I need to show that $$ \int\limits_1^{\infty}x^\alpha\sin(x^\beta)dx $$ converges if and only if $\alpha + 1 < \beta$. I used substitution and integration to get $$ \lim\limits_{t\to\infty}\int\limits_1^tx^\alpha\sin(x^\beta)dx \overset{u = x^\beta}{\underset{du = \beta x^{\beta-1}}{=} }\lim\limits_{t\to\infty}\left(\frac{1}{\beta}\int\limits_1^{t^\beta}u^{\frac{\alpha + 1 - \beta}{\beta}}\sin{u}du\right) $$ If $\alpha + 1 -\beta < 0$, then we have a product if a function with bounded anti-derivative and a differentiable decreasing function which tend to 0, and from Dirichlet's criterion, the integral converges.   For the converse, I used integration by parts $$  = \frac{1}{\beta}\lim\limits_{t\to\infty}\left(\left.-u^{\frac{\alpha + 1-\beta}{\beta}}\cos{u}\right|_1^{t^\beta} + \frac{\alpha+1-\beta}{\beta}\int\limits_1^{t^\beta}u^{\frac{\alpha + 1-2\beta}{\beta}}\cos{u}du\right) $$ For $\alpha + 1 -\beta\geq 0$, I get that the first term indeed diverges, but this is not enough to show total divergence. How can one show it?


careful looking at the linear map dNp with its correspondence matrix

Here, I have some question that remain unsolved for quite a long time. My question is about the differential of the gauss map $dN_{p}$, to start the convenient expression of the symbol and formula, I have to construct some functions(maps).  First, there is a one dimension parameters line and I use the parameter as $t$, and the function $\overline{α}(t)=(u(t),v(t))$ maps $t$ to $uv$ plane, and which is a plane curve on $uv$ plane.  Second, there is a function $\mathbf{x}$ that takes $\overline{α}(t)$ to a curve on a regular surface, $α(t)=\mathbf{x}(\overline{α}(t))=(x(u(t),v(t)),y(u(t),v(t)),z(u(t),v(t)))$.  Final, there is a map $\mathbf{N}$ represents the unit normal vector on each point of the surface (x,y,z), $N(x,y,z)=(X(x,y,z),Y(x,y,z),Z(x,y,z))$.  And, in most of the books, they start to discuss $dN_p$, and I used to learn that the linear map $dN_p$ corresponds a 3x3 matrix: \begin{bmatrix}X_x&X_y&X_z\\Y_x&Y_y&Y_z\\Z_x&Z_y&Z_z\end{bmatrix}  The matrix derive from the chain rule in calculus: $\frac{dN(α(t))}{dt}=(X_{x}*x'(t)+X_{y}*y'(t)+X_{z}*z'(t), Y_{x}*x'(t)+Y_{y}*y'(t)+Y_{z}*z'(t), Z_{x}*x'(t)+Z_{y}*y'(t)+Z_{z}*z'(t))=\begin{bmatrix}X_x&X_y&X_z\\Y_x&Y_y&Y_z\\Z_x&Z_y&Z_z\end{bmatrix}\pmatrix{x'(t)\\y'(t)\\z'(t)}=(dN)_{3x3}(α'(t))$, here, $x'(t)=\frac{dx(u(t),v(t))}{dt},y'(t)=\frac{dy(u(t),v(t))}{dt},z'(t)=\frac{dz(u(t),v(t))}{dt},$  Now ,I have the question about the partial derivative $\pmatrix{X_x\\Y_x\\Z_x}$,  the definition of it is  $$\lim_{\Delta t\to 0} \frac{(X(x+Δt,y,z),Y(x+Δt,y,z),Z(x+Δt,y,z))-(X(x,y,z),Y(x,y,z),Z(x,y,z))}{\Delta t},$$  but even $(X(x+Δt,y,z),Y(x+Δt,y,z),Z(x+Δt,y,z))$ may not defined because the domain of the map $\mathbf{N}$ is only defined on the surface, not a solid domain, so if we move a little $Δt$, it may go out of the domain(the domain is on the surface).This is my personal thinking.   If my consideration has some mistake, please correct me, thanks!


There are four types of chomsky hierarchy (specified for formal languages):  Type-0  Recursively enumerable Type-1  Context-sensitive Type-2  Context-free Type-3  Regular   I consider that, it should be the type-0. This type is represented by Turing machine. I think, that it is because of the dynamic changing tokens during runtime, dynamic changing of the meaning of macros, calculating Lambda calcul (what should be the most important).  Do you have any advice?


how to tell which statistics SQL server references in query

Is there a way to check in SQL Server 2016 which statistics the optimizer referenced when compiling a particular query?  My question is similar to , except that I am using SQL Server 2016, which doesn't appear to support trace flags 9204 and 9292 as listed in  by Paul White. I tried them and nothing showed in my SSMS.  I googled to check why - and it sounded as if 2016 doesn't support them?


Prove that every number has a unique representation in base 3.

How do I use induction to show this? From what I understand we want to prove $\forall m \in \mathbb{N}$, $$ m = \sum_{i=0}^{n}{a_i.3^i} = a_0.3^0 + a_1.3^1 + a_2.3^2 + \dots + a_{n-1}.3^{n-1} + a_n.3^n $$ where $n \geq 0$ is unique and so is $a_i$, for $a_i = 2, 1$ or $0$.  The base case is simple for $m=1$: Let $a_0 = 1$. Then  $1 = 1.3^0$ which is true. How do I proceed after assuming the inductive hypothesis? Adding $1$ to show the expression for $m$ to show the result for $m+1$ seems a bit trivial..


I have a CPT for events. I need to display future events for people to register, while hiding past events.  What is the easiest date format for both (1) entering date when creating new event and (2) comparing event dates with current date ?


Received a new comment reply notification about a comment reply posted 10 months ago

This morning, I received a notification of a new reply to a comment I made.  But that reply was made 10 months ago, yet the inbox says it was made 5 hours ago.    The question in question is .  I'm not sure whether or not I received a notification when the reply was actually posted.


Was the blue fire from Crimes of Grindlewald Fiendfyre?

In Crimes of Grindlewald, Grindelwald uses a powerful blue flame that takes on the shape of monsters. Was this Fiendfyre?


I want to split a string in the first space it has, but when I try to use the splited string in the condition "if" it doesn't work.  String parentName = new String(); String[] fullName = a.getPathComponent(1).toString().split("\\s+"); //also try with split (" "); parentName = fullName[0]; if (parentName == "DBPedia"){    ...  }   for example, fullName will take the string "DBPedia (23)", and the splited string "parentName" will have only the string "DBPedia", but when I use the string on the "If" it does not enter to the condition. What can be the problem?


How to connect OpenLayers to PostGIS data?

I have read in OpenLayers how to load KML, GeoJSON etc. vector files in OpenLayers. But how can I connect to PostGIS data. If not, why should I upload my data to PostGIS then instead of directly putting my data using WebServices. Am I missing anything?   And I want to load this vector data so that one can see the attributes by clicking on the features.  I need PostGIS because in future I want to enable queries. I think it's only possible by maintaining a database like PostGIS. But how using OpenLayers?   I have read OpenLayers Beginner's Guide, but nowhere it is mentioned. Please help!!


I often read through many threads and websites when trying to solve a problem, and only later realize that the first thing I read actually had the answer, or was key to eventually finding it (which is more often than not a SE thread).   Often I have closed the tab and forgotten the title of the thread, so I can't easily go back and upvote the question/answer, or I just plain forget to do so.   I think that if I could view my visitation history, I would upvote a lot more stuff. I can see a privacy concern with tracking this type of information, but I would find it useful. I suppose I could just filter my browser history, but I'm lazy and I'm probably not the only one.  Edit: I did notice the previous similar thread, but I decided to make this one because I want this feature for a specific purpose. It would also be useful to highlight in some way my most visited threads, but that would require keeping a history. So the first step would be to record that information.


Is it more difficult to earn reputation on SO than couple of years ago?

It seems that all good questions that could be asked have been already asked. Also it seems all good answers that could appear have already appeared. Existing questions/answers base probably covers most of the programming topics. And, therefore, it is more difficult to ask an interesting question that bothers everybody than, for example, couple of years ago when SO was comparatively empty. Do only I get this feeling or not? Are there any metrics for proving/disproving that it is more difficult to get more reputation on SO as time passes? I want to get rid of the feeling that all questions have been asked and answers have been already answered.  UPD: Maybe Jon Skeet would be great candidate for the experiment of getting statistical data about SO reputation dynamics? We can track dynamics of his reputation over the last (two) year(s). Maybe it could tell us much. Is there any right way to get such data easily?  UPD2: Here is some info about Jon Skeet dynamics:


Should you ever use protected member variables?  What are the the advantages and what issues can this cause?


Everytime I use my terminal, I am always put into the dash shell instead of bash. Is there any way to change this even just for my user only? Tried apt-alternatives but setting the default shell can't be found.   I am using Debian Jessie testing btw.


Russian characters in equations without \textup in XeLaTeX

I want to change LaTeX engine from PdfLaTeX to XeLaTeX.  There are a lot of formulas and equations with Russian text inside. And it used without any commands.  MWE for pdflatex:  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[russian]{babel} \usepackage{mathtext}  \usepackage[T2A]{fontenc}   \begin{document}      Формула: $F_{подпись} = Ф$      Уравнение:     \begin{equation}     X_{первый} = Y_{второй}     \end{equation}  \end{document}   I tried the same example with XeLaTeX. There is no errors, but Russian characters are displayed only with \textup command, like it was said in this answer:  \documentclass{article} \usepackage{unicode-math} \usepackage{polyglossia}   \setdefaultlanguage{russian}   \setmainfont{Liberation Serif}  \setmathfont{Asana Math}  \begin{document}      Формула: $F_{подпись} = Ф$      Уравнение:     \begin{equation}     X_{первый} = Y_{\textup{второй}}     \end{equation}  \end{document}   Are there any ways to do it without \textup?


Proving number of subsets of a set size $n$ via induction

I am trying to prove by induction that number of subsets of a set is equal to $2^n$. I start with the base case when n=1, for example, and the number of subsets is clearly 2. When we go to n=2, the number of subsets increases to 4, and I can see that this way: the empty subset is still there, the subset that has all elements is still there, the number of subsets that have only 1 element increases by 1, since we add another element, not sure about sets that have multiple elements in them (this is for $n \geq 3$; does it have to do with $\textrm{C}$ombinations? How can I write a mathematically rigorous inductive proof for this? Thanks!


Can one travel with xerox copy of photo iD

My mother in law forgot her original PAN Card. She has a photocopy of the same. Can she fly in domestic airline with this Photocopy of PAN Card? She has her flight tomorrow i.e. on 5 April from Ahmedabad to Pune. She is from Jalgaon.


Availability of MXD file for OpenStreetMap data in Esri Geodatabase?

From what I understand, an ArcGIS mxd file contains the "styling" information on how to show data.  I downloaded and imported OpenStreetMap data into my geodatabase. Now I need to show them.  Is there any available mxd file match the OpenStreetMap fields/values that I can use?  I check this question(), but the links are all dead.  ps: right now the all the highway/roads/trail display as a single line in my map. I want to use mxd to show them in a better way, like Mapnik or google.


What is the sum this series involving sum of reciprocals of natural numbers?

