused copy of Mass Effect 2 Collector's Edition bought via Amazon.com in the US, including a special code for Inferno Armour (also unused).  Will it work fine if I install and start playing the game in the UK? Does geographical location matter?  Thanks!


Hi all, Tonight I'm going to see a 3D film so I thought I'd check whether I had any old 3D glasses around the house. Found a pair of "RealD" glasses.  Anyhow, I assume that the glasses use some kind of polarisation to work. So I played around with looking through them in the bathroom mirror.  The first picture shows me holding the glasses facing towards the mirror, and looking through one of the lenses at the reflection in the mirror. One of the reflected lenses looks black and the other looks transparent. Cool! Polarisation in action.  However, the right-hand picture shows me holding the glasses facing away from the mirror - and in that picture, when I look through one of the lenses at the reflection, both reflected lenses appear transparent.  What on earth is going on? Dumbed-down explanation suitable for a mere mathematician, please :-)


Is it possible to have distinct scrolling while editing a response?

When editing a post, you've got a markdown edit area, then some kind of preview packed below. If the post happens to be long - and actually about a few tens of lines make it long - it becomes impossible to see both what you are editing and the rendering, as scrolling the preview does remove the markdown from your sight.  This is I think a feature request: is it possible to have at least the preview scroll on its own? Or better, have it scroll on its own and focus at the very point we've just made some modification?  Or is it a problem with my browser? Or did I not search the site with adequate keywords?


I need to make a bash script wait for a while, then resume running.  Shebang ./script Wait 10m ./thing


the use of 'would' in the following sentence

Can we use 'would' rather than 'might' in the following sentence?      Some students find it more difficult to sustain their motivation online than they might as part of a real learning group.


Ubuntu 18.04: Changing dock location on monitor rotation

In my current configuration, I have a dock (which shows application icons) on the left of the screen. I was wondering whether it is possible to move the dock to the top when the monitor is rotated 90 degrees (so to avoid narrowing down the width of the screen). Also, I want the dock to be back in the original position when I go back to the horizontal monitor orientation. Could someone help me do this?  Environment  I am running Ubuntu 18.04 and using the default gnome desktop environment. My computer is a 2-in-1 laptop which automatically rotates screen based on device orientation.   Current Attempt  I looked into possible gnome extensions that would do this, but  did not have such options.


I found a bug today in Stack Exchange's Code Snippet. Kindly check this. While inserting code snippet, this happens:    Please try to solve this.     Note: I am not exactly sure how to recreate. It just happened. I happened to see few just recently. I will surely explain, if I get a chance to replicate.   Reference Post:


I can´t get the minipages title to align with one another, as you can see in the images. Already tried align*. Thanks for the help! \documentclass  \begin{minipage}{0.4\textwidth}  \cvsection{Software}  \cvtag{Excel}  \cvtag{Word}  \cvtag{Eviews}  \cvtag{LaTex}  \cvtag{Haskell}  \cvtag{Access}  \cvtag{R}  \cvtag{PowerPoint}  \end{minipage}  \hfill  \begin{minipage}{0.5\textwidth}  \cvsection{Languages}  \begin{itemize}       \item Portuguese (Native)      \item English (Fluent)  \end{itemize}  \end{minipage}  \end{document}


When does $P(x)=\sum_{n=0}^{\infty}{\frac{n!}{n^n}\cdot x^n}$ with $x\in \mathbb{C}$ converge?   My Attempt:$$\bigg |\frac{a_n}{a_{n+1}}\bigg |=\left(1+\frac{1}{n}\right)^n\to e$$ So it converges for $|x|<e$. Now I wanted to check wheter the series converges for $e$ or $-e$.  I fail to either prove the divergence or convergence. Can you help?


Regarding three R packages for Bayesian analysis

There are several R packages for Bayesian analysis, i.e., RBugs, JAGS,MCMCPack. Are there any pros and cons for each of these packages?


I now have a 1 TB , but I can't change that with gparted.   How can I partition the hard disk into 600GB and 300GB? Should it stay as ext4 or should I change it to NTFS? I have only one OS installed.


