(Java begineer) "this" keyword discussion
How do I call one constructor from another in Java?
I just read this very insightful post , where the author stated that the variance of $\hat\beta$ is:  $$\text{var}(\hat\beta) = \sigma^2(\textbf{X}^\prime \textbf{X})^{-1}.$$  I couldn't figure out why it is like this. Can anyone elaborate a bit? Will free-fall object into black hole exceed speed of light $c$ before hitting black hole surface? In Newtonian mechanics, if we throw an object in against direction of gravity with speed $v$ and it achieve max height of $h$. Now if we allow object to fall from that height $h$, it will eventually attain speed $v$ when it reach position where we launch it.   Now applying same idea to a black hole in general relativity. Speed require to escape black hole gravity is greater than $c$, so if we throw something into black hole with almost the speed of light, the object speed will exceed speed of light $c$ before hitting black hole surface! How relativity explain this? Can space-time curvature reduce speed of this freely falling object from attaining speed of light? Seeing as C# can't switch on a Type (which I gather wasn't added as a special case because is relationships mean that more than one distinct case might apply), is there a better way to simulate switching on type other than this?  void Foo(object o) {     if (o is A)     {         ((A)o).Hop();     }     else if (o is B)     {         ((B)o).Skip();     }     else     {         throw new ArgumentException("Unexpected type: " + o.GetType());     } } Is "education" a count noun? Do you really answer "How do you do?" with "How do you do?" Can anyone help me out with how to make Bing Picture to my Desktop Wallpaper?    So it works by downloading the highest quality of todays picture. Then storing it ex in the Picture folder of your account. After that automatically changing the picture itself.  It should continue the same everyday without hassle in the background.  Probably something I have to add in the Startup Applications. Any differences between Ubuntu versions?    -Do I have to write a script?  This would be appreciated by many others too! Thank You in Advance :) Let $H$ be a subgroup of $G$ with $[G:H]=n$. Let $N$ be the kernel of the left-multiplication action on the cosets of $H$. Show $[G:N]$ divides $n!$ Let $H$ be a subgroup of $G$ with $[G:H]=n$ and $G$ finite.  Let $G$ act on left cosets of $H$ by left multiplication.  Let $N$ be the kernel of the action.  Show that $[G:N]$ divides $n!$.  Ok so I have a theorem that says that if $G$ is simple then it embeds into $S_n$.  So if $G$ is simple than I'm done because $G$ divides $n!$ and thus $N$ divides $n!$ and hence $[G:N]$ divides $n!$.  Now I also know that $N$ is the largest normal subgroup of $G$ contained in $H$.  Thus if $G$ isn't simple then it contains some non-trivial normal subgroup $K$ and thus $K\cap H$ is normal in $H$ and by the 2nd Iso Theorem $H/K\cap H\cong KH/H$...    As you can see I'm not sure where to go from here. I was hoping to prove that $K\cap H$ wasn't trivial and thus that $N$ couldn't be trivial since it must contain $K\cap H$, but I'm not sure I can, and even if I could I'm not sure that would help me in showing that $[G:N]$ is small enough to divide $n!$.  Can anyone give some guidance?  Thanks. Assume $\bar A\cap\bar B=\emptyset$. Is $\partial (A \cup B)=\partial A\cup\partial B$, where $\partial A$ and $\bar A$ mean the boundary set and closure of set $A$?   I can prove that $\partial (A \cup B)\subset \partial A\cup\partial B$ but for proving $\partial A\cup\partial B\subset \partial (A \cup B)$ it seems not trivial. I tried to show that for $x\in \partial A\cup\partial B$ WLOG, $x\in \partial A$ so $B(x)\cap A$ and $B(x)\cap A^c$ not equal to $\emptyset$ but it seems not enough to show the result. How can I clear event subscriptions in C#? Take the following C# class:  c1 {  event EventHandler someEvent; }   If there are a lot of subscriptions to c1's someEvent event and I want to clear them all, what is the best way to achieve this? Also consider that subscriptions to this event could be/are lambdas/anonymous delegates.  Currently my solution is to add a ResetSubscriptions() method to c1 that sets someEvent to null. I don't know if this has any unseen consequences. Get polynomial interpolation formula Is there any way to check whether a file is locked without using a try/catch block?    Right now, the only way I know of is to just open the file and catch any System.IO.IOException. In Windows there’re perhaps only a couple of important folders (by important I mean important in my logical picture of the Windows file system) in the installation drive (in my case C:\). Namely Program Files and Windows. I simply stay away from Windows folder and the “add remove program files” is good enough to handle the program files folder of Windows. Of course there’s a folder named Users where the users (who are not admins) can access only their folders.  Thus there’s a clear picture at some level in my mind of the Windows file system. In Ubuntu, when I reach the location /, there’s a huge list of folders, most of which I have no clue as to what they contain. The /bin folder seems to be the equivalent of the Windows folder in windows. The /usr folder seems like it’s the equivalent of the Users folder in Windows. But even the /home folder looks like it can fit the bill.  