Let $S =^nC_1 - (1+\frac{1}{2}) ^nC_2 + (1+\frac{1}{2}+\frac{1}{3}) ^nC_3 + … (-1)^{n-1}(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...\frac{1}{n}) (^nC_n)$ I have to prove that $S = \frac{1}{n}$, I thought of writing the general term like this,   $T_r=(-1)^{r-1}(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...\frac{1}{r}) (^nC_r)$ and then multiplying each term by $^nC_r$ and then take sum of each, but that led me nowhere. I tried the reversal method too, but the terms weren't adding up. I want to know if there is a easy way of doing this. Thanks.


How does google regard subdomains with regard to SEO?

For example, in the past, links to www.example.com wouldn't have meant Google would pass any value to say, forum.example.com. What is the current status of this? (Please provide a reference if possible).


Why are snaps and regular apt packages both provided in ubuntu 18.04

When I wanted to install Skype on my system, I ended up with my first snap.  Interestingly, it mounted itself as a loopback device and broke my script to mount a crypto filesystem as /dev/loop1.  But Skype was only available as a snap, and I needed it, so...  Since then, I've installed a few open source packages that I would not have expected to be snaps, but were.  Specifically GIMP and the Clementine music player.  Again, I didn't notice they were snaps until I had to move my crypto filesystem to another higher /dev/loop... device.  I had moved it from loop1 to loop9, and thought that would hold me, but having installed the 'visual studio core' text editor to play with I ended up with 6 additional loopback filesystems, in addition to Skype's 3 and GIMP's, and Clementine's.  Personally, I find that really messy.  If a project is truly open source and can be built from source by the distro maintainers, why release it as a snap?  To me, snaps are a necessary compromise for 3rd party closed source developers to get their apps onto multiple distros.  So, Skype I get.  GIMP, no.  It turns out that having uninstalled GIMP and Clementine, I see that Ubuntu (actually Kubuntu - if that makes a difference) has non-snap versions included as well.  Why would they do that - and why would anybody choose the snap over the 'build for the distro'?


When and how to use the "be + they + noun" structure

Can you please explain this structure?     I can't forget the looks on faces of people who've lost hope. Be they gay, be they seniors, be they blacks looking for an almost-impossible job, be they Latins trying to explain their problems and aspirations in a tongue that's foreign to them.   *This is also from Harvey Milk's "The Hope Speech"


Understanding transverse oscillation in 1 mass, 2 spring systems

Lately I have been working through some nice problems on mass-spring systems. There are tons of different configurations - multiple masses, multiple springs, parallel/series, etc.   A few possible configurations are listed here: . I think the most interesting one is the 1 mass, 2 spring system with transverse motion:    It is written on that page:  "If the springs are initially stretched a great deal from their relaxed length (but not distorted), the vibration frequency is nearly the same as for longitudinal vibrations.  If the springs are initially stretched very little from their relaxed length, the "natural" frequency is much lower and the vibrations are nonlinear (nonsinusoidal) for all but the smallest of $y$-axis displacements."  If I understand correctly, this means that the system approaches simple harmonic motion when the initial displacement $y_0$ is either very small, or very large.   I tried to see if I could prove this myself by looking at the period of oscillations as a function of the initial displacement $y_0$, but I am having some trouble:  Suppose the mass is a distance $\Delta y$ from the equilibrium position. Then each spring has length $\sqrt {a^2+\Delta y^2}$, so each spring is stretched by $\sqrt {a^2+\Delta y^2}-a$ from its original length. Therefore, each spring exerts a restoring force of $k(\sqrt {a^2+\Delta y^2}-a)$. The magnitude of the net restoring force on the mass is then   $|F_r|=2k(\sqrt {a^2+\Delta y^2}-a)\sin(\theta)=2k(\Delta y-a\sin(\theta))$  Substituting $\sin(\theta)=\Delta y/\sqrt {a^2+\Delta y^2}$, we get:  $|F_r|=2k\Delta y(1-a/\sqrt {a^2+\Delta y^2})$  So we have the differential equation:  $y''=-(2k/m)y(1-a/\sqrt {a^2+y^2})$.  If $y$ is very large, then $y''\approx -(2k/m)y$, which is simple harmonic motion with period $2\pi\sqrt{2k/m}$. This makes sense, because if $y$ is very large, the two springs essentially act in parallel, so we effectively have a 1 spring system in longitudinal motion with spring constant $2k$, which gives the same result.  Now if $y$ is very small, I'm not sure which approximation formulas to use to make things come out nicely. According to the web page, I should get the result that the period will be larger than $2\pi\sqrt{2k/m}$.


What exactly does "it's down the street" mean?

When giving addresses, what exactly is the meaning of "it's down the street" ?        Go straight along the street and it's a little further.     It's at the end of the street.     It's somewhere in the end.


I have to calculate the volume of the solid bounded by $$x^{2}+y^{2}+z^{2}=6 \qquad z=x^{2}+y^{2} \qquad z\geq0$$ using double integrals.  When I drew it, I could see that a part of the sphere is above the paraboloid. So, for me, it should be something like that: $$V=\iint_{B}\left[\sqrt{6-x^{2}-y^{2}}-\left(x^{2}+y^{2}\right)\right]dx\,dy$$ But my problem is to find these integrals. I think I'm supposed to not use spheric coordinates (since I'm calculating a double integral, not a triple one), but even the polar ones, I don't know how to find them.


Hibernate computer with a timeout from command line on Windows 7

I am trying to hibernate my computer from the command. I was using shutdown /s /t 20 to shutdown the the computer. I change /s to /h to hibernate and now it just returns the usage text as if it doesn't recognise what I have entered. In this is does say  /h         Hibernate the local computer.   Is there something else that I need to use with /h to get it to hibernate?


Accepting one's own answer does not move it to the top of the answers list

I have the following question: . I've posted my own solution after a while and accepted it.  The expected behavior is that even though it doesn't have the highest vote count, it's on top of the list since it's accepted and should be correct, (like it does on normally accepted answers), but if the accepted answer is my own (a.k.a. OP), it doesn't move to the top of the list, staying somewhere near the bottom with the lower voted answers.  Why is that so? Is it a bug or is it by design?


How can a file's size on disk be 0 bytes when there's data in it?

I have a file in Windows 10 with 362 bytes of data, but the "size on disk" is just 0 bytes. It's a simple "Hello world" program written in assembly, and saved in .  How is it possible that the size on disk is zero when the size of the file is 362 bytes?  I have an SSD, not a normal hard disk.  Screenshot of the Properties dialog:


How should I create URLs for database generated content that can be indexed by search engines?

I have learned how to retrieve data from a database to a single page by using a form, so I would not need to create many pages to show the elements of a catalog. The concern that I have is how to make this database content available for search engines.   I have read that I need my site to generate different URLs for each search result, but in my test, the webpage always has the same URL without any additional parameter. I know that sites like Facebook and similar generate particular URLs for each profile and they are indexed, but I don't know if "physical" files exist for them or how this is done. I have read similar questions to this, but still can't figure how to generate the URLs.


What package is tail (the command-line tool to see the end lines of a file) included with in the latest stable version of Ubuntu, if I want to install or uninstall it (and does it come installed by default)?  I already have it installed; I just don't remember if I installed it or it was already there. I made a program that requires it as a dependency (so that's why I ask).


Hint to prove that $\exp : M_n(\mathbb{C}) \rightarrow GL(n,\mathbb{C})$ is surjective.

I'm trying to prove that $\exp: M_n(\mathbb{C}) \rightarrow GL(n,\mathbb{C})$ is surjective , but I can't seem to have an idea. Can somebody give me a hint, please?


Why is 600 out of 1000 more convincing than 6 out of 10?

Look at this excerpt from "The study skills handbook", Palgrave, 2012, by Stella Cottrell, page 155:     Percentages Notice when percentages are given.   Suppose, instead, the statement above read:           60% of people preferred oranges; 40% said they preferred apples.         This looks convincing: Numerical quantities are given. But is the difference between 60% and 40% significant? Here we would need to know how many people were asked. If 1000 people were asked of whom 600 preferred oranges, the number would be persuasive. However, if only 10 people were asked, 60% simply means 6 people preferred oranges. "60%" sounds convincing in a way that "6 out of 10" does not. As a critical reader, you need to be on the lookout for percentages being used to make insufficient data look impressive.   What is this characteristic called in statistics? I would like to read more about it.


How to determine whether critical points (of the lagrangian function) are minima or maxima?

$f(x,y) = 2x+y$ subject to $g(x,y)=x^2+y^2-1=0$. The Lagrangian function is given by  $$ \mathcal{L}(x,y,\lambda)=2x+y+\lambda(x^2+y^2-1), $$  with corresponding   $$ \nabla \mathcal{L}(x,y,\lambda)= \begin{bmatrix}  2 + 2\lambda x \\ 1+2\lambda y \\ x^2+y^2-1 \end{bmatrix}. $$  From the latter we can see that $x=\frac{-1}{\lambda}$ and $y=\frac{-1}{2\lambda}$, which we can substitute into $x^2+y^2=1$ to obtain $\lambda = \pm\sqrt{\frac{5}{4}}$. Meaning that $x = \pm \dfrac{2}{\sqrt{5}}$ and $y= \pm \dfrac{1}{\sqrt{5}}$. We find the critical points $(\frac{2}{\sqrt{5}}, \frac{1}{\sqrt{5}})$ and $(\frac{-2}{\sqrt{5}}, \frac{-1}{\sqrt{5}})$.  I am confused on how I should proceed to check wether these points or minima or maxima? I know the Hessian is involved, but which one?


How to see terminal commands generated by GUI actions

I am new to Linux and only know my way around because of the GUI.  Is there a way to see the equivalent commands on the terminal to do the same things as using the GUI?  Thanks


How can I install open JDK 7 on Ubuntu 18.04?

I need openjdk to build my Android ROM, but I can't install it. I installed Oracle JDK but it doesn't work.


Let $A$ be a set that is countable. Let there be a function mapping $A$ onto a set $B$. Is $B$ countable?

Let $A$ be a set that is countable. Let there be a function mapping $A$ onto a set $B$. I'm asked to prove the statement "$B$ is countable".   This is my attempt at a solution.   Since $A$ is countable it is either finite or countable infinite.  If it is finite the statement is obvious. If it is countably infinite, it is by definition in one-to-one correspondence with the set $N$ consisting of positive integers. Since there exists a function mapping $A$ onto $B$, every element in $B$ has a direct relation to atleast one element in $A$, which in turn has a relation to $N$. And thus it $B$ must be countable since by proxy it is in one-to-one correspondence with $N$.  Does this logic prove anything, am I missing something? Am I completely on the wrong track and if so, how would I go about proving it? What happens in extreme cases if every element in $B$ is the image of a lot of elements in $A$?


How to create dependent picklist in salesforce lightning component?

