I have this array declared. While you can possible tell that I'm playing with Google Maps, the contents of this array are not really important, it's just an array.  var mapData =[{"id":1,"name":"Love.Fish","address":"580 Darling Street, Rozelle, NSW","lat":-33.861034,"lng":151.171936,"type":"restaurant"},{"id":2,"name":"Young Henrys","address":"76 Wilford Street, Newtown, NSW","lat":-33.898113,"lng":151.174469,"type":"bar"},{"id":3,"name":"Hunter Gatherer","address":"Greenwood Plaza, 36 Blue St, North Sydney NSW","lat":-33.840282,"lng":151.207474,"type":"bar"},{"id":4,"name":"The Potting Shed","address":"7A, 2 Huntley Street, Alexandria, NSW","lat":-33.910751,"lng":151.194168,"type":"bar"},{"id":5,"name":"Nomad","address":"16 Foster Street, Surry Hills, NSW","lat":-33.879917,"lng":151.210449,"type":"bar"},{"id":6,"name":"Three Blue Ducks","address":"43 Macpherson Street, Bronte, NSW","lat":-33.906357,"lng":151.263763,"type":"restaurant"},{"id":7,"name":"Single Origin Roasters","address":"60-64 Reservoir Street, Surry Hills, NSW","lat":-33.881123,"lng":151.209656,"type":"restaurant"},{"id":8,"name":"Red Lantern","address":"60 Riley Street, Darlinghurst, NSW","lat":-33.874737,"lng":151.21553,"type":"restaurant"}];   Now later on, I want to get some information out of each of the objects in that array and I do so with a for in loop like so:  for(marker in mapData){     console.log(mapData[marker]); }   I understand that according to ,     for..in should not be used to iterate over an Array where index order is important.   But I don't really care about the order, so that being the case, are there any disadvantages to iterating over my array with a for in loop?

I've been told not to use for...in with arrays in JavaScript. Why not?


In my blender 2.8 version the "convert to", which is present in Search option is not there.  What should I do?

I want to convert my text object to mesh. In 2.79 it was Alt-C, are the keys changed for 2.80?    I browsed it externally and I got some thing like this image as answer..   but any shortcut-keys will be easy to work! If you know one, you can comment below.


As per maxwells distribution law the molecule of gas will have speed across zero to infinity with some probability function. I want to know that why the speed above speed of light is possible (i know that its probability will be very less i mean really less, but it would be non zero.). Doesn’t it violet Special theory of relativity?

The Maxwell-Boltzmann velocity distribution in 3D space is $$ f(v)dv = 4\pi \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 \exp\left(-\frac{m v^2}{2k_B T}\right)dv$$ It gives the probability for a single particle to have a speed in the intervall $[v,v+dv]$. But this probability is not zero for speeds $v > c $ in conflict with special relativity.  Is there a generalization of the Maxwell-Boltzmann velocity distribution which is valid also in the relativistic regime so that $f(v) = 0$ for $v>c$ ? And how can it be derived? Or can a single particle distribution simply not exist for relativistic speeds, because for high energies, we always have pair-production meaning the particle number is not conserved and a single particle distribution can not be defined in a consistent way?


While I was in edit mode I tried to extrude but accidentally pressed W instead of E and now I don't know how to turn this thing off.  It makes my cursor select everything inside the little circle, making it very hard for me to model something with many vertices.

I was editing a curve for hair, and pressed W to bring the specials menu and Subdivide it, but instead everything but the curve I had active dissapeared, and my cursor turned into a circle like the one from the circle select mode.  I'm guessing they changed the specials menu and I'm inside some unknown to me function, but I'm not sure how to turn everything back to normal.


Do I need to pay a fee or tax at the airport when leaving Malaysia to Australia?

I'm about to leave Malaysia and expect to get a much better rate for my Ringgit here in Chinatown than at the airport.  So after having paid for my plane ticket and transportation to the airport, are there going to be any surprise fees or costs between getting to the airport and departing?  (In other countries over the years there have been things such as departure taxes and airport improvement taxes that I was not expecting.)


Today I have created a new user for my wife on my Windows 10 PC. And when I launched Google Chrome, it started with launchpage.org which is known as a kind of virus that is easy to remove via Regedit. However, next, I clicked the "show desktop icons" option on the settings page, instead of showing the dialog box to choose icons I would like to pin to the desktop, it opened the "Which app would you like to open with" menu which is way weird. I can't see any sign of these ridiculous things when I switch to my own account, it only shows itself on the new account. Any idea what can it be?

What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.


Let $X \rightarrow Y$ be a finite surjective and generically one to one morphism between algebraic variety of characteristics $0$. Is it biraitonal? This question is from the answer of Jason Starr , where he asserted the answer of my question is yes. While he said that this is false in positive characteristics case. How will the counter example be like?

Let $X,Y$ be varieties over $\mathbb{C}$, $k(X), K(Y)$ be function fields of $X, Y$. Suppose $\pi: X \to Y$ is a dominant,  $\textit{injective}\ $ morphism, why the degree of the function field extension $[K(X) : K(Y)] =1$?  If $\phi : X \to  Y$ is a finite morphism, then the fibre is finite, and by semicontinuity theorem, let $n$ be the number of the points in the generic fibre, then I feel one should similarly have $[K(X) : K(Y)] =n$. But I don't know how to show that. Any suggestions or reference on this question?  $\textbf{Edit}$: I really want the morphism $\phi$ to be a morphism between locally finite type and finite morphism. To be precise, for any affine open set $U=\rm{Spec}(B) \subset Y$, there is an affine open over of $\pi^{-1}(U)$, such that each $\rm{Spec}(A_i)$ in this cover has the property $A_i$ is a finitely generated $B-$module. I don't know the corresponding definition of this sort of morphism, or is it just a finite morpism?


I have Flipkart Digiflip Pro XT911 Tab, which have old version of android like Marshmlow, Now I am looking for a way to update it to latest android version, How can I do that.  Thank you

This Community Wiki question is designed to be the "canonical question" for questions asking how to upgrade one's device to a new Android version.   I want to get a newer version of the OS for my Android device. How can I do that?  See also:


My project is to create a program which reads a number the user inputs and return relevant information corresponding to the input. I've finished my code and it compiles, but when I enter a room number it returns this error:  Exception in thread "main" java.lang.NullPointerException                at Room.setDirection(Room.java:93)                at Room.roomNumber(Room.java:29)                at Room.main(Room.java:18)   My complete program is below. I've looked at the lines corresponding to the errors but can't tell whats wrong. Any help?  import java.util.Scanner;  class artGallery {     String direction;     String title;     String artist;     String year;     String height;     String width; }  public class Room {     public static void main(String[] param)     {                artGallery room;         room = roomNumber();         System.out.println("The painting " + getDirection(room) + " is called " + getTitle(room) + " and is painted by " + getArtist(room) + ". It was painted in " + getYear(room) + " and is approximately " + getHeight(room) + "cm tall and " + getWidth(room) + "cm wide.");     }     public static artGallery roomNumber()     {         int number;         Scanner scanner = new Scanner(System.in);         System.out.println("Are you in room 1, 2 ,3 or 4?");         number = scanner.nextInt();         artGallery[] room = new artGallery[5];          room[1] = setDirection(room[1], "in front of you");         room[1] = setTitle(room[1], "The Starry Night");         room[1] = setArtist(room[1], "Vincent Willem van Gogh");         room[1] = setYear(room[1], "1889");         room[1] = setHeight(room[1], "73.7");         room[1] = setWidth(room[1], "92.1");          room[2] = setDirection(room[2], "to the left of you");         room[2] = setTitle(room[2], "The Persistence of Memory");         room[2] = setArtist(room[2], "Salvador Domingo Felipe Jacinto Dalí i Domènech");         room[2] = setYear(room[2], "1931");         room[2] = setHeight(room[2], "24");         room[2] = setWidth(room[2], "33");          room[3] = setDirection(room[3], "to the right of you");         room[3] = setTitle(room[3], "Liberty Leading the People");         room[3] = setArtist(room[3], "Ferdinand Victor Eugène Delacroix");         room[3] = setYear(room[3], "1830");         room[3] = setHeight(room[3], "260");         room[3] = setWidth(room[3], "325");          room[4] = setDirection(room[4], "above you");         room[4] = setTitle(room[4], "The Creation of Adam");         room[4] = setArtist(room[4], "Michelangelo di Lodovico Buonarroti Simoni");         room[4] = setYear(room[4], "1512");         room[4] = setHeight(room[4], "280");         room[4] = setWidth(room[4], "570");          return room[number];     }       public static String getDirection(artGallery v)     {         return v.direction;     }      public static String getTitle(artGallery v)     {         return v.title;     }      public static String getArtist(artGallery v)     {         return v.artist;     }      public static String getYear(artGallery v)     {         return v.year;     }      public static String getHeight(artGallery v)     {         return v.height;     }      public static String getWidth(artGallery v)     {         return v.width;     }      public static artGallery setDirection(artGallery v, String direction)     {         v.direction = direction;         return v;     }      public static artGallery setTitle(artGallery v, String title)     {         v.title = title;         return v;     }      public static artGallery setArtist(artGallery v, String artist)     {         v.artist = artist;         return v;     }      public static artGallery setYear(artGallery v, String year)     {         v.year = year;         return v;     }      public static artGallery setHeight(artGallery v, String height)     {         v.height = height;         return v;     }      public static artGallery setWidth(artGallery v, String width)     {         v.width = width;         return v;     } }

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


I know to install software from terminal using some sudo apt-get stuffs but I can't install utorrent by terminal. So, I download .tar.gz from their website. So please instruct me how to install .tar.gz or say the way to install it from terminal friends.

I am trying to install utorrent instead of using the torrent apps and I just came off windows seven can someone help me?


A metric space is a set M together with a function $d:M \times M \rightarrow \Bbb{R} $, where $d$ satisfies:   $d(x,y)\ge 0$ $d(x,y)=0 \Leftrightarrow x=y$ $d(x,y)=d(y,x)$ $d(x,z) \le d(x,y)+ d(y,z)$    $\forall x,y,z \in M.$  Naively it seems that $\Bbb{R}$ has too much structure than what is required of it to satisfy these axioms and $d$ could map to any ordered ring.  So my question is why is $\Bbb{R}$ chosen and not a more general ring? Has there been any research on metrics that map to sets other than $\Bbb{R}$?  I have searched Google and not found anything useful. My question title seems similar to this  but after reading the full question text I believe they are asking different things.

Usually we define a metric on a space $X$ to be a map $X\times X\to\mathbb{R}$ that satisfies a few axioms. $\mathbb{R}$ has of course a total order. What if we instead have a metric $X\times X\to A$ where $A$ is a monoid with some kind of weaker order on it (I say monoid because the triangle inequality requires addition, and we'd also need a zero). It seems to me that if $A$ is a monoid and directed set, and if we define open sets as sets for which every point has a ball around it contained in the set, then this generalized metric induces a topology on $X$.  Is this a thing already? Which topological spaces can be endowed with this kind of metric? This feels natural because when going from metric spaces to topological spaces we have to talk about nets (maps from directed sets) rather than sequences (maps from the natural numbers). This is in a way analogous.  Edit: Changed group to monoid.