Please understand that I do understand, that Ubuntu (Linux) has a different character than that of Windows, i.e., there need not be exact equivalent of Windows functions, in Ubuntu. All I am looking for is a bit more clearer picture of the Ubuntu file system.   This question is a part of a bigger question which I am splitting up to make it more answerable. The original question can be found here: How to get/suppress french spacing before punctuation in `\href` Attention I have already a possible answer and will add it soon. I thought it would be useful to have a solution about it on the site. (Other answers are naturally welcome too).  Question How to activate or suppress the french spacing before some punctuations like a colon in the text argument of \href locally (for one specific \href) and globally? Switching the language is not an answer!  Minimal examples for tests (the argument of \href should normally be a valid url, so it is a bit unfair to add an example without a colon in the link):  pdflatex  With pdflatex it depends on the link how the argument of \href is printed:  \documentclass{article} \usepackage[french]{babel}  \usepackage{hyperref}  \begin{document} With pdflatex no french spacing in links with colons:   \href{link}{a:b}  \href{link:colon}{a:b}  \end{document}     lualatex  With lualatex the spaces are always there:  \documentclass{article} \usepackage[french]{babel}  \usepackage{hyperref}  \begin{document} With lualatex always spaces:  \href{link}{a:b}  \href{link:colon}{a:b}  \end{document} Alignment of equals sign in multiple align environments How to manually typeset text in parallel on facing pages in (Lua)LaTeX? I want to typeset a bilingual text in parallel on facing pages using LuaLaTeX. The existing solutions to automate this task have proven unsatisfactory as they don't allow for footnotes (parallel), don't allow for different font sizes of the two parallel texts (), or generally provide a poor result of aligned text chunks (eledpar).  As the text is not too long, I really came to consider breaking the pages myself. For this to do, I have to solve the following problem(s):  Consider two facing pages with ending paragraphs of different length. The following paragraphs should then begin at the same vertical position such that the beginnings of these following paragraphs face each other. For this to accomplish on has   to determine the position of the end of the longer paragraph on its page to have the means to let the next parallel paragraphs both begin at the identified position.   Is this something which is doable? Are there mechanisms provided by (Lua)LaTeX to determine positions on a page and to begin typesetting at a specific position on a page?  EDIT: The following example illustrates the task. Here the latin paragraph starting with "O tempora, o mores" (third chunk of text in the code) should begin at the facing position of the beginning of the paragraph "Shame on the age..." (fifth chunk).  \documentclass[a6paper]{scrbook} \usepackage{fontspec} \usepackage[latin,english]{babel} \begin{document} \mbox{}\pagebreak  \noindent\selectlanguage{latin}{\large quo usque tandem abutere, Catilina, patientia nostra? quam diu etiam furor iste tuus nos eludet? quem ad finem sese effrenata iactabit audacia? nihilne te nocturnum praesidium Palati, nihil urbis vigiliae, nihil timor populi, nihil concursus bonorum omnium, nihil hic munitissimus habendi senatus locus, nihil horum ora voltusque moverunt? patere tua consilia non sentis, constrictam iam horum omnium scientia teneri coniurationem tuam non vides? quid proxima, quid superiore nocte egeris, ubi fueris, quos convocaveris, quid consili ceperis quem nostrum ignorare arbitraris?\par\newpage}  \noindent\selectlanguage{english}When, O Catiline, do you mean to cease abusing our patience? How long is that madness of yours still to mock us? When is there to be an end of that unbridled audacity of yours, swaggering about as it does now?  Do not the nightly guards placed on the Palatine Hill — do not the watches posted throughout the city — does not the alarm of the people, and the union of all good men — does not the precaution taken of assembling the senate in this most defensible place — do not the looks and countenances of this venerable body here present, have any effect upon you? Do you not feel that your plans are detected? Do you not see that your conspiracy is already arrested and rendered powerless by the knowledge which every one here possesses of it? What is there that you did last night, what the night before — where is it that you were — who was there that you summoned to meet you — what design was there which was adopted by you, with{\parfillskip0pt\relax\par}  \noindent\selectlanguage{latin}{\large O tempora, o mores!\par\newpage}  \noindent\selectlanguage{english}which you think that any one of us is unacquainted?  