I Have written following code  Component --   <aura:handler name="init" value="{!this}" action="{!c.doInit}"/>  <aura:attribute name="country" type="Lead"/> <ui:inputSelect label="Country" class="dynamic" aura:id="InputSelectDynamic" value="{!v.leadObj.Country__c}" change="{!c.onSelectChange}"/>  <aura:if isTrue="{!v.InputSelectDynamic != '--None--'}" >     <ui:inputSelect label="States" class="dynamic" aura:id="states" value="{!v.leadObj.States__c}" />  </aura:if>   Java Script Controller -   ({     doInit : function(component, event, helper) {         var action = component.get("c.getLeadCountry");         var inputsel = component.find("InputSelectDynamic");         var opts=[];         action.setCallback(this, function(a) {             for(var i=0;i< a.getReturnValue().length;i++){                 opts.push({"class": "optionClass", label: a.getReturnValue()[i], value: a.getReturnValue()[i]});             }             inputsel.set("v.options", opts);          });         $A.enqueueAction(action);     },     onSelectChange : function(component,event,helper){         var action = component.get("c.getLeadState")         var inputsel = component.find("states");         var opts=[];         action.setCallback(this, function(a) {             for(var i=0;i< a.getReturnValue().length;i++){                 opts.push({"class": "optionClass", label: a.getReturnValue()[i], value: a.getReturnValue()[i]});             }             inputsel.set("v.options", opts);          });         $A.enqueueAction(action);     } })   Apex Controller -   public class DependentPicklistDemoController {     @AuraEnabled     public static List<String> getLeadCountry(){         List<String> options = new List<String>();         options.add('--None--');         Schema.DescribeFieldResult fieldResult = lead.Country__c.getDescribe();         List<Schema.PicklistEntry> ple = fieldResult.getPicklistValues();         for (Schema.PicklistEntry f: ple) {             options.add(f.getLabel());         }         return options;     }     @AuraEnabled     public static List<String> getLeadState(){         List<String> options = new List<String>();         Schema.DescribeFieldResult fieldResult = lead.States__c.getDescribe();         List<Schema.PicklistEntry> ple = fieldResult.getPicklistValues();         for (Schema.PicklistEntry f: ple) {             options.add(f.getLabel());         }         return options;     } }   I am not able to filter child picklist value on the basis of parent picklist values. Please help--


For which countries does tourist visa apply after the end of a long-stay visa in Schengen countries?

According to this  it is possible to stay legally in the Schengen Area after the expiration of a long visa for 90 days.   is the ammendment from where this quote comes from:     For the purposes of implementing paragraph 1, the date of entry shall be considered as the first day of stay on the territory of the Member States and the date of exit shall be considered as the last day of stay on the territory of the Member States. Periods of stay authorised under a residence permit or a long-stay visa shall not be taken into account in the calculation of the duration of stay on the territory of the Member States.   So this pretty much settles the case, but I don't know to which exact countries this applies.  I am from Brazilian nationality and my country is part of the  countries that don't need a visa to enter the Schengen Area.  However, according to the User manual for the short-stay "Schengen" calculator (cannot post more than 2 links), Antigua and Barbuda, The Bahamas, Barbados, Brazil, Saint Kitts and Nevis, Mauritius, and Seychelles are somewhat different because they hold a visa waiver agreement with the EU.  In the same guide it is stated that for these countries     the old definition ("3 months during a 6 months period following the date of first entry") continues to apply   So finally my question is: Does the full old interpretation of the date of first entry (Verification of the length of previous and intended stays under the old rules) still applies to these countries or just the 90 days/180 days part (or any other possibility I haven't thought of)?  I would also like some reliable links to support the answer. This guide is unclear as to how they define the day of first entry and is not an official document    Update: I left Europe to Brazil through the Charles de Gaulle airport at Paris. At first I presented my passport and the border guard asked for my titre de séjour (French long-term visa), which was expired for about 2 months at that time. The guard didn't even comment that it was expired and he let me pass.  So nothing happened to me but I still don't know exactly if I was illegally staying in the country or not.


What theorems depend on the unproven Riemann Hypothesis?

I heard that many theorems in modern mathematics depend on the unproven Riemann Hypothesis. What are some examples of such theorems, and what will be the impact on these results if the Riemann Hypothesis is proven to be true?


In my website have two types people login one is designer another is reader, i want people come to login my website by role. Mean designer go to design login form to login. Reader go to reader login form to login. my question is:   how to show two login forms in same page? how to check the role when the visiter login at the same time in login form? is it any module i can use or i need do something customize the user module and how    customize?   Plz help!


What is this random name in my command-line prompt?

I'm trying to figure out what this (obretschlt2-w7) is, from my command-line prompt.  I'm using a conda environment, with the name µ_env, with my Username mu. However I can't figure out where the 2nd field is coming from.  I'm logged into a secure server VPN, through my work, but I don't ever recall seeing this.  What is this name and where is it coming from?   (µ_env) obretschlt2-w7:~ mu$ pwd /Users/mu   Output from echo $PS1, as asked for (in comment).  (µ_env) \h:\W \u\$


Show that $\sqrt{6+4\sqrt{2}}-\sqrt{2}$ is rational using the rational zeros theorem

Let $r=\sqrt{6+4\sqrt{2}}-\sqrt{2}$, then $r+\sqrt{2}=\sqrt{6+4\sqrt{2}}$. Squaring both sides, we get $$r^2+2r\sqrt{2}+2=6+4\sqrt{2}$$ which is the same as $r^2-4=2\sqrt{2}$. Squaring both sides again, we get $r^4-8r^2+16=8$ or $$r^4-8r^2+8=0.\tag{$\star$}$$   The rational zeros theorem tells us that the only possible rational solutions to ($\star$) are $±1$, $±2$, $±4$, $±8$. I do not know where to go from here. Please help me complete this proof.


Mathematical form of the de facto repulsive "force" associated with the Pauli Exclusion Principle

One of the principles of General Relativity is that test objects follow a geodesic unless otherwise acted upon by a force. From this perspective, it is clear that physicists, consciously or unconsciously, view the Pauli Exclusion Principle (PEP) as a force, since it is intrinsically involved in the processes that prevent us, for example, from following a geodesic through the earth's surface. If this interpretation is considered incorrect, so be it.  There are other instances where physicists treat PEP as a force. Semantic arguments aside, PEP is in fact a repulsive phenomenon that that keeps fermions from occupying the same state. It behaves like a de facto force, and can be overcome by sufficient pressure. What is the mathematical form, in terms of $r$, of PEP repulsion? Have experiments been done to determine this?  Regarding the fall-off with $r$: note that one electron approaching another electron must "know" at some distance that it is being repulsed; the two electrons need not come in contact.  [Author's note: Since several readers claim this is a duplicate question, official forum guidelines require I explain why it is not. First, I see nowhere else the question as to the mathemetical form of the EFFECTIVE repulsive force f(r). Thus, the question is new on this forum. Second, whether PEP repulsion is a "true" force, a "fundamental" force, or a "pseudo" force is a matter of semantics, discussions of which do not answer the question. In any case, PEP repulsion is an EFFECTIVE force, and therefore in principle can be described by some function f(r), even if only statistically.]


Compute the complex integral $\int_{|z|=1} \frac{1}{z^2+1}$

As one can easily see the function $\displaystyle f(z)=\frac{1}{z^2+1}$ has two poles $i$ and $-i$ which both lay on the circle with $R=1$ in the complex plane.  Does the residue theorem hold for such cases and thus $$\int_{|z|=1} \frac{1}{z^2+1}= 2 \pi i \left[ Res(f,i) + Res(f,-i) \right]?$$


What the difference between 'it exists' and 'it does exist'? I want to know.


If $A, B$ and $A + B$ are all $n × n$ invertible matrices. Prove that $A^{−1} + B^{−1}$ is invertible and the inverse is $A(A + B) ^{−1}B$.  I am afraid I am really stuck on this one, and I haven't really tried much because I don't know what to try.  Thanks for all the help guys, I understand now.


Why do we need to use chain rule of differentiation

For example, here we have $y = \sin(x^2 + 5x -6)$. So, it’s answer will be $\cos(t)\cdot(2x+5)$, where $t= x^2 + 5x -6$. But I want to know what if we solve it directly I.e $\cos(2x+5)$ wrong? What’s the reason? Why choose the 1st approach?


Uncompressing .tar.gz archive to specific directory

How does tar.gz file gets uncompressed with all contents to arbitrary directory, existing or not using tar using single line command? If it does not exists, then is created (directory). To clarify, let consider example: I've downloaded archive-latest.tar.gz from internet into directory /home/user/Downloads. I have microSD card target partition mounted on /mnt/archive. Once downloaded, I want to extract downloaded /home/user/Downloads/archive-latest.tar.gz directly on /mnt/archive using single line command. I've read man tar manual, but I cannot find option for specifying target dir.


I am Python amateur and was trying to write a code to generate a Fibonacci Series when I came across a weird behaviour.  >>> def F(num):                    #line1     a,b = 1,2                      #line2                           yield a                        #line3     yield b                        #line4     while num>2:                   #line5         a,b = b,a+b                #line6         yield b                    #line7   >>> gen = F(10)                    #line8 >>>                                #line9   The while loop in the code is an infinite loop. My question is if the loop does not end then how did #line8 complete execution?  Thanks!!


$n$ balls are thrown randomly into $k$ bins - how many are empty?

A large number of variants of this question were already asked here, including these - , , which are close, but none seem to answer my question. Assume that $n$ balls are thrown randomly and independently into $k$ bins.  What is the probability of finding $x$ empty bins? What is the expectation of the number of empty bins?


Is Stack Overflow's (SSL) log-in process optimal from a UX perspective?

Does Stack Overflow use SSL when transmitting passwords during the log-in process? This question comes up when you log-on, because there is no green lock in the browser when logging in.   I do use the Stack Exchange OpenID provider and my browser stays on that page during the log-in process and hence the connection seemingly stays insecure, because there is no green browser lock.    Edit:  I had a look now into the network stream and saw there is indeed a https connection taking place to Stack Exchange after having entered my credentials.   However the common Web user won't do a network trace each time when he enters credentials into a HTML form on the Web. Therefore not seeing a green browser lock nor being able to verify the certificate should ring alarm bells and could be considered a problem at least from an UX point of view. I do not find this behaviour to be optimal.


Screen detection and mouse reverse (x & y axis) kali linux

I installed kali linux OS on my laptop.  The installation went well but when I booted in kali linux the screen was backwards. I signed in as root and the screen flipped back but the mouse is reverse (x & y axis).  When I move my mouse left it moves right when I move it down it moves up. If I want to press a button at the upper right I need to press it at the down left.  The screen is acting backwordes (x & y axis)but I see the graphics straight and the mouse is acting backwordes.  I installed kali linux again with a fresh installation. I have the same problem as before.  I installed kali linux again with a fresh installation. I have the same problem as before.   I searched the web And I don't find information on a problem like this


Is there anything I can do if I get 3rd party about my SO question?

I posted a question on StackOverflow:    Then I got spam from a 3rd party trying to get me to go to their site to get an answer, instead of SO. I know SO can't stop the email spam from a 3rd party, but is there someway to find if they have any SO accounts and nuke this f'ing spammer?


I am trying to use <template></template> tags in my HTML to hold content that can then be displayed in the page. I am currently grabbing the template contents using html() and writing them to the div using html(). This all works as expected, but when the content is displayed in the div, things like button click events are not triggering. So the content seems to be out of scope. I assume this may be because it was loaded using html(). Is there a better method I can use or is the problem caused by something else?  Example code  window.launcher = function(){     $('#launch').on('click', function(){         var content = $('#content').html();         $('#container').html(content);     }); };  window.launcher2 = function(){     $('#launch2').on('click', function(){         alert('You clicked me!');     }); };   The second function will not fire.    Edit: fixed typo


Is it OK to include my own library in my answer to my own question?

I wanted to do something in a programming language once. The only way to do it back then was pretty verbose, so I created an open source library to make it much easier.   It's encouraged to answer your own questions here, but is it also OK to mention your own library in the answer? Of course I want to list several ways of achieving the task at hand (including the verbose method and some other open source libraries) in my answer. But still: it's kinda self promoting.  So: OK or not OK?


There are functions for is_home(), is_blog() is_single() etc...  What's the best way to tell if I'm on a page that is requesting that I login? I guess that would just be the wp-login.php page.


