We would like to perform a statistical test to assess that a subsample of a global population has significantly a different mean than the global population. In this context, we are convinced that a statistical test where the null hypothesis H_0 is {means are equal} is what we would like to perform.  To know more about our samples:   the whole population contains more than 60000 values, it passed Gaussian testing and can be considered Gaussian. the subpopulation contains less than 1000 samples. Based on some criteria that we will not discuss here this subpopulation is varying, but most of the time it can also be considered Gaussian. Let us assume that this subpopulation is Gaussian.   For now on, we did not change the variances of our samples but we could divide the global population results by its standard deviation in order to achieve normalization.  We hesitate between the three following tests:   One sample T-Test. Two sample T-Test.  We have absolutely no knowledge that our subpopulation and the global population have equal variance. Practice showed that they have not. However, "equal variances" is one of the t-Tests assumptions see .    Welsh Tests looks more appropriate but the independence of the sample is not verified as well. The subpopulation and globalpopulation are by definition dependent. Should we remove our subpopulation from the global population in order to have non overlapping samples?   Among these three tests which one is recommended? Is there a better test in the litterature for what we are trying to achieve?

I want to perform a two sample test, to see whether theirs means are equals. One of the sample is rather big (#60000 values) and represents the scores of a whole population. This population is partitioned in small classes of less that 1000 people. The other sample of the test is a subsamble of the former. It corresponds to people of the same class. So, each time, there is less than 1000 values in it. I have no idea about the variances, so I'd think of using Welch's t-test.  But I'm concerned regarding the independence hypothesis: can it be valid, considering that the second sample is negligible when compared to the overall population?


I'm having hard time on this localstorage array. Hope you can help me .  here is my code..  var bank = document.getElementById('name_bank').value;  function AddBank(bank){    var data = JSON.parse(localStorage.bank);      if(!$.inArray( bank, data )){     data[]=bank;   }    localStorage.setItem("bank", JSON.stringify(data));  }   and i have a error Uncaught SyntaxError: Unexpected token ]

How do I append an object (such as a string or number) to an array in JavaScript?


What's the runtime (in Big O notation) for Array reversal for the below java code?  void reverse(int[] array){    for(int i=0;i<array.length/2;i++){      int other = array.length-i-1;      int temp = array[i];      array[i] = array[other];      array[other] = temp;    } }

Most people with a degree in CS will certainly know what . It helps us to measure how well an algorithm scales.   But I'm curious, how do you calculate or approximate the complexity of your algorithms?


The sequence is defined: $$u_1=1, u_{n+1}=1+\dfrac n {u_n}$$  The question asks to find an asymptotic development of 2 terms for $n\to+\infty$. I have got $u_n\sim_\infty\sqrt{n} $, but how to derive the 2nd term?


I am trying to set up a bibliography with BibLatex. Even a single \cite{} statement causes an error upon second compilation with pdflatex after running biber.  The sequence of running the commands is as follows:  pdflatex mwe.tex biber mwe (optionally multiply by 2 and/or add a bcf extension) pdflatex mwe.tex   After running biber and trying to run pdflatex for the second time the engine errors at \cite{aa} and no bibliography gets printed.  Here is the minimal (not yet) working example:  \documentclass{article} \usepackage[backend=biber, date=short, style=apa]{biblatex} \title{some title} \author{Authorov A. A.} \date{\today} \addbibresource{references.bib} \begin{filecontents}{references.bib} @misc{aa,   author = {Some Author A.},   title = {Some title},   year = {2016} } \end{filecontents} \begin{document} \maketitle Some sentence\cite{aa}  \printbibliography \end{document}   Blg file output:  [0] Config.pm:354> INFO - This is Biber 2.7 [1] Config.pm:357> INFO - Logfile is 'mwe.blg' [28] biber-MSWIN64:303> INFO - ===  [51] Biber.pm:359> INFO - Reading 'mwe.bcf' [136] Biber.pm:835> INFO - Found 1 citekeys in bib section 0 [149] Biber.pm:3670> INFO - Processing section 0 [168] Biber.pm:3840> INFO - Looking for bibtex format file 'references.bib' for section 0 [171] bibtex.pm:1435> INFO - Decoding LaTeX character macros into UTF-8 [176] bibtex.pm:1292> INFO - Found BibTeX data source 'references.bib' [187] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' [187] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized' [188] Biber.pm:3499> INFO - Sorting list 'apa/global/' of type 'entry' with scheme 'apa' and locale 'en-US' [189] Biber.pm:3505> INFO - No sort tailoring available for locale 'en-US' [191] bbl.pm:608> INFO - Writing 'mwe.bbl' with encoding 'ascii' [192] bbl.pm:712> INFO - Output to mwe.bbl   I am running MikTex 2.9 (64-bit), Biber 2.7 and Windows 10.  Having had a look through similar questions, they either do not use Biber or the problem seems to have a different root. Would appreciate any hints and tips. Thank you in advance!

biblatex-apa gives me this:  ! Undefined control sequence. <argument> \mkbibdateapalongextra                                {labelyear}{labelmonth}{labelday}\iffieldu...   I'm using the default (english) language, and have done the:  \DeclareLanguageMapping{norsk}{norsk-apa} \DeclareLanguageMapping{english}{american-apa}   thing.   Here's a short example:  \documentclass[english]{memoir} \usepackage{babel} \usepackage{roffe} \usepackage[backend=biber,date=short,maxcitenames=2,style=apa]{biblatex}  \DeclareLanguageMapping{norsk}{norsk-apa} \DeclareLanguageMapping{english}{american-apa} \addbibresource{Papers2.bib} \addbibresource{R.bib}  \begin{document} \cite{R-base}  \printbibliography \end{document}   This one replicates the problem.


I can't make a Google account in Pokemon GO i can only make a Pokemon go trainer club account and on my phone that's not works... Are there someone whit the same problem or is it only me? What are I'm doing wrong and are there someone out there there can help me? I hear thousand of things about Pokemon GO and I will very very very like to play it, but I can't, plzz help me😢

Recently I downloaded Pokemon GO but when I try to sign up with google account,the option isn't there. Help please. I use a LG G2 mini


I am trying to write a Unicode character in Microsoft Word by using its hex code; e.g., WHITE SQUARE (◻) code 25A1?  How do I do it?

How to type directly with keyboard the U+200C character in Notepad or other places... in Windows 8.1? (without depending on a certain font)  I don't want to copy and paste ways. I don't want any complicated ways. I just want something like Alt+### for typing U+200C Directly at any text area in windows 8.1 without depending to a certain font. Just like ALT+129 for U+200B.  (I do not need ALT+129, That's for U+200B. I need U+200C)  the U+200C character name is: ZERO WIDTH NON-JOINER (ZWNJ)  Here is the U200C character info:


I am trying to work out a regular expression on strings such as below:  DDR3 4Gb 512Mx8 1600/1866MHz	   I am interested in the sub-string DDR3 4Gb 512Mx8 1600/1866MHz	 And specifically DDR3 4Gb 512Mx8 1600/1866MHz or in other words, removing the  tag and get text up to the  tag  When look at the substring  DDR3 4Gb 512Mx8 1600/1866MHz	   The expression \w+?[^<>]+?(?=(?:<)) works well for me and I successfully pick up   DDR3 4Gb 512Mx8 1600/1866MHz  So I added the substring method to  the end of my whole regex for the original string as below:  \s*(){0,1}\w+?[^<>]+?(?=(?:<))   But this no longer works on the whole string   (please see the screenshot) As you may see, the third one fails (circled in red).  I have looked around on a few stackoverflow on many topics regarding this skip of specified characters but was not able to find a resoluton.  Please help and sincere thank you in advance.

I'm looking for a library/method to parse an html file with more html specific features than generic xml parsing libraries.


I want to set bounty for a question asked by me but I couldn't. I can't understand why. Here is the question:

It's possible to offer and award bounties of reputation on questions.   What is a bounty? How can I find questions that have a bounty attached? How do I start a bounty? When can I start a bounty? Why is the system requiring me to choose a bounty amount that's higher than the minimum? Can I use Markdown formatting in the bounty remarks? Can I edit the remark? How long is the bounty period? How do I award a bounty? Can I award a bounty to my own answer? Can I award a bounty to an old answer? If I offer a bounty on someone else's question, can I award the bounty to their answer? After awarding the bounty, can I remove it or move it to another answer at a later time? What happens if there's no answer after the bounty period? What happens if I feel my question is still unanswered? What is automatic awarding? Are bounty awards exempt from the 200 points/day reputation limit? How does Community Wiki mode affect bounties? How does user deletion or post dissociation affect bounties? Can I award a bounty to an answer from a deleted user or one where the author was dissociated? Can I offer a second bounty after the first one has expired? Can I raise my bounty? What happens if a bounty question is closed or deleted? Why can't I vote to close or migrate a bounty question? What happens if I delete my account while I have an active bounty? Do I keep an awarded bounty when I delete my answer? What happens if a question where I awarded a bounty later gets deleted or migrated? Can I cancel my bounty? Can I affect / divide / share part of my bounty to two (or more) users? How many outstanding bounties can a single user have?      See also:  in the Help Center


I know that for an lm model is enough to run plot(model_lm) to get diagnostic plots. I am dealing with high-dimensional count data, so I am using Poisson, Quasipoisson, Negative Binomial and Zero Inflated . Is there a way to compare different glm outputs to see which one fit the data better? Moreover, how can I plot diagnostic plots?  My question is a bit different from:  since my X is made of five numeric variables.

What diagnostic plots (and perhaps formal tests) do you find most informative for regressions where the outcome is a count variable?  I'm especially interested in Poisson and negative binomial models, as well as zero-inflated and hurdle counterparts of each. Most of the sources I've found simply plot the residuals vs. fitted values without discussion of what these plots "should" look like.  Wisdom and references greatly appreciated. The back story on why I'm asking this, if it's relevant, is .  Related discussions:


Prove that If gcd$(a,2)=1,$ and $p$ is an odd prime, then $(a^{p-1})-1$ is divisible by $8$.

I am trying to show that if $n$ is an odd natural number, then $8$ divides $n^{2}-1.$ I was able to prove that because I know that if $n$ is an odd natural number, then $n^{2}$ can be written as $8k+1$ for some $k\in \mathbb{N}.$ I would like to show this question by using the Euclidian division. Then I wrote $n^{2}-1=8k+r$, where $0\leq r  < 8.$ When $r=2$ we get $n^{2}-1=8k+2.$ Since $n$ is odd, then $n^{2}-1$ is even and I got stuck. Is there way to fix that?


