There is a function: $f: \mathbb{R} \to [1 ; + \infty) $ that is continous in $\mathbb{R}$. Prove that for every chosen set of $x_i \in \mathbb{R}$ for $i \in \{1, 2, ..., n \}$ there exists a point $x \in \mathbb{R}$ such that: $$f(x) = \sqrt[n]{f(x_1) \cdot f(x_2) \cdot f(x_3) \cdot ... \cdot f(x_n)}$$  That exercise seams quite basic: if function is continuous in $\mathbb{R}$, then, for every set of values, there exists a value equal to geometric mean of values in the set that is reached by that function. I know that geometric mean is a continous function + that a function $f(x)$ is continous. How do I prove then that a combination of those functions is continous? As I carry on my research, any help would be much appreciated - answers providing materials on similar problems would be great.

I tried to solve this problem but I could not continue  Let $f: [a, b]\to \mathbb{R}$ be a continuous function.  Prove that if $x_1, x_2,\ldots,x_n  \in (a,b)$, then exists $x_0 \in (a, b)$ such that $$f (x_0) =\frac{f (x_1) + f (x_2) +\cdots + f (x_n)}{n}$$  the function is continuous, so $\forall\ x_1, x_2,\ldots,x_n  \in(a, b)$ $$\begin{align*} \lim_{x \to \ x_1}f(x)&=f (x_1)=L_1\\ \lim_{x \to \ x_2}f(x)&=f (x_2)=L_2\\ \lim_{x \to \ x_3}f(x)&=f (x_3)=L_3\\ &\vdots\\ \lim_{x \to \ x_n}f(x)&=f (x_n)=L_n\\ \end{align*}$$  We have that:  $$\lim_{x \to \ x_0}f(x)=f (x_0)=\frac{f (x_1) + f (x_2) +\cdots + f (x_n)}{n}= \frac{1}{n}\sum_{j=1}^n f(x_j)$$ Now $$\min\left \{ L_1,L_2,L_3,\cdots,L_n \right \}\le\frac{1}{n}\sum_{j=1}^n f(x_j)\le\max\left \{ L_1,L_2,L_3,\cdots,L_n \right \}$$  and at this point I'm lost ...


If you would like to describe a place where two different waters meet together and form a new stream, what word would you choose? I looked it up online and found word "confluence" can be the choice but I got the feeling that it is  describing about the phenomenon of the conflux rather than the geographical feature of the stream.  That being said, I don't think saying like     XXXX stream is a water confluence       or      XXXX confluence(conflux) is named because it is where two different water bodies meet   will successfully describe what I intend.  Thank you!

I'm seeking a word that best describes the point of land created by the confluence of two rivers. The parcel of land in question would be situated in between the two rivers as their flow combined to form one river. Is there such a name?  This is not a duplicate of the question asking about the word confluence. This question refers to the point of land created by the confluence.


I am using the following template in order to create a letter  \documentclass[version=last]{scrlttr2} \usepackage[ngerman]{babel} \begin{document}  \begin{letter}{   Petra Mustermann\\   Vor dem Berg 1\\   12345 Musterhausen } \opening{Liebe Vereinsvorsitzende,} \end{letter} \end{document}   I would like to have the date to be in german, but the date in the output is in english, as shown in the following picture.  On page 179 of the , the date is correctly printed in german. I am using Linux and pdflatex.

Whenever I try to compile my .tex file, I get the following error:      ! LaTeX Error: File ngerman.sty not found.   Type X to quit or  to proceed,   or enter new name. (Default extension: sty)   Enter file name:   ! Emergency stop.      l.3 \begin   Here's a MWE:  \documentclass[a4paper,12pt]{article} \usepackage{ngerman} \begin{document} xyz \end{document}   This happens even though the ngerman.sty package can be found in the following directories:   /usr/share/texlive/texmf/tex/latex /usr/share/texmf/tex/latex   I also tried running the texhash command.


This community is introduced by a friend of mine about a week ago and I hope I can write my questions clearly (English is not my first language and I normally have poor communication skills...)   My story: I started my BSc in mathematics about 22 years ago (when I was age 9) and I decided (had to) quit after one painful semester that I still remember it. I studied on my own and a few years later I decided to solve the notorious impenetrable problem the Hodge conjecture. I have not achieved that goal yet but (I think) I have more than enough that people get a fields medal for that. And with my past experiences I believe that I am most probably not wrong in the technicalities (peer review need to be done though)... Nonetheless I can't continue working hard on the problem as I used to because of spending a lot more time on making money (from teaching to laboring jobs) so better to publish whatever I have to possibly get a research job than living a fading life and every-day-increasing severe-depression. But there are many obstacles I believe:   1- Can I publish an article without having an academic position and even without a university degree, at all?   2- I never care about fame and I absolutely don't care if solving some unsolved problem is attached to a particular name (=person) but handing over 18 years of my research to someone who have authority to easily publish it has a high risk of his/her plagiarism temptation thus ruining a possible would-be good life of mine. How can I trust someone?  3- Evaluation of my results is a necessity before I have any claim of that but if it turns out to be valuable enough can I get an academic position without having a physical degree and not going through all many years of official undergraduate and graduate programs in mathematics?     By the way, I hold an Iranian passport which means that I cannot travel Europe/US/Canada/... to present my research with just an invitation for a conference. (Visa-on-arrival is available for Iranian citizens in Mozambique or Samoa airports but I don't think that be helpful; no offense).    PS Please feel free to edit my post if my English is not clear. Thank you all in advance. :)

Assume you have already completed your undergrad and have been working for a number of years. Does one need to be part of a university or a learning institution to publish papers?


Much to my chagrin, I've discovered that the question/answer editor view implements a keyboard shortcut of Cmd-G (on OS X, can't speak to other platforms) for adding images to posts. I'm sure this is very useful for folks who add lots of images to their posts, but for my part, I far more often want to use the OS X platform-standard text searching command, "Find Next", that is normally bound to Cmd-G.  Is there a way to turn off this "override" behavior? (And preferably any other overrides of platform-standard key bindings related to text editing?)

I navigate with Ctrl-n,p,f,b (readline/ keys), so that I don't have to move my hands too much and get  again. Is there a way to disable Ctrl-b being hotkey for bold?  Note that this is not just an Emacs thing. Standard web browsers, like Firefox and Chrome, use things like  Ctrl + K and Ctrl + L to navigate to the Google search bar and address bar respectively.


I got this bright pixels, what is reason? , any one can help me for this

I often use Cycles' built in Glass BSDF shader to achieve realistic refraction effects, but in many cases, it seems that Cycles' glass caustics creates an unfortunately large number of fireflies (pixels that are abnormally bright relative to their surroundings). In some models of mine, even when I render for 3000 or more samples/pixel, my final image is still covered in fireflies. While I can improve this in many cases by increasing the total amount of light available in the scene, this loses a lot of the potency of the refractive effects I'm looking for, especially in scenes with low light levels.  So my question is, how can I reduce the amount of fireflies while using Cycles' caustics without sacrificing the quality of the refractive effects?  Note: I am aware that Cycles' caustics will perform much better once Cycles has full support for bidirectional path-tracing, but it looks unlikely that that will become , unfortunately.


Below are all the linux kernels that are running on my machine. I am trying to make a debian base install as light as possible. The kernel I am running is linux-image-2.6.30-vortex86mx-apm. I am wondering will it be safe to remove all others using apt-get remove kernel-image-xxxxxx       ||/ Name                               Version                      Description     +++-==================================-============================-===================================================================     un  linux-image                        <none>                       (no description available)     un  linux-image-2.6                    <none>                       (no description available)     ii  linux-image-2.6-486                2.6.32+29                    Linux 2.6 for old PCs (meta-package)     un  linux-image-2.6-686                <none>                       (no description available)     un  linux-image-2.6-686-bigmem         <none>                       (no description available)     un  linux-image-2.6-amd64              <none>                       (no description available)     un  linux-image-2.6-k7                 <none>                       (no description available)     un  linux-image-2.6-openvz-686         <none>                       (no description available)     un  linux-image-2.6-vserver-686        <none>                       (no description available)     un  linux-image-2.6-vserver-686-bigmem <none>                       (no description available)     un  linux-image-2.6-xen-686            <none>                       (no description available)     ii  linux-image-2.6.30-vortex86mx-apm  1.1                          Linux kernel binary image for version 2.6.30-vortex86mx-apm     ii  linux-image-2.6.32-5-486           2.6.32-41                    Linux 2.6.32 for old PCs


I am trying to choose between the two correlation tests. I am trying to see if a trait is correlated with the area of a habitat patch for a number of different habitat types. The data is non-parametric and cannot be made normal through transformation, so the choice is between Spearman's or Kendall's  As it is comparing areas numerous data points will have the same area value which means there will be lots of ties in the data. I understand that Kendall's tau handles ties far better than Spearman's does.  However, some of the data sets are very large including one that is approximately 500,000 data points, and I understand that the cost of Kendall's is O(N^2) so it could potentially be very computationally demanding.   How do I make the choice between the two correlation statistics in this case?

In which cases should one prefer the one over the other?  I found someone who claims an advantage for Kendall, , are there other reasons?


If $\|u\| \leq \|u+av\|$ for all $a \in F$,   How can I show that $\langle u,v\rangle=0$?  I know a standard solution uses $\operatorname{Re}$ and $t =$ something but was wondering if there was perhaps an easier solution? Thanks!

Prove that $\langle u,v\rangle=0\Longleftrightarrow \|u\|\leq \|u+av\|$.  So far I can get the $\Longrightarrow$ very easily, but I need some help with the $\Longleftarrow$ implication, any hints would be greatly appreciated.  Please no answers, I just want a small nudge to get me in the right direction, I've been stumped on this for a little bit.  Here's what I have so far:  ($\Longleftarrow$)  Assume $\|u\| \leq \|u+av\|$  $\|u+av\|^2=\langle u+av,u+av\rangle=\langle u,u\rangle+ \langle u,av\rangle+\langle av,u\rangle+\langle v,v\rangle=\|u\|^2+\bar{a} \langle u,v\rangle+a\langle v,u\rangle+\|v\|^2=\|u\|^2+ \bar{a}\bar{\langle v,u\rangle}+a\langle v,u\rangle+\|v\|^2$  Thoughts/ideas?


On a PAL xbox system - I can run some NTSC games. Is there a way to know which NTSC game will run on the PAL console just by its cover?

I just bought a  game (Forza 4) for my Xbox 360 (bought in the US). When I tried to play the game, it wouldn't load because of region issue. Is there a legal way to solve this (no crack)?


Does anyone know how to do this without the use of addition rules? We have not covered that in class, and all the info I can find online suggests that as a solution. Thanks]

Obviously since A → C and B → D then if A v B one of C or D must be true.   My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?