Prove that $ \frac{1}{1*5} + \frac{1}{2*7} + \frac{1}{3*9}+... = \frac{8}{9} - \frac{2}{3}\ln(2)$  I got the answer using the hint given in the question  It mentioned to consider the integral$\int x^2 \ln(1-x^2)dx$. I evaluated the integral by integration by parts.  Then I again evaluated by applying Taylor series. I equated both expressions and took limits of integration from 0 to 1 to obtain the result.  Is there any other way to solve this question? Without the hint, I would never have thought of considering that Integration.  What I tried: $\sum_{i=1}^{\infty} \frac{1}{i(2i+3)} = \frac{1}{3} \sum_{i=1}^{\infty} \frac{1}{i}-\frac{2}{2i+3}$  But both of the above series diverge


Show revision history link on question for any moderation action (edit, closure, deletion, etc)

Background Many events are included in the revisions list, primarily:  edits deletions closures  However, the only thing that creates the link to the revisions list is edits. This link is in the form of "edited x minutes ago". This means an  assortments of events can occur to a question that has never been edited without any evidence of that fact. I tested this on a question of my own which I had never edited, but probably needed a minor edit. You can see the . I deleted it then undeleted it, all without any revision list link appearing, I finally edited it and the full revisions list was available How this affected me This affected me when I asked a question regarding an on going event. I was criticised for posting a duplicate of a question that was "still on the front page!". However what had actually happened (I eventually found out) was that the original was posted, self deleted and then undeleted a few minutes later (for whatever reason). I posted my duplicate while the original was deleted but there was no (available) record of that until the question was later edited. Request Have any event that are included in the revisions history also generate an appropriate link to the revisions list on the question


Is it possible to simulate key press events programmatically?

Is it possible to simulate key press events programmatically in JavaScript?


How do I prove that if $A\setminus C = B\setminus C$ and $A\cap C = B\cap C$ then $A = B$?

I am stuck. I know that I need to prove $A$ is a subset of $B$ and that $B$ is a subset of $A$, and that in each case all elements in A are elements in $B$, but I don't know where to go from there. Any help is appreciated!


Estimate total song ('coupon') number by number of repeats

If shuffle-playing playlist ×100 resulted in [10 13 10  3  2  2] different songs being repeated [1 2 3 4 5 6] times, what is the estimate for the total number of songs? (assuming shuffle play was completely random)  Update: (R code)  k <- 50 # k number of songs on the disk indexed 1:k n <- 100 # n number of random song selections m <- 20 # m number of repeat experiments colnum <- 10 mat <- matrix(data=NA,nrow=m,ncol=colnum) df <- as.data.frame(mat) for(i in 1:m){   played <- 1+floor(k*runif(n)) # actual song indices (1:k) selected    freq <- sapply(1:k,function(x){sum(played==x)})   # = number of times song with index x is being played   histo <- sapply(1:colnum,function(x){sum(freq==x)});   for(j in 1:colnum){    df[i,j] <- histo[j]   } } df   Resulting in: e.g. 20 distributions (V1=number of single plays, V2=number of double plays, etc):     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 1  15 13 11  1  2  2  0  0  0   0 2  15 12 10  1  4  0  1  0  0   0 3  12 14  7  6  3  0  0  0  0   0 4  17 16  6  4  2  0  1  0  0   0 5  17 10 12  5  0  0  1  0  0   0 6  13 15 11  6  0  0  0  0  0   0 7  10 14  9  3  2  1  1  0  0   0 8  12 17  5  6  3  0  0  0  0   0 9   9 19  8  3  1  2  0  0  0   0 10 13  9 11  6  1  0  1  0  0   0 11 16  9 12  5  2  0  0  0  0   0 12 15  9 11  6  2  0  0  0  0   0 13 19  9  7  4  4  1  0  0  0   0 14 17 11  4  7  3  1  0  0  0   0 15 11 20  8  1  3  1  0  0  0   0 16 14 12 10  5  0  2  0  0  0   0 17  9 12  8  7  3  0  0  0  0   0 18 10 15  9  4  2  0  1  0  0   0 19 14 11 12  7  0  0  0  0  0   0 20 16 14 11  3  1  1  0  0  0   0   Now I need to get from here to the Poisson modelling--my R is a bit rusty (?lmer)...--Any help would be appreciated...  Attempted Poisson modelling: disappointing fit?!  plot(1:colnum,df[1,1:colnum],ylim=c(0,30),    type="l",xlab="repeats",ylab="count") for(i in 1:m){   clr <- rainbow(m)[i]   lines(1:colnum,df[i,1:colnum],type="l",col=clr)   points(1:colnum,df[i,1:colnum],col=clr) }  df.lambda=data.frame(lambda=seq(1,5,0.1),ssq=c(NA));df.lambda for(ii in 1:dim(df.lambda)[1]){   l <- df.lambda$lambda[ii]       ssq <- 0       for(i in 1:20){         for(j in 1:10){           ssq <- ssq + (df[i,j] - n*dpois(j,l))^2         }       }       print(ssq)       df.lambda$lambda[ii] <- l   df.lambda$ssq[ii] <- ssq     }     df.lambda     lambda.est <- df.lambda$lambda[which.min(df.lambda$ssq)] lambda.est # 2.4 points(x <- 1:10, n*dpois(1:10,lambda.est),type="l",lwd=2)  100*dpois(1:10,3) n/lambda.est   the estimated lambda stays around 2.3, with an n estimate of around 43; the fitted curve seems very discrepant, and seems to worsen with rising n !?  Doesn't this have to do with the fact, that our repeats are different from the 'classical' Poisson distributions: it's not just ONE event that repeats itself x number of times, but the sum of repeats of different items (songs)?!


Blender 2.8 does not render current camera view

Why doesn't blender 2.8 render the view from the currently selected camera; this view:  produces:  How can I render an image viewed from a specific camera?


Javascript: Why does ["2","3"].map(parseInt) return [2, NaN]?

Since map callback gets called on each element, I would have expected [2,3] as the return value based on the documentation .


I'm an absolute beginner at writing programs in C, and I'm having difficulty compiling a simple program. Here's my code:  /* This code is a .c file that prints out the words hello, world. */  # include <stdio.h> int main() {     printf("Hello World! \n"); }   Here's the error I get when compiling:  Ubuntu:~/Desktop/cFiles$ gcc -Wall hello.c -o hello.out -lmls  hello.c:5:1: warning: return type defaults to ‘int’ [-Wreturn-type] hello.c: In function ‘main’: hello.c:7:3: warning: implicit declaration of function ‘print’ [-Wimplicit-function-declaration] hello.c:8:1: warning: control reaches end of non-void function [-Wreturn-type] /usr/bin/ld: cannot find -lmls collect2: ld returned 1 exit status   I'm not sure what I'm doing wrong. Can anyone help?


Prove that : $\Omega \operatorname{reducible}\implies k\equiv 435\pmod{1163}$

Let the fraction :   $$\Omega =\frac{2k^{7}+1}{3k^{3}+2},k\in\mathbb{N}$$ Prove that :      $$\Omega \operatorname{reducible}\implies k\equiv 435\pmod{1163}$$    My try as following :   Let $d=gcd(2k^{7}+1,3k^{3}+2)$   So : $d$ divide $2k^{7}+1$ and $3k^{3}+2$ this mean :   $d$ divide   $$3(2k^{7}+1)-2k^{4}(3k^{3}+2)=3-4k^{4}$$  Then $d$ divide  $4k(3k^{3}+2)+3(3-4k^{2})=8k+9$$  How I complete ? And where I atop ?


memoryless property of exponential distributions with random variables

It is true that $P(X>t+s|X>t)=P(X>s)$ for certain values $t$ and $s$.  However, how can I show that this still holds if:   $T$ is a continuous random variable. That is $P(X>T+s|X>T)=P(X>s)$ Both $T$ and $S$ are continuous RVs: $P(X>T+S|X>T)=P(X>S)$   All the random variables are independent.


How to enable top bar background opacity?

There is a way to change top bar background opacity in ubuntu 20.04 lts.  I installed the hide top bar extension but is not a option to change it.


Find the value of the following integral  $$ \int_{-\pi/2}^{\pi/2} \frac{\cos^3 x}{e^x+1} dx $$  I tried to use the twin integral with sin and get some result but nothing obvious came out. Also, Mathematica gives a very bizarre result! Any ideas how to solve analytically?


Some hints for "If a prime $p = n^2+5$, then $p\equiv 1\mod 10$ or $p\equiv 9\mod 10$"

I tried to prove this question by first considering the possible last digit of $p$ when $p=n^2+5$, but that reasoning got me nowhere. Then I tried to prove it by contrapositive, and however I just couldn't really find where to start. Hence I'm here asking for some hints (only hints, no solution please).  Many thanks, D.


What is the cause for the validity of Newton's third law?

What, specifically, causes newton's third law?  For instance, if I push on a wall, why is it that I experience a force in the opposite direction?    I seem to vaguely understand that is has something to do with electronic repulsion or molecular compression (maybe that's completely wrong, I don't know).  As a related question, what would happen if two objects that were /infinitely/ immovable (at the molecular level, it cannot be broken or compressed) collided with each-other?


X ∪ (Y ∩ Z) = (X ∪ Y) ∩ Z  If it were true I'd know how to prove that it is, but if it's not how do I go about finding a counter example?


Nodejs Nginx error: (13: Permission denied) while connecting to upstream

I'm trying to run multiple Nodejs applications on Nginx server running on CentOS 7. I noticed that when I run a Nodejs app on some ports I get an 502 Bad Gateway error in the browser so I checked the error logs:  [notice] 12806#0: signal process started [crit] 12807#0: *13 connect() to 127.0.0.1:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://127.0.0.1:7777/", host: "myapp.com" [crit] 12807#0: *13 connect() to [::1]:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://[::1]:7777/", host: "myapp.com"   when I change the app to listen to 8008 for example everything is working fine. I checked permissions and if the process is running as root and everything seems ok. I played with the timeouts as well but no result. Can anyone help?


Find N Distinct Evenly Spaced Perfect Squares

I understand that it's possible to find 3 distinct evenly spaced square numbers is possible by finding a rational solution to the equation: $x^2+y^2=2r^2$ Where $r$ is a rational number. But I have no idea how to apply this to finding a larger amount of evenly spaced perfect squares, or if it is even possible.


If $|f'(c)| \leq M$ and $ M < 1$, the sequence defined by $a_{n+1} = f(a_n)$ converges

Let $f$ be a real function such that $f$ is differentiable and $|f'(c)| \leq M<1$. Let $a_1$ a real number and define $a_{n+1} = f(a_n)$. Then $(a_n)$ converges.   My attempt:   By the mean theorem, we have that $|a_{n+1} - a_n| = |f(a_n) - f(a_{n-1})| \leq M|a_n - a_{n-1}|$.  Then, $|a_{n+1} - a_n| \leq M^{n-1}|a_2 - a_1|$.  As $M < 1$, we know that $M^{n-1}$ converges to $0$.


How can one pass the contents of a LaTeX environment to a macro?