I would like to make the background transparent. In Texmaker, if I right-click on the TikZ picture, I can save it as a png image as follows     If I save this picture, I get the white background. Is there a way to remove it?   \documentclass[border=10pt,tikz]{standalone} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{calc,fit,arrows.meta, positioning} \usepackage{graphicx} \usetikzlibrary{calc}  \begin{document}  \begin{tikzpicture}[auto,node distance=3cm,>={Stealth[width=4mm, length=6mm, fill=red]}] \coordinate (O) at (5,0);   \draw [very thick,fill=green,fill opacity=.2]  (-4, 4) circle (2.0cm) node [fill opacity=1]{\textbf{A}};  \end{tikzpicture}  \end{document}

I do not know what is the official term for such images, but if I make an image in TikZ or pstricks then I want it to have no background; for example I might post it on a webpage with a different background than white, then it should blend in nicely.   I have seen a couple of images in wikipedia that are like this (), and they show up on image viewers to have some kind of a checkered background.


simply put, I have a file with lines of text that are unknown to me, something like  abaa dddd bbbb cccc abaa aaaa abaa   the result I'd like to get is  dddd bbbb cccc aaaa   where all the duplicates are completely removed. if one line of text is duplicated anywhere else, remove this line and any repetitions that follow. is this possible to do? all of my searches show output with duplicates removed, leaving one instance, which I would like removed.

Is there some better solution for printing unique lines other than a combination of sort and uniq?


Why are boolean operations so slow? If I try to cut into an object that has subdivisions or I array the cutter, Blender will freeze for up to 10 seconds, even though I have a 12 core CPU and a powerful GPU. Also, after adding the boolean to the modifier stack, the viewport will stall whenever I switch between Object and Edit Mode or toggle between some other settings.

Hi, I'm on a 3.2Ghz 6core AMD processor, 16Gb Ram, GTX 1050Ti vid card. Blender 2.91, via Steam ( so auto updates) usually works fine, so I'm suspicious of how i'm working. The mesh was a curve, converted to mesh, cleaned of excess Verts and extruded. The cylinders (holes 6mm/8mm/10mm) are the default 32 sided, I've changed the dimensions and applied transforms. Difference boolean calls on the 'Holes colection' which has the cylinders in it. a couple of arrays spread out the cylinders/holes which display as wire. it.. chuggs.. soo... slow.. is 32 sides on the cylinders considered excessive? should I get rid of the arrays and make instances of the cylinders? have i missed something obvious?


i am using Math.random() method but method return a double Value so wana Convert 0.345 to 345 and between ranges like 50 --- 100 only.

How do I generate a random int value in a specific range? I have tried the following, but those do not work: Attempt 1: randomNum = minimum + (int)(Math.random() * maximum);  Bug: randomNum can be bigger than maximum. Attempt 2: Random rn = new Random(); int n = maximum - minimum + 1; int i = rn.nextInt() % n; randomNum =  minimum + i;  Bug: randomNum can be smaller than minimum.


In what way are the Laplacian operator (defined on functions from $\Bbb{R}^n$ to $\Bbb{R}$ which are twice-differentiable) and the Laplacian matrix (defined on simple graphs) similar or related?

I was wondering if anybody would explain (or please point me to a nice reference) as to why the ``discrete Laplacian" on a graph is actually called a Laplacian. Namely, how is it related to the standard Laplacian on $\mathbb{R}^n$ ? Is there a sense in which the discrete Laplacian on say, a square lattice, would converge to the standard Laplacian as the lattice spacing tends to $0$ ?


I attempt to solve the equation    $(z+1)^5=z^5$.  My first approach is to expand the left hand side but ı get more complicated equation. So I couldn't go further. Secondly, I write equation as, since $z\neq0$,   $(\frac{z+1}{z})^5=1$, put $\xi=\frac{z+1}{z}$   and attempt to solve equivalent equation $\xi^5=1$. But this time it requires more computation to find solutions $z$. Can anyone suggest a simple way to solve this equation? Thanks in advance..

The question says to solve this equation: $(z+1)^5 = z^5$  I did. Just want to find out if I did it properly and if my run-around logic makes sense.  First I begin my writing the equations as:  $$ (z+1)^5 = z^5$$ $$ \mathbf{e}^{5 \mathbf{Log}(z+1)} = \mathbf{e}^{5 \mathbf{Log}(z)} $$ So $$  \mathbf{Log}(z+1) = \ln|z+1| + \mathbf{Arg}(z+1)i $$   $$  \mathbf{Log}(z) = \ln|z| + \mathbf{Arg}(z)i $$   Now, because the natural logarithm is one-to-one, I write:  $$ \ln |z| = \ln |z+1| \Rightarrow |z| = |z+1|$$   So assign $ z = a +bi$   So that $|z| = \sqrt{a^2 +b^2} = |z+1| = \sqrt{(a+1)^2 +b^2} \Rightarrow a^2 +b^2 = (a+1)^2 +b^2 \Rightarrow a^2 = (a+1)^2 \Rightarrow a = -\frac12 $  So, $z = -\frac12 + bi$ and $z+1 = \frac12 + bi$ for some $b \in \mathbb R$  Now to find $b$  $$ \mathbf{Arg}(z+1) = \mathbf{Arg}(z)$$ $$ \tan^{-1} \frac{b}{\frac12} = \pi - \tan^{-1}\frac{b}{-\frac12}$$  I have a feeling this last part isn't quite right, so I just want to find out if I'm approaching this question properly?  Ultimately, I get $ z = -\frac12$ which upon inspection...is wrong...


I have several Redstone contraptions on my map, but while trying to build another, I'm having problems with pistons deploying once and getting stuck deployed, even when power is removed. they will not reset or function properly. I don't understand why it won't work anymore.

I've lately become hooked into building computers in Minecraft and today I decided to build a giant hard drive. I've built HDDs before, but not at the scale I'm currently attempting, and I anticipated problems. As I was wiring some pistons, they activated and pushed forward oddly. As far as I can tell, there's nothing powering them.    I thought at first that it might be the redstone torches (top left of above pic) but they aren't powered.   Here's a top view of the same pistons. I also thought the line of redstone above  them might be the problem (middle of above pic), but when I destroy it, the pistons stay extended.  Is there a reason why my pistons are extending? If so, is there a way to get them to power (when I want them to) without disturbing the pistons above?


When recently discussing with others how young we'd first read stories with apocalyptic themes, I was reminded of a story I'd found in a middle-school library, circa 1984-1986. The protagonist was a boy or young man in a world that was about to end. I don't recall the reason, but either their looming demise seemed not to be general knowledge in his world, or they didn't believe there was any hope of avoiding it.  He encountered members of a secret group planning to survive/escape by recruiting people of every skill and talent necessary to repopulate the world (don't think it was a different planet) without sacrificing accumulated technology/knowledge. They told him about a secret (underground?) place to which the chosen few would be summoned at the appropriate time, where they could safely hide before emerging to start the world over. Since I can't recall his skills, I'm not actually certain whether he'd been selected himself or was so young he was merely family of someone who had been.  To prevent spies or those not chosen from discovering or stampeding to the protected place, there was some sort of antechamber/elevator which could destroy people with some sort of (green light?) radiation or gas--unless you wore a magic ring (or some other amulet/device). Near the end of the story, a bad guy chases our hero into the chamber and is indeed vaporized.  I recall this book's plot not because it was any good (I remember thinking much of it cheesy even at the time), but because I read it at exactly the time in my life where I was ready to ponder all the fascinating what-ifs surrounding the apocalyptic genre. Been hooked on scifi/fantasy ever since, and later studied engineering partly due to not wanting to be "that person" who knew nothing useful should the world need a fresh start. ;)  Can anyone point me to the title/author? Thanks in advance!

I'm hoping someone can identify this young-adult/children's sci-fi book. I read it in 1996-1997, but I remember thinking it was written in the 1980s.   The main character was a boy (maybe in his early teens) and over the course of the book he gained a female companion of the same age. I think the boy and his father had a vegetable garden growing in their basement, but it was illegal for them to grow their own food so they hid the trapdoor to the basement under their refrigerator. The boy's father was an important scientist (or something of that nature) and he goes missing (taken by the evil government?) and the boy has to find him.   There is a scene where the boy is at school and is sent to the school counselor or doctor to be given an anti-depressant or tranquilizer pill, the counselor (a male) is sympathetic to the boy and tries to help him and the girl to find the boy's father (and possibly the girl's parents too?). There was also a scene where the boy and girl go to an abandoned building/warehouse to meet someone who can give them information on their parents (maybe they meet each other for the first time at the building?). It seems like there was also a mention of golf clubs in relation to the boy's father and a mention of Crackerjack rings in relation to the girl, but I know a Crackerjack ring played a part in another book I read around the same time so I could be confused:).   Sorry this is so long, I only read part of the book and would like to find out how it ends.


I often hear that partitioning huge tables should significantly increase query speed and insert/update speed, because indexes are proportionally smaller. I'm struggling to understand why that should be the case. In my understanding operations on an index should be of log(N) complexity, so even if we partition a huge table into 100 smaller items then we just partitioned a single index into 100 smaller ones. If queries frequently access items from the entire dataset, then these 100 indexes will compete for processor cache anyway, so I don't see why database will be hitting the disk less often. If we are usually only requesting some portion of the data - for example if we have a table with timestamped data and are more often interested in latest data - then the B-tree node count that we have to traverse will be 1 or 2 less. But in un-partitioned table scenario top-most nodes of B-tree will be cached anyway, so the fact that B-tree is slightly higher shouldn't have significant impact on performance. Variation on previous scenario: if we are commonly accessing ranges of data that are on the same "axis" as the partition key - again, if we have a table paritioned by timestamp and run reports on date ranges - then partitions will provide natural clustering for the data, thus reducing disk accesses and improving query performance. But I don't see how this will improve insert/update performance? And why should it improve performance on queries that do not filter by partition key? I realize that partitions are useful in some other cases (dropping old data, lock contention with many users, backups, aforementioned clustering, etc) - but I commonly hear that query or update performance should increase as well, hence this question. I'm most familiar with PostgreSQL, but I suspect the underlying concepts are similar between many relational databases.