The first half of this works correctly. $selectedVerb and $verbNum both come back fine and are displayed. When I try to use $verbNum in the next query, it keeps resulting in error:      Fatal error: Uncaught Error: Call to a member function fetch_array()   on boolean; Stack trace: #0 {main} thrown.   Code:  if ($stmt = $dbc->prepare("SELECT verbNum FROM verblist WHERE mainVerb = ? ")){      $stmt->bind_param("s", $selectedVerb);      $stmt->execute();      $stmt->bind_result($verbNum);      $stmt->fetch();      echo ''.$selectedVerb.' is part of verb number: '.$verbNum. '';      settype($verbNum, "integer");      $verbListarray = mysqli_query($dbc, "SELECT mainVerb FROM verblist WHERE verbNum = $verbNum");      while($row = $verbListarray->fetch_array())     {         echo $row['mainVerb'];         echo "
";     }          $stmt->close(); }

I am trying to execute my PHP code, which calls two MySQL queries via mysqli, and get the error "Commands out of sync; you can't run this command now".  Here is the code I am using  <?php $con = mysqli_connect("localhost", "user", "password", "db"); if (!$con) {     echo "Can't connect to MySQL Server. Errorcode: %s\n". Mysqli_connect_error();     exit; } $con->query("SET NAMES 'utf8'"); $brand ="o"; $countQuery = "SELECT ARTICLE_NO FROM AUCTIONS WHERE upper(ARTICLE_NAME) LIKE % ? %"; if ($numRecords = $con->prepare($countQuery)) {     $numRecords->bind_param("s", $brand);     $numRecords->execute();     $data = $con->query($countQuery) or die(print_r($con->error));     $rowcount = $data->num_rows;     $rows = getRowsByArticleSearch("test", "Auctions", " ");     $last = ceil($rowcount/$page_rows); }  else {  print_r($con->error); } foreach ($rows as $row) {     $pk = $row['ARTICLE_NO'];     echo '
' . "\n";     echo ''.$row['USERNAME'].'	' . "\n";     echo ''.$row['shortDate'].'	' . "\n";     echo 'DELETE RECORD	' . "\n";     echo '
' . "\n"; } function getRowsByArticleSearch($searchString, $table, $max) {     $con = mysqli_connect("localhost", "user", "password", "db");     $recordsQuery = "SELECT ARTICLE_NO, USERNAME, ACCESSSTARTS, ARTICLE_NAME, date_format(str_to_date(ACCESSSTARTS, '%d/%m/%Y %k:%i:%s'), '%d %m %Y' ) AS shortDate FROM AUCTIONS WHERE upper(ARTICLE_NAME) LIKE '%?%' ORDER BY str_to_date(ACCESSSTARTS, '%d/%m/%Y %k:%i:%s')" . $max;     if ($getRecords = $con->prepare($recordsQuery)) {         $getRecords->bind_param("s", $searchString);         $getRecords->execute();         $getRecords->bind_result($ARTICLE_NO, $USERNAME, $ACCESSSTARTS, $ARTICLE_NAME, $shortDate);         while ($getRecords->fetch()) {             $result = $con->query($recordsQuery);             $rows = array();             while($row = $result->fetch_assoc()) {                 $rows[] = $row;             }             return $rows;         }     } }   I have tried reading up on this, but I am unsure of what to do. I have read about store result and free result, however these have made no difference when using them. I am unsure at exactly which point this error is being caused, and would like to know why it is being caused, and how to fix it.  Going by my debug statements, the first if loop for countQuery is not even being entered, because of an error in my sql syntax near near '% ? %'. However if I just select * instead of trying to limit based on a LIKE clause, I still get the command out of sync error.


I've been an ESRI user and a Carto user and like both tools but I am now hoping to build my own web-mapping platform. The issue is, I have no web-development experience other than the little I've taught myself. I want my mapping platform to be able to run SQL queries and to store data safely (some datasets I only want to make available via a link, and not make the data shareable/scrapeable).   Am I even looking in the right direction?   Can this GeoServer + PostgreSQL mix get me what I want?

I want to start working on a web map at work to map some of our statistics by city.    I have an idea, but I'm not exactly sure where to start.   Are there any definitive resources that provide step by step guidance on how to do this?


Hi,  My book on analogue circuits has this question and I have been stuck  at it for the past three days or so. I am supposed to figure out the transfer function for the network as well as the cutoff frequency and the angle. I am just having hard times figuring out how to solve it. I tried nodal analysis and the two poles theory but I get a different result every time.  Here are the values for resistors and capacitor: R1=R3=4.7KOHM, R2=10KHOM and C=4.7 nF

I have  (link to multisim) and i am asked to find the transfer function, the max and min value, the cutoff frequency, angle and the type of the filter.   [the actual problem][2]][2]   I have done the calculations and found that the circuit is a low pass filter, and its cutoff frequency is  26842 Hz which is awfully high and therefore i am very worried that i have gotten something wrong. I also found that when w=0 the value for the transfer function = 0.6803 and when w approaches infinity the value for the transfer function =0 and hence i concluded that it was a low pass filter. here is my calculate for the transfer function:   $$H_w=\frac{1}{(((R1+R3)*(j*w*C))+(((R3*R1)/(R2))*(j*w*C))+(R1/R2)+1)}$$  here is how it looks after i plug in the values for the resistors:  $$H_w= \frac{1}{(1.47 + j*w*0.000054562299999999998836925505310975)}$$  j represents the imaginary number. Basically you can see that if w=0 i get 1/1.47= 0.6803  Anyone can varify this is correct for me? and if so any chance that that "anyone" knows how verify that with multisim as i cant read the graph it produce. Please help.  [2]:


I opened , authenticated using Google OpenID, and was returned to   When using HTTPS Everywhere, authentication fails because of this:  Unable to log in with your OpenID provider:  The openid.return_to parameter (http://meta.stackoverflow.com/users/authenticate/?s=46229692-b92a-4e47-9221-1bc8a2ea72c1&dnoa.userSuppliedIdentifier=https%3A%2F%2Fwww.google.com%2Faccounts%2Fo8%2Fid) does not match the actual URL (https://meta.stackoverflow.com/users/authenticate/?s=46229692-b92a-4e47-9221-1bc8a2ea72c1&dnoa.userSuppliedIdentifier=https%3A%2F%2Fwww.google.com%2Faccounts%2Fo8%2Fid&openid.ns=http%3A%2F%2Fspecs.openid.net%2Fauth%2F2.0&openid.mode=id_res&openid.op_endpoint=https%3A%2F%2Fwww.google.com%2Faccounts%2Fo8%2Fud&openid.response_nonce=2014-01-08T16%3A28%3A08ZYkthQjdVkVBcoQ&openid.return_to=http%3A%2F%2Fmeta.stackoverflow.com%2Fusers%2Fauthenticate%2F%3Fs%3D46229692-b92a-4e47-9221-1bc8a2ea72c1%26dnoa.userSuppliedIdentifier%3Dhttps%253A%252F%252Fwww.google.com%252Faccounts%252Fo8%252Fid&openid.assoc_handle=1.AMlYA9UYcnrN8ok5c7u7N_0w6xqXecfeGurDPvv2sfif3KdJrrpG8PqSCA4TQKcw&openid.signed=op_endpoint%2Cclaimed_id%2Cidentity%2Creturn_to%2Cresponse_nonce%2Cassoc_handle%2Cns.ext1%2Cext1.mode%2Cext1.type.alias4%2Cext1.value.alias4&openid.sig=l19x4Zy0MYR0EYaHgoDzk6yZKV0%3D&openid.identity=https%3A%2F%2Fwww.google.com%2Faccounts%2Fo8%2Fid%3Fid%3DAItOawmMuRNLMJTQVB_HNcT1Vp5FzBfvKQHXIEc&openid.claimed_id=https%3A%2F%2Fwww.google.com%2Faccounts%2Fo8%2Fid%3Fid%3DAItOawmMuRNLMJTQVB_HNcT1Vp5FzBfvKQHXIEc&openid.ns.ext1=http%3A%2F%2Fopenid.net%2Fsrv%2Fax%2F1.0&openid.ext1.mode=fetch_response&openid.ext1.type.alias4=http%3A%2F%2Faxschema.org%2Fcontact%2Femail&openid.ext1.value.alias4=dserodio%40gmail.com) the request was made with.   This problem seems to be new since I've been using HTTPS Everywhere for a while and this error manifested for the first time last week IIRC.

I can't seem to log in with my Stack Exchange OpenID. When I try, I get the error message:     Unable to log in with your OpenID provider:      The openid.return_to parameter (.) does not match the actual URL (.) the request was made with.   It works if I disable the HTTPS-Everywhere plugin in Firefox, but if I then re-enable the plugin and go to a site on which I am not logged in (in which case login is normally nearly seamless), it fails again with the same error message, or at least something very similar.  I'm not aware of having done anything that might have caused this, although I will admit I don't recall seeing https:// in the address bar on Stack Exchange before (I do now, and that's a good thing IMO!). I was using the site  and it worked fine then, but not now...


I am a filipino citizen. I will be travelling to Fiji Island and my layover is in Korea. Do I need to get a transit visa in Korea? Thanks.

I am a Vietnamese citizen. I am planning to buy a round-trip flight ticket from Taipei to Los Angeles (America) and I will transit in Seoul airport.   Do I need a visa if I want to enter Seoul (not over 72 hours)?   My first route is TPE-ICN-LAX, do I need a visa if I stay one night in Seoul? My second route is LAX-ICN-TPE, do I need a visa if I stay one night in Seoul?  Of course, I have a valid US visa, and onward ticket that I booked.


After exporting HISTTIMEFORMAT='%F %T' I tried to query history  But the result shows all the commands are executed on same day.  How can I check the actual date and time of actual command execution?


I regularly write chemistry documents with odd words in them. Is there a way to know if LaTeX knows it can hyphenate a word? I'm wondering as the person beside me just discovered that the person whose thesis he is using as a base told LaTeX how to hyphenate polymer, which he thought would be common enough that LaTeX would know it already.

When TeX produces Overfull box, is puts something like this in the log:  Overfull \hbox (15.47195pt too wide) in paragraph at lines 7--9 []\OT1/cmr/m/n/10 I re-ally re-ally want to get dis-played the op-tions for  hy-phen-ation xxxxxxxxxxxxxx |   I would like a macro \showhyphens that would for an entry like \showhyphens{hyphenation} display its hyphenation options, i.e. hy-phen-ation. This should be displayed either in the document (preferred) or in the log.  (Background: I need this for sumbitting a paper that contains many multi-part words and similar stuff like $(2,3)$-representation etc. I know that there are ways to modify - with \discretionary to make the word breakable, but it makes the code extremly unreadable and I'm not allowed to make this a macro definition.)


I want to know what to use in C# to format my output in my console window I tried to use \t but it did not work  I know there is printf in C to format my output  check this image

Is there something similar to sprintf() in C#?  I would for instance like to convert an integer to a 2-byte byte-array.  Something like:  int number = 17; byte[] s = sprintf("%2c", number);


The common equations to calculate the sound speed in an ideal gas use macroscopic quantities, e.g.:  $$c = \sqrt{\frac{\gamma RT}{M}}$$  What I am interested in is an equation that determines the sound speed in an ideal gas from a microscopic perspective. My reasoning is as follows: Sound propagates through an ideal gas by means of collisions between molecules. Since molecular movement is random, information that propagates from point A to point B via molecular collisions does not travel in a straight line but with an average angle of 45°.  The sound speed in an ideal gas should then be given by:  $$c = v_{rms} \space \sin{45°}$$ where $v_{rms}$ is the root-mean-square speed of molecules.  This equation gives results that are very close to the results given by the above formula (approx. 3% difference). Is my reasoning solid or what is a correct microscopic equation for sound speed in an ideal gas?