I'm working on an exam document class where the user enters in questions something like this:  \multiplechoice{Question} {Answer #1} {Answer #2} {Answer #3} {Answer #4} {Correct answer} {Explanation}   I'd like to process this information in various ways in one LaTeX run (to create an answer sheet, key, and the test itself), so the questions need to be stored in a macro. The awkwardness comes when one defines:  \newcommand{\sectionA}[1]{\newcommand{\putsectionA}{#1}}   and then asks the user to put 15 questions as an argument to \sectionA. I'd much rather have those questions be the contents of an environment, like so:  \begin{sectionA} lots of questions \end{sectionA}   Mostly because I find it much easier to keep track of environment declarations than curly brackets. Is it possible to have the contents of an environment get packaged up into a macro?  Edit:  The solution would seem to be to us the environ package, but it doesn't seem to be working. Here's what I'm trying:  \documentclass{article} \usepackage{environ} \NewEnviron{foo}{\edef\foot{\BODY}} \begin{document} \begin{foo}   Store This \end{foo} \foot \end{document}   However when running this code \foot remains undefined. It actually seems impossible to define any macro using environ. Even when not using \BODY. For example, replacing the definition above with  \NewEnviron{foo}{\newcommand{\foot}{Print me}}   still fails. I've also tried \Collect@Body from the environ package with similar results. Does \NewEnvrion somehow prohibit defining new commands?


I timed both range() and xrange() expecting range() to be faster. But I got surprising results.  $ python -m timeit 'for i in range(1000000):' ' pass' 10 loops, best of 3: 39.9 msec per loop $ python -m timeit 'for i in xrange(1000000):' ' pass' 10 loops, best of 3: 20.2 msec per loop   If I'm not mistaken, range() stores the whole list in memory while xrange() lazily evaluates the list.  So shouldn't accessing elements from the already generated list be faster than lazily evaluating the list and getting required elements? I don't get it.


Canonical Correlation analysis without raw data (algebra of CCA)

I want to run a Canonical Correlation (in R) but I don't have the original (raw) data. I have only the correlation matrix of all the variables.  I have seen some questions here about this, but my question continue unsolved. A user gave a parcial solution (), but I need the canonical loadings, the percentual of variance in set Y that was explained from set X, and the variables significance.  Does anyone here could help me?  P.S.: I am a new R user. I have experience only on Eviews, GRETL and SPSS (also a little bit in Stata).


Add multiple figures from a single pdf page to a List of Figures

I have inserted a pdf document using \includepdf. The document has several figures to a page that I want added to a List of Figures. Is there any way to do addtolist={} several times for the same instance of \includepdf? Any other solutions?


Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$

I came across this question:   From the comments, Joren said:     L'Hopital Rule is easiest: $\displaystyle\lim_{x\to 0}\sin x = 0$ and $\displaystyle\lim_{x\to 0} = 0$, so $\displaystyle\lim_{x\to 0}\frac{\sin x}{x} = \lim_{x\to 0}\frac{\cos x}{1} = 1$.   Which Ilya readly answered:     I'm extremely curious how will you prove then that $[\sin x]' = \cos x$   My question:  is there a way of proving that $[\sin x]' = \cos x$ without using the limit $\displaystyle\lim_{x\to 0}\frac{\sin x}{x} = 1$. Also, without using anything else $E$ such that, the proof of $E$ uses the limit or $[\sin x]' = \cos x$.    All I want is to be able to use L'Hopital in $\displaystyle\lim_{x\to 0}\frac{\sin x}{x}$. And for this, $[\sin x]'$ has to be evaluated first.    Alright... the definition that some requested.   Def of sine and cosine: Have a unit circumference in the center of cartesian coordinates. Take a dot that belongs to the circumference. Your dot is $(x, y)$. It relates to the angle this way: $(\cos\theta, \sin\theta)$, such that if $\theta = 0$ then your dot is $(1, 0)$.  Basically, its a geometrical one. Feel free to use trigonometric identities as you want. They are all provable from geometry.


Plotting a function with singularities in TikZ/pfgplots

Essentially I want to plot a function with singularities like   $\frac{1}{(x-0.5)^2+(y-0.5)^2}\cdot \frac{1}{(x+0.5)^2+(y+0.5)^2}$    at a higher sampling rate.  I tried to avoid the singularities by capping with some value ($20$):  \begin{tikzpicture} \begin{axis}[view={55}{45}] \addplot3[surf, colormap/jet, samples=50, domain=-1:1] {min(1/((x-0.5)^2+(y-0.5)^2)* 1/((x+0.5)^2+(y+0.5)^2),20)}; \end{axis} \end{tikzpicture}   Which yields    But that really does not stop TikZ/pfgplots from having to evaluate the function near its singularities, so it gets quite slow at compiling. So here is my question:  Is there a better/faster way to plot functions that contain singularities? Or do i have to precompute the data and give it to TikZ/pfgplots manually?


Why is $\lim\limits_{n\to\infty}\frac{3e^n}{n!}=0$?  $e^n=e\cdot e\cdots e$, $n$-times. I tried to find  a constant $C>0$ and a $N\in \mathbb{N}$ such that $\frac{3e^n}{n!}\le C\frac{e}{n}$ for $n\ge N$, to apply the squeezing lemma afterwards. But I don't know how to estimate the fraction $\frac{3e^n}{n!}$, how can I estimate $\frac{3e^n}{n!}$ from above? Thank you.


Proving $\{a+b\sqrt{-7}, a,b\in\frac{\mathbb{Z}}{2}\}$ is a euclidean domain

I am having a bit of difficulty showing that the set $A=\{a+b\sqrt{-7},a,b\in\mathbb{Z}/2\}$ (i.e. using integers+half integers) is a euclidean domain.  I see how a lot of the proofs work, like for $\mathbb{Z}[i]$ and $\mathbb{Z}[\sqrt{-2}]$.  However, I am a bit confused, as it seems that the trick that happens doesn't work for me.  In those proofs, you show that some remainder $r$ and elements $z,w$ such that $z=qw+r$.  With this, you can show that $N(r)\leq\frac{3}{4}N(z)$.  I am not getting this $\frac{3}{4}$, I am getting $\frac{8}{4}$, or just some constant that isn't less than 1.  Furthermore, I've looked at some of the other posts when your $d=1$mod$4$, but it looks like they're using the same norm, so I don't know.  Here's my work: Let the norm of an element in $A$ be $N(a+b\sqrt{-7})=4(a^2+7b^2).$ Now I am not entirely sure about multiplying this by 4, but it seems that the norm function has to map into $\mathbb{N}\cup{0}$, so in order to guarantee that this happens I need the 4 to account for the half integers being squared (does it matter that $\mathbb{N}$ has a bijection with $\frac{\mathbb{N}}{4}$?  Let $z,w\in A$.  Then there are real numbers $c,d$ such that $\frac{w}{z}=c+d\sqrt{-7}$.  Let $q_1,q_2\in\frac{\mathbb{Z}}{2}$ be the closest elements to $c,d$ respectively.  Then we have $|q_1-c|\leq\frac{1}{4}$ and $|q_2-d|\leq\frac{1}{4}$.  Setting $q=q_1+q_2\sqrt{-7}$ and $r=\frac{w}{z}-q$, so $w=qz+rz$.  Now it remains to show that $N(rz)=N(r)N(z)\leq N(z)$, and this is where my problem is.  For $N(r)$, my first question is why in the world can I even apply the norm to $r$ since it must not even belong to my set $A$.  Ignoring that technicality, we have that $r=(q_1-c)+(q_2-d)\sqrt{-7}$, so $N(r)=4[|q_1-c|^2+7|q_2-d|]\leq 4[(1/4)^2+7(1/4)^2=2.$  If my 4 from the norm wasn't part of my norm function, then I would be good to go, but I've explained why I'm not sure that works.  Can someone help me figure out where I'm going wrong?  Thanks.


changing a value inside a Map also change it on another Map

Edit : Question marked as duplicate, but the duplicated post is not helping me fixing this issue. How can I modify the value of the map2 without changing the one from map1 ? (  ) I have 2 maps. The first one can be considered as a "Source of truth" that is initialized at loading of the page. I want to duplicate the content of the first map into a second one. So all my changes will be applied to the second map, and I will use my first one if I want to revert my changes. But duplicating a map is the cause of a weird bug that change the content of the first map when the second one is changed.   var map1 = new Map() var map2 = new Map()  map1.set('1', 'one') map1.set('2', {alpha:"NOT",beta:"MODIFIED"}) map1.set('3', 'three')      // Duplicate the content of the first map into the second one // map2 = new Map(map1) //<-- this is probably because of that assignment       var x = map2.get('2') x.alpha = "why???" x.beta = "how???" //Why does the value of the map change when I edit the 'x' variable ? // map2.set('2', x); is not required ?  console.log("MAP1 : " + JSON.stringify(map1.get('2'))) console.log("MAP2 : " + JSON.stringify(map2.get('2')))    But the snippet blow work well and won't modify the value of the first map (but I can't modify only a part of the content inside map2 with this method)   var map1 = new Map() var map2 = new Map()  map1.set('1', 'one') map1.set('2', {alpha:"NOT",beta:"MODIFIED"}) map1.set('3', 'three')      // Duplicate the content of the first map into the second one // map2 = new Map(map1) //<-- this is probably because of that assignment       map2.set('2', {alpha:'but this', beta:'work ???'})  console.log("MAP1 : " + JSON.stringify(map1.get('2'))) console.log("MAP2 : " + JSON.stringify(map2.get('2')))    What is happening ?


Has anyone has managed to install the iBurst USB drivers? I went through the steps and when I want to start the connection I get the following error:  Plugin rp-pppoe.so loaded. /usr/sbin/pppd: in file /etc/ppp/peers/dsl-provider: unrecognized option ''


Partial Derivatives : Show that $\frac{∂x}{∂y}\frac{∂y}{∂z}\frac{∂z}{∂x}=-1$

Let $f : \mathbb{R}^3 \rightarrow \mathbb{R}$. How can i show that       If $f(x,y,z)=0$ then $$\frac{∂x}{∂y}\frac{∂y}{∂z}\frac{∂z}{∂x}=-1 $$   Any help will be appreciated.


Looking for missing files in a directory of files via wildcard inputs

I currently have a directory with 100 files of 4 types, for a total of 400 files. I would like to find which ones are missing. My current script is:  for((i=1; i<=100; i++)); do name="File_Type_1_${i}.RData";  [[ ! -e "$name" ]] && echo "missing $name"; done  for((i=1; i<=100; i++)); do name="File_Type_2_${i}.RData";  [[ ! -e "$name" ]] && echo "missing $name"; done  for((i=1; i<=100; i++)); do name="File_Type_3_${i}.RData";  [[ ! -e "$name" ]] && echo "missing $name"; done  for((i=1; i<=100; i++)); do name="File_Type_4_${i}.RData";  [[ ! -e "$name" ]] && echo "missing $name"; done   which is annoying to have to run 4 times. Is there a way to run everything at once? The


$ KC $ spaces imply $ US $ spaces , but vise versa is false.

In the $ US $ space , each convergent sequence has unique limit.      In the $ KC $ space , every compact subset is closed.      It easy to show that $ KC $ spaces imply $ US $ spaces.   The example below show that $ US $ spaces do not imply $ KC $ spaces.      Let $ X = [ 0, 1 ] $ with the the usual topology and attach  a new point z whose neighborhood are open dense subsets of $ [ 0,1 ]$. Observe $ [ 0,1 ]$ is a compact non-closed  of $X$ and then $X$ is not a $KC$ space. However no sequence in $ [ 0,1 ]$ converge to $z$ and in particular  all convergent in $X$ have unique limits.   can you give me more details?   Why $X$ is not closed? Why no sequence in $ [ 0,1 ]$ converges to $z$ and in particular all convergent sequences in $X$ have unique limits ?