I have just been involved in a project on which I will have to develop a data migration process and a web interface that uses an already existing SQL Server DB. This DB was developed by another person several years ago, it has around 100 GB of data and it is increasing every 10 minutes (it stores 10 min data from several units -> 144 records per day per device). Several tables have around 10 milion rows. The point is that I think the main tables have been designed in a way that is not the most efficient or appropiate for the kind of queries that will be usually executed. Now I need to proof if what I say is better than what it is already implemented. The DB is extensive in number of tables, but the structure can be simplified by the following diagram:   The Date_Id field is generated automatically by a function using the DateTime field. There are two indexes in both tables. The cluster index for each table contains the PK fields in the same order. The second index for the Unit table contains only the Unit_Id field, while the second index in UnitData contains the Unit_Id and DateTime fields in this order.  However, I think the design should be this one:   In this case only a clustered index for the PK fields will be needed. For this DB design the usual query would be something like:  SELECT ud.* FROM Unit u, UnitData ud WHERE u.Unit_Id = ud.Unit_Id and ud.DateTime >= 'dd-MM-yyyy' ORDER BY ud.Unit_Id, ud.DateTime   Now comes the thing that I really don't understand: I've been told that the only reason for having a Date_Id column is to use it as partitioning column for this table. I've asked about the real necessity of having this table partitioned and the asnwer was "to run queries more efficiently when wanting daily or monthly data". I didn't know to much about partitioning before this, so I checked these links:        Considering that the ideal query would be filtering by device and datetime, the questions are:   What do you think would be the most efficient and ideal query for the first DB design (with partitioning)? Do you really think that the most efficent query against the first DB design is better than the second one (the one I wrote above)? If the previous one was affirmative, do you really think the improvement is worth enough having two extras fields (Id and Date-Id) and an extra index?   Thank you very much!!


There is a column containing following e.g. abcd/ef/g/hij. Characters between the / are dynamic not fix. I want to split in a select query the content into 4 separate new columns.  The already answered question is different, I want to split the content in a string seperated by / into new columns.

Using SQL Server, how do I split a string so I can access item x?  Take a string "Hello John Smith". How can I split the string by space and access the item at index 1 which should return "John"?


In the final battle, Scarlet Witch pinned Thanos upon which he told Corvus Glaive to...      "Rain Fire!"   ... which seemed to open fire like Gatling guns and nearly injured all parties fighting. However, it quickly shifts and started firing towards the clouds where Captain Marvel was emerging from.    Why did the Sanctuary II focus its attack on Captain Marvel?

In Avengers: Endgame      Thanos and his spaceship jump into the future and fight the Avengers.   Towards the end of the battle the ship's cannons rotate upwards and begin firing at the approaching       Captain Marvel.   This was a direct contradiction of the order Thanos himself gave when he commanded the ship to fire at the ground, regardless of whether he was hitting his own troops or not.  Clearly someone on board the ship had the authority to ignore the order and decide to fire somewhere else instead.  Who was it?  Presumably some information exists in the MCU about who is in charge of the ship when Thanos isn't on board.


In the books, Harry consistently takes seemingly Muggle routes to Platform 9 3/4, to Hogwarts by train (which has been boarded before), or at his place on Privet Drive, (just to name a few of the times) as it seems that he was (nearly) unprotected (magically) most of the time.   Why don't the DE just Apparate in and kidnap him while he's at his most vulnerable?  Edit for clarity: Per the comments and answers, Voldemort was highly against any of the Death Eaters killing Harry, but why not kidnap him directly, rather than put his name in the Triwizard cup? For instance, why not on the train to Hogwarts among other such places? I have reworded the question to lose the specifics (as they seem to get my questions in trouble) and make it more general. I hope this clears up some of the confusion, but if anyone has any edits to make this question more legible, I'd be more than happy to see them.  Also to note, there is protection against Harry dying at Privet Drive, but kidnapping is not listed as something that can't be done from what I can deduce. There may be evidence to the contrary, but I am unable to find it.

Voldemort mentions several times during the books (in particular at the ‘rebirthing party’ in the graveyard at the end of Goblet of Fire) that he has spent quite a lot of his time over the years plotting ways to get at Harry.  It is of course clear that Voldemort cannot get to or harm Harry while he is at 4, Privet Drive, because he is under the protection of ‘old magic’ there. It also makes sense that getting to him while he is at Hogwarts under Dumbledore’s protection would be rather more of a risk than Voldemort is willing to run.  The dénouement of Goblet of Fire describes Voldemort’s plan as hinging upon Harry being in a specific place at a specific time (at the Triwizard Cup), so that Voldemort could get him on his own, away from the protection of Dumbledore and old magic.  But there is one time when Voldemort (and everyone else) knows, basically, that Harry will be alone (apart from the Dursleys, and who cares about them?) and unprotected, in a specific place, at a specific time: when the Hogwarts Express has taken him back to London and the Dursleys are driving him back home to Surrey.1  We know from Deathly Hallows that the charm hiding Harry while at Privet Drive extends only to the boundaries of the house/property, so while the Dursleys and Harry are driving along the M3 (or whatever way they take home), he’s quite exposed.  Why not target him there?     1 There are other times when he’s unprotected, of course, but they’re less predictable and harder to plan for.


In both Tolkien’s and Jackson’s The Lord of the Rings there are beacons for Gondor to call for aid in times of need. Only in the Peter Jackson film of Return of the King do the beacons go from Gondor to Rohan but is there a name for the people manning them or are they 'employed' from the local area? E.g. In the books the Red Arrow took the message to Rohan and not the beacons so is there a term similar to those who light the warning fires?

Following this image I found online:    Do the beacon lighters really live on top of the mountains?  It seems really cold on top of some of these mountains and there are no villages or whatsoever.


when i use morekeys in the lstdefinestyle it succesfully adds any word but it doesn't work with some characters like +,<, etc. this is the style: \lstdefinestyle{ligth}{ morekeywords = [1]{}, keywordstyle = [1]\color{red}, morekeywords = [2]{otherwise,\_, |, >, ==, :: }, keywordstyle = [2]\color{blue}}  This adds perfectly fine the word otherwise and _ but it doesn't add any of the others: , >,==,:: How can I fix this?? Thanks for your time

I want to put some symbols in green color with lstdefinelanguage in latex, but it seems that symbols are not recognized.  The symbols I need to be colored are =, > and <. Is it possible? How can I do this?  The main file:  \documentclass{article}   \usepackage{graphicx,color} \usepackage{booktabs} \usepackage{listings}   \lstdefinelanguage{NeoIDL}{   sensitive = true,   keywords = [1]{module, resource, enum, annotation, for, import, entity, path,   @get, @post, @put, @delete, require, ensure, otherwise, call},   %ndkeywords={int, \char{}  },   %ndkeywordstyle=\color{blue}\bfseries,   morekeywords=[2]{>, <, ==},   keywordstyle=[2]\color{green},   numbers=left,   numberstyle=\scriptsize,   stepnumber=1,   numbersep=8pt,   showstringspaces=false,   breaklines=true,   frame=top,   comment=[l]{//},   morecomment=[s]{/*}{*/},   commentstyle=\color{purple}\ttfamily,   stringstyle=\color{red}\ttfamily,   morestring=[b]',   morestring=[b]"   }  \begin{document}  \begin{figure}[htb] \begin{small} \lstinputlisting[language=NeoIDL,firstnumber=1]{store_pos_servico.neo} \end{small} \caption{Service 1} \end{figure}   \end{document}   The file to be formatted:  module store {    (...)     resource order  {      path = "/order/{id}";       @post   int postOrder (Order order)     require (call store.getOrder(id) == "NotFound"),     otherwise "InvalidPrecondition"    }; }


Since the domain of $f(x)$ is $(-\infty, 1) \cup (1, \infty)$ is there any point discontinuity in $f(x)= \frac{x^2-1}{x-1}$?

$$\lim _{x\rightarrow 5}\frac{x^2-25}{x-5}  = \lim_{x\rightarrow 5} (x+5)$$  I understand that to evaluate a limit that has a zero ("hole") in the denominator we have to factor and cancel terms, and that the original limit is equal to the new and simplified limit. I understand how to do this procedurally, but I'd like to know why this works. I've only been told the methodology of expanding the $x^2-25$ into $(x-5)(x+5)$, but I don't just want to understand the methodology which my teacher tells me to "just memorize", I really want to know what's going on. I've read about factoring in abstract algebra, and about irreducible polynomials (just an example...), and I'd like to get a bigger picture of the abstract algebra in order to see why we factor the limit and why the simplified is equal to the original if it's missing the $(x-5)$, which has been cancelled. I don't want to just memorize things, I would really like to understand, but I've been told that this is "just how we do it" and that I should "practice to just memorize the procedure." I really want to understand this in abstract algebra terms, please elaborate. Thank you very much.


I have a beamer frame with six fairly short footnotes on it.  This takes up a fair bit of vertical space and not much horizontal space, so I'd like to put the footnotes into a two-column layout (even though the frame content itself is one column).    I tried dblfnote package (had no discernible effect) and the eledmac advice seen in , but I couldn't even get the document to compile with eledmac package included (something about \lemma being already defined).    How can I get Beamer to use a two-column environment for footnotes?  Ideally I would like to be able to switch this on or off for different frames, but I'd settle for a document-wide solution.  PS: I know footnotes are discouraged in Beamer, but I'm not asking for presentation design advice here.

Hi I am wondering whether it is possible to place the beamer footnotes into multiple columns or display as horizontal, instead of vertical.   \documentclass{beamer} \usepackage{booktabs} \begin{document}  \begin{frame} \begin{table}[htbp]   \centering %  \caption{Add caption}             \resizebox{\textwidth}{!}{%     \begin{tabular}{rrr}     \toprule     \centering     Animal estimated by tracking  & \textbf{2 Equation approach} & 1 Equation \\     50\%   & $\frac{\partial C\footnote{dye }(t,\vec{x})}{}$      &  \\      &  $\frac{\partial \alpha\footnote{age }(t,\vec{x})}{}$     & $\frac{\partial A\footnote{A refers to "animal"}}{}$ \\     \bottomrule     \end{tabular}}% %  \label{tab:addlabel}% \end{table}% \end{frame} \end{document}   I would appreciate if anyone could explain me how to get the horizontal footnotes.


I want to create a database shape in tikz that looks something like this:    I need the two arcs in the middle, so I cannot directly use cylinder, as suggested in .  Ideally, I would like to start from the cylinder shape and just add a few arcs, but I cannot figure out how to do this? Is the code of the cylinder shape available somewhere? Or is there a better way to achieve this?  I have looked at  that asks how to create a shape for a camera, but it is quite far from what I want.

I'm trying to display all of my corporate database instances and their relationship to each other, so to speak the database links. I found the geometry shape cylinder using TikZ \usetikzlibrary{shapes.geometric}, but I'm new to the whole TikZ stuff and it doesn't worked out that well so I thought maybe you could help me getting something like the following figure:    There will be a ton of instances and arrows, but I hope that you guys could give me a start so that I could do the rest on my own.


I'm having this problem where the mesh appears to change whenever I leave edit mode. Some extra faces seem to be there but when I go back to edit mode they just disappear.

I have append a mesh (rex) from this .blend .  In edit Mode I see different vertices from objcet mode (see pictures). The vertices of belt are missing!  OBJECT MODE:   EDIT MODE:   How can I edit vertices of belt? Is It a bug?  This is my .blend  maybe can help.


