showing the group is abelian
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
ARMA/GARCH estimation in sequence I have a time series that shows a nonstationary seasonal autoregressive component as well as known heteroshedasticity. In order to model the series, I have fit a seasonal ARIMA model for the mean with the auto.arima model in the forecast package in R and a GARCH model on the residuals of the ARIMA model.   Is the procedure of sequentially estimating ARIMA and GARCH model correct or would it have been better to jointly model the mean and the variance of the series? If this were correct, is there a (possibly R) function to do it? I am travelling from Singapore to San Francisco and the airline has a layover of 7.5 hours at Tokyo Airport (NRT). I am wondering if I would be allowed to go out to experience the city for a while in some form a visitor visa.  I know Singapore has such facilities, but does anyone know if I can do it in Tokyo? Any suggestions or pointers are welcome. Note - I do not have a visa for Japan yet, but I am hoping that 1 day visitor visa could be possible at airport. How can I reduce the file size of a scanned PDF file? I have a 72.9MB PDF file that I need to shrink into under 500KB.  The file was a JPEG image that I had scanned, and then converted to pdf. What happens to Zhang ziyi (Jen) in  when she jumps off the cliff .. she dies? becomes immortal? Just before jumping what does she want Lo to become - a master?  Why does she jump off, guilt? HTTP request parameters are not available by request.getAttribute() Syntax error on print with Python 3 Showing OSM source acknowledgment on the map in QGIS? I am using OpenStreetMap as a base layer via XYZ tiles in QGIS 3.01.  I can't seem to find a way of having source acknowledgement appear on the lower right corner of the map.  Can somebody point me in the right direction? Debugging a custom-bib bst file that crashes on book items I created my own bibliography file with custom-bib (makebst), but when I run it with a reference to a book I get:  $ bibtex PhD [...normal output] Database file #1: PhD.bib You can't pop an empty literal stack for entry oecd2001brc while executing---line 1504 of file wdsphd.bst   The only thing on that line is a high-level ITERATE call.   The style was created with these options:  %% merlin.mbs  (with options: `head,exlang,annote,seq-no,nm-rvvc,dt-beg,yr-par,xmth,tit-qq,qx,bt-qq,vol-bf,volp-sp,num-xser,pub-date,isbn,issn,doi,english,pp,ord,url,url-nl,nfss,,{}') %% english.mbs  (with options: `exlang,annote,seq-no,nm-rvvc,dt-beg,yr-par,xmth,tit-qq,qx,bt-qq,vol-bf,volp-sp,num-xser,pub-date,isbn,issn,doi,english,pp,ord,url,url-nl,nfss,,{}') %% merlin.mbs  (with options: `tail,exlang,annote,seq-no,nm-rvvc,dt-beg,yr-par,xmth,tit-qq,qx,bt-qq,vol-bf,volp-sp,num-xser,pub-date,isbn,issn,doi,english,pp,ord,url,url-nl,nfss,,{}')   The code for book items looks like:  FUNCTION {book} { output.bibitem   author empty$     { format.editors "author and editor" output.check     }     { format.authors output.nonnull       crossref missing$         { "author and editor" editor either.or.check }         'skip$       if$     }   if$   format.btitle "title" output.check   crossref missing$     { format.bvolume output       new.block       format.number.series output       new.sentence       format.publisher.address output     }     {       new.block       format.book.crossref output.nonnull     }   if$   format.edition output   format.isbn output   format.doi output   new.block   format.note output   fin.entry   write.url }   And this is the entry:  @book{oecd2001brc,  author = {OECD},  doi = {10.1787/9789264193550-en},  isbn = {9789264186903},  publisher = {OECD Publishing},  title = {{Biological Resource Centres: Underpinning the future of life sciences and biotechnology}},  url = {http://www.oecd-ilibrary.org/science-and-technology/biological-resource-centres\_9789264193550-en},  year = {2001} }   Is there a way to get a better stacktrace from bibtex? What I have now doesn 't really tell me what is going on. If it can be fixed simply, help would also be appreciated. I am trying to add a list into an another nested list before adding values of a list to nested list it is getting the correct value but after adding i am getting (already output) in debug log when i checked.    