Why did I get a different name?
Something weird is going on with my login on at least one site
Fix terminal after displaying a binary file Evaluate forecasting ability of GARCH models with RMSE and MAE I am evaluating different forecasting models and their ability to forecast index volatility during period of market turmoil, using two measurements, Root Mean Square Error and Mean Absolute Error. For the previous evaluated models, ARMA (1,1) as an example, I was able to obtain the residuals and calculate the RMSE quite easily in Stata.   When estimating the GARCH (1,1) model in Stata I am however not able to correctly obtain the residuals in the post estimation procedure, no option to directly obtain the RMSE is available. Perhaps I have misunderstood how one should evaluate the forecasting ability of GARCH models, since the models specifies the conditional variance unlike ARMA which specifies the conditional mean.   Does anyone have a suggestion on how to obtain these evaluation measurements after estimating a GARCH model? And preferably how to do it in Stata. Energy-Momentum Tensor in QFT vs. GR What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu f_i - \eta^{\mu\nu}\mathcal{L}$$ (the four conserved Noether currents corresponding to four possible spacetime translations)  where $\{f_i\}_{i=1}^N$ are the $N$ matter fields in the theory, and we assume $f_i\mapsto\alpha^\nu\partial_\nu f_i$ for translations,  and stress-energy tensor from the Einstein-Hilbert action, which is: $$ T_{\mu\nu}\equiv-\frac{2}{\sqrt{-g}}\frac{\delta\mathcal{L}_{Matter}}{\delta g^{\mu\nu}} $$   In particular, how do you get that the two are equal (are they?) for Minkowski space, for which there is no variation in the metric? Product of elements of a finite abelian group Suppose $G=\{a_1,...,a_n\}$ is a finite abelian group, and let $x=a_1a_2\dotsm a_n$.   Prove that if there is more than one element of order $2$ then $x=e$.   What I've done so far: (#1 is just for illustration, There should be at least $3$ such elements)   $G$ has an even number of elements with order $&gt;2$ (They are paired so: $(a,a^{-1})$ ). And then there are $e$ and $\{b|o(b)=2\}$. Also, if $G$ has at least one element of order 2 then $|G|$ is even (Lagrange). Thus $|\{b|o(b)=2\}|$ must be odd. If there is exactly one element $b$ of order $2$ then $x=b$. That's because $G$ is abelian, and we can write: $x=e\cdot b\cdot(a_1 a_{1}^{-1}\dotsm a_n a_{n}^{-1})=b\cdot(e\dotsm e)=b$. If there are exactly $3$ such elements $a,b,c\in G$, then, as shown above, $x=abc$ and thus $x=e$ (That's because $(abc)^2=a^2b^2c^2=e$ which means $abc\in \{a,b,c,e\}$. If $abc=a$ then $b=c^{-1}=c$ which is false, same goes for $abc=b,abc=c$.)   I haven't managed to find a reason why the claim must hold for $5, 7, ...$ (i.e. All other odd integers). Does anyone have an idea?  Thanks in advance. Please excuse my English.  edit: Not a canonical answer but a simple one (if such even exists). Consider an inviscid Burgers equation:  $u_t + u u_x = 0.$  With the initial data:  $ u(x,0) = \left\{ \begin{array}{ll}              0  \quad  &amp; \text{if} \quad x &lt; 0, \\[0.5em]              1  &amp; \text{if} \quad x &gt; 0.\end{array} \right. $  Possible weak solutions to this problem include, for example:  $ u_1(x,t) = \left\{ \begin{array}{ll}              0  \quad  &amp; \text{if} \quad x &lt; t/2, \\[0.5em]              1  &amp; \text{if} \quad x &gt; t/2.\end{array} \right. \hspace{10mm} $   $ u_2(x,t) = \left\{ \begin{array}{lll}              0  \quad  &amp; \text{if} \quad x &lt; 0, \\[0.5em]                      x/t &amp; 0 &lt; x &lt; t,\\[0.5em]              1  &amp; \text{if} \quad x &gt; t.\end{array} \right. $  Every material that provides such examples states that it is easy to check that these are both solutions of our problem. I do not see how that is done.  I know how to obtain the equation:  $ \int_{0}^\infty \int_{-\infty}^\infty [ q \phi_t + f(q) \phi_x ] dx dt + \int_{-\infty}^\infty q(x,0) \phi(x,0) dx = 0,  $  But I do not see how to "test" if the weak solutions provided above satisfy this. I tried writing the solutions as Heavside functions and integrating them, but I am not sure how to handle an arbitrary test function.  I assume there are some solution I could construct that would not be the weak solution to our initial data, how to check that? Prove that in any GCD domain every irreducible element is prime Remove dots & Page numbers from TOC I am using example given here by @stephan .  Works great however I want to get rid of dots and page numbers.  I added this to the preamble   \let\Contentsline\contentsline  \renewcommand\contentsline[3]{\Contentsline{#1}{#2}{}}   that removed the page numbers, but do not know how to remove the dots. I would appreciate your help. Its hard to get result without understanding the basics. String Comparison in Java How can I merge properties of two JavaScript objects dynamically? I need to be able to merge two (very simple) JavaScript objects at runtime.  For example I'd like to:  var obj1 = { food: 'pizza', car: 'ford' } var obj2 = { animal: 'dog' }  obj1.merge(obj2);  //obj1 now has three properties: food, car, and animal   Does anyone have a script for this or know of a built in way to do this?  I do not need recursion, and I do not need to merge functions, just methods on flat objects. Should I keep my swap file on an SSD drive? I'm considering getting an SSD drive to run as the primary OS partition.  