In an ideal gas, the speed of sound $v_s$ is related to the r.m.s. molecular speed $v_m$ by  $$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}} \qquad ,$$  where $\gamma=C_p/C_v=7/5$ for a diatomic gas. I understand how to prove this relation from first principles. However, it seems mysterious to me that it pops out like this in the end.  I suppose it's inevitable for dimensional reasons that there will be some relation of this form, since if we want to describe a sample of an ideal gas, a sufficient set of unitful parameters is $m$ and $kT$, and there is a unique way of combining these to give units of velocity. (In a solid or liquid, we have other parameters such as the Young's modulus.) However, this type of dimensional argument doesn't prove that the ratio of the speeds is of order unity.  Is there any straightforward physical plausibility argument for the fact that this ratio of speeds is constant, and for the fact that the ratio is of order unity? I guess it's implausible to have $v_m \gg v_s$, since it seems like then a sound wave would sort of get scrambled and lose its identity because of molecular motion, and this scrambling would take place in much less than a period.


Can anyone say whether the complete recount of question voting changed counters such as the one for the Legendary badge?

When the recalc runs what happens regarding rep capping on particular days? Say I earned 200 solely from questions on one day, will I earn a further 200 when the recalc runs or will I earn zero?  On a similar note if I got no rep from a question upvote on a day will the recalc give me 10, 5 or 0 rep?


Problem statement  6 scientists are working on a secret project. They wish to lock up the documents in a cabinet so that cabinet can be opened when and only when 3 or more scientists are present. What is smallest number of locks needed? What is smallest number of keys each scientist must carry??  Let $n$ be the number of locks. Let us name each scientist as $1,2,3,4,5,6$.Let $S_i$ be the set of keys that scientist $i$ is carrying and each scientist carries $k$ number of keys.we would get following results  $|S_i|=k$ $|S_p \cup S_q \cup S_r|=n$ $n=3k-(|S_p \cap S_q|+|S_p \cap S_r|+|S_r \cap S_q|)+|S_p \cap S_q \cap S_r|$  I tried manipulating the above results in hope of finding solutions but failed.Is there anything I am missing or is this approach entirely wrong?

There are 8 crew members, The leading member wants that only a crew of 5 people or more could open a safe he bought, To each member he gave equal amount of keys, and locked the safe with several locks.  What's the minimal number of locks he should put:   at least 5 crew members would be required to open the safe? Any team of 5 crew members could open the safe, but none of the 4 team crew members.   1,2 stands individually of course.


As of 8/2 I'm still unable to upgrade from 16.04 to 18.04 using the do-release-upgrade command. Still "No new release found." I don't remember it ever taking this long before. And I'd rather not use -d , cause I want to stay on the LTS.  I know they said it'd be a few days, but it's been like a week.. Was there an unexpected delay or something?

I'm following the , but on launching the upgrade tool I get this response:  Checking for a new ubuntu release No new release found   Am I doing something wrong? Is there a workaround?


How do we calculate this?  $ \displaystyle \sum_{n=1}^{\infty} (-1)^{n-1} \frac{H_{2n}}{2n} $  I am stuck that the integrals isn't converging for harmonic (even) numbers . somebody please help .

I would appreciate to understand the main steps giving the evaluation of this series: $$ S=\sum_{n=1}^{\infty} (-1)^{n-1}\frac{H_{2n}}{n}$$ where $H_n$ is the harmonic number. I've tried with no success to obtain this sum with the help of Wolfram Alpha.


The sentence I was writing is: "I thought tubes and bike ... synonymous" is it: "are" or "were"? Thought process is, I am reporting what I thought at the time, which is that they are synonymous, but as a native English speaker it sounds wrong. edit: I think I answered my question in the first sentence but I'll wait for an official answer...

I know the past tense carries the past tense in every dependent clause, but referring specifically to places or to things that are eternal, like the Earth, seems a bit weird and therefore we sometimes (I believe incorrectly) say     He didn't know that New Jersey was actually on the East Coast.   Because it still is. Or     He thought the Earth was round.   So is it square now?  Logically speaking, would you consider the use of past tense here a bit confusing in a day-to-day speech in these examples? Would you instinctively opt for using the present tense?


If I have a card out like  and my opponent cast a  and targets Animar, would I be able to morph my  and give Animar hexproof in response so that he doesn't die, or does he still die?

I'm a relatively new player to Magic: the Gathering. I was reading  to try to understand exactly when it's okay to cast instants (e.g. ) and use some abilities (e.g.  should be tappable sometime during other peoples' turns), but I don't seem to be making much progress: as I come to understand some things, others make less sense.  My confusion is boundless  For instance: to cast  one needs priority. Spells go on the stack, and priority gets passed at some points (I have no idea when), and effects on the stack are resolved when both players have passed priority. But when is that? I can't find any mention of when the other player gets the priority to cast an instant, except on their own turn. Furthermore,  states that during the Main Phase:     505.4. Second, the active player gets priority. Players may cast spells and activate abilities. The active player may play a land.   So players (plural) may cast spells, but only the active player has priority, so only the active player can cast an instant. The turn rules, and the rules on , never mention any point at which the other player gets priority, so when can they possibly Cancel?  In addition, you can only cast a spell when the stack is empty, so the entire stack must be able to be resolved in your turn at some point.  I need an explanation!  I could go on a bit more. There is also  which can be overloaded to "Counter each spell you don't control", which seems like it could only possibly work with an understanding of the stack.  Could someone explain, in simple English:   When can Instants be cast? When can tap abilities be used? What do Instants and abilities have to do with the Stack and Priority?


I am traveling to India(New Delhi) On 29th December 2020. And I have Belgian -PR Card Holder with electronic Chip, but I have an Indian Passport. My Flight is from Brussels to London Heathrow Via British Airways with 6 Hours Layover and then connecting flight via Air India to Delhi. Do I need a Transit Visa for changing my Flight at London Heathrow airport or Not ? also I have to change terminal T5 to Terminal T2 for connecting flight. please advice!

Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.


I did use to live in London. I did used to live in London.  Which one is correct? According to the usage of emphatic do with past tense (eg "I lived in London/I did live in London"), did should change ‘used to’ to ‘use to,’ but I didn't find anything about it except in English Grammar Today by Cambridge. However, Cambridge used did with ‘used to.’ Shouldn't emphatic did change ‘used to’ to ‘use to’?  used to From  Emphatic did We can use the emphatic auxiliary did with used to:  We never used to mix very much with the neighbours, but we did used to say hello to them in the street. (Don't use this form in written exams.)  —

Which is the correct sentence, if there is a correct one?     I use to be a hitman.        I used to be a hitman.   I've read the second sentence recently in a book, but I was sure it should be I use to be a hitman.


In "Future's end, part 2", the doctor is fired upon by two Earth militants and the bullets pass through his holographic matrix. Only two scenes prior, with his new holographic projector, he receives and gives punches with starlings associate. How?

In the Voyager episode: "Future's End, Part II" the doctor rescues B'elanna and Chakotay.     PORTER: They've got lasers! A black man and some bald guy.  (The EMH   enters. Porter and Butch's bullets go straight through him.)       PORTER: God in heaven help us.       EMH: Divine intervention is unlikely.  (The EMH phaser stuns them,   then unties Torres and Chakotay.)   In an earlier episode of Voyager, "Phage":     PARIS: But a hologram is just a projection of light held in a magnetic   containment field. There's no real matter involved. (The EMH slaps   Paris.)       EMH: Now, you hit me.  (Paris's hand passes through the EMH's head.)       EMH: The magnetic containment field that creates the illusion of my   body can be modulated to allow matter to pass through it or be   stopped. I might be able to modulate the holographic lungs in the same   way, allowing oxygen and carbon dioxide to pass from the lungs to the   blood stream.   In order to make the above adjustments the doctor had to touch several buttons on a control panel. I realize the time I refer to above he was using the holo-emitter instead.    How does it work exactly that the doctor can have bullets pass straight through him but he's able to hold on to a phaser without it falling out of his hand? Can he simultaneously have part of his body be transparent and the rest be more like matter at the same time? What if the bullets hit the hand holding the phaser? I think one had a shotgun as I recall so there probably would have been pellets going all over the place.


In algebra we consider two structures to "equivalent" iff they are isomorphic. But apparently in the category of categories, equivalent categories needn't be isomorphic. This goes against my intuition of isomorphism, which I so far thought to be the category theoretic "definition" of equivalent. Why, and what's the right way to think about isomorphisms/equivalences?

I am learning category theory using Basic Category Theory by Tom Leinster as my main source. In the chapter on natural transformations he says that isomorphism of categories is unreasonably strict for the notion of the sameness of two categories. Isomorphism would require functors, $$ F:A\rightarrow B,G:B\rightarrow A $$ such that $$ G\circ F=1_A, F\circ G=1_B $$  Instead he says that for equivalence we loosen the requirement on these functors to be isomorphic, $$ G\circ F\cong 1_A,F\circ G\cong 1_B $$ Then this is better. This section threw me for a loop. I don't understand the difference between the equivalence and the isomorphism statements. Any help clarifying what is trying to be said here is greatly appreciated.


I want to compute  $$\iint_A \frac{1}{x^2+y^2}\,\mathrm dx\,\mathrm dy$$ where $A:=\left[\frac{1}{a},a\right]\times[0,1]$.  I got that this is equal to $\int_{1/a} ^a \frac{1}{x}\arctan \Big(\frac{1}{x}\Big) \mathrm dx\ $ and I don't know what to do from here. Can somebody help me, please?

In there any way to calculate Integral          $$\int_{\frac{1}{2014}}^{2014} \frac{\tan^{-1}x}{x} dx$$      by using simple properties of definite integration. I used substitution $\tan^{-1}x=t $ and applied by parts but then I am stuck at $\int\int \csc(2t)dt$ How should I proceed? What is the most appropriate method to solve this question?


I'm not even sure how to approach this problem. Kunen defined for arbitary sets $B$ and cardinals $\theta$,  $$ [B]^\theta = \{ x \subseteq B : |x| = \theta \} $$ $$ [B]^{< \theta} = \{ x \subseteq B : |x| \leq \theta \} $$ And the problem (working in ZFC without foundation) I'm stuck on is the second part of lemma I.13.19: if $B$ is infinite and $\aleph_{0} \leq \theta \leq |B|$, then $$ |[B]^\theta | = |B|^\theta $$ And $$ |[B]^{< \theta} | = |B|^{< \theta} $$ Here $B^A$ is the cardinal exponentiation, and $B^{< A} = | \{ f: C \to B : C$ is an ordinal and $C < A\}|$ I've only managed to show the trivial inequalities like $|[B]^\theta | \leq |B|^\theta$. I'm sure the proof is probably pretty simple, but I'm pretty clueless about what I should do next, any hints would be appreciated!

