Which sans-serif fonts are best suited for body text? Currently I think about Gill Sans, Proxima Nova or Frutiger, but since I'm not full-stack graphic designer or typographer, I'm not sure in my choice.  The text should be easily read in large amounts, from screen, with long lines, also it should have hightly distinctive bold and italic versions.  But it's not for website. It's for Word documents, for personal use. I write a lot of stuff for myself and I want to read it in easy way.


I often catch myself trying to write ?explaination, phonetically spelling the word in my head. To my chagrin I get part way through and have to stop myself.  So I’m wondering why is the i dropped? I can’t think of other words ending ‑ain that take the ‑ation suffix for comparison.


I’ve found a small, yet annoying, CSS-error in the mobile view of Stack Exchange. It seems like long titles breaks the style, which causes the up-vote arrow and the answer button to break the row and fall beneath the intended spot. From the looks of it, the title cell, or the tags, increase too much and causes this minor CSS-error.    Is it possible to fix this?


Android development - Access JSON within fragment - java.lang.NullPointerException

I am new with android development. I am using TABLayout and I am having a problem getting information from the JSON data set inside a fragment.  Inside the fragment, I implement an AsyncTask that is evoked inside the fragment’s method onCreate.  In doInBackground I save the JSON data in an object (eventsDetail) that is public for the fragment class.  Inside of onCreateView I use eventsDetail to populate various string widgets. Also, I populate longitude and latitude data to a map (SupportMapFragment).   When I first enter at onCreateView I have no issues. Then I leave the fragment. When I go back into the fragment again, I receive the error (java.lang.NullPointerException) on the eventsDetail object.  Has anyone encountered this problem? I think the problem is that I am accessing the JSON incorrectly.


Basis of $\mathbb{R}^2_{\rm discrete}$ with the lexicographic order topology

I have a homework problem that asks us to find the basis $\mathbb{R}^2_{\rm discrete}$ with the lexicographic order topology. I actually have no idea, so any help is greatly appreciated. Thank you!


How to run two-way ANOVA on data with neither normality nor equality of variance in R?

I am working on my master thesis at the moment and planned on running the statistics with SigmaPlot. However, after spending some time with my data I came to the conclusion that SigmaPlot might not be fit for my problem (I may be mistaken) so I started my first attempts in R, which did not exactly make it easier.  The plan was to run a simple TWO-WAY-ANOVA on my data which results from 3 different proteins and 8 different treatments on those, so my two factors are proteins and treatments. I tested for normality using both  > shapiro.test(time)   and  > ks.test(time, "norm", mean=mean(time), sd=sqrt(var(time)))   In both cases (maybe not surprising) I ended up with a non-normal distribution.  Which left me with the first questions of which test to use for equality of variances. I came up with  > chisq.test(time)   and the result was, that I don't have equality of variance in my data either.  I tried different data transformations (log, center, standardization), all of which did not solve my problems with the variances.  Now I am at a loss, how to conduct the ANOVA for testing which proteins and which treatments differ significantly from each other. I found something about a Kruskal-Walis-Test, but only for one factor (?). I also found things about ranking or randamization, but not yet how to implement those techniques in R.  Does anyone have a suggestion what I should do?  Edit: thank you for your answers, I am a little overwhelmed by the reading (it just seems getting more and more instead of less), but I will of course keep going.  Here an example of my data, as suggested (I am very sorry for the format, I couldn't figure out another solution or place to put a file. I am still new to this all.):    protein treatment   time   A   con 2329.0   A   HY  1072.0   A   CL1 4435.0   A   CL2 2971.0   A   CL1-HY sim  823.5   A   CL2-HY sim  491.5   A   CL1+HY mix  2510.5   A   CL2+HY mix  2484.5   A   con 2454.0   A   HY  1180.5   A   CL1 3249.7   A   CL2 2106.7   A   CL1-HY sim  993.0   A   CL2-HY sim  817.5   A   CL1+HY mix  1981.0   A   CL2+HY mix  2687.5   B   con 1482.0   B   HY  2084.7   B   CL1 1498.0   B   CL2 1258.5   B   CL1-HY sim  1795.7   B   CL2-HY sim  1804.5   B   CL1+HY mix  1633.0   B   CL2+HY mix  1416.3   B   con 1339.0   B   HY  2119.0   B   CL1 1093.3   B   CL2 1026.5   B   CL1-HY sim  2315.5   B   CL2-HY sim  2048.5   B   CL1+HY mix  1465.0   B   CL2+HY mix  2334.5   C   con 1614.8   C   HY  1525.5   C   CL1 426.3   C   CL2 1192.0   C   CL1-HY sim  1546.0   C   CL2-HY sim  874.5   C   CL1+HY mix  1386.0   C   CL2+HY mix  364.5   C   con 1907.5   C   HY  1152.5   C   CL1 639.7   C   CL2 1306.5   C   CL1-HY sim  1515.0   C   CL2-HY sim  1251.0   C   CL1+HY mix  1350.5   C   CL2+HY mix  1230.5


13.10 BCM4313 network problems after update

I have a problem with my network adapter after upgrading from 13.04 to 13.10. The adapter works for literally several seconds after I establish the connection but then it looks as if it got clogged somehow.  This is what I see amongst my devices:  ~$ lspci | grep -i wireless 02:00.0 Network controller: Broadcom Corporation BCM4313 802.11bgn Wireless Network Adapter (rev 01) ~$ uname -a Linux bubek 3.11.0-12-generic #19-Ubuntu SMP Wed Oct 9 16:12:00 UTC 2013 i686 i686 i686 GNU/Linux ~$ lsmod | grep 80211 lib80211_crypt_tkip    17387  0  lib80211               14040  2 wl,lib80211_crypt_tkip cfg80211              401436  1 wl   Now, how does is behave. Let's assume I connect to my wireless network and straight after I get connected I ping the default gw:  ~$ ping 10.1.0.1 PING 10.1.0.1 (10.1.0.1) 56(84) bytes of data. 64 bytes from 10.1.0.1: icmp_seq=1 ttl=64 time=226 ms 64 bytes from 10.1.0.1: icmp_seq=4 ttl=64 time=222 ms 64 bytes from 10.1.0.1: icmp_seq=7 ttl=64 time=260 ms 64 bytes from 10.1.0.1: icmp_seq=11 ttl=64 time=265 ms 64 bytes from 10.1.0.1: icmp_seq=16 ttl=64 time=117 ms From 10.1.0.16 icmp_seq=45 Destination Host Unreachable From 10.1.0.16 icmp_seq=46 Destination Host Unreachable   What has happened over here? Is there any possibility I can get it working? The only way I could write that post was that I used my phone and USB tethering :)  Thanks for any tips in advance!


Ubuntu 16.04 not mounting windows partitions

I have a problem with Ubuntu mounting windows partitions. When I turn on the computer, Ubuntu is not mounting my windows partition (sda3). It gives this error message:  Unable to access "Main memory"


I'm currently peer-reviewing a paper (for a computer science conference; review is double-blind). While reading it, I came up with a method for the problem they're solving, somewhat inspired by their approach but fairly separate. I haven't implemented and tested it yet, but I expect it to be better than their approach, and it is definitely (in my mind) simpler. The idea came from slightly reframing their approach based on papers that they've cited in their submission, so they had the tools to do so, but they may not be as familiar with as I am (it happens to be right in my wheelhouse).  I see two options here:   Suggest the reframing and the new method to them in the review. They may or may not do anything about it, but if they do, all I get is thanks to an anonymous reviewer in their acknowledgements, assuming the paper gets in. (In my opinion, their paper is probably borderline for this conference.) If they don't use the idea, then it just goes away. Don't say anything about it in the review; develop the method independently. think, at this early stage, that it's reasonably likely a whole new paper can be written based on this method and related improvements I have in mind. If their paper gets in to this conference, or is put online / gets in somewhere else before I'm done with my paper, cite them. If it doesn't, I could either ignore their paper and write my own – which feels somewhat dishonest, though I wouldn't really be using their results in my new paper – or ask the PC to get me in touch with the authors for possibly collaborating on a single joint paper with both methods. I don't know if that kind of thing is ever done.   Option 1 is clearly ethical, but if option 2 is also ethical, it's both better for my career and possibly better for scientific progress as a whole (if they don't end up using the idea). So my question is: is option 2 okay? What do I do in the case where their paper doesn't get in?


I'm searching on internet but I can't find anything about it.  Is there a way to do a scan for a wifi connection and to connect to one with a C/C++ program in Linux?


Exchanging US dollars for Australian Dollars

Traveling to Australia, where is best place to exchange money?  US Bank?  Airport in LAX?  SLC airport or in Australia


Does DVI carry audio?  My monitor has 4 HDMI inputs and I am going from a device that only has DVI output will the audio follow on the DVI to HDMI adapter?


How to logout an user from the connected app?

NOTE: I am not interested in calling /secur/logout.jsp since it ends all the active salesforce sessions.  I am developing a web application that is registered on salesforce as a connected app, so I am using salesforce credentials to authorize the user.  Application is developed in REST API and the communication with salesforce is happening in restful manner.   Auth url:   Authorization:  Method 1: If there is no salesforce session active, The user is taken to salesforce login page, where he enters his salesforce details to be authorized and after which he is taken to home page of my web application.  Method 2: If there is already a salesforce session active in another tab, the user is directly authorized and is taken to home page of my web application.  Now I am trying to implement logout button for my application, such that the following scenarios are covered,  Scene 1: The user is authorized using method1, and the user press the logout. Upon trying to logback the user is prompted for credentials.  Scene 2:  The user is authorized using method2, and the user should use logout to logout of the web application (not from active sessions). Upon login, the user should be again able to login using method2.  Can someone help me on how to implement the logout button such that it covers scenario 1 & 2.  Thanks in advance.


How can I automatically log out the guest account after a period of inactivity?

As part of a kiosk system, I have set up a Guest account on a Mac OS X Snow Leopard computer. This account is cleared every time someone logs off the computer. However, plenty of people don't. Is there any way that I can automatically log out this guest account after a period of inactivity?  I tried using the security preferences pane, but that just causes the confirm logout dialog to show up.  I have hacked around the /System/Library/User Templates/ folder, so I can set the screensaver, desktop background, &c. If something like ScriptSaver can solve my problem, I will gladly use it.


How can I change my name on a Stack Exchange site?

How can I change (or remove / reset ) my name on a site in Stack Exchange network?


Changing the position of right click menu items

I would very much like to reposition the AMD Radeon Settings option to be lower in the list. Is this even possible?    Thanks


How to type commands in PuTTY by creating batch file?

I have created a .bat file which automatically takes the SSH server (Jump Server) access. Now, I have couple of commands which I would like to hit in that window.  For an ex. (To take root access)  usrun -u root rush   With this command, it'll ask me to enter the password.  So, how can I achieve this entirely through .bat file?