When studying modulation of radio waves (or of most electromagnetic waves for that matter) I came across that question. Why are FM waves less susceptible to interference than AM waves? I know that in FM waves the frequency has been modulated to carry the signal by superimposing the signal wave to the carrier wave and for AM the amplitude has been varied by a similar process however what I don't understand is why FM radio waves are less susceptible to interference. Is it because when two waves interfere it is easier to change the amplitude as compared to the frequency, if so why? I can't think of any proper explanations so any help would be appreciated.  EDIT: This question has been marked as a duplicate however I don't understand the solutions from the other question. Also I fear that asking for clarification on that question will not gain the attention necessary as it is from 2 years ago.

Frequency modulated waves are less susceptible to noise compared to amplitude modulated signal. This is because the information in an FM signal is transmitted through varying the frequency, and not the amplitude. But why does noise affect changing amplitude and not frequency or other characteristics?


I've been stuck on this for the longest time and it's driving me nuts. I've tried a dozen different methods and can't figure out how to get it to work. Any help would be appreciated!! Thanks  Here's my code:

I have an HTML string representing an element: '
text
'. I'd like to append it to an element in the DOM (a ul in my case). How can I do this with Prototype or with DOM methods?  (I know i could do this easily in jQuery, but unfortunately we're not using jQuery.)


After I got message about existing conflicts, I found that files with conflicts contain marks like  <<<<<<<<<<<<<<<   or   >>>>>>>>>>>>>>>   Is this correct? What is the name of this file format?

I want to resolve merge conflicts in my Git repository. How to do that ?


Anyone know how to completely get rid of the Windows 10 upgrade prompt so I can install critical updates? I seemingly deleted all the necessary files and folders including the $WINDOWS.~BT folder but every time I uncheck the optional "Upgrade to Windows Home" update and attempt to install the important ones, I immediately get prompted to install the upgrade now or schedule it for later. Is there something that needs to be deleted or modified in registry to make this go away for good? What am I missing? I'm on Windows 8.1, by the way.

I cancelled the Microsoft Windows 10 Reservation and uninstalled KB3035583, but Windows 10 is still trying to install.   After I uninstalled KB3035583 and restarted my laptop as instructed, I could not find KB3035583 to hide it.   Now Windows 10 is sitting in my Windows Update saying that it will install when I restart my computer.


I have a Linux guest virtual machine under VirtualBox, on Windows 7 Professional, which exports its disk as a Samba share.  When I connect to \\SHARENAME after booting, though, while the share does appear, and the files are there, they are greyed out with a fat grey "X" overlaid. If I click on any of them (file or folder), I'm informed that the item is not available and Windows suggests I run a Diagnose Network.  If I choose not to, and cancel, nothing happens; the share remains unavailable for up to ten minutes, after which it'll stabilize and start working for no apparent reason. During this ungrace time, connecting to the IP address, restarting Samba, twiddling with NET.EXE from command line, etc., all avail nothing.  If I accept, the Diagnose Network applet starts (d’oh), and after four or five seconds it reports that nothing is wrong. And it's right: because just an instant before it terminates, the icons become fully visible and the X overlay disappears. Nothing's wrong, but that's because it just got fixed!  So I deduce that Windows Diagnostics does something without even being aware it's doing it, to the point that it uncharacteristically doesn't even boast of having solved anything.  I'd therefore very much like to be able to run this something, whatever it is, directly from a shell script, instead of having to run the tiresome connect-doesntwork!-wannadiagnose?-yesdamnyoureyes-nothingwrongyouninny gauntlet. Or having to wait ten minutes before being able to do anything.  But what is it that Windows Diagnostics fixes, rather than just diagnosing?   Or equivalently, is there a way of making the share become "available", whatever this means?   lists what Windows Diagnostics claims to be doing, but that's not what I want. The official Microsoft answer states,     The following table contains a list of issues that the Fix My Network   Wizard can check for and fix. The list is not exhaustive, and there   are many more issues that the wizard can fix   While not claiming it's a complete list (rather, stating the contrary), the problem here is that Fix My Network can't be just checking things, it must be actively doing something, even when it doesn't say so.  More to the point, I've tried checking those same things that appear in MS's list. My checking has had no effect.  Following the advice of , I've tried the "running nbtstat -R to purge and reload the name cache" thing, with no results.  Update (and fix)  Following @DanielB's hint, I was able to fix everything by disabling Offline Availability that I must have turned on somehow on the VM's share.  My guess is that O.A. is checking every ten minutes whether the files are there or not; that if they are not, the disk is shown as unavailable, even if it meanwhile it's become available; and that Fix My Network somehow teases the check into running immediately.  So probably tinkering with Offline Availability would also have fixed my problem. This can be useful to someone with the need for O.A.; I did not have such need, so I just disabled O.A. altogether and the share now comes up at once.

When a network connection doesn't connect to the internet, Windows pops up a dialogue, asking whether you want to "Fix network problems".  What does it actually do when you click "yes"?


On the  says that  was opened 2014 years ago. Can this be fixed please?

In what I assume is a repeat of , the  shows that Rus.SE is 2014 years, 3 months old (click for full resolution):


When I hit on the show 9 more (or with whatever number), the container expands but goes behind the footer.  Here's a snapshot (from the JavaScript room):    This screenshot is taken on a 1440x900 resolution screen. As you can see, the scrollbar is way off.  (It seems more of a CSS issue to me.)

In chat, when clicking on the "show X more" link to show more recently starred messages, the new entries are added beyond the exiting view and are tucked away under the footer.   The scrollbar is useless in this case since it only scrolls the chat section. So how do I get at the messages?  (See also: . Possibly the same issue but hard to tell based on the information provided)  I can get at the hidden content by enlarging the browser window or zooming out, but considering the number of items initially shown is already scaled based on the available space, I'd expect the "show more" link to indeed show more items irrespective of my screen resolution.  Is this a bug, or am I missing something obvious?


This may be a bit of an odd question, but is it possible to make it to Japan without using an airplane. I have an inner ear disease and the last time I flew, it literally left me incapacitated for a week. My doctor said it's just not a good idea to take a chance. I want to visit Japan and possibly move there, however I cannot fly.   Does anyone on here know of ways around this? I have done some googling, but they all seem to be "Stupid" answers like "Sneak into a shipping container". I could easily go by way of boat or ship, but the only things I've seen are private charter and cost upwards of $20,000 to rent them.   I know this is a unique situation, but I'm going to possibly get a job there so I need a method other than flight to get back and forth from the states.  Thanks ahead of time for any suggestions.

This question is similar to  but broader.  If you depart from North America, how can you reach any East Asian destination by cruise, ferry, cargo ship or anything that doesn't fly?   Are there regular cruises Seattle - Hawaii - Tokyo? Or something similar?


We are looking into scaling our servers and I am not sure where load will fall as visitor count increases.  I have one HAProzy load balancer, that proxies to two Varnish Nginx static content servers. As our load increases, which server(s) will take the largest hit in terms of resource impact? They are all Digital Ocean droplets so I can scale them up as needed. Would the load be highest on the HAProxy server, or the Varnish servers?

This is a  about  Related:      I have a question regarding capacity planning. Can the Server Fault community please help with the following:   What kind of server do I need to handle some number of users? How many users can a server with some specifications handle? Will some server configuration be fast enough for my use case? I'm building a social networking site: what kind of hardware do I need? How much bandwidth do I need for some project? How much bandwidth will some number of users use in some application?


My professor said (hesitantly)  $\textit{If it works in 1-D, it is likely that it also works in N-D}$  Hesitantly because, she remarked, it is not true for everything (which is expected).  After some research, I found one such example:  In 1-D and 2-D, if you start at the origin and continually do random unit steps in each of the cardinal directions (north, south, east, west, etc.), you will return to the origin with probability one. This fails for dimensions three and higher, in fact, you return to origin with probability zero in those cases.  What are some other striking examples of this?

A number of economists do not appreciate rigor in their usage of mathematics and I find it very discouraging.  One of the examples of rigor-lacking approach are proofs done via graphs or pictures without formalizing the reasoning. I would like thus to come up with a few examples of theorems (or other important results) which may be true in low dimensions (and are pretty intuitive graphically) but fail in higher dimensions.  By the way, these examples are directed towards people who do not have a strong mathematical background (some linear algebra and calculus), so avoiding technical statements would be appreciated.   could be such an example (though most economists are unfamiliar with the notion of a homeomorphism). Could you point me to any others?  Thanks.


I want a package that is not part of the MacTeX distribution.   I'm running Lyx 2.1.1 (on OSX) and want to use icml2013.sty I followed , which said to make local additions to MacTeX in Library/texmf. I did this. My package is presumably in the correct place: Library/texmf/icml2013.sty  I reconfigured LyX and then created a document with:  \usepackage[accepted]{icml2013}   When I try to view the document, I get an error:     LaTeX error: File 'icml2013.sty' not found.   Where does the package need to be (e.g., a sub-directory of Library/texmf/)? Or this is a problem with MacTeX?

I know how to define a package or a class, but how do I make it available (to myself) at all times?  Say I have the package file commonstuff.sty (or myprettyclass.cls), that I want to be able to include in any .tex file I create on my computer. Where do I put it? Do I need to run some installer on it, or is it enough to keep it in a certain folder?  Note: I know I can just place it in the same folder as the .tex file, but that's not what I'm after here. I'm looking for a way to "install" the package centrally on my computer.


