I have a question on the use of article &quot;the&quot; in scientific paper. The following is my paragraph that includes my question. ... This process is given by x+ y + z = 1.                                                    (10) It was proved that: (a) the equation (10) has two solutions. (b) Equation (10) has two solutions. (c) equation (10) has two solutions. ... My question is that (a), (b) or (c) is written correctly. More clearly, we use “the” before “equation” or not? I think (a) and (b) are true but many people also used (c). Could you please let me know an explanation for that question. Thanks.
In many scientific papers, the article before the word "Equation" is omitted. Is there any grammar statement behind this? For instance:     "Equation (8) contains various approximations, and we have to check their consistency."
Is it possible to make macros give different results at the beginning of a new sentence? Suppose that I want the macro "\secname" to write "Section" at the beginning of a new sentence, and "section" anywhere else. How can I do so? Why did the Tethered form a line in Us? In Jordan Peele's  we see that the Tethered plan a revolt, rise above ground and start murdering everyone in sight and then they form a line by holding hand in hand.   What was the purpose of that? Validate decimal numbers in JavaScript - IsNumeric() Is it possible to call a non-exported function that resides in an exe? how can i automatically record every terminal session? Is there a way to solve this integral?  $$\int \frac{dx}{\sqrt{-ax^2 + bx +c}}, \;\;\;\;\; \forall\; a,b,c \in (0,+\infty) \;in\;R$$  I have tried it by changing of variable and by parts, but no result. I don't know what else to do.  Thanks in advance. Both are in the present perfect, but one uses the verb 'to go' and the other 'to be'. Is there a rule for this?  Is there any chance that the differences between "I have been" vs. "I have gone", are differences in English dialect (I don't know if this is the right word).  Edit Could I say that North American English speakers use "I have gone", and maybe U.K speakers say "I've been"? Or vice versa. I'll be arriving at Heathrow in June 2015 with my current girlfriend for a holiday in the UK. I've been trying to find out which immigration queue to join at Heathrow Passport Control without much luck. I have a British passport, my girlfriend has a non-EU passport.     Should I join the EU queue and she the non-EU queue or should we both queue together (and if so, which of the queues should we join)? Currently I'm running Linux-3.0 and I want to update it to Linux-3.3.1 the latest stable kernel release as mentioned at . Can I update to 3.3.1 in Ubuntu without any risk of crashes? I'm updating my kernel regularly as provided by the Update Manager..Currently I have Linux-3.0.0.17..Can I update?  NOTE:  The latest kernel version any user is supposed to use in Ubuntu is updated automatically via the Update Manager, so no action is normally required by user regarding kernel upgrades. What the question author is referring to is mainline kernel, see: How can I do development on my Android device? I have a pretty long commute to work and own an android phone. I figure it would be nice to do some simple programming on the way. I'm not picky on which language to code on. I usually have an internet connection on the train.  I've been looking through the android market but haven't found any apps that offer a "development environment" or an editor with a compiler. Is any development ON the Android possible? Does an app for this exist? better Curve/Text to Mesh generation? The triangulation process of Text to Mesh or Curve to Mesh generates some nasty topology.   I get why, but maybe it could be done a bit nicer? Since text is flat, have ngons instead of hundreds of triangles you'll need to modify anyway?  Another issue is when you then want to use the text as a Volume for particles, which for some reason behave weird when you have unusual topology even though they should be using the volume, not vertex or face positions. How to convince longtable to do a page break earlier using the longtable package to typeset page spanning tables, I run into a nasty behaviour: only a dummy table head and the caption are put on the following page. The contents of the table is extracted from program sources. I don't have much influence here.  \documentclass[a4paper,twoside,DIV10,BCOR1.5cm]{scrbook} \usepackage{longtable} \newlength{\tablcol} \setlength{\tablcol}{4.7cm} \newlength{\tabrcol} \setlength{\tabrcol}{8.1cm} \itemsep0ex plus0.2ex % \begin{document} \begin{longtable}{p{\tablcol}p{\tabrcol}}% % \hline \multicolumn{1}{l}{{\bfseries Feld}} &amp; \multicolumn{1}{l}{{\bfseries Beschreibung}}\\ \hline \endfirsthead % \hline \multicolumn{2}{l}% {{\small\slshape Fortsetzung der vorherigen Seite}}\\ \hline \multicolumn{1}{l}{{\bfseries Feld}} &amp; \multicolumn{1}{l}{{\bfseries Beschreibung}}\\ \hline \endhead % \hline \multicolumn{2}{l}% {{\small\slshape Fortsetzung auf der n\"achsten Seite}}\\ \hline \endfoot % \hline \caption[show user output]{Beschreibung der Output-Struktur des show user Statements} \endlastfoot % \label{tucshowxuser}% {\scshape id} &amp; Die Nummer des Repository Objektes \\ {\scshape name} &amp; Der Name des Objektes \\ {\scshape creator} &amp; Name des Benutzers der dieses Objekt angelegt hat \\ {\scshape create\_time} &amp; Datum und Uhrzeit der Erstellung \\ {\scshape changer} &amp; Name des Benutzers der dieses Objekt zuletzt ge\"andert hat \\ {\scshape change\_time} &amp; Datum und Uhrzeit der letzten \"Anderung \\ {\scshape privs} &amp; Zeichenkette die K\"urzel f\"ur die Benutzerrechte auf dieses Objekt enth\"alt \\ {\scshape commenttype} &amp; Typ des Kommentars \\ {\scshape comment} &amp; Kommentar zum Objekt, wenn vorhanden \\ {\scshape id} &amp; Die Nummer des Repository Objektes \\ {\scshape name} &amp; Der Name des Objektes \\ {\scshape creator} &amp; Name des Benutzers der dieses Objekt angelegt hat \\ {\scshape create\_time} &amp; Datum und Uhrzeit der Erstellung \\ {\scshape changer} &amp; Name des Benutzers der dieses Objekt zuletzt ge\"andert hat \\ {\scshape change\_time} &amp; Datum und Uhrzeit der letzten \"Anderung \\ {\scshape privs} &amp; Zeichenkette die K\"urzel f\"ur die Benutzerrechte auf dieses Objekt enth\"alt \\ {\scshape commenttype} &amp; Typ des Kommentars \\ {\scshape comment} &amp; Kommentar zum Objekt, wenn vorhanden \\ {\scshape id} &amp; Die Nummer des Repository Objektes \\ {\scshape name} &amp; Der Name des Objektes \\ {\scshape creator} &amp; Name des Benutzers der dieses Objekt angelegt hat \\ {\scshape create\_time} &amp; Datum und Uhrzeit der Erstellung \\ {\scshape changer} &amp; Name des Benutzers der dieses Objekt zuletzt ge\"andert hat \\ {\scshape change\_time} &amp; Datum und Uhrzeit der letzten \"Anderung \\ {\scshape privs} &amp; Zeichenkette die K\"urzel f\"ur die Benutzerrechte auf dieses Objekt enth\"alt \\ {\scshape commenttype} &amp; Typ des Kommentars \\ {\scshape comment} &amp; Kommentar zum Objekt, wenn vorhanden \\ {\scshape id} &amp; Die Nummer des Repository Objektes \\ {\scshape name} &amp; Der Name des Objektes \\ {\scshape creator} &amp; Name des Benutzers der dieses Objekt angelegt hat \\ {\scshape create\_time} &amp; Datum und Uhrzeit der Erstellung \\ \end{longtable}  \end{document}   The problem is that I don't find a method to force a page break earlier. A page that isn't filled entirely, followed by a page with the last part of a table is better than this.  I tried to add "\needspace{someLength}" at the beginning or end of the rows, but that doesn't work either. It simply makes the rows someLength high instead of forcing a page break if there's no more than someLength room left on the page.  I'd be more than grateful for some solution or even a good hint.  TIA Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer Let $a,b$ be positive integers.  When $$k = \frac{a^2 + b^2}{ab+1}$$ is an integer, it is a square.    Proof 1: (Ngô Bảo Châu): Rearrange to get $a^2-akb+b^2-k=0$, as a quadratic in $a$ this has two values: $a$ and $kb - a = (b^2-k)/a$. (The second root is determined in two different ways from the expansion $(x-r_1)(x-r_2) = x^2 - (r_1 + r_2)x + r_1 r_2$.)  Now suppose we have $a,b$ such that $k$ is an integer but not a square, by the investigation about roots we have that the second root is a nonzero integer since $k,b,a$ are integers and $k \not = b^2$, futhermore it is positive which is easily seen from its defining equation.  WLOG assume $a \ge b$ so that the second root is strictly smaller than $a$. This leads to a decent, replacing $a$ with the second root.    Proof 2 (Don Zagier): Apply reduction theory (specifically, Sätze 1 and 2 of Section 13 of my book on quadratic fields) to the quadratic form $x^2 + kxy + y^2$, which is the unique reduced quadratic form in its equivalence class.    Note that Proof 2 is pretty much the same as Proof 1 when written out in explicit detail, but I could not read Zagier's book because I cannot read German.  I would like to know more approaches to this and other alternative proofs of this result if possible! Thanks in advance.  