This is from Putnam:     If a function $f: \mathbb{R} \to [-1, 1]$ is such that $f''(x)$ exists for all $x \in \mathbb{R}$ and $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then prove that there is a point $c$ such that $f(c) + f''(c) = 0$.   Now the condition concerning values of $f(0), f'(0)$ (and the fact that range of $f$ is subset of $[-1, 1]$) implies that $f'(0) \neq 0$ so that function is not a constant. If we take $g(x) = \{f(x)\}^{2} + \{f'(x)\}^{2}$ then we can see that $g' = 2f'(f + f'')$. One hope of solving the problem is to show that $g$ attains local extrema at some point different from an extrema of $f$. This would ensure that $g'$ vanishes without making $f'$ vanish and that will lead to $f + f'' = 0$. However the constraint on $f(0), f'(0)$ does not help in analyzing the extrema of $f$ or $g$.  Another line of thought which could be helpful here is to consider $F(x) = f'(x)\sin x - f(x)\cos x$ so that $F'(x) = \sin x\{f(x) + f''(x)\}$ but in this case I am not able to see how to use the condition on values $f(0), f'(0)$ to impose some constraint on $F(x)$.  Perhaps both the approaches which came to my mind are not in right direction (or may be they are, but I am unable to see). Please provide any hints.  Update: Based on the answer by Sandeep Thilakan, I have dropped the requirement for continuity of $f''(x)$.


Strange behaviour "for in" statement (NodeJS)

I think I miss something into the use of "for in" statement. I have a JSON document returned from a mongoDB query (nodejs + mongoose), his structure is like the following:    [{     "_id":"596f2f2ffbf8ab12bc8e5ee7",   "date":"1500458799794",   "questionId":4249,   "__v":0,   "myArray":[        "1234567",      "8901234",      "5678901"      ]   },   {     "_id":"596f2f2ffbf8ab12bc8e5ee5",   "date":"1500458799795",   "questionId":4245,   "__v":0,   "myArray":[        "1234565",      "5678905"      ]   }]   In a "for in" cicle I get each document and into another I want to iterate the array "myArray". The problem is when I try to iterate the array "myArray". If I iterate it with "for in" statement I receive a lot of other wrong stuff, like if I am iterating the document returned by the query:    [null,{},{"_id":"596f2f2ffbf8ab12bc8e5ee7","date":"1500458799794","questionId":4249,"__v":0,"myArray"["1234567","8901234","5678901"]},null,null,....,"myArray",true,[],{"caster":{"enumValues":[],"regExp":null,"path":"myArray","instance":"String","validators":[],"setters":[],"getters":[],"options":{},"_index":null},"path":"whoDislikes","instance":"Array"....etc etc... ]   If I iterate it with a classic for statement everything is good:       ["1234567","8901234","5678901"]  Why? The code is the following:     for(question in data){       var myArray=data[question].myArray;       console.log(JSON.stringify(myArray));   //this print ["1234567","8901234","5678901"]        for(var i=0;i<myArray.length;i++){          console.log(myArray[i]);   //this print ["1234567","8901234","5678901"]        }        for(element in myArray){           console.log(myArray[element]);   //this print a lot of wrong stuff!        }   }


I would like to solve for $x$ in $a = x^b\ (mod\ n)$ given $a$, $b$, $n$. How might I go about doing this?


$[L:K]$ dividing $n!$ with $L=K(\alpha_1,...\alpha_n)$, and $L$ a splitting field of $f$ with $\alpha_1..\alpha_n$ zeros of $f$

I have just proven the following statement:  Let $K$ be a field and $L$ the splitting field of a separable polynomial $f\in K[X]$ of degree $n$. Denote the zeros of $f$ in $L$ by $\alpha_1,\alpha_2,...,\alpha_n$. Then for $i=1,2,...,n$: $$ [K(\alpha_1,...,\alpha_i):K]\leq n(n-1)...(n-i+1). $$  I now need to show that $[L:K]$ divides $n!$.  What I figured out and I think I have to use:   $|\text{Gal}(L/K)|=[L:K]$  $L/K$ a normal and separable extension $|\text{Gal}(L'/K)|$ equals the number of distinct zeros of $f$ which lie in $L$ if $L'/K$ is a simple extension And as a hint: The Galoisgroup permutes zeros of polynomials


My profile picture in the top bar is distorted

So this is what it looks like for me, there's a gray square which is not supposed to be there. This is persistent across computers and reboots and cache refreshes:


How to recover contacts from an Android phone whose screen has died?

My daughter's Samsung Galaxy S4 has a faulty screen - it is completely non-functional. As it died the remainder of the phone functionality appeared to be completely fine. Now the screen is dead. So there is no way to see what is displayed nor interact with it.  She got a new phone and was dismayed to learn that most of her contacts did not appear. Apparently, unbeknownst to her, they were saved to the phone (not SIM) rather than Google.   Is there a way for her to recover those contacts from the screenless, but otherwise still-functioning, phone?  It does not appear that simply connecting it to USB will work. I thought about installing over-the-air the app AirDroid - but it appears it is too late to do that, since some of the setup appears to need to be done on the phone itself.  Any other solutions?  Thanks.


How do I make the FaceTime.app sound output louder on my MacBook?  It's too quiet for me to hear what the people on the other end are saying. Way quieter relative to every other app I use (YouTube in Safari, Discord calls, Microsoft Teams calls, etc.)  macOS Catalina 10.15, FaceTime 5.0


How do you determine if the series $\sum\limits_{k=1}^\infty \left(1-\frac1k\right)^{k^2}$ converges?

$$\sum_{k=1}^\infty \mathrm{(1-\frac{1}{k})}^{\mathrm{k}^{2}}$$ I tried using the limit comparison test with $$\sum_{k=1}^\infty \mathrm{(1-\frac{1}{k})}^{\mathrm{k}^{}}$$ but this leads to a limit of 0, which doesn't help. I think this may involve some use of  $\mathrm{e}^x$, but I don't know where else to start. Any suggestions?


I don't know how to prove that $$\lim_{n\to\infty} \frac{n}{\sqrt[n]{n!}} =e.$$ Are there other different (nontrivial) nice limit that gives $e$ apart from this and the following $$\sum_{k = 0}^\infty \frac{1}{k!} = \lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n = e\;?$$


How can I recover my BitLocker recovery key

my laptop has freezed, I restart it with power button but now, at start up, BitLocker said that:     You need to enter your recovery key because Secure Boot has been disabled. Either Secure Boot must be re-enabled, or BitLocker must be suspended for Windows to start normally.   I gone to UEFI settings and define a password to re-enabled Secure Boot but BitLocker when I restart comptuer said that Bios secure parameters has changed... It doesn't solve the problem.  The problem is I don't have my recovery key. I tried to recover my recovery key using Microsoft account but I had to update my phone number and so my security settings are locked for one month. My question is :   Is it possible to boot on Ubuntu USB key or plug HDD to an Ubuntu computer, copy files and decrypt them one by one with my password session ? Is it possible to retrieve my recovery key using Windows command line and session password ? (I can access to Windows recovery menu so I have access to commands line.) Is a program to decrypt completely my hard drive exists ? I will write it on a USB key, start it, enter my session password and it will decrypt all the disk or something like that.   Thanks a lot.


Can I disable GNOME legacy tray in 17.04?

The legacy tray (see the screenshot below) will be removed in GNOME 3.26. I want to wean myself off it before the change arrives in Ubuntu (17.10 or 18.04).    Can I disable the legacy tray in Ubuntu GNOME 17.04?


I want to prove the variation from      $$\int_{0}^{1}{(x-1)^2\over \sqrt{2^x-1}\ln(2^x-1)}dx=\color{blue}{\pi\over \ln^2{2}}\tag1$$   Sub $u=2^x-1\rightarrow du=2^x\ln{2}dx$  $x=1\rightarrow u=1$ and $x=0\rightarrow u=0$  $(x-1)^2={1\over \ln^2{2}}\ln^2\left({1+u\over 2}\right)$  $$I={1\over \ln{2}}\int_{0}^{1}{(x-1)^2\over \sqrt{u}(u+1)\ln{u}}du\tag2$$  $$I={1\over \ln^3{2}}\int_{0}^{1}{\ln^2\left({u+1\over 2}\right)\over \sqrt{u}(u+1)\ln{u}}du\tag3$$  Sub $u=e^z\rightarrow du=e^zdz$  $u=1\rightarrow z=0$ and $u=0\rightarrow z=-\infty$  ${e^z+1\over 2}=e^{z/2}\cosh(z/2)$  $$I=-{1\over \ln^3{2}}\int_{0}^{\infty}{\ln^2(e^{z/2}\cosh(z/2))\over ze^{-z/2}(1+e^z)}dz\tag4$$  $e^{-z/2}(1+e^z)=2\cosh(z/2)$  $$I=-{1\over \ln^3{2}}\int_{0}^{\infty}{\ln^2(e^{z/2}\cosh(z/2))\over 2z\cosh(z/2)}dz\tag5$$  I am stuck! Can anyone demonstrate how to prove I in step by step manner please, thank.  I try to understand their proofs From , but couldn't follow.


connected sets dont have subsets that are both open and closed

My problem states the following:  A topological space $X$ is connected if and only if there are no nonempty proper subsets of $X$ that are both open and closed in $X$.  Here is my proof:  Since the theorem is if and only if statement, we must prove it in both directions.  ($\Rightarrow$) Let $X$ be a connected topological space and for the sake of contradiction, suppose $U$ is an open and closed proper subset of $X$. Because $U$ is open, nonempty and proper subset of $X$, it must be the case that $X-U$ is closed and likewise nonempty and proper subset of $X$; because $U$ is closed, it follows that $X-U$ is open. But now we have that $U \cup (X-U) = X$, $U \cap (X-U) = \emptyset$ and $U$, $X-U$ are open, nonempty subsets of $X$, which means that $X$ is not connected. This is a contradiction, because we assumed $X$ to be connected; therefore, it must be the case that if $X$ is connected, then there are no nonempty proper subsets of $X$ that are both open and closed in $X$.  ($\Leftarrow$) We will prove this direction by contrapositive method.   Let $X$ be a topological space and suppose that $A$ is a nonempty proper subset of $X$ that is both open and closed in $X$. But since $A$ is open, it must be the case that the complement of $A$, i.e. $X-A$ is closed; similarly, since $A$ is closed, $X-A$ must be open. Also, since $A$ is a nonempty proper subset of $X$, it follows that so is $X-A$. Observe, that $A \cap (X-A) = \emptyset$, and $A \cup (X-A) = X$. So now we have that both, $A$ and $X-A$ are open nonempty proper subsets of $X$ that are disjoint and $A \cup (X-A) = X$. Hence, it must be the case that $X$ is not connected.  My question is: Both directions look almost identical, is this ok, or shall I work on this in some another way?


I am new to TeX. Should I use LaTeX, XeLaTeX, ...?