Initially assume ZFC.  Let $\binom{\kappa}{\lambda}$ denotes $\left|[\kappa]^{\lambda}\right|$ where $[\kappa]^{\lambda}$ is the collection of all subsets of $\kappa$ with cardinality $\lambda$. That is, the number of subsets of $\kappa$ of size $\lambda$.  Let $\kappa$ be any infinite cardinal number. Then it is easy to see that   $\binom{\kappa}0=1$ $\binom{\kappa}n=\kappa$ for all positive natural number $n$.  $\binom{\aleph_0}{\aleph_0}=\beth_1$ $\binom{\kappa}{\lambda}\le \kappa^\lambda$ when $1\le \lambda \le \kappa$   3 is due to $\beth_1=\sum_{\lambda=0}^{\aleph_0}\binom{\aleph_0}{\lambda}$ and others besides $\binom{\aleph_0}{\aleph_0}$ sums $\aleph_0$(since countable infinite countable infinites sums to countable infinite)  $\left({}^{\kappa}_{\lambda}\right)\le \kappa^\lambda$ is due to an injection can be made from $[\kappa]^{\lambda}$ into $\kappa^{\lambda}$(maps $\{a_i|i<\lambda\}$ to $\langle a_i\rangle_{i<\lambda}$ where $a_j<a_k$ iff $j<k$)  I hypothesize that   $$\binom{\kappa}{\lambda}=\begin{cases} \kappa^\lambda,&\lambda \le \kappa \\ 0,& \lambda>\kappa  \end{cases}$$  It holds when $\kappa=\aleph_0$, but hard to induct for larger cardinals without assuming GCH. So I need some helps.


why echo (int) ((0.1 + 0.7) * 10); result is 7 ?  I was surprised when get value 7 ? I dont understand why ?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


info.name and info.phone are changing after passing to defaultEntry(Info infoObject) but reference not changing to null why? can anybody please explain this scenario as well as working of java methods. Is there any difference between c functions and java methods working mechanism? Thanks in advance :)         class Info {         String name = "Sagar Pudi";         String phone = "9999999999";     }      public class MemberDetails {         public void defaultEntry(Info infoObject) {             infoObject.name = "DEFAULT_MEMBER";             infoObject.phone = "NO_PHONE";             infoObject = null;         }          public static void main(String[] args) {              Info info = new Info();             System.out.println("Before : " + info.name + "<->" + info.phone);              MemberDetails md = new MemberDetails();             md.defaultEntry(info);             System.out.println("After  : " + info.name + "<->" + info.phone);             if (info != null)             System.out.println("info  is still an object of " + info.getClass());         }     }   Output:  Before : Sagar Pudi<->9999999999 After  : DEFAULT_MEMBER<->NO_PHONE info  is still an object of class Info

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


I am pretty sure that it has been already discussed many times, but I couldn't find.     Well, the problem is to show that $\mathrm{Hom}(\mathbb Z/n\mathbb Z, \mathbb Z/m\mathbb Z)\simeq\mathbb Z/(n,m)\mathbb Z$.   I have proven that $Hom(Z/nZ, Z/mZ)$ is precisely $Ann(nZ) = \{x \in Z/mZ: nx = 0\}. $ Thus my problem reduces to proving $Ann(nZ) = Z/(n,m)Z$, but I haven't gotten success so far.

My algebra is weak I need help computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z)$, $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ and also $\mathrm{Hom}(\mathbb Z,\mathbb Z)$ as $\mathbb Z$-modules. Also books suggestion to improve my basic. Thank you.  Regards


So, I am lost and tried to work it out through definitions, but am unsure where to go to solve.  If G and H are groups, a homomorphism from G to H is a function $f:G→H$ such that for any two elements $a,b∈G$, $f(ab)=f(a)f(b)$.  If the commutative law holds in a group G, such that a group is called a commutative group or, more commonly, an abelian group,

I'm working on the following problem:     Let $G$ be a group. Prove that $G$ is abelian if and only if   $\varphi(g) = g^2$ is a homomorphism.   My solution: First assume that $G$ is an abelian group and let $g, h \in G$. Observe that $\varphi(gh) = (gh)^2 = (gh)(gh) = g^2h^2 = \varphi(g)\varphi(h)$. Thus, $\varphi$ is a homomorphism.  I'm having trouble completing the proof in the reverse direction. Assume that $\varphi$ is a homomorphism. We then know that $\varphi(gh) = \varphi(g)\varphi(h)$ and $\varphi(hg) = \varphi(h)\varphi(g)$. However, I don't see a way to use this to show that $gh = hg$.  Could anyone lend a helping hand?


I'm trying to return a list of IDs from a variable, however I have more than one User ID. It works just fine with one user ID, however when there is multiple it doesn't work at all. Variables: var AuthorizedIDs = ["473903419497775114", "460188583043530762"]  Code: if (userData.id === `${AuthorizedIDs}`) {     response.redirect('/access/login') }  Any help would be greatly appreciated.

What is the most concise and efficient way to find out if a JavaScript array contains a value? This is the only way I know to do it: function contains(a, obj) {     for (var i = 0; i < a.length; i++) {         if (a[i] === obj) {             return true;         }     }     return false; }  Is there a better and more concise way to accomplish this?


LFSR characterized by $p_2 = 1$, $p_1 = 0$, $p_0 = 1$.  I've computed that, the corresponding polynomial is $P(x) = x^3 + x^2 + 1$  What is the sequence generated from the initialization vector $s_2 = 1$, $s_1 = 0$, $s_0 = 0$?

Say you have a characteristic polynomial of an LFSR:  $$f(X) = X^4 + X^3 + 1$$  How can I use this function f to get the output of the LFSR, given some initial state?  Obviously I can create the LFSR diagram based on the function, since this function describes where the "taps" are (see .e.g the Wikipedia article ):  |----+--------+ |    |        | +-->[0][1][1][0]-->   Then calculate it iteratively like this: 0, 1, 1, 0, 0, ... (here the initial state is as in the diagram, 0,1,1,0).  I know you can also get this output from the equation:  $$s_j \equiv c_1s_{j-1} + c_2s_{j-2} + \dots + c_2s_{j-2} \pmod 2$$  Which gives the same result as calculating it from the diagram "by hand".  However my question is how to get this from the characteristic polynomial. Also what purpose does the characteristic polynomial have, beyond describe the taps in this way? If you give f some arbitrary argument, what are you really doing? What is the argument X?  I have a feeling this should be covered pretty well in some readily accessible online guide or tutorial that I cannot find, however I have read several such texts and searched through several more, and this is still not clear to me.


my question is based on newton's 3rd law . An elephant pushes a rabbit with $250 N$ force , then the rabbit should also apply $250 N$ force but the rabbit is only capable  to apply $25 N$ force . Why does this happen? . According to Newton's 3rd law the rabbit should also apply this much of force .

If an elephant can apply 250N force and a rabbit can apply 25N force , and if they are pulling each other , then elephant will pull with 250N force and according to newtons third law the rabbit should also pull the elephant with 250N force.then from where do the rabbit got the extra 225N i.e.(250-25=225) force??? can anyone please explain.


I am using biblatex with biber as backend and natbib loaded. What I am trying to achieve is appending an author's name with 's, e.g. in a situation like:     [...] as outlined in Krugman's (1989) early work   I could use \citeauthor{krugman89}'s (\citeyear{krugman89}), I suppose, but I was wondering whether there is a more direct way of appending the 's directly to the author's name. \citet[]['s]{krugman89} would not work, since this adds the 's after year in parenthesis, i.e. Krugman (1989, 's).

When using biblatex I often use \textcite. Sometimes I want to write things like "Smith's (2000) formulation of x is" instead of "Smith (2000) formulates x as". How do I achieve this? Or more generally, how do I make the author's name output by \textcite to be in the ? I'm mainly looking for a looking for an English variant. This mean that I want \textcite to be able to add "'s" to the author's name, e.g. to output     Knuth's (1984)   instead of     Knuth (1984)   Ideally I want a solution to be able to put any author's or authors' name in the possessive case and for it to be able to cope with other languages than English.  The following example might clarify what I'm asking for:  \documentclass{article}  \usepackage[style=authoryear-comp]{biblatex}  \usepackage{filecontents}  \begin{filecontents*}{database.bib} @book{texbook,     author  = {Donald E. Knuth},     title   = {The {{\TeX}book}},     publisher   = {Addison-Wesley},     date    = {1984}     } \end{filecontents*}  \bibliography{database.bib}  \begin{document}  \textcite{texbook}% Standard use. Output: "Knuth (1984)"  \textcite{texbook}'s% Failed try to get output in the possesive case. Output: "Knuth (1984)'s"  Knuth's (1984)% The ouput that I want  \end{document}


Naruto's father's name is Minato Namikaze, and mother is Kushina Uzumaki. So, why is Naruto's surname Uzumaki? Shoudn't it be Namikaze?

Is there any logical and canonical reason to why Naruto used his mother's family name, Uzumaki, instead of his father's family name?


I am using Ubuntu, and I am trying to install virtualbox. But I get this error. If anyone knows how to solve this, please, tell me.  Error: WARNING: The vboxdrv kernel module is not loaded. Either there is no module available for the current kernel (2.6.32-042stab092.2) or it failed to load. Please recompile the kernel module and install it by     sudo /etc/init.d/vboxdrv setup  You will not be able to start VMs until this problem is fixed.   *Edit: After ThomasW's answer this showed up:  ERROR ON LOG: Error log file: Uninstalling modules from DKMS Attempting to install using DKMS Failed to install using DKMS, attempting to install without Makefile:183: *** Error: unable to find the sources of your current Linux kernel. Specify KERN_DIR=<directory> and run Make again. Stop

I did upgrade VirtualBox from 4.1 to 4.2  wheneverver I want to load my Win XP VDI, it gives me the following error:     Kernel driver not installed (rc=-1908)   The VirtualBox Linux kernel driver (vboxdrv) is either not loaded or there is a permission problem with /dev/vboxdrv. Please reinstall the kernel module by executing  /etc/init.d/vboxdrv setup   as root. If it is available in your distribution, you should install the DKMS package first. This package keeps track of Linux kernel changes and recompiles the vboxdrv kernel module if necessary.  I ran the suggested step to reinstall the kernel module, and the log file is as follow:  Makefile:181: *** Error: unable to find the sources of your current Linux kernel. Specify KERN_DIR=<directory> and run Make again.  Stop. Makefile:181: *** Error: unable to find the sources of your current Linux kernel. Specify KERN_DIR=<directory> and run Make again.  Stop. Makefile:181: *** Error: unable to find the sources of your current Linux kernel. Specify KERN_DIR=<directory> and run Make again.  Stop.   I still unable to re-run my win virtual XP vdi file.  Anyone have any clue?


I'm a bit confused about the true meaning of imaginary number. It's my understanding that a complex number is a number of the form $a+ib$, where $a$ and $b$ are real numbers. A pure imaginary number is a complex number where $a=0$. However, when they say that a number is an "imaginary number", without the "pure", what do they mean exactly?