The terms $a,b,c$ of quadratic equation $ax^{2}+bx+c=0$ are in A.P. and positive. Let this equation have integral root $\alpha,\ \beta$. Then find the value of $\alpha+ \beta + \alpha \cdot \beta$ ?   please point where I'm wrong:  Let common difference be $d$  $\implies \alpha+ \beta + \alpha \cdot \beta=\dfrac{c-b}{a}=\dfrac{d}{a} \implies a|d \ \ \ \ \longrightarrow  \ \ \ \ \              \because (b=a+d$, $c=a+2d)$  Also , $ax^{2}+(a+d)x+(a+2d)=0$.   $\implies$ $\alpha,\ \beta=\dfrac{-(a+d) \pm \sqrt{(a+d)^{2}-4\cdot a \cdot (a+2d)}}{2a}$.   For this to be integer $\sqrt{(a+d)^{2}-4\cdot a \cdot (a+2d)}$ must be perfect square.  $\implies$ ${(a+d)^{2}-4\cdot a \cdot (a+2d)}=p^{2}$ for some $p$.  $\implies -3a^{2}+d^{2}-6ad=p^{2}$  $\implies -3a^{2}+a^{2}q^{2}-6a^{2}q=p^{2}$ $\because$ $a|d \implies aq=d$ for some $q$.  $\implies a^{2}(-3+q^{2}-6q)=p^{2}$   $\implies -3+q^{2}-6q\ $  has to be perfect square. By trial $q=7$  But I need to get this without trial, please help.


Is there a way to install and remove packages in a single yum command?

Is there a way to add and remove packages at the same time with a single yum command? For example, installing postfix and removing sendmail without running two separate commands/transactions.


MacOS Kindle version 1.12.0 no longer seems to keep downloaded books in the My Kindle Library location, no new files are showing up there. Does anyone know where they are being stored now? Without these files to find and remove the DRM for use on other non-kindle readers I'll probably just go back to finding my books on DRM free sites 8(


Could functions change the content of a variable?

I wanted my variable play to change whenever the turn changes so I made a function. If turn is even play will be variable O="O", vice versa for odd then I used the function even(turn) with turn=1, it displays O even though it should be X. Is my code below wrong in some way or it just doesn't work like that?  I'm making a tic tac toe program on repl.it, I've tried using manual change as in making 9 different copies to change the turns but its just too much work, I wanted to make a simpler code.   play=0 X="X" O="O"  turn=1   def even(turn):   if turn%2==0:     play=O    else:     play=X    even(turn) print(play)   I expect the output to be either O or X according to if the number is even or odd respectively.


How did “to doctor” come to mean “to falsify"?

as a noun originally comes  from French “doctour” from Latin “docere”, to teach; all terms with a positive connotation:         c. 1300, "Church father," from Old French doctour, from Medieval Latin doctor "religious teacher, adviser, scholar," in classical Latin "teacher," agent noun from docere "to show, teach, cause to know,"      The meaning of doctor as a verb is related to the original noun. But from the late 18th century it develops a negative connotation:        1590s, "to confer a degree on," from doctor (n.). Meaning "to treat medically" is from 1712; sense of "alter, disguise, falsify" is from 1774.       (Etymonline)   :        To alter or tamper with something dishonestly; cook: We doctored the receipts/ He doctored the booze (1774+).      (The Dictionary of American Slang)  This later meaning appears to be English specific, as the negative connotation does not appear to present in other European languages such as French, Spanish or Italian.   How did the term doctor develop the decidedly negative meaning  of alter, falsify?


"Can you tell me what this is?" or "[...] what is this?"

As written in the title, my question is, which version of the sentence is grammatically correct, if not both. I've been arguing with some guy on 9gag for roughly 10-15 minutes already, and I'm not sure myself anymore by now. Again, which of the following is correct?   Can you tell me what this is? Can you tell me what is this?   In my opinion, the first version is correct, and the second version lacks a colon, like this:   Can you tell me: What is this?   I would be delighted to hear your opinions.  PS: Please note that I did some research online, also with the help of "online grammar checks", but a) couldn't find anything or b) both sentences were identified as correct.


Please show me how to calculate the folowing limit of a sequence

I think should be something very simple... $$\lim_{n\to\infty}nq^{n}$$ wher $|q|<1$ i tried to use binomial theorem, but no success... I know that $q^{n}$ is convergent to $0$, but can't deal with this $n$


Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a continuously differentiable function such that $\underset{x\rightarrow\infty}{\lim}\frac{f(x)}{x}=0$ and suppose $\underset{x\rightarrow\infty}{f'(x)}$ exists. Then Prove that $\underset{x\rightarrow\infty}{f'(x)}=0$    I can see that if we apply L'hoptal's theorem directly to $\frac{f(x)}{x}$ then we can get the answer. But is it possible to do so without knowing the value of $\underset{x\rightarrow\infty}{f(x)}$  On the similar problem: , they have given the existence of $\lim_{x\rightarrow\infty} f(x)$. But in this particular problem they haven't