I am starting to learn LaTeX and I really like what I am seeing. However, I get the feeling I should actually start with another 'TeX' version. I've been reading about different options. Some references:      These questions and answers are very helpful, but I'd like to check to see if my findings are correct. I get the feeling that XeLaTeX is more of the 'improved' version that provides easier/more font options and makes it easier when using weird characters. Most people talk about 'converting' from one TeX to another, but given the fact that I am a beginner I am looking for the proper TeX flavor right now, so that I do not need to change preambles and such when I am learning about new things that are only available when using other TeX engines. Some details about my usage:  I visualize using TeX mostly for business reports, memos, and investigations. I also might use it for presentations and publishing in book-format. I will not be using advanced math nor Chinese or other very non-Latin symbols. Being a beginner, I do not need to convert any old documents. I have been reading about , however, and this seems like a version that will be superior to the existing TeX options. So when this becomes available, I envision switching to this. So if that is of any validity, I'd say that easy conversion to / compatibility with LaTex3 would be important.  Also, I read about an issue with 'microtype' in XeTeX, but I do not really get what that is and if this would affect me. To quote from  related to another beginner's question:  XeLaTeX would be (especially) suitable to you, for better (Unicode) multilingual support and easy font switching. And it supports more image format and PSTricks code.  I feel this also applies to my situation, so I am about to use XeLaTeX instead of LaTeX, and learn using this instead. Is this a good idea given my situation, or am I overlooking something important?


Evaluate $\int\frac1{1+x^n}dx$ for $n\in\mathbb R$

I was wondering on how to evaluate the following indefinite integral for all $n\in\mathbb R$.  $$\int\frac1{1+x^n}dx$$  It seems to be peculiar in that we have  $$\begin{align} \int\frac1{1+x^{-1}}dx&=x-\ln(x+1)+c\\ \int\frac1{1+x^0}dx&=\frac12x+c\\ \int\frac1{1+x^{1/2}}dx&=2\sqrt x-2\ln(1+\sqrt x)+c\\ \int\frac1{1+x^1}dx&=\ln(x+1)+c\\ \int\frac1{1+x^2}dx&=\arctan(x)+c\\ \int\frac1{1+x^3}dx&=\frac13\ln(1+x)-\frac2{3\sqrt3}\arctan\left(\sqrt{\frac43}\left(x-\frac12\right)\right)+c \end{align}$$  Naturally, there appears to be some combination of $\ln$ and $\arctan$, though no simple formula arises to solve the general case.  It is, however, easy to see that  $$\int\frac1{1+x^{-n}}dx=\int1-\frac1{1+x^n}dx$$  So there is an easy enough connection between positive and negative $n$.  Also, it is easy enough to find the series expansion, taking advantage of the above connection we just made to circumvent problems concerning convergence.  $$\frac1{1+x^n}=1-x^n+x^{2n}-x^{3n}+\dots\forall\ |x|<1$$  $$\int\frac1{1+x^n}dx=c+x-\frac1{n+1}x^{n+1}+\frac1{2n+1}x^{2n+1}-\dots$$  $$=c+\sum_{k=0}^\infty\frac{(-1)^k}{kn+1}x^{kn+1}\ \forall\ |x|<1$$  Though this isn't very much along the lines of closed form.  For $n=\frac ab$, where $a$ and $b$ are whole numbers, we can use the substitution $x=u^b$ to get  $$\int\frac1{1+x^n}dx=\int\frac{bu^{b-1}}{1+u^a}du$$  though I'm unsure where that could lead.  This reduces the integral down to  $$\int\frac1{1+x^n}dx=b\int P(u)+\frac{u^{b-1-ak}}{1+u^a}du,\quad k\in\mathbb N$$  for some polynomial $P(u)$.  Though I'm still clueless as to how this can be advanced.     How can I evaluate $\int\frac1{1+x^n}dx\ \forall\ n\in\mathbb R$ in closed form?  Can someone prove there at least exists some closed form solution for all $n\in\mathbb Q$ if the above is not possible?  If possible, use real numbers.


$f'' + f =0$: finding $f$ using power series

How can one solve the following differential equation   $$f'' + f =0$$   with the usage of power series?  Writing:   $$f(x) = \displaystyle\sum_{k=0}^{\infty} a_k x^k$$  $$f'(x) = \displaystyle\sum_{k=1}^{\infty} a_k k x^{k-1}$$  $$f'' (x) = \displaystyle\sum_{k=2}^{\infty} k (k-1) a_k x^{k-2}$$  How to continue?


I accepted an objective from the religious leader that required issuing an edict.  After looking at the consequences of the edict I decided I want to back out of this. Is there a way to cancel a mission?


Is it safe to install windows updates on Server 2008 without restarting it?

I've got a windows 2008 production server which I'm planning to install windows updates on, without restarting it for several weeks.   Is this a good idea? (This is a production server, which is on continuously, but I'd like to download & install updates now, so that when reboot time comes, I can reboot it right away, without first installing updates.)   Thoughts? ( & Thanks!)


I have a Qualcom Atheros AR9485 Wireless Network Adapter on a Samsung laptop and running 14.04.   My laptop can see the wireless network, but it keeps asking for the password and I can't connect. I know for a fact that it's not my router because my phone can connect and so can my tablet.  I have Wireless N only running on 20 MHz.  wlan0     IEEE 802.11bgn  ESSID:off/any             Mode:Managed  Access Point: Not-Associated   Tx-Power=16 dBm              Retry  long limit:7   RTS thr:off   Fragment thr:off           Power Management:off


Doubt regarding work done in separating capacitor plates

Suppose there is a parallel plate capacitor with distance between plates $d$ and it is charged to a potential difference $V$ and then charging battery is disconnected. Then the plates are further separated by a distance $d$. We need to calculate work done in doing this.  Now, I did this problem in two different ways, and they are giving contradictory results.  The first solution involves finding change in electrostatic energy of the capacitor and accordingly find the work done which is $CV^2/2$. This gives the right answer.  But, here's another solution which I think is perfectly justified and want your help in finding what is the fault in this approach.  Consider one plate to be at rest and the other one moving. Now the change in potential is from $V$ to $2V$ as the distance is doubled while field is same between the plates. Therefore, the work done should be the charge on capacitor plate times the potential difference, i.e  $QV$. Now $Q=CV$ which gives the work done as $CV^2$.  Now, I know that this answer is incorrect, but even after spending quite a time on this, I cannot figure out the fault.  So, please help.  Thanks.


Add my own bounty to a question with bounty outstanding

I've seen questions that have a bounty on them, but I'm interested in the answer as well, and I've wanted to augment with the bounty with some points of my own. Can we get a way to do this?  For example:  I see a question with a 100 point bounty on it, and I'm willing to throw 50 of my own points into the mix to make the bounty 150. I recognize that I won't get any control over the question/answer selection as a result, but it lets me do something more than just upvote a question if I want it answered.


Is there a way to make CSS dynamic? I want to set a variable in the CSS file. Something like this:  var baseColour = #000;  body{   background-colour: baseColour; }   I want to let the user choose a colour. Then I want to set the variable in CSS to the user input with JavaScript.  Is that possible? Or at least that one with the variable?


What does it mean to take the tensor product of two reps of the Lorentz group?

If I reduce the Lorentz group to the representation $\mathfrak{su}(2)\oplus \mathfrak{su}(2)$, I can write left and right-handed Weyl spinors respectively as $\left( \frac{1}{2},0 \right)$ and $\left(0, \frac{1}{2} \right)$. I can get a Dirac spinor by summing them, i.e. $\left( \frac{1}{2},0 \right) \oplus \left(0, \frac{1}{2} \right)$.  In my lecture notes, it is said that one can obtain higher representations by taking the tensor product. As an example, my prof gives $\left( \frac{1}{2},0 \right) \otimes \left(0, \frac{1}{2} \right) = \left(\frac{1}{2}, \frac{1}{2} \right)$, and he says that this corresponds to spin $1$ with $4$ components. I don't really understand what are the numbers on the right-hand side, and how I can relate this object to spin $1$. What does this notation mean, and how does the calculation work?


Convince grep to output all lines, not just those with matches

Say I have the following file:  $ cat test  test line 1 test line 2 line without the search word another line without it test line 3 with two test words test line 4   By default, grep returns each line that contains the search term:  $ grep test test  test line 1 test line 2 test line 3 with two test words test line 4   Passing the --color parameter to grep will make it highlight the portion of the line that matches the search expression, but it still only returns lines that contain the expression. Is there a way to get grep to output every line in the source file, but highlight the matches?  My current terrible hack to accomplish this (at least on files that don't have 10000+ consecutive lines with no matches) is:  $ grep -B 9999 -A 9999 test test     If grep can't accomplish this, is there another command-line tool that offers the same functionality? I've fiddled with , but it doesn't seem to have an option for it either.


How to insert a break line in LaTeX just like hr tag do in HTML?

In HTML, I can insert a line below any text using <hr> tag.        How can I do same thing it in LaTeX?


Ubuntu hosed my Windows 10 EFI partition

I attempted to install Ubuntu 15 on a separate drive that I set aside just for Ubuntu, and for whatever reason, Ubuntu decided to make changes to my Windows 10 EFI partition on a completely separate drive. Now neither OS will boot. Can anyone help me figure out how to fix this and allow windows to boot again?


Example of a relation that is reflexive but not symmetric

By definition, $R$, a relation in a set X, is reflexive if and only if $\forall x\in X$, $x\,R\,x$, and $R$ is symmetric if and only if $x\,R\,y\implies y\,R\,x$.   I think $x\,R\,x$ can also be symmetric when I read the definition, but I also feel there's something wrong or missing in my understanding.   Can you give an example of a relation that is reflexive but not symmetric?


I SSH into a multitude of different servers every day and some of them have different filesystem structures for their websites. Each time I change server, I have to work out where I'm going to get to the files I really want (because it's very rarely that I want to be in ~). I use Fabric files to automate all my actions (pushing to git, automated SSH to the server to pull from git, restarting the web application, changing dependencies, etc), so I was wondering if I couldn't also tell it that I want to SSH into the right directory so I can run fab ssh and be in a normal SSH session, just in the right place and start working immediately. This is not about Fabric though; please ignore it. Fabric is just running a batch of commands. My argument is with the ssh command. That's what I'll be telling Fabric to run. So how I can get ssh to cd into a specific directory on login? Note: this cannot be a server or user-wide thing. I have multiple websites under one user on some servers so sticking something in ~/.bashrc would not work for me.


Review test catching people indiscriminately for duplicate questions

I occasionally get flagged for not passing a review audit test because of duplicate questions.   In nearly all cases for a duplicate answer vote the easiest way to see the candidate questions is to choose "Close" button, then click "Duplicate of...", then it will show you the question previous people think is the duplicate. If I read it and I do not think it is a duplicate, I hit the "X" button in the upper right to cancel the operation and go back to the question. If I do think it is a duplicate, I click the "Vote to Close" button.  The problem is that the current auditing system thinks you are voting to close as soon as you click the first "Close" button (which is not true), thus you get falsely criticized by the system for trying to make an invalid close when all you were trying to do was see the duplicate question.  I would suggest fixing this by making the audit only complete when the person clicks the "Vote to Close" button, not when they click the "Close" button.


The quotient ring $\mathbb{Z}[i]/(1 + i)$

Let $n = |\mathbb{Z}[i]/(1 + i)|$. Determine the value of $n$ and show that $\mathbb{Z}[i]/(1 + i)$ is isomorphic to a field of order $n$. Justify your answer.   I have an exam tomorrow so every minute counts.   Am I right in saying that $\mathbb{Z}[i]/(1+i)$ is just $(a+bi)(1+i)$ but then surely the cardinality is infinite. Also am I right in saying that the ideal is not principal due to its norm being root 2.