I've used the following code to create a table. This is roughly what I want, and it looked close enough with a different page size.   Now with a new page size, the cells in the bottom right are too narrow. I need each of them to each have width = 1/8 of the overall table width.   Is there a better way to scale them according to a fraction of the page size?  \documentclass[letterpaper,10pt,english]{article} \usepackage{tabularx} \newcolumntype{Y}{>{\centering\arraybackslash}X}  \title{My Awesome Table} \author{Kyle Gregory} \begin{document} \pagenumbering{arabic}     \maketitle     \begin{tabularx}{\textwidth}{| *8{Y} *8{Y} |}         \multicolumn{1}{l}{\tiny $_{31}$} & \multicolumn{14}{Y}{ } & \multicolumn{1}{r}{\tiny $_{24}$} \\         \hline         \multicolumn{16}{| c |}{Reserved} \\         \hline         \multicolumn{16}{| c |}{\tiny N/A}  \\         \hline     \end{tabularx}     \begin{tabularx}{\textwidth}{| *8{Y} *8{Y} |}         \multicolumn{1}{l}{\tiny $_{23}$} & \multicolumn{14}{Y}{ } & \multicolumn{1}{r}{\tiny $_{16}$} \\         \hline         \multicolumn{16}{| c |}{Reserved} \\         \hline         \multicolumn{16}{| c |}{\tiny N/A}  \\         \hline     \end{tabularx}     \begin{tabularx}{\textwidth}{| *8{Y} *8{Y} |}         \multicolumn{1}{l}{\tiny $_{15}$} & \multicolumn{14}{Y}{ } & \multicolumn{1}{r}{\tiny $_8$} \\         \hline         \multicolumn{16}{| c |}{Reserved} \\         \hline         \multicolumn{16}{| c |}{\tiny N/A}  \\         \hline     \end{tabularx}     \begin{tabularx}{\textwidth}{| *8{Y} |}         \multicolumn{1}{l}{\tiny $_7$} & \multicolumn{6}{Y}{ } & \multicolumn{1}{r}{\tiny $_0$} \\         \hline         \multicolumn{4}{| Y |}{Reserved} & \multicolumn{1}{c |}{XPPS} & \multicolumn{1}{c |}{SROL} & \multicolumn{1}{c |}{ROG} & \multicolumn{1}{c |}{FRWL}  \\         \hline         \multicolumn{4}{| Y |}{\tiny N/A} & \multicolumn{1}{c |}{\tiny R/W (0)} & \multicolumn{1}{c |}{\tiny R (0)} & \multicolumn{1}{c |}{\tiny R (0)} & \multicolumn{1}{c |}{\tiny R (0)} \\         \hline     \end{tabularx} \end{document}   Column type Y is defined as follows. I tried setting all of the columns as type Y, but I found that it would scale the \multicolumn{4} cells to be the same width as a single cell.  \newcolumntype{Y}{>{\centering\arraybackslash}X}   It produces the following output:

So I have this table, which I just used an online tool to create, but I want the columns to wrap. So, I just change \begin{tabular} to \begin{tabularx} and then the last column vertical line is about 1cm from the table... How can I fix that gap? \begin{tabularx}{\textwidth}{|X|X|X|X|} \hline Name:                                      & Donald Trump                              & Student ID:                                         & 99999999                                     \\ \hline \multicolumn{2}{|p{0.5\textwidth}|}{Feedback focus:}                                                 & \multicolumn{2}{p{0.5\textwidth}|}{asoidjfaopsidjfp oiajdfpo iasjdfp oiasjdfpo ij}                                \\ \hline \multicolumn{2}{|p{0.5\textwidth}|}{askdljf ;laksjdf;l aksjdf;lkajsd;:}                          & \multicolumn{2}{l|}{as;ldifja;lsdkfja;lsdkfja; slkfj; aldkjf ;aslkdj ;alk}                         \\ \hline \hline \multicolumn{4}{|p{\textwidth}|}{as;ldkf;lkj: aklsduhf asldkj f;alskdjf ;alskdjf ;alskdf }                                                                  \\ \hline Fully Met                                  & Met                                      & Partially Met                                       & Not Met                                      \\ \hline Comments:                                  & \multicolumn{3}{l|}{}                                                                                \\ \hline \multicolumn{4}{|p{\textwidth}|}{asldkjf;alksdj f;laksjdf:as;dlk ja;lsdk fjas;ldkfj a;slkdfj ;lakasdlk;jkdj }                                                                               \\ \hline Fully Met                                  & Met                                      & Partially Met                                       & Not Met                                      \\ \hline Comments:                                  & \multicolumn{3}{l|}{}                                                                                \\ \hline \multicolumn{4}{|p{\textwidth}|}{a;lsdkjf; lakj;l3: alkjdsf l;aksjdf;l kasjd;lf kjasd;l fkjas;ldkfjas;ldkf jas;ldkf ja;sldkfj asldkfj alksjferopijp34qjp asdf} \\ \hline Fully Met                                  & Met                                      & Partially Met                                       & Not Met                                      \\ \hline Comments:                                  & \multicolumn{3}{l|}{}                                                                                \\ \hline \multicolumn{4}{|p{\textwidth}|}{as;ldkfjal;kej ;l4: alskdjf ;lasdkjf ;alskdjf ;laskd}                                                                                \\ \hline Fully Met                                  & Met                                      & Partially Met                                       & Not Met                                      \\ \hline Comments:                                  & \multicolumn{3}{l|}{}                                                                                \\ \hline \multicolumn{4}{|p{\textwidth}|}{asl;dkjf;lk4j: asl;dkjfaslkdjf eirkajp (asl;dkfj a) aslkdjf l}                                                                                \\ \hline Fully Met                                  & Met                                      & Partially Met                                       & Not Met                                      \\ \hline Comments:                                  & \multicolumn{3}{l|}{}                                                                                \\ \hline \end{tabularx}  Gives:


heres the issue- the image shown is in rendered mode and in material mode the background IS visible

I made a character, and its one of my first times texturing, and I saved my character into a new folder, and when I came back to the model ALL the textures were pink, I used to know what to do, but I stopped texturing, how do I bring my textures back?


I already have IPTables blocking all unnecessary traffic.  Is mod_evasive the best solution for something like this?  What do you use on your server?

This is a  about DoS and DDoS mitigation.   I found a massive traffic spike on a website that I host today; I am getting thousands of connections a second and I see I'm using all 100Mbps of my available bandwidth.  Nobody can access my site because all the requests time out, and I can't even log into the server because SSH times out too!  This has happened a couple times before, and each time it's lasted a couple hours and gone away on its own.  Occasionally, my website has another distinct but related problem: my server's load average (which is usually around .25) rockets up to 20 or more and nobody can access my site just the same as the other case.  It also goes away after a few hours.  Restarting my server doesn't help; what can I do to make my site accessible again, and what is happening?  Relatedly, I found once that for a day or two, every time I started my service, it got a connection from a particular IP address and then crashed.  As soon as I started it up again, this happened again and it crashed again.  How is that similar, and what can I do about it?


I need to call a method from a fragment and also pass a string value as a parameter. But I am getting NullPointerException and it's showing currenttodat is static content.On the internet i have got only how to call a method from the fragment.But i need to pass a parameter along with it.While passing parameter i am getting the nullpointer exception.   Calendar calendar = Calendar.getInstance();     calendar.add(Calendar.DAY_OF_YEAR, count);     currenttoday = dateFormat.format((calendar.getTime()));     tv_date.setText(currenttoday);     Toast.makeText(LandingActivity.this, currenttoday, Toast.LENGTH_SHORT).show();      ManageCustomersFragment manageCustomersFragment = (ManageCustomersFragment) getSupportFragmentManager().findFragmentByTag("managecustomerTag");      manageCustomersFragment.getApplicationList(currenttoday);

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


Let $f(z)$ be an analytic function defined on the unit disk $\mathbb{D} = \{z : |z| < 1\}$ so that $f(0)=0$ and $−1<Re\{f(z)\}<1$ for all $z \in \mathbb{D}$. Prove that $|Im\{f(z)\}|≤ $$\frac{2}{\pi} \log \frac{1+|z|}{1 - |z|},$ $z \in \mathbb{D}$.  I want to use the fact that $Imf$ and $Ref$ satisfy maximum modulus principle (strong version.  But not sure if that is useful or not.  Would love some help.  Thanks

Let $f$ be holomorphic in the unit disk $D(0,1)$, and $f(0)=0$. Suppose $|\Re f(z)|\leq 1$ for all $|z|<1$. Show that  $$|\Re f(z)|\leq\frac{4}{\pi}\arctan|z|;$$ $$|\Im f(z)|\leq \frac{2}{\pi}\ln\frac{1+|z|}{1-|z|}.$$  What I could do is just to observe that $$\frac{e^{i\frac{\pi}{2}f(z)}-1}{e^{i\frac{\pi}{2}f(z)}+1}:D(0,1)\to D(0,1)$$ with $0$ being fixed. And Schwarz lemma applies. However, I could not get any information on the real and imaginary part of $f$.


I am using this function to reverse text but I am having a little issue with speed. for testing I have 130,000 characters text and its taking about 10 seconds. is it possible to speed it up? This questions is different than C# as its a vb.net  Function ReverseString(ByRef strString As String) As String         Dim NextChr, TempString As String, StringLength, Count As Integer, NewString As String = Nothing          TempString = strString         StringLength = Len(TempString)         Do While Count <= StringLength             Count = Count + 1             NextChr = Mid(TempString, Count, 1)             NewString = NextChr & NewString         Loop         ReverseString = NewString End Function

I've just had to write a string reverse function in C# 2.0 (i.e. LINQ not available) and came up with this:  public string Reverse(string text) {     char[] cArray = text.ToCharArray();     string reverse = String.Empty;     for (int i = cArray.Length - 1; i > -1; i--)     {         reverse += cArray[i];     }     return reverse; }   Personally I'm not crazy about the function and am convinced that there's a better way to do it. Is there?


I have a (still relatively new) acer predator laptop (G9-593-7757 15,6"/i7-7700/32 GB RAM/512 GB SSD/1 TB HDD/GTX1070) running 16.10 and noticed that the sound sounds far more hollow then when I use windows. It appears as if the laptop is only using the subwoofer rather then the 2 other speakers making the sound distorted.   Here is my /etc/pulse/deamon.etc file   # This file is part of PulseAudio. # # PulseAudio is free software; you can redistribute it and/or modify # it under the terms of the GNU Lesser General Public License as published by # the Free Software Foundation; either version 2 of the License, or # (at your option) any later version. # # PulseAudio is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # General Public License for more details. # # You should have received a copy of the GNU Lesser General Public License # along with PulseAudio; if not, see <http://www.gnu.org/licenses/>.  ## Configuration file for the PulseAudio daemon. See pulse-daemon.conf(5) for ## more information. Default values are commented out.  Use either ; or # for ## commenting.  ; daemonize = no ; fail = yes ; allow-module-loading = yes ; allow-exit = yes ; use-pid-file = yes ; system-instance = no ; local-server-type = user ; enable-shm = yes ; shm-size-bytes = 0 # setting this 0 will use the system-default, usually 64 MiB ; lock-memory = no ; cpu-limit = no  ; high-priority = yes ; nice-level = -11  ; realtime-scheduling = yes ; realtime-priority = 5  ; exit-idle-time = 20 ; scache-idle-time = 20  ; dl-search-path = (depends on architecture)  ; load-default-script-file = yes ; default-script-file = /etc/pulse/default.pa  ; log-target = auto ; log-level = notice ; log-meta = no ; log-time = no ; log-backtrace = 0  ; resample-method = speex-float-1 ; enable-remixing = yes ; enable-lfe-remixing = no ; lfe-crossover-freq = 0  flat-volumes = no  ; rlimit-fsize = -1 ; rlimit-data = -1 ; rlimit-stack = -1 ; rlimit-core = -1 ; rlimit-as = -1 ; rlimit-rss = -1 ; rlimit-nproc = -1 ; rlimit-nofile = 256 ; rlimit-memlock = -1 ; rlimit-locks = -1 ; rlimit-sigpending = -1 ; rlimit-msgqueue = -1 ; rlimit-nice = 31 ; rlimit-rtprio = 9 ; rlimit-rttime = 200000  ; default-sample-format = s16le ; default-sample-rate = 44100 ; alternate-sample-rate = 48000 ; default-sample-channels = 2 ; default-channel-map = front-left,front-right  ; default-fragments = 4 ; default-fragment-size-msec = 25  ; enable-deferred-volume = yes deferred-volume-safety-margin-usec = 1 ; deferred-volume-extra-delay-usec = 0   here are my devices  $ cat /proc/asound/devices    1:        : sequencer   2: [ 0]   : control   3: [ 0- 0]: digital audio playback   4: [ 0- 0]: digital audio capture   5: [ 0- 0]: hardware dependent  33:        : timer  $ cat /proc/asound/cards  0 [PCH            ]: HDA-Intel - HDA Intel PCH                       HDA Intel PCH at 0x83620000 irq 134   Anybody got any ideas?