Finding if which users have a record type available to them using SOQL

I would like to be able to execute a SOQL query that will allow me to see which users have access to a certain record type for a certain object.  For example, if I have a case record type called Phone Team, I would like to make a query that returns the names of all the users that have been assigned the Phone Team record type, as can be seen in the native user interface in a profile's Object Settings page.  So far I have managed to get a query that can get the names of all the users that have, for example, read access to the case object:  SELECT Assignee.Name FROM PermissionSetAssignment      WHERE PermissionSetId IN          (SELECT ParentId FROM ObjectPermissions WHERE SObjectType = 'Case'               AND PermissionsRead = true AND Parent.IsOwnedByProfile = true)   However, there doesn't seem to be any way to access record type assignment in the same way that you can object permissions.  I see from  that the info can be obtained via the metadata API, but I would much prefer to do it by SOQL if possible.  Thanks


For $H,K \triangleleft G$ and $H\cap K=\{1\}$ show $hk=kh \ \forall k \in K, h\in H$

Let $H$ and $K$ be normal subgroups of $G$ with a trivial intersection. $H \cap K = \{1\}$. Where $1$ is the unit. Show that $hk = kh$ for every $k \in K, h \in H$. Additionally, it asks if the statement still holds if only one of $K$ and $H$ is a normal subgroup.  Firstly, does $hk = kh$ for every $k \in K, h \in H$ mean $HK = KH$? It means that every element from $H$ commutes with every element from $K$. But does these two things tell the same thing?    What I did: Since $ H \triangleleft G$ Let $h \in H$ for every $g \in G: ghg^{-1} \in H$.  Similarly,  $k \in K \  \forall g \in G : gkg^{-1} \in K$    It is also true that $khk^{-1} \in H$ and $hkh^{-1} \in K$. So there exist such $h' \in H$ and $k' \in K$ that $khk^{-1} = h'$ and $hkh^{-1} = k'$.    $kh = h'k$ $hk = k'h$.      I do not know how to use that the intersection is trivial nor how to continue as I can't get anything out of this.


Is it acceptable to omit "I" when it's the subject?

Possible Duplicate:          Is it correct English to omit I from the beginning of a sentence when it's clearly implied?  For example...     How are you? Hope everything's okay?   as opposed to     How are you? I hope everything's okay?


I want to be able to play sound files in my program. Where should I look?


What order do triggered abilities happen in if multiple things trigger at the same time?

I had several humans on the battlefield.  On turn three, I played . On turn four, I played . On turn five, during my upkeep, this question came up.  At this point, I need to draw/reveal three cards. If I reveal a human, Descendants' Path will allow me to cast it without paying its mana cost.  So, does it matter when I draw the human?  The static abilities state "at the beginning up your upkeep..." which leads me to believe that those two draws/reveals would happen before my normal draw. If that's the case, does the draw order happen in the same order that I played the enchantments?  In the end, that's how we decided to do it. I drew first for Triumph of Ferocity, then I revealed for Descendants' Path, then I drew for my turn. Did we do it right?


SetWindowsHookEx, KeyboardProc and Non-static members

I am creating a keyboard hook, wherein KeyboardProc is a static member of a class CWidget.  class CWidget {    static LRESULT CALLBACK KeyboardProc(int code, WPARAM wParam, LPARAM lParam );  };   I want to call the non-static members of CWidget inside the CWidget::KeyboardProc.   What is the best way to do it?   KeyboardProc does not have any 32 bit DWORD where I can pass the 'this' pointer.


Install WhatsApp on Android x86 virtual machine

I installed  on   $ virtualbox -help Oracle VM VirtualBox Manager 5.1.22_Ubuntu   using:  $ lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 17.04 Release:    17.04 Codename:   zesty   If I open Play Store app and select WhatsApp, there is no option to install it. Only the option "add to wishlist" appears.  Is it possible to install WhatsApp via Play Store app on Android x86 virtual machine?


Should I take down-votes as a personal insult?

I have read many posts on the pros and cons of the down-vote system. Reputation points have no real value, yet I feel insulted when a question I asked is down-voted. From a personal point of view, I feel as though my input is being rejected by an entire community.   It is hard to describe how it makes me feel when I pose a question that I would want to know the answer to, only to be subjected to hostility. This may not be the intent but it's most definitely the message I receive.    Should I take down-votes personally?


What is the C# version of VB.net's InputDialog?

What is the C# version of VB.net's InputBox?


