Elliptical orbit in Newtonian gravity
Why don't planets have Circular orbits?
The equivalence of sample correlation and R statistic for simple linear regression What exactly is the difference between a parametric and non-parametric model? I am confused with the definition of non-parametric model after reading this link  and .   Originally I thought "parametric vs non-parametric" means if we have distribution assumptions on the model (similar to parametric or non-parametric hypothesis testing). But both of the resources claim "parametric vs non-parametric" can be determined by if number of parameters in the model is depending on number of rows in the data matrix.  For kernel density estimation (non-parametric) such a definition can be applied. But under this definition how can a neural network be a non-parametric model, as the number of parameters in the model is depending on the neural network structure and not on the number of rows in the data matrix?  What exactly is the difference between parametric and a non-parametric model? Top of answer covered by sticky top bar after clicking direct link With the introduction of the network-wide sticky top bar , I noticed a bug that's happening on every site (except for Stack Overflow). When you click on an answer link (of the form https://site.stackexchange.com/a/####), the very top of the answer and the upvote button are covered by the top bar:    Stack Overflow shows the correct behavior: Can I use two different cards with the same name in Commander? The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$ is _____ I tried by taking the odd $n$ values as in that case, the integral I suppose was easier to calculate. So, denote $I_n=n\int_{0}^{1}e^{x^2}x^ndx$, then we have : $I_1=\frac{e-1}{2},\\I_3=\frac{3}{2},\\I_5=5(\frac{e}{2}-1),\\I_7=7(3-e)$ Then I tried calculating (random) values using calculator as integration was getting cumbersome. $I_{31}=2.488$, $I_{51}=2.57$. I do not see any kind of recurrence so that I can find a general term for odd $n$. I also tried the method given . The idea was that since integral doesn't depend on $n$ considering $I(n)=\int_{0}^{1}e^{x^2}x^ndx$, then $I'(n)=\int_{0}^{1}x^n\ln(x)e^{x^2}dx$, but this also doesn't lead me to any conclusion as well. I believe I couldn't get to a proper approach to tackle this question. Can someone please help with the idea that involves in solving these type of questions? Cardinality of equivalence relations in $\mathbb{N}$ I came across this long proof on this site:    But I would like to know whether my direction can work.  Say we want to find the cardinality of all equivalence relations in $\mathbb{N}$. Since it is a subset of all relations in $\mathbb{N}$, I conclude it has a cardinality smaller or equal to $\aleph$. Now, define an injective function from $P(\mathbb{N})$ to the set of equivalence relations by matching each subset of $\mathbb{N}$ with the identity relation (which is an equivalence relation in $\mathbb{N}$.  Therefore the cardinality of all equivalence relations in $\mathbb{N}$ is greater or equal to $\aleph$ and using CSB we get the desired result.  Seems legit? Class moderncv moving footer I am using documentclass moderncv to style my resume, and I'd like to put the information that normally goes at the bottom of the document, such as phone number and email, to the space next to the name aligned on the left of the document. I'm a beginnner user, so I'd love to get some enlightenment on this.  \documentclass[11pt,letterpaper,sans]{moderncv}  % moderncv themes \moderncvstyle{casual} \moderncvcolor{blue} \usepackage[scale=0.75]{geometry}  % personal data \firstname{John} \familyname{Doe} \mobile{+1~(234)~567~890}  % content  \begin{document} \makecvtitle \pagestyle{empty}  \section{Education} \cventry{1998-2007}{Degree}{Institution}{City}{\textit{Grade}}{Description}   \section{Computer skills}  \thispagestyle{plain} \end{document}    Simply put, I want to move \mobile from the bottom to the top left. Database schema documentation for the public data dump and SEDE Stack Exchange releases "data dumps" of all its publicly available content roughly every three months , and also makes that information queryable over the Internet at the  (SEDE) (updated weekly, on Sunday). Over time, as new features and other bits of data are introduced to Stack Exchange sites, the "anatomy" of the data dump is likely to change. Why didn't Harry die in the dark forest? Constructing an explicit isomorphism between finite extensions of finite fields Suppose $K$ is a finite field, $K = \mathbb F_{p^s}$. If we take an irreducible polynomial $f$ of degree $d$ over $K$, then the splitting field $L$ of $f$ is $K(\alpha)$ where $f$ is the minimal polynomial of $\alpha$. But then $L = \mathbb F_{p^{sd}} $. Since $\mathbb F_{p^{sd}}$ is unique, we see that this is the splitting field of every irreducible polynomial of degree $d$ over $K$.   