Can I install both RTX 2080 ti and GTX 1080 ti on same machine

I have a spare 1080 ti GPU, can i install it along with RTX 2080 ti on the same machine? Will it be effective in rendering?


choose the elements from a set to form a group

let $p$ and $q$ be distinct primes. supose $H$ is a proper subset of integers and $H$ is a group under addition that contains exactly $3$ elements from $[p,p+q,pq,q^p,p^q]$. we have to choose any 3 such that it forms a group under addition. i honestly don't know where to start. firstly for addition identity $0$ is not in the set.     Also $<p,q>$=$1.Z$ so each element is in $H$??


Hello,  So recently I dual-booted my Windows system with Ubuntu, then I decided remove Windows and install Ubuntu 14.04.  Before that, I'm using Windows 7 and upgraded to Windows 8. I have a Toshiba laptop, which is by pressing 0 when booting will lead you into Factory Restore.  In Ubuntu installation options, I choose Replace Windows 7 With Ubuntu, then all my Windows files removed.  Today, I decided to go back to Windows 7 by using the Factory Restore, but when I pressed 0 button, it boot straight to Ubuntu/Grub. I have no idea, is my Factory Restore partition got wiped out by Ubuntu installation?  Please help, thanks in advance.


How to agree verb with has and will in same sentence?

The sentence is-  The management has never and will never close the door to negotiations.  Textbooks says closed should be use instead of close.  I am confused as it sounds strange to ears.  Which one is grammatically correct?


How can I send mail from an iPhone application

I want to send an email from my iPhone application. I have heard that the iOS SDK doesn't have an email API. I don't want to use the following code because it will exit my application:  NSString *url = [NSString stringWithString: @"mailto:foo@example.com?cc=bar@example.com&subject=Greetings%20from%20Cupertino!&body=Wish%20you%20were%20here!"]; [[UIApplication sharedApplication] openURL: [NSURL URLWithString: url]];   So how can I send an email from my app?


What is a valid use case for an "execute only" file permission?

I was reading up on chmod and its .  I saw that 1 is execute only.  What is a valid use case for an execute only permission?  To execute a file, one typically would want read and execute permission.  $ echo 'echo foo' > say_foo $ chmod 100 ./say_foo $ ./say_foo bash: ./say_foo: Permission denied $ chmod 500 ./say_foo $ ./say_foo foo


Matching multiple occurrences with regex

I'm building an extractor in Graylog to pull tac_plus syslog data.  I have a log:  <70>Oct 13 10:10:05 auth tac_plus[17354]: 2015-10-13 10:10:05 -0500#01110.10.89.1#011jmartinez#011tty132#01110.10.1.27#011stop#011task_id=146#011timezone=CDT#011service=shell#011start_time=1444747732#011priv-lvl=15#011cmd=show running-config <cr>   I want to extract the indvidual statements between the #011 markers. I was able to get the first section, the IP with:  (?<=#011)(.*?)(?=#011)   Now I want to extract the 'jmartinez'. I'm trying:  #011.*?#011(.*)(#011)   but it matches:  jmartinez#011tty132#01110.10.1.27#011stop#011task_id=146#011timezone=CDT#011service=shell#011start_time=1444747732#011priv-lvl=15   if i do:  #011.*?#011(.*)(#011tty)   it seems to work but i'd rather it not rely on seeing #011tty because it might be something else in another message.  what about the next one? how can I extract tty132, 10.10.1.27, stop, task_id=146, etc  any help would be greatly appreciated!


To which level can an antecedent of "which" be a phrasal noun? Can an entire clause be the antecedent?

I see many answers on the antecedent of "which", but not with this level of detail. In this sentence:  The values of MAE and RMSE obtained for the validation phase are similar, which confirms the method is robust.  Is the sentence correct? If yes, is the phrasal noun the entire first clause "Values of MAE and RMSE obtained for the validation phase are similar"? Or is the meaning of "which" more like "which fact", with "fact" understood? Basically: To which level can an antecedent of "which" be a phrasal noun (i.e. a set of more words)?


If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?

Let $f:[0,\infty)\to [0,\infty)$ be a continuous function such that $\displaystyle \int_0^{\infty}f(t)\,dt<\infty$. Which of the following statements are true ?   (A) The sequence $\{f(n)\}$ is bounded.  (B) $f(n)\to 0$ as $n \to \infty$.  (C) The series $\displaystyle \sum f(n)$ is convergent.  I am unable to prove directly but I am thinking about the function $f(x)=\frac{1}{1+x^2}$. For this function all options are correct. Is it correct ? I think not , as I have no proof in general.  Please help by giving a proof or disprove the statements.


Past Perfect or Past Simple in the sentence where there are two events

which option is correct in the following sentence?     I ___ for my exam all morning so I was really upset when I didn't do   well.      a) revised      b) had revised   I would say that both options make sense. How can I understand whether I have to use past perfect (which I use for a sequence of events which happened in the past, therefore I had revised for my exam and I was really upset) or past simple (which I use for something that happened in the past, therefore I revised for my exam...) in such cases?  Does that so (so I was...) in the sentence make me somehow understand that I should opt for past simple, which claims to be the correct answer?  Thank you for your attention!


How hot is it in Italy on June? Can I wear tank tops and short pants? Please consider that I'm from South East Asia with very hot weather.  These are the places where I'm going:   Pisa Cinque Terre Florence Venice Rome   I checked the weather online but not really sure on how it feels like.


How do you read/write a Map, specifically a LinkedHashMap, from/to a text file? I've tried to use the Iterable interface, but that doesn't work because i have Map and Iterable can only take one argument.   Map code:  Map<String, String> m1 = new LinkedHashMap<String, String>(16, 0.75f, true);  m1.put("John Smith", "555-555-5555"); m1.put("Jane Smith", "444-444-4444");   I know I have to create a PrintWriter + BufferedWriter/PrintReader + BufferedReader objects to read/write to this text file, and then use some version of the hasNext() method to read until the file ends, I just am not sure how. Please help!  EDIT: I can't use the Serializable interface for this either, because I'm trying to write a Map to the text file, not individual entries, and there's no indexOf() method for Maps.


why n>=30 for central limit theorem to hold?

From population choosing samples(size n=30) and calculate its mean then repeating it N times will converge to normal distribution as N->inf when mean of each sample is plotted as a histogram. From my understanding as size of n increase normal distribution will have smaller standard deviation, this makes sense because using larger sample size will be better at estimating population mean than smaller sample. is my understanding correct? edit: for clarification I am referring to n,N as follows:  n = number of data in a sample N = number of time sample(of size n) is sampled


What are good software-solutions in recovering deleted files in Ubuntu on ext3-/ext4- and ntfs-filesystems?  I've been looking for diverse programs, but I couldn't find good ones so far.  TIA


Toroid with variable current and Ampere's Law

Say you have a current $I(t)$ (notice the time dependence) flowing through a Toroid with $N$ total loops and all the usual approximations: $(b-a) \ll r,\; B=0$ outside.   (source: )    You are asked to calculate the magnetic field $B$. Could you apply Ampere's Law to obtain the familiar form of $B$ found for example ?:  $$B~=~\frac{\mu N I}{2\Pi r}.$$


It is given a continuous function $f$ on $[0,1]$. Assuming that $$\int_{0}^{1} x^n f(x) \ dx = 0$$ for every $n\in\mathbb{N}$, how to prove that $f(x) = 0$ on $[0,1]$?


Can a unemployed student who is not working used his guardian's or parents' bank statement from his own country or the unemployed student must have his or her own bank statement? Even when the sponsor who lives in UK will sponsor the trip?


I had Windows 10 Home (it was preinstalled on my notebook), but I needed Hyper-V to try something, so I found university which has a CD key for Windows 10 Student version on their website and I used it.  Everything worked fine for a few hours, but now I get the well known message to activate Windows. I now understand that I can't use the education version from a different college, but it's a little bit too late.  Is there any way I can restore my old serial key? It's not anywhere in my box from notebook.


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


rmod iwlagn error message (it is not loaded)?

I'm trying to fix my slow wifi connection and when I typed  the command I got an error message.  rmmod iwlagn: rmmod: ERROR: Module iwlagn is not currently loaded


Adding a variable in multiple regression - interpretation?

Suppose that I try to explain $Y$ with $X_1$ and run a simple regression $y_i = \beta_0 + \beta_1x_{1,i}+e_i$. The result is that $\beta_1$ is not significant, so we conclude that $X_1$ does not explain $Y$.  Then I add another independent variable, $X_2$, in the regression. This time, $\beta_1$ is significant but $\beta_2$ is not(!). Is this kind of a situation possible or perhaps have I made a mistake? If it is possible, what is the interpretation? What could explain the observation that $X_1$ alone does not explain $Y$, but with an additional variable $X_2$, $X_1$ becomes meaningful, yet $X_2$ itself is not explaining $Y$?


Weird pointer-to-something template parameter

I found this snippet online  union U { int a; int b; }; template<int U::*> void f();          ^^^^^^^^   I had never seen int U::* as a template parameter, what does it mean?


Prove that $43^{101}+23^{101}$ is divisible by $66$ using modular arithmetic

Prove that $43^{101}+23^{101}$ is divisible by 66. I was able to find it to be divisible by 22 but not by 66. Please help


Show formatted decimal rounding to specific amount of digits

I'm working with .net core, and I having some issues formatting one number.  I have a decimal like this   decimal d = 362250;   And i want to show it rounded to 4 digits   3623    I was reading both  and  but i wans't be able to do it  I try :  Console.WriteLine($"{d:####}"); //show 362250 Console.WriteLine($"{d:####,}"); //show 362   How can i achieve that?  I know its so simple, but I fighting with it for 2 hours!


File extensions and association with programs in linux

In windows we can associate a file's extension with programs. E.g. a file test.pl can be run by the installed Perl interpreter due to the pl extension. In linux though it needs #!/usr/bin/perl as the first line. Is this because there is no association between file extensions and programs in Linux?


Why does the billiard multiprocessing module require the "if __name__=='__main__'" line?

If I have the following code:  def f():     print 'ok!'     import sys     sys.exit()  if __name__=='__main__':     import billiard     billiard.forking_enable(0)     p = billiard.Process( target=f)     p.start()     while p.is_alive():         pass   The script behaves as expected, printing "ok!" and ending. But if I omit the if __name__=='__main__': line and de-indent the following lines, my machine (OS X) goes crazy, continually spawning tons of Python processes until I killall Python. Any idea what's going on here?  (To those marking this as a duplicate, note that while the other question asks the purpose of  if __name__=='__main__' generally, I'm specifically asking why failure to use it here causes dramatically unexpected behaviour)


jquery function does not work after creating an element

I want to add a function after I create an input element. but it didn't work. this is my code.
      <input type="button" onclick="add();" value="Add Template"/>
     Photo: <input type="file" id="chooseFiles" name="photo[]"  class="inputFile">

         the existing input works. but after createElement, function add() doesn't work..


What situations in classical physics are non-deterministic?

In Sean Carroll's book "The Big Picture," he states ():      Classical mechanics, the system of equations studied by Newton and   Laplace, isn't perfectly deterministic. There are examples of cases where a unique outcome cannot be predicted from the current state of the system. This doesn't bother most people, since cases like this are extremely rare—they are essentially infinitely unlikely among the set of all possible things a system could be doing. They are artificial and fun to think about, but not of great import to what happens in the messy world around us.   What are some of these situations he is referring to?   My first guess was something like the conceptual equivalent of a ball sitting exactly atop a hill and asking which direction it will roll. But that doesn't seem right—this would be a case where the "true" solution is that the ball wouldn't roll at all, while in reality there will always be tiny disturbances that cause the ball to roll in some direction. I don't think this is what Carroll is referring to. He seems to suggest that the "true, exact mathematical outcome" is not uniquely determined for certain classical systems.  I've heard that uniqueness theorems for solutions to differential equations don't generally apply to non-linear equations, and wonder if this may have something to do with it. Elucidation and examples would be much appreciated.