I have a laptop Acer Predator G9-792  It has 2 or 4 speakers (there is 5 holes but not sure are all holes have speaker inside) and subwoofer  On windows 10 everything working as expected, but in Ubuntu 16.10 only subwoofer being used to output sound  I've tried recommendations here -   including enabling 3,4,5,6 channels - sound either stop working or keep working through subfoower  alsamixer with extra driver support also didn't work  Is there anything I can try to enable normal sound on the laptop?


With my 37 base features, I obtain a PCA 7 components whose explained variance is 62584.661. Below is my code (I use scikit-learn):  >> pca = decomposition.PCA() >> X = set_1.to_dataframe().drop(['user_id', 'TARGET'], axis=1) >> pca.fit(X)  >> print pca.explained_variance_    [6.14280876e+04   4.54217662e+01   2.72989436e+01   2.67631322e+00    1.82282196e+00   1.21712136e+00   1.14632304e+00   9.78220983e-01    5.29859226e-01   4.46864198e-01   2.20896621e-01   1.35477040e-01    1.24036813e-01   1.16983213e-01   9.77577393e-02   9.52879856e-02    6.33013163e-02   5.11503915e-02   4.46737594e-02   4.17721621e-02    3.62836939e-02   2.81101420e-02   2.40227513e-02   1.73247899e-02    9.59248897e-03   5.97952400e-03   2.32278409e-03   1.53377399e-03    1.13924785e-03   3.69972626e-04   5.94762833e-28   5.94762833e-28    5.94762833e-28   5.94762833e-28   5.94762833e-28]   >> pca.explained_variance_[:7].sum()  62584.661944243671   Using these 7 PCA variables in my linear regression model, I obtain 0.20 as the r2 value.  To improve the results, I add 39 more features (76 in total). Following the same steps, PCA results indicate 71052.64 as the variance explained with 76 components. However, when I run linear regression using these 76 components, I obtain a r2 of 0.06 that is less than 0.20 of the previous model.  I wonder if I am doing something wrong in my experiment. Is this behavior expected? I thought I would get a better model with a PCA that explains more variance.

Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$?   I understand that from dimensionality-reduction/feature-selection point of view, if $v_1, v_2, ... v_k$ are the eigenvectors of covariance matrix of $X$ with top $k$ eigenvalues, then $Xv_1, Xv_2 ... Xv_k$ are top $k$ principal components with maximum variances. We can thereby reduce the number of features to $k$ and retain most of the predictive power, as I understand it.   But why do top $k$ components retain the predictive power on $Y$?   If we talk about a general OLS $Y \sim Z$, there is no reason to suggest that if feature $Z_i$ has maximum variance, then $Z_i$ has the most predictive power on $Y$.   Update after seeing comments: I guess I have seen tons of examples of using PCA for dimensionality reduction. I have been assuming that means the dimensions we are left with have the most predictive power. Otherwise what's the point of dimensionality reduction?


Can we use two verbs together?  We recognize those who help prepare America's future leaders for a life filled with meaning, purpose and success.

What is the correct way to use infinitive after the verb "help": with or without "to"?  For example:     Please, help me to understand this.   or:     Please, help me understand this.


Calculating the limit as $x$ approaches $0$ using L'Hospital's rule or series expansion is straightforward, but how to evaluate the limit without either of those techniques.  How to calculate the following limit as $x$ approaches $0$:  $\dfrac{\ln(x+1)+1-e^x}{x^2}$

Is it always possible to find the limit of a function without using  or ?  For example,   $$\lim_{x\to0}\frac{\tan x-x}{x^3}$$  $$\lim_{x\to0}\frac{\sin x-x}{x^3}$$  $$\lim_{x\to0}\frac{\ln(1+x)-x}{x^2}$$  $$\lim_{x\to0}\frac{e^x-x-1}{x^2}$$  $$\lim_{x\to0}\frac{\sin^{-1}x-x}{x^3}$$  $$\lim_{x\to0}\frac{\tan^{-1}x-x}{x^3}$$


How do I split the partition without loosing my windows OS and files .I am mainly concerned about the new table.

I wanted to create more space for Ubuntu on my hard disk in favor of my Windows partition. I booted the livecd and resized the NTFS partition to 100 GB. Then I wanted to resize my Ubuntu (ext4) partition to fill up the created unallocated space.  A screenshot of my current disk. (With the livecd there's no 'key' icon after sda6)    My first thought was just right click on sda6 → move/resize → done. Unfortunately I cannot resize or move the partition. However I can resize the NTFS partition.  I guess it is because the extended sda4 partition is locked. I couldn't see an unlock possibility though…  So how do I resize the ext4 partition anyway, probably by unlocking the extended partition, but how?


This is from the song ‘‘happier”.     I know that there's others that deserve you.   Shouldn't it be there're?

For example:     There's two options here   or     There are two options here   I hear a lot of people say the first line (or something similar), but isn't that incorrect? Isn't it plural and therefore you should use "there are"?


I'm curious to know the difference between these two commands in Linux:  $ cat ./boot.bin ./kernel.bin /dev/zero | dd bs=512 count=2880 of=devos.img   and  $ cat ./boot.bin ./kernel.bin > devos.img

I recently realized we can use cat as much as dd, and it's   I know that dd was useful in dealing with tapes where block size actually mattered in correctness, not just performance. In these days, though, are there situations where dd can do something cat can't? (Here I would regard a less than 20% performance difference irrelevant.)  Concrete examples would be nice!


I have proven that the sum of any two irrational numbers is not always irrational and that a rational plus an irrational is irrational, however I am not sure how to prove this specific case.  I was thinking along the lines of: $\sqrt{2}+\sqrt{3}=n$   where $n$ is an element of rationals. By squaring both sides  $$(\sqrt{2}+\sqrt{3})^2 = n^2$$ $$7 + 2\sqrt{2}\sqrt{3} = n^2$$ I have proven the sum of a rational and irrational is irrational yet it is too long and complicated to prove that root two and root three make root six. Moreover, it will be an additionally difficult to prove that two times root six is irrational so I was wondering if there was a quicker less complex way to finish this proof?

Can the expression $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m \in \mathbb{N}$ are perfect squares? It doesn't seem likely, the only way that could happen is if for example $\sqrt{m} = a-\sqrt{n}, \ \ a \in \mathbb{Q}$, which I don't think is possible, but how to show it?


I am studying a game-engine codebase and trying to figure out what the last line of the following function does: template<typename FuncT>     static void Submit(FuncT&& func)     {         auto renderCmd = [](void* ptr) {             auto pFunc = (FuncT*)ptr;             (*pFunc)();              // NOTE: Instead of destroying we could try and enforce all items to be trivally destructible             // however some items like uniforms which contain std::strings still exist for now             // static_assert(std::is_trivially_destructible_v<FuncT>, "FuncT must be trivially destructible");             pFunc->~FuncT();         };         // storageBuffer here is a void* pointing to a memory location in a buffer         auto storageBuffer = GetRenderCommandQueue().Allocate(renderCmd, sizeof(func));         new (storageBuffer) FuncT(std::forward<FuncT>(func));     }  I have honestly never come across such a syntax in C++ so any help to decipher it would be appreciated. What I am really trying to figure out is the last line of code new (storageBuffer) FuncT(std::forward<FuncT>(func)); the syntax (i.e., new (void*) FuncT(std::forward<FuncT>(function))) of which is confusing. The Allocate function: void* RenderCommandQueue::Allocate(RenderCommandFn fn, uint32_t size) {     // TODO: alignment     *(RenderCommandFn*)m_CommandBufferPtr = fn;     m_CommandBufferPtr += sizeof(RenderCommandFn);      *(uint32_t*)m_CommandBufferPtr = size;     m_CommandBufferPtr += sizeof(uint32_t);      void* memory = m_CommandBufferPtr;     m_CommandBufferPtr += size;      m_CommandCount++;     return memory; }

Has anyone here ever used C++'s "placement new"? If so, what for? It looks to me like it would only be useful on memory-mapped hardware.


I've tried out a few pairs of numbers for $a$,$b$ where I have combinations of prime-prime, prime-non prime, non-prime-non-prime, and I know the statement is true, but how should I go about proving this?   I know that if $\gcd(a,b)=1$ and $a|mb$, then $m=a$, $m=2a$, $m=3a$ etc. Does this then prove that $a|m$?

Well I thought this is obvious. since $\gcd(a,b)=1$,  then we have that $a\not\mid b$ AND $a\mid bc$. This implies that $a$ divides $c$. But apparently this is wrong. Help explain why this way is wrong please.   The question tells you give me two relatively prime numbers $a$ and $b$ such that $a$ divides the product $bc$, prove that $a$ divides $c$. how is this not obvious? Explain to me how my "proof" is not correct.


My Windows installation is on C drive, and I want to install a new Ubuntu installation on D drive. I have some downloads on my D drive like anime and stuff (nothing directly relating to the windows installation).   Is it possible?  I've been googling everywhere but the forums are down and I'm a complete newbie. Keep in mind I would rather not format my D drive but if it comes down to it I can. Both drives have 300GiB free space. Even if you forward me onto another site any help would be greatly appreciated!!

Okay, so here's the story.  I am trying to install Ubuntu 13.04.  I currently have a 2TB drive in my computer where Windows 7 boots from, and a secondary 500GB drive that also has a bootable installation of Windows 7, because the version on the 2TB is a clone of what was on the 500.. I do not need any information on the 500 as I already have it moved over to the 2TB.  What I want is to completely reformat the 500 so that it has about 300GB for NTFS and the rest for Ubuntu.  However, I can't seem to find a straightfoward way to do that in the Ubuntu installer.  If I click on "Install Ubuntu alongside them," it does not give me the option to select my 500GB drive, only my 2TB.  I do NOT want any linux partitions on my 2TB drive.  I do not want to click, "Erase disc and install Ubuntu" for obvious reasons.  Finally, clicking "something else" brings up a menu that is quite confusing.  I can kind of figure out how to use it, but it's not as straightfoward as I'd like..  Further, I know that Ubuntu requires a SWAP partition, but I do not know how much, or even how, to allocate that with the stupid dropdown menus it gives me.  So, to get to the point..  What is the easiest, safest way to do what I want to do?  That is, allocate approximately 200G for Ubuntu on my 500G drive, and be able to choose between Windows 7 on my 2TB drive and Ubuntu at startup - all, of coarse, without touching the 2TB drive at all.  Thanks!


In the movie Terminator why was only one Terminator allowed to be brought back at a time?

Since the first Terminator failed, Skynet sent back .  Another strategy would have been to send back multiple Terminators. Why was that not attempted? Was there a cost (e.g. power) to sending them back in time?