Suppose that $R = S × T$ is a direct product of rings with $S$ and $T$ each having at least two elements. Prove that $R$ has zero divisors.

I have a question, and this is it in entirety:     Let R be a non-zero ring(that is, R contains at least one element other than the zero element). Prove that $R \times R$ is NOT an integral domain.   Now I haven't done a problem like this before, and it seems to be(from the Wikipedia definition) that this ring $R$ needs to be commutative to be an integral domain. Which it isn't stated to be here. What exactly am I meant to do? I haven't been given anything else than the area in grey.


I'm an almost complete novice in Ubuntu installation. I use some program since years, but never install it myself, and I would like to start to learn and be able to do so myself. I would like to install Ubuntu on a USB device first, but I don't know:      What version of Ubuntu to install?   Where to find and download this version   Where to find some explanations about how to prepare the USB device for that?

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


I have a string that represents a command. Each command can be a different length. For example here are some commands   showmessage "hello im the message" exit showmessage "im the message" "im the title" playsound /path/to/sound/file   My function takes a string that has the whole command and currently splits the string into a string array using split("\\s+").   However this splits the command at every whitespace. What I need to do is split the command at each space UNLESS something in the command started with " and ends with ". In this case I'd need to split the string so that the string array contains a string that is the whole part of the command that is in quotes.  So if the input command was:   showmessage "the message"   the split string array would contain the strings:   showmessage, "the message"  and if the command was:  showmessage the message  the split array would contain:  showmessage, the, message  Is there a way to do this with regexes?

I'm new to regular expressions and would appreciate your help.  I'm trying to put together an expression that will split the example string using all spaces that are not surrounded by single or double quotes. My last attempt looks like this: (?!") and isn't quite working. It's splitting on the space before the quote.  Example input:   This is a string that "will be" highlighted when your 'regular expression' matches something.   Desired output:  This is a string that will be highlighted when your regular expression matches something.   Note that "will be" and 'regular expression' retain the space between the words.


I am a low reputation user (103 points)  on this community. However, I am able to downvote questions and answers. I thought I needed 125 points for downvoting. On other communities, I need 125 points for downvoting but not on this one, why?

To make your opinion known on MSE you need both up and downvotes. Given at the moment you need 125 rep to downvote on this site, the voting patterns will be skewed positive because not everyone is active on the site.   This is to be expected for regular Stack Exchange sites as you are expected to be involved in the community before you are deemed knowledgeable enough to be part of the community voice. However, MSE is different because you are voting for the entirety of the Stack Exchange network and you shouldn't need to be active on MSE itself to have a voice on changes to the entire network.  This is especially important for questions like  because it will effect every network to do with coding at all. This was brought up in .  I would suggest reducing the rep required to downvote on MSE down to 100 (or 101) rep. This is the amount you get for the site association bonus. This is given once you achieve 200 rep on any network site and shows that you are active in at least one community. I think this would be the perfect use of the association bonus in showing that you are a member of the Stack Exchange community.


Most operating systems do not use 100% of the available RAM all the time, having said that I am unable to find an approximation for this over provisioning. CPU cores is not a constraint for me,  I have a 64 GB KVM host, I would like to provision multiple 8GB machines, the machines remain under utilized for most of the time but always in running state, I would like to know the maximum acceptable number of VM's that can be provisioned on this setup, without hitting any bottlenecks. The underlying storage is hard disk drives, with no SSD so there is little room for swap memory as it may impact performance

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


I want that when my users clicks on a link who is near to a text box, the content of the text box gets copied to the clipboard. How can I do this?

What is the best way to copy text to the clipboard (multi-browser)? I have tried: function copyToClipboard(text) {     if (window.clipboardData) { // Internet Explorer         window.clipboardData.setData("Text", text);     } else {         unsafeWindow.netscape.security.PrivilegeManager.enablePrivilege("UniversalXPConnect");         const clipboardHelper = Components.classes["@mozilla.org/widget/clipboardhelper;1"].getService(Components.interfaces.nsIClipboardHelper);         clipboardHelper.copyString(text);     } }  But in Internet Explorer it gives a syntax error. In Firefox, it says unsafeWindow is not defined. A nice trick without using :


The script is not working correctly. Even if the service is not running, then also the output is ok stating that service is running.  #!/bin/sh is_running=`ps aux | grep -v grep | grep "$1" | wc -l` echo $is_running if [ "$is_running" > 0 ]; then    echo "OK: $1"    exit 0 else    echo "Problem: $1 is not running"    exit 2 Fi   Ran it using: sh scriptname couchbase-server

I am trying to create a event handler for icing. My Bash script looks like this right now:  #!/bin/bash # Event Handler for loggin out inactive RDP users  # $1 is $SERVICESTATE$ (OK WARNING UNKNOWN CRITICAL) # $2 is $SERVICESTATETYPE$ (SOFT HARD) # $3 is $SERVICEATTEMPT$ (1 through 4) # $4 is $SERVICDOWNTIME$ (0 no Downtime, >0 Downtime active) # $5 is SRV29  # $6 is $host.name$ (1 through 4)   if  [ "$4" > 0 ];  echo "in downtime, exit";  then exit fi  case "$1" in OK) echo "ok!" ;; WARNING) echo "warning!" ;; UNKNOWN) echo "unknown!" ;; CRITICAL) echo "critical!" ...   When I execute this script without my if statement at the top, everything works fine. But I want to check if $4 is greater than 0. This test condition always returns true and no matter what I enter inside this condition it always results in "in downtime, exit".  So even if [ "hello" = "hallo" ] it will go inside and exit right away. I also tried pretty much every variation with quotes, without, double brackets... and so on. I am obviously doing something wrong. Can anyone spot it?  Thanks in advance!


I have a smal laptop Acer aspire and I wish to install ubuntu from a flash drive how do I proceed?


I created new project in QGIS (v3.2.1) Added a OSM Standard layer with QuickMapServices plugin. Current CRS is EPSG:3857   Now I want to use map in degree units. As far as I understand I need to convert CRS to WGS 84. So I pressed the button:  Project Properties | CRS dialog box appeared. I filtered CRS by string '84'. There were two potential candidate geographic coordinate systems in that list: EPSG:4326 and IGNF:WGS84G  It looks like both of them do not fit because of the map distorted in both cases. The original view (EPSG:3857) was following:  After changing to CRS to EPSG:4326 it became look like:    How to solve my problem with degree coordinate systems?    The following is the image of layer context-menu:  It has not Save as element.

Using QGIS 2.6.1 Brighton. I am trying to set the CRS for the project to display Decimal Degrees, where it is defaulting to Feet. I can change it in the Properties Dialog, but it does not change it, it is just staying on Feet. How do I change it?  Edit: this layer was imported from a shapefile where it was internally set to Feet. I was able to get the vendor to supply one with Decimal Degrees so my problem is gone. Still would love to know if there was a way to do it myself from within QGIS.


I downloaded this file.   Then, maybe there is some eye pattern.   But, I don't know how to change eye. How to change? Thank you.   supplementation -     In this topic, the facial expression image is displayed large, but I do not know where this image is in the first place.How can I make the same screen as this?

I'm trying to animate a mesh with different eye textures but it's not working.     This is a texture made by me to animate but I still couldn't figure out how to do it. I've seen tutorials on the internet but they don't work to me.


I'm sure this is an easy question, but I am somewhat confused. I'm considering here a measure space $(X, \mathcal{A}, \mu)$, and the functions are real valued. Given a sequence of functions $(f_n) \in L_p$ that converges almost everywhere to a function $f$ and converges in $L_p$ to a function $g$, is it true that $f=g$ almost everywhere?

If I know $\| f_n - f \|_{L^p(\mathbb{R})} \to 0$ as $n \to \infty$, do I know that $\lim_{n \to \infty}f_n(x) = f(x)$ for almost every $x$?


Use the area interpretation of integrals to prove that; $$\int_{0}^n \lfloor t \rfloor dt = \frac{(\lfloor n\rfloor-1)\lfloor n\rfloor}{2}$$ for all integers n $\ge$ 0, and hence find a formula for $\int_{0}^x \lfloor t \rfloor dt$.  I assume for the second part that the formula is  $$\int_{0}^x \lfloor t \rfloor dt = \frac{(\lfloor x\rfloor-1)\lfloor x\rfloor}{2}$$  For the first part I have assumed that since n is an integer $\lfloor n\rfloor$ = n  Therefore we have $$\int_{0}^n \lfloor t \rfloor dt = \frac{(n-1)n}{2}$$ This is the solution to that summation of (i-1) from i=1 to n if I am remembering correctly, and matches the area of all the rectangles from 0 to n right?  Any help would be greatly appreciated!  Edit: Okay just to clarify I am confused with the first at of how to actually use the area interpretation. The duplicate only really deals with the second part!

I am having difficulties understanding and solving the following problem.    So far I think I understand the first line. I know what the graph of floor[t] looks like and I understand they're asking to integrate from 0 to some value of n and that integral always equals the equation on the right. I do not really understand what they are asking for in the second line or how that differs from the first equation.  I have checked through my notes and various online sources and we've just covered the fundamental theorem of calculus and discussed integration using partitions on an interval to calculate area but I am also unsure about how to relate these to this problem if they are even needed.  Any pointers, explanations or solutions would be greatly appreciated.  Thank you.


This question follows from a . I am using the OSCOLA BibLaTeX style file. In the bibliography, when citing the same author more than once, the author's name should be replaced with a double em-dash. This works except when the author has co-authored works. In that case, the first author name is printed in full.  This is a minimal working example. First, a .bib file:  @phdthesis{Author2002,  Author = {Author, An},  School = {Department of Something, University College Somewhere},   Title = {A PhD thesis}, Year = {2002}}  @article{Author2003,    Author = {Author, An}, Journal = {Some Journal}, Number = {2}, Pages = {163}, Title = {An Article},Volume = {27}, Year = {2003}}  @incollection{Author2009,   Author = {Author, An},  Booktitle = {Some Book},    Publisher = {Some Publisher}, Title = {Book Chapter}, Year = {2009}}  @article{Author2013,    Author = {Author, An and AnotherAuthor, An},Journal = {Another Journal},Number = {1},Pages = {55--69},Title = {Another Journal Article},    Volume = {45}, Year = {2013}}   And the .tex file:  \documentclass[12pt, a4paper]{article} \usepackage[style=british]{csquotes} \usepackage[style=oscola,   ibidtracker=true,          backend=biber,       autolang=hyphen]{biblatex}  \addbibresource{Test.bib} % fixes a bug identified in a previous StackExchange question \usepackage{xpatch} \xpatchbibdriver{thesis}{\printnames{author}}{\usebibmacro{author}}{}{}  \title{Test Document}  \begin{document} \maketitle  First citation.\autocite[66]{Author2013} Second citation.\autocite[31--2]{Author2002}  Third citation.\autocite{Author2009}  \printbibliography[nottype=commentary,nottype=jurisdiction,nottype=legislation,nottype=misc,nottype=legal] \end{document}   The bibliography looks like this, at least on my system:     Author A, ‘A PhD thesis’ (PhD thesis, Department of Something, University College Somewhere 2002).      — ‘Book Chapter’, in Some Book (Some Publisher 2009).      Author A and AnotherAuthor A, ‘Another Journal Article’ (2013) 45(1)   Another Journal 55.   The last reference listed should start with — — and AnotherAuthor A. Does anyone have any idea how to fix this issue?