I defined a Table with lable the following way:  \begin{table}[t]    \centering    \begin{tabular}{|c|c|}       \hline Transaktionsnummer & Enthaltene Items \\        \hline 1 & f,a,c,d,g,i,m,p \\        \hline 2 & a,b,c,f,l,m,o \\        \hline 3 & b,f,h,j,o \\        \hline 4 & b,c,k,s,p \\        \hline 5 & a,f,c,e,l,p,m,n \\        \hline     \end{tabular}     \label{tab:transaktionsdatenbank}    \caption{Transaktionsdatenbank nach \cite{han2000mining}} \end{table}   The caption shows:  Tabelle 5.1: Transaktionsdatenbank nach [HPY00]  When using the reference:  \begin{figure}[t]     \centering     \includegraphics[width=0.5\textwidth]{img/FrequentPatternTree58.png}     \caption{Frequent Pattern Tree aus Transaktionsdatenbank in Tabelle \ref{tab:transaktionsdatenbank}}     \label{fig:frequentPatternTree} \end{figure}   I get: Abbildung 5.1: Frequent Pattern Tree aus Transaktionsdatenbank in Tabelle 5.2.2 where 5.2.2 is the subsection the table was defined in instead of 5.1.  What could I have done wrong?


Where do I get a SIS mirage 672 vga driver?

I need to obtain a display adapter for SiS mirage +3 gpu (closed source), so I can run a stable system on Ubuntu.  I need to find a driver for this adapter that is open source and gives completely stable video playback.


Simple question here that I can't Google and have the time for to look it up through all the info on the web available... I also don't know how to import mathematical signs. Could you maybe explain that as well? Sorry for  the inconvenience.  The "f" sign in calculus is used to denote the integral, and I know it in the standard form with b above the f and a under the f, next to the f the function and then dx after that to express the integral of a function on the interval [a, b]. Now I met a another way to note it, its the same f with a circle in the middle (?) and a f with a collection of coordinates called sigma under the f and an alpha after the f, to express some kind of "volume" of a polygon? BTW it is on this site  in case this is really unreadable for you. I could understand that.  gr. and thanks


Gravitational shielding and equivalence principle

I read on wiki that gravitational shielding is considered to be a violation of the equivalence principle. Is that so, How? A conceptual description without lot of mathematics will be helpful.   I am not sure whether the wiki article refers to shielding only by materials, or it also includes mechanisms - e.g a rotating disk. I know rotating disk does not shield gravity, but just to describe what a mechanism could mean.  It goes on to say that any evidence of gravitational shielding would falsify GR, is this true?  It is hard for me to believe because - suppose gravitational shielding is demonstrated somehow, then how GR can be falsified all of a sudden, which has been verified by so many experiments and phenomena. So, that makes me think gravitational shielding would not invalidate GR.


Ubuntu 15.10 No interface, just the wallpaper

I just installed Ubuntu 15.10 and after login, i do have only the new wallpaper, I do only have that, no menus, no interface, nothing...  I see the login screen, once I log in, just the wallpaper. If i connect a USB the explorer opens and I can see all the folders, including the root.  Any suggestion?   UPDATE:   I have tried to reinstall, reset, remove and install both Ubuntu-desktop and unity fully and no solutions.  I have tried to activate the unity plugin. (was already activated). I have tried to reset the user files. tried to reinstall everything (.iso and OS).   None of those worked for me.


Encrypted Home... Forgotten Password, but no Passphrase

I am using a cloned hard drive in attempts to restore some old files.   The cloned drive has 2 users, one with an encrypted home drive, one without. Both are administrators. When I couldn't get into the main user (with the encrypted home directory), I logged in as the 2nd user and changed the password.   It seems that I somehow broke the relationship between the encryption passphrase and the user. I'm pretty sure I have the passphrase. Is there a way to get to the data?


how to make /usr/lib owned by root again

I chowned -R username /usr/lib and now i cannot sudo or do any thing really due to sudoers.so belonging to username.  How do i fix this and make /usr/lib owned by root again?


how do I set up the auto redirect with apache2. I have got SSL working and want to redirect all to the SSL side. I added Redirect /  but takes me to the wrong site directory whereas https takes me to the right spot. Is that the right thing to add for the redirect? (its in VirtualHost *:80)  Current VirtualHost file:  ServerName fraffel.tech   <VirtualHost *:80>     ServerAdmin webmaster@localhost     DocumentRoot /var/www/fraffeltech     Redirect / https://fraffel.tech/     ErrorLog ${APACHE_LOG_DIR}/error.log     CustomLog ${APACHE_LOG_DIR}/access.log combined  </VirtualHost>  <VirtualHost *:443>      DocumentRoot /var/www/fraffeltech      SSLEngine on      SSLCertificateFile /etc/ssl/fraffel_tech.crt      SSLCertificateKeyFile /etc/ssl/private/fraffel.tech.key      SSLCertificateChainFile /etc/ssl/fraffel_tech.ca-bundle  </VirtualHost>


Ubuntu 14.04 update-pci ids /usr/share/misc/pci.ids.new is read-only

I try to install cuda 7.5 on Ubuntu 14.04. To verify that your GPU is CUDA-capable, I write   $ lspci | grep -i nvidia    command. I don't see anything. Then i write   update-pciids   I take   update-pci ids /usr/share/misc/pci.ids.new is read-only   message. I login as a root but i can not do. Are there anyone who solved this problem? I also new in ubuntu.