At school, I really struggled to understand the concept of imaginary numbers.  My teacher told us that an imaginary number is a number that has something to do with the square root of $-1$.  When I tried to calculate the square root of $-1$ on my calculator, it gave me an error.  To this day I still do not understand imaginary numbers.  It makes no sense to me at all.  Is there someone here who totally gets it and can explain it?  Why is the concept even useful?


Two questions;    Are spouses of permanent residents currently allowed to travel to the US? I want to get back to my husband as I do not want to be separated at the moment. If they are exempt, how do I go about getting an ESTA or would it be better to have another type of visa? My ESTA was cancelled when the travel ban came into place.   Thanks in advance.

This community wiki explains the current restrictions by the United States of America on the entry of individuals who may pose a risk of transmission of the SARS-Cov2, the virus which causes the Covid-19 disease.


I was  the algorithm on  for polynomial long division works for $\mathbb{Q}, \mathbb{R}, \mathbb{Z}$.  Using  I now understand it over $\mathbb{Q}, \mathbb{R}$, however am having challenges using the same steps over $\mathbb{Z}$.   I will provide an example with questions.  has another base-2 code example that shifts bits and also has a recurrence relation $r_{j+1} = B r_j - q_{n-(j+1)} b$ where $r_j$ is the partial remainder, $B$ the base, $q_{n-(j+1)}$ digit of the quotient, $n$ number digits and $b$ divisor.  I'm assuming $r_0 = 0$.  I don't understand why $b$ is in the first term. For such a widely used algorithm, there are many step by step explanations on "how to do it" but very little algebraic explanation with explicit proof of what is occuring.  So I appreciate your guidance. QUESTIONS  Can anyone describe algebraically or with set theory the integer algorithm?  Perhaps using the recurrence relation above?  Maybe I'm overlooking something. I'm curious for the base-2  algorithm.  Does anyone know why it shifts higher order bits numerator to low order in the denominator? An example follows where I'm getting stuck using  suggested algorithm which seems suited for $\mathbb{Q},\mathbb{R}$.  Does anyone know where I'm going wrong?  Example Using  algorithm. $bq + r = a$ $a = 1*10^1 + 8*10^0, b=9*10^0$ The first steps is to divide the highest degree terms $\frac {1*10^1}{9*10^0} = 0$ because we are over a field of $\mathbb{Z}$.  Now $r = a = 1*10^1 + 8*10^0$.  This process seems to continue forever with $q = 0$.

In  in these notes, it is said that  Since $x − a$ has leading coefficient $1$, which is a unit, we may use the Division Algorithm...  Why is this true? I thought that the Division Algorithm is only guaranteed to work in Euclidean domains not any integral domain.


Recently I bought a laptop which is running in Ubuntu 14.04 LTS. Now I wants to move back to Windows 7 64 bit. Regarding same I created a boot-able USB and thinking to boot from USB. In new machine boot settings are not taking from USB and UBUNTU is getting loaded automatically , In boot setup I kept USB as primary option - Even though no luck . Any ideas how to remove UBUNTU completely and install windows 7 ?

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


to make my cv, to give educational information in a table with box box, I have used this   \begin{document}   \begin{tikzpicture}     \draw[help lines] (-5,0) grid (4,4);       \end{tikzpicture}   and got   but I want to write my university name marks etc etc inside those boxes and I want to make bit wider boxes, I want proper latex commands for such table .. thank you for helping.

I need to copy a table from a pdf file to my LaTeX document. I know I have to do it by hand but still don't understand how to create a table with LaTeX.


How would I use the array modifier to duplicate this pattern all the way around the top and bottom circle faces? Whenever I try to use the array modifier, the pattern just copies next to itself. Its hopefully going to be a grenade. Ive added the blend file in case anyone can help. Thanks

We know that the there is an Object Offset option for Array modifier, but when trying to make a circular array with that offset object as the center of the array circle, it always doesn't behave quite like what's expected. So how to make a nice and controllable circular array?  P.S.: There is an old  about moving the object's origin. I wonder if there is any way to do this without changing the location of the origin. :)


The question count in the network profile's account tab is sometimes incorrect.  E.g.:     vs. :

While I'm writing this question, I've written  on this site:  Yet my network profile shows :  I don't think it's a caching issue, as I've checked the profiles of users who posted something today and their counts have been properly updated. My  is ~30 hours old. Deleted posts might play a role, but my  is from last November, and none of my questions has been Roomba'ed since. My  is somewhat newer (24 hours).  After I posted this (my 302nd) question, the number of questions on my network profile had immediately increased by 1, to 301, so it is updated but it's still off by one. A year later, the problem still persists, but I now noticed it also happens to my MathOverflow account; the network profile says 16 answers:  one more than my site profile (15 answers):


In my .bash_profile file, I have this, which works fine to execute that script in the same process that I'm launching my shell...  . ~/Code/iOS/CommunityDemo/APIMocker/mockutil.sh   I realized for part of that script, I need the path where it resides to be used within it.  Normally, you'd just do this...  MOCKUTIL_PATH=$(dirname "$0")   However, since I'm not spawning the script into its own process, but rather including the script in my profile script, the above understandably yields /bin, not ~/Code/iOS/CommunityDemo/APIMocker as I need.  "No worries!" I figured... I'd just export the path from within my profile, like this...  export MOCKUTIL_PATH="~/Code/iOS/CommunityDemo/APIMocker" . ${MOCKUTIL_PATH}/mockutil.sh   but I'm getting this...  bash: ~/Code/iOS/CommunityDemo/APIMocker/mockutil.sh: No such file or directory   Now I can just do this, but I really hate redundancy!  export MOCKUTIL_PATH="~/Code/iOS/CommunityDemo/APIMocker" . ~/Code/iOS/CommunityDemo/APIMocker/mockutil.sh   So... is there a way to define that path once, then use that definition in the source (.) command?

When I open up a bash prompt and type:  $ set -o xtrace $ x='~/someDirectory' + x='~/someDirectory' $ echo $x + echo '~/someDirectory' ~/someDirectory   I was hoping that the 5th line above would have went + echo /home/myUsername/someDirectory.  Is there a way to do this?  In my original Bash script, the variable x is actually being populated from data from an input file, via a loop like this:  while IFS= read line do     params=($line)     echo ${params[0]} done <"./someInputFile.txt"   Still, I'm getting a similar result, with the echo '~/someDirectory' instead of echo /home/myUsername/someDirectory.


I just tried to update to Ubuntu 14.04.5 on my Dell Inspiron 8600 running Ubuntu 12.02 LTS, and I received an error saying that PAE is not enabled. I looked at the support for enabling PAE on Pentium M systems, but when I tried to run the command  apt-get install linux-image-generic-pae , I received an error saying:   E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   I've tried to find answers to this in the forum, however I cannot find the solution to this. Is there any way to fix this issue? Do I need to run this as a superuser?

I get this error whenever I try to install programs using the terminal:  home@ubuntu:~$ apt-get install myunity E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   Also I'm unable to install updates using the terminal.


If I have a card like  or  that says if I tap this card, I add one green mana to your mana pool, from where I can get this card green mana?

What is the relationship between lands and mana in Magic and what do each of them do?  A good answer should especially include how a new player should think about them.    Note:  This is an attempt to create a canonical question about the relationship between lands and mana in Magic.  Beginners are often confused about this given the same symbols are used to mean different things across basic lands, non-basic lands, and mana costs.  This can lead to confusion about , about , or even about .


I am learning python,and I am confused about how the index of an array woks in python.  Following is my code  test_var = "hello how are you"  print(test_var[-1], ",", test_var.find('t'))   The output of this program is.     u , -1   Now I understand that negative indexing is allowed in python unlike java and it most probably works in cyclic manner so that -1 indicates the last character.  But when it comes to find method and it does not match any character 't' it again gives -1. So does it imply that -1 is like the null value in python? And it does not mean that find has returned the position of the last character?  Is it just me or would it be less confusing if an unsuccessful find would return None?

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


So now what?  Old HP with XP, running IE8 and had to put Chrome into the mix because Yahoo quit working in IE. Still use the IE, because my online shop won't load with Chrome. My AVG antivirus began having conniptions and to get System Restore to work again, Microsoft said to erase the antivirus software, which doesn't want to go (maybe another problem in itself?).  How do I open U and 'run it alongside' the others? I downloaded the 32 bit 12 LTS. Not as tech savvy as I should be for this, but was hoping to keep it all working at least until I can afford another computer. Thank you!

I would like to see a full how-to guide on how to install Ubuntu.


I have a program class and a student class, the student constructor creates a student and stores it in the array, the problem is when I try to print the array I get the following printed out:  metClassTwo.Student@5c74c3aa   How can I get the program to print the array details correctly?  print method:    public static void listStudent() {     for (int i = 0;i < myClassCount;i++) {       if (myClass[i] != null) {         System.out.println(myClass[i]);       }     }   }   myClassCount is incremented by one each time a student is added.  Array:    static final Student[] myClass = new Student[6];

In Java, arrays don't override toString(), so if you try to print one directly, you get the className + '@' + the hex of the  of the array, as defined by Object.toString():  int[] intArray = new int[] {1, 2, 3, 4, 5}; System.out.println(intArray);     // prints something like '[I@3343c8b3'   But usually, we'd actually want something more like [1, 2, 3, 4, 5]. What's the simplest way of doing that? Here are some example inputs and outputs:  // Array of primitives: int[] intArray = new int[] {1, 2, 3, 4, 5}; //output: [1, 2, 3, 4, 5]  // Array of object references: String[] strArray = new String[] {"John", "Mary", "Bob"}; //output: [John, Mary, Bob]


How can I avoid getting the error:  Could not resolve 'us.archive.ubuntu.com'   when executing the command:  sudo apt-get install [package name]

I need to configure proxy. There wasn't apt.conf file in etc/apt/ so I've created it using nano.   But I don't understand what I need to write there. I've written  http_proxy = http://lgn:pwd@192.168.1.254:8080/ there and then restarted networking. But when I try to apt-get update - it doesn't work.   Actually I don't understand what port and ip I should write in apt.conf file(there was example with 192.168.1.254 ip and 8080 port so I decided to use them).


This isn't a regular, let's stop curse words post. Please read on. This post was precipitated by a report that came to my attention from the  in  which is a bot that, I am grateful, alerts users to possible spam and abusive posts on the site. This post could easily have been filtered out on the keywords alone, let alone how they were put together. This is a link that will not be able to be observed by most people WARNING: NSFW, de-linkified to avoid accidental clicking. parenting.stackexchange.com/questions/24995 It is so offensive it really caused pain for the handful of people who read it. It is taking a while to recover. This post is at the very least a fantasy of written child pornography, at the worst a story of horrific child abuse. I had difficulty finding someone or enough people to flag it to delete it. Which leads me to the question. Can we increase the filters of what is posted on these sites to assist in preventing this kind o f thing occurring again rather than wait to be alerted to it after the fact? This post isn't about preventing curse words on the site, it's about setting a filter to prevent extreme NSFW and material that is so abhorrent it should not be too difficult to filter. As the post I am using as an example, would have been relatively simple to filter on. Or at least make the poster task of posting such matter more difficult. Within the content of that post there were multiple words and phrases that could easily be flagged and especially when put together in such number, there is no reason such content should make it on the site. At least if content needs to be re-written in such a way that it is not so graphic, it will assist in keeping the site cleaner from the outset. FYI I am forwarding a link to this post and the parenting post to SE employees for forwarding to the appropriate authorities.