public List&lt;String&gt; fieldName {get;set;}  public List&lt;List&lt;String&gt;&gt; fileValuesXML; // To get the field values of xml  for(Dom.XMLNode child : SalesforceObjecet.getChildElements()) {                        objecetName = child.getText();             system.debug('Object Name in XML field  ' + objecetName );              for(Dom.XMLNode subchild : child.getChildElements())              {                 system.debug('Sub child ' + subchild.getText() );                 for(Dom.XMLNode subchildfield : subchild.getChildElements())                 {                     system.debug('Sub child Field ' + subchildfield );                     fName  = subchildfield.getText();                     fieldName.add(fName);                     //fileValuesXML.add(fieldName);                     //system.debug('Filed Name in XML field  ' + fieldName);                 }                  system.debug('Filed Name before affing to filevalueXML  ' + fieldName);                                     fileValuesXML.add(fieldName);                 fieldName.clear();                 system.debug('Filed Name after affing to filevalueXML  ' + fileValuesXML);             }    }    I am getting values in debug log as:     Filed Name before affing to filevalueXML  (AccountSource, field3)   Filed Name after affing to filevalueXML  ((), (already output),   (already output)) Expected value of subset of variables in Bayesian setting Assume we have $N$ random variables $X_1, \ldots, X_N$ with known (posterior) distributions that are easy to sample from. For simplicity, assume that I am interested in the expected value of the ten largest of these random variables. There will be some uncertainty surrounding this expected value as there is uncertainty with respect to the rank of a given $X_i$ in case the distributions of $X_1, \ldots, X_N$ overlap. I want to use simulation based methods. My approach is to simulate $M$ samples from the distributions of $X_1, \ldots, X_N$, where in each iteration, I construct a binary indicator of length $N$ indicating whether random variable $i$ is within the set of the ten largest samples or not. Averaging over these $M$ draws gives me the probability that random variable $i$ is member of the top ten group. Denote this probability as $\pi_i$. Define a binary random variable that indicates membership in the top ten group as $S_i$. $S_i$ follows a Bernoulli distribution s.t. $S_i \sim Ber(\pi_i)$. In a second step, I draw $L$ samples from the distribution of $S_i$ and from the distributions of $X_1, \ldots, X_N$. Given a draw of $S_i$, I can select the top ten out of the samples of $X_1, \ldots, X_N$ in each iteration and average the respective samples within the top ten group. I save this average, so the result after $L$ iterations will be the distribution of the average outcome within the top ten group, taking into account all relevant sources of uncertainty. My questions are: Is this simulation approach valid in general? From a Bayesian perspective, is this simulation valid or do I need to treat additional quantities (e.g. $S_i$ or $\pi_i$) as random variables that need a prior? Past tense: learned/learnt, dreamed/dreamt? In my very first question, Carlo made an edit stating that learnt is a rare past tense of learn. I am accustomed to using learnt for past tense and learned as an adjective (as in He is a learned scholar.) I checked into a couple of dictionaries and they say both are valid past tenses. Do I stand a risk of not being understood if I use learnt?  In a similar vein, should dreamed be used as a past tense for dream instead of dreamt? I can't think of other such conflicts, but I guess there must be more. Can we say that $\frac{0}{0}$ is every number? text-overflow: ellipsis in table-cell without width LaTeX/BibTex not arranging citations by order of appearance I am having an issue with LaTex/Bibtex presenting my citations in order of appearance. I know there a plenty of questions on this and I have read some of them, but the solutions posted don't seem to do me any good. I am using MacTeX and TeXmaker.  I am writing a large document, like a Thesis. Chapters are split between individual Tex files and included using the \include command.  I have a large .bib file that is maintained by Mendeley (program I use for storing my references and producing a BibTex file).  I am using the package, cite (mainly for doing references like [1-3,6,9])  I have a pretty standard looking document.  \documentclass[11pt,a4paper]{report} \setcounter{secnumdepth}{3} \setcounter{tocdepth}{3} \newcommand{\doubleSignature}[3][Alex Mason]{% \parbox{\textwidth}{ \centering #3 \today\\ \vspace{2cm}  \parbox{7cm}{   \centering   \rule{6cm}{1pt}\\    #1  } \hfill \parbox{7cm}{   \centering   \rule{6cm}{1pt}\\   #2 } } } \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} %\usepackage[sorting=none]{biblatex} %\bibliography{Alex} % Where journals.bib and phd-references.bi \usepackage[pdftex]{graphicx} \usepackage{enumerate} \usepackage{nomencl} \usepackage{wasysym} \usepackage{booktabs} \usepackage{cite} \usepackage[left=1in,right=1in,top=1in,bottom=1in]{geometry} \graphicspath{{./Diagrams/}} \usepackage[labelfont={sf,bf}, margin=1cm]{caption} \usepackage{subcaption} \renewcommand{\figurename}{Fig.} \renewcommand{\tablename}{Tab.