\chapter* with a titletoc entry and a running head

The answer referred to above involves Koma and deals with a single chapter. I have not been able to make any use of the answer in my case where the document class is book and where I want to deal with all chapters.  I would like to define a titletoc command which, like \chapter* suppresses the word Chapter and the chapter number in the title of the chapter but produces both a table of content entry and a running head, both without the word Chapter and the chapter number.  As it turned out, though, the question had indeed been asked and, as @Johannes_B finally pointed out in a comment, an answer given at  To wit, \chapter* need not be redefined but two lines need to be added. Seems a bit clunky but a macro to insert chapter* along with the two lines can do the job.  Correction: The two lines were given in the question referred to above, by @egreg, but hidden in a comment. :-(  Here is a MWE with the additional two necessary lines indented:  \documentclass[11pt]{book} \usepackage{titletoc} \usepackage{hyperref} \begin{document} \tableofcontents \chapter*{One}     \addcontentsline{toc}{chapter}{One}     \markboth{\MakeUppercase{One}}{\MakeUppercase{One}}  Text   \newpage Text  Text  \newpage Text  Text  Text \end{document}


Render layers with and without HDR background

I have a scene with a house in front of the camera and behind the house some trees. I want to render them in separate layers, but I want the HDR image in the background for the first render and without in the second render with only the trees.  I can only check the Transparent in the Film section in the Render tab, but that affect both render layers. I guess I can render them manually one by one and change the settings for Transparent, but perhaps there are some other alternative?  EDIT: I'm not asking HOW to render a background with HDR image! I have two render layers. The first render layer I want to render with the HDR background and in the second render layer without the HDR background. But if I enable the Transparent option, both render layer are affected by this settings and the HDR background isn't visible in any render layer. How to fix this was my question.


Bind Middle mouse button + Left click to pan

I want to pan when holding down the middle mouse button and the left click at the same time.


I need to show that $$ 1-x\leq e^{-x} (*) $$ Now we know that $e^x:=\sum_{k=0}^\infty \frac{x^k}{k!}$, which means $$ e^{-x}:=\sum_{k=0}^\infty \frac{(-x)^k}{k!}=1-x+\frac{x^2}{2!}-\frac{x^3}{3!}+\frac{x^4}{4!}-\frac{x^5}{5!}... $$ So after we subtract $1-x$ from both sides of the inequation (*) we have to show: $$ 0\leq \sum_{k=2}^\infty \frac{(-x)^k}{k!}=\frac{x^2}{2!}-\frac{x^3}{3!}+\frac{x^4}{4!}-\frac{x^5}{5!}... $$  1.) $x=0$ : $\sum_{k=2}^\infty \frac{(-x)^k}{k!} = 0$  2.)$x=1$: $\frac{1}{2n+1}\leq \frac{1}{2n}$ for all $n\in\mathbb{N}$  3.) $x<0$: This is obvious since ever summand is positive.  4.) $0<x<1$: This is also obvious (?) because for such $x$ it holds that $x^{2n}>x^{2n+1}$ for all $n\in\mathbb{N}$ and also $\frac{1}{(2n)!}>\frac{1}{(2n+1)!}$. So $\sum_{k=2}^\infty \frac{(-x)^k}{k!}=\sum_{n=1}^\infty \frac{x^{2n}}{(2n)!} - \frac{x^{2n+1}}{(2n+1)!}>0 $ since all summands are positive.  5.) $x>1$: Here is where I struggle and need help please. This is the a bit of the opposite of 4 maybe.


Someone edited my message on StackOverflow, but it really bugs me out.  I'm not sure what's wrong with it:   As you see, the bigger the circle becomes, the more vertices I need for hiding the straight lines. As you see, the bigger the circle becomes, the more vertices I need to hide the straight lines.   The latter (corrected) sentence just bugs me out for some reason. It would sound better if there was a comma after the word "need", perhaps, but I guess that would be even worse in means of grammatical correctness.  Can someone explain why is the first sentence bad and the second sentence correct? And could there even be better solution to fix the first sentence?


There were two posts from back in 2011 about the  and . It's been 8 years since and I'm wondering if there might be an update since gvSIG and QGIS (at time of writing) are at v2.4 and v3.5, respectively.  Particularly, I'm interested to know what processes one software does better in than the other and how/why so (e.g. for Plugins, QGIS wins hands-down as the community is larger which has led to more plugins being developed).  Outside of the actual technology, I'm also curious as to how the community help has evolved. QGIS has a vast amount of help forums, websites, and tutorials, and I'm wondering if the response of the gvSIG community or if the resources available are equivalent or near equivalent to QGIS.