Shame on the age and on its principles! \end{document} Can we use curved spacetime to measure the one-way speed of light? This is related to  and  The idea is to shine a beam of light from a clock towards a heavy mass, like a black hole, in some manner such that the curvature of spacetime around the mass is sufficient to &quot;bend&quot; the light directly back to the clock. That is, to send the light along a self-intersecting geodesic using a sufficiently curved spacetime. Note that in this case the source and the detector are the same object, so no clock synchronization is required. Hypothetically, this should measure the one-way speed of light. None of the given refutations from the similar posts on this site are convincing. Here are some of the main refutations, as I understand them, and my counter to them: (1) In being curved by spacetime, the light is actually changing direction, hence this is not the one-way speed. To my understanding of General Relativity, the light travels along a geodesic; that is, a curve such that, ignoring technicalities of Differential Geometry, its tangent direction is constant. There is no reflection or acceleration. So in this sense, how can the light with a constant tangent direction be said to change direction? One might say that the path deviates from a straight line in Euclidean space, but given that spacetime is not Euclidean, has no , and has no global notion of direction, this is the only definition of straight or &quot;one direction&quot; that makes sense. Thus, either the light does not change direction and is &quot;one-way,&quot; or we need to be clearer about what exactly we mean by &quot;one-way&quot; in the context of General Relativity. (2) Such an experiment would be impossible or impractical. I think some posters were saying this because the original questions implied that the clock would have to be at the event horizon of a black hole, which is of course impossible or impractical; however, I don't think such an extreme closeness to the black hole is required. Given that the  of a black hole, where light orbits in a circle, is outside of the event horizon, shining the light at some distance outside of the photon sphere should be sufficient to curve the light back to the clock, regardless of the distance of the clock from the black hole (see my rough illustration). At the extreme, we could place the clock directly on the photon sphere, which should be theoretically possible. Regardless, the question is not about practicality, but whether the one-way speed is theoretically measurable.  Update: Essentially what this argument boils down to, I think, is that the average speed of light along a single self-intersecting geodesic may differ from the average speed of light along a non-geodesic self-intersecting path, which is always c. Put that way, however, it does seem a little ridiculous. It is hard to see how the anisotropy of the speed could be defined in such a way as to be consistent with this pathological case. Presumably, we could approximate a single self-intersecting geodesic with a non-geodesic path arbitrarily closely, so, logically, the average speeds over each path should be approximately the same, i.e., c. Furthermore, how would the &quot;preferred direction&quot; of the speed of light behave around a black hole, for instance? Regardless, I still think this experiment does actually solve the problem for the given notion of &quot;direction&quot;. Though the problem is usually posed in the flat spacetime of Special Relativity, with a global notion of direction, so the apparent unanswerability of this question should be seen as a limitation of Special Relativity only, which is then solved by General Relativity. I keep running into a problem: How can I rotate an UV island by exactly 90 or 180 degrees? The same applies for scaling it to double in size, etc. Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? My final goal is to generate Impulse Response Functions in R.  I have variables that are non stationary when I set k = 5 in a Unit Root test, and they are cointegrated which to my understanding prompts the use of the VECM, from which the Vec2Var argument is used to then generate IRFs. However, my response functions from this methodology do not decay over time and mostly do not revert to the zero line.  Furthermore, I noticed that when I input first differenced variables into the VECM as opposed to level data above, response function do revert to the zero line. Therefore my first question is: 1) is it appropriate to use differenced variables in a VECM model?  Secondly, as an alternative I am considering restricting the number of lags used in the Unit Root tests so that the variables are not all non-stationary; in this case 2) would the use of VECM be void and the VAR with first differences be a more appropriate model? Again, using differenced data is giving me better response functions that revert to zero in the long run. However, 3) is it ok to use the VAR for stationary/non-stationary data in levels where these variables are still cointegrated?  Also, I am using growth rate variables, 4) should I still long transform all variables and use logs in all tests?  Thank you for the help! How can I prove that $\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain?  Also, I need to prove that its field of fractions is isomorphic to the field of rational functions $\mathbb{Q}(t)$?    (The question is taken from ) Wacom Graphics Tablet CTH-480 / CTL-480 Not Detected In Ubuntu 13.10 My Wacom tablet (CTH-480) is not detected by the Wacom Tablet option under settings. The Tablet shows up when I run lsusb but does not show up under settings. Again Thanks.