With biblatex, the author can be replaced by a dash (or “idem”) in the bibliography. Is it possible to have this replacement also if there are multiple authors, and the first of these multiple authors is the same as the author of the book listed before? (It is somewhat difficult to describe, see the attached example instead, where “Buchautor, Hans-Wilhelm” should be replaced in book3 as well.)   I assume that it should be possible by customising \DeclareNameFormat, but I don’t know how.  Minimal example:  \documentclass{scrartcl} \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} \usepackage[english]{babel} \usepackage{csquotes} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @BOOK{book1,   author = {Buchautor, Hans-Wilhelm},   title = {Irgendein Buch},   location = {Buch am Wald},   date = {2000} } @BOOK{book2,   author = {Buchautor, Hans-Wilhelm},   title = {Ein anderes Buch},   location = {Berlin},   date = {2001} } @BOOK{book3,   author = {Buchautor, Hans-Wilhelm and Zweitautor, Zoran},   title = {Noch ein Buch},   location = {London and New York},   date = {2010} } \end{filecontents}  \usepackage[ style=authortitle, backend=bibtex8 ]{biblatex} \bibliography{\jobname}  \renewcommand*{\bibnamedash}{%   \bibstring[\mkbibbold]{idem\thefield{gender}}}  \begin{document} \nocite{*}  \printbibliography \end{document}   Edit 15/02/2011 17:14   I should have added that there was a feature request for biber which pointed back to biblatex. See .  Edit 21/06/2011 9:26  Is this somehow possible now with biblatex 1.4/1.5? I played a bit with uniquename/uniquelist, but I could not get it to work.


Consider the following situation. A block slides on a rough surface. We have already given it an initial velocity. I consider my system to include only the block. Due to friction, the table performs work on the block, thereby reducing its kinetic energy. On the other hand, the block performs no work on the table, since the table surface does not get displaced at all. So, isn't it incorrect to say that work done on the system is the negative of the work done by the system?  If the work done by a system is not always the negative of the work done by the system, then how can both versions of the first law of thermodynamics hold true? The first law of thermodynamics in the physics point of view is: $\Delta U=Q-W,$ and in the chemistry perspective is: $\Delta U=Q+W.$  Both of these seem to be correct, as in the first case we are considering the work done by the system on the surroundings, and in the second case we are considering the work done on the system by external forces. But, if the work done by a system is not equal to the negative of the work done on it, then I have a feeling that the chemistry definition might be a better one. Please clarify.  Kindly note that I am already aware of the different conventions  used in physics and chemistry, and I completely understand their intended meanings. My question is not really related to thermodynamics, but something more fundamental. I have just taken the first law of thermodynamics as an example.

What is the sign of the  done on the system and by the system?  My chemistry book says when work is done on the system, it is positive. When work is done by the system, it is negative.  My physics book says the opposite. It says that when work is done on the system, it is negative. When work is done by the system, it is positive.  Why do they differ?


I have proven that the Cantor set is uncountable using Cantors diagonalization argument in base $3$. Now I have to prove that it has cardinality $\mathfrak{c}$ due to the fact that it is uncountable  but I am struggling to even get started.   Any help would be appreciated.

Let $S_0=[0,1]$ and define every $S_k$ for $k\geq 1$  \begin{align*} S_1&=\left[0,\frac{1}{3}\right]\cup\left[\frac{2}{3}, 1\right],\\ S_2&=\left[0,\frac{1}{9}\right]\cup\left[\frac{2}{9}, \frac{3}{9}\right]\cup\left[\frac{6}{9}, \frac{7}{9}\right]\cup\left[\frac{8}{9},1\right],\\ S_3&=\left[0, \frac{1}{27}\right]\cup\left[ \frac{2}{27}, \frac{3}{27}\right]\cup\left[ \frac{6}{27}, \frac{7}{27}\right]\cup\left[ \frac{8}{27}, \frac{9}{27}\right]\cup\left[ \frac{18}{27}, \frac{19}{27}\right]\cup\left[ \frac{20}{27}, \frac{21}{27}\right]\cup\left[ \frac{24}{25}, \frac{25}{27}\right]\cup\left[ \frac{26}{27},  1\right]\\ \vdots \end{align*}  Now let $C=\bigcap_{k=0}^\infty S_k$. This is known as a Cantor set.  I have to prove that C is non-empty, by showing that 1/4 is in C. I also have find the cardinal of C and prove my answer.   I have some ideas how to prove non-emptiness, but I am stuck as to how to specifically prove that 1/4 is in C. Also I think that the cardinal is equal to the cardinal of the reals $2^{\aleph_0}$. I probably need to find a bijection to prove this right?


i've been trying to mount an .iso according to a guide i read here, but every time i run the command sudo mount -o loop /home/varbo/Downlaods/Windows 7 Ultimate SP1.iso /media/iso i get the same (usage) error:  Usage: mount -V                 : print version  ... usage and options deleted ....  Other options: [-nfFrsvw] [-o options] [-p passwdfd]. For many more details, say  man 8 mount .   Any kind of help would be appreciated.

I'm running into trouble trying to mount a large iso:  dev@dev-OptiPlex-745:~$ sudo mount -o loop /home/dev/Hämtningar/matlab2011a_64.iso /cdrom mount: warning: /cdrom seems to be mounted read-only. dev@dev-OptiPlex-745:~$    Can you tell me how I should do it?


we gets (sinx)'=cosx from lim x→0 sin(x)/x=1  Geometric proof of it is based on the fact that the area of sector of unit circle with central angle x is x/2  However, when we calculate the area of unit circle, we use the integral of trigonometrical function which derive from (sinx)'=cosx. That is an circulation logic!  Also, area formula of polar coordination also derives from area of sector, so we can't use it to proof lim x→0 sin(x)/x=1  I tried many other methods, but I can't find any process.  I want to know rigorous proof of lim x→0 sin(x)/x=1 not using the differential and integral of trigonometrical function.  Thank you.

How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution.  This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, that proving the above statement is enough for proving the continuity of $\sin$, but I can't find out how. Any help is appreciated.


Let $f$ be in $L^1(\mathbb{R}). $ Show that $$\lim_{a\to 0}\int_{\mathbb{R}}|f(x)-f(x-a)|dx=0.$$  As $f\in L^1(\mathbb{R})$, we have $\int_{\mathbb{R}}|f(x)|dx<\infty. $ Define $f_n(x):=f(x-a_n)$. For each fixed $n$, $f_n(x)\in L_1(\mathbb{R}).$ I don't know how to solve this kinda of problems. Should I apply Fatou's lemma or the dominated convergence theorem? But I'm not evey sure if $f$ is bounded. I appreciate any help for this problem. I don't undstrand the proof provided in the mentioned link. I'm very new in measure theory and I think there must be some easier solution for this question.

Let $f:\mathbb{R^+}\to\mathbb{R}$ be an integrable function ($f\in L^1(\mathbb{R}^+,\mathbb{R})$). Do we have $$\lim_{h\to 0^+}\int_0^\infty|f(t+h)-f(t)|dt=0$$ ? How can we prove it ?


Im looking for help left aligning and vertically aligning a image in this header.    @import url("https://fonts.googleapis.com/css?family=Open+Sans:400,300,600,700"); * {   box-sizing: border-box; }  img {   float: left;   vertical-align: middle; }  .header {   padding: 5px;   text-align: center;   background: #222222;   color: white;   font-size: 20px; }  h2 {   color: white; }  title {   color: white; }  body {   font-family: 'Open Sans', sans-serif;   background-color: #2C2C2C; }

This should be center

     Here is my code for the image (currently its left-aligned but i can't seem to align it vertically. And then it also moves my text to the right when the text should stay in center of div horizontally)  img {     float:left;     vertical-align: middle; }   I basically need the red image to stay the same size, i just need it to be left-aligned (maybe 50px from left) and be vertically aligned with the header div. But i also need the text to stay in the center of the div, vert and horz.

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...


How do I efficiently compute $a^b\bmod c$:  When $b$ is huge, for instance $5^{844325}\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, for instance $5^{69}\bmod 101$? When $(a,c)\ne1$, for instance $6^{103}\bmod 14$?  Are there any other tricks for evaluating exponents in modular arithmetic?  This is being asked in an effort to cut down on duplicates, see  and .


Tried to enter in Boot setup using F2 and updated grub .But not able to enter into bootsetup nothing work.After pressing F2 it direcly get into Ubuntu .If it is fastboot pls guide me to disable it . As its my second day in ubuntu

I have a laptop with Ubuntu installed as the only OS. I also have a USB stick with a Windows 7 installation on it. I want to install Windows from the USB stick on my laptop but when I try to restart the laptop to get access to BIOS, I can't seem to find the command for it, its like it skips everything and just says Ubuntu and then takes me to the login screen.  How do I change the boot priority to USB in Ubuntu?


The book is about alien birds that must dock and flap their wings to keep islands afloat on their home planet. All of a sudden aliens attack them and slaughter most of them. The birds have at least one space ship, and a few escape on that.   The birds find a water planet, and decide to explore it. They notice a large object under water; when they try to check it out, they crash. Only one bird survives the crash; he finds some sort of tentacle monster (?), and survives off it.  The bird eventually leaves the water planet, becomes part of a space ship, and battles other aliens. Both sides have powerful ships which end up destroying galaxies.  The birds in the beginning also play a VR game about being god. They try to help one race become more powerful. A more detailed bit of the game is they main protagonist, the bird, has these animals that cannot lookup so he clears the sky so that they can look up which leads to the enemy destroying them because the enemy can finally see a race to kill (all in the simulation VR game). The game is something the birds have on their homeworld; I think it's implanted in their heads. It's an activity for them to do while they're docked, keeping the islands afloat.  As far as I can recall, the birds were presented as looking much like actual birds here on Earth, with wings and talons (no hands, for example).  I read the book in 2017; I'm not sure how old it was then, and I don't remember anything about the cover.  Extra detail: There might have been crystals on the islands crystals that helped keep them floating.

