Check the stationarity of a time series
How to know if a time series is stationary or non-stationary?
$A \oplus B = A \oplus C$ imply $B = C$? I don't quite yet understand how $\oplus$ (xor) works yet. I know that fundamentally in terms of truth tables it means only 1 value(p or q) can be true, but not both. But when it comes to solving problems with them or proving equalities I have no idea how to use $\oplus$.  For example: I'm trying to do a problem in which I have to prove or disprove with a counterexample whether or not $A \oplus B = A \oplus C$  implies $B = C$ is true.   I know that the venn diagram of $\oplus$ in this case includes the regions of A and B excluding the areas they overlap. And similarly it includes regions of A and C but not the areas they overlap. It would look something like this:    I feel the statement above would be true just by looking at the venn diagram since the area ABC is included in the $\oplus$, but I'm not sure if that's an adequate enough proof.  On the other hand, I could be completely wrong about my reasoning.    Also just for clarity's sake: Would $A\cup B = A \cup C$ and $A \cap B = A \cap C$ be proven in a similar way to show whether or not the conditions imply $B = C$? A counterexample/ proof of this would be appreciated as well. Make your own .sty files Sorry to start a subjective question, but want to understand "own.sty" file.  Other than all \usepackage{} what sort of other commands can be added to the makeyourown.sty file.  Can you include \let command, and \newcommands in it.   What sort of precaution / structure newbies should follow. Mixed content on many SE sites Many SE sites (like math.SE) have a problem with mixed content, which causes display bugs in recent browsers. This is particularly evident with math.SE (because of the huge use of MathJax) and with chat sections.  Will this be fixed?  How to reproduce  Visit  or   What happens  Mixed content is blocked, output is missing pieces of code (MathJax):    This picture also includes my main Firefox addons (top right), it relevant. It shows missing styles:    The white on the left is my tab list. I understand that the eigenvectors of a linear transformation are the vectors that, when transformed, are simply scaled by a factor of the corresponding eigenvalue. Therefore $$ A\vec{x}=\lambda\vec{x}. $$ We can replace the scaling of the vector $\vec{x}$ by $\lambda$ with its equivalent linear transformation, $\lambda I$. Then we can rearrange this equation as follows: $$ A\vec{x}-(\lambda I)\vec{x}=\begin{bmatrix}0\\0\end{bmatrix}\\  (A-\lambda I)\vec{x}=\begin{bmatrix}0\\0\end{bmatrix}\\  $$ For this to be true either $\vec{x}$ must be a zero vector or the transformation $A-\lambda I$ must have $\vec{x}$ in its null-space. The course I'm following says that we can solve for $\lambda$ by finding when the determinant of $A-\lambda I$ is zero, but why does that guarantee that $\vec{x}$ will become the zero vector when transformed by $A-\lambda I$? I understand that for $\vec{x}$ to be an eigenvector this transformation must have a determinant of zero, but I don't see how the inverse can be true; having a determinant of zero doesn't gaurantee that $\vec{x}$ will be transformed into the zero vector. For example, let $$ (A-\lambda I) = \begin{bmatrix}1&amp;2\\0&amp;0\end{bmatrix}, \vec{x}=\begin{bmatrix}1\\1\end{bmatrix} $$ Then, although $\det\begin{bmatrix}1&amp;2\\0&amp;0\end{bmatrix} = 0$, it does not gaurantee $(A-\lambda I)\vec{x}$ to be the zero vector. $$ \begin{bmatrix}1&amp;2\\0&amp;0\end{bmatrix}\begin{bmatrix}1\\1\end{bmatrix}=\begin{bmatrix}3\\0\end{bmatrix}  $$ We can see that the transformation gives us $\begin{bmatrix}3\\0\end{bmatrix}$ and not the zero vector. Why does finding when the determinant of this transformation is equal to zero help us find the eigenvectors? Am I missing something? A bit of background, I am doing research in atmospheric physics and detection systems  Recently, I received a paper submission back with revisions suggested by a couple of reviewers.  For the most part, the revisions were definitely constructive, justified and most importantly, helpful.    That is, except on one particular crucial aspect of the paper where both reviewers made suggestions, that they labelled as critical for the paper's success.  However, the suggestions were directly opposite.  i.e. Both suggestions are mutually exclusive, but equally feasible.    What is an effective means to address this conflict?  I have spoken to my academic supervisor and he is not sure how to proceed either and we have double checked and both suggested paths are feasible. I have 2 columns in Excel: the first contains a list of employee names who perform function A, and the second contains a list of employee names who perform function B.  What I want is to identify, in one cell, if there is one employee whose name appears in both the first and second columns. It does not have to show which name(s) appears in both columns, it just needs to identify IF there are any names that appear in both columns. The set of homotopy classes login and payoff are nouns. But can they be used as verbs? I know that words like login and payoff are properly nouns but I increasingly notice many (not at all uneducated) people use them as verbs:     Will you payoff your credit card this month?   and     Please check this when you login.   To me (a non-native English user), that seems incorrect because separating the core noun from a preposition is what I was taught: Please check this when you log in. (My emphasis)  Is this use proper or not? 1970s or 80s kids book: girl's life taken over by a robot doppelganger version of herself I read this book between 1980-82 but it could have been written earlier.  It's about a girl who is dissatisfied with her life, as her parents have her on a diet and she wants to be able to eat what she wants. Someone offers her a solution: to come live in this large building where she can eat all the chocolate eclairs and other junkfood she wants, while a robot doppelganger android version of herself will take her place at home and at school.  The girl agrees, but finds that after week of eating mainly eclairs, she is sick and wants to eat a decent meal. But she is not allowed to eat anything else and has found herself to be a prisoner, so she sets out to get rid of the android and get her life back.   I don't recall the ending but it seemed the 'people' behind it all might have been aliens and the building might have been a kind of ship that then disappears. booting windows 10 spends too long I've always wondered how to write the "A ? B : C" syntax in a C++ compatible language.  I think it works something like: (Pseudo code)  If A &gt; B    C = A Else    C = B   Will any veteran C++ programmer please help me out? fitting a smaller range when we bought our house, it had a very used 40" gas range. now that range has died. replacing with a new 40" range is very pricey ($2k+), and our cooking needs don't justify the size anyhow.  i'm looking for ideas on how to fit a smaller range. i would imagine that extending the counter top and cabinets would be a pretty extensive change. we've found we can get a 36" range for around 1/2 the cost. would it be feasible to add some sort of storage along side the smaller range to fill in the space?  thanks. i know this is an open-ended question with no specific answer, i'm just looking for ideas. What is vector division? My question is:  We have addition, subtraction and muliplication of vectors. Why cannot we define vector division? What is division of vectors? Run script as root at login (no sudoer user, shell session) Much like /etc/profile and ~/.profile but ran by root instead of the user is doing login. /etc/rc.local runs after boot but I need running the script before login. The user is not a sudoer one.   Thanks! Is it possible to follow a user automatically? I've been looking around and I can't seem to find an automatic (i.e. buzz- or Twitter-like) way to follow users inside Stack Exchange. Why haven't the developers added such a feature? It could help beginner users follow other beginners with the same interests. We would be able to learn from each others' questions and pitfalls. Also, it would reduce double posting. I'm trying to use the Bash parameter expansions to modify the output of a command substitution or another parameter expansion. The following nested expansions work quite well in Zsh; but result in a &quot;bad substitution&quot; error in Bash: ${${PWD##*/}//trunk/latest}  or ${$(basename $PWD)//trunk/latest}  the output should be the last folder of the $PWD, replaced by latest when my current directory is trunk so /home/user/trunk should become latest Is there a Bash equivalent allowing to chain expansions without relying on variables or pipes? Or do Bash expansions only allows the input to be a string or a plain variable? I admit this feature request is probably somewhat limited in useful scope, but I'm throwing it out there anyway. Inspired by , and because I want to use it on , I'm requesting that name be supported on a tags in posts.  On very long answers, such as the closing/migration guidance answer, this would allow direct linking to the specific closure reason. This would then allow us, when someone , to link directly to the appropriate reason and description thereof.  I recognize the limited scope of this, however, I have seen other long answers that could stand to have that kind of "deep" linking ability as well.  (The original incarnation of this post had either name or id, but preferenced name. Per Koper's answer, which I agree with, I took out the idea of supporting id, because Koper's right -- too dangerous.) To EAV or not to EAV? biblatex: Cite commands with the same author prints authors name twice I'm using biblatex 1.4b, and Biber 0.9. However, I think the problem is with my settings, not with the versions of those programs.  I'm trying to cite a single author, and produce their name, followed by the dates of two papers, using the authoryear-ibid style, and natbib compatability. Here's my biblatex preamble:  \usepackage[style=authoryear-ibid,natbib=true,backend=biber]{biblatex}   What I want is for the following command: The works by \citet{Blau81, Blau88} ... to produce: The works by Blau (1981; 1988) ... however, what I'm getting is: The works by Blau (1981); Blau (1988)...  I know that biblatex knows they're the same author, since in the bibliography they fall under the same name (i.e. after the first instance of the name, there's just a dash instead of the name)  What am I doing wrong here? I've also tried it with the commands \cite and \cites, and neither produces what I want.   (crossposted with comp.text.tex) Can you retrain the Magic Initiate spell using the Spellcasting feature? got me thinking about the mechanics of the Magic Initiate feat when you have class levels in the class into which you were inducted.    Among the classes you can pick with this feat are the Bard, Sorcerer, and Warlock, which know a limited number of spells and all have the same statement under Spells Known.     Additionally, when you gain a level in this class, you can choose one of the [class] spells you know and replace it with another spell from the [class] spell list , which must also be of a level for which you have spell slots.   The term "learning" is used both to describe new spells acquired on level-up and the spell acquired through the feat. This would seem to indicate your Magic Initiate spell counts among the spells you know, and is thus eligible for retraining if you learned it as a spell of your class.  An odd change in wording occurs during the Magic Initiate feat description (emphasis mine):     In addition, choose one 1st-level spell from the same list. You learn that spell and can cast it at its lowest level.   This generalization in describing the learned spell's level seems to imply that there exists a scenario where it would not be appropriate to restrict the spell to being cast as a 1st-level spell.  Could one of the charisma casters retrain Magic Initiate into a higher level spell, which they could then cast once per long rest without using a slot?  This would turn an otherwise unexciting feat into, effectively, a Mystic Arcanum for Bards and Sorcerers. This seems too powerful to be intentional,  but the feat description appears to have gone out of its way to permit it.