Almost the same website problem as   server: Windows 2008 with IIS7  Router: Dlink DIR-615  Configured: Port 80 forwarded, ddns OK  Shield Up: Port 80 test ok  Online Browser: PC outside network can access the website   And my Problem:   PC outside private network - Access using external ip or ddns hostname: OK PC inside private network - Access using internal ip (192.168.0.x): OK From the server - Access using "localhost": OK PC inside private network - Access using external ip or ddns hostname: failed   Just wonder why pc in the same network can not access to web server using external ip while those external pc can do so? Well I found some points from the post above:   Such access confuse router: well I can not get the point. Some said some DNS settings in router can fix that but I can not find how to do that Change host table and map hostname to internal ip: this of course works (even without internet connection) , just no difference from accessing with "192.168.10.x". Such solution make no sense, I want to access the server via internet to make sure what external user will get in their browser   Thanks advance for your help !

This is a  about Hairpin NAT (Loopback NAT).   The generic form of this question is:  We have a network with clients, a server, and a NAT Router. There is port forwarding on the router to the server so some of it's services are available externally. We have DNS pointing to the external IP. Local network clients fail to connect, but external work.   Why does this fail? How can I create a unified naming scheme (DNS names which work both locally and externally)?   This question has answeres merged from multiple other questions. They originally referenced FreeBSD, D-Link, Microtik, and other equipment. They're all trying to solve the same problem however.


I use Windows 10 Enterprise and the Windows 10 Anniversary Edition update still doesn't appear in Windows Update  Is anyone else having this problem?  How can I get the Anniversary Edition update for Windows 10 Enterprise Edition?

I have a laptop with Windows 10 Enterprise edition installed (64bit).  I haven't got the Windows 10 Anniversary Update from the normal Windows Update (I have clicked Check for updates). So I want to install it manually.  I have downloaded the the update from . However when I run it, the Update Assistant says     But I'm my own system administrator. I've installed Enterprise Edition from MSDN Subscriber downloads.  How do I update to the Anniversary Edition?


I want to restore my contacts in the left side of my emails and not separate on the right corner.

I've turned on the , and now notice that my Contacts button has disappeared. It used to be above Compose. Does anyone know where it has gone to?


I see a CONFIGURE, autogen.sh and a makefile but I can't seem to figure out how to install this.   Can someone help explain what I need to do to install this?

Trying to install  from source. I did try the usual methods like using make. There is nothing related to installing in the readme file and could not find a configure folder.  So how do I install this?


Basically we are over limit and I did some investigating but I am still baffled as to how.  I checked contact builder - email and mobile and we have a total of 1.7 million contacts.  Our limit is 1.5 million, but apparently we are over by 400,000 (1.54M)?  MC counts Contact Keys as individual records and they are unique, so by that logic there should be no duplicates correct?   My question is, is there a way for me to figure out if there are any duplicates and to gain a much more specific answer as to how our total is calculated.  I see 1.7 contacts total in Contact Builder - All contacts, but apparently we are at 1.54m total contacts.  If someone uploads a list of contacts as a DATA EXTENSION using say an email, would that be counted towards our limit?

Salesforce bills Marketing Cloud on total number of Contacts within the system. I'd like to know what exactly is used to count these? Is this the Email Studio > All Subscribers list or the Contact Builder > All Contacts list?  When we have Marketing Cloud connector and synchronise the Contacts object, is this counted towards that number? (or only when they have been inserted into the All Subscribers / All Contacts list, as they are not done so automatically)


I have 1 SSD and 2 HDDs - each has a capacity of 1 TB. Windows 10 is installed on the SSD while Ubuntu 18.04 is on one of the HDDs. I need to be able to access the HDD from Windows, but I currently can't because its file system is EXT4, obviously. I need to be able to access the HDD from Windows for a number of reasons:   I want to install some of the storage-eating software for Windows on that HDD, as I don't intend to use Ubuntu on daily basis anyway. I plan to record some videos on Ubuntu, hence I need to access the video files from Windows in order to edit them in a video editor program.   What I had been trying so far to do, unsuccessfully, are the following:   Using  - it successfully granted me access to the HDD, but also , and maybe even the whole Ubuntu partition. (though I didn't it, because whenever I came across that screen - I couldn't type anything to the command-line interface) Tried to reinstall Ubuntu, but this time to first set via the installer to format to FAT32 - it refused to. (thought of this idea because I read online that Ubuntu can read FAT32)   So now I'm lost.  What solution can I have? Thanks!

I have two questions on ext4:   Is there currently a way to mount an ext4 partition in Windows (XP/Vista/7) to get basic read support? If not, are there any plans to support this someday?


If I wanted to say: this folder contains the links to all the programs,  should I use: this folder contains the program links or this folder contains the programs links ?

Possible Duplicates:             I'm wondering whether or not I should use a plural form noun with a collection name. For example, which one is correct, bookList or booksList (obviously they are variables in a programming language)?


I was reading a Calculus book and I saw this problem which looks easy: $$\lim _{x \rightarrow 0} \frac{2 x \cos x- \sin 2x}{x^3} = ?$$ It's a 0/0 limit and it's using some of the Taylor series of $\sin$ and $\cos$ expressions to solve the problem. I know that the First and Second way should be correct because it's using more expressions of the Taylor series around 0. What I can't figure out is WHY using fewer expressions of the Taylor series in the Third way doesn't give 0/0 but gives a wrong answer? First way: $$\lim _{x \rightarrow 0} \frac{2 x \cos x-2 \sin x \cos x}{x^3}=\lim _{x \rightarrow 0} \frac{2 \cos x(x-\sin x)}{x^3}=\lim _{x \rightarrow 0} \frac{2 \cos x\left(x-x+\frac{x^3}{6}\right)}{x^3}=\lim _{x \rightarrow 0} \frac{2 \cos x\left(\frac{x^3}{6}\right)}{x^3}=\frac{1}{3}$$ Second way: $$\lim _{x \rightarrow 0} \frac{2x(1-\frac{x^2}{2})-(2x-\frac{8x^3}{6})}{x^3}=\lim _{x \rightarrow 0} \frac{2x-x^3-2x+\frac{8x^3}{6}}{x^3}=\lim _{x \rightarrow 0} \frac{\frac{x^3}{3}}{x^3}=\frac{1}{3}$$ Third way: $$\lim _{x \rightarrow 0} \frac{2 x \cos x- \sin 2x}{x^3} =\lim _{x \rightarrow 0} \frac{2 x \cos x-2x}{x^3}=\lim _{x \rightarrow 0} \frac{2x(\cos x -1)}{x^3}=\lim _{x \rightarrow 0} \frac{2x(-\frac{x^2}{2})}{x^3}=-1$$

I got a limit:  $$\lim_{x\to\infty}\frac {(2x+3)^3(3x-2)^2} {(x^5 + 5)}$$  As far as $x$ approaches infinity, can I just forget about 'small' numbers (like $3$, $-2$ and $5$ in this example)? I mean is it legal to make a transition to:  $$\lim_{x\to\infty}\frac {(2x)^3(3x)^2} {x^5}$$  Or if it is not always okay — in what cases such transitions are okay?


I installed ubuntu 18.04 on HP envy. However I am getting issue setting up wifi :-  No Wi-Fi adapter found  The output of following command is :-  lspci -nnk | grep -A2 0280  Kernel driver in use: iwlwifi  I tried steps mentioned in  with no success.  Could anyone please help me with the issue.

My wifi card is an Intel® Wireless-AX200 (802.11/a/b/g/n/ac/ax), Bluetooth® 5, and bluetooth is working. I've tried following various guides, however these drivers are apparently yet to make it into the kernel.  Their product brief states linux is supported:    And yet their driver page has no listing for them:    sudo lshw -c network => mark@m-blade-2019:~$ sudo lshw -c network   *-network UNCLAIMED               description: Network controller        product: Intel Corporation        vendor: Intel Corporation        physical id: 0        bus info: pci@0000:02:00.0        version: 1a        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix cap_list        configuration: latency=0        resources: memory:cf300000-cf303fff   *-network        description: Ethernet interface        physical id: 2        logical name: enx0050b6b47e72        serial: 00:50:b6:b4:7e:72        capabilities: ethernet physical        configuration: broadcast=yes driver=cdc_ncm driverversion=22-Aug-2005 firmware=CDC NCM ip=192.168.1.17 link=yes multicast=yes   I'm running kernel version Linux 5.0.0-13-generic, any help is greatly appreciated.  EDIT: results of lspci -nnk | grep 00280 -A3:  mark@m-blade-2019:~$ lspci -nnk | grep 0280 -A3 02:00.0 Network controller [0280]: Intel Corporation Device [8086:2723] (rev 1a)     Subsystem: Intel Corporation Device [8086:0084]     Kernel modules: wl, iwlwifi 03:00.0 Non-Volatile memory controller [0108]: Samsung Electronics Co Ltd NVMe SSD Controller SM981/PM981 [144d:a808] mark@m-blade-2019:~$


How to block the renaming of a Particular Folder by Ubuntu Users ?

For some special purpose, I want to prevent non-root users of the Linux Server from changing or renaming the filenames. However, they can modify and write to the contents of the file. How to do this from command line.


Currently I have two monitors (1 and 2) as on the picture:   When I am moving the windows on the screen I can stick them to the left of monitor 1 and to the right of monitor 2 (the window is resized to half of the screen and stick to edges of the screen) but can not stick them to the right of monitor 1 and left of monitor 2.  Is there a simple way to achieve this?

As the question states... In Windows 7 with a single screen, you can drag a window to the right and a window to the left to maximize them both at half the screen, letting you quickly and neatly see two windows simultaneously.  If I have 2 monitors, is there a way to do this with 4 windows, where each monitor gets 2 windows split across each screen?


So the question is pretty straightforward. Is there a way to know which is the route followed by a Flixbus bus from city A to city B, before buying the ticket?

Is there any way to see the timetable for a  bus route?  On their website I can see the routes map, but I'd me more interested in seeing where the bus is going to stop for a given route.  E.g. if a bus goes from Rotterdam to Amsterdam, I'd like to see each stop.


Because of distributive properties we know this is true, but I am stuck on showing the proof. I know: Let $x\in A\times (B-C)$. This means $x\in\mathbb{A}$ and $x\in B$ but $x\ not in C$. Assume $x\in A$ then from here im not sure where to go.

This is what I have come up with so far, but I am rather lost at lines 3-4...  $$\begin{align} (a,b)\in A\times (B\setminus C)\iff& a\in A \land b\in (B\setminus C)\\ \iff& a\in A \land (b\in B \land \lnot(b\in C))\\ \iff& (a\in A \land b\in B) \land (a\in A \land b\notin C)\\ \iff& (a\in A \land b\in B)\setminus (a\in A \land b\in C)\\ \iff& (a,b)\in (A\times B)\setminus ((a,b)\in A\times C)\\ \iff& (a,b)\in (A\times B)\setminus (A\times C) \end{align}$$


In Gmail, how does one determine which email messages are in All Mail, but nowhere else? I'm referring to email messages that are not in the Inbox (or another folder) and do not have any labels assigned.