} \renewcommand{\bibname}{References} \author{NAME (MEng)} \title{TITLE} \date{\today} \makenomenclature %------------------------------------------------ \begin{document} \maketitle \pagenumbering{roman} %-----------------------------------------------certificate of originality----------------      -------------------------------------------- \input{CertofOrigin} \begin{abstract} ABSTRACT \end{abstract} %-----------------------------------------------contents------------------------------------------------------------ \tableofcontents \listoffigures \addcontentsline{toc}{chapter}{List of Figures} \listoftables \addcontentsline{toc}{chapter}{List of Tables} \chapter*{Acknowledgements} \addcontentsline{toc}{chapter}{Acknowledgements} ACKNOWLEDGEMENTS \printnomenclature[1.5in] \addcontentsline{toc}{chapter}{Nomenclature} \pagebreak \pagenumbering{arabic} \include{2ndYearReport_CHAP1} \include{2ndYearReport_CHAP2} \include{2ndYearReport_CHAP3} \bibliographystyle{unsrt} \bibliography{Alex} %\printbibliography \end{document}   The goofy looking part at the top (\newcommand{doubleSig.....) is just for when i input a special page I made containing a certificate of originality spiel with two boxes for signatures and my university logo.  As you can see I am using the standard bibtex way of doing bibliographies by stating the style then the stating the bib file to use right at the end of the document. I have tried biblatex but can't get it to work. It says it hasn't produced the bib file but doesn't really state why.  As far as I am aware everything was working A-OK until I started on the second chapter and began adding citations in there. Now my citations are all messed up and won't correct. My first citation starts with [9]!!!  [1] appears in a figure caption later down the page, after 10, 11 and 12 have been called!  I have tried deleting all the working files (bbl, aux, log etc) but nothing happens. I get the same result. IIRC I used to have this problem with MS Word and is part of the reason why I switched to LaTex...yet it seems to have followed me!   bibtex does through a few warnings when it runs stating that some references are missing journal names or volume numbers. Would that be a reason?  What have I done wrong with my code? How do I copy an entire directory into a directory of the same name without replacing the content in the destination directory? (instead, I would like to add to the contents of the destination folder) I want to write a survey on one emerging research topic in wireless communications (It can be applied to any field!). There are almost 500 papers on this topic as published or in early access. And the publishing rate in this topic is increasing day by day. So, I want to write a survey on this topic keeping in mind that it will get high citation and it will help new scholar who are in struggle with this topic. I found only one survey written by some reputed authors, however it lacks in many ways, like detailed information related to particular direction, it just assembles the papers in a good manner. I want to pick some directions and discuss  important approaches with good connection between them. However, I find it very difficult to proceed with large number of papers. Is there any good way to handle the survey process in a good efficient and quick way? PS. According to me, many people have already started to write this. Is there a way to get trig functions without a calculator? In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calculator?  Sometimes I don't feel right when I can't do things out myself and let a machine do it when I can't.  Or, if you could redirect me to a place that explains how to do it, please do so.  My dad said there isn't, but I just had to make sure.  Thanks. Alright, so the idea of an exponent, $x$, is that you are multiplying its base by itself $x$ number of times. With base $5$ and $x=3$, we have that $5^3$ = $5 \cdot 5 \cdot 5$  I understand that the logarithm with base $a$ of $x = c$,  tells us that  $$a^c = x$$  and for $c =$ positive; values for $x$ are greater than $1$, and for $c =$ negative; values for $x$ are less than $1$,  and for $c = 0$, values for $x$ are...$1$.  So in short, I understand how, by means of observation of the graph of $f(x) = \log x$, we can see that $f(1) = 0$, BUT, I see no other way to understand why $x^0 = 1$, apart from the graph and everything around that very point.  I honestly cannot get my head around the idea, "$5$ times itself $0$ times... is one".  Is it that there is no fundamental answer for this but that we simply know by the graph? Or can I truly understand $x^0 = 1$ on its own? How to find the mime type of a file in python? “How to Ask Questions in Private Beta” is listed in every site’s help centre When I go to /help/asking on any Stack Exchange site (), there is a link to How to Ask Questions in Private Beta (). It starts with:  Welcome to the private beta for [site] The tone and quality of the questions asked during this temporary private beta are critically important. If the private beta doesn't produce enough high quality expert level questions, it won’t proceed onward to the public beta. To help ensure your site makes it out of private beta, here are some tips:  There is no disclaimer or similar that this is outdated. This may lead to unnecessary confusion. I understand that that it is useful to keep this page in public pages for documentary purposes, as it may be linked in early Meta discussions, but it should:  not be listed in the table of contents (/help/asking) have a disclaimer