I searched SE.Meta and was unable to find such question.  Someone just swore at us in a  as an  (warning: profanity, may be NSFW), sure, Arqade (profanity in phrases in games) or some SE (ELU, ELL or Anime.SE maybe?) can sometimes contain profanity as a small parts of question.  I think that a part should be added to the review system that will automatically hide questions/answers with profanity, just like the close vote system, the question/answer will be on hold and will be voted to be shown or be deleted.  Tip, if this gets implemented, u can be typed as \/ or v, and most other can be written as leet (l = 1 etc). Maybe it can be called "suspicious activity", and can be triggered when there is too many number or Unicode characters. (I can write hi as |-| |, |-|I, |-|l, l-li, hî, 1-1i, H1 and many more)


Newton's second law  $$\mathbf{F} = m\mathbf{a}$$  where $\mathbf{F}$ is the force, $m$ the mass, and $\mathbf{a}$ the acceleration, seems at first blush to be a simple tautology, since $\mathbf{F}$ and $m$ are not defined anywhere else in the formalism. Of course we can use the more general formulation  $$\frac{d\mathbf{p}}{dt} = \frac{d(m\mathbf{v})}{dt}$$  with $\mathbf{p}$ the linear momentum and $\mathbf{v}$ the velocity, but given the usual elementary definition of linear momentum $$\mathbf{p} \equiv m\mathbf{v}$$  this seems hardly an improvement.   Have I missed something? Perhaps in the Lagrangian or Hamiltonian formulation one can use Noether's theorem etc. to give a less trivial definition of $\mathbf{p}$? Or is there something even more elementary than that which I've missed?  Now, the law is clearly not tautologous in concert with some kind of force law, such as Coulomb's law or the law of universal gravitation. In that case we know what force means independently of mechanics. I'm just wondering if mechanics can be viewed as logically self-contained without recourse to such an addition.

If you consider  as laws, then there must be independent definitions of  and  but I don't think there's such definitions.  If you consider them as definitions, then why are they still called laws?


Since Yosemite, the Script Editor allows using javascript.  What is the best way to execute javascript from an applescript?  My use case is an existing applescript which needs to send some parameters over to a piece of javascript code, which makes a complex calculation and returns a result to be used as part of some appplescript-powered automations.  For clarity, I'm looking for an alternative to a tell application [browser] to execute the javascript using the new native javascript support of Yosemite, NOT for an alternative to a do shell script.

Support for javascript automations .  How could I run using javascript an external command? (i.e. the equivalent of do shell script of applescript?


i do not know what this site is expecting to write. i've written my question above . saw in a question paper. again writing it.   is intersection of a countable collection of dense, open subsets of a complete metric space also dense in X?

Consider the following theorem known as Baire's Category Theorem (BCT).   Theorem.[BCT] A non-empty complete metric space $X$ is not a countable union of nowhere dense sets.  I am interested on how to prove the following using BCT.  The intersection of every countable collection of dense open subsets of a complete metric space is dense.  My draft: Let $(A_k)$ be a sequence of dense open sets in $X$. Then for each $k$, we get $$ A_k \mbox{ is dense }\Leftrightarrow \overline{A_k}=X \Leftrightarrow \mbox{int }A_{k}^c=\varnothing.  $$ Since $A_k$ is also open, we get $$ \mbox{int }\overline{A_{k}^c}=\mbox{int }A_{k}^c=\varnothing   $$ and so $A_{k}^c$ is nowhere dense. We now consider the set $$\bigcup_{k=1}^{\infty}A_{k}^c.\qquad \qquad \qquad(*)$$  I am convinced that upon taking the complement of (*), the resulting set must be dense. But I don't know how to verify that step. Any tips?


This code was working at one point.  I'm not sure what broke it, but basically on postback I'm looking for the existence of a submit button key in the FormsCollection.  Depending on the existence, I perform different operations.  The custom attribute to handle this is getting hit.  When I step through it and look at the FormsCollection, I can see all key/values from the form except for the submit button which submitted the form.  Looking at the submission via Fiddler2, it doesn't even look like the submit button is being sent to the server with the rest of the values.  If I put in a hidden field with the same name I am looking for (and hard coded value) I can successfully hit the "if exists" logic branch because the hidden field's value is sent to the server.  Here's my form:  @using (Html.BeginForm("Respond", "AccountInvitations", new {id = Model.Invitation.InvitationCode, ReturnUrl = Request.QueryString["ReturnUrl"] ?? string.Empty}, FormMethod.Post, new {@class = "invitation-details-form"})) {

                  You have been invited to join @Model.Invitation.AccountName.         Create your profile below to join this account.
      @Html.AntiForgeryToken()     @Html.ServerValidationSummary()     @Html.EditorFor(model => model.InvitationResponse, "InvitationResponseDto", "")

         <input type="submit" name="accept" value="Accept Invitation" class="btn btn-secondary" />         <input type="submit" name="decline" value="Decline Invitation" class="btn btn-link cancel" />

 }   Neither "accept" nor "decline" shows up in the FormsCollection when I press on either (the form is submitted and all fields from the editor template show, but not the submit inputs).  I do not want to handle this with javascript setting a hidden field value.

Is there some easy way to handle multiple submit buttons from the same form? For example:  <% Html.BeginForm("MyAction", "MyController", FormMethod.Post); %> <input type="submit" value="Send" /> <input type="submit" value="Cancel" /> <% Html.EndForm(); %>   Any idea how to do this in ASP.NET Framework Beta? All examples I've googled for have single buttons in them.


I would like to know how to draw the "less than" or "greater than" lines in a tikz graph. i found this nice graph but am unable to draw the "zebra-lines". Is there a package for this?  For my plots I'm currently using pgfplot \documentclass[12pt, a4]{article} \usepackage{pgfplots} \pgfplotsset{compat=1.16}  \begin{document} \begin{figure}[h]     \begin{tikzpicture}         \begin{axis}[             axis x line=center,             axis y line=center,             xlabel=$x_1$,             ylabel=$x_2$,             xmin=-1,             ymin=-1,             xmax=8,             ymax=15,             xtick={-1,0,1,2,...,8},             ytick={0,2,3,4,6,8,10,12}         ]         \addplot[mark=none, domain=-1:8] {-4*x + 8}; % -4x_1 -x_2 <= -8         \addplot[mark=none, domain=-1:8] {x + 3};         \addplot[mark=none, domain=-1:8] {2};         \addplot[mark=none, domain=-1:8] {-2*x + 12};         \addplot[fill=blue!20,draw=blue]coordinates{(1,4)(3,6)(5,2)(1.5,2)};         \draw[red, ->](3,6)--(3,9);         \node[label={180:{(3,6)}}, circle, fill=red, inner sep=2pt] at (axis cs:3,6) {};                  \end{axis}     \end{tikzpicture} \end{figure}  \end{document}  which looks like this:

I want to draw the shapes of airspaces according to the german VFR map style and I have problems with the restricted areas, ED-R44 in this picture:  (source: ) I already found out how to do the airspace A and B,C,D but the fill mechanism doesn't transpose to the hatch pattern I am looking for: \documentclass{minimal} \usepackage{tikz} \usetikzlibrary{patterns}  \tikzstyle{EDR}=[draw=red,line width=1pt,preaction={clip, postaction={pattern=north west lines, pattern color=red}}] \tikzstyle{D}=[draw=blue,line width=1pt,preaction={clip, postaction={draw=blue,opacity=0.5,line width=12pt}}]  \begin{document} \begin{tikzpicture} \draw[EDR] (1,0) -- (4.5,1.5) -- (4,4) -- (1,3.5) -- (2.5,2) -- cycle;  \node at (6,2) {$\rightarrow$};  \draw[EDR] (8,0) rectangle (12,4); \draw[fill=white,draw=none] (8.5,0.5) rectangle (11.5,3.5);  \draw[D] (13,0) rectangle (17,4); \end{tikzpicture} \end{document}   The problem is, that the white fill doesn't work for arbitraray polygons, but I am unable to think of a way for preaction, postaction or decoration, to make it work.


Trying to use comparison test, but can't find a good candidate to compare with. Rather without use of Taylor series.

A student was recently asked this question by his instructor:  $$\sum_{n=1}^\infty{\left(\sqrt[n]{n}-1\right)}$$  Converge or diverge?  I feel a little dumb for not being able to answer it. The following tests fail to prove convergence or divergence:  nth term test for divergence (limit is 0), ratio test (limit is 1), root test (see ratio test), limit comparison with $\sqrt[n]{n}$ (not sure why I thought that'd work)  Something I did try was using the fact that  $$x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+x^{n-3}y^2+\cdots+x^2y^{n-3}+xy^{n-2}+y^{n-1})\;,$$  to rewrite $\sqrt[n]{n}-1$ as  $$\frac{n-1}{n^{1-1/n}+n^{1-2/n}+\cdots+n^{2/n}+n^{1/n}+1}\;.$$  However, I'm not sure what to compare this to. According to wolfram alpha this series "diverges by the comparison test", but comparison to what? There is a similar problem in Baby Rudin, but for $(\sqrt[n]{n}-1)^n$, and a simple nth root test resolves that series [convergence] in a hurry. Any ideas? Have any of you encountered a similar looking series before? Thanks.


I am trying to install some packages but i receive message error:  E: Unable to locate package libodbcinstq4–1  E: Unable to locate package libodbcinstq4–1:i386 E: Unable to locate package libzthread-2.3–2 E: Couldn't find any package by glob 'libzthread-2.3–2' E: Couldn't find any package by regex 'libzthread-2.3–2'   As repository, I added:  echo ‘deb http://cz.archive.ubuntu.com/ubuntu precise main universe’ >> /etc/apt/sources.list.d/extra.list   with the response of N0rbert, I have the following output:  libodbcinstq4-1 is already the newest version (2.3.0-4). libodbcinstq4-1:i386 is already the newest version (2.3.0-4). You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies:  libodbcinstq4-1:i386 : Depends: odbcinst1debian2:i386 (>= 2.2.14p2) but it is not going to be installed  libqtcore4 : Breaks: libqtcore4:i386 (!= 4:4.8.7+dfsg-5ubuntu2) but 4:4.8.5+git192-g085f851+dfsg-2ubuntu4.1 is to be installed  libqtcore4:i386 : Breaks: libqtcore4 (!= 4:4.8.5+git192-g085f851+dfsg-2ubuntu4.1) but 4:4.8.7+dfsg-5ubuntu2 is to be installed  libqtgui4:i386 : Depends: libqt4-declarative:i386 (= 4:4.8.7+dfsg-5ubuntu2) but it is not going to be installed                   Depends: libqtcore4:i386 (= 4:4.8.7+dfsg-5ubuntu2) but 4:4.8.5+git192-g085f851+dfsg-2ubuntu4.1 is to be installed                   Depends: libtiff5:i386 (>= 4.0.3) but it is not going to be installed                   Depends: libxext6:i386 but it is not going to be installed                   Depends: libxi6:i386 (>= 2:1.2.99.4) but it is not going to be installed                   Depends: libxrender1:i386 but it is not going to be installed                   Recommends: libcups2:i386 but it is not going to be installed                   Recommends: qt-at-spi:i386 but it is not going to be installed E: Unmet dependencies. Try 'apt-get -f install' with no packages (or specify a solution).   I tried apt-get -f install to correct the problem, but among the results I got this error message:   Errors were encountered while processing: /var/cache/apt/archives/libqtcore4_4%3a4.8.7+dfsg-5ubuntu2_i386.deb  E: Sub-process /usr/bin/dpkg returned an error code (1)

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


I intent  to travel  to  US  from India  in the last  week of September 2016  for  20 days and  have valid  US visa till November 2016. Will this visa be acceptable ?