I would also be interested in related problems (especially easier ones of a similar nature) and texts which cover the reduction theory in English. Elsevier has started circulating  as a consequence of the  to the editors of their journals:     Subject: US editors and reviewers can no longer handle submissions by   authors employed by the Government of Iran            Dear Dr Bruno Granier,      The Office of Foreign Assets Control (OFAC) of the US Department of   the Treasury administers and enforces economic and trade sanctions. As   a result of OFAC sanctions we have been made aware that US editors, US   Elsevier staff and US reviewers are now unable to handle scientific   manuscripts where any of the authors are employed by the Government of   Iran. This includes the research departments of the various oil and   gas companies which are deemed to be entities of the Government of   Iran. We realize that this OFAC regulation will cause some   inconvenience in your role as an editor but Elsevier is legally   obliged to ensure that all reasonable efforts are made to avoid   submissions from Iranian government agencies and companies being   handled by US editors, US Elsevier staff and US reviewers. Please be   aware that editors, Elsevier staff and reviewers from outside the US   may still handle these manuscripts and that this OFAC regulation does   not pertain to manuscripts where the authors are based at Iranian   academic and research institutes. Manuscripts originating from a   clinical setting that are not government run, for example, a hospital   or clinical practice are also exempt from this regulation.      To view the official OFAC regulation, please click here. In practice   the result of these sanctions will mean that:      • Submissions where any author is based in Iran, and is not at an   academic and research institution, cannot be handled by US-based   editors, US Elsevier staff, US reviewers, or any US citizens based   outside of the US.      • If an Iranian author has dual affiliations (eg. university and   government), their submission cannot be handled by US-based editors,   US Elsevier staff, US reviewers, or any US citizens based outside of   the US.      • Affiliations of Iranian authors should therefore be checked, and any   manuscripts which fall under this OFAC regulation delegated to a   non-US editor, before handling.      • When assigning reviewers, affiliations of Iranian authors should   also be checked, and any papers which fall under this OFAC regulation   should only be sent to non-US reviewers. (As an editor you should do   what is reasonable to determine the nationality of a reviewer e.g.   check their email address. This check does not extend to emailing   reviewers directly to confirm their nationality or location). Unless   there is specific knowledge that a non-US-based reviewer is a US   citizen, editors can send such submissions to reviewers based outside   the US.      • If your journal workflow involves all submissions being handled by   US-based Elsevier staff, they will reject these manuscripts outright   before they reach you.      • Should there be no suitably qualified editor or reviewer, please   reject the manuscript outright.      When rejecting manuscripts which fall under this OFAC regulation   please use the new EES Decision Term "Reject - OFAC Sanctions" and the   following text:      "As a result of OFAC sanctions all editorial staff who are US-based/US   nationals are unable to handle scientific manuscripts which are   authored by Iranian scientists, employed by the Government of Iran.   Based on this OFAC regulation we are unfortunately unable to handle   your manuscript. We wish you success with your submission to another   Journal."       We apologize for the inconvenience this may cause. If you do have any   questions please contact your Publisher.       Sent on behalf of Dan Lovegrove      Cretaceous Research   Has there been any public response, by US editors or reviewers, stating whether they will obey (or not) the instruction? Also, does this letter conflict with the  of the  (all Elsevier journals are members of COPE as of January 2008)? If I want to add more RAM to my computer, how can I buy something compatible? What kinds are there? How do I determine which kind my computer will accept and how much I can add? I have a virtual machine running ubuntu and I am trying to host some files on ubuntu and map the drive in windows PC.  Following the steps , I am able to see (from windows) the "work" folder after typing in \ubuntu_ip. But when trying to access or map it with "svc_acct" from windows, I get "0x80070043 error the network name cannot be found". I guess I am not accessing correctly from windows.   SAMBA config below (svc_acct is an account set up under linux). When accessing the folder from windows, I get prompted for username/password. Not sure what credential to type in exactly.  samba config: [work] path = /home/svc_acct/work valid users = svc_acct available = yes read only = no browsable = yes public = yes writable = yes force user = svc_acct create mask = 0777 directory mask = 0777   UPDATE:  All I did to resolve this is by changing samba config's path from path = /home/svc_acct/work to path = /home/svc_acct following  post  (last sentence). Then no more prompt for password in windows when I try to click into the folder. Thanks to @sancho.s for suggesting the link. For which $n$ does $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ imply $\frac{1}{a^n}+\frac{1}{b^n}+\frac{1}{c^n}=\frac{1}{a^n+b^n+c^n}$ I'm having trouble finishing a problem on an old national competition.  As the title states, the question says asks:  Given $a,b,c \neq 0,a+b=c$ such that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$,  Find all integers $n$ such that $\frac{1}{a^n}+\frac{1}{b^n}+\frac{1}{c^n}=\frac{1}{a^n+b^n+c^n}$.  I know that if it is true for $n$, it is also true for $-n$ since $(a^n+b^n+c^n)(\frac{1}{a^n+b^n+c^n})=1$ and $(a^n+b^n+c^n)(\frac{1}{a^n}+\frac{1}{b^n}+\frac{1}{c^n})=1$ and the statment follows for $-n$ given that we can make the substitution for $n$. Thus I found out that $n=-1$ satisfies the equality.  I also know that it fails for all even $n$. If $n$ were even, $(a^n,b^n,c^n)$ would all be positive, and Titu's Lemma asserts that $\frac{1}{a^n}+\frac{1}{b^n}+\frac{1}{c^n}\geq \frac{9}{a^n+b^n+c^n}$. Thus $n$ must be odd.  I also observed that $(2,-1,1)$ was a solution, and from here noted that this particular solution satisfies all odd $n$.  I have been trying to prove that all other solutions satisfy all odd $n$ with no success.  Any help would be greatly appreciated. Thanks! How to check if a macro value is empty or will not create text with plain TeX conditionals? I have a macro which holds some text value, e.g. \macro{some text}. If it is empty, I would like for nothing to appear in the document, but it has some content of any kind which would produce text displayed in the document, I would like a message to appear, "Text: some text".   \macro{} would be considered empty. \def\somedata{}, \macro{\somedata} would be considered empty. \macro{0} would be considered not empty.   I have tried making a TeX conditional which can check if the value is not empty, but nothing I tried works, e.g.:  \ifx #1 {} \else     Text: #1 \fi  \ifx#1{} \else     Text: #1 \fi  \ifx #1 \nil \else     Text: #1 \fi  \ifx#1!="" \else     Text: #1 \fi   What is the correct syntax for creating a conditional in plain TeX with checks if a value is not empty? I just started trying to undestand the notion of stationary in time series. Basically I have 2 questions:  Can stationary time series contain regulary cycles and thus seasonality patterns? For exmaple in this tutorial it is stated that stationary time series can not have seasonal components (predicitable cycles)  whereas in this figures () the green time series that clearly has cycles (and thus seasonality) is labeled as 'stationary' (and I have seen these kind of figures quite often if you just google 'stationary time series) Can a stationary time series have periods with no fluctuations and periods with high fluctuations? As far as I understood the variance and the (aut)covarianz should not change over time making such a time series not stationary. But here in this picture () the time series below is labeld as stationary altough it has periods with changing fluctuations.  I hope you can help me as I am confused about the concept of stationarity. I'd appreciate every comment. The bounty is to expire quite soon. So I'd be happy if some could at least give me one answer to my questions. It will help me a lot. Why is nobody answering the questions? Are they not clear enough? If so, please tell me. I think they are important and fundamental as the concept of stationarity is quite important. In Magic: The Gathering, the rules for a player losing in a multiplayer game are quite complex, so I'd like to try to understand them by example. I would be happy to ask each of these situations as a separate question if that is preferred, but they all seem related, and I would love to have one place to look up all of these answers.  Let's say I'm playing with two friends, Bob and Chloe, in a simple free for all. Unfortunately, I lose. When I lose, suppose the following:   I controlled an  which has exiled Bob's , does he get his bear back? I have a  on the stack targeting Chloe, does Chloe take the 2 damage still? Earlier in the turn I cast  to prevent damage to one of Bob's . If it later takes 3 damage, will that damage be prevented? Something I controlled gave Bob a 1/1 soldier token. What happens to the token? Something Chloe controlled gave me a 1/1 soldier token. What happens to the token? I had a  enchanting one of Bob's army of . What happens to the bear? I had also played  on Bob's final . What happens to the last bear? Chloe had  my . What happens to the Clone? Are there any other situations specifically addressed by the rules?