How do you add more than one phone number on iMessage?

My sisters and I all have iPhones under the same account. I also have an iPad under the same account. I am trying to get the iMessage on my iPad compatible with my phone number, not email address.   The only phone number choice to choose from is my sister's iPhone number. How can I choose my phone number for iMessage on my iPad?


How can I apply a basic material to an object using python in cycles render?

I would like to be able to apply and edit a material to objects I have create using python script. I am using the cycles render engine but can't find a way to get this to work.  I've tried a bunch of the answers already given in other threads but none of them seem to work.  I would like to: create and apply a new material for each object and adjust the colours using rgb, using nodes or otherwise.  Sorry if this is a stupid question, I'm very new to blender scripting!


I am supposed to create a log analysis software for my Master Degree thesis.  Currently I am in the data collection phase :) so I need a way to read a file in real time. For example I have to monitor the "/var/log/auth.log" file and to look for failed logins (just an example among the 1000000s to come for my program:) ). So I need to read the file line by line. OK, if I were to use a scripting language (Python, Ruby) this would be really easy, but since I am in JAVA, I wasn't very lucky. Anybody gotta clue how to read a file in Real Time, maybe an example? Thanks in advance.


What is the meaning of ./ before a given path?

I've been told to run this:  ./yiic message ./app/messages/config.php   But I don't understand the ./ meaning, can anyone clarify please.  Note: Believe me, we can't google that. I've tried:  ./ meaning ./ ubuntu  It was the same as nothing. :(


I have some struggles with this exercise. Let $X$ and $Y$ be infinite dimensional Banach spaces. Show that no $T\in \mathcal{K}(X,Y)$ is onto. We know that $T$ is compact why $T\in \mathcal{L}(X,Y)$ and I think I can show it by contradiction assuming that it is onto, whereby open, but I am not sure how to show that $T$ is open. Or I dont know is their any easier way to solve this problem.


I am trying to check for integers, "" and " " when a user inputs a string. Every thing is working as expected but when I pass an empty field it validates and prints invalid input. Apart from that it also prints the println statement from the catch. Below is my code and actual output. package com.assessment;  import java.util.Scanner;  public class MaxCharString {      public static void main(String[] args) {         int i, j, count = 0, maxcount = 0;         System.out.println("Enter a string to find the maximum character.");         Scanner input = new Scanner(System.in);         String character = input.nextLine().toLowerCase();         try {             if (character == "") {                 System.out.println("Invalid Input");             }             int inputCharacter = Integer.parseInt(character);             System.out.println(inputCharacter + " is not a valid Input. Please try again.");         } catch (NumberFormatException e) {             char result = 0;             char ch[] = character.toCharArray();             for (i = 0; i < ch.length; i++) {                 count = 0;                 for (j = 0; j < ch.length; j++) {                     if (ch[i] == ch[j]) {                         count++;                     }                     if (maxcount < count) {                         maxcount = count;                         result = ch[i];                     }                 }             }             System.out.println("Maximum count of occuring character in the string is: " + result);             input.close();         }     } }  Output: Invalid Input Maximum count of occuring character in the string is:    Could anyone please help me out with this problem. Thank you.


Keep in mind: I'm still in high-school so forgive my poor maths. Also remember that I'm in HIGH-SCHOOL so nothing to complex I like to mess around with equations and I find it quite fascinating the results I can somehow come up with. Recently, I found  and started to mess around with this. Somehow I can up with the following result: $π = 0.$ I thought to myself, as anyone would, how is this possible? I then decided to show my proof to my maths teacher and my parents and neither one could show me where I went wrong so I was hoping someone here could. This is my proof: $$e^{iπ} + 1 = 0$$ $$e^{iπ} = -1$$ $$e^{2iπ} = 1$$ $$2iπ = \ln(1) = 0$$ $$4\times-1\timesπ = 0$$ $$-4π^2 = 0$$ $$0 = 4π^2$$ $$0 = 2π$$ $$0 = π$$ Edit As I pointed out above, my maths knowledge isn't that advanced, compared to people on this site. Therefore the answer(s) I accept and/or upvote will be based on understandability as well as how well they answer the question.


Find all pairs of integers $(n,k)$  that satisfy $(n+1)^k - 1 = n!$  It is easy to see that (1,1) and (2,1) are solutions by inspection,  but how do we prove that these are the only solutions? After sometime, I also saw that $(4,2)$ was also a solution, as it wasn't so obvious.  I was thinking that maybe $n! + 1$ cannot be a perfect power of a number? Though I also can't prove it. I also tried binomial theorem but still cant see anything.