How to make a new command similar to \author

I'm preparing a new template for our students' projects based on memoir. All this projects are supervised (directed) by one or more professors so I would like to declare a command like \author but called \director.   This way the student can declare \director{My professor} and the template will place and format the name.   I would like to be like \author and not just a simple \newcommand because it can include affiliation, several names, etc.  I don't know where is \author declared, where should I look?


Get all the Table names in particular database SQL Server

I am using SQL Server 2014 and want to get all the tables name in a particular database STUDENT through a SQL query.   How is it possible?  Thanks


How to add normal brackets around a tabular environment or create similar effect?

I want to mimmick this layout:    But I do not have access to the source code. My best guess is that this is a tabular environment with brackets typeset arround it.


Large table cannot be inserted in document with normal font size

In LaTeX when I insert a table in my document, the font size in table gets very small compared to the normal font of document. Definitely Table is large in width as well as in length. How I can insert large tables with normal font size, as it used to be in remaining document?  Thanks  Here is my document class:  \documentclass[a4paper, 12pt, twoside, openright, cleardoublepage=empty, numbers=noenddot, appendixprefix, BCOR1.5cm, bibliography=totoc ]{scrbook}   here is how I insert table  \begin{table}[h!] \centering \caption{My caption} \label{my-label} \resizebox{\textwidth}{!}{% \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline


Gravity force strength in 1D, 2D, 3D and higher spatial dimensions

Let's say that we want to measure the gravity force in 1D, 2D, 3D  and higher spatial dimensions.   Will we get the same force strength in the first 3 dimensions and then it will go up? How about if we do this with Electromagnetic force?   I've include the Electromagnetic force just to see if I can find an analogy to the gravity force behavior.


Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$

Let $N$ be a positive integer. Then, we have  $\sum\limits_{j=1}^{N} \binom{j}{6} = \binom{N+1}{7}$.  Could anyone explain this equation a little bit? I wrote out the left hand side as $\binom{1}{6} + \dots + \binom{N}{6}$, but it did not help at much.  UPDATE  From lecture notes, I found a proposition says:     $\sum\limits_{0\leq k\leq n} \binom{k}{m} = \binom{n+1}{m+1}$.   Could anyone give a hint on how to prove it?


What is the SObject for a private message?

I want to monitor private message and want to check and store at admin side. so admin can see who doing message to whom and make the policy for to sending the message.


Small caps font warning in beamer using biblatex

Consider the following MWE  \documentclass{beamer} \usepackage{silence} \WarningFilter{biblatex}{Patching footnotes failed}  \usepackage{lmodern} \usepackage[T1]{fontenc}  \usepackage[style=authoryear-comp,backend=biber]{biblatex} \addbibresource{biblatex-examples.bib}  \begin{document} \begin{frame}   \fullcite{sarfraz} \end{frame} \end{document}   This generates the warning:  LaTeX Font Warning: Font shape `T1/lmss/m/sc' in size <10.95> not available (Font)              Font shape `T1/lmr/m/sc' tried instead on input line 28.   Is there a way to avoid the warning without using the silence package?


Recovering a password protected LibreOffice Writer document

A year ago I started a memoir and wrote 120000 words, which I password protected in LibreOffice 3 writer. I took a break of many months, and intended to resume writing the document a couple of days ago.  However..  I have forgotten my password.  This is a complete disaster.  I made my wife aware of the password (just in case !) But she has also forgotten it.  Here is my rather obvious question - Is there some way of accessing the memoir with out the password?  I'm very non technical, and following a search I discovered a possible means of using xmlcopyeditor to turn off the password and thereby access the document.  But this doesn't work - the xmlcopyeditor doesn't seem to open.  There are three copies of the memoir, one on a flashdrive thing, one on a cd rom, and one in the laptop, all are protected by the same password.  Very frustrated indeed.


Skewing/Shearing Text On A Path In Photoshop or Illustrator?

How can I skew or shear text on a circular path in either photoshop or illustrator? I need the text running along the bottom outside of the circle to skew the opposite direction of italics (slanting to the left). Apparently, this is something that has never been done before because I can't find anything on it anywhere.      If that makes sense, I want the text slanted as if it was showing motion by following the rotation of the gear.


I have found out the formula of a_n by recursion method but after that I am being unable to show that it converges.


Hard drive full, but files / folders don't add up to used drive space

My harddrive is full, but according to the size of all my folders, I should have more than half of my drive left over.


I am trying to prove that $n^2 \leq 2^n$ for all natural $n$ with $n \ne 3$. My steps are:    induction base case: $n=0:$ $0² \leq 2⁰$ which is okay.    inductive step: $n \rightarrow n+1:$ $(n+1)²\leq2^{n+1}$ $$(n+1)^2 = n^2 + 2n + 1 = ...help...\leq 2^{n+1}$$   I know the bernoulli inequality but don't know where to use it, if I even need to. I have problems when it comes to proving things which are based on orders..


How can I delete items from my list of tuples?

I want to use a list of indices to remove items from my list of tuples:  mytupList = [(1,2),(2,3),(5,6),(8,9)] indxList = [1,3]   I have tried using numpy like so:  newtupList = numpy.delete(mytupList,indxList).tolist()   but it has not worked.   I want my newtupList = [(1,2),(5,6)]  what am I doing wrong? I have also tried:  a = np.array(mytupList)  newtup = np.delete((a),indxList)   but this does not produce the desired result.


How do questions on the "Tour" page get chosen?

Every SE site has a  page. This page exhibits various actual Q&A from the site.  On Lifehacks.SE,  uses one of my questions. Was this manually selected by somebody on the SE Community Team, or automatically?


this is my code and I don't know why    "one == null" and "two == null"    are always False and I can't send any Null argument to my method! please help me public class RepeatInString {     public int StringInString(String one, String two) {         if (one.equals("") || two.equals("") || one == null || two == null){             return 0;         }         else{             char[] oneChar = one.toCharArray();             char[] twoChar = two.toCharArray();             int repeatCounter = 0;             int matchChars = 0;             for (int i=0 ; i < (one.length()-two.length()+1) ;i++ ){                 matchChars = 0;                 for (int j=0; j<two.length() ;j++) {                     if (oneChar[i + j] == twoChar[j])                         matchChars += 1;                     else                         break;                 }                 if (matchChars == two.length())                     repeatCounter += 1;             }             return repeatCounter;         }     }


populate drop down list and display on screen?

//asp <asp:DropDownList ID="ddlGroups" runat="server"></asp:DropDownList>  //code behind  protected void SelectAccessLevel()         {             List<string> ADGroups = new List<string>();             ADGroups.Add("Group1");             ADGroups.Add("Group2");             ADGroups.Add("Group3");              ddlGroups.DataSource = ADGroups;             ddlGroups.DataBind();         }   Create a drop down list in ascx page, bind to list in code behind and display on screen. Nothing displays in DD on screen..as to why? is it correct to bind the drop down or do I need to create another dd in code behind it to that?


This has been asked  but marked as answered and I don’t feel like the question was ever answered, or at least was not clear to me. I don’t understand why the set consisting only of the element $\{0\}$ along with the usual $+$ and $×$ does not satisfy the criteria, since $0$ acts as both the additive and multiplicative identity. That is, letting $G = \{0\}$, then  $∀ g ∈ G, 0+g = g$ and  $∀ g ∈ G, 0·g = g$ (Since $0·0 = 0$ )   Similarly, it is both its own additive and multiplicative inverse. What is the problem at only the field level, without wishing it satisfy some additional properties for category theory or algebraic/arithmetic geometry?


Why doesn't bash expand this variable when I prefix a command with a "one time variable assignment"

If I run this bash command and prefix the statement, so that the variable fruit should exist, but only for the duration of this command:  $ fruit=apple echo $fruit  $   The result is an empty line. why?  To quote a comment from wildcard on :     parameter expansion is done by the shell, and the "fruit" variable is   not a shell variable; it's only an environment variable within the   environment of the "echo" command   An environment variable is still a variable, so surely this should still be available to the echo command?


Topological group admits up to isomorphism only one smooth structure turning it into a Lie group.

proposition : Let $G$ be a Lie group.  Then $G$ as a topological group admits, up to isomorphism, only one differentiable structure turning it into a Lie group.  I think I have to use the fact that if $f : G\to H$ is a continuous homomorphism between Lie groups then $f$ is smooth. In particular, I should apply this to $\operatorname{Id}_G : G\to G$ but I am not sure how this gives us the result.


Material Shader not fully applied to selected faces? Why?

I am adding materials to my model but the bottom edges of faces do not show the colour/material even if the rest of its faces are coloured. Why is this?  As you can see by the picture, the grey area above the indent is part of the face of the red material but it is not shaded red along with the rest of the face. The indented section only coloured the middle red and left the top and bottom material-less. How do I fix this?


Cannot delete file "This action cannot be completed because the file is open in Event Log Watch"

I'm trying to delete a file called lic98.dll and I fail to do so, I tried cutting the file somewhere else in it works, then I tried deleting and nothing happens, so I'm kinda stuck now on how to delete it.


I just want to check this:  If I have a derived class that has no new members. In case that the base class has already a long constructor (many parameters), the creation of the constructor in the derived class that just throws all the parameters to the base constructor is somewhat a boring (and obviously not necessary) process. Is there a way to tell the compiler to do it automatically? I suppose not, but just needed to check. I haven't found anything on this topic but still sorry for a duplicate if this is the case...  //I'm not interested in IDE automatic generation features (although I would welcome an advice of that type either), just a compiler...


Recurrence Relations: general process for solving first order

So I had asked a question prior to this one about recurrence relations, but apparently it was a bad one to ask. So I'm trying again to understand how to solve these babies... Here it is:  $$ 3a_{n+1}-4a_n=0, n>=0, a_1=5 $$  What is the general process for solving a relation like this?


Logo and two text div centering verically and horizontally on the page

What is the best way and best practice to achieve this layout? Meaning it will stay consistent on iPad, Android or desktop. CSS Grids? Flexbox? Logo div should be centered on the page vertically and horizontally. Text divs should be centered in the middle of the logo div.


Suggest an algorithm for factorizing an integer such that each of its factor is .  Thanks,


"this is my string".myfunction(argument)   This is very simple in javascript. With the keyword this i can access to my string directly. Is that possible with python?


How can I have yes, flagged and no buttons in a column

I have a document library where the CEO wants to see three buttons. If he has read the document he wants to click on Yes, otherwise it will always be No. If he clicks Flag it means it needs to be discussed. How can I have three buttons where he can simply push it and he wants that to be color coded. He is using safari on ipad and would not change that; therefore all the easy options I had for him are not going to help . Is there a javascript I can use so when he clicks the Yes button it turns green and when he clicks No it remains red. I have searched everywhere for an answer and I can't find one. I am not good at coding and just a beginner so still learning but this one is becoming a hard task doesn't seem hard but for me it is.   He does not want to go into edit view to complete the task as he says its too many clicks and of course since its its on ipad it is bit harder than working a computer.  I am thinking of adding one button with three colors, First one will always be no so red and onclick it will become green and if he clicks it again it will become black. Is there a javascript that can add a button in a column and have the user just click on it with their mouse and no editing required?   Thanks in Advance.