I am a Mexican citizen with a visa that expires May 31, 2015. I need to enter the US for five days in the last week of January.    Can I do so or do I need to renew it before entering the US?


I have tried frying salmon filet and besides the fact it was very raw on the inside it fell apart when I tried to flip it over. Why?  *Skin was on.

We sometimes buy trout from a local breeder who'll get them fresh out of the water for us, and then cook them a few hours later. They taste great, but the flesh tends to fall apart in a way that doesn't happen with fish from the super market. It's often barely even possible to get them out of the pot without them completely coming apart. We tried leaving them in the fridge for a day so they wouldn't be quite as just-killed-an-hour-ago-fresh, but that didn't help.   We usually prepare them by cooking them in simmering (not boiling) water.  Is there some way to prevent this?


I am using JFileChooser to get a directory path in a project of mine. It is working perfectly, but there is a little problem. Suppose this is the directory structure:  ->Home   ->Documents     ->Java   This is the code:  JFileChooser fileChooser=new JFileChooser();         fileChooser.setFileSelectionMode(JFileChooser.DIRECTORIES_ONLY);         int userSelection=fileChooser.showSaveDialog(this);         if(userSelection==JFileChooser.APPROVE_OPTION){             try{File fileTosave=fileChooser.getSelectedFile();                 File newFile=new File(fileTosave.getAbsolutePath()+"satish.txt");                 System.out.println(newFile);                 this.dispose();}             catch(Exception e){}         }   If currently i am inside the java folder, it gives me the path Home/Documents/Java(or Home:\Documents\Java) in windows. What I want is that it should return the path which includes single forward slash or double forward slash (according to plaform) such that it looks like Home/Documents/Java/. I want to do this because later I have to append a file name to this path such that file path becomes Home/Documents/java/file.txt.  Any Idea on how to do this?  I don't want to add slashes manually because then I would also have to keep the platform in mind.  Thank you!

Is there a Java equivalent for  in C#/.NET? Or any code to accomplish this?  This static method combines one or more strings into a path.


We are writing a book about an amateur dramatic group called 'Richmond Players'. The title is "The Richmond Players Story".  There is a hot debate in the group about whether a possessive apostrophe is needed after "Players".  One school of the thought is that one is not needed because of the inclusion of "The".  Thoughts?

In the following is it better to use a possessive noun with an apostrophe or an attributive noun without an apostrophe?     The following list details the assumptions that have been made in   conjunction with the Dell Company’s staff.   Or      The following list details the assumptions that have been made in   conjunction with the Dell Company staff.   Assume Company is the name of a company, such as Dell.


I forgot my Yahoo! password. I tried many times to recover it but I can’t. I called Yahoo! customer service who they said that I have to pay for it.  Please help me to recover it.

One of my friends just got hacked on her PC and her Yahoo account password was stolen. Now the hacker use her account under her name for bad reason. He may have change alternative email, security question, etc.  What can we do about that? We need her account back. Is it possible?   ps. I tried to google search for Yahoo contact information but I'm not sure where to knock Yahoo door.


I need help with this problem  Let $X$ be a reflexive Banach space and $T: X \to X$ a linear operator. Show that $T$ belongs to $\mathcal{L}(X,X)$ if and only if whenever $\{x_n \}$ converges weakly to $x$, $\{T(x_n)\}$ converges weakly to $T(x)$.  any hints or suggestions, thank you!

Suppose I have a weakly sequentially continuous linear operator T between two normed linear spaces X and Y (i.e. $x_n \stackrel {w}{\rightharpoonup} x$ in $X$ $\Rightarrow$ $T(x_n) \stackrel {w}{\rightharpoonup} T(x)$ in $Y$). Does this imply that my operator T must be bounded?


I'm looking for a way to redirect visits to facebook to another website. It's to stop a child from wasting all his time on facebook. We can't use extensions because they are simple to disable so I'm looking for something along the lines of the hosts file from windows which redirects all visits to a ip to another ip.  I know of iptables but I can't quite figure out how to redirect all visits to facebook to another webpage.  I'm using ubuntu 13.04.

I have an Ubuntu machine that I'm using as my home Internet router.  It uses a USB mobile broadband modem as its Internet connection, and shares this with another router (via the router's "Internet" port) which I use as my LAN.  How do I redirect requests from within my LAN for a given URL to a custom IP address (ex have google.com redirect to x.x.x.x)?


I just downloaded Blender, testing to render animation. But there seem to be something missing under Output > File format. Here is my version     Greatful for help...:-I!

Even when I start a brand new file in Blender, I only get four video output file options: AVI raw, AVI JPEG, Frame Server, FFMpeg Video.  I am running version 2.78.5 (I'm using the beta so that I can use denoising.  How can I get access to all the other video outputs other people have? Like this:


I have simple class written  class Test:      stat = 0      def __init__(self):         self.inst = 10      def printa(self):         print Test.stat         print self.inst   Now I've created two object of this class  $ a = Test() $ b = Test()   When I say a.printa() or b.printa() it outputs 0 10 which is understandable.  But when I say   $ a.stat = 2 $ print a.stat   It'll output   2   But when I say a.printa() It'll output   1 10   What's the difference between saying objInstance.staticVar and ClassName.staticVar?? What it is doing internally?

Is it possible to have static class variables or methods in Python? What syntax is required to do this?


Look here:    And now here:    Can you see what I mean? One upvote, 10 points. I can remember though that at first 5 points were awarded, which changed into 10. Why?

This is an unofficial list/changelog of new features and various changes to Stack Overflow and the Stack Exchange network.  It is maintained by the community, while a Stack Exchange employee changes the accepted answer to ensure that the latest changes remain on top (given default user settings).  To see the list in reverse chronological order (latest entry on top), .  For those adding new features here: please post only feature changes that affect the whole network and have some global impact. i.e. bug fixes don't belong here, nor do mobile app updates.


I was solving a recurrence problem which had a sequence such as $y = (1+2+4+8+...)\sqrt n$, and I wanted to find what $x = 1+2+4+8+...$ was. So consider $x = 1+2+4+8+...$ as an infinite series.  $$x-1 = 2+4+8+...$$  $$2(x)=2(1+2+4+8+...) = 2+4+8+... = x-1$$  $$2x = x-1 \Rightarrow x=-1$$  What does $x=-1$ represent? Have I made a mistake in my calculations? Of course, we expect that $x=\infty$ since the sum grows by a factor of $2$ with each term.

I puzzled two high school Pre-calc math teachers today with a little proof (maybe not) I found a couple years ago that infinity is equal to -1:   Let x equal the geometric series: $1 + 2 + 4 + 8 + 16 \ldots$  $x = 1 + 2 + 4 + 8 + 16 \ldots$ Multiply each side by 2:  $2x = 2 + 4 + 8 + 16 + 32 \ldots$ Again from the equation in step 1, move the $1$ term to the left hand of the equation:  $x - 1 = 2 + 4 + 8 + 16 + 32 \ldots$ So the following appears to be true:  $2x = x - 1 \implies x = -1$   This is obviously illogical. The teachers told me the problem has to do with adding the two infinite geometric series, but they weren't positive. I'm currently in Pre-calc, so I have extremely little knowledge on calculus, but a little help with this paradox would be appreciated.


Missing underline for "Sign up" tab on the :        Observed on Stack Overflow and its international clones: , , , and   Tested on FF, Chrome, IE.

There is some alignment issue in the following trilogy or  site's account recovery page. The Sign up link's border bottom is missing.   You can find the issue in the following links:            Can be able to reproduce this in the following browsers:  Firefox: 49.0.1 Chrome: 51.0.2704.103 m OS: Windows 8  Screenshot for reference:        Update: The border bottom issue is in Stack Apps account recovery page too. There extra border is displaying under the Login tab.


Im starting to learn a bit of xml and xslt, and I read on w3c W3Schools that they recommend you use elements instead of attributes. Whats your practice and why would you not want attributes -  is there any point where you want them really?

At work we are being asked to create XML files to pass data to another offline application that will then create a second XML file to pass back in order to update some of our data. During the process we have been discussing with the team of the other application about the structure of the XML file.   The sample I came up with is essentially something like:  <INVENTORY>    <ITEM serialNumber="something" location="something" barcode="something">       <TYPE modelNumber="something" vendor="something"/>     </ITEM> </INVENTORY>   The other team said that this was not industry standard and that attributes should only be used for meta data. They suggested:  <INVENTORY>    <ITEM>       <SERIALNUMBER>something</SERIALNUMBER>       <LOCATION>something</LOCATION>       <BARCODE>something</BARCODE>       <TYPE>          <MODELNUMBER>something</MODELNUMBER>          <VENDOR>something</VENDOR>       </TYPE>    </ITEM> </INVENTORY>   The reason I suggested the first is that the size of the file created is much smaller. There will be roughly 80000 items that will be in the file during transfer. Their suggestion in reality turns out to be three times larger than the one I suggested. I searched for the mysterious "Industry Standard" that was mentioned, but the closest I could find was that XML attributes should only be used for meta data, but said the debate was about what was actually meta data.  After the long winded explanation (sorry) how do you determine what is meta data, and when designing the structure of an XML document how should you decide when to use an attribute or an element?


I have a question. I am using an Intel Compute Stick pre installed with Ubuntu 14.04 LTS 64-bit using a remote access software. And when the Compute Stick is sitting idle the Compute Stick disconnects from the wireless network and I need to hard reboot the stick to work. Does Ubuntu have a power saving option that turns off the Wifi to save power or turns off the Wifi connection when the stick goes on standby? If yes, is there a way to disable it.   TIA

I am affected by this bug: .  A workaround which seems to stop the kernel panics for me is to disable wlan0 power management:  sudo iwconfig wlan0 power off   However it seems to automatically turn power management back on when I unplug the power cable and I think at many other times, too.   Is there something that might be causing this? Does anyone know how I can prevent it?


Using the package bbold changes the look of \mathbb{R} which I dont want. However, I do want the look of \mathbb{1} from the package bbold. Is there some way to have both or am I too greedy :)  \documentclass[10pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx}  %\usepackage{bbold}   <------ CHANGE HERE      \begin{document}          $\mathbb{1}$              $\mathbb{R}$      \end{document}

A solution I saw somewhere suggested to use   \usepackage{bbold} $\mathbb{1}$   which works well and I get what I want. However, now other symbols used to represent real numbers, natural numbers, etc look ugly.    I'd like them to look (without using bbold)    I'd like to only use that package to achieve that strange double one. Is there any way I can do that?


Consider the random experiment in which three fair dice are rolled simultaneously (and independently).  Let X be the random variable defined as the sum of the values of these three dice.  Let $Y_1$ be the maximum of the three values, let $Y_2$ be their product, and let $Y=Y_1+Y_2$.  Finally, define Z=𝔼[X∣∣Y] (the conditional expectation of X given Y).   Find the expected value of the random variable Z. Enter your answer as a fraction, such as $\frac{3}{2}$.

Consider the random experiment in which three fair dice are rolled simultaneously (and independently).  Let $X$ be the random variable defined as the sum of the values of these three dice.  Let $Y_1$ be the maximum of the three values, let $Y_2$ be their product, and let $Y=Y_1+Y_2$.  Finally, define $Z=E[X∣Y]$ (the conditional expectation of $X$ given $Y$).   Find the expected value of the random variable $Z$. Enter your answer as a fraction, such as $\frac{3}{2}$.  I would like some help on where to start this problem, please. I know $X$ can be any value between $3$ and $18$ and $Y_2$ could be (most of the values) between $1$ and $216$; i.e., $Y_2$ will never be $7$, $11$, $13$, etc. since those numbers are prime and are greater than $6$.  Thanks!


I want to change the shortkey Ctrl+C which is used to kill process in terminal. Could you please give me some clue or directions to do this? Thank you so much. Here is the background I use some simulation with other tasks in terminal. However, I am habitual to use Ctrl+C to copy stuff and then paste it. Same thing happened with me in terminal and I accidentally killed the simulation. How can I change the shortkey for killing the process?

I'm using Ubuntu 14.04 LTS with Unity right now. I've changed my copy and paste keys to Ctrl + C and Ctrl + V respectively.  The command I've used is this:   gconftool-2 -t str -s /apps/gnome-terminal/keybindings/copy "<Control>c"   Now I'm looking for a way to change the interrupt / kill process key from Ctrl + C to (for example) Ctrl + I. The problem is that I can't find the appropriate keybinding name for it.  Any help would be appreciated.


I am novice to Lyx. I have used standard report for the document class. I created a gather equation. The equation numbering includes the number of the chapter which I do not want. I just want to number my equations 1,2,3 .........

I have an equation, such as:  \documentclass{report}  \begin{document}  \chapter{hello} \begin{equation} x=1 \end{equation}  \end{document}   And the equation appears as "x=1 (1.1)".    What I want is "x=1 (1)" ignoring the chapter number.  How do I get that?  Thank you.


"This page intentionally left blank" is a common sentence at the start of books/documents. I know it is correct, but why is it not expressed as "This page has been initially left blank"?   Is there a term to describe this phenomenon in English grammar? A useful link for further study will be appreciated. I have already read this relevant .

The sentence below often appears in a "blank" page of books.  "This Page Intentionally Left Blank"  Why there's no linking verb after the subject (Page)? e.g.:  This Page Was Intentionally Left Blank   If the adverb in the original sentence is removed, we only have:  This Page Left Blank  So I wonder why the original sentence without a linking verb often appears in books. Is it not odd without a linking verb? Based on my understanding of the original sentence, it means that the page left itself blank, which is odd for me. Hope to get some clarifications about this.


I am working with the following data:  Fixed effect:   GROUP (each subject only in one group) CONDITION (within subject variable, there are 2 conditions (1) baseline - same for all the groups, and (2) experimental - different for each group) GENDER (of the speaker from the stimuli) GENDER_S (of the subject)   Random Effects:   Subject Item (the audio stimuli)   Response Variable: accent ratings converted to z-scores  Research Question: Will the accent ratings differ between the groups in the experimental condition - and if so, between which? (all the groups listened to the same audio BUT with different visual stimuli)  I have 100 response total per participant = 80 x 100 -> 8000 (40 in one condition and 60 in the other) and model including all these Fixed Effects seems to be the best one based on AIC/BIC (prioritizing BIC in my case), hence in the final model I decided to include both GENDERs.   Since I was first interested only in the group:condition interaction (and which groups differ if any) I used a mixed design ANOVA which showed that it is NOT significant.  I have then moved to LMM, I choose "the best" model which seems to include the genders as well. I tried Anova() on the single model and got SIGNIFICANT group:condition interaction. However, when I did pairwise comparison with glht() and Holm's adjustment there are no significant pairs for group:condition only (averaging on the gender variable). The same happens when I fit a new model with group and condition as the only fixed effect. Also the same outcome even if I use NO adjustment at all.  Any ideas what should one do in a situation like this? Is it OK to ignore ANOVA and use the pairwise comparison since I am interested in which groups differ in the experimental condition (and I need to make sure that they don't in the baseline condition)?

i created a simple anova with three groups in R and get a significant Result. After that i do a Tukey HSD Test and now nothing is significant. How can that be?  Pr(>F): 0.0316  Group |   p adj  1 - 2    |  0.0689014  2 - 3     | 0.0847163  3 - 1      | 0.8909709


I am trying to write a software that can identify simple variants of passive voice in an english sentence.  I found multiple resources that state that to be + a past participle is an indication that the sentence is in passive voice.  My question is, is this a reliable rule? Are there any false positives, i.e. are there sentences that contain a construct of to be + past participle that are not in passive voice?

How can I reliably and accurately identify the passive voice in writing or speech? I'm not interested in advice about whether or not to use it yet... I just want to know for sure what it is, so that I don't look as stupid as .


How to compute     $$S=\csc^2\frac{\pi}{14}+\csc^2\frac{3\pi}{14}+\csc^2\frac{5\pi}{14}$$   I tried to rewrite it in terms of $\sin$  $$ \csc^2\frac{\pi}{14}+\csc^2\frac{3\pi}{14}+\csc^2\frac{5\pi}{14}= \frac{1}{\sin^2\frac{\pi}{14}}+\frac{1}{\sin^2\frac{3\pi}{14}}+\frac{1}{\sin^2\frac{5\pi}{14}}=\\ \\  \frac{\sin^2\frac{3\pi}{14}\sin^2\frac{5\pi}{14}+\sin^2\frac{\pi}{14}\sin^2\frac{5\pi}{14}+\sin^2\frac{\pi}{14}\sin^2\frac{3\pi}{14}}{\sin^2\frac{\pi}{14}\sin^2\frac{3\pi}{14}\sin^2\frac{5\pi}{14}}$$  then i used  $$2\cos x\cos y=\cos(x-y)+\cos(x+y)\\ 2\sin x\sin y=\cos(x-y)-\cos(x+y)$$  then i found \begin{align} S &= 2\frac{\left(\cos\frac{\pi}{7}-\cos\frac{4\pi}{7}\right)^2+\left(\cos\frac{2\pi}{7}-\cos\frac{3\pi}{7}\right)^2+\left(\cos\frac{\pi}{7}-\cos\frac{2\pi}{7}\right)^2}{\left(\cos\frac{\pi}{7}-\cos\frac{4\pi}{7}\right)\left(\cos\frac{2\pi}{7}-\cos\frac{3\pi}{7}\right)\left(\cos\frac{\pi}{7}-\cos\frac{2\pi}{7}\right)} \end{align}  i made a simplification and used again the transformation of product on sum and arrived at \begin{align} S &= 4\frac{6-5\cos\frac{\pi}{7}+2\cos\frac{2\pi}{7}-4\cos\frac{3\pi}{7}+2\cos\frac{4\pi}{7}-4\cos\frac{5\pi}{7}+\cos\frac{6\pi}{7}}{5-8\cos\frac{\pi}{7}+6\cos\frac{2\pi}{7}-5\cos\frac{3\pi}{7}+4\cos\frac{4\pi}{7}-3\cos\frac{5\pi}{7}+\cos\frac{6\pi}{7}} \\  & \cos\frac{6\pi}{7}=-\cos\frac{\pi}{7} \hspace{5mm}  \cos\frac{5\pi}{7}=-\cos\frac{2\pi}{7} \hspace{5mm} \cos\frac{4\pi}{7}=-\cos\frac{3\pi}{7} \\ S &= 4\frac{6+6\left(-\cos\frac{\pi}{7}+\cos\frac{2\pi}{7}-\cos\frac{3\pi}{7}\right)}{5+9\left(-\cos\frac{\pi}{7}+\cos\frac{2\pi}{7}-\cos\frac{3\pi}{7}\right)} \end{align}     $$-\cos\frac{\pi}{7}+\cos\frac{2\pi}{7}-\cos\frac{3\pi}{7}=-\frac{1}{2}$$   $$S=4\frac{6-3}{5-\frac{9}{2}}=4\frac{3}{\frac{1}{2}}=4\cdot3\cdot2=24$$

How do I show that:  $$\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$$  This is actually problem B $4371$ given at this . Looks like a very interesting problem.   My attempts: Well, I have been thinking about this for the whole day, and I have got some insights. I don't believe my insights will lead me to a $\text{complete}$ solution.   First, I wrote $\sin\frac{5\pi}{14}$ as $\sin\frac{9 \pi}{14}$ so that if I put $A = \frac{\pi}{14}$ so that the given equation becomes, $$\frac{1}{\sin^{2}{A}} + \frac{1}{\sin^{2}{3A}} + \frac{1}{\sin^{2}{9A}} =24$$ Then I tried working with this by taking $\text{lcm}$ and multiplying and doing something, which appeared futile. Next, I actually didn't work it out, but I think we have to look for a equation which has roots as $\sin$ and then use $\text{sum of roots}$ formulas to get $24$. I think I haven't explained this clearly.         $\text{Thirdly, is there a trick proving such type of identities using Gauss sums ?}$ One post related to this is:  I don't know how this will help as I haven't studied anything yet regarding Gauss sums.


If $p$ is a prime number, then $\sqrt{p}$ is irrational.  I know that this question has been asked but I just want to make sure that my method is clear. My method is as follows:  Let us assume that the square root of the prime number $p$ is rational. Hence we can write $\sqrt{p} = \frac{a}{b}$. (In their lowest form.) Then $p = \frac{a^2}{b^2}$, and so $p b^2 = a^2$. Hence $p$ divides $a^2$, so $p$ divides $a$. Substitute $a$ by $pk$. Find out that $p$ divides $b$. Hence this is a contradiction as they should be relatively prime, i.e., gcd$(a,b)=1$.

It is well known that $\sqrt{2}$ is irrational, and by modifying the proof (replacing 'even' with 'divisible by $3$'), one can prove that $\sqrt{3}$ is irrational, as well.  On the other hand, clearly $\sqrt{n^2} = n$ for any positive integer $n$.  It seems that any positive integer has a square root that is either an integer or irrational number.        How do we prove that if $a \in  \mathbb N$, then $\sqrt a$ is an integer or an irrational number?      I also notice that I can modify the proof that $\sqrt{2}$ is irrational to prove that $\sqrt[3]{2}, \sqrt[4]{2}, \cdots$ are all irrational.  This suggests we can extend the previous result to other radicals.        Can we extend 1? That is, can we show that for any $a, b \in \mathbb{N}$, $a^{1/b}$ is either an integer or irrational?