In Gmail, the inbox view only contains mail which has not been archived. I'm looking for a particular conversation I had with someone a while ago to find a quote, but I can't remember the exact topic or person I was emailing. I know it has been archived but I cannot find a way of viewing only archived email—it appears I have to browse through many months of All Mail in order to find that particular conversation.  Is there a more effective way of viewing only archived mail?


I am not able to create a regex from a variable, using template literals  What is wrong and how to fix it?  const myValue = 'a.b' const reg = new RegExp(`/^${myValue}$/`); /*   /^a.b/ */

I would like to create a String.replaceAll() method in JavaScript and I'm thinking that using a regex would be most terse way to do it.  However, I can't figure out how to pass a variable in to a regex.  I can do this already which will replace all the instances of "B" with "A".  "ABABAB".replace(/B/g, "A");   But I want to do something like this:  String.prototype.replaceAll = function(replaceThis, withThis) {     this.replace(/replaceThis/g, withThis); };   But obviously this will only replace the text "replaceThis"...so how do I pass this variable in to my regex string?


I am looking for any rules to give developers how they can differ between Errors, Warnings and Notifications. I haven't found something in literature or the web.  Is there a standard that needs to be followed?

I designed a program that is used to send data through the socket. In each program action, I display a message about process state.  I'm confused by when to display a Notice message or Info message. Some of the programs that I have encountered use both terms.  What is the difference between Notice and Info messages? And when this increased to a Warning?


I would like to change the default bullet style for the itemize environment in beamer to be a dash (or double dash). It seems that labelitemi is not defined in beamer so  \renewcommand\labeli{-}   does not work. How can I solve this?

To modify the definition of a command we use \renewcommand, but how about modify a beamer template. For example if we change itemize item like this:   \defbeamertemplate{itemize item}{triangle} {\scriptsize\raise1.25pt\hbox{\donotcoloroutermaths$\blacktriangleleft$}}   We get the error:     ! LaTeX Error: Command \beamer@@tmpop@itemize item@triangle already   defined.   This is an example of that:  \documentclass{beamer}  \defbeamertemplate{itemize item}{triangle}     {\scriptsize\raise1.25pt\hbox{\donotcoloroutermaths$\blacktriangleleft$}}  \begin{document}  \begin{frame} \setbeamertemplate{itemize item}[ball]  \begin{itemize} \item  text  \item  text \end{itemize}  \setbeamertemplate{itemize item}[tiangle]  \begin{itemize} \item  text  \item  text \end{itemize}  \end{frame}  \end{document}


So here's my problem: I am trying to use \cite{} in a beamer. I would like the output of \cite{{AB_00} to be either something like [1] or Author A \& Author B, which is essentially what I've written in brackets. Below is my code and its output:  \documentclass[10pt]{beamer} \mode<beamer>{\usetheme[hideothersubsections, right, width=22mm]{Goettingen}}  \usepackage[english]{babel} \usepackage{biblatex}   \begin{document} \begin{frame} Test \cite{AB_00} \end{frame}  \begin{frame} \begin{thebibliography}{} \bibitem[Author A \& Author B]{AB_00} A \& B 2000 \end{thebibliography}{} \end{frame} \end{document}     Any help or suggestion is greatly appreciated.  P.S. I've tried turning my code into a m.w.e. If however something is unclear, please let me know so I can try clearing it up.

I have the following problem: I correctly obtain a numbered bibliography at the end but along the text the cite_key appear instead of a number. How to fix this problem?   \documentclass[11pt]{book}  \usepackage[]{biblatex} \begin{document} %some text  ... \cite{ABKM2015}... %some text  \begin{thebibliography}{99} \bibitem{ABKM2015} Arroja, F. and Bartolo, N. and Karmakar P. and Matarrese, S. (2015). \newblock The Two Faces of Mimetic Horndeski Gravity             \newblock {\em ArXiV}, 1506.08575 (2015). \end{thebibliography} \end{document}   After compiling I get ... [ABKM2015] ... while I want for example  [1].


When I started learning Java I was always asked to set the environment variable PATH before using the compiler. Now, I know why I have to do so.   But why does the Java installation wizard not do it by itself as other software do?  EDIT: Before this question gets closed as primarily opinion based; I'm looking for an authoritative answer, from one of the Oracle folks here.

I always wondered why I have to manually set the JAVA_HOME environment variable after installing the Java SDK.     JAVA_HOME=c:\Program Files\Java\jdk1.6.0_12   Visual Studio at least provides a batch file to set these kind of environment variables:     call "c:\Program Files\Microsoft Visual   Studio 9.0\VC\vcvarsall.bat"   Does Java have something similar? I'm trying to make a build script that should simply work after installing the Java SDK. I don't want people to mess with environment variables on their PC.


How to use the  method?  Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$,  where $x_i\in\mathbb{N}$.  Is this the correct time to apply the method?  This is being repurposed in an effort to cut down on duplicates, see here:     and here:


I want to make a rocket engine nozzle but I don't know how to curve a cone into its point and make it hollow. I thought about using a torus or cylinder but I wouldn't know how to recreate the shape. (Google Raptor Engine)

I'm really new to Blender and for my next project I need to create a cone with curved edges. I've searched online and messed around with Blender but I can't find a way. What could I try?  EDIT  Sorry I wasn't clear, what I mean is something like this :


Is there a way for me to get to Greenland from Canada without flying? Basically I'm looking for it to be as cheap as possible.

Are there any roads (or ferry service) that would allow a person to travel from Canada to Greenland without taking a plane?


Say I have a platform, and I want to store a password.   Is it more secure to store the password prefixed with the users email, then to hash it then just hashing the password?  Example,  $hash = md5($email.$password);   Rather then just  $hash = md5($password);   Then to store the variable $password.

It is currently said that MD5 is partially unsafe. Taking this into consideration, I'd like to know which mechanism to use for password protection.  This question,   suggests that hashing multiple times may be a good idea, whereas  suggests using salt.  I'm using PHP. I want a safe and fast password encryption system. Hashing a password a million times may be safer, but also slower. How to achieve a good balance between speed and safety? Also, I'd prefer the result to have a constant number of characters.   The hashing mechanism must be available in PHP It must be safe It can use salt (in this case, are all salts equally good? Is there any way to generate good salts?)   Also, should I store two fields in the database (one using MD5 and another one using SHA, for example)? Would it make it safer or unsafer?  In case I wasn't clear enough, I want to know which hashing function(s) to use and how to pick a good salt in order to have a safe and fast password protection mechanism.  Related questions that don't quite cover my question:


In all terminals I can think of, tput reset is much faster than reset, why? (sh, bash, xfce4-terminal, lxde-terminal, gnome-terminal, and probably others)   I know the technical reason, reset issues a nanosleep() sleep syscall, while tput reset does not, but what is the logical reason? why was/is it implemented this way?   For the record, tput reset is over 1000 times faster than reset in my xfce4-terminal:   time reset: real    0m1.002s time tput reset: real   0m0.001s   Edit: also, any reason to NOT add alias reset='tput reset' to ~/.bashrc ?

The reset command includes a delay, between clearing the screen and returning.  This is even on the latest terminal type xterm-256color.  Why?  man reset does not mention a delay, only the printing of special strings.  (It doesn't mention clearing the screen either.  I assume this is included under the terminal initialization string).  I notice the follow output in strace -f reset:  nanosleep({tv_sec=1, tv_nsec=0}, 0x7ffe1964f100) = 0 ioctl(2, SNDCTL_TMR_STOP or TCSETSW, {B38400 opost isig icanon echo ...}) = 0


I am using the jQuery validation plugin. How to validate ISBN number formats in jQuery rule or pattern or Regular Expressions? Is there any Regular Expressions to achieve this? Please share your idea.  jQuery.validator.addMethod("isbnNo", function(value, element) {     return isValidISBN(value); }, "Please enter valid ISBN number");  // ISBN Number validationValidation function isValidISBN(isbn) {       isbn = isbn.replace(/[^\dX]/gi, '');       if(isbn.length < 10 || isbn.length > 13){         return false;       }       var chars = isbn.split('');       if(chars[9].toUpperCase() == 'X'){         chars[9] = 10;       }       var sum = 0;       for (var i = 0; i < chars.length; i++) {         sum += ((10-i) * parseInt(chars[i]));       };       return ((sum % 11) == 0);      }

How do you create a simple, custom rule using the jQuery Validate plugin (using ) that doesn't use a regex?  For example, what function would create a rule that validates only if at least one of a group of checkboxes is checked?


My textbook defined general cartesian products as: Let $\{A_\alpha| \alpha\in\mathbb{A}\}$ be a family of sets. The the cartesian product $\prod_{\alpha} A_\alpha$ is the set of all maps $c$: $\mathbb{A}\rightarrow\cup_{\alpha} A_\alpha$ having the property $\forall\alpha\in\mathbb{A}: c(\alpha)\in A_\alpha$.  Since the cartesian product $A*B\neq B*A$, I was wondering is index set $\mathbb{A}$ always has some order to make sure the general product, for example, is $A_{\alpha 1}*A_{\alpha 2}*A_{\alpha 3}*\dots$ not  $A_{\alpha 2}*A_{\alpha 1}*A_{\alpha 3}*\dots$, or the general cartesian product includes both the cases $A_{\alpha 1}*A_{\alpha 2}*A_{\alpha 3}\dots$ and $A_{\alpha 2}*A_{\alpha 1}*A_{\alpha 3}*\dots$.   It somehow seems in either case the map $c(\alpha)\in A_\alpha$ is defined. Thanks!

In Introduction to Topology, Mendelson defines the Cartesian Product of an Indexed Family as follows:     DEFINITION  Let $\{X_\alpha\}_{\alpha \in I}$ be an indexed family of sets. The product  of the sets $\{X_\alpha\}_{\alpha \in I}$,    written  $\prod_{x\in I}X_\alpha$ consists of all functions $x$ with domain the indexing set $I$ having the property that for each $\alpha \in I$, $x(\alpha)\in X_\alpha$.    Halmos, in Naive Set Theory, makes the following observation about this sort of product:     Ordered triples, ordered quadruples, etc., may be defined as families whose index sets are unordered triples, quadruples, etc.   However, it is not immediately apparent to me why this is true. It makes sense if we understand the prior assertions in Halmos that $\prod_{i \in I} X_i = X_i$ and that $\prod_{i \in I} X_i = X_a \times X_b$ when $I = \{a, b\}$, but these already pose difficulty for me.  Let $I = \{0, 1\}$, let $X_0 = \{A, B\}$, and let $X_1 = \{C, D\}$. Then by Mendelson's (and Halmos's) definitions, it would seem to me that . . .  $$\prod_{i \in I} X_ i = \{\{(0, A), (1, C)\}, \{(0, A), (1, D)\}, \{(0, B), (1, C)\}, \{(0, B), (1, D)\}\}$$  This would appear to me to be the set of all functions matching the definition given, but it is not equal to $X_0 \times X_1$. Moreover, extending this to a case where the index set $I$ is a triple, we would not end up with ordered triples, but with each subset of the product containing three ordered pairs.  When Halmos posits the equalities he does, the idea seems easy to grasp, but the peculiar wording of Mendelson's definition suggests something different to me.