Coloring problem with equilateral triangles

Prove:  If we color the plain with three different colours, then there will always be an equilateral triangle which has three vertices of the same colour.  I have proved it for two colours but I just can't solve this one.


I am a PhD student and hate it here. How can I warn prospective students during admit weekend without ruining my reputation?

On the one hand, I want to warn students not to come to my program.  On the other hand, I don't want to be "that one," and I also don't want to tarnish the reputation of the specific people I worked with (who I mostly like).  More specifically:  I want to warn students about lack of funding, administration being uncaring towards students, certain PhD requirements being a lot more onerous than they say they are, general departmental atmosphere and culture among the grad students, general culture of the school, poor location, etc etc.  Also my school is the only top school in my field that has a "rotation system" for picking advisors, and that is generally framed as a benefit, and a reason to choose the school.  But I don't think students really realize how much rotations suck until after they've come here.


SOQL to get Assets with AccountId different from Parent.AccountId

I need to get all Assets X with X.ParentId != NULL, and the X.Parent.AccountId != X.AccountId.  SELECT AccountId,Id,ParentId,Parent.AccountId,RecordTypeId,RootAssetId FROM Asset WHERE ParentId != NULL AND Parent.AccountId != AccountId AND RecordType.DeveloperName='RecTypeABC' limit 10   The SOQL above fails with a MALFORMED_QUERY error.  Any idea how to do this?  Thanks


Does a full frame lens require more light on a crop body?

When using a full frame lens on a crop body, does the lens require more light?  If I use an f/2.8 full frame lens on a crop body, does it become an f/4.2 (*1.5)?


Do Users assume that company logos link to the "home" page?

I have limited space on the top navigation of my bootstrap website and among other links, I have both the company logo and home (index) link, Both logo and index scroll to the top of the page.  I want to add another link and its going to take up space.  Can I safely get rid of the "Home" link assuming the user will click on the company logo?


Use the Cayley-Hamilton Theorem to find the inverse of this $3$-by-$3$ matrix

$A=\begin{pmatrix} 2&0&0\\ 1&3&0\\ -3&5&3 \end{pmatrix}.$  I can find the characteristic polynomial $C_a(A)= -A^3 + 8A^2-21A+18$.  How to continue from here to use the Cayley-Hamilton theorem to find the inverse matrix, $A^{-1}$?


Installed Mint on external SSD, now Ubunty won't boot without SSD plugged in

So, I installed Mint on an external SSD just because I had it laying around, and I found it entertaining to do so.  Now when I boot my laptop without the external Mint SSD plugged in, it goes to GRUB and won't boot Ubuntu.  Once Ubuntu boots with the SSD, I can eject and remove it, and the system continues to run absolutely fine. I don't want to have to lug the hard drive around with my laptop everywhere I go...


How to turn off this pop-up PowerShell notification that appears at start-up?  When trying to install Photoshop from torrents, I had to disable Windows real time Defender, and the msvcr100.dll file was missing. I got both .dll files from dll-files.com. I incorrectly replaced the msvcp110.dll file, but figured out my mistake soon enough and put back the original file. When installing Photoshop it didn't work, so I replaced both the new .dlls with the original files. Now my computer is asking me to do click yes every time I start my computer up. I would appreciate any answers or just a way to stop me from clicking the Yes button in the PowerShell pop-up all the time. Nksvoo is causing my problems:


While in manual mode with auto focus, could not get the camera to focus for night astrophotography.  Tried different combinations of ISO, TV and AV.  I noticed that the EV was all the way to the right.  What does that tell you? Could the combination cause the camera not to focus?  Thanks


How do black holes form without violating the uncertainty principle?

Many videos on YouTube while discussing black holes mention that it's born out of a heavy star when it collapses into a single point and that infinitely curves spacetime around it.   When all the mass is getting confined to one point isn't it violating the uncertainty principle?


Why is the 'System' process listening on port 443?

I am having problems starting my Apache server, because port 443 is already in use.  It turns out, the system process (PID 4) uses the port 443. I don't have IIS installed, the services.msc shows (predictably) no Exchange server running, nor WWW-Services, nor IIS. I have no idea how to find out what service uses that port, short of just disabling each service one after the other, and I am not even sure that would help.  I would be grateful if someone could point me towards how I can get my SSL port back, thank you :)  P.S.: Of course "just switch Apache to another port for SSL" would solve the problem of not being able to start Apache. But I'd still like to know what is so insistent about hogging port 443. :)    I by now took the 'hard route' and disabled services one after the other. It turned out that the "Routing and RAS" service was the culprit.  Thank you all for the valuable input and the new tools in the combat against "WTF does my system do now?".


Does $\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converge? Converge absolutely?

Per the title, does $\displaystyle\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converge? Converge absolutely?   I'm stuck on this question, not sure how to approach it.  Thank you!


Use of Custom Object to authenticate Users

We have public website built with Salesforce.  Public(guest) users can view the images and short description of products. To view price, they need to register and login to website.  So, for this if we create an custom object called "Site Users" and when click on "View Price", if we authenticate those users by "Site Users", is it recommended?  My intention to this question is, couple of years back I read that it is not legal to create your own user authentication in Salesforce. We must use Salesforce authentication for site users as well.  I am searching that link, but I am not able to find similar article. If someone has idea on this, please provide some feedback/suggestion.  Thanks and Regards,  Ashish Shukla


I have a file, called "some.img", created with fallocate, that has a filesystem on it. I can mount the img file using mount -o loop some.img /media/where, and I see the filesystem. When I reboot, however, the file is no longer mounted.  How do I automatically mount this at boot?  Update: SuSE Linux


Are plusses a good second character to use for spaces in URLs for SEO when dashes are already in use?

I was wondering if the following is good for SEO. I have a webshop with categories and products. Products can contain - themselves.  For example, one of the URLs would be:  http://SITE/products/CATEGORY/this+is+something+1-layer   Where the product name is "This is something 1-layer"  Now, I understand it's better to use - as space replacement, but since my product names can contain a - I was wondering if just using + would be good.  If not, what would be a better way to display it?


Is a URI (specifically an HTTP URL) allowed to contain one or more space characters? If a URL must be encoded, is + just a commonly followed convention, or a legitimate alternative?    In particular, can someone point to an RFC that indicates that a URL with a space must be encoded?  Motivation for question: While beta-testing a web site, I noted that some URLs were constructed with spaces in them. Firefox seemed to do the right thing, which surprised me! But I wanted to be able to point the developers to an RFC so that they would feel the need to fix those URLs.


Let $M=\big( \begin{smallmatrix} A & B \\ C & D \end{smallmatrix} \big)$. Prove $\det(M)=\det(A)\cdot \det(D-C·A^{-1}·B)$.

Let  (shown in matrix blocks) $M=\big( \begin{smallmatrix} A & B \\ C & D \end{smallmatrix} \big)$ a square matrix such that $A$ is invertible and $D$ is a square matrix. I have to prove that  $$\det(M)=\det(A)\cdot \det(D-C·A^{-1}·B)$$  I also have an indication to use it: Consider previously these cases: \begin{align*} A_1 &= \begin{pmatrix} A & 0 \\ 0 & I \end{pmatrix},\\ A_2 &= \begin{pmatrix} I & 0 \\ 0 & D \end{pmatrix},\\ A_3 &= A_1·A_2,\\ A_4 &= \begin{pmatrix} I & A^{-1}·B \\ 0 & I \end{pmatrix},\text{ and}\\ A_5 &= A_3\cdot A_4. \end{align*}   The problem is difficult in general for me and I don't even know how to use the indication.


I cannot see my imported DXF mesh/object in Blender. How can I make it visible?

I have been trying to open and see the visualization of a DXF file in Blender with the DXF importer addon. I managed to get it working once and I could see the details properly in the 3D viewport but now when I import the file it just appears in the outliner but no model is actually visible. What to do? It's basically a point cloud height map from a mapping service. Here is the file:


If current is same, is it correct to say that the speed of charge passing through a resistor is more than that of a normal wire?

It took me a long time to understand that current is constant throughout the circuit. And now I am stuck at one last thing: The speed of charge. Here is what I am thinking:  Current is defined as quantity of charge passing through a point at a given time, and from this we can deduce that current is constant throughout a circuit. But, if this is true, then wouldn't the speed of charge through a resistor be increased? Let us think about an analogy, water flowing through a pipe. Suppose water is flowing through a broader pipe(analogous to a less-resistance wire), and  a greater quantity of water can flow past a point because of larger cross-sectional area. Now, suddenly water encounters a smaller pipe(analogous to the resistor). So, less quantity of charge can flow through it because of less cross-sectional area. But, if the volume of water flowing in a time $T$(analogous to current) is same, won't the rate of flow of water in the narrower pipe(the resistor) be more?  I am asking this question because while seeing some answers for the question that "Why is current constant?" , I saw some people saying that speed of charge slows down a bit through a resistor, which seems incorrect to me.


Infer the shape of a solid given the moments of inertia

Let's say we have a solid with uniform mass distribution, but we don't know its shape. However, we know the moment of inertia of the solid with respect to as many axes of your choosing as you want (e.g. you know $I_{Ox}$, $I_{Oy}$ and $I_{Oz}$). Is it possible to deduce the shape of the solid based on the moment of inertia $I_{Ox}$, $I_{Oy}....$? And if so, what would be the minimum number of axes required to do it ?  Do note that the mass is supposed to be evenly distributed, otherwise we could have a cube with the bulk of the mass concentrated in a sphere within, for example, and thus the different moments of inertia would not take into  account the "lightweight corners" of the cube.  Then, there is the parallel axis theorem, which reduces the scope of the problem, as we could therefore only choose axes going through the center of mass, for  example. Other than that, I'm completely stumped.


I'm using a rooted Google Nexus 4 (mako) with CyanogenMod 11 and adb 1.0.32 on OS X. I also use disk encryption.  adbd is running as root. I'm trying to create a full backup using:  adb backup -apk -obb -shared -all -nosystem   However, regardless of the options passed to adb backup, it asks me to enter my backup password on the phone and then exists, showing Backup finished on the phone. It only leaves a 549 bytes backup.ab file.  Using the wrong or no backup password does the same but leaves a 0 bytes file.


How to enable Contact to allow login on SF org - Lightning LEX

How to enable Contact to allow login on SF org .  I think this was available in classic but could not find in Lightning LEX


Note: despite the linked duplicate not being a duplicate (it explicitly asks about casting to int and float separately) I still mark it as duplicate because it contains wonderful information about the subject (and an answer similar to my solution) Summary: I am looking for a pythonic way to convert a string into a number (an integer or a float). I currently use a waterfall function but while it works, it is not particularly aesthetically pleasant: def convert_to_int_or_float(a):     # maybe an integer     try:         return int(a)     except ValueError:         # nope - so can be a float or a str         try:             return float(a)         except ValueError:             # must be a str             return a  for s in ["0", "12", "-13", "14.7", "-14.7", "hello"]:     print(s, type(convert_to_int_or_float(s)))  # outputs  # 0 <class 'int'> # 12 <class 'int'> # -13 <class 'int'> # 14.7 <class 'float'> # -14.7 <class 'float'> # hello <class 'str'>  Is there a better way to do that? (ideally though a module) I had  look at math but did not find anything there.