Things I remember   I read this book in elementary school, but I don't know how much of a "kid's" book it is. Main character was male, and I think the title of the book may have been his name. I picture him as owl-like, but I know he had talons and wings at least. The book possibly started on his race's home planet, and they had to leave to live on space stations for some reason. Once they leave their home planet, there is a comment that their children will be born with flatter feet to accommodate walking on metal of the space station instead of gripping branches. I'm forgetting a chunk of the book, but the main character becomes separated from everyone else, possibly left behind somewhere on purpose. Somehow the main character becomes extremely powerful. He is able to fly through space on his own without a ship. Near the end of the book, he engages in a prolonged battle with some other hyper-powerful character (The fight might start on a water planet). Their fight spans the galaxy. Main character ends up in a black hole, omniscient and observing a planet (possibly Earth?). A boy from the planet dies and shows up where our main character is. Main character and boy talk about whether anything in life has meaning or affects anything.


I have been doing a lot of problems regarding calculus. An utmost basic question I stumble upon is "when is a continuous function differentiable?" (irrespective of whether its in an open or closed set).

Why does differentiability implies continuity, but continuity does not imply differentiability?   I am more interested in the part about a continuous function not being differentiable.  Well, all I could find in regards to why continuous functions can not be differentiable were counter- examples...   I just wanted to know if there was a more detailed way of explaining this.


I need to install Python 3.7 in order to run a library that requires it, but I don't want to replace my system's native Python 3 installation (which is an earlier version) as I'm afraid to break system dependencies.   How do I install it in parallel?

I want to install the latest Python tarball on Ubuntu, downloaded from .  Is this is a correct way to install?  ./configure make make install   If not, how do I do that?


So for example I have a model chair which includes the arms, piston (that type of chair), base etc. How do I select all parts including the parent item for duplicating the model? Shift+G only allows me to select the children but not parent. I'm fairly beginner with Blender.  Thanks

Say I have a set of objects parented to another object, for the sake of this example say they are parented to an empty.  If I have the empty selected, is there a way of quickly selecting all the objects parented to it?


Why must unexposed and undeveloped film be handled in total darkness? Why can analogue, unexposed and undeveloped monochromatic photographic paper be handled in red/ yellow safelights without getting fogged?

I'm no expert in darkroom photography, but it seems a little odd that there is a type of light that doesn't affect film or developing paper etc. The only way that I could think to explain it is:   The low frequency red photons don't have enough energy to raise electron states in the film/paper, or Magic   either way, I'm curious to know how this handy tool is, as per title, safe.


Find all natural numbers $n$ and $m$ for which $$n^m=(n-1)!+1.$$  By the Wilson theorem, $n$ is prime. Obviously, $m < n$.  For example, some solutions $(n, m)$ are $(2, 1)$, $(3, 1)$ and $(5, 2)$.

How to find all positive integers $n$ such that $(n-1)!+1$ can be written as $n^k$ for some positive integer $k$?


My wife was cooking a turkey leg/thigh quarter in the oven at 350.  She turned off the oven after cooking and mistakenly left it in there for two days(!).  If the leg/thigh was cooked to the right safe temperature to kill bacteria, and if 350 is hot enough to kill any bacteria in the oven, and if the oven was never opened after turning the gas off, would the turkey still be safe to eat?

If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?


If I have 2 same capacity/model of power bank and combine the output via Y connector (parallel), will there be any issue?

Can I run two 5v power packs in parallel to give me more mAh's (Time)? Or will one try and charge the other?    I.E. connect both 5V lines together, both GND lines together to my device


I want to change the Sections and subsection spacing, therefore I use "\usepackage{titlesec}". However, at the moment I import the "titlesec" package I lose my section and subsection numbering.  I am aware of the "titleformat", however, I have not been able to combine the spacing and the format together in order to have numbering and the spacing I add to my example.  I must add that I'm compiling in Ubuntu 16, using TeXMaker.  \documentclass[a4paper, 11pt, twoside,openright]{report} \usepackage{lipsum}  \usepackage{titlesec}  \titlespacing\section{0pt}{8pt plus 2pt minus 2pt}{0pt plus 2pt minus 2pt} \titlespacing\subsection{0pt}{8pt plus 2pt minus 2pt}{0pt plus 2pt minus 2pt} \titlespacing\subsubsection{2pt}{8pt plus 2pt minus 2pt}{0pt plus 2pt minus 2pt}   \sloppy %avoid word passing the limits of page aligment. \begin{document}   \chapter{uno prueva}  \section{uno Section} \lipsum[1] \section{dos Section} \lipsum[2] \section{tres Section} \lipsum[3] \chapter{dos prueva} \section{uno Section}q qsdfdqsf \section{dos Section} qsdf \section{tres Section} \lipsum[1]  \end{document}   EDIT 1:  As Requested by @egreg I added \listfiles at the beginning of the document and here they are the log results:  This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex 2017.11.1)  24 JAN 2018 14:28 entering extended mode  restricted \write18 enabled.  %&-line parsing enabled.   *File List*   report.cls    2014/09/29 v1.4h Standard LaTeX document class    size11.clo    2014/09/29 v1.4h Standard LaTeX file (size option)     lipsum.sty    2014/07/27 v1.3 150 paragraphs of Lorem Ipsum dummy text  titlesec.sty    2016/03/15 v2.10.1 Sectioning titles  ***********

After reinstalling TeXLive distribution (install-tl-20160318, Ubuntu 14.04), a issue occurs with the updated version of the titlesec package: the section numbering is lost.  What could it be missing? Is there a modification I have not seen?  Below is a MWE comparison of the two versions. The prevtitlesec package is a reinstall of the previous version (2011/12/15).  \documentclass{book} \usepackage[margin=2cm,a4paper]{geometry} %\usepackage{prevtitlesec}% 2011/12/15 version \usepackage{titlesec}% 2016/03/15 version \usepackage{lipsum}  \begin{document}  \chapter{Title of the first chapter} \lipsum[1] \section{A test section} \lipsum[4] \subsection{A test subsection} \lipsum[4] \subsection{A test subsection} \lipsum[4]  \end{document}   titlesec package 2011/12/15:    titlesec package 2016/03/15:


I have been on eBay, looking for a used Mac mini and to my surprise it said, the system comes without any operation system (disk erased). It is still an Apple product and I wonder, is it possible to not have a "right" to at least an older (original sold) version of macOS?  A good answer would hence point out the aspects:   Can Apple computers be bought without a license? Can Apple macOS licenses be transfered in a way that a Apple Computer ends up without an OS?   update  A comment suggested specifying the model of the Mac Mini. As suggested the product was seen on ebay, where vendors not always care/are able to provide a model number. This being said, the Mac Mini in question was described as only using its hardware attributes:      Apple MAC MINI 1,66 GHz Intel Core Duo   Considering the comment/ request about the model, an answer could highlight if the OS / OS license is depending on the model/product?

I just got off a very long and very frustrating phone call with Apple support.  I purchased a used Apple computer which came installed with Mountain Lion. Meaning that the computer was shipped by Apple with Mountain Lion installed, and received by me with that same installation.  As a precaution, I tried to reinstall Mountain Lion via Recovery mode. This failed because my Apple ID hasn't purchased Mountain Lion.  Apple insisted that because I didn't purchase the computer new, I don't have a license for OS X. I don't believe this is correct, or even legal. This means that anyone using a used computer is doing so illegally, unless they've purchased a separate OS license.  Am I way off-base here? I'm pretty sure I now "own" a copy of Mountain Lion, and Apple is in the wrong. If this is correct, what are my options?


Let $A,B,C,D$ be four complex $n\times n$ matrices such that $AB^T$   and $CD^T$ are symmetric and $AD^T-BC^T=I$. Show that $A^TD-C^TB=I$.   The point is that I can't see how any theory can be used here. It appears to be a mere exercise of calculus which, either way, I'm not able to solve.  I think that some multiplications must be done, in order to use the fact that the identity is involved (and not just show that $A^TD-C^TB=AD^T-BC^T)$. I tried to get help from particular cases, but found nothing.

Let A,B,C,D be complex matrices $n \times n$ such that $AB^T,CD^T$ are symmetric and $AD^T-BC^T=I$. Prove that $A^TD-C^TB=I$. Can anyone give me any idea? Thank you.


What are the roots of $ x^{2} = 2^{x} $? I drew the graphs and found $ x = 2 $ and $ x = 4 $, and there is one other root in $ [-1,0] $. Can anyone describe an algebraic method to obtain all roots?

How to solve this equation $$x^{2}=2^{x}$$   where $x \in \mathbb{R}$.  Por tentativa erro consegui descobri que $2$ é uma solução, mas não encontrei um método pra isso. Alguma sugestão?(*)  (Translation: By trying different values I've found that $2$ is a solution, but I couldn't find any method to this though. Any suggestions? )


The factorisation thm for polynomial in one variable $p \in F[x]$ says that if $p(\alpha)=0$, then there is $r \in \mathbb{N} $  s.t $p(x)=(x-\alpha)^rh(x)$ where $h(\alpha)\neq0$. Is there is similiar thm for polynomial in 2(or n) variables? i.e for polynomials in $F[x,y]$?

I've been searching around for a formal definition, but I haven't found one yet. There are a few examples of how to use it, namely . I've been playing around with possible statements myself, and I've come up with two candidates, the second a generalization of the first. I'll phrase each in terms of polynomials in $\mathbb{C}[x,y,z]$ because they're easily generalizable to $n$ variables if true.     If $f(x,y,z)$ is a polynomial, and $P(y,z)$ is a polynomial satisfying $f(P(y,z),y,z)=0$ for all complex $y$ and $z$, then $x-P(y,z)$ is a factor of $f(x,y,z)$.   This one I think I've successfully shown, just by using the remainder theorem where the remainder is designated to have smaller $x$-degree.     If $f(x,y,z)$ and $P(x,y,z)$ are polynomials such that for any $x,y,z\in\mathbb{C}$ the following implication holds:   $$P(x,y,z)=0\Longrightarrow f(x,y,z)=0,$$   then $P(x,y,z)$ is a factor of $f(x,y,z)$.   This I have less of an idea how to show, because the remainder theorem is trickier for multivariable polynomials. It still looks true to me.