Take $K = \mathbb F_2$ and let $P(X) = X^3 + X + 1$, $Q(X) = X^3 + X^2 + 1$. Let $L$ be the splitting field of $P$ and $L&#39;$ be the splitting field of $Q$. The above tells us that $L$ and $L&#39;$ are isomorphic. I would like to construct an explicit isomorphism between $L$ and $L&#39;$.   I know that $L \cong \mathbb F_2[X] /(X^3 +X + 1)$ and $L&#39; \cong \mathbb F_2[X] / (X^3 + X^2 + 1)$. Intuitively, I want to find an isomorphism $\phi : \mathbb F_2[X] \to \mathbb F_2[X]$ such that $\phi((X^3 + X + 1)) = (X^3 + X^2 + 1)$. A little playing around gives me $\phi(X) = X+1$. It now feels like I'm falling at the last hurdle: how do I finish the construction of an isomorphism between $L$ and $L&#39;$? I don't think $\phi$ makes sense as a map from $L$ to $L&#39;$, yet it seems the map I want. How can I solve this quantum mechanical "paradox"? Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard deviation of momentum is $0$, but $\sigma_x$ must be finite. So we find that $\sigma_x\sigma_p=0$. Is something wrong with the uncertainty principle? What are the differences in targets, and when should I switch to one? So I get the 4 options for target selection are:   Attackers Badges Randoms K.O.s   What I don't understand is the pros/cons for selecting each one, and what situations would make each one useful.  Things like Badges and K.O. makes no sense to start off with because nobody starts off with badges, and nobody is going to start off near death unless they are purposely trying to lose (by hard dropping int he same position). I've tried the strategy then of just sticking with Attackers, but then I all of sudden get wave after wave of garbage late into the game.    So it begs the question -- what are the differences in target choices, and how can I use that to my advantage to become a Tetris 99 champion? It is known that a superconductor is a material with electrical resistance zero. My question is, it is exactly zero, a theoretical zero, or for practical realistic reasons it is effectively zero? ISO image integrity check (new try)? When you open an .iso file with e.g. 7-zip, the tool lets you test the ISO file, just like you can test any RAR or 7Z or ZIP file that the file is still ok.  If that test finishes successfully, does that mean the .iso file data and all the files within the ISO disc image are fine and not corrupted (bitrot)?   I am a bit confused because elsewhere I saw it mentioned that the ISO (raw disc image) format doesn't contain any data integrity checksums, so I am unsure what the 7-zip tool is testing while testing an ISO disc image file. Repeated ANOVA unbalanced data I did experiment on one group of rats, the group was tested during 8 days, this is the first stage. The same group was also tested again but this time the test phase was 7 days. I tried to do my analysis using ANOVA repeated measures but I had a problem with the days.. I want to know the difference in the 2 tests but the days are not the same number. I don't know how to handle it. If there is any way to do the analysis using repeated measures ANOVA.   I tried to use repeated measure anova within subjects effect. My first factor will be test with 2 levels (test 1 &amp; 2),second factor is day with the level of ?? Here is the problem! if I write 8 there will be extra day in test 2 and the analysis cant carry!! bibtex and genitive / possessive 's: the proper way to obtain "Kuran's (1989) model" Using ArcMap 10.0, I am working on a map that shows many villages. Each village has a name attribute that I want to use for a label, but in some areas there are so many villages that not all can be labeled. I am using the Maplex label engine and have not checked the "Never Remove (allow overlap)" box.  I am quite happy that not all village names are displayed as this would be way too much. And it is ok that Maplex chooses which labels to display, as I have no way to know which village is more important than another one. This also means that I can't base the labeling on a field such as population or something else, even though that would be less random.  However, I would also like the village points that are not labeled to similarly not be displayed. I think it unlikely that someone would want to see the point without knowing the name of the village. If all points are shown, it is also difficult to tell which point a name label goes with in crowded areas. So instead of choosing just labels not to be shown, I also want the computer to chose features not to be shown.  To give you a better idea on what I mean:    Is there a way to make these features/points not draw if their label is not shown? Invisible software updates list in Software Updater Today I received an update notification for three updates but update manager doesn't say what updates are they.    Does anyone have a clue what this is about? How am I to check what is to be updated? Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$ I've tried getting everything on the left side and transforming it into something squared so that I can prove it's bigger or equals to 0 but I've been unsuccessful. php - Should I encrypt email addresses?