Different ways to tackle the integral $\int_0^1\sqrt\frac x{1-x}\,dx$

$$\int_0^1\sqrt\frac x{1-x}\,dx$$ I saw in my book that the solution is $x=\cos^2u$ and $dx=-2\cos u\sin u\ du$. I would like to see different approaches, can you provide them?


Why do I see router and not my real IIS?

I am trying to access IIS through web but unable to do so. Basically I have a router (which functions as router and modem) that is given by ISP and I have another router connected to the router given by ISP. My ISP's router can be visited through 192.168.0.1 and the router that I connected to ISP's router can be visited through 192.168.1.1  Please see my ISP's router:    As you can see I have DMZ enabled for my router of 192.168.1.1  Now please see my router of 192.168.1.1:    As you can see I added a virtual server for port 80 where 192.168.1.125 is my private IP.  I rebooted both of my modems an tried to visit my IP from:   and after doing so, when I type my live IP I still see my router of 192.168.0.1 instead of my IIS. What am I missing?  Note: I have disabled Firewall on both of the routers.  Any help would be appreciated.  EDIT:  When I go to WAN in ASUS I see this:    Does that help?


If $A \in M(n,\mathbb{C})$ with $A^2 =A$ , then $rk(A)= tr(A)$ . Is it true if yes then how can anyone explain?


I was working on a small Integration problem, where i was needed to solve another integral:  $$I= \int_0^{\pi} \frac{1}{1+\cos^2x} dx $$  Working:  $$\int_0^{\pi} \frac{1}{1+\cos^2x} dx=\int_0^{\pi} \frac{\sec^2x}{\sec^2x+1} dx$$ $$=\int_0^{\pi} \frac{\sec^2x}{2+\tan^2x} dx$$  Substituting, $\tan x=t, \sec^2x dx=dt$  $$\implies \frac{\sec^2x}{2+\tan^2x}dx=\frac{dt}{2+t^2}$$ which gives us $$I= \left[       \begin{array}{cc|c}{\frac{1}{\sqrt2}\tan^{-1}\frac{\tan x}{\sqrt2}}       \end{array}     \right]_0^\pi$$ I think the answer should be zero. After seeing the answer at , i think i am doing a serious mistake. Ay help will be appreciated.


Adding Google star Rating to the search Result

I need to add star rating to my site for showing the star image rating in search results. I did a search on the internet and read a few articles on it. It is basically Microformats and the related tags. I'm still confused about the review. What if I need to use the tripadvisor review and rating on the search results. How can I do that or can anybody tell me about the code that I need to put in to my pages. I'm sorry for not being sound to this question.


Reference to a figure uses the section's number

One of my sections seems to be using the section number rather than the appropriate figure number for \ref's that point to figures. (Theorems and the like work fine.) As far as I can tell, there's nothing differentiating the problematic section from the other sections, but there must be as the problem doesn't go away when I compile that section on its own. Any ideas?  Edit: an example of a broken figure. (Every figure in the section is broken.)  \begin{example}   Figure~\ref{fig: hasse} depicts ... \begin{figure}[htbp]\label{fig: hasse} \begin{center} \begin{tikzpicture}     \tikzstyle{every node}=[draw,circle,fill=black,minimum size=4pt,                             inner sep=0pt]     [bunch of lines for the picture]     \end{tikzpicture} \caption{Hasse diagram} \end{center} \end{figure} \end{example}   This particular instance had the figure inside the example, but that doesn't make a difference.


A free book/resource for learning genetics?

I took an undergrad class in genetics. I felt it was not too intensive and I do not feel prepared for grad school (if I can manage to get in.)   Does anyone know of a preferably free resource for learning genetics?   I know the field is very large, but I would like to be competent in the field, considering I also want to learn more about genomics as well. And I figure one must first have a fundamental understanding of either computer science or biology to be successful in genomics, both of which I lack.


Prove that $1+r+r^{2}+...+r^{n-1}=\frac{r^{n}-1}{r-1}$, $r$ a positive integer, $r \neq 1$


Can someone let me know how/if possible to append “.log” to the end of the file when using logging.timedrotatingfilehandler? By default, when rotating happens, logging module append the date in format %Y-%m-%d_%H-%M-%S at the and of the file, but I want to append .log at the end.


The other day, my family chose to make something akin to "roast beef" for the holidays. Since most markets were closed, we found a small shop which sold a limited selection of beef cuts. The one we eventually picked up was labeled "Bottom Round Roast". Needless to say, upon roasting it, it didn't exactly turn out as planned. While the end-product was quite juicy and flavorful, it was also also uncomfortably tough. Since this isn't a cut we've used before, I'm curious to know if anyone can help us troubleshoot.  Here's how it was cooked:   Salted about 2 hours in advance Roasted--mid-rack--in a conventional oven at 225 degrees Removed from the oven when a thermopen read about 125-130 degrees F, and rested for 20 minutes. Finished stovetop in butter and thyme, about 45 seconds to a minute per side, until a thermopen confirmed the middle was medium rare. Sliced against the grain--visibly medium rare.   Does this cut simply need more time? Clearly it doesn't behave like a prime rib. Any tips for next time?


How to use a gerund with 'my' in a sentence?

I am trying to say, "this led to my working as a research assistant with ...". I think something's awry in this phrase. Am I right?


What is $$\sum_{n=1}^\infty\frac{1}{n^2+1}$$ I know that  $\sum_{n=1}^\infty\frac1{n^2}=\frac{\pi^2}6$ but what about if we add a one to it in the denominator, can we still figure it out?


Let $x \in \mathbb{N}$ and let $p$ be a prime divisor of $x^4+x^3+x^2+x+1$, prove that $p = 5$ or $p \equiv 1 \mod{5}$   Note that $(x^4+x^3+x^2+x+1)(x-1) = x^5 - 1$.  I tried reducing the equation $\mod{5}$, which gave me some information on $x$, but I was not able to utilize this information.


What are the situations where Kirchoff laws cease to be valid? How we can create circuits based on lumped element discipline, and that can work in real life? We take ideal conditions, but they just are not like that in real life.


I am unable to pick a nickname for my trainer. When I use names like Ash, Millby, or anything else, the game says that it is not availible. What should my nickname be then?


Proving the general limit $\lim_{n\to\infty} \frac{an+c}{bn+d} = \frac{a}{b}$

I'm trying to prove the general      $$ \lim_{n\to\infty} \frac{an+c}{bn+d} = \frac{a}{b} $$   using the definition of the limit of a sequence, for any $\varepsilon > 0 \,\, \exists N \in \mathbb{N}$ s.t. for every $n \geq N$ $|a_n - a| < \varepsilon$. My (not so valiant) efforts:  \begin{align*}  \left| \frac{an+c}{bn+d} - \frac{a}{b} \right| &< \varepsilon \\ \left| \frac{abn + bc - abn - ad}{b^2n+bd} \right| &< \varepsilon \\ \left| \frac{bc-ad}{bn+d} \right| &< \varepsilon \left| b \right| \\ \left| bn+d \right| &> \left| \frac{bc - ad}{\varepsilon b} \right| \\ \left| bn+d \right| &> \left| \frac{c}{\varepsilon} - \frac{ad}{\varepsilon b} \right| \end{align*}  I'm used to being able to manipulate constants or remove absolute values when solving these kinds of problems, but with general constants I'm not sure what to do next.


Insert Login IP Ranges using apex in salesforce

Is it possible to insert to Login IP ranges via apex?


I've known that the possessive case of the proper noun ending in "-s" such as "James" is formed by adding just "an apostrophe" or "an apostrophe and -s". Is it right? Then what's the possesive case of "Mars"? Mars'    and     Mars's Are they both "grammatically" correct?


Counting Principles. Selecting, while having constants

A committee of five people is to be selected from a class of 12 boys and 9 girls. How many such committees include at least one girl? Can't find the right method on other forums.


Can you suggest me some problem solving books for quantum mechanics ;that will help me develop more physical intuition along with mathematical reasoning.


I came across this question in some extracurricular problem sets my professor gave me: what is the closed form notation for the following sum:  $$S_n = 1\cdot1!+2\cdot2!+ ...+n \cdot n!$$  I tried computing some terms, and the only "vague" thing I noticed was that maybe I should be subtracting a term, but I'm really not sure. I went around looking on StackExchange's archives for a closed form of $S_n = 1!+2!+ ...+ n!$ but that didn't help me with my problem much.   Any pointers?


Is the kernel of a map to a finitely presented module finitely generated?

Let $R$ be a ring (unital, not necessarily commutative), $M$ a finitely presented left $R$ module. Suppose $m_1,\ldots,m_n\in M$ generate $M$. This determines a surjection $f:R^n\to M$.     Must the kernel of $f$ be finitely generated?   This is true by definition if the generating set $m_1,\ldots,m_n$ is the one coming from the finite presentation of $M$.


How do I set preferences for the Guake Terminal?

Just installed guake - terminal emulator.  How can I get to preferences to customize it?  I don't seem to have any if the normal menu's available.  I searched everything on their help site to no avail.  I use Ubuntu 11 (now Ubuntu 16 in 2016)


Can I get System Variable path to read/write xml to?

I want to use a path set in my system variable to read/write data to.  System variable is called "LUCTEST" and has value "C:\Users\Luc" XML is in C:/Users/Luc/test.xml  My code does read the XML OK, but how does it know to choose the test.xml??  Can I specify exactly what the xml should be called if there are multiple in "C:\Users\Luc"  Below is my current code:     private void Form1_Load(object sender, EventArgs e)     {         string path = Environment.GetEnvironmentVariable("LUCTEST",EnvironmentVariableTarget.Machine);         if (File.Exists(path))             App.Phonebook.ReadXml(path);         phonebookBindingSource.DataSource = App.Phonebook;         panel1.Enabled = false;     }


How to integrate $\int_0^{2\pi} \frac{1}{(k\cos\theta + 1)^2} d\theta$

I have the following identity in a derivation I'm trying to understand:  $\int_0^{2\pi} \frac{1}{(k\cos\theta + 1)^2} d\theta = \frac{2\pi}{(1-k^2)^\frac{3}{2}}$  and I cannot see how this is true.  I'm sure it is - I just can't figure out how to integrate the LHS.  I've tried using tangent half-angle substitution, and although that gave me something I could integrate, the definite integral ended up being $0 - 0 = 0$, which wasn't entirely helpful...  Can anyone help?


How can I turn a creature with Su and Ex abilties into armour that grants those abilities?

Could someone describe to me a method for changing a corporeal creature with Supernatural and Extraordinary racial abilities into a set of armor that would grant those same racial abilities to the wearer?  Neither the setting, nor the magic, nor crafting matter so long as it is not built from an inherited template, as I am trying to achieve something unique to happen in game.  I am imagining that it would work similarly to Fusion Spell for Psionics.  I am the DM for one scenario and would be a player for another.    DM PoV  I need to create a villain whose in game & story abilities can be defeated by destroying different sections of the armor, which can cost any amount but not be made of a material that is so unbreakable that it could not be destroyed. The details would be tailored to whatever they are wearing.  I'm designing an NPCs as if he were originally a Player Character. In terms of Su & Ex abilities, armor that grants the wearer Mountain Walk or Awesome Beauty, or something more random is what my concept needs.  This isn't about focusing on the numbers or what the story would look like, I don't have strong preferences: it is about having fun.  In creating the NPC, I hope to be able to create multiple other NPCs that use different methods as part of a group the party must face.  Examples:   The villain sends some would-be adventurer to gather his materials for him or A hero decides to join forces with a dying whachamacallit.   Notes:   Rough Cost Estimate: equivalent to the party's current collective fortune of 900,000 gp. Armor quality would be masterwork. The current party is equivalent to a level 20 party.   Player Character POV  Meanwhile from a player character's PoV, this character benefits others by creating that  sort of armor during the main campaign.