I want to prove the following:  Let $m_0,...m_r$ be pairwise coprime integers . Show that there exists a sequence of consecutive integers $s, s+1,...,s+r$ such that $m_i\vert s+i, i =0,...,r$  I know that consecutive number are coprime and then $gcd(s_j,s_{j+1}) =1$ . Because the mi's are pairwise coprime I thought about the Chinese Remainder Theorem but I don't  think it's the right way  Any hint on how to proceed ?


How can I kill a process by name instead of PID, on Linux?

Sometimes when I try to start Firefox it says "a Firefox process is already running". So I have to do this:  jeremy@jeremy-desktop:~$ ps aux | grep firefox jeremy    7451 25.0 27.4 170536 65680 ?        Sl   22:39   1:18 /usr/lib/firefox-3.0.1/firefox jeremy    7578  0.0  0.3   3004   768 pts/0    S+   22:44   0:00 grep firefox jeremy@jeremy-desktop:~$ kill 7451   What I'd like is a command that would do all that for me. It would take an input string and grep for it (or whatever) in the list of processes, and would kill all the processes in the output:  jeremy@jeremy-desktop:~$ killbyname firefox   I tried doing it in PHP but exec('ps aux') seems to only show processes that have been executed with exec() in the PHP script itself (so the only process it shows is itself.)


Is using mid 2012 MacBook Pro RAM in mid 2011 iMac 27" an option?

I recently came into possession of a 27 inch mid 2011 iMac. It only has 4GB RAM and I have been pricing compatible memory modules online.  I  then remembered I also have a 13 inch mid 2012 MacBook Pro that was damaged some time ago. It has 8GB RAM that I have no reason to suspect has any faults as it worked fine before the damage which was not anywhere near the bottom case. So I thought I would investigate the types of memory modules the iMac and MacBook Pro use.   I found the iMac uses 204 pin PC3-10600 (1333 MHz) DDR3 SO-DIMM modules. I found the MBP uses 204 pin PC3-12800 (1600 MHz) DDR3 SO-DIMM modules.   Obviously I'm thinking that if I can use the MacBook Pro RAM in the iMac I can save some money and it's a good way of recycling.  I understand this RAM would not operate at 1600 MHz in the iMac. My questions are:   Would the MBP RAM work okay otherwise? If it would work, does it make a difference if I add them to the original RAM so I have 12GB in total, or will I have to remove the old modules and just use the 8GB instead?


NPE whenever I want to run Intent from my class

I'm a beginner when it comes to Android app development. I have finished some Udemy courses, but then I realized that the Android Docs might actually be better for building a good foundation on app development. I'm trying to build my own app now but I encountered this problem.    My Class  public class deleteInfluencer extends AppCompatActivity {  private Repository instanceOfRepository;  public static final int EDIT_BLOGGER_ACTIVITY_REQUEST_CODE = 1;  deleteInfluencer(Application application) {     super();     instanceOfRepository = new Repository(application); }  void callDeleteInfluencer(int id) {     instanceOfRepository.deleteInfluencerCalledFromRepository(id); }  void callUpdateInfluencer() {     Intent intent = new Intent(this, EditBloggerActivity.class);     startActivityForResult(intent, EDIT_BLOGGER_ACTIVITY_REQUEST_CODE); }  @Override protected void onActivityResult(int requestCode, int resultCode, @Nullable Intent data) {     super.onActivityResult(requestCode, resultCode, data);      if (requestCode == EDIT_BLOGGER_ACTIVITY_REQUEST_CODE && resultCode == RESULT_OK) {         int id = 0;         Tables tables = new Tables(                 id, // Blogger ID                 data.getStringExtra(EditBloggerActivity.EXTRA_EDIT_REPLY_NAME),                 data.getStringExtra(EditBloggerActivity.EXTRA_EDIT_REPLY_ADDRESS),                 data.getStringExtra(EditBloggerActivity.EXTRA_EDIT_REPLY_MOBILE_NUMBER),                 data.getStringExtra(EditBloggerActivity.EXTRA_EDIT_REPLY_FB),                 data.getStringExtra(EditBloggerActivity.EXTRA_EDIT_REPLY_IG),                 data.getStringExtra(EditBloggerActivity.EXTRA_EDIT_REPLY_EMAIL));         instanceOfRepository.updateInfluencerCalledFromRepository(tables);     } else {         Toast.makeText(this, "Save Failed! fill out all fields", Toast.LENGTH_LONG).show();      } } }   LOGCAT  2020-02-28 16:10:06.071 4258-4258/com.kurtsample.digitalcirclesprototype E/AndroidRuntime: FATAL EXCEPTION: main Process: com.kurtsample.digitalcirclesprototype, PID: 4258 java.lang.NullPointerException: Attempt to invoke virtual method 'java.lang.String android.content.Context.getPackageName()' on a null object reference     at android.content.ContextWrapper.getPackageName(ContextWrapper.java:142)     at android.content.ComponentName.<init>(ComponentName.java:130)     at android.content.Intent.<init>(Intent.java:6082)     at com.kurtsample.digitalcirclesprototype.deleteInfluencer.callUpdateInfluencer(deleteInfluencer.java:31)     at com.kurtsample.digitalcirclesprototype.Adapter$2.onClick(Adapter.java:95)     at android.view.View.performClick(View.java:6597)     at android.view.View.performClickInternal(View.java:6574)     at android.view.View.access$3100(View.java:778)     at android.view.View$PerformClick.run(View.java:25885)     at android.os.Handler.handleCallback(Handler.java:873)     at android.os.Handler.dispatchMessage(Handler.java:99)     at android.os.Looper.loop(Looper.java:193)     at android.app.ActivityThread.main(ActivityThread.java:6669)     at java.lang.reflect.Method.invoke(Native Method)     at com.android.internal.os.RuntimeInit$MethodAndArgsCaller.run(RuntimeInit.java:493)     at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:858)