I am using texmaker, which is based on Tex Live 2013. I have just downloaded a package, i.e. mathpro2 (lite version).   Question 1: Where should I put my package files into?   I have seen answers to this question, but I am still entirely not sure where exactly should I put my mtp2lite folder. Right now, I have the following file path  `\usr\local\texlive\`   Inside texlive, there are 2 folders 2013 and texmf-local.   2013 contains texmf-config, texmf-dist and texmf-var.  Inside texmf-local, there are 6 other folders; bibtex, dvips, fonts, metapost, tex, and web2c.  But I am not sure where to place my "mtp2lite" folder in?   Question 2: My mtp2lite folder 2 folders, template and texmf. And the texmf contains several other folders doc, dvips, fonts, source, tex, and tpm but I was expecting files with .sty extension. Not sure where they are? Am I suppose to extract something from these folders? Put simply, what should I do such that when I compile my TeX files in Texmaker with the following command, everything will work smoothly?  \usepackage[lite]{mtpro2}   I am just really confused here.  UPDATE: Someone said that it suffices to unzip the mtp2lite.zip file. However, I am not sure which file path should I unzip the file ?    \usr\local\texlive\2013\texmf-config \usr\local\texlive\2013\texmf-dist \usr\local\texlive\texmf-local   I unzip the files in all 3 paths, and in the terminal I ran the following command:  sudo mktexlsr /usr/local/texlive/2013/  and  sudo updmap-sys --enable Map=mtpro2.map  The terminal output gave me this after the second command:  updmap is using the following updmap.cfg files (in precedence order):   /usr/local/texlive/2013/texmf-config/web2c/updmap.cfg   /usr/local/texlive/2013/texmf-dist/web2c/updmap.cfg updmap is using the following updmap.cfg file for writing changes:   /usr/local/texlive/2013/texmf-config/web2c/updmap.cfg /usr/local/texlive/2013/texmf-config/web2c/updmap.cfg unchanged.  Map files not recreated.  I am Not sure if this is actually a problem.   But when I tried to compile my tex file, I am still getting error message:    I can't find file `mt2exa'. <*> ...:=ljfour; mag:=1; nonstopmode; input mt2exa Please type another input file name ! Emergency stop. <*> ...:=ljfour; mag:=1; nonstopmode; input mt2exa Transcript written on mfput.log.  grep: mt2exa.log: No such file or directory

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


I decided to look up my username for kicks, and found .   They seems to be scraping SO for questions with a security tag. Those questions listed appear to be every "security" related post I've been involved with on SO.   Last time I reported a similar site, it was well recieved, so it seems this is an appropriate channel to report though.

of Stack Overflow, all content posted on Stack Exchange sites by their users (i.e. you wonderful people) has been provided to the whole universe under . For my fellow non-lawyers, that license basically means:   Anyone can use any Stack Exchange posts at any time without having to ask for permission Making money off of the copied content is permitted You don't even have to copy stuff from here verbatim; you can just use it as a starting point and make whatever edits you want There are just two rules you have to follow:   You have to provide . Simple links to the original post and author info are just fine. You have to  and allow other people to use your content, as long as they follow these very same rules. How meta!    (If you ever forget any of that, and want to refresh your memory, the license info is linked to in the footer of every page.)  There are, in fact, a lot of people who republish varying amounts of our content for assorted reasons. Unfortunately, there are some Stack Content Republishers Attributing Poorly and/or Excelling at Ranking (SCRAPERs, for short).  In this context, "attributing poorly" means any use that doesn't follow our attribution rules or make any other reasonable attempt at give credit. This can get pretty egregious; I've seen SCRAPERs that not only don't link back to SE originals, but also use fake author info and post dates to make it harder to find originals. By "excelling at ranking," I'm referring to copycat sites that end up higher in Google results than the original SE sites do for the same content. That's not necessarily wrong, but in some cases, it indicates inappropriate SEO hackery.  So, the question is: what can you do if you spot a SCRAPER?


This is what  looks like on a desktop browser (Windows 10, Chrome 84.0.4147.135):  This is what it looks like on a mobile browser (Android 8, Firefox 79.0.5):  Italic text is not formatted on the mobile.

Update 3 It took me longer than I wanted, but I’ve got some updates for you on our s-prose component. You can see the  with my thinking over at our design system’s repo. It does the following:  Spreads s-prose headers out from paragraphs for better grouping. Tightens up s-prose paragraphs a bit, and made sure spacing under headings are more consistent. Replaces all s-prose margins internal to the component with a CSS variable var(--s-prose-spacing) so our users can more easily tinker with it in their browsers and user scripts. Kills trailing margins in s-prose  You can see  of content at our Stacks documentation.  Update 2 I’ve split the difference between the original 1.3 line-height and the proposed 1.6 line-height. We’re now at 1.5, with additional refinements to spacing between elements. I’ve also reduced line height within code blocks back to near the original value.  Update 1 This is now live.  We’re doing a bit of refactoring on our post formatting. Currently, we apply a single class with both layout and styling called .post-text. Our first goal is to separate layout from our text styles. Simple enough! However, our current post styling has a few missing spots and areas for improvements. Using our  as a sandbox, we’ve beefed up our styling and created a new component called .s-prose. It’s designed to offer styling for everything the  spec allows. This should allow us to add Stack Overflow-flavored styling anywhere we need to consume Markdown—questions and answers, of course, but also things like user profiles. Our .s-prose component adds:  Proper formatting for   Further header support and better spacing there  Additional blockquote refinements.  Refinements for revealing spoilers. We now reveal this on click / tap for a more consistent experience across devices—fewer accidental reveals as well, since it’s no longer a :hover interaction. Clicking again does not hide the spoiler. We also now add a badge to the top right corner. You can see how these work on our . It looks something like this:   This is a spoiler  It has two lines   General refinements to spacing including nested lists, images within lists  Sizing variations for different contexts. We offer xs, sm, and md variations of the .s-prose component.   As with everything, our prose component is a work in progress. We think we’ve got a heck of a start to a reusable component. We plan on going live with the new component network wide on Thursday, August 27, 2020. We’ll edit this post if that changes. If you see something funky, let us know. Some things are intended but might feel like regressions—images have a slightly different baseline—but others may have slipped through the cracks.


I am now using this command to select in MySQL 5.7: SELECT game_id         FROM platform_reward_record         WHERE hub_sync = 0         GROUP BY game_id         LIMIT 100  when I create index like this: ALTER TABLE `packet_db`.`platform_reward_record`  ADD INDEX `idx_hubsync_gameid` (`game_id`, `hub_sync`);  the query is very slow, but using this index: ALTER TABLE `packet_db`.`platform_reward_record`  ADD INDEX `idx_hubsync_gameid` (`hub_sync`, `game_id`);  it is fast, why the field sequence affected whe slect speed? What should I learn from it?

I have the following covering indices:  INDEX (col1, col3); -- index 1 INDEX (col1, col2, col3); -- index 2   because I would like to support the following type of queries:  1)    SELECT col3     FROM my_table    WHERE col1 = ... AND          col2 = ... ORDER BY col3   2)    SELECT col3     FROM my_table    WHERE col1 = ...  ORDER BY col3   I am unfamiliar with how a covering index works.  Is index 1 redundant? Or does a covering index requires that the columns be side by side?


Well everything is in the title. Why is StackOverflow showing up with a indent and why don't I see my rep next to it like on the other websites.

EDIT Dec 4 -  We're doing it live! Please post bugs or concerns as questions tagged [top-bar]  We have rolled out our 95% completed top bar for feedback.  Note:   We are still adding a few final features, so if you have a request for a feature that is not there you might hold off on that for a day or two Yes, the bar is black1. Also give that a day or two to sink in.   I also want to specifically address the meta/main/chat links.  I'm very aware that many of you like having the links at the top of the page and that this new version is different.  The thought process behind moving these links is that the "site switcher" should be an automatic place to go when you are on a site and want to go to another one. If you haven't already developed the muscle memory for these links, getting between them required a bit of a cognitive load: You must first decide that you want to switch sites and then you have to decide which area to go to to switch.  Also, we find that less familiar users aren't entirely clear what a standalone link that says "main" or "meta" actually does... Not to mention that it hurts my UX sensibilities that we are dynamically changing links in an element that should be fixed.  It is true that we have added a click in the process, but we have also removed a lot of clicks for other common actions that are much more frequent than switching between main and meta.  All I ask is that you give it a few days and see if the new "switch sites at the top left" paradigm grows on you.  What do you think?  1.  points out that technically it's not quite black.


I'm searching the 5 bottles in The Legend of Zelda: A Link Between Worlds, but I've just found the one in the empty house. Where are the other bottles?

In Zelda games, bottles are pretty useful and often there are one or two that are well-hidden. I'm a bit surprised in this one that I've only done 3 dungeons of the game and already found 4 bottles.  How many are there, and where can I find them all?


Given $a,b,n \in \mathbb N$, prove that $a-b|a^n-b^n$. I think about induction. The assertion is obviously true for $n=1$. If I assume that assertive is true for a given $k \in \mathbb N$, i.e.: $a-b|a^k-b^k$, I should be able to find that $a-b|a^{k+1}-b^{k+1}$, but I can't do it. Any help is welcome. Thanks!

I did some mathematical induction problems on divisibility   $9^n$ $-$ $2^n$ is divisible by 7. $4^n$ $-$ $1$ is divisible by 3. $9^n$ $-$ $4^n$ is divisible by 5.   Can these be generalized as $a^n$ $-$ $b^n$$ = (a-b)N$, where N is an integer? But why is $a^n$ $-$ $b^n$$ = (a-b)N$ ?  I also see that $6^n$ $- 5n + 4$ is divisible by $5$ which is $6-5+4$ and $7^n$$+3n + 8$ is divisible by $9$ which is $7+3+8=18=9\cdot2$.  Are they just a coincidence or is there a theory behind?  Is it about modular arithmetic?


I notice that  is showing up on the homepage, but not on the newest java questions. Can someone fix this soon?  This question is in fact a recurrence of my other question with the same name.

What can cause a question to be "bumped" to the first page in the Active tab of a Stack Exchange site? (Changing the "Last Active" date.)  .


I am trying to grow my C: drive to use the unallocated space on Disk 0. Is it safe to throw away the Recovery Partition (i.e. make it unallocated)? And if so, is GParted an ok tool to do that with? And after I delete it, if I leave enough unallocated space after joining pertitions, is there a way to have it build a new recovery partition?

I am trying to grow my C: drive to use the unallocated space on Disk 0. Is it safe to throw away the Recovery Partition (i.e. make it unallocated)? And if so, is GParted an ok tool to do that with? Or do I need to move that, and if so, is the way to do that to reduce the size of the unallocated partition so there is empty space at the end, then move it there?