As I understand, this should provide a substantial improvement in performance.     My question is this: Should I leave the swap file on that drive?     The swap partition will be largely random seeks and so should benefit from the speed.  On the other hand, it will be constantly written to which will wear out the drive faster. Two sidebars in Beamer for two presentations in one tex file Beamer, Babel and Tikz conflict Exporting multi layered Illustrator to Photoshop SEO safe way to run beta of new site on seperate domain Proving that a doubly-periodic entire function $f$ is constant. Let $f: \Bbb C \to \Bbb C$ be an entire (analytic on the whole plane) function such that exists $\omega_1,\omega_2 \in \mathbb{S}^1$, linearly independent over $\Bbb R$ such that: $$f(z+\omega_1)=f(z)=f(z+\omega_2), \quad \forall\,z\in \Bbb C.$$Prove that $f$ is constant.   The intuition seems clear to me, we have the three vertices of a triangle given by $0$, $\omega_1$ and $\omega_2$. All points in the plane are one of the vertices of that triangle under a suitable parallel translation. The constant value will be $f(0)$, fine. Throwing values for $z$ there, I have found that $$f(n\omega_1) = f(\omega_1) = f(0)=f(\omega_2) = f(n\omega_2), \quad \forall\, n \in \Bbb Z.$$  I don't know how to improve the above for, say, rationals (at least). Some another ideas would be:   Checking that $f' \equiv 0$. I don't have a clue of how to do that. Write $w = a\omega_1+b\omega_2$, with $a,b \in \Bbb R$, do stuff and conclude that $f(w) = f(0)$. This approach doesn't seem good, because I only have a weak result with integers above. Finding that $f$ coincides with $f(0)$ on a set with an accumulation point. This seems also bad: the set on with $f$ coincides with $f(0)$ by which I found above is discrete.    Nothing works and this is getting annoying... And I don't see how analyticity comes in there. I'll be very thankful if someone can give me an idea.  (On a side note.. I know that this title is not informative at all. Feel free to edit if you come up with something better.) Let me begin by stating that I did google the answers (and I'll reference to them soon). Yet each of the resources I found discussed one particular method, I'm interested in a comparison of the approaches.  So far, I've found three ways to deal with this problem:   split the number into two columns (integer and fractional parts), as documented  or . The LaTeX code is simple, but the approach is a pain when it comes to copying and pasting tables from external sources. use  manually use Mike Zhang's automatic  (). I have yet to test it.   What do most people use? dcolumn? Are there other options? Does Java have buffer overflows? In An Introduction to Statistical Learning (James et al.), in section 3.7 exercise 5, it states that the formula for $\hat{\beta}_1$ assuming linear regression without an intercept is  $$\hat{\beta}_1 = \dfrac{\displaystyle\sum\limits_{i=1}^{n}x_iy_i}{\displaystyle \sum\limits_{i=1}^{n}x_i^2}\text{,}$$ where $\hat{\beta}_0 = \bar{y}-\hat{\beta}_1\bar{x}$ and $\hat{\beta}_1 = \dfrac{\displaystyle S_{xy}}{S_{xx}}$ are the usual estimates under OLS for simple linear regression ($S_{xy} = \displaystyle\sum\limits_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})$).  This is not the actual exercise; I am merely wondering how to derive the equation. Without using matrix algebra, how do I derive it?   My attempt: with $\hat{\beta}_0 = 0$, we have $\hat{\beta}_1 = \dfrac{\bar{y}}{\bar{x}} = \dfrac{S_{xy}}{S_{xx}}$.  After some algebra, it can be shown that $\displaystyle S_{xy} = \sum\limits_{i=1}^{n}x_i^2 - n\bar{x}\bar{y}$ and $\displaystyle S_{xx} = \sum\limits_{i=1}^{n}x_i^2 - n\bar{x}^2$. From here, I'm stuck. How to disable Import option in LibreOffice Calc while pasting text in a cell? I'm making a table in which I have to copy few lines from pdf to a table. I'm using LibreOffice calc for table making purpose. Problem is that even though I am copying simple text from the pdf, when I paste it to LibreOffice, Import Option keeps on poping up(randomly-sometimes it pop up sometime it does't). And due to this pasted text's font size also very small. Desired result is that when I paste the text in the cell, it just got pasted in the cell, without any time wasting popup which also disturbs the font size. Same question is asked here but no solution. Is there a word for someone with the same name? If a person shares my name, in Dutch there is the word &quot;naamgenoot&quot;, meaning roughly 'member of the same name'.  John A: Hi, my name is &quot;John&quot;  John B: O, then we're insert solution word here!  Similarly,  'classmate' is 'klasgenoot' in Dutch 'roommate' is 'kamergenoot' in Dutch  I'm pretty sure I cannot call someone with the same name as mine a 'namemate' :)  Edit Because sceptics appear to be frustrated mightily by an apparent lack of research, there was  in chat, with no satisfactory conclusion. /Merriam Webster namesake appears to be linked to intentional name correspondance (being named after someone). There may be a US/UK English divide there.  &quot;I was named after my grandfather. I am his namesake.&quot; -   Also, the introduction seems to hint at much broader meaning:  &quot;Namesake is a term used to characterize a person, place, thing, quality, action, state, or idea that has the same, or a similar, name to another&quot;   Do you know of a better word/phrase to describe this succinctly?