I installed Ubuntu 12.10. Is django installed by default on my Ubuntu? If not, how can I install it?


Why does removing the intercept in my categorical GLM result in the same model?

I'm trying to understand what is going on when I remove the intercept in my model using y ~ x + 0  Why do these models have the same predicted values despite one not having the intercept?  glm1 <- glm(Survived ~ Pclass + Sex + Age, family = binomial(link = "logit"), data = titanic_train) glm2 <- glm(Survived ~ 0 + Pclass + Sex + Age, family = binomial(link = "logit"), data = titanic_train)  > summary(glm1)  Call: glm(formula = Survived ~ Pclass + Sex + Age, family = binomial(link = "logit"),      data = titanic_train)  Deviance Residuals:      Min       1Q   Median       3Q      Max   -2.7270  -0.6799  -0.3947   0.6483   2.4668    Coefficients:              Estimate Std. Error z value Pr(>|z|)     (Intercept)  5.056006   0.502128  10.069  < 2e-16 *** Pclass      -1.288545   0.139259  -9.253  < 2e-16 *** Sexmale     -2.522131   0.207283 -12.168  < 2e-16 *** Age         -0.036929   0.007628  -4.841 1.29e-06 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for binomial family taken to be 1)      Null deviance: 964.52  on 713  degrees of freedom Residual deviance: 647.29  on 710  degrees of freedom   (177 observations deleted due to missingness) AIC: 655.29  Number of Fisher Scoring iterations: 5  > summary(glm2)  Call: glm(formula = Survived ~ 0 + Pclass + Sex + Age, family = binomial(link = "logit"),      data = titanic_train)  Deviance Residuals:      Min       1Q   Median       3Q      Max   -2.7270  -0.6799  -0.3947   0.6483   2.4668    Coefficients:            Estimate Std. Error z value Pr(>|z|)     Pclass    -1.288545   0.139259  -9.253  < 2e-16 *** Sexfemale  5.056006   0.502128  10.069  < 2e-16 *** Sexmale    2.533875   0.456247   5.554 2.80e-08 *** Age       -0.036929   0.007628  -4.841 1.29e-06 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for binomial family taken to be 1)      Null deviance: 989.81  on 714  degrees of freedom Residual deviance: 647.29  on 710  degrees of freedom   (177 observations deleted due to missingness) AIC: 655.29  Number of Fisher Scoring iterations: 5   And a summary of the resulting predictions:  > summary(predict.glm(glm1, newdata = titanic_test))    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's  -3.5660 -1.9688 -0.5642 -0.3827  0.7782  3.1027      86  > summary(predict.glm(glm2, newdata = titanic_test))    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's  -3.5660 -1.9688 -0.5642 -0.3827  0.7782  3.1027      86   if it simply reparamartarizes the model is there any advantage to having the intercept term or can I safely use the second model for increased interpretability?


Why does Stack Overflow only allow one @User per comment?  This restriction lead me to a non-comment like :     @MiMo - seem my previous comment (Only one @ user per comment)   Which left me wondering why Stack Overflow is blocking me from notifying two users of a response.  I am sure there is a reason for this, can some one share it with me?


//Shows automatically the width and height from images                 $(document).ready(function () {                     //Select all the images on the page                     var img = $("#resultsFromSearch3").find('.oa-panels-col-33').find('img');                     //For every image the code below will run                      $(img).each(function() {                         //The code below select the p that belongs to the image.                          var description = $(this).closest('.oa-panels-row').find('.views-field-file-field-oa-body-value .field-content p:last-child');                         //Create a new img element with the src of the orinial image.                          $("").attr("src",$(this).attr('src')).load(function () {                             //Print the width and height, of this clone image, in the description of the orinial image.                              description.after(''+'Width=' + '' +  this.width + 'px '+ '
' + ''+'Height='+''+  this.height + 'px' + '
');                         });                     });                 });   I want to display the original image size on my screen in a list. Now it shows the width en height of the thumbnails. Anyone familiar?


Why are there two different XIAOMI Stocks?

I'd like to buy Xiaomi Stocks. When I search in my Brokers List, i find two different Stocks: ISIN:US98421U1088 Symb: 3CPA & ISIN:KYG9830T1067 Symb: 3CP I figured that this is with quite a lot of Coorps so. What does it explaination for that? Which one should i buy?


How to remove duplicate id updates in batch job?

I got this error while executing my batch job     Duplicate id in list: 0062800000AqfihAAB   Here is my batch job:  Global class OpportunityStageChanges implements Database.Batchable<sObject> {  Global Database.QueryLocator start(Database.BatchableContext BC) {    //String query = 'Select id,Amount, (Select OldValue, NewValue From Histories) From Opportunity where stage <> NULL';    //String query  = 'Select Id, CreatedById, CreatedDate, Field, NewValue, OldValue from OpportunityFieldHistory ';      String query = 'Select Id,Name,Amount,LightiningEd__Stage_change_from_Prospecting__c,(Select ID, CreatedDate,OldValue, NewValue from Histories)from Opportunity';             return Database.getQueryLocator(query); } Global void execute(Database.BatchableContext BC, List<Opportunity> scope) {   List<Opportunity> opplist = new List<Opportunity>();   for(Opportunity opp : scope) {      for(OpportunityFieldHistory opfh : opp.Histories){           system.debug(opfh.oldValue+'----'+opfh.NewValue+'-----'+opfh.CreatedDate );           if(opfh.OldValue == 'prospecting' && opfh.NewValue == 'Qualification '|| opfh.NewValue == 'Closed Won'){                opp.LightiningEd__Stage_change_from_Prospecting__c = opfh.CreatedDate;               System.debug('Date Value' + opp.LightiningEd__Stage_change_from_Prospecting__c);               opplist.add(opp);          }             }     if(opplist.size()>0){           update(opplist);      }    }  } Global void finish(Database.BatchableContext BC) {     } }


Based on a   Does the automated jerk detector also double as an automated nice-guy detector?  I was under the impression it just blew out serial-downvotes.  What all is caught by the system?


Increase progress bar each second -- error

it's my first experience with C#, I'm trying to make a progress bar that increases each second on a value (a part of program, it receives current value from another object and sets it to the progress bar).  My simplified object source:  public delegate void LoadingProgressChanged(int percents); public event LoadingProgressChanged loadingProgressChanged;  public void Enable() {     loadingTimer = new Timer(1000);     loadingTimer.Elapsed += new ElapsedEventHandler(IncreaseLoadingPercentage);     loadingTimer.Start(); }  private void IncreaseLoadingPercentage(object source, EventArgs e) {     loadedPercents += getLoadingPercentsPerSecond();     loadingProgressChanged(loadedPercents); }   Form sources: In constructor  router.loadingProgressChanged += new AbstractRouter.LoadingProgressChanged(percentageChanged);   Body of percentageChanged  public void percentageChanged(int percs) {     progressBar1.Value = percs; }   And I get error     An exception of type 'System.InvalidOperationException' occurred in   System.Windows.Forms.dll but was not handled in user code      Additional information: Cross-thread operation not valid: Control   'progressBar1' accessed from a thread other than the thread it was   created on.      If there is a handler for this exception, the program may be safely   continued.   I understand why it happens: it seems that percentageChanged form is called in timer thread. But how to implement it correctly? Thanks!


Get 'TerminalServicesHomeDirectory', 'TerminalServicesHomeDrive' properties using DirectorySearcher

I have a c# .NET 3.5 application which retrieves various user properties. Out of them 'TerminalServicesHomeDirectory', 'TerminalServicesHomeDrive' are 2 properties I need to fetch. On the DirectorySearcher, if I add these 2 propertiesToLoad property and do a FindAll(), the SearchResult object does not contain these properties.   I will have to do SearchResult.GetDirectoryEntry() and from the obtained directory entry, when I do InvokeGet, I get the values.  My question is, is there a way I can get value for these properties without having to create directory entries for each SearchResult ?  Is there anything I am missing? Thanks!


Decode & restore files from /dev/md3 (Hacked server)

My not exposed MongoDB has hacked to ransom, my files stored on /home/mongo/store has deleted, i use foremost, ext4magic , extundelete , nothing is happening , backups on the same server are deleted too... I have only 1 earlier month backup, its not possible for me to announce that to my customers.  I try my last solution and cat /dev/md3 ( -> /home) and my data partialy encoded appear   Do you know how to decrypt encoded values ?  Thanks all to save me.


Mechanically Speaking, What is the Best Alignment for a Cleric?

So I for a while now I've thought that from a purely mechanical standpoint true neutral is the best alignment as a cleric; you can worship any deity because they will always be within 1 step; similarly, with aligned spells you are not restricted so long as you either worship a concept or have a true neutral deity.  Chaotic, Evil, Good, and Lawful Spells: A cleric can’t cast spells of an alignment opposed to her own or her deity’s (if she has one). Spells associated with particular alignments are indicated by the chaotic, evil, good, and lawful descriptors in their spell descriptions.   Alignment: A cleric’s alignment must be within one step of her deity’s, along either the law/chaos axis or the good/evil axis.  Well, that's more or less my own theory on it but I tend to overlook stuff in the rules quite frequently and wanted confirmation from someone more familiar with this kind of stuff than me. Out of all the alignments, what is the best one for cleric, mechanically speaking? By "best" I mean in a typical pathfinder setting which alignment offers the most benefits in most situations if you only consider the effects alignment has on a clerics mechanics and class features. This is distinct from  because  this question is about pathfinder, not including 3.5 material that question is primarily from a role-play perspective it cites things like reasoning with people which is not what I'm asking about I'm asking about clerics specifically; it barely mentions spellcasters in general and Clerics are primarily commented that their aura is more likely to raise flags than other types of spellcasters.  While I am well aware that optimization does not automatically make a good character, this question is specifically out of curiosity. I want to know if there is/what is the mechanically superior alignment is best for a Cleric.


Lowercase letter at the beginning of a question which is following another question?

I read philosophy, and a great deal of philosophical texts, including those by Nietzsche, Plato, Hume, and a great deal of others include a similar grammar that I do not understand: that an independent clause which is a question may begin with a lowercase letter if it is following another question.  Here is an example from Phaedo (by Plato):     "And is the soul in agreement with the affections of the body? [or]   is she at variance with them?   Why is it permissible to lowercase 'or'?  Unfortunately I cannot recall any specific examples of this, but I remember having the exact same question when reading Nietzsche's Genealogy of Morals.   Is there any grammatical rule sanctioning lower case letters at the beginning of questions following other questions (perhaps if that question begins with a conjunction, or is directly related to the preceding question?)?  Not that it matters, but I quite like it. It looks unique and interesting to me.


How to encrypt a text file in a portable manner based solely on a password?

I used to use openssl aes-256-cbc, but the problem I have with this is when I try to decrypt in a different version of the distro it fails, as if it depends also on some internal key or something, instead of depending solely on the password. So I have to keep a different encrypted file for each version of the distro, which is annoying and bad. Any suggestions?