I just followed a tutorial on how to create a nice and round Earth. Here are my 3 spheres (1 for the ground, 1 for the clouds and 1 for the atmosphere) in camera view.    When I press F12 to render my image, here is what I get : a sphere... which is not round  It might be a detail but I just can't figure out this deformation after rendering...   Anyone ?   Thanks guys

Why would there be a difference in aspect ratio between a rendered image, and the camera perspective in the viewport? My render is getting squashed to fit a different aspect ratio.  Here is a scene with a circle and emission shader.  Camera perspective in the viewport:   Render:


Could someone please explain to me which of these sentences is correct and why?        Only one out of three respondents (29%) thinks otherwise.     Only one out of three respondents (29%) think otherwise.      I understand that the subject of this sentence is singular, and therefore, theoretically, the verb should be singular, but this just doesn’t sound right.  Could someone please help?

Take the examples:   "One in ten children are dyslexic."  "One in ten children is dyslexic." "One in ten children has dyslexia." "One in ten children have dyslexia."   The "one" is singular so 2 and 3 should be correct. But the "one in ten" is a fraction" so 1 and 4 should be correct. And yet I think I usually say 1 and 3. Which is/are correct?!


i want to fix first column (ex: Title column) of my sharepoint list view, so  that whenever the user scroll horizontally the first column should be fixed.   Thanks in advance for your support.

I am working in SP2013 , in a particular list view  we want to freeze first column on horizontal scrolling.  Please help on this if any one having idea/code/any reference URLS.


Question:    simplify $$\frac{(k-1)!}{(k+2)!}$$   What I did was:  $$\frac{(k - 1)!k!}{(k + 2)! \cdot (k + 1)!}$$ This I did following the rule $n! = n \times (n - 1)!$.  can this be simplified further? Thanks.

Question: simplify $$\frac{(n-1)!}{(n-2)!}$$   What I did was:  $$\frac{(n - 1)!}{(n - 2)! \times (n - 3)!}$$ This I did following the rule $n! = n \times (n - 1)!$.  But my answer just doesn't look correct and I don't have a solution guide that tells me the correct answer. This is why I don't know whether my answer is correct or not.


When I run sudo visudo , what should it contain? Please give me an example of what it should have normally for a sudo user.

I clean-installed Ubuntu 11.10 today, and then installed VirtualBox.  This required me to add myself to the vboxusers group, and since 11.10 seems to no longer have a graphical app to add users to a group, I ran the following command:  sudo usermod -G vboxusers stephane   This is a problem.  I now see what I should have run instead is:  sudo usermod -aG vboxusers stephane   The end result is I'm no longer in the groups I should be in.  Including whatever group is required to run "sudo".  When I run any command as sudo now, I get the following:  $ sudo ls [sudo] password for stephane:  stephane is not in the sudoers file.  This incident will be reported.   Is there a way to fix this, or do I need to re-install from scratch again?


I sent an email to some professor about a month back for some research paper. He reply to me that he will scan the research paper and send me in few weeks. I think he has forget to send the scanned document. Should I send him a gentle reminder?

When needing to ask a professor about something important and potentially delicate, what is an appropriate way to phrase the question or write the email?  Examples include:   Requesting a recommendation letter Asking for exceptions to policy (e.g., ignoring a course prerequisite, rescheduling an exam) Asking if you can do research with them, join a group, get into a program Scheduling a meeting, exam, or defense Letting them know about a change of plans Letting them know about a life event affecting your work or studies (e.g., wedding, funeral, sickness, vacation)


I installed ubuntu and erased windows data and didn't made partitions while installing ubuntu. I had 2 partitions in windows 7 and now i have just one 245gb partition. I need one partition which i can use seperatly.  How do i create partitions now?

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


I see presently that many countries outside the U.S. have negative rate government bonds. So you buy one for $101 and in 5 years you get $100 back (face value). (I picked numbers for simplicity).  I understand the bond would be more difficult for someone to steal and cash; but that does not seem a large value.  If you just hold cash you can use it at anytime. There is no inflation protection.  What am I missing?

The only reason that I can think of is because I expect the bond to appreciate in price thus offsetting the loss in yield. I could still end up with less money than I started with, if I hold the bond until maturity. Ultimately, the only scenario where I would want to buy a bond with a negative yield is because I anticipate deflation and even lower rates in the future. Is this correct, or is there another reason?  Currently, a lot of the global government bond market is trading on negative yield, and there are even some corporate bonds that are too.


I was interested in studying whether or not if when we remove an arbitrary two edges from $K_5$, we get a planar graph. I understand that a planar graph has at most $3v-6$ edges, where $v$ is the number of vertices in the graph. Hence, given that $K_5$ has $\binom{5}{2} = 10$ and because it is apparent that $10 > 9 = 3(5)-6$, $K_5$ is obviously not planar. However, given the fact that this is not necessarily an "if-and-only-if" assumption on the bounds of the edges of a planar graph, I wasn't entirely sure if removing edges on a graph such that $E(G) \leq 9$ was going to be a simple solution. Is there an induced subgraph of $K_5$ that has $8$ edges and is not planar?

this question might be simple to others, but I'm stuck on this question. "prove that when I deleted an edge from $K5$, it has planar sub-graph .  So, I know that G is planar if and only if G contains no sub-division of $K5$ or $K3,3$. So that means when I delete an edge from K5, I no loger have sub-division of K5 and therefore, the subgraph is planar. But how do I show that explicitly that when I remove edge from $K5$, it will have planar subgraph? (I think this question is somewhat related to Kuratowski's theorem)


It's a report chart showing the evolution of construction sector through the years . The titles of the columns read:  "2017", "2018f" and "2019f".   Does this mean the numbers below the titles are not final and could vary?  Thank you for your help!

What does the term F[YY]e mean in financial reporting in India? I have seen reports these days to use the term F15e. Does this mean Financial Year end? Googling on this does not yield a relevant result.


I have the quaternions $q = x_0 + ix_i + jx_2 + kx_3$ where $x_i \in \mathbb{R}$ and $i,j,k$ satisfy the relations $$ i^2=j^2=k^2 = -1, \hspace{0.3cm} ij=-ji=k,\hspace{0.3cm}  jk=-kj=i,\hspace{0.3cm}  ki=-ik=j$$ I also have that $f(q) =q^2$ defines a smooth map from $\mathbb{R}^4 \cup \{\infty\} \cong S^4$ to itself. I have to find how many solutions are there to the equation $q^2 = 1$. Can someone help me ?

In class we saw that $-1$ has infinitely many square roots in the ring of quaternions. Is it possible to compute the square roots of a given nonreal quaternion? What do they look like?


Have a look at .  To expand / collapse each day to show / hide the breakdown, you have to click the triangle. However, wherever you hover on the line you get the hand cursor, suggesting you can click.  Please can we be able to click anywhere on the line?

Steps to reproduce:   Open the reputation on a profile () Click on the date next to the arrow.   The details aren't expanded, even though the td has cursor:pointer. If you click the arrow, the details are toggled as expected.  I think the click function should be bound to the parent td rather than the arrow a.    Note this issue still exists on the  since  rolled out on Meta.


I know that \tilde{x} will produce  but how do I make it that \tilde will be below  ?

It is very easy to put a tilde over the symbol in math mode. Simply type $\tilde{a}$. But how to put a tilde under the symbol in math mode?


Let $\{X\}_{\alpha\in\mathscr{A}}$ be a collection of metrizable spaces and consider their disjoint union $$X:=\bigsqcup_{\alpha\in\mathscr{A}}X_{\alpha}.$$ Show that $X$ is metrizable.  Not sure where to begin. I figured some employment of a theorem is need; such as, the Urysohn Metrization Theorem, but I don't see how that could be used. Any help is appreciated.

I have encountered this question while tring to figure out why every sequential space $X$, is a quotient spaces of a metric space. If I understand correctly, given a sequential space, every sequence (including it's limit) can be identified with the space $Y=\{0\} \cup \{\frac1{n+1}|n \in N\}$. So The space $X$ can viewed as a quotient space of $\bigoplus_{(x_n) \in C} \{(x_n) \} \times Y$ where $C$ is the set of all converges sequences in $X$. My question is, How can I show that this space is metrizable?  Thank you! Shir


In classical mechanics we talk about Lagrangian, but when we talk about fields (in example- electromagnetic fields), we consider the Lagrangian density instead of "just" the Lagrangian. I didn't understand why? In addition I didn't understand the differences between the relativistic Lagrangian formalism and classical Lagrangian formalism when we are considering fields.

My question is: Why do we consider Lagrangian densities in  field theory (as opposed to Lagrangians as in point mechanics)? Is it simply because of the following? We wish the theories to be Lorentz invariant and as in Special Relativity space and time are no longer independent of one another we must consider the physics at each spacetime point $x^{\mu}$, implying that the theory should be locally described by a density. Additionally, to obey Poincare invariance the Lagrangian density should not be explicitly dependent on $x^{\mu}$, and for it to be Lorentz invariant it must be dependent on spatial derivatives $\nabla\phi$ of the fields as well as temporal derivatives $\partial_{t}\phi$ (as time derivatives in one reference frame will correspond to a combination of time and spatial derivatives in another frame). (Physically does the fact that $\mathscr{L}$ depends on $\nabla\phi$ as well as $\partial_{t}\phi$ because the field $\phi$ is defined at each spacetime point and so a fluctuation in $\phi$ at a point $x^{\mu}$ will produce temporal and spatial derivatives at that point which will affect fields in its immediate neighbourhood (i.e. infinitesimally close to it)?)


Let's say in the exponential distribution, the cdf if $$f(x|\lambda)=\frac{1}{\lambda}\exp\left\{-\frac{x}{\lambda}\right\}$$ If we have $n$ observations: $X_1, X_2, \cdots, X_n$. Then we know since it belongs to the exponential family we have the UMVUE for $\lambda$ is $$T({\bf X})=\sum^n_{i=1}X_i$$ And $$E(T)=E\left(\sum^n_{i=1}X_i\right)=\sum^n_{i=1}E(X_i)=n\lambda$$ Then  $$\hat{\lambda}_{UMVUE}=\frac{T}{n}=\bar{X}$$ Then, what if we want to find the UMVUE of $\frac{1}{\lambda}$?

Hi I'm solving some exercise problems in my text : "A Course in Mathematical Statistics".  I'm in the chapter "Point estimation" now, and I want to find a UMVUE of $\theta$ where $X_1 ,...,X_n$ are i.i.d random variables with the p.d.f $f(x; \theta)=\theta e^{-\theta x}, x\gt0$.   I know that $E(X_i)=1/\theta,$ for each $i$, and also have that $\bar{X}$ (or equivalently $\sum_1^n X_i$) is a complete sufficient statistic for $\theta$. But I cannot go any further here. Somebody can help me?


Ever since I updated from Blender 2.77 to 2.79, my Codec menu in the Render tab looks like this:  .  I'd like to render a scene in H.264 and I have no idea why it is missing in the menu. This doesn't seem to be a common problem, I haven't found any forums threads about this issue at all. I would be very grateful for your help!

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: