I'm having trouble finding a pattern by calculating each step of the sum from $j=0$ to $j = p-1$.

How do I prove the formula $\newcommand{\jaco}[2]{\left(\frac{#1}{#2}\right)}\sum\limits_{a=1}^{p-2} \jaco{a(a+1)}p = -1$ where a varies from 1 to p-2 and p is a prime  I got as far as $\jaco{p-a}p = \jaco{-1}p \jaco ap$ so I can reduce the sum but that does not seem of much help.


quick question, i was just wondering when cononical made and released snaps, I checked the wikipedia  and i couldn't find it, thank you

I've been trying snappy Ubuntu core on a Raspberry Pi 2 device, and I've heard I can use Snapcraft to do development on it. Now I hear that snaps are available on the desktop and server for Ubuntu 16.04 and other distros.  What is Snapcraft and how can I use it?


Many a times I leave the laptop connected to the charger with the switch on for the entire day. When it becomes fully charged does it still consume electrical energy?

Quite similar to . If I'm not mistaken any impulse mobile device charger is still consuming power, when plugged into socket, but when cable is disconnected from charged device. Correct?  Does the same rule goes for power sockets equipped with USB ports for charging mobile devices ( to Polish seller):    I was wondering, if this kind of construction means that my socket(s) will be continously draining power, 24 hours a day, no matter if anything is connected to it or not? Or do these have some kind of power-off "switch" (meaning stops draining power when everything is disconnected)?


I have been trying to resize my /home partition (/dev/sda5) with the unallocated space (325 GiB), I tried gparted but it seems that I can't add the unallocated space.    The fdisk -l output:    Can someone help me?

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?


Prove that $-x\sin x<\frac{x^4}{6}-x^2$ for all $x\in(0,\pi)$.  My approach is that for similar type of problem I used two function $f(x)=y=-x\sin x$ & $g(x)=y=\frac{x^4}{6}-x^2$   $f(x)-g(x)<0$ for $x\in(0,\pi)$ After this step I am confused.

Prove that $x - \frac{x^3}{3!} < \sin(x) < x$ for all $x>0$   This should be fairly straightforward but the proof seems to be alluding me.    I want to show $x - \frac{x^3}{3!} < \sin(x) < x$ for all $x>0$.  I recognize this shouldn't be too difficult but perhaps finals have fried my brain.


The APA style manual website says:     [A]rticles with one or two authors include all names in every in-text citation; articles with three, four, or five authors include all names in the first in-text citation but are abbreviated to the first author name plus et al. upon subsequent citations; and articles with six or more authors are abbreviated to the first author name plus et al. for all in-text citations.   Is there a way to   manually cite all authors in a citation of a paper with 5 authors, using \cite{...}  have the above-described rule automatically performed by latex, so that I don't have to do it manually?

I am really new to LaTeX and I need a comprehensive solution for my Thesis  I have this problem since two days and I couldn't find any solution in any other post.  I work with BibDesk on Mac  And I used Packages apacite and natbib  @article{Ha89, Author = {Peter M. Haas}, Date-Added = {2017-02-06 21:15:57 +0000}, Date-Modified = {2017-02-06 21:45:06 +0000}, Journal = {International Organization}, Lastchecked = {03/02/2010 12:54}, Number = {3}, Pages = {377-403}, Publisher = {Peter Haas}, Read = {0}, Title = {Do regimes matter? Epistemic communities and Mediterranean pollution control}, Urldate = { http://www.jstor.org/stable/2706652}, Volume = {43}, Year = {1989}}   this is a stripped version of my document:  \documentclass[11pt, oneside]{article}  \usepackage{lipsum} \usepackage[margin=1in, left=1.5in, includefoot]{geometry}   \usepackage{ragged2e} % REFERENCE PREAMBLE %\usepackage{url} \usepackage{apacite} \usepackage{natbib} %\usepackage{biblatex-apa}                                                   % Bullet preamble \renewcommand{\labelitemi}{$\bullet$} \renewcommand{\labelitemii}{$\diamond$} \renewcommand{\labelitemiii}{$\circ$} % graphics preamble \usepackage{graphicx}   %Allows you to import images \usepackage{float}      %Allows for control of float positions %HEADER AND FOOTER STUFF \usepackage{fancyhdr}  \pagestyle{fancy} \usepackage{graphicx}        \usepackage{amssymb} %Zeilenabstand 1,5 wenn aktiviert  \usepackage{setspace}\makeatletter\newcommand{\MSonehalfspacing}{\setstretch{1.44}\ifcase \@ptsize \relax\setstretch {1.448}\or\setstretch {1.399}\or\setstretch {1.433}\fi}\newcommand{\MSdoublespacing}{\setstretch {1.92}\ifcase \@ptsize \relax\setstretch {1.936}\or\setstretch {1.866}\or\setstretch{1.902}\fi}\makeatother\MSonehalfspacing %Zeilenabstand Code fertig \usepackage[hidelinks]{hyperref}   %allows for clickable reference %                       BEGIN OF DOCUMENT \citeA{source} %                       REFERENCES  \renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}} \fancyhf{} \rhead{\fancyplain{}{Identifying the Regime}} \lhead{\fancyplain{}{List of References}} \cfoot{\fancyplain{}{\thepage}}  \setlength\bibitemsep{1.9\itemsep} \bibliography{/User/Desktop/Thesis/references/mybib.bib}                   \bibliographystyle{apa} \addcontentsline{toc}{section {\numberline{}References}                                                       \end{document}   I would like to have the bibliography entry include a retrieved from    I tried to deactivate hyperref – as suggested in another post – but it didn't work. I also tried to activate and deactivate natbib and apacite as well.   I would really appreciate any help...


I have a cloud application which uses git and maven, so the source code is uploaded by Eclipse using GIT, and the required libraries are downloaded to the server by maven.  But I have one library not in maven, it's downloaded as a source and also run time jar, xxx.jar and xxx-source.jar.  When I upload the source, the reference libraries are not uploaded to the server, so the compile will fail on the server.  I could unzip it and package in the source folder and upload altogether.  However, is there a simpler way just to put the source.jar as part of the project so Eclipse can upload that jar file as part of the project to the GIT server? and then the server will use that jar for compile?

I'm just starting to use , (evaluating it, really) and I need to be able to quickly generate a  file for my application and a directory with all the dependencies (for example, lib) so that I can deploy those two to be run in a stand-alone manner.  Generating the JAR file with the proper manifest is easy, but I do not know how to get Maven to copy the dependencies for the current project into a lib directory that I can deploy.    Since this is for a stand-alone Java applications, I am not interested in deploying to a Maven repository, that is also fairly trivial, or at least easily googleable.  I've found out how to do everything except copy the dependent JAR files into some specified directory.  This is the workflow I'm looking for:  $ mvn clean $ mvn package $ cp -r target/{lib,myApp.jar} installLocation   Then, running myApp.jar from installLocation as a JAR file should "just work" regardless of my $CLASSPATH.  To try and pre-empt some answers:   I do have a Main-class: set, and it works fine. I've also set the classpath in the MANIFEST.MF, and that works fine too. I've found out how to use <classpathPrefix> and <classpathMavenRepositoryLayout> to make this work -- but only on my machine. (via: <classpathPrefix>${settings.localRepository}</classpathPrefix>)


I have a table with a column name that includes a single quote '. I do not manage this table so I cannot change the column name. How do I select a value from my query?  Example: $sql['This Column's Name']

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


I consulted some textbooks about string theory, but they only told me that the Nambu-Goto action and the Polyakov action is equivalent. So I searched relevant questions here and got some ways of derivation however I want to know relation between the two actions and lagrangian multiplier.

I've read that the Polyakov action using an intrinsic metric $h_{\alpha\beta}$  $$\tag{1} S_P ~=~ -\frac{T}{2}\int d^2 \sigma \sqrt{-h}h^{\alpha\beta} \partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu} \eta_{\mu\nu}$$  can be converted into the Nambo-Goto action containing the induced metric $\gamma_{\alpha\beta}$  $$\tag{2} S_{NG} ~=~ -T\int_{\tau_i}^{\tau_f} d\tau \int_0^{\ell} d\sigma \sqrt{-\gamma}.$$  How this conversion is done is not further explained in my book so my question is if somebody can give or point me to some more explicit hints how this can be done?


I pressed Ctrl + Alt + F1 (while I was logged in) and got the console interface.  After logging in, I wanted to go back to GUI, so I typed startx. It didn't work, so I pressed Ctrl + C and logged in and out a couple of times, and repeated the process, after which I typed sudo reboot to reboot computer.  After that, Ubuntu booted normally, but when I try to log into my account, it just returns me back to the login screen. I entered the console intreface again, tried pressing Ctrl + Alt + F1, but in vain. Logging in into other accounts including the guest account is successful, but I cannot log into my account.  Fortunately, I have cloned the entire HDD about a month ago, so should I restore the backup, or is there a quick solution? I'm not willing to do some advanced programming or so, because it would take much less effort to install some missing updates and some programs after the restore than to mend my system and make it unstable, if it's seriously broken. I also have all my data backed up on spideroak, so it's not a problem too. Please help. Thanks!

My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M


It is sometimes seen that people divide power series of two functions $f$ and $g$ to get the power series representation of $\frac{f}{g}$.  For example, $\tan x=\frac{\sin x}{\cos x}$, so compute $\frac{x-\frac{1}{3!}x^3+\frac{1}{5!}x^5-\cdots}{1-\frac{1}{2!}x^2+\frac{1}{4!}x^4-\cdots}$ as if it were two finite polynomials by long division, and get the quotient of first few terms, and see the pattern of what this whole power series are.  However, I haven't read any analysis books which mentioned the division of power series.  What justifies doing so? Why is it valid? Is there something we should be careful when doing this? Why we can do the traditional long divison on infinite terms polynomials?

I have this book Calculus, Ninth Edition by Varberg, Purcell, and Rigdon; there's a particular point of a theorem (and another line after that) about Infinite Series that I really don't understand. I quote from Section 9.7, Operations on Power Series:     Let $$f(x) = \sum_{n=0}^{\infty} a_n \cdot x^n$$ and $$g(x) =\sum_{n=0}^{\infty} b_n x^n$$, with both of these series converging at least for $|x| < r$.    If the operations of addition, subtraction, and multiplication are performed on these series as if they were polynomials, the resulting series will converge for $|x| < r$ and represent $f(x) + g(x)$, $f(x) - g(x)$, and $f(x) \cdot g(x)$, respectively. If $b_0 \neq 0$  the corresponding result holds for division, but we can guarantee its validity only for $|x|$ sufficiently small....We mention that the operation of substituting one power series into another is also legitimate for $|x|$ sufficiently small, provided that the constant term of the substituted series is zero.   What does it mean by "sufficiently small"? How do I find the limit of how large $|x|$ can be before divisions and substitutions between power series become invalid? My book doesn't go into detail on the exact nature of this restriction and doesn't include a proof of the theorem. If I were dividing one power series by another I don't really know what I should be looking for. I wasn't able to find information about convergence sets for a series generated by two power series divided by each other.


I am really unsure of how to answer this as I have tried taking out n and using the ratio lemma and am still confused!

I have two limit problems which are quite similar, so I've put them both into this post.   $((4^{10}+2^{n})^{\frac{1}{n}})$ $((3n^{2}+n)^{\frac{1}{n}})$   Attempt:  For 1, I'm not sure if this is permissible. I know that $\lim_{n \to \infty}(x^{n}+y^{n})^{\frac{1}{n}} = \max\{x,y\}$. Obviously $4^{10}$ is a constant so it's not quite in the same form, but I believe it is still okay to use this result, and so the limit is $2$.  For 2, I've got $((3n^{2}+n)^{\frac{1}{n}}) = (n(3n+1)^{\frac{1}{n}})$, but then I'm not too sure how to proceed.   I also thought of taking the log and proceeding that way, however in the notes I'm learning from they haven't covered l'hopital yet, so I'm trying to not use it.  Thanks.


A few months ago my iPhone was stolen... a few days ago I recieved a facetime call from a weird email at 4am so I didnt pick up then a message that says add +57(318)xxx-yyyy for iMessage and Facetime then it says This phone number was associated with the Apple ID (my email address) on Iphone (my Name)... What this means? Is the person who stole my iPhone?

Hello I received this notification, I would like to know what to do next if I do not know the MacBook Pro the notification is referring to?  I have checked my icloud and do not see this device in the list.  I have since changed the password to the icloud and my email.  Any direction would be helpful.   Thank you


Can we make changes in uk visa new application form for reapplying for tourist visa after refusal of visa? Do they compare previous application with the new application?      Additional info from comments which explain the corrective measures (edit by Gayot)  My college letter clearly says that i am enrolled in 4 years program and he has completed 3 years and 1 more year to go.I will also attach my exam results to prove the number of semesters i have cleared. The letter also says that i want to travel to uk during my vacation as the college is having holiday from 2 june to 4 july 2016 and the college has no objection. I have also attached bonafide letter from college. My Father has savings of 2900 pounds and mother has savings of 1600 pounds.  I have a joint account with my father worth 1500 pounds and we are also showing my fathers fixed deposits worth 12000 pounds. And public provident funds worth 5600 pounds in my name,fathers and mothers name combined.That should be enough?    For those having a problem with the poor resolution of the scan, it is all very standard formulae...  First dot point: she accepts that the cousin has the capacity to provide accommodation, but she needs to evaluate his (the applicant's) personal circumstances (standard text for sponsored applications)  Second dot point: she explains that he is a student with GBP 1k to spend, but she doubts his financial capacity is sufficient and notes that he did not provide sufficient evidence (standard text for student applicants).  Third dot point: she explains that the father sponsor is diving deep into his life savings to pay for the trip. (standard text for disproportionate expenditure)  Last dot point: based on all of that she thinks he will go underground and try to live in the UK (V 4.2 (a) & (c)) and moreover will become reliant on public funds (V 4.2 (e)). Text straight from the manual.  (edit by Gayot)

I applied for UK visa and was rejected on 16th June on the grounds that I have not provided documents to verify my personal circumstances.  I'm planning to reapply. My question is when completing the new application form can I change figures like my monthly income after taxes must correct what I have done wrong last time?


I was first denied the B1/B2 visa. On my second attempt, I was given the visa for 3 months with an annotation “CPA EXAM - Maryland.” I took the exam and, out of two parts, I passed one part. But, in the same interview, the officer had told me you have to attempt all four parts and I am giving you one chance.  I returned within the stipulated time. Since then, I have reapplied five more times for a visa (on average once a month) and I have not been given the visa.  One more thing: after coming back, I told the officer that I would like to stay for 5 months as I want to pass my remaining exams during the stay. Also, the officer misunderstood my results and he recorded as if I had failed the two parts.  In my last interrview, the visa officer told me to "try to change your circustances and apply after a long time.  What should I do?

Over the course of time here on TSE, I have observed individuals whose pattern of visa applications is best described as ''...     serial refusals - Two or more consecutive visa refusals issued by the same regime to the same person. Commonly for the same, or nearly the same, reasons. In some visa regimes Serial refusals can have a cumulative effect wherein the applicant's credibility is increasingly eroded, especially when the application pattern suggests a secondary agenda.   A common thread appears to be the need to visit the destination country (especially Schengen, the USA, or the UK) with a special sense of urgency. Also common in these cases are the following types of questions...   Should I just reapply once again? What are my chances? What can I do to improve my odds in the future? Can I somehow address the previous refusals to avoid them being a burden on all future applications? How can I break the pattern?      NB: This question is intended as a canonical about serial refusals. I have never been personally denied a visa.


I want to start a process which outputs to a text file. I want to be able to start it and have seperate button to stop it. I have tried using popen, exec, passthru but my understanding is they all wait till the process exits to return data to php? Is there any way i can just start  a process and leave it running. All i want returned is the pid. Here is what I have tried so far.  <?php $data=$_POST['data']; $args = escapeshellarg($data); $cmd = "./fw {$args}". " 2&>lg.log & echo $!"; passthru($cmd, $output);   $arr = array("pid"=>$output); echo json_encode($arr); /* $handle = popen('./fw {$args} 2>&1', 'r'); echo "'$handle'; " . gettype($handle) . "\n"; $read = fread($handle, 209600); echo $read; pclose($handle); */  ?>   Solution suggested in the linked question works with this  $cmd = "./fw {$args}". " >lg.log & echo $!"; exec($cmd, $output);   but if i want stderr redirect too and change it to  $cmd = "./fw {$args}". " 2&>lg.log & echo $!"; exec($cmd, $output);   it stops working. Then i get the return value for pid only after I kill the process.

I need to execute a directory copy upon a user action, but the directories are quite large, so I would like to be able to perform such an action without the user being aware of the time it takes for the copy to complete.  Any suggestions would be much appreciated.


I often need to edit my video and update the new version on YouTube, but on the same address.  It seems not possible, so is there a way maybe to create some automatic redirection feature from old to new address?

I need to make a small correction in a video I uploaded to YouTube. Googling shows that this is not possible. However, I remember seeing it done before. I posted a comment on a video saying that a certain part of the video was missing. I got a reply back that it was fixed, and when I went to see the video again, it was changed. How was this done?


If my teacher says :     "I am closing down all online assignments up to Module 3"    Is she closing Modules 1, 2, AND 3, or just Modules 1 and 2 ? Thanks everyone!

Consider the sentence: "The boxes must be filled up to the last box".  Does this mean 'including' the last box or all 'but' the last box?  If I ask you to start with 1 and count up to 8, you'll likely say "1,2,3,4,5,6,7,8".   But, if I lay a Black, Blue, Red and Yellow marker in front of you and ask you to start with the Black marker and take the caps off up to the Yellow marker. Do you take the cap off the Yellow marker?


I imagined a system of $n$ "things" that are ordered: each "thing" has a specific place. Also, the $n$th thing is the last thing in the system, meaning that there is always a "thing" to which number $1$ is assigned. Given such a system, we can "mess it up" — put things in wrong order. Now we must put them back. Like so (an example):    We see that in this case, we have a system $n = 5$. If all the "things" are in their spots, then the output of the function I wanted to deduce (but failed) is $0$. But if they are not, my "function" adds $1$ to its output for each place a misplaced "thing" must travel to get to its original location. In the above case, the output of function in order to "clean up the mess" is $8$.  The question is: for some system $n$ (where $n \in \mathbb{N}$), what is the maximum of the function $f$?  I already found $f_{\text{max}}$ for $n = 1$ ($f_{\text{max}}(1) = 0$), $n = 2$ ($f_{\text{max}}(2) = 2$) and $n = 3$ ($f_{\text{max}}(3) = 4$). But it is quite clear that this problem needs a different approach; bruteforce won't do any good. So, my main interest is to know what a formula for $f_{\text{max}}(n)$.  I am very eager to see the answer. I tackled a few hard problems, but this one (and the strange thing is that I made it up myself) is one tough cookie, at least for me.

For each permutation $\sigma$ of $ \left\{ 1, 2, \dots, n \right\}$ define  $$\operatorname{dist}(\sigma)=\sum_{i=1}^{n}\left| \sigma (i)-i \right|$$  For each $n\in\mathbb{N}$, I'm interested in finding the maximum value this function can score, namely $$M_n=\max_{\sigma\in D_n}\left\{\operatorname{dist}(\sigma)\right\}$$  Does $M_n$ has a conventional name? Uses? Is there a formula to find it?  I've noticed that $M_n$ grows "in pairs", meaning that for each odd $a\in \mathbb{N}$ it holds that $$M_{a+1}-M_a=M_{a+2}-M_{a+1}$$  I guess it can represent some kind of measure for hardness to sort.


I am confused about the notation.  What's the differences between $(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},0)\bigoplus  (0,\frac{1}{2})$, or maybe $(\frac{1}{2},0)\bigoplus  (\frac{1}{2},0)$ ?  (1) $so(1,3)=su(2) \bigoplus su(2)$ has different representations, I don't understand why  $(\frac{1}{2},\frac{1}{2})$ is irreducible, since we already have direct sum  $\bigoplus$ between two $su(2)$, and direct sum usually means reducible.   The Schwartz book (page 163) says $(\frac{n}{2},\frac{n}{2})$ These are each irreducible representations of the Lorentz algebra, but reducible representations of the $su(2)$ subalgebra corresponding to spin.  (2) The group elements are acting on some space, then $\bigoplus$ means the direct sum of these spaces, like $(\frac{1}{2},0)\bigoplus  (0,\frac{1}{2})$. Then what does $(\frac{1}{2},\frac{1}{2})$ means, a direction product $(\frac{1}{2},0)\bigotimes  (0,\frac{1}{2})$ ?

EDIT:  The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain unanswered.  The definition of a representation is a map (a homomorphism) to the space of linear operators over a vector space. My question is: What are the corresponding vector spaces for the   $(0,0)$ Representation $(\frac{1}{2},0)$ Representation  $(0,\frac{1}{2})$ Representation $(\frac{1}{2},0) \oplus (0,\frac{1}{2}) $ Representation $(\frac{1}{2},\frac{1}{2})$ Representation infinite dimensional Representation?


In a few of the kinematic equations there is a $2$ or a $0.5$ coefficient. Why is this?  For example the kinematic equation for distance is:  $$\text{previous velocity} * \text{time} + \frac{1}{2} * \text{acceleration} * \text{time}^2$$  But why the $\frac{1}{2}$?  If I use the equation for acceleration to get to that equation I don't have a $\frac{1}{2}$? Here:  $$\frac{\Delta v}{t} = a  | \cdot t$$  $$v_{new} - v_{old} = a \cdot t | + v_{old}$$  $$\frac{s}{t} = a \cdot t + v_{old} | \cdot t$$  $$s = a \cdot t^2 + v_{old} \cdot t$$  Are my calculations wrong? If so, could someone please show me where I went wrong or explain to me how the $\frac{1}{2}$ comes into play?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?


I have a problem with a data merge. On several tutorials if they selected the CSV file, all the data loads up separately but when I select the CSV file, all data loads like this:     So I can't load them up separately. What I'm doing wrong?  My steps:   make excel file with all my data  save this file save the CSV file open InDesign document select data source then I see this...

I am trying to import an Excel CSV into InDesign Data Merge. Everytime I try to export the csv, it appears in Data Merge as only one field, with fields separated by semicolons, although in Excel I have multiple, comma separated fields.  I've done this plenty of times and have never experienced this problem. I have checked the language and regional settings on my laptop and these are set as comma separated. I've tried to use a txt file version, but Indesign won't accept it. I am now very much stuck! any suggestions?


I have some measurement results (about 10000 or even more). How can I say (which methods should I use and how to apply them) to check if my data is time series or is a statistical sample?

I have some set of random data. I would like to check if this data constitute a time series. I know how to apply a simple moving average method to the data. But after applying it, how can I say if the data is time series or not?


Let $F|K$ be a field extension and $a \in F$ such that $[K(a):K]$ is odd integer,          then prove that $K(a)=K(a^2)$.

Let $K\subseteq K(\beta)$ be a finite  of odd degree. Does this imply $K(\beta)=K(\beta^2)$?


How would one potentially split the accounts that one owns in relation to the different Stack Exchange sites? I would like to separate one of them out from my other accounts (that is to say, remove it from my profile, but not actually delete it). My profile is linked to my Gmail account, so I sign into all my accounts using SSO. Apologies if this has been asked before.

I would like to unlink my  and  accounts from other Stack Exchange accounts. These accounts have some information to the incidents in my workplace and personal life which I would like to keep confidential to the group who knows my Stack Exchange ID and user name.   Many potential employers are also asking about my account name in Stack Exchange to assess my knowledge levels. I am happy to share my Stack Exchange,  and  accounts. At the same time I would like to keep my Workplace and Personnal Productivity accounts confidential as I see potential risk if they know incidents about my WorkPlace and Personal Productivity. Hence I would like to unlink these two accounts from other accounts. However, I learned from the post  that unlink is not possible.  Since unlinking is not possible, what are the possible alternatives to maintain separate accounts for Workplace and Personal Productivity?  Edits Based on answers: As per the answer of Knights who say Ni, I have tried to add more logins. How ever if I add login or remove login, this change is reflecting in all accounts. Hence as a result all of my accounts are linked to single login and single account.


I have only been a pokemon trainer for about two weeks, so I admit that I lack the experience of a veteran trainer. However, I have already defeated the eight gym leaders in my region (including my father!) and disrupted the criminal actions of a group of scientific thug fanatics.  Despite my obvious natural talent, I feel like I have made a blundering mistake. In my eagerness to save the world from the aforementioned apocalyptic extremist group, I defeated their cataclysmic Primal Groudon without a moments hesitation. It was then I realized the unfortunate selflessness of my actions--I should have captured the beast for my own use!  I returned to the Cave of Origins, but I can't find him in either of the two placed I confronted him earlier. Is there any way to re-encounter this leviathan, or have I entirely wiped the legend from the face of the earth?  Thanks in advance!

I've heard that legendary Pokemon such as Kyogre/Groudon respawn after you defeat the Elite Four (if you didn't catch them). The only information that I can find seems to relate to the original version of the game.  Can players faint legendary Pokemon in order to progress the story and come back later to capture them? And are there any exceptions?  The reasoning for this is some players, myself included, wish to finish the game in order to unlock post-game features before investing time/effort soft resetting for ideal natures in legendary Pokemon.  Please avoid spoilers where possible.


Do physicists know what the expansion rate of the Universe was at the beginning of the matter dominated era?

There is something I don't understand about the  $H$, as it seems to clump two concepts together that I can't quite unify in my head. On the one side, we have  $$V = D H$$  which means that for a given distance $D$, there is a certain amount of new space created over time - and $H$ is simply the factor that makes this relationship work. So, for example, say we have two points 1 Mpc apart, this would mean they recede at about 70 km/s away from each other  (given our current approximation of $H$).  Now the thing I can't wrap my head around is that   $$T =\frac{1}{ H}$$  is also the age of the universe. Contrary to claims made on, say, Wikipedia this means that $H$ cannot possibly have been a constant throughout the past 13 billion years, because mathematically $1/H$ means that $H$ must be continually shrinking as the universe ages.  So if $H$ did start out as some huge value and is now shrinking over time, doesn't this mean the expansion of the universe is slowing down? Because if $H$ is shrinking, I'll get a lower value of $V$ today than I'll get tomorrow. Shouldn't the notation then be more like  $$V = DH(t)$$  So which one is it? If $1/H$ is simply the solution for $D=0$, how can we use it as the expansion-velocity-per-unit-of-distance at the same time? What's worse, how can literature say $H$ has probably been more or less constant forever and simultaneously assert that $1/H$ is the current age of the universe? What am I missing?


I have fail2ban up and running, but my Failregex doesnt match anything, something is wrong.  Request which i like to ban look like this:  186.6.65.199 - - [06/May/2013:18:46:21 +0400] "GET / HTTP/1.1" 200 10488 "coolsearch37845.com/b/eve/618aef08...... 186.6.65.199 - - [06/May/2013:18:46:21 +0400] "GET / HTTP/1.1" 200 10531 "liteapps.mcafee.com....... 186.6.65.199 - - [06/May/2013:18:46:21 +0400] "GET / HTTP/1.1" 200 10531 "jfueznxchgsef.pl......   What i got so far:  /etc/fail2ban/filter.d/apache-attackers.conf :  failregex = <HOST> - - [[^]]+] "GET / HTTP/1.1"   /etc/fail2ban/jail.local :  [apache-attackers] enabled = true port    = http,https filter  = apache-attackers bantime = 25920000 logpath = /var/www/mysite/log/access.log maxretry = 2 findtime = 1   When i do a   fail2ban-regex /var/log/auth.log /etc/fail2ban/filter.d/apache-attackers.conf   i get  Failregex |- Regular expressions: |  [1] <HOST> - - [[^]]+] "GET / HTTP/1.1" | `- Number of matches:    [1] 0 match(es)   So my regex fails and it does not match anything.  I want to match any IP which requests "GET / HTTP/1.1" twice or more in 1 second.  What i am doing wrong ?

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


I'm referring to this question here:    At the time this question was answered, back in 2011, the term "Hydration" was new.  It is still very young now even, but the use of this term has matured somewhat.  Now it is clear that the fundamental part of the answer, that hydration is a synonym for deserialization, is patently false.  However by now almost three years later it has a bunch of upvotes and is the accepted answer.  This question comes up pretty prominently in google when you search on things like "hydrate an object".  I'm concerned that people visiting the site will see this and be misinformed.  I think it's important that people using StackOverflow to learn have confidence that they are learning correct things.  But this answer is not correct, and I'm concerned because it looks correct on the page.  What can we do to address something like this?  I have downvoted the answer and upvoted the correct answers below it, but there are still 15 votes on the accepted answer, and it is accepted, and only 6 on the next choice.  Is there anything else we can do to address something like this?  Edit: I have already communicated with the original poster of the answer, and he doesn't agree with me entirely.  He self-described himself as being "catty or combative" about it.  I do not believe a bounty is appropriate, as two people now (myself being one) have submitted answers below it which have garnered upvotes.  Ideally, I would just edit the answer to improve it, but I'm concerned that the original author will simply revert my changes.  So I'm just not sure the best approach here to deliver a good quality answer to google searchers without starting some kind of an edit war or confrontation.

Due to changes in technologies, many answers were outdated. However, these answers were very good for the past, and they might also be useful for the same cases, but not for most. An example is a depreciated  extension that was replaced with , and the older PHP date time function whose use should be replaced by the newer (PHP date time class).  I am putting myself in a scenario: I do all my best to answer a question, my answer will be accepted and upvoted, but after one year, someone might write a comment and say:     This is a bad answer, outdated.   This is ethically right, notifying about an outdated answer is not a bad thing, but I am sure we can do this in another way, that does not destruct the person, considering that the answer was good in the past. My aim in this discussion is: What is the best etiquette for doing that? Is there any systematic procedure to be taken for improving the quality of answers?  Another issue here is someone that is searching for an answer. In case that we post an updated answer to the question, it might not get any upvotes, and then the user will probably chose the one with a high number of upvotes (considering that it's peer reviewed).


McDonald's use "I'm lovin' it." slogan. As we all know that love is a stative verb and young people, too, use stative verbs in the continuous form. Can usage of 'ing' with Stative verbs grammatically correct?

My friend had a homework exercise about stative verbs in their English class and asked me to help with it. The task was to mark sentences that were correct. There was one difficult sentence there:     I am preferring fish to meat.   In the other column, there was the same sentence in Present Simple:     I prefer fish to meat.   To me, it looks like the sentences are both correct. The latter means "I always/usually prefer fish to meat", the former means "Right now I am choosing fish, not meat, while I could usually prefer meat to fish.".   So, can I use "prefer" as a dynamic verb, meaning something along the lines of "choose", not "like"?


I want to upgrade my laptop hard drive to one with more space.  I dont want to reinstall everything.  Can I "clone it" to a new drive so that the laptop doesnt know the difference ?  Can this be done ?  Thanks.

I'm upgrading my Windows 7 laptop to a new hard drive.  How can I clone or image the old hard drive over to the new hard drive, so that it looks like nothing has changed (other than the new hard drive) to my operating system and applications?  Can I use what is built into Windows 7 Backup or should I use something else?


This is the first time I've used a sugar daddy site and I have little idea what I'm doing. I was smart enough to set up a PayPal account so he wouldn't have any of my personal information. He set an amount at which he would send, assuming I "passed his tests". Then he asked me to start by sending $29 to his account manager's PayPal so he would have my information. Am I right to think this is a scam?

I met a guy on a sugar daddy dating site and we talked, I told him my situation and he said he would help.   He asked for my bank account information and I told him you can use cash app or PayPal to go through. He said his account manager deals with his finances. So I set up an account with a bank that I don’t use so that my primary account isn’t used.  Eventually he was in the process of sending me money and we had agreed on a amount that wasn't crazy. But then he asked for my address and I asked why and he said just wondering. Then said he wanted to send me a surprise for being his baby. Which I didn’t give.  Then later on he sent the money and said he sent me a bonus and that I was supposed to use that to pay his mothers caregiver, which he didn’t mention until after.  I kept questioning him and he was saying that he works in construction and he’s trusting me to carry out the errand. Then he said don’t let him down and I asked him if he was threatening me and he kept saying I need this done but didn’t really answer my question.  Am I being scammed? I’m about to change my password but is this a scam?


I'm not sure how to find the degree of the ratio $\frac{p(x)}{q(x)}$ of polynomials $p(x)$ and $q(x)$ when $\deg(q(x)) > \deg(p(x))$. I couldn't find an answer. For example, $\deg(p(x))=10$ and $\deg(q(x))=26$. Intuitively the degree of the ratio should be $-\infty$, and the degree of the remainder should be $10$.  Want to be sure if I'm right. Any help appreciated, thanks!

This might sound like a very trivial question but I found different answers on the web.     Assume one has a rational function $$\frac{f(x)}{g(x)} ,$$ where $f(x)$ and $g(x)$ are polynomials. What is the degree of the rational function?   Is it the maximum degree of $f$ and $g$? Or is it $\deg(f) – \deg(g)$?  Thanks


Let $X \sim \text{Uniform} ( -1,3)$.  Find the PDF of $Y= X^2$.   Solution: The  density of $X$ is $$f_x(x)  = \begin{cases}    \frac {1}{ 4} &  \text{if }  -1< x  < 3  \\ 0 & \text{otherwise} \end{cases} $$   $Y$ can only take values in $(0,9)$. Consider two cases: (i) $0 < y < 1$ and (ii) $1 < y < 9$. For case (i), $A_{y1} = [-\sqrt{y}, \sqrt{y}]$.  For case (ii) $A_{y2} = [-1,\sqrt{y}] $  $$F_Y(y) = \int _{A_{y1}} f_X(x)dx  =  (1/2)\sqrt {y} $$  $$F_Y(y) =  \int_{A_{y2}} f_X(x)dx   = (1/2)(\sqrt {y} + 1)$$  Differentiating $F$ we get    $$f_Y(y) =   \begin{cases}  \frac {1}{ \sqrt y } & \text{ if } 0 < y < 1  \\   \frac {1}{8 \sqrt y }  & \text{ if } 1 < y < 9 \\ 0 & \text{otherwise } \end{cases}$$   I don't get how the two cases were considered and then from those two cases limit of integrals $A_{y1} $ and $A_{y2} $ were calculated?

The continuous random variable $X$ has a $\text{Uniform}[-1, 3]$ distribution and let $Y = X^2$ .  Find the probability density function of $ Y$.    My attempt.  I know that it has to be between $0 < y < 1$. So $F(Y = y) = P(Y \leq y) = P(X^2 \leq y) = P(-\sqrt{y} \leq X \leq \sqrt{y}) = \frac{2\sqrt{y}}{3+1} = \frac{\sqrt{y}}{2}$  I'm not sure how to go forward from this


I have a line whose length is "a". Can anyone explain procedure of drawing following lines?  1-line whose length is "a^2"  2-line whose length is "sqrt(a)"

The author is trying to prove it is impossible to square a circle of radius $1$ under the assumption that $\pi$ is transcendental. Even with this assumption, the author explains that if the circle can be squared, then we could draw a line with distance $\pi^{1/2}$. Everything good at the moment. Then he claims that, if such construction is possible, we could also draw a line of distance $\pi$, and that the proof would, under the stated assumption, be complete.     The thing I don't get is how, from a line with distance $\pi^{1/2}$, we could create a line with distance $\pi$.


Is it possible to use sed to replace the entire example bracketed line below? I seem to be running into trouble finding out a delimiter to use since / and many other special characters exist in the actual line I want to replace. Line needing replacing: This is a random example since the actual line I want to use is much less friendly to the eyes. [...] <example>=(a,b,c);{!@#$%^&*?/};</example> [...]  If there is any tool better suited for this please let me know. Any help would be greatly appreciated.

Take the following script:  #!/bin/sh sed 's/(127\.0\.1\.1)\s/\1/' [some file]   If I try to run this in sh (dash here), it'll fail because of the parentheses, which need to be escaped. But I don't need to escape the backslashes themselves (between the octets, or in the \s or \1). What's the rule here? What about when I need to use {...} or [...]? Is there a list of what I do and don't need to escape?


I just got started on Stack Exchange. What happens to your reputation after deleting a question on a Stack Exchange website?  Do you lose the reputation associated with the deleted question? If yes: If you go below a privilege threshold, do you lose that privilege too?

What circumstances can cause a question or answer to be deleted, and what does that actually mean?    How can a post be deleted? When can't I delete my own post? Can I still see my post even after it's deleted? Can I see a list of my deleted posts? How can I undelete one of my posts? What does deletion mean for a post? How do votes to delete work? What are the criteria for deletion? What else should I know about deleted posts? If I flag my question with a request to delete it, what will happen?       For more information, see the articles about  and  in the .


When I try to hibernate my computer I receive 2 messages and computer turns off:   pnp_bus_resume+0x0/0X70 returns -19 PM: Device 00:08 failed to thaw error -19   Can something be done?  UPD: Thanks to the @minerz029 the message about free swap has disappeared. But computer still can't hibernate.

I have, by default, 250MB of swap space in Ubuntu, and I want to expand it to a larger size. I need 800MB, which I think will be enough to open several applications without having to hit the current limit of swap. I hope someone can help me.


I am learning programming for computer games and it seems i am struggling to work out an equation for a steering behaviour.  I have a vehicle that navigates around objects. Some times it has to take a really sharp turn and so has to slow down before it approaches this turn to take it without over/under steering. It may even need to stop completely whilst its rotating (like a tank would).  I am wondering how you can calculate the best approach speed to take a given corner/angle.  I have 3 properties for the vehicle, a max speed, an acceleration (same for increasing and decreasing the speed) and a rotation speed.  Is there any general equation that can help with this that i can then try to translate into code.

It is given here that the maximum safe speed of a vehicle on a banked road having coefficient of friction $0$, is $V =\sqrt{R g \tan \theta}$, where $\theta$ is the angle of banking. I can't understand how circular motion is possible without friction.


My 17-year-old daughter's passport expired on April 1, 2015. She is a U.S. citizen. I need to know if she will be allowed to across the border from Rochester, New York to Canada and back from Canada to Detroit. She has with her the expired passport and her original birth certificate, and will be traveling with her mother.

Is it possible to leave and re-enter the US through the land border with Canada with an expired (US) passport? My passport expired in December and I didn't realize that until now. In addition to the expired passport, I have my naturalization certificate and Tennessee issued drivers license to prove citizenship and residency. Re-entry will be by road from Canada.  UPDATE:  I made some calls and was told that I needed a passport -- I was told to contact the regional passport agency in New Orleans (about 6 hours by road for me) get an appointment and show up in person with proof of imminent travel outside the country. After searching on the web, I located a few agencies who claimed that they could help with this for a charge of around $199. I picked the one that had good reviews and they helped take care of the problem. On Monday they walked me through different documents they needed, asked me to go to a "Passport Verification" agent in a post office to get everything verified and sealed in an envelope, had to FedEx the package to them. On Tuesday they got it, processed the passport and shipped it back to me. I got it Wednesday. In all it cost me $170 (Govt Passport Fee) + $25 (Verification fee at the post office) + $199 (Agency charge) + $90 (Shipping). Glad i got this taken care of. Thanks to everyone who helped with responses.


Hi I am a newbie typesetting a book with the Memoir class (texlive 2014 and LyX).  I would like to place chapter titles on a (verso) page of their own, with the text of the chapter starting on the next recto page.  In the Memoir manual I found some mention of this with an example code, but given my lack of experience I don't seem to be able to achieve the desired result.  This is a sample document:  \documentclass{memoir}  \makeatletter \renewcommand\memendofchapterhook{% \clearpage\m@mindentafterchapter\@afterheading} \makeatother  \begin{document}  \chapter*{Three Worlds} Text of my chapter...  \end{document}   Supposedly that should start new page (\clearpage) after the chapter title, but it doesn't.  Can you please show me how to achieve my aim properly?  Many Thanks Martin

I'm writing a book using memoir, and I'd like each chapter's text to begin on a new page after the chapter headings (so each chapter heading stands on a page by itself).  Is there a way to make this automatic, so I don't have to add the \newpage command after each instance of \chapter{}?  I tried \renewcommand{\chapter{}}{\chapter{} \newpage}, but it doesn't seem to work...  Here is my MWE as it stands with my current chapter header customizations:  \documentclass{memoir} \usepackage[american]{babel}  % Chapter headers customize \setsecnumdepth{none} \setlength\beforechapskip{6\baselineskip} \renewcommand*{\chaptitlefont}{\sffamily \HUGE \bfseries}  \begin{document} \chapter{Chapter 1} My text. \end{document}


I'm not talking about Domino Effect or Murphy's Law, it's something else. I used to know it, but for the life of me, I can't seem to remember. Any help would be greatly appreciated. I think it was "something" effect. Lol. Please help guys or I won't be able to sleep tonight.

Something small goes wrong, and this triggers something slightly bigger, which triggers something slightly bigger, and so on and so forth until you end up with a chain of problems of increasing severity until it ends in catastrophy.  Something like the old saying "for want of a nail the battle was lost", only highlighting that each intermediate issue was a problem in its own right, not just a stepping-stone to the final disaster.  Is there a common word/phrase that specifically describes this? I'm thinking "cascade of ever-increasing problems", but this seems clumsy, and I suspect there might already be a neat word or expression that covers it.


I have been using sendmail as MTA & SquirrelMail for webmail. I used to have following setup to restrict recepient in SquirrelMail. SquirrelMail had a plugin called Recepientrestrictions which can check two php files   Config.PHP - contains list of different domains where my domain user can send mails (sysadmins & Directors of company can send mails to anybody) recepientrestrictions.php - contains list of specific addresses such as user@gmail.com or user1@yahoo.com to whom my domain user can send mail.(again sysadmin & Directors of company can send mails to anybody)   Now the problem is:  I am migrating to Zentyal as email server. Zentyal uses Postfix in background & Roundcube for webmail.  I have got a partial solution which is a general rule for all users in my domain (couldn't seperate sysadmin/ directors to send mail to anybody on internet)  which restricts mails delivered to specific domains which is as follows.    Add this into main.cf:   smtpd_recipient_restrictions = check_recipient_access              hash:/etc/postfix/recipient_domains, reject   /etc/postfix/recipient_domains is the whitelist file:   mycompany.com OK  anotherdomain.com OK   Generate hash file: postmap /etc/postfix/recipient_domains Restart postfix service.    Even after this it doesn't block a mail sent to anybody@gmail.com or anybody@yahoo.com . Also I want to enable sending mail to few mail id's on webmail providers with the help of a whitelist file. e.g.  somebody@gmail.com OK somebody@yahoo.com OK foo@gmail.com OK   In short the scheme is :   Group1 sends mail to anybody on the planet. Group2 sends mail thro' two whitelists 1) domain wise 2) specific users of webmail.   Question is how to achieve this scheme?

I want to configure postfix to only send mail to addresses in a whitelist. I have tried to use smtpd_recipient_restrictions in main.cf like so:  smtpd_recipient_restrictions =     reject_unauth_destination     check_recipient_access hash:/path/to/whitelist   The whitelist file is of the format  address@example.com    OK another@example.com    OK   And then translated into a hash with the postmap command.   Still, the relay is sending mail to non-whitelisted addresses. What am I missing?  Edit: I am sending this mail via the sendmail command, which apparently bypasses the smptd restrictions. Is there a way to deal with this?   Edit 2/The rest of the story: I spent quite a bit of time trying to make sendmail send via SMTP only to discover the command I was using was not sendmail, but postfix's sendmail compatibility interface which mimics functionality but can't be told to use SMTP as far as I could tell.   84104's solution worked perfectly though.


I found this command used to find duplicated files but it was quite long and made me confused. For example, If i remove -printf "%s\n", nothing came out. Why was that? Besides, why they used xargs -I{} -n1?  Is there any easier way to find duplicated files?  [4a-o07-d1:root/798]#find -not -empty -type f -printf "%s\n" | sort -rn | uniq -d | xargs -I{} -n1 find -type f -size {}c -print0 | xargs -0 md5sum | sort | uniq -w32 --all-repeated=separate 0bee89b07a248e27c83fc3d5951213c1  ./test1.txt 0bee89b07a248e27c83fc3d5951213c1  ./test2.txt

Is it possible to find duplicate files on my disk which are bit to bit identical but have different file-names?


I have tried multiple things that were used in earlier versions but they no longer work as commands have changed a lot so I was wondering how I can delay them for my adventure map

I found 11 questions like this on gamingSE already, but none of them have proper and up-to-date answers. So I'm creating this Q&A:  How do you either activate a command x seconds/minutes/hours/… in the future or every x seconds/minutes/… in a loop?  Repeating command blocks and ticking functions execute 20 times per second, redstone is  in many situations and most of the extremely fancy solutions, like falling blocks in cobwebs, have broken over time or are needlessly complicated.


So my professor talked about one example of improper integrals and I'm having difficulty understanding the general proof outline for proving convergence.   I was given the problem to prove that $$f(x) = \begin{cases} \frac{\sin x}{x}, & x>0 \\ 1, & x=0 \end{cases}$$ converges . The proof then goes like (proof is in blockquotes and my question/comments follow underneath it):     $f$ is continuous at $x \ \forall \ x >0$ and $f$ is continuous at $x=0$.   My question: I know how to show continuity with the epsilon-delta argument, but other than that how can I tell if something is continuous? Specifically for this case, why do we have continuity for all $x>0$ and $x=0$?      Therefore $f$ is RI on $[a,b] \ \forall \ b>0$. In particular, $f$ is RI on $[0,1]$. So $\displaystyle \int_0^{\infty} f(x) dx$ converges iff $\displaystyle \int_1^{\infty} f(x)dx$ converges.   I'm guessing that this is from the comparison test for improper integrals where if $|f(x)| \leq g(x)$ then $\displaystyle \int_a^{\infty} g(x) dx$ converges. Clearly the integral from $1$ to infinity is smaller than the integral from $0$ to infinity.     And so we look at   \begin{align*} \lim_{b \rightarrow \infty} \int_1^{b} \frac{\sin x}{x} dx &= \lim_{b \rightarrow \infty} \left[-\frac{1}{x} \cos x\right]_1^{b} - \int_1^{b} \frac{\cos x}{x^2} dx \\ &= \lim_{b \rightarrow \infty} \left(\frac{-\cos b}{b} +\cos(1)\right) - \int_1^{\infty} \frac{\cos x}{x^2} dx. \end{align*}   I understand this is done by integration by parts.      Finally, we have that $\displaystyle \int_1^{\infty} \frac{\cos x}{x^2} dx$ converges because $\displaystyle \left|\frac{\cos x}{x^2}\right| < \frac{1}{x^2}$ and $\displaystyle \int_1^{\infty} \frac{1}{x^2}$ converges.   Does $\displaystyle \int_1^{\infty} \frac{1}{x^2}$ converge from the fact that $\displaystyle \sum \frac{1}{n^p}$ converges if $p>1$?

In  wikipedia article for improper integrals,  $$ \int_0^{\infty}\frac{\sin x}{x}dx $$ is given as an example for the integrals that have an improper Riemann integral but do not have a (proper) Lebesgue integral. Here are my questions:   Why does this one have an improper Riemann integral? (I don't see why $\int_0^a\frac{\sin x}{x}dx$ and $\int_a^{\infty}\frac{\sin x}{x}dx$ converge.) Why doesn't this integral have a Lebesgue integral? Is it because that $\frac{\sin x}{x}$ is unbounded on $(0,\infty)$ and Lebesgue integral doesn't deal with unbounded functions?


This is probably going to turn out to be an embarrassment for me (took me an hour to get the courage to post this), but I can't figure this out.  Using the , we have $$\mathbb R^3=\big\{(x_1,x_2,x_3); x_1,x_2,x_3\in \mathbb R \big\}$$ $$\mathbb R^2=\big\{(x_1,x_2); x_1,x_2\in \mathbb R \big\}$$ $$\mathbb R^2 \times \mathbb R^3 = \big\{\big((x_1,x_2),(x_3,x_4,x_5)\big); (x_1,x_2) \in \mathbb R^2, (x_3,x_4,x_5) \in R^3 \big\} $$  Which does not seem to be equal to $\mathbb R^5$, which has $(x_1,x_2,x_3,x_4,x_5)$ as elements instead of ordered pairs of 2-tuples and 3-tuples.  Please make the universe functional again, thanks!

I have a basic doubt about the associativity of the cartesian product. Well, first wikipedia says that the cartesian product isn't associative, and there's a good argument for it: if $x\in E$, $y\in F$ and $z \in G$ the identity $((x,y), z)=(x,(y,z))$ would imply that $(x,y) =x$ and $(y,z) = z$ so that $((x,y),z)=(x,y,z)$ would mean nothing.  That's fine, I like this argument. However, in his book Calculus on Manifolds, Spivak says that the cartesian product is associative. He says: if $A \subset \mathbb{R}^m$, $B\subset \mathbb{R}^n$ and $C \subset \mathbb{R}^p$ then $(A\times B)\times C = A \times (B \times C)$, and both of these are denoted simply by $A \times B \times C$.  Well, this confuses me because Spivak is always very rigorous, so that he wouldn't state something that's not true in such way. Is Spivak or Wikipedia right ? Or Spivak's statement only works for subsets of euclidean spaces ?  Thanks in advance and sorry if this question is too basic.


Ignoring the reduction in fuel weight as it burns, does the weight on a car's wheels decrease with increasing speeds? If so, by how much and is there a fomula for calculating that?  At what speeds does it then become zero?

I've been researching the physics involved with spoilers and I've just been turning up the same information about spoilers giving the back wheels of a car more traction by acting as an up side down airfoil.   So my question is, what exactly causes the car to apparently gain lift while moving quickly, so as to merit the use of a spoiler, and is this entirely due to the aerodynamics of the vehicle in question?   Edit: Clarity of question.


I recently bought a DnD 5e starter set and with it came the adventure book of the Lost Mine of Phandelver. It had a few maps with it. Now the problem is, I'm not sure how I should get those maps on a separate physical grid.

I have a bunch of different ways I use to make maps for my tabletop game.  Sometimes I draw one on graph paper.  Sometimes I use .  Sometimes I copy a map from a published adventure or use the  random generators.  These all have the same output:  a piece of paper (or maybe two) with a map on it, and the map is usually quarter inch squares, or so.  When it's time to put minis on a mat, though, I need to copy over the relevant details of the map to our battle mat.  (We use Tact-Tiles.)  This is fine when most of our map is overland detail and I'm just copying down one or two rooms in which combat will occur.  For dungeon crawls, where there are more random encounters or where combat can chase through many rooms, it can lead to a pretty tedious drawing of the whole dungeon as we go.  I feel foolish for having to ask, but is there some trick, technique, or something to make it less tedious to transcribe maps from printed pages to the battle mat?  EDIT:  Answers in general are great, but I should note that the best answers, for me, will be informed by this previously-unmentioned fact:  the game venue is not my house, so I have limited prep time on site.


I am trying to install ubuntu-desktop on 14.04 but when I run apt-get install ubuntu-desktop it gives error:  Some packages could not be installed. This may mean that you have  requested an impossible situation or if you are using the unstable  distribution that some required packages have not yet been created  or been moved out of Incoming.  The following information may help to resolve the situation:  The following packages have unmet dependencies:  ubuntu-desktop : Depends: ubuntu-session but it is not going to be installed  E: Unable to correct problems, you have held broken packages."   With synaptic, it shows red mark on this package. I tried with apt-get clean as well as apt-get update but no success.

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


I think I asked a question about 21 hours ago. It is my second questions in Philosophy Stack Exchange (I asked more, but they were deleted). But in 'Network profile' in the 'accounts' tab it shows '1 questions' in the Philosophy part. Is something wrong with my account?

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


Some people are named "Dick". What does "Dick" mean when it is a name?

How did Peter, the surname, Johnson, and the nicknames for William(Willy) and Richard(Dick), come to mean penis?  Was the first instance of these usages, related to a specific person?  Are there more examples in this area? Is this exclusive to English?


How can I prove that: $\operatorname{trace}(A^\top B) > \sum_i -\sigma_i(A)\sigma_i(B) $

Let $A,B$ have the appropriate size. How can we show Von Neumann Trace inequality $ \text{Tr}(AB) \leq \sum_{i=1}^n \sigma_{A,i}\sigma_{B,i} $?  Also, what is the intuition behind this inequality?


As you all know, when we study analytical mechanics and similar courses, the phase space representation is always employed. It's of course a nice representation to see how particles and things are behaving, but I'm wondering, what is the necessity behind a phase space representation? In other words, why do we truly use it and do we actually need it? I hope my question doesn't sound stupid and you get what I mean.

I've just finished a Classical Mechanics course, and looking back on it some things are not quite clear. In the first half we covered the Lagrangian formalism, which I thought was pretty cool. I specially appreciated the freedom you have when choosing coordinates, and the fact that you can basically ignore constraint forces. Of course, most simple situations you can solve using good old $F=ma$, but for more complicated stuff the whole formalism comes in pretty handy.  Then in the second half we switched to Hamiltonian mechanics, and that's where I began to lose sight of why we were doing things the way we were. I don't have any problem understanding the Hamiltonian, or Hamilton's equations, or the Hamilton-Jacobi equation, or what have you. My issue is that I don't understand why would someone bother developing all this to do the same things you did before but in a different way. In fact, in most cases you need to start with a Lagrangian and get the momenta from $p = \frac{\partial L}{\partial \dot{q}}$, and the Hamiltonian from $H = \sum \dot{q_i}p_i - L$. But if you already have the Lagrangian, why not just solve the Euler-Lagrange equations?  I guess maybe there are interesting uses of the Hamiltion formalism and we just didn't do a whole lot of examples (it was the harmonic oscillator the whole way, pretty much). I've also heard that it allows a somewhat smooth transition into quantum mechanics. We did work out a way to get Schrödinger's equation doing stuff with the action. But still something's not clicking.  My questions are the following: Why do people use the Hamiltonian formalism? Is it better for theoretical work? Are there problems that are more easily solved using Hamilton's mechanics instead of Lagrange's? What are some examples of that?


Installing Ubuntu 20.10, but do not have any network other than Wi-Fi. Please, can anyone assit me to find the root cause to use a nic ???  there is no /etc/network/interfaces file /etc/resolv.conf contains  nameserver 127.0.0.53 options edns0 trust-ad   sudo lshw -class network shows the following lines    *-network                         description: Wireless interface        product: Wi-Fi 6 AX201        vendor: Intel Corporation        physical id: 14.3        bus info: pci@0000:00:14.3        logical name: wlo1        version: 00        serial: f8:e4:e3:81:e0:f2        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical wireless        configuration: broadcast=yes driver=iwlwifi driverversion=5.8.0-31-generic firmware=55.d9698065.0 QuZ-a0-jf-b0-55.u ip=10.0.0.69 latency=0 link=yes multicast=yes wireless=IEEE 802.11        resources: irq:16 memory:53514000-53517fff   *-network UNCLAIMED        description: Ethernet controller        product: RTL8125 2.5GbE Controller        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:05:00.0        version: 05        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix vpd cap_list        configuration: latency=0        resources: ioport:3000(size=256) memory:53300000-5330ffff memory:53310000-53313fff   lspci show the following lines  00:00.0 Host bridge: Intel Corporation Device 9b33 (rev 05) 00:01.0 PCI bridge: Intel Corporation Xeon E3-1200 v5/E3-1500 v5/6th Gen Core Processor PCIe Controller (x16) (rev 05) 00:12.0 Signal processing controller: Intel Corporation Comet Lake PCH Thermal Controller 00:14.0 USB controller: Intel Corporation Comet Lake USB 3.1 xHCI Host Controller 00:14.2 RAM memory: Intel Corporation Comet Lake PCH Shared SRAM 00:14.3 Network controller: Intel Corporation Wi-Fi 6 AX201 00:16.0 Communication controller: Intel Corporation Comet Lake HECI Controller 00:17.0 RAID bus controller: Intel Corporation SATA Controller [RAID mode] 00:1b.0 PCI bridge: Intel Corporation Comet Lake PCI Express Root Port #17 (rev f0) 00:1b.4 PCI bridge: Intel Corporation Comet Lake PCI Express Root Port #21 (rev f0) 00:1c.0 PCI bridge: Intel Corporation Device 06b8 (rev f0) 00:1c.4 PCI bridge: Intel Corporation Device 06bc (rev f0) 00:1d.0 PCI bridge: Intel Corporation Comet Lake PCI Express Root Port #9 (rev f0) 00:1d.4 PCI bridge: Intel Corporation Device 06b4 (rev f0) 00:1f.0 ISA bridge: Intel Corporation Device 0685 00:1f.3 Audio device: Intel Corporation Comet Lake PCH cAVS 00:1f.4 SMBus: Intel Corporation Comet Lake PCH SMBus Controller 00:1f.5 Serial bus controller [0c80]: Intel Corporation Comet Lake PCH SPI Controller 01:00.0 VGA compatible controller: NVIDIA Corporation TU117 [GeForce GTX 1650] (rev a1) 01:00.1 Audio device: NVIDIA Corporation Device 10fa (rev a1) 02:00.0 Non-Volatile memory controller: Samsung Electronics Co Ltd NVMe SSD Controller SM981/PM981/PM983 05:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8125 2.5GbE Controller (rev 05) 06:00.0 Non-Volatile memory controller: Samsung Electronics Co Ltd NVMe SSD Controller SM981/PM981/PM983  thanks in advance. Regards Rainer

So I did a fresh install of Ubuntu 20.04 on a computer with the new RTL8125B Realtek network card and I cannot get the network to work. I was very suprised since this is supposed to be the new feature of the 5.4 kernel (I have 5.4.0-26-generic installed). Does anyone have any idea on how to get it working? Thank you. $ lspci -knn | grep Eth -A3 06:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8125 2.5GbE Controller [10ec:8125] (rev 04) Subsystem: ASUSTeK Computer Inc. RTL8125 2.5GbE Controller [1043:87d7] Kernel modules: r8169 07:00.0 VGA compatible controller [0300]: Advanced Micro Devices, Inc. [AMD/ATI] Ellesmere [Radeon RX 470/480/570/570X/580/580X/590] [1002:67df] (rev e7)  $ dmesg | grep -i r8169 [    0.911236] r8169 0000:06:00.0: unknown chip XID 641


I have seen way of querying in many ways but does that really make a difference or its  just a way of coding  List<CustomObj__c> CustObj = new List<CustomObj__c>(); CustObj = [Select id, Name, CustField1__c, CustField2__c from CustomObj__c];   And  for(CustomObj__c i : Select id, Name, CustField1__c, CustField2__c from CustomObj__c){}   Is there a difference or just a way of writing a code.

Some of code I read in trigger is like this    for(account a: [select id  from account where id in: mapAccount.keySet()]) {     //code      }    some are like   List<Account> listAccount = [select id  from account where id in: mapAccount.keySet()];   for(Account a: listAccount ){   //coode   }   Are those same from performance view?which one is better?


I've been try to make my content stay centred at all time. I have the width centred with: text-aligned, but I can't figure out how to vertically centre my content. Here is the code for the element:  HTML:

HELLOWORLD

CREATED BY JOHN DOE
     <button class="btn">Signup</button>
   CSS:   .content {   text-align: centre; }  .content h1{   color: white;   font-family: NoveBold;   font-size: 150px;   line-height:94% }  .content p{   color: white;   font-family: NoveLight;   font-size: 30px; }  .content img{ }  .content btn { }   Does anyone know a fix on how to automatically vertically align this content so its centred on the page?

I want to center a div vertically with CSS. I don't want tables or JavaScript, but only pure CSS. I found some solutions, but all of them are missing Internet Explorer 6 support.
Div to be aligned vertically
   How can I center a div vertically in all major browsers, including Internet Explorer 6?


I have a variable '2019-05-30 21:01:09' that needs to be converted into 2019-05-30 21:01:09. What is the best way to go about this.

I've got a huge list of date-times like this as strings:  Jun 1 2005  1:33PM Aug 28 1999 12:00AM   I'm going to be shoving these back into proper datetime fields in a database so I need to magic them into real datetime objects.   This is going through Django's ORM so I can't use SQL to do the conversion on insert.


Sci-fi/time traveller cartoon from the early to mid 2000's.  The plot goes like this:  A time traveler was in some sort of training mission. Whilst he was on this mission he witnesses this girl that was going to get killed (I think this was taking part during the French Revolution). He saves the girl but it somehow causes the Earth to just disappear as if it had never existed. After this they go on an journey to find out what happened.     I remember seeing it when I was growing up in Portugal and I think it either aired on .

I scarcely remember this animated series.  The gist of it is in the title: Earth vanishes (I can't remember the reason now but it was probably explained) and the only surviving humans were two astronauts on an interstellar spaceship. They decide to explore space and meet up with different aliens, hoping that one day they'll find out what happened to Earth.


I've recently discovered Bayesian statistics, currently I am experimenting with Openbugs, yet I cant grasp the concept of what happens with the inputted data. I understand mcmc, yet all of examples I've seen were connected with some sort of integration, not the actual fitting of model to data.  Can someone explain to me, what happens with the inputted data in context of Gibbs Sampler?  Thank you.

Maybe the concept, why it's used, and an example.


I need to get name and supervisor name  Table name:user  id | name | -----------  1 | David   2 | Frank  3 | Shane  4 | Franchich   Another table name: details  user_id | supervisor_id| ----------------------------   1 | 4   2 | 3   3 | 4   I have tried like :  select      name as user name  from user, details  WHERE details.user_id=user.id    but failed   Now I want to get result like  User Name | Supervisor Name ------------------------------ David | Franchich Frank | Shane Shane | Franchich   So how is it possible ?

I have 2 tables. One (domains) has domain ids, and domain names (dom_id, dom_url).  the other contains actual data, 2 of which columns require a TO and FROM domain names. So I have 2 columns rev_dom_from and rev_dom_for, both of which store the domain name id, from the domains table.  Simple.  Now I need to actually display both domain names on the webpage. I know how to display one or the other, via the LEFT JOIN domains ON reviews.rev_dom_for = domains.dom_url query, and then you echo out the dom_url, which would echo out the domain name in the rev_dom_for column.  But how would I make it echo out the 2nd domain name, in the dom_rev_from column?


I have been trying to get back to work for several years now. I'm an architect (or was) with children and where I am they don't cater for long hour day care facilities. So here we are me over sharing and still seven years later still without a job. I like photographing things. I own a canon Rebel TSi 550D. It's a superficial hobby. Superficial in the sense that it's genuine just lacks the proper knowledge and understand of the various AV TA ISO combinations. Can you kindly please point me to good website good techniques, anything that can expand my knowledge with photography. I need a good place to start.

What are good resources (tutorials/books/videos/etc) for a beginning photographer?  Keep in mind that this is for a beginning photographer, who has recently moved from a point-and-shoot to an entry-level DSLR, and is interested in digging deeper into photography in general.  Examples of good topics for the resources to cover:   what's aperture?, and other camera basics  color temperature and lighting composition and visualization etc.


Let's say I have a thread including while loop and I want to stop it "from outside".  public class MyThread extends Thread {      private boolean running = true;      @Override     public void run() {         while (running) {             // do something         }     }      public void setRunning(boolean running) {         this.running = running;    } }   And here is the Main class:  public class Main {     public static void main(String[] args) {         MyThread mt = new MyThread();         mt.start();         // do something         mt.setRunning(false);     } }   It seems to be stopping properly, but I have read that the boolean should be also volatile. Why? Will it quicken the stopping?

At work today, I came across the volatile keyword in Java. Not being very familiar with it, I found . Given the detail in which that article explains the keyword in question, do you ever use it or could you ever see a case in which you could use this keyword in the correct manner?


In an inner product space,  $\langle x,y \rangle + \langle y,x \rangle = 2\operatorname{Re}\langle x,y \rangle$  and  $\langle x,-y \rangle + \langle -y,x \rangle = -2\operatorname{Re}\langle y,x \rangle$  Why are these two identities true? What is the significance of writing Re instead of leaving the sum as $\langle x,y \rangle + \langle y,x \rangle$?

What are the benefits of using a conjugate linear inner product in a complex vector space vs a simple linear inner product?  That is, why do we demand that $(y,x) = \overline{(x,y)}$ as opposed to $(y,x)=(x,y)$?  Of course, this ensures that $(x,x)$ is real and thus makes an easy definition of norm, but is that necessary?


My old graphics card hase just died. So I ordered a new MSI Radeon HD6450. What is the best way to install the AMD drivers?  Thank you.  Regards,  Richard

I am planning on doing a fresh install of Ubuntu and want to know what is the correct way to install ATI Catalyst Video Driver?      There are multiple valid answers for this question spanning over several versions of Ubuntu. For your convenience an index of each below:


NOTE: I am reposting this question as this was , claimed being a duplicate. However, please note that this is not, as the question doesn't at all talk of how the statement holds if we assume the alternative definition below, which is entirely what I ask. Before closing this again, please look carefully.  I am studying Abraham and Marsden's Foundations of Mechanics. They define a covering $\{U_\alpha\}$ of a set $S$ to satisfy $S = \bigcup_\alpha U_\alpha$, and NOT $S\subseteq\bigcup_\alpha U_\alpha$. Their definitions of compactness of a topological space, and its subsets (involving the relative topology) are the usual ones. Then they casually remark  It follows easily that a closed subset of a compact space is compact.  However, I'm not able to prove this with the given definition of cover. (I can prove it using the latter definition though.) I'm even skeptical if that holds with the given definition.  Got an answer! User Vercassivelaunos's comment below answers the question.

I am studying Abraham and Marsden's Foundations of Mechanics. They define a covering $\{U_\alpha\}$ of a set $S$ to satisfy $S = \bigcup_\alpha U_\alpha$, and NOT as $S\subseteq\bigcup_\alpha U_\alpha$. Their definitions of compactness of a topological space, and its subsets (involving the relative topology) are the usual ones. Then they casually remark  It follows easily that a closed subset of a compact space is compact.  However, I'm not able to prove this with the given definition of cover. (I can prove it using the latter definition though.) I'm even skeptical if that holds with the given definition.  I really don't think that this is a duplicate!


I'm trying to get a user's proxy information using a simple TK GUI with the following code:  def getProxyCredentials(proxy, username, password):     root = Tk()      #define the entry boxes for username password and proxy     proxyBox = Entry(root)     proxyBox.insert(0, 'some.default.proxy:8080')     userBox = Entry(root)     pwdbox = Entry(root, show = '*')     Label(root, text = 'Proxy Server').pack(side = 'top')     proxyBox.pack(side = 'top')     Label(root, text = 'Username').pack(side = 'top')     userBox.pack(side = 'top')     Label(root, text = 'Password').pack(side = 'top')     pwdbox.pack(side = 'top')      def onokclick():         proxy = proxyBox.get()         username = userBox.get()         password = pwdbox.get()         root.destroy()         return None      Button(root, command=onokclick, text = 'OK').pack(side = 'top')     root.mainloop()     return True   When I call the function outside, all the string fields do not change.  proxy = '' username = '' password = ''  getProxyCredentials(proxy, username, password)   The passed in variables are still blank even though they are assigned within the function. Strings are passed by reference, so they should no longer be blank. What am I missing/not doing correctly?

How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access?


I am using beamer overlays within tikz nodes, which yields the  expected result, except for a growing indent.   Here is a minimalistic example showing the behaviour.  \documentclass{beamer} \usepackage[utf8]{inputenc} \usepackage{tikz} \usepackage{blindtext} \begin{document} \begin{frame}   \begin{tikzpicture}     \path[draw] (1,0) -- (1,2);     \node [text width=3cm, anchor=west] at (1,1) {       \only<1>{Here}       \only<2>{There}       \only<3>{Away}     };   \end{tikzpicture} \end{frame} \end{document}   This results in the text moving across the slides:    I did not expect or intend this. Any help towards avoiding this behaviour is appreciated.

My document has lots of extra whitespace appearing between various elements. The problems appear around one macro which appears multiple times. After every line in the macro, I've placed %'s, however, extra white spaces are still appearing.   What method can I use to track what is causing these white spaces? Is it possible that items such as ifstrequal (from etoolbox), macros referenced inside macros,  mathmode-textmode switching, glossary entries, \pageref's and other cross-referencing and labeling commands. or indented space before code will cause these problems?


I am confused about the expression "fixed effect" in the context of mixed models. I am more familiar with the terms like "fixed effects" and "random effects" in context of econometrics and the analysis of panel data.  The understanding of "random effects" seems similar in both disciplines and the "random effects model" in econometrics is equivalent to a "mixed model with random intercept". See for example:   But what is about the "fixed effect". In econometrics, with the help of fixed effects e.g. all time invariant effects will be absorbed. Or in other words, a dummy variable for each individual is introduced.  But, what is "fixed effect" in context of mixed models? In simple words? Hereby, I mean more the intuition and not the mathematically way.  It is not the same as a fixed effect in econometrics. That is what I understand, but I have no clue what it is instead.  EDIT:  Meanwhile I found this explanation in context of mixed models:  "The fixed effects are analogous to standard regression coefficients and are estimated directly."  This means to me, that a fixed effect in mixed models is not the same as fixed effects in econometrics. Or in other words: Fixed effects are the variables that are not declared as random effects (--> standard regression coefficients as in linear regression).  Source (slide 2):

I used to think that "random effects model" in econometrics corresponds to a "mixed model with random intercept" outside of econometrics, but now I am not sure. Does it?  Econometrics uses terms like "fixed effects" and "random effects" somewhat differently from the literature on mixed models, and this causes a notorious confusion. Let us consider a simple situation where $y$ linearly depends on $x$ but with a different intercept in different groups of measurements:  $$y_{it} = \beta x_{it} + u_i + \epsilon_{it}.$$  Here each unit/group $i$ is observed at different timepoints $t$. Econometricians call it "panel data".    In mixed models terminology, we can treat $u_i$ as  a fixed effect or as a random effect (in this case, it's random intercept). Treating it as fixed means fitting $\hat \beta$ and $\hat u_i$ to minimize squared error (i.e. running OLS regression with dummy group variables). Treating it as random means that we additionally assume that $u_i\sim\mathcal N(u_0,\sigma^2_u)$ and use maximum likelihood to fit $u_0$ and $\sigma^2_u$ instead of fitting each $u_i$ on its own. This leads to the "partial pooling" effect, where the estimates $\hat u_i$ get shrunk toward their mean $\hat u_0$.  R formula when treating group as fixed:    y ~ x + group R formula when treating group as random:   y ~ x + (1|group)  In econometrics terminology, we can treat this whole model as a fixed effects model or as a random effects model. The first option is equivalent to the fixed effect above (but econometrics has its own way of estimating $\beta$ in this case, called "within" estimator). I used to think that the second option is equivalent to the random effect above; e.g. @JiebiaoWang in his highly upvoted answer to  says that      In econometrics, the random-effects model may only refer to random intercept model as in biostatistics    Okay --- let us test if this understanding is correct. Here is some random data generated by @ChristophHanck in his answer to  (I put  for those who do not use R):    @Christoph does two fits using econometrics approaches:    fe <- plm(stackY~stackX, data = paneldata, model = "within") re <- plm(stackY~stackX, data = paneldata, model = "random")   The first one yields the estimate of beta equal to -1.0451, the second one 0.77031 (yes, positive!). I tried to reproduce it with lm and lmer:  l1 = lm(stackY ~ stackX + as.factor(unit), data = paneldata) l2 = lmer(stackY ~ stackX + (1|as.factor(unit)), data = paneldata)   The first one yields -1.045 in perfect agreement with the within estimator above. Cool. But the second yields -1.026, which is miles away from the random effects estimator. Heh? What is going on? In fact, what is  plm even doing, when called with model = "random"?  Whatever it is doing, can one somehow understand it via the mixed models perspective?  And what is the intuition behind whatever it is doing? I read in a couple of econometrics places that random effects estimator is a weighted average between the fixed effects estimator and the "between" estimator which is more or less regression slope if we do not include group identity in the model at all (this estimate is strongly positive in this case, around 4.) E.g. @Andy :     The random effects estimator then uses a matrix weighted average of the within and between variation of your data. [...] This makes random effects more efficient[.]   Why? Why would we want this weighted average? And in particular, why would we want it instead of running a mixed model?


Suppose I have a noiseless Signal, which has been filtered with a 2nd order Bessel low pass. I know the filter's transfer function. How can I obtain the unfiltered signal? Thanks!

A signal from a measurement is filtered with an analog 2nd order low pass filter. The original signal which consists of the sum of two exponentials (one positive amplitude the other one negative amplitude) slightly changes its shape. Since the information of important parameters can only be extracted from the unfiltered signal, I would like to undo the filtering digitally. I am aware that it is not possible to obtain the full original bandwidth, but could I theoretically increase the bandwidth? The filter's transfer function numerator is 1 while the denominator is a 2nd order polynomial.  Added:  My goal is to determine the values of an RC low pass (life science application). A voltage pulse is applied to the low pass filter. The arising current (which is a mono-exponential and contains the information of the R,C values in its time constant) is converted to a voltage (with an I-V-converter). The signal is then low-pass-filtered with a 2nd order Bessel filter. The sampling rate of the system is 20 kHz while the cutoff frequency of the filter is 3 kHz. Fitting algorithms are used to cancel noise in the output. My goal is to obtain the mono-exponential for any output signal.   Added: This is the actual circuit I wish to analyze.   I would like to obtain the current input at the ampere-meter for any output voltage. Of course in this simulation there is no noise. Before I apply the method to the real system I would like to make it work for the simulation. I've been using the MATLAB system identification toolbox in order to estimate the transfer function. By applying the inverse transfer function to the output I should be able to recover the original current input.


In  by Hastie and Tibshirani, it is mentioned that with case-control samples, we can estimate the logistic regression parameters accurately, but the intercept term is incorrect. It also gives a formula to correct the intercept term.  Could you please mathematically explain why this happens?  Additionally, could you please explain why exactly case-control sampling is necessary, and which methods of classification are particularly sensitive to imbalanced priors?

If I have a dataset with a very rare positive class, and I down-sample the negative class, then perform a logistic regression, do I need to adjust the regression coefficients to reflect the fact that I changed the prevalence of the positive class?  For example, let's say I have a dataset with 4 variables: Y, A, B and C.  Y, A, and B are binary, C is continuous.  For 11,100 observations Y=0, and for 900 Y=1:  set.seed(42) n <- 12000 r <- 1/12 A <- sample(0:1, n, replace=TRUE) B <- sample(0:1, n, replace=TRUE) C <- rnorm(n) Y <- ifelse(10 * A + 0.5 * B + 5 * C + rnorm(n)/10 > -5, 0, 1)   I fit a logistic regression to predict Y, given A, B and C.   dat1 <- data.frame(Y, A, B, C) mod1 <- glm(Y~., dat1, family=binomial)   However, to save time I could remove 10,200 non-Y observations, giving 900 Y=0, and 900 Y=1:  require('caret') dat2 <- downSample(data.frame(A, B, C), factor(Y), list=FALSE) mod2 <- glm(Class~., dat2, family=binomial)   The regression coefficients from the 2 models look very similar:  > coef(summary(mod1))               Estimate Std. Error   z value     Pr(>|z|) (Intercept) -127.67782  20.619858 -6.191983 5.941186e-10 A           -257.20668  41.650386 -6.175373 6.600728e-10 B            -13.20966   2.231606 -5.919353 3.232109e-09 C           -127.73597  20.630541 -6.191596 5.955818e-10 > coef(summary(mod2))               Estimate  Std. Error     z value    Pr(>|z|) (Intercept) -167.90178   59.126511 -2.83970391 0.004515542 A           -246.59975 4059.733845 -0.06074284 0.951564016 B            -16.93093    5.861286 -2.88860377 0.003869563 C           -170.18735   59.516021 -2.85952165 0.004242805   Which leads me to believe that the down-sampling did not affect the coefficients.  However, this is a single, contrived example, and I'd rather know for sure.


Suppose that $f$ is a continuous function on $[0,2]$ such that $f(0)=f(2)$.We have to show that there is a real number $c$ in the interval $[1,2]$, such that $f(c)=f(c-1)$.  I am completely lost on this question. I have tried fiddling with Rolles theorem and the Mean Value Theorem but it hasn't worked.

Let $f \in C[0,1]$ and $f(0)=f(1)$.   How do we prove $\exists a \in [0,1/2]$ such that $f(a)=f(a+1/2)$?  In fact, for every positive integer $n$, there is some $a$, such that $f(a) = f(a+\frac{1}{n})$.  For any other non-zero real $r$ (i.e not of the form $\frac{1}{n}$), there is a continuous function $f \in C[0,1]$, such that $f(0) = f(1)$ and $f(a) \neq f(a+r)$ for any $a$.  This is called the Universal Chord Theorem and is due to Paul Levy.  Note: the accepted answer answers only the first question, so please read the other answers too, and also this answer by Arturo to a different question:     This is being repurposed in an effort to cut down on duplicates, see here: .  and here: .


My Goal is to make a root beer with a ABV similar to your everyday beer or maybe stronger. (4-10%) I am newer to homebrewing so most of my experience comes from using Kits. My approach was going to be to use a Wheat Beer Kit (ABV 5.2%) and before starting the Fermentation process I would add some Root beer extract. Any suggestions or Tips would be Greatly appreciated!

I picked up some rootbeer extract at my local brewshop, and I've made a few batches in old soda bottles... but is it possible brew it with an alcohol content similar to that of beer?


I came across a question for which I have the correct answer. But since the question is a duplicate and the answer only requires a link to that question, the best way to provide the link would be in comments. Since I don't have enough reputation to flag it as a duplicate nor to comment, what can I do?

I've been trying to break the 15 barrier for about 2 years now (much less the 50 barrrier!), and I want to try and answer this question:    But the question needs some clarification before I can answer it. How can I get this clarification if I can't post a comment? Or do I just have to sit this one out?


A class of 60 students has three sections. Summary statistics for   scores on a quiz:           Section 1: 25 students, mean $\mu_1$ = 23, SD $\sigma_1 = 3$     Section 2: 20 students, mean $\mu_2$ = 25, SD $\sigma_2 = 2$      Section 3: 15 students, mean $\mu_3$ = 27, SD $\sigma_3 = 4$         Let $S$ be the quiz score of a student picked at random from the   class.   Found this problem in a textbook. The question was looking for something else, but I want to find $E(S)$ and $Var(S)$. How would I do that? This is what I think so far:    Let $\mathbb{I}_x$ be the event that Section $x$ is picked from the 3 sections with probability $p$, where $p$ is the $\frac{\text{number of students in that section}}{60}$ and $x \in [1,2,3]$.    Then, $$ E(S) = E(E(S|\mathbb{I}_1) + E(S|\mathbb{I}_2)+ E(S|\mathbb{I}_3))   $$  $$ = \frac{25}{60} \cdot 23 + \frac{20}{60} \cdot 25 + \frac{15}{60} \cdot 27  $$    Then, to find $Var(S)$:    $$ Var(S) = (\mu^2_1 + \sigma^2_1)\frac{25}{60} +(\mu^2_2 + \sigma^2_2)\frac{20}{60} + (\mu^2_3 + \sigma^2_3)\frac{15}{60} - E(S)^2 $$    $$ = (23^2 + 3^2)\frac{25}{60} + (25^2 + 2^2) \frac{20}{60} + (27^2 + 4^2) \frac{15}{60} - E(S)^2 $$    Does this look correct?

I'm calculating the covariance of a distribution in parallel and I need to combine the distributed results into on singular Gaussian. How do I combine the two?  Linearly interpolating between the two almost works, if they are similarly distributed and sized.   provides a forumla at the bottom for combination but it doesn't seem right; two identically distributed distributions should have the same covariance, but the formula at the bottom of the page doubles the covariance.  Is there a way to combine two matrices?


Applied for a visa to visit my uncle in the UK but was refused giving the following reasons:  They said I applied to to visit my aunt (which I never stated in my application) but brought supporting documents from my uncle stating his willingness to bear the cost of my trip, meaning there's no personal or professional relation between us (actually when filling the form there was a question that went like what's the relation of the person in the UK to you but there wasn't uncle in the options provided so I chose other relative and added his contact details and address so I don't know where the aunt came from, does choosing other relative mean aunt or something?)  Secondly they said I stated in my application I'm a non working student and that I attached a bank statement with a closing balance of over 200GBP and that they aren't satisfied with the evidence of the source or the money is for my exclusive use (I don't really get this point, are non working students required to have a specific amount before applying or what?)  Lastly they said I said the cost of the trip to me personally was 300GBP but I had less than that in my account so I can't sustain myself in the UK does it not contradict the second reason?) they also said I stated I had 300USD for the trip but the cost of flight was 285USD and my living expenses 200USD meaning I'm short of 185 (I thought they just needed an information about these so provided them because my uncle was bearing the cost of my trip so attached all the necessary documents to the invite not knowing they calculated using the money my account, how was I supposed to answer the questions under income in expenditure in the case where my sponsor that's my uncle was bearing all the cost of my trip? Can I apply again? And how many times can I apply after refusal?

My daughter wanted to travel to UK on tourist visa as her student visa expired. She wanted to go there to meet her sister working there on tier 2 (general visa). She by mistake showed my bank statement instead of her own as she had her current account in Lloyd bank in the UK. Visa was denied to her on the ground that in India she did not show any evidence that she is able to maintain herself – No evidence to show that she will leave england at the end of visit.   Is it ok to buy ticket before getting visa? How long should she wait before reapplying for visa?


I have a bash script that is named reader. It reads user input:  #!/bin/bash read -p "What is your name?" username echo "Hello, ${username}"   Running the script by source reader (EDIT: from the zsh shell), I get the error reader:read:2: -p: no coprocess. It doesn't give this error when I run it as ./reader.   Other read options do not produce this error. For example, I could have done:  #/bin/bash echo -n "What is your name?" read username echo "Hello, ${username}"   Where does the no coprocess error come from? What does it mean? And what should I do about it?

In zsh, running the command read -p 'erasing all directories (y/n) ?'  ans, throws the error,  read: -p: no coprocess   But in bash, it prints a prompt. How do I do this in zsh?