I'm trying to make a fountain and I have finished the fluid baking...Now I want to bake the mesh it doesn't allow me to bake it. I have to bake it in the domain


Statistical Learning book with theoretical content

I'm currently reading the book 'An Introduction to Statistical Learning with application in R(ISLR)', it is very helpful for learning the applications of statistical model, but less complement of theoreotical content or mathematical proof/derivation of formulas. I'm often confused with some conclusion/formulas provided in that book without theoretical explanation. Does anyone can give me some resources or books that emphasizes on theoretical aspect of statistical learning? Or other statistical learning book with theoretical problems is OK as well.


I've ran into an unexpected behavior when using a nested list in python, that took a while to debug. If a list is initialized like this:  a = [[None] * 2] * 2 a [[None, None], [None, None]]   and another list initialized like this:  b = [[None, None], [None, None]] b [[None, None], [None, None]]   I would expect the same behavior from both these lists, but if I do:  a[0][0] = 3 a [[3, None], [3, None]]   and if I do:  b[0][0] = 3 b [[3, None], [None, None]]   Can someone explain the reason why this happens? thanks


When installing or booting from USB flash drive screen goes blank

When I was installing Ubuntu 11.10 64-bit on my new PC from a flash drive since the only computers I have do not have disk drives, I ran into a problem.  After the ASUS logo when switching on the PC, and pressing F8 to select the USB flash drive, there was the options thing as normal that allows me to select to either boot form the flash drive or install on the HDD, when I do either of these, there is a bunch of text on a black background, as I would expect, but after a few seconds the screen goes blank and the monitor says No signal.  I have previously installed Ubuntu with a flash drive to fix issues caused my Windows and ran into no problems.  Is it a problem with the pen drive I am using? Or maybe a problem with the system? I tried it in my USB 3.0 ports at the back and the USB 2.0 ones as well.  My Specs are:     AMD Phenom II x4 965BE   ASUS AMD Radeon HD 6670   ASUS M5-L75 USB3 (typing this from memory, it's an AM3+ ASUS board with USB3.0 in the AMD700 chipet or something)   Corsair XMS3 DDR3 4GB(2x2GB) 1333MHz RAM    I ran the memtest program on the flash drive as well, and it came out clean.


Evaluating $\lim_{n \to \infty} \int_{0}^{1} n(2^x-1)^n dx$

I tried to calculate this dominant convergence theorem to solve this limit. Evaluate the following limit for $x=0$ and for $x>0$: $$\lim_{n \to \infty} \int_{0}^{1} n(2^x-1)^n dx$$ and I got the limit value : $\frac{1}{2\ln{2}}$ did I do the right thing?


Relation between number of digits of a number and its logarithm?

I found a couple of questions where, for example, they ask you to calculate the number of digits in $18^{200}$ and only the value of $\log 18$ is given. Can anyone tell me a way?


How can I read a dash file from the terminal other than delimiting it with ./  For example to read a - file we can read it by   cat ./-file_name  Q: Is there an alternative way to achieve the same thing?


Rigorous book on probability theory and statistics

I would like some examples of very rigorous books on probability and statistics. I know there are lots of rigorous books on probability by itself, but I am also looking for a book that makes rigorous the theory behind statistics. From my understanding, there is a difference between probability theory and statistics.


I'm trying to get the Hairnet add-on installed on Blender 2.8.1, but it won't show I've had the same issue since I found out about add-ons.  It shows that it's in my Blender folder, but it doesn't show up in my preferences not even if I I scrolled down.


Can I use my auto-generated SO gravatar in other places?

I have an auto-generated gravatar as my display on SO. I wish to associate that unique, but non-descriptive, gravatar in other places (such as github). I have grown rather fond of it. Is there anyway to do this? Do I have to go to  and actually sign up for an account?


Do the close votes disappear if the duplicate question reference is deleted?

I voted to close the following question because the OP posted the exact question couple of days ago before posting this question. I remember that because I edited the original question with formatting. OP copied the edited question and posted a new question with couple of changes on the title. Below given question was posted only yesterday (February 17, 2013).    I am sure that the question that I used for the duplicate reference had 1 answer. The answer did not have any upvotes though.   What I noticed:   The question used for duplicate reference has been deleted. I don't know who deleted the question (whether OP or moderator). Close votes (there were two votes) on the above mentioned question have disappeared.   Searches on Meta:  Below Meta post shows that when someone can delete their own question.     Below Meta post shows when a close vote will disappear.    Questions:   Did the OP delete the original question because it had only one answer with no upvotes?  My understanding: The Meta searches show that only questions with multiple answers cannot be deleted even none of them had up votes. I assume that OP can delete the question since there was only one answer with no upvotes. Did the close votes disappear from the above-mentioned questions because the question used for duplicate reference was deleted?   My understanding: The Meta searches show the close votes will disappear only if there were at least 100 views or the last close vote had elapsed 4 days. In this case, the above-mentioned question has only 29 views as of writing this post and the question itself was posted only yesterday. These conditions do not meet the criteria to expire the close votes.   Update: (17:45 UTC)  I just noticed that when I click Close link, I get the below message but there are no close votes count displayed on next to the link. I don't find anything on the revision history of the question that suggests a moderator modified something.   Is this behavior because a user is allowed to close a question only once and I already voted to close this question?


My professor never answered my email. What should I do?

I'm having trouble submitting an assignment into turnit in and my professor never replied back to my email. The assignment had 3 different parts to it and I was only able to submit one of the parts because I tried to submit them separately instead of together. I asked my professor if I could just email him the other 2 parts of the assignment and he never answered back. I emailed him 4 days ago.


How many memory copies do object variables in Python have?

I am new to python recently. Previously all my programming knowledge are limited on Java. So here I have a question about object variables in Python. I know that object variables in Python share on class instances. For example.  class A:     list=[]  y=A() x=A()  x.list.append(1) y.list.append(2) x.list.append(3) y.list.append(4)  print x.list     [1,2,3,4] print y.list     [1,2,3,4]   So my questions is that how many memory copies does A.list have? only 1 or just as many as number of instances? object variables in python sharing behavior is just like Java's static class variables,  are these two concepts same or different? if different, what's diff between them?


I was thinking of random math problems to myself when I came across this:  $x^2 = 2^x$  It seemed very simple at first, but after trying multiple ways to solve it, I had no idea what to do.  So, I began doing a lot of searches for this problem, and I found out that in order to solve $x^2 = 2^x$, you have to use some function of which I have never heard before. So, I have three main questions regarding this problem.  1) is it possible to solve $x^2 = 2^x$ arithmetically? If so, how would one do so? If not, why not? In other words, why would it be impossible to solve this problem arithmetically?  2) Why is it that addition and multiplication are commutative, but exponentiation is not? I understand not all forms of multiplication in mathematics are non-commutative, but for the sake of this problem, exponentiation feels like the "next step" right after multiplication. Here's what I mean by this:  Addition is just adding a number to a number.  Multiplication is just adding a number $N$ times to a number.  Exponentiation is just multiplying a number $N$ times by a number.  3) Would it be possible to invent your own function to solve $x^2 = 2^x$, or rather, $x^y = y^x$? And after you found a way to represent your answer, how could you go about evaluating your answer without using a calculator?  If anything doesn't make sense above, I can do my best to clarify. I also know some of these questions have been asked before, but I didn't really understand any of the answers, and the questions weren't as specific as mine.


Can inductor voltage and capacitor current change abruptly?

I understand that inductor current and capacitor voltage cannot change abruptly, but can inductor voltage and capacitor current change abruptly?  I have a feeling the answer is no but I cannot explain why.


Not able to Install Teamviewer on Ubuntu 14.04

I have a Ubuntu 14.04 LTS System and I am not able to install Teamviewer 10 and is throwing :   dependency not satisfiable lib32asound2   Have somenone worked on it before?


Can $g_0 \mapsto g_0^{-1}$ always be extended to an automorphism?

Let $G$ be a group and $g_0\in G$ be a fixed element of that group. I'm wondering if $g_0 \mapsto g_0^{-1}$ can always be extended to a group automorphism $G \to G$. My feeling tells me yes. For abelian groups the map $g \mapsto g^{-1}$ is already an automorphism, so there it's trivial. But what about non-abelian groups?


This is one of the most entertaining movies that has/have appeared this year.   Can't figure out with certainty whether the subject is singular or plural. Seems like has is the obvious answer but presence of that is making me falter.


Run for loop for list with diminishing values

I'm looking to run an operation on all values of a list but 10 at a time. The problem is that on the final cycle of the for loop there are less than 10 values in the list. My current solution to this is to do the following:  for i in range(len(my_list) // 10):      for i in range(10):          # do operation  for i in range(len(my_list) % 10):      # do operation   Or another solution would be:  while True:      for i in range(10):          if not my_list:              break           # do operation      if not my_list:          break   My question is if there's a better (and probably quite obvious) solution to this. I wasn't sure how to describe the issue, so there may be another question that already answers this if I had known the right terminology to look with. Sorry if this is the case.


Unable to open /var/lib/apt/lists/in.archive.ubuntu.com_ubuntu_dists_eoan_InRelease - fopen (13: Permission denied)

This type of question has been asked, But the error that person got was also different. I don't want to take no chances with my computer so asking it here again.  I was working on my stuff when this error sign occurred on the top of the screen, I clicked on it. This is the screenshot :    After that I ran the command apt-get update as asked by this error. This is what I got as output :  I am also pasting the same thing here in case the image is not loading  Reading package lists... Error! E: Could not open lock file /var/lib/apt/lists/lock - open (13: Permission denied) E: Unable to lock directory /var/lib/apt/lists/ E: can not open /var/lib/apt/lists/in.archive.ubuntu.com_ubuntu_dists_eoan_InRelease - fopen (13: Permission denied) E: The package lists or status file could not be parsed or opened.     What I have tried :  Looked for the directory which was causing the problem which was /var/lib/apt/lists/ It looked something like this :    I noticed 3 files including a folder have a cross sign on them, and these are the three files terminal showed in the error ! Please help me solve this problem, I am new to Ubuntu and so, don't know about it a lot, probably you can help me.  My system information that you might need   OS : Ubuntu 19.10 GNOME : 3.34.1 OS -type : 64-bit  This information may not be useful but I still added, just in case.


Does matrix multiplication preserve positive semi-definiteness [PSD]?

If $A,B$ are two PSD matrices, will $AB$ also be PSD?


Why is an $RLC$ resonance curve asymmetric?

When I was measuring the current with varying frequency of an series RLC circuit, I noticed that the graph produced is asymmetric:  Is there any reason for this? (inductance=8.29mH) The Q-factor is 2.75 (3 s.f.)