Can anyone help with this sentence? Is my punctuation here correct?  If you sell bicycles, sell as many accessories as you can; water bottles; pumps; and biking gear, such as shoes, gloves, caps and more.

While writing a proposal at work today I needed to mention a list of things and within that list were multi-part items. It seems like replacing the comma with a semi-colon in this situation would make the sentence easier to understand, but is it correct usage?  With standard punctuation this could get confusing:       Some of my favorite things to do are   camping, playing football and   baseball, watching Laurel and Hardy   Movies, and traveling.   Proposed alternative. Is this acceptable usage?       Some of my favorite things to do are   camping; playing football and   baseball; watching Laurel and Hardy   Movies; and traveling.


Show that $\left(\frac{n^{\frac{3}{2}}}{2^n}\right)_{n\geq 0}$ is a null sequence. A null sequence is a sequence tending to $0$.   We need to find a $N\in \mathbb{N}$ for every $\varepsilon >0$, such that $n\geq N:|a_n-0|<\varepsilon$.  Usually, I first try to simplify the argument, but that does not work, since we have $n$ as the exponent and as a base. Secondly, I'll try to achieve an inequality like $n>...$. Tis sadly doesn't work out aswell. This expression is way to hard to simplify.  Is there another method, an easier way to solve this problem?

In other words, how to prove:  For all real constants $a$ and $b$ such that $a > 1$, $$\lim_{n\to\infty}\frac{n^b}{a^n} = 0$$  I know the definition of limit but I feel that it's not enough to prove this theorem.


I have this string in php  $tagged   and I want to put it in my javacript script inside the ' '  tagName: '',   how do I do this

What is the easiest way to encode a PHP string for output to a JavaScript variable?  I have a PHP string which includes quotes and newlines.  I need the contents of this string to be put into a JavaScript variable.  Normally, I would just construct my JavaScript in a PHP file, à la:  <script>   var myvar = "<?php echo $myVarValue;?>"; </script>   However, this doesn't work when $myVarValue contains quotes or newlines.


I want to create a new linux distro with customized name,customized wallpaper,customized packages etc.Can i do it keeping ubuntu 14.04 as base and installing packages etc on it.  Also i have successfully created a livecd using ubuntu uck but when it boots it shows ubuntu photos while installing operating system.  I want my customized photos should be displayed while installing my created operating system.  I know its kind of weard but appreciate if someone can help me... : )  Regards

I would like to know how can I customize the Ubuntu installer NOT customize Ubuntu, I just want to modify the installer.  We have a large environment here with lots of developers and since we don't use Windows, I want to customize the installer to automatically set the timezone to NYC, the keyboard layout to English USA, put the company logo in the installer etc...


I used WuBi to install Ubuntu. I did this after I did a factory restore on my Windows 7 Desktop, and cleaned out unnecessary junk, defragged, etc. I also did some hardware tests, and everything seems to work. This is my first experience with Ubuntu or any Linux system.  It shows the grub screen where it's asks if I want windows or ubuntu, and I select Ubuntu. Then Ubuntu crashes at the login screen(or just prior to it), makes repeated beeping noises(in a loop), and has these strange diagonal lines through the screen.  Any suggestions on how to fix the problem?

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


So i've tried so find something about this but without any success. Does anyone know what this essentially does (e.g. inside a loop)?  static bool thing = (someFunction(), true);

How does the comma operator work in C++?  For instance, if I do:  a = b, c;     Does a end up equaling b or c?   (Yes, I know this is easy to test - just documenting on here for someone to find the answer quickly.)  Update:  This question has exposed a nuance when using the comma operator.  Just to document this:  a = b, c;    // a is set to the value of b!  a = (b, c);  // a is set to the value of c!   This question was actually inspired by a typo in code.  What was intended to be  a = b; c = d;   Turned into  a = b,    //  <-  Note comma typo! c = d;


It is well known that a subgroup of $PSL(2,\mathbb{R})$ is discrete iff it acts properly discontinuously on the hyperbolic plane $\mathbb{H}$.  I wounder - does the same hold for a discrete group of isometries of $\mathbb {H}^n$ for $n>2$?  Also, a reference regarding hyperbolic isometries of high dimension would be of help, even not only about this specific question.

I was reading the article "The Geometries of 3-manifolds" by Peter Scott and in the end of page 406 he states the following:     If $G$ acts properly discontinuously on a space $X$, then $G$ is a   discrete subset of the space of all continuous functions $X \to X$   with the compact-open topology. The converse is false, in general, but   is true if $X$ is a complete Riemannian manifold and $G$ is a group of   isometries of $X$.   How do I prove the last statement?     If $X$ is a complete Riemannian manifold and   $G$ is a group of isometries of $X$ acting properly discontinuously on $X$, then $G$ is discrete.    Observation: We say a group $G$ of homeomorphisms of $X$ acts properly discontinuously on $X$ if for every compact $K \subset X$ the set $$\{g \in G: gK \cap K \neq \emptyset\}$$ is finite.


I am trying to install the desktop environment of lubuntu on Ubuntu 18.04.02 but I am getting the following error:  $ sudo apt install -y lubuntu-desktop Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  lubuntu-desktop : Depends: lubuntu-gtk-core but it is not going to be installed                    Depends: lubuntu-gtk-desktop but it is not going to be installed E: Unable to correct problems, you have held broken packages.   Any idea how to address this?

After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.


I have a list of arbitrary length, and I need to split it up into equal size chunks and operate on it. There are some obvious ways to do this, like keeping a counter and two lists, and when the second list fills up, add it to the first list and empty the second list for the next round of data, but this is potentially extremely expensive.  I was wondering if anyone had a good solution to this for lists of any length, e.g. using generators.  I was looking for something useful in itertools but I couldn't find anything obviously useful. Might've missed it, though.  Related question:


I am confused with the input and output, can anyone tell me why I get such output.  #include<iostream> #include<stdlib.h> using namespace std;  int main() {     int ival, oddcnt(0), evencnt(0);     while (cin >> ival) {         switch (ival) {         case 1, 3, 5, 7, 9:             oddcnt++;             break;         case 2, 4, 6, 8, 10:             evencnt++;             break;         }     }     cout << "Quantity of odd number:" << oddcnt << "\n"         << "Quantity of even number:" << evencnt << endl;     system("pause");     return 0; }   This is the result I get: Input:1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 6 6 6 7 7 7 7 8 8 9 9 10 10 10 EOF Output:Quantity of odd number:2        Quantity of even number:3


On pg 195 of the book "Algebraic Topology", Hatcher says the following:     Every abelian group $H$ has a free resolution of the form $0\to F_1\to F_0\to H\to 0$, with $F_i=0$ for $i>1$.    He justifies this by saying that the kernel of the map $F_0\to H$ is a subgroup of the free group $F_0$, and hence also free. This would imply that $F_1$ is free, and hence the map $F_1\to F_0$ would have a trivial kernel.   Why isn't this true for non-abelian groups? Wouldn't the same argument be applicable even there?

This is probably a very easy question but I think I am missing some background regarding free abelian groups to answer it for myself.  In Hatcher's Algebraic Topology, the idea of a free resolution is introduced in the section on cohomology.       A $\textbf{free resolution}$ of an abelian group is an exact sequence $$F_2 \to F_1 \to F_0 \to H \to 0$$ such that each $F_i$ is free.    Let $f_0:F_0 \to H$ and choose a set of generators of $H$. Let $F_0$ be the free abelian group with basis in one-to-one correspondence with this set of generators.   Then we can easily form the two term free resolution   $$\to 0 \to Ker(f_0) \to F_0 \to H \to 0$$  Why is $H$ an abelian group a necessary condition so that there necessarily exists resolution of the form $0 \to F_1 \to F_0 \to H \to 0$?   For what non-abelian group does such a free resolution not exist?


I am getting null pointer exception problem on MyFirebaseInstanceIDService class. I have used try catch but still there exist the problems. Please help me find the problem. Thanks in advance.  public class MyFirebaseInstanceIDService extends FirebaseInstanceIdService {     Response response;     SharedPreferences sharedPrefs;     SharedPreferences.Editor ed;     @Override     public void onTokenRefresh() {          String token = FirebaseInstanceId.getInstance().getToken();          sharedPrefs = getSharedPreferences("settings", MODE_PRIVATE);         ed = sharedPrefs.edit();         ed.putString("tokana", token);         ed.commit();         registerToken(token);     }      private void registerToken(String token) {         OkHttpClient client = new OkHttpClient();         RequestBody body = new FormBody.Builder()                 .add("Token",token)                 .build();          Request request = new Request.Builder()                 .url("http://example.com/register.php")                 .post(body)                 .build();          try {             response = client.newCall(request).execute();            // System.out.println("working...");          } catch (IOException e) {             e.printStackTrace();         }finally {             response.body().close();         }      } }   This problem is shown on some devices. The following is the crash report from play store.  java.lang.NullPointerException:   at com.ramropatro.app.MyFirebaseInstanceIDService.onTokenRefresh (MyFirebaseInstanceIDService.java) or                     .registerToken (MyFirebaseInstanceIDService.java)  at com.ramropatro.app.MyFirebaseInstanceIDService.onTokenRefresh (MyFirebaseInstanceIDService.java) or                     .registerToken (MyFirebaseInstanceIDService.java)  at com.google.firebase.iid.FirebaseInstanceIdService.onTokenRefresh (FirebaseInstanceIdService.java) or                     .zza (FirebaseInstanceIdService.java) or                     .zzbI (FirebaseInstanceIdService.java) or                     .zzca (FirebaseInstanceIdService.java) or                     .zzhi (FirebaseInstanceIdService.java) or                     .zzo (FirebaseInstanceIdService.java)  at com.google.firebase.iid.FirebaseInstanceIdService.handleIntent (FirebaseInstanceIdService.java) or                     .zzbK (FirebaseInstanceIdService.java) or                     .zzbZ (FirebaseInstanceIdService.java)  at com.google.firebase.iid.zzc.run (zzc.java)  at java.util.concurrent.ThreadPoolExecutor.runWorker (ThreadPoolExecutor.java:1112)  at java.util.concurrent.ThreadPoolExecutor$Worker.run (ThreadPoolExecutor.java:587)  at java.lang.Thread.run (Thread.java:818)

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


I'm trying to install the hardware enablement stack onto 12.04 but I'm running into the following dependency issue:  The following packages have unmet dependencies:  libgl1-mesa-glx-lts-trusty: Depends: libglapi-mesa-lts-trusty (= 10.1.3-0ubuntu0.1~precise1) but 10.1.3-0ubuntu0.1~precise1 is to be installed                             Depends: libx11-6 (>= 2:1.4.99.1) but 2:1.4.99.1-0ubuntu2.2 is to be installed                             Depends: libxdamage1 (>= 1:1.1) but 1:1.1.3-2build1 is to be installed xserver-xorg-lts-trusty: Depends: xserver-xorg-core-lts-trusty (>= 2:1.11) but 2:1.15.1-0ubuntu2~precise1 is to be installed   How can I circumvent this and get the HWE to install?

Occasionally, when I'm installing stuff, I get an error like the following:  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  package1 : Depends: package2 (>= 1.8) but 1.7.5-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.   How can I resolve this?


I'm trying to use a single array across multiple methods; when I try to print the values of the array after I have defined them in another method I get the error Exception in thread "main" java.lang.NullPointerException     at shop.main(shop.java:130)  public static int[] discount; public static double[] price; public static String[] name;  public static void setup(Scanner input, String[] name, double[] price, int[] discount) {     System.out.print("Please enter the number of items to setup shop: ");     do {         CheeseNum = input.nextInt();         if (CheeseNum < 0) {             System.out.print("Invalid Input. Enter a value > 0: ");         }     } while (CheeseNum < 0);     System.out.printf("\n");      discount = new int[CheeseNum];     price = new double[CheeseNum];     name = new String[CheeseNum];      for (int i = 0; i < CheeseNum; i++){         System.out.print("Enter the name of the " + numSuffix(i + 1) + " product: ");         name[i] = input.next();         System.out.printf("Enter the per package price of " + name[i] + ": ");         price[i] = input.nextDouble();         System.out.printf("Enter the number of packages ('x') to qualify for Special Discount (buy 'x' get 1 free) for " + name[i] + ", or 0 if no Special Discount offered:");         discount[i] = input.nextInt();     } }  public static void buy(Scanner input, String[] name, int[] purchased) {     purchased = new int[CheeseNum];     for (int i = 0; i < CheeseNum; i++){         System.out.printf("\nEnter the number of " + name[i] + " packages to buy: ");         purchased[i] = input.nextInt();         shopBuyIns = shopBuyIns + purchased[i];     } }   So whats happening is the user inputs the values for the array in setup, and when I try to use those values in buy it tells me the arrays are null.


Let $G$ be a Lie group with Lie algebra $\mathfrak g$. I'm trying to prove the first two terms of the Baker-Campbell-Hausdorff formula for $\exp(tX)\exp(tY)$ satisfy $$ (\exp tX)(\exp tY) = \exp\big(t(X+Y) + \frac 1 2 t^2 [X,Y] + t^3 \hat Z(t)\big)  $$ for some smooth function $\hat Z: (-\epsilon, \epsilon) \to \mathfrak g$ and some $\epsilon > 0$, for every $X, Y \in \mathfrak g$.   What I've tried: Since $\exp : \mathfrak g \to G$ restricts to a diffeomorphism from a neighborhood of $0 \in \mathfrak{g}$ to a neighborhood of $e \in G$, the map $\phi : (-\epsilon, \epsilon) \to \mathfrak g$ defined by  $$ \phi(t) = \exp^{-1}(\exp tX \exp tY) $$ is smooth for some $\epsilon > 0$. So the problem amounts to proving $\phi''(0) = [X,Y]$ and applying Taylor's theorem. But I'm not sure how to do this without knowing the derivative of multiplication $G \times G \to G$ at general points $(g,h) \in G \times G$. I'm wondering if there's a more clever approach having something to do with the adjoint representations $\mathrm{Ad}: G \to \mathrm{GL}(\mathfrak g)$ and $\mathrm{Ad}_* = \mathrm{ad}: \mathfrak g \to \mathfrak{gl}(\mathfrak{g})$ since $\mathrm{ad}(X)Y = [X,Y]$. Any advice would be appreciated.

Problem 20-9 in Lee's Introduction to Smooth Manifolds (2nd Ed.) asks to prove that for a Lie group $G$, and for $X, Y\in \text{Lie}(G)=\mathfrak g$, there is $\epsilon>0$ and a smooth map $Z:(-\epsilon, \epsilon)\to \mathfrak g$ such that   $$(\exp tX)(\exp tY) = \exp\left(t(X+Y) + \frac{1}{2}t^2[X, Y] + t^3 Z(t)\right)$$   What we want to show is that the first and second term in the Taylor expansion of $\exp^{-1}\left((\exp tX)(\exp tY)\right)$ are $t(X+Y)$ and $\frac{1}{2}t^2[X, Y]$ respectively.  Calculating the first term is easy since we just need to differentiate $\exp^{-1}((\exp tX)(\exp tY))$ with respect to $t$ at $t=0$ once, and this gives the desired result.  But for the second term we need to take the second derivative at which I am stuck.


Let $A_n$ denote an $n \times n$ tridiagonal matrix.  $$A_n=\begin{pmatrix}2 & -1 & & & 0 \\ -1 & 2 & -1 & & \\ & \ddots & \ddots & \ddots & \\ & & -1 & 2 & -1 \\ 0 & & & -1 & 2 \end{pmatrix} \quad\text{for }n \ge 2$$  Set $D_n = \det(A_n)$  Prove that $D_n = 2D_{n-1} - D_{n-2}$ for $n \ge 4$.

How to show that the determinant of the following $(n\times n)$ matrix  $$\begin{pmatrix} 5 & 2 & 0 & 0 & 0 & \cdots & 0 \\ 2 & 5 & 2 & 0 & 0 & \cdots & 0 \\ 0 & 2 & 5 & 2 & 0 & \cdots & 0 \\ \vdots & \vdots& \vdots& \vdots & \vdots & \vdots & \vdots \\ 0 & \cdots & \cdots & 0 & 2 & 5 & 2 \\ 0 & \cdots & \cdots & \cdots & \cdots & 2 & 5 \end{pmatrix}$$  is equal to $\frac13(4^{n+1}-1)$?    More generally:     How does one compute the determinant of the following  (where the three diagonals are constant)?      $$M_n(a,b,c) = \begin{pmatrix} a & b & 0 & 0 & 0 & \cdots & 0 \\ c & a & b & 0 & 0 & \cdots & 0 \\ 0 & c & a & b & 0 & \cdots & 0 \\ \vdots & \vdots& \vdots& \vdots & \vdots& \vdots & \vdots \\ 0 & \cdots & \cdots & 0 & c & a & b \\ 0 & \cdots & \cdots & \cdots & \cdots & c & a \end{pmatrix}$$      Here $a,b,c$ can be taken to be real numbers, or complex numbers.   In other words, the matrix $M_n(a,b,c) = (m_{ij})_{1 \le i,j \le n}$ is such that $$m_{ij} = \begin{cases} a & i = j, \\ b & i = j - 1, \\ c & i = j + 1, \\ 0 & \text{otherwise.} \end{cases}$$  There does not seem to be an easy pattern to use induction: the matrix is not a diagonal  of the type $M = \bigl(\begin{smallmatrix} A & C \\ 0 & B \end{smallmatrix}\bigr)$ (where we could use $\det(M) = \det(A) \det(B)$ for the induction step), and there are no lines or columns with only one nonzero entry, so  gets complicated quickly.  Is there a general pattern that one could use? Or is the answer only known on a case-by-case basis? It's possible to compute the determinant by hand for small $n$:  $$\begin{align} \det(M_1(a,b,c)) & = \begin{vmatrix} a \end{vmatrix} = a  \\ \det(M_2(a,b,c)) & = \begin{vmatrix} a & b \\ c & a \end{vmatrix} = a^2 - bc \\ \det(M_3(a,b,c)) & = \begin{vmatrix} a & b & 0 \\ c & a & b \\ 0 & c & a \end{vmatrix} = a^3 - 2abc \end{align}$$  But there is no readily apparent pattern and the computation becomes very difficult when $n$ gets large.


I am looking at a valid question with 4 votes to close on a site. I think the collective conscious has edited the question to make it appropriate, and there are answers for that question now.  With one more vote that question will be closed, creating cognitive dissonance about acceptable questions on that site.  The current recourse is to wait for the question to be closed, and then begin voting to reopen.  Instead there should also be a way to negate a vote to close, with a vote to keep open.  Thoughts?

My request is simple: Many times, there will be a question where some people feel like it should be closed. At the same time, I'll feel like it's a perfectly legit question, and it should therefore NOT be closed. Right now, I have to wait till it gets enough close votes (which it always does for some reason, as soon as 1 or 2 people vote to close, e/o else decides to vote as well) and then vote to re-open. How about, as soon as there's one vote to close, there should be an option to counter the close vote, something like "vote not to close" or whatever. This would then bring the "Vote to close" number down by one. Only when the vote to close outnumbers the vote not to close by 5, that's when a question is indeed closed. Any thoughts?


I'm currently going through University Physics by Young & Freedman, and there's one paragraph (13th edition, end of section 4.5, page 123), I just can't wrap my head around - why is the tension in the rope $50\ \mathrm N$ and what is the equation giving us "the magnitude of force acting at that point", when obviously, from what it says in this paragraph, it is not the net force?    (Background: I am a mathematics student on a year abroad in the UK who made the questionable decision to take an introductory physics module covering the entire contents of the textbook, assuming that the theory would be covered in the lectures, but apparently the knowledge of A-level physics is assumed and my prior knowledge of physics at the beginning of the term basically boils down to "what is uniform motion?", so at the moment I spend most of the day reading through Y&F and watching Walter Lewin's lectures.)

I'm going to provide my argument for why I think the tension in a rope should be twice the force exerted on either side of it.  First, let's consider a different example. Say, there is a person named A and a block in space. A pushes on the block with a force of 100 N. Then, the block will also push A with a force of 100 N by Newton's third law. Now, consider the case where instead of the block, there is a person B who is also pushing on A with a force of 100 N while A is pushing on him. A will experience a force of 100 N because he pushed on B, AND another 100 N because he is being pushed by B. Hence he will experience a force of 200 N. Similarly, B also experiences 200 N of force.  Now, back to the original problem. There are two people A and B in space with a taut rope (no tension currently) in between them. If only A is pulling and B is not, then I agree that the tension is equal to the force A exerts. This situation (in my opinion) becomes analogous to the above if B is also pulling. So, say both of them pull from either side with a force of 100 N. Then the rope at the end of B will pull B with a force of 100 N (this pull is caused by A). By Newton's third law, the rope will experience a pull of 100 N. But B is also pulling his end of the rope with 100 N. Therefore, the tension should be 200 N. Similarly, the end of the rope at A must pull A with 100 N of force (because B is pulling from the other side) and hence experience a force of 100 N itself by Newton's third law plus another 100 N because A is pulling on the rope.  Apparently, the answer is not this (according to my searching on the web). So, could anyone tell me why this reasoning is wrong? Thanks.  EDIT : So apparently people don't agree with my first example, leave alone the second. This is to the downvoters and the upvoters of the highest-rated answer: You all agree that if only A pushes B with a force of 100 N, then A and B both will get pushed by a force of 100 N in opposite directions, right? Then, in the case where B is also pushing with a force of 100 N, it doesn't make sense that the answer would be exactly the same. It doesn't seem right that no matter what B does, B and A will always experience the same force as they would have if B hadn't applied any force.  EDIT 2 : I'm going to provide here a link to a question that I posted:  According to the answer and the comments there, the reason as to why my first example is incorrect is different to the one provided here. So maybe you should all read the answer and the comments provided by the person and reconsider what you think.