I would like to abbreviate \begin{frame} \end{frame} environment of Beamer. For most Latex environments, I could do this using a basic \def command: \documentclass{article}  \def\be{\begin{enumerate}\item} \def\ne{\item} \def\ee{\end{enumerate}}  \begin{document}  \be One \ne Two \ne Three \ee  \end{document}  This works and is much more compact than the full syntax. But if I try to do something similar for Beamer it doesn't work: \documentclass{beamer}  \def\be{\begin{frame}} \def\ee{\end{frame}}  \begin{document}  \be A frame \ee \be Another frame \ee  \end{document}  Runaway argument? \let \AtEndDocument \@firstofone \@enddocumenthook \@checkend {docume\ETC. ! File ended while scanning use of \beamer@collect@@body. <inserted text>                 \par  Why wouldn't this work for the frame environment in particular?


Kernel of $T$ is closed iff $T$ is continuous

I know that for a Banach space $X$ and a linear functional $T:X\rightarrow\mathbb{R}$ in its dual $X'$ the following holds: \begin{align}T \text{ is continuous } \iff \text{Ker }T \text{ is closed}\end{align} which probably holds for general operators $T:X\rightarrow Y$ with finite-dimensional Banach space $Y$. I think the argument doesn't work for infinite-dimensional Banach spaces $Y$. Is the statement still correct? I.e. continuity of course still implies the closedness of the kernel for general Banach spaces $X,Y$ but is the converse still true?


How to make something transparent while still keeping the effect intact

So I am literally a illustrator noob with literally 4 hours of experience since writing this post. I am creating a logo for my school robotics team and I wanted to make the background of the logo transparent for our team website but realized that while I can make the background of the logo transparent the objects cannot be transparent. I was wondering how can I keep the effects of the objects while still making them transparent.  Here are some images of my logo and my situation.   The first image is what I have on Ai.       This is my image converted to the pdf file, as you can probably tell I want the white parts to be transparent (sorry for the bad image on the 2nd one btw).     if image does not show


`ls / | wc -l` tells more lines than `ls /` shows

ls / outputs two lines.  $ ls /  bin   cdrom  etc   initrd.img      lib    lost+found  mnt  proc  run   share  sys  usr  vmlinuz boot  dev    home  initrd.img.old  lib64  media       opt  root  sbin  srv    tmp  var  vmlinuz.old   But why does ls / | wc -l tell 26 lines?  $ ls / | wc -l 26


I'm doing some tests on postfix and I've read the following log message: status=sent (delivered via filter service) Can someone tell me what does that mean?


#!/bin/bash var=1 if [[ $var -eq 0 ]] then     echo "No students" elif [[ $var -eq 1 ]] then     echo "1 student" elif [[ $var -eq 2]] then     echo "2 students" elif [[ $var -eq 3 ]] then      echo "3 students" elif [[ $var -eq 4 ]] then     echo "4 students" else     echo "A lot of students" fi   I've written this bash script . But it throws this error:   Failed test #1. Runtime error: main.sh: line 11: syntax error in conditional expression main.sh: line 12: syntax error near `then' main.sh: line 12: `then'


I got stuck on this inequality for a day. If $p$ is positive integer, then the problem becomes too easy, but I can't find how we deal with the general case when p can be any positive number. Can someone give me a hint? I really appreciate     Prove that $|x^p - y^p| \le p|x-y|(x^{p-1} + y^{p-1})$ provided that $1 \le p \lt \infty$ and $x, y \ge 0$