Let's raise the privilege to set bounties to something that needs having been active in the site

In  a case is being discussed about a user that got 200 reputation in one of the Stack Exchange sites and hence he gets the  whenever they sign up in a new one. Then, they have a reputation of 101 points and they offer a 100 bounty to some question.  As of writing, this has been done in over 100 sites, and in most of them they just joined today and their first action was offering such bounty. Sometimes, also a comment was written down. Nothing else in most of the cases.  A bounty has a big impact: it attracts a lot of traffic, which in a sense is "taken" from others in the front page. Thus, placing one is a big action towards the site.  While the purpose of these bounties can be OK and offered to questions that are worthy, this very specific case has showed that the system can be a bit perverted and a non-experienced user can have a big impact on a site (or multiple ones).  Currently, the  is set to  (beta and graduated). This means that you have this privilege if you ever when signing up in a site if you ever got 200 in any other site. That is, if you are granted the association bonus.  For this, I suggest raising the reputation for the bounty privilege to something that involves having been somehow active in the site, for example 125, to the same level of the privilege of .


Statistical evidence that the AUC was not overfitted to the model. With N=119, C-stat = 0.81 seems optimistic. Optimism-adjusted?

My data have 119 cases and we did ROC for x (continuous variable) to predict postoperative y (categorical variable) available , we got a comment from a reviewer asking:       Please provide statistical evidence that the AUC was not overfitted to the model. With N=119, C-stat = 0.81 seems optimistic. Optimism-adjusted?    I found some : basically I split my cohort into train set (n=107) and test set (n=12), did 2 ROC curves and compared AUC for both using this command:  testobj <- roc.test(rocobj0, rocobj1);testobj    and this was the output  DeLong's test for two ROC curves  data: rocobj0 and rocobj1 D = 0.44822, df = 12.488, p-value = 0.6617 alternative hypothesis: true difference in AUC is not equal to 0 sample estimates: AUC of roc1 AUC of roc2 80.26961 72.22222   Regarding the optimism adjustment, I did it using the following code copied from .    library (pROC);library (kimisc)    auc.adjust <- function(data, fit, B){   fit.model <- fit   data$pred.prob <- fitted(fit.model)   auc.app <- roc(data\[,1\], data$pred.prob, data=data)$auc # require 'pROC'   auc.boot <- vector (mode = "numeric", length = B)   auc.orig <- vector (mode = "numeric", length = B)   o <- vector (mode = "numeric", length = B)   for(i in 1:B){         boot.sample <- sample.rows(data, nrow(data), replace=TRUE) # require 'kimisc'     fit.boot <- glm(formula(fit.model), data = boot.sample, family = "binomial")     boot.sample$pred.prob <- fitted(fit.boot)     auc.boot\[i\] <- roc(boot.sample\[,1\], boot.sample$pred.prob, data=boot.sample)$auc     data$pred.prob.back <- predict.glm(fit.boot, newdata=data, type="response")     auc.orig\[i\] <- roc(data\[,1\], data$pred.prob.back, data=data)$auc     o\[i\] <- auc.boot\[i\] - auc.orig\[i\]   }   auc.adj <- auc.app - (sum(o)/B)   boxplot(auc.boot, auc.orig, names=c("auc.boot", "auc.orig"))   title(main=paste("Optimism-adjusted AUC", "\nn of bootstrap resamples:", B), sub=paste("auc.app (blue line)=", round(auc.app, digits=4),"\nadj.auc (red line)=", round(auc.adj, digits=4)), cex.sub=0.8)   abline(h=auc.app, col="blue", lty=2)   abline(h=auc.adj, col="red", lty=3) }  model <- glm(data$y ~  data$x, data = data, family = "binomial") auc.adjust(data, model, B=200)   But it gave me this weird figure below in which AUC is > 1:       I should conclude that AUC was not overfitted based on the splitting of the data that I did and P value of 0.66 from DeLong's test for two ROC curves, Right? How to fix the optimism adjusted AUC figure to get it <=1?


Cannot favorite a question in android app

I tried to favorite , it kept giving me an error saying the question is already favorited.


Existence of injective homomorhism and surjective homomorphism of free modules implies isomorphism

Given an integral domain $R$, we have that $R^n$ embeds in $R^{n+1}$ as free modules over $R$. Can we have a surjective $R$-homomorphism from $R^n$ to $R^{n+1}$? Or more so, given two free $R$-modules $A$ and $B$ where there is an injective homomorphism from $A$ to $B$ and also a surjective homomorphism from $A$ to $B$, can we conclude that $A \cong B$?


Move wireless passwords to another computer

I am going to reinstall Ubuntu soon and want to move my wireless passwords I have to the new installation. What do I need to backup to put on the new installation?


How can we implement a CurveMapping widget in a script using python api?

How do we implement a CurveMapping widget (similar to RGB curves) in our own scripts using the python API to remap a range of values?


Can I create a shortcut to open a specific application on OS X?

I want to create a keyboard shortcut to i.e. open Firefox while I am working in another application. I know I can use ⌘ CMD+T when I am in Firefox to open a new tab.   I haven't found a way to create that kind of shortcuts in System Preferences.  Any ideas?


Postive-semidefiniteness of matrix with entries $1/(a_i+a_j)$

Let $a_1, \ldots, a_n$ be a set of positive numbers. Define a matrix $M_{ij} = \frac{1}{a_i+a_j}$. I'm trying to prove that $M$ is positive-semidefinite. The hint says to use the fact that $\int_{0}^{\infty} e^{-sx}\; dx = \frac{1}{s}$ if $s > 0$. However I don't know how this hint is useful. I've tried choosing an arbitrary vector $x$ and substituting $x^{\intercal}Mx = \sum_{i}\sum_{j} \frac{x_ix_j}{a_i+a_j}$ into $s$ and using properties of exponents to simplify the equation into something that is clearly positive, but without any luck. The denominator $\frac{1}{a_i+a_j}$ is simply too difficult to work with. At this point I think I'm just missing some trick that I don't know. Any help would be appreciated.


I tend to overuse the hyphen as a pause, and would appreciate some feedback on this

An example of the way I tend to use the hyphen would be:     Some people are genetically predisposed to build muscle - I am not one of them.   I usually do this more often when I am in a hurry. Still, I use it this way regularly. The comma is not a candidate otherwise I would just make the trailing phrase into another sentence. An ellipsis would seem to be the correct choice to indicate the pause, but I want it to seem as if I interrupted myself out of my own existential angst over it (in that example).


In java we can create String in the following 2 ways -    String str1 = new String("first string");  //1  String str2 = "second string";  //2   Is there any difference in performance  with these 2 approaches? And in the second case is there any new String object created? Thanks in advance.


I notice that I lost a hat, before I had 18 hats:  but now I can just see 17 hats.  I notice this because I open multiple tabs in my navigator. My question: Can we lose our hats after we get them, or is this a bug?


How to properly align a set of very long equations

I do have a term and would like to show several steps of a derivation, just like here:  \documentclass{IEEEtran} \usepackage{amsmath} \begin{document} \begin{align} thisIsATerm \\ &= \framebox[\columnwidth]{long equation 1}\\ &= \framebox[\columnwidth]{long equation 2} \end{align} \end{document}   Here, the equations 1 and 2 are filling up a single (double-column) line. which looks like:     How to I get something that looks better? Maybe something like this (please suggest something more beautiful or how you would do it):


How do readied actions involving movement interact with being charged?

Situation:  On her turn, Alice uses the  action.  She specifies the condition "a creature attacks me," and an action that would take her out of melee range (like teleporting away with ).  On Bob's next turn, he  Alice.  The attack he would take at the end of his charge meets the trigger conditions for Alice's readied action, so she teleports away.  What exactly happens?   Does Bob get to make his melee attack before Alice teleports? Does it matter whether Alice teleports somewhere that would have been within Bob's original charge range, versus somewhere he could not have charged in the first place? If Bob doesn't get to attack, does he still lose his entire full round action for charging?  Or has he only spent a move action if he never gets to attack?  What if he's already moved farther than he could have with a single move action (since you can charge twice your speed)? Would it matter if Alice had chosen a different trigger condition for her readied action, like "a creature comes within 20 feet of me?"


List of icons for Moto G 2nd Generation running Android 5.0.2

I have a Moto G (2nd Generation) running Android 5.0.2.  I am new to both the device and to the Android OS, and would like to understand the meanings of the various notification icons present across the top of the home page of the device. Is there a list provided by Motorola or Google?  Note: I know about this related  but that link is specifically for a Samsung Droid Charge model, and is also dated.  Update: The link mentioned in the possible duplicate is a list of "suggested" icons from Google, and is not helpful.


How to negate the definition of continuity using Generalized De Morgan's Law.

The difinition of the Continuity is the following. $f(x)$ is continuous at a point $a$ means for every $\epsilon > 0$ , we will get a $\delta > 0$ such that $|f(x) - f(a) < \epsilon|$ for all $x$ satisfying $|x - a| < \delta .$ By using quantifiers , we can write $(\forall \epsilon > 0) (\exists \delta > 0 ) [ \forall x ( |x- a | < \delta \implies |f(x) - f(a) | < \epsilon )]$ The negation of the above statement will be '$( \exists \epsilon > 0) ( \forall \delta > 0 ) [\exists c (|c - a | < \delta \implies |f(c) - f(a)  | \geq \epsilon )]$ .' But I want to know how to do that using generalized De morgan's Law. Can anyone please help me?


making a div "hug" its contained components

If I have HTML that looks like this:

Fig. 1: Some caption

   Is there a way to use CSS so that the div with class figure has a width that is only large enough to contain the image and caption? I want to put a rectangular border around both, but I don't want to have to guess the div's width in pixels.  example below (div.figure has a width that seems to expand to fill its available width)    div.figure {    border: 1px solid black;  }

Fig. 1: Some caption


I have a Nikon D5100, and would like to be able to hold a speedlight in my hand, or place it behind my subject. I'd like to avoid cables, but don't know which specific products I should get. I currently have an SB-400, which I'm willing to replace.  Any recommendations?


Let $k$ be an algebraically closed field. How do we show $Y=\{(t, t^2, t^3) \mid t \in k\}$ is an algebraic set?

There is an exercise in Hartshorne's Algebraic Geometry with says to show that $Y=\{(t, t^2, t^3) \mid t \in k\}$ is an affine variety of dimension $1$. But I actually don't even know how to show that it is algebraic set. The easiest polynomials I thought of that vanish on $Y$ are: $x^2-y, x^3-z, y^3-z^2$. How do we show that $Y$ is affine algebraic set? How do we come up with the polynomials to define $Y$? How would we go about showing that $Y$ is the zero set of these polynomials?


Java convert String to XML Document Null pointer Exception in StringReader

Getting a xml document from the http url, and printing of the documents works perfect (System.out.println(xmlResult)), but when I convert  string into xml Document it produces an Null Pointer exception  Java code  public static void main(String[] args) throws MalformedURLException, IOException, ParserConfigurationException, SAXException {         DocumentBuilderFactory builderFactory = DocumentBuilderFactory.newInstance();         DocumentBuilder documentBuilder = DocumentBuilderFactory.newInstance().newDocumentBuilder();         URL url = new URL("http://ops.epo.org/3.1/rest-services/published-data/publication/epodoc/US7039403/biblio");          HttpURLConnection epo = (HttpURLConnection) url.openConnection();         epo.setRequestMethod("GET");         epo.setRequestProperty("ContentType", "text/xml;charset=\"utf-8\"");         epo.setRequestProperty("Accept", "text/xml");          InputStream inputstream = epo.getInputStream();         BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(inputstream,"UTF-8"));              String xmlResult = "";             while ((xmlResult = bufferedReader.readLine()) != null) {                             }                        InputSource inputSource = new InputSource();             inputSource.setCharacterStream(new StringReader(xmlResult));             Document xmlDocument = documentBuilder.parse(inputSource);              System.out.println("Root element :" + xmlDocument.getDocumentElement().getNodeName());             }   Exception details  Exception in thread "main" java.lang.NullPointerException     at java.io.StringReader.<init>(StringReader.java:50)     at ExtractBiblio.Teser.main(Teser.java:62)  Line:inputSource.setCharacterStream(new StringReader(xmlResult));   help me to resolve it.


If $F$ and $G$ are adjoint functors, why are $\operatorname{Nat}(G,G)\simeq\operatorname{Nat}(F,F)$ as algebras?

Suppose $F\colon\mathcal{A}\to\mathcal{B}$ and $G\colon\mathcal{B}\to\mathcal{A}$ are adjoint functors between some $R$-linear abelian categories ($R$ a ring), via a fixed counit-unit adjunction $\epsilon\colon GF\Rightarrow 1$ and $\eta\colon 1\Rightarrow FG$. Why is the following an isomorphism of $R$-algebras?  $$ \operatorname{Nat}(G,G)\to\operatorname{Nat}(F,F):\alpha\mapsto (F\ast\epsilon)\circ (F\ast\alpha\ast F)\circ (\eta\ast F) $$  My primary issue is I don't see how to invert it, since the counit-unit equations $F\epsilon\circ \eta F=1$ and $\epsilon G\circ G\eta=1$ don't seem to allow me to "undo" the $F\ast\epsilon$ and $\eta\ast F$ from the left and right.


Cannot boot ubuntu without usb plugged in and cannot use the usual way to install grub

I installed ubuntu automatically using a jump flash, however it cannot boot without usb. I tried the way of typing "sudo grub-install/dev/sda", and it just doesn't work! Also I am still confused where I install the grub2. Hope someone can help me. The terminal screen is showed as followed:  ubuntu@ubuntu:~$ sudo fdisk -l  WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk doesn't support GPT. Use GNU Parted.   Disk /dev/sda: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders, total 1953525168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0xa62b4079  Device Boot      Start         End      Blocks   Id  System /dev/sda1               1  1953525167   976762583+  ee  GPT Partition 1 does not start on physical sector boundary.  Disk /dev/sdb: 7858 MB, 7858028544 bytes 90 heads, 30 sectors/track, 5684 cylinders, total 15347712 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0xc3072e18  Device Boot      Start         End      Blocks   Id  System /dev/sdb1   *          24    15347711     7673844    c  W95 FAT32 (LBA)  ubuntu@ubuntu:~$ sudo grub-install/dev/sda sudo: grub-install/dev/sda: command not found


How to show that $e$ is irrational by studying $\sum^{n}_{k=1}\frac{1}{k!}$ and $\sum^{n}_{k=0}\frac{1}{k} + \frac{1}{n \cdot n!}$?

Suppose you have $$a_n = \sum^{n}_{k=0}\frac{1}{k!}$$ and $$b_n = a_n + \frac{1}{n \cdot n!}. $$  By using the fact that $a_n <e <b_n$, which is true $\forall n \in \mathbb{N}$, conclude that $e \not \in \mathbb{Q}$.  And I am unable to do anything. I tried to get something absurd by supposing that $e = \frac{a}{b}$ with $a,b \in \mathbb{Z}$, but didn't get anywhere. A hint would be highly appreciated.


Is a citizen of Canada required to apply for a US visitor visa after visiting Iran?

Under new rules, non-US citizens from Visa Waiver Program countries who have visited Iraq, Syria, Iran, Sudan, Libya, Somalia, or Yemen are required to apply for a proper visa because they are no longer eligible for the VWP.   Does the above apply to citizens of Canada also? Canada is not a Visa Waiver Program country, but instead Canadian citizens can enter the US visa-free. If a Canadian citizen has visited Iran for example, is the entry procedure to the US any different?  I have looked through  but that page does not mention Canada.


How to get values from JTable's row then assign them to an array?

[Fixed! There was a typo error. I wrote productsTable1 when it was supposed to be productsTable2] I'm trying to assign the values of a JTable's row (which was created from a 3d array) to an array, invoiceDump, after I click on the row, but I get an error Exception in thread "AWT-EventQueue-0" java.lang.NullPointerException: Cannot invoke "Object.toString()" because the return value of "javax.swing.JTable.getValueAt(int, int)" is null when I selected the 1st row and this error Exception in thread "AWT-EventQueue-0" java.lang.ArrayIndexOutOfBoundsException: 1 >= 1 when I select the 2nd row. Here's is what I did private void productsTable2MouseClicked(java.awt.event.MouseEvent evt) {                                                 int[] selectRow = productsTable2.getSelectedRows(); // array that stores selected row's data     // Displays the selected row's data to text fields     invoiceDump[0] = productsTable1.getValueAt(selectRow[0], 0).toString();     invoiceDump[1] = productsTable1.getValueAt(selectRow[0], 1).toString();     invoiceDump[2] = productsTable1.getValueAt(selectRow[0], 2).toString();     invoiceDump[3] = productsTable1.getValueAt(selectRow[0], 3).toString();     invoiceDump[4] = productsTable1.getValueAt(selectRow[0], 4).toString();     invoiceDump[5] = productsTable1.getValueAt(selectRow[0], 5).toString();     invoiceDump[6] = productsTable1.getValueAt(selectRow[0], 6).toString();     System.out.println(Arrays.toString(invoiceDump)); }     I replaced int[] selectRow = productsTable2.getSelectedRows(); with int selectRow = productsTable2.getSelectedRow();, but it generated the same errors. This block of code works fine when I want to set text fields from the row's values. However, I want to get the values directly from the table and assign it to my array. How to make it work?


Let A be a nonsingular square matrix with integer entries. Prove that inverse of A contains only integer entries if and only if det(A) = ±1.

How can we describe the enteries of a matrix by just knowing the determinant of it?


SQL Server UNION SUM misses repeated values

I have 3 independent querys that I would like to sum the values obtained in each query. These querys obtain a count value for each day of a month:  query one  day|val|  1  | 2  2  | 6  3  | 5*  4  | 2  5  | 7   query 2  day|val| 2  | 1 3  | 5* 10 | 5 11 | 2 12 | 7   I am using the instruction:  select day, SUM(val)  from query1 UNION query2 group by day   I found out that when a value is repeated instead of sum it would use one of the repeated values, for axample the days number 3 both have value 5. the instruction would give onlye value 5 instead of 10.  This is supposed to give me a report of total of values per day in a month but the report is wrong because of this problem caused by UNION How can i fix it?


BibLaTeX: Combine same author, different years into one citation

In the MWE below, \citet{macdonald2015, macdonald2016} becomes "MacDonald (2015) and MacDonald (2016)". \citep{macdonald2015, macdonald2016} becomes "(MacDonald, 2015; MacDonald 2016)". How do I make it print "MacDonald (2015, 2016)" and "(MacDonald, 2015; 2016)?  \documentclass{scrartcl} \usepackage{fontspec} \usepackage[style=authoryear,natbib=true,backend=biber,sorting=nyt,mincitenames=1,maxcitenames=2,url=false,giveninits=true,uniquename=false,maxbibnames=100,uniquelist=false,dashed=false]{biblatex} \begin{filecontents}{\jobname.bib} @article{macdonald2015,   title = {On Having a Farm},   volume = {42},   journaltitle = {Journal of Science and Stuff},   author = {MacDonald, O.},   date = {2015} } @article{macdonald2016,   title = {Noise reduction in livestock},   volume = {43},   journaltitle = {Journal of Science and Stuff},   author = {MacDonald, O.},   date = {2016} } \end{filecontents} \addbibresource{\jobname.bib} \title{A document} \begin{document} \maketitle In this text I cite \citet{macdonald2015, macdonald2016} for the mwe.  And now i cite the same clever fellow \citep{macdonald2015, macdonald2016} again. \printbibliography \end{document}


I need to subscribe to specific tags, for example:  If I need to subscribe to the [android] tag I just go through this tag and subscribe to it. What if I need to make it more specific, like [android][java] which will send me emails with the questions containing these tags only (meaning I won't receive separate emails for [android] only or [java] only)?  Is that possible or not?


Inductive step of $2^2 + 4^2 + \cdots + (2n)^2$

I am trying to prove that $\sum_{k=1}^n (2k)^2 = \frac{2n(n+1)(2n+1)}{3}$. I managed to do the base case but I am stuck at the inductive step. Am I doing it wrong? This is what I need to prove: $$2^2 + 4^2 + \cdots + (2n)^2 = \frac{2n(n+1)(2n+1)}{3}$$ Here is the working I did. I feel that I did something wrong but I am not sure which portion. Show $k+1$ is true: $$2^2 + 4^2 + \cdots + (2k)^2 + (2(k+1))^2 = \frac{2(k+1)((k+1)+1)(2(k+1)+1)}{3}$$ $$\frac{2k(k+1)(2k+1)}{3} + \frac{3(2(k+1))^2}{3} = \frac{2(k+1)((k+1)+1)(2(k+1)+1)}{3}$$


trigger command over network from/to Linux

I have two linux (gentoo) boxes A and B. Both are connected via LAN.  A has a camera with motion detection. If motion was detected I can trigger a command on A.  I want to send a ? message/packet to B so that B plays a sound on every motion event that occurs on A.  (paplay /usr/share/sounds/freedesktop/stereo/complete.oga)  How can I do this (without passwordless SSH setup), maybe netcat?


Where is system.log in TimeMachine backup

I would like to get older versions of /private/var/log/system.log files from TimeMachine.  Is this possible?  How?   I see current system.log files. I went to folder /private/var/log then invoked TimeMachine.     When I go back to previous backup, I do not see system.log files.    relates to    User want to look through macOS log files to see history of external drive mounting. Data is in "/private/var/log/system.log".  Needed data is a month old. A month is longer than normal backup of system.log is keep.  Attempted to look in timemachine backup but it seems the older system.log files are not kept.


Java Pass By Value and Pass By Reference

i have done the following sample with to check my knowledge   import java.util.Map;  public class HashMap {     public static Map<String, String> useDifferentMap(Map<String, String> valueMap) {         valueMap.put("lastName", "yyyy");         return valueMap;     }      public static void main(String[] args) {         Map<String, String> inputMap = new java.util.HashMap<String, String>();         inputMap.put("firstName", "xxxx");         inputMap.put("initial", "S");         System.out.println("inputMap : 1 " + inputMap);         System.out.println("changeMe : " + useDifferentMap(inputMap));         System.out.println("inputMap : 2 " + inputMap);     } }   the output is :   original Map : 1 {initial=S, firstName=xxxx} useDifferentMap : {lastName=yyyy, initial=S, firstName=xxxx} original Map : 2 {lastName=yyyy, initial=S, firstName=xxxx}   this method useDifferentMap gets the map and changes the value and returns back the same. the modified map will contain the modified value and the scope of it is local for the useDifferentMap method.  my question is if java is pass by value is the modified value should not be affected in the original map.  so is java pass by value or pass by reference ???  thanks