I know velocity and acceleration are higher order derivatives of the position vector. Any other examples? What is the physical significance of higher order derivatives.?
Specific derivatives have specific names. First order is often called tangency/velocity, second order is curvature/acceleration. I've also come across words like Jerk, Yank, Jounce, Jolt, Surge and Lurch for 3rd and 4th order derivatives. Is there a widely agreed list of names for these? How many orders have specific names?  In this case, I'm dealing with NURBs curves, so the "tangency" and "curvature" related words are to be preferred over "velocity" and "acceleration" words.
Aliens abduct mathematician, astronomer, woman Bits I remember about this SF movie which probably originated in late 50s / early 60s:   Humans are flying in a light, general aviation, high winged, single engine aircraft. An alien in a flying saucer abducts the whole kit &amp; kaboodle (plane &amp; passengers). Takes them to a secret terrestrial base Eventually tells them that his computer is damaged and he needs their help to get back to his planet. He needs an astronomer for planetary masses &amp; other information. He needs a mathematician to calculate trajectories and perform other calculations. He needs the woman as eye candy, lol They eventually make it back to the alien home planet which is under attack by its enemy. The attacking aliens are bombarding the original alien's home planet with meteors / asteroids.   That's about all I remember. Test of whole distribution for two samples It seems that KNN is a discriminative learning algorithm but I can't seem to find any online sources confirming this.  Is KNN a discriminative learning algorithm? Multiple citations: citation order different to bibliography order I wish to cite several sources at once and sort my in-text citations in a different manner to how they appear in my bibliography. I want my citations to be sorted by year and my bibliography to be sorted by author. I am using BibLaTeX with Biber. I used  to achieve this with TeX Live 2015 but since upgrading to 2016 (as well as upgrading all my packages) this does not work.  Below is a minimal working example (with a second bibliography for illustrative purposes). I wish for the citations to be sorted ascending by year (2001, 2002, 2003) and the bibliographies to be sorted alphabetically (a, b, c) and descending by year (2003, 2002, 2001) respectively, but below is an image of the result; the bibliographies stay true to the desired sorting but the citations in-text are sorted descending by year.  If I remove the last \newrefcontext then everything (citations and bibliographies) is sorted alphabetically, and if I remove both \newrefcontexts then everything is sorted ascending by year (which was the option specified when originally calling BibLaTeX). It seems that the citations follow the last sorting referenced; ynt as per BibLaTeX options when both \newrefcontexts are removed or else whatever sorting is specified in the last \newrefcontext.  I am compiling in order pdflatex, biber, pdflatex, pdflatex and am on MacTeX.  It seems this would have worked as desired in TeX Live 2015 so is this a bug or has something changed which requires the citation sorting to be set in some other way?  \documentclass{article}  \usepackage[            backend=biber,            style=authoryear,            sorting=ynt,            sortcites,            ]{biblatex}  \usepackage{filecontents} \begin{filecontents}{lib.bib} @article{test1,   author = {b},   title = {b},   year=2003, } @article{test2,   author = {c},   title = {c},   year=2001, } @article{test3,   author = {a},   title = {a},   year=2002, } \end{filecontents}  \addbibresource{lib.bib}  \begin{document}      Hello World! \parencite{test1,test2,test3}      \newrefcontext[sorting=nyt]     \printbibliography      \newrefcontext[sorting=ydnt]     \printbibliography  \end{document}     Edit  I have a workaround but it's super crap: Typeset the document with global sorting=ynt, copy the pdf to another file, then typeset the document with global sorting=nyt; using a PDF editing tool (Apple's Preview suffices) cut the pages containing the bibliography with the desired sorting from one PDF and paste into the other. As I said super crap. I'm not sure if I'd even do this as I'd feel dirty, but it's a workaround nonetheless.  If a solution does not exist or this is a bug without a patch, then what would be similar but much better would be some kind of package (which probably doesn't exist) which only changes certain pages at a time within the PDF (while still actually 'compiling' the whole document so that all the citations are done). It might look something like:  % document preamble % ...  \usepackage{onlychange} \onlychangerange{10,12}  % Bibliography found on pages 10--12 % On next compilation will typeset all pages except 10--12  % ...   It's a long shot but maybe someone knows of such a package or this rambling has inspired an actual solution. Im trying to craft a regex that only returns &lt;link&gt; tag hrefs  Why does this regex return all hrefs including &lt;a hrefs?       (?&lt;=&lt;link\s+.*?)href\s*=\s*[\'\"][^\'\"]+        &lt;link rel="stylesheet" rev="stylesheet"      href="idlecore-tidied.css?T_2_5_0_228" media="screen">     &lt;a href="anotherurl">Slash Boxes&lt;/a>   thank you I use a 7805 for a project where the circuit needs a higher current (~2.8&nbsp;A) at 5&nbsp;V. So I assume that if I use both ICs in parallel I can increase the maximum current capacity. Would it work? Question on showing a bijection between $\pi_1(X,x_0)$ and $[S^1, X]$ when X is path connected. I am trying to do this question taken from Hatchers algebraic topology and I am struggling to understand the notation and the concepts.  As far as I know $\pi_1(X,x_0)$ is the set of end point preserving homotopy classes of loops in X based at $x_0$ and a loop is just a path    $f:I \rightarrow X$ with $f(0)=f(1)$. The question says we can regard $\pi_1(X, x_0)$ as the set of basepoint preserving homotopy classes of maps $(S^1, s_0) \rightarrow (X, x_0)$.   This confuses me, does it mean the set of basepoint preserving homotopy class on maps $g:S^1 \rightarrow X$ which map loops in $S^1$ based at $s_0$ to loops in X based at $x_0$?  Then how can $\pi_1(X,x_0)$ be regarded as this set?  If someone could explain this it would be really useful execute drush command from devel/php drupal Can any one please tell me how can I execute drush command from devel/php?  I can execute PHP codes from devel/php. But I don't know how can I execute drush command from devel/php. (As we know "devel/php" URL coming from devel module).  I have written some custom drush command for cron purpose. I can able to run those commands from command line.  &gt; drush my-cmd or drush cc all or drush status , etc ... I can run it through command line.   Expecting some function as mentioned below to run from devel/php  some_function("drush cc all"); Can someone show me a straightforward proof that  $\lim_{m\to\infty}(1+\frac{r}{m})^{mt}=e^{rt}$  Thanks! Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$ How does "Reputation" work? My mortgage came up for renewal right at the time in 2009 when UK interest rates hit rock bottom. This was unprecidented, and most financial advice was to take out a fixed-rate mortgage. So I perhaps went overboard and got one for ten years.  Five years on, interest rates haven't moved and I'm losing money on it to the tune of £100 a month. Obviously, this is ongoing: so that decision has cost me about £5000 in real terms so far. It'll come to a lot more by the end of the mortgage, unless interest rates rise.  Being fixed rate, it's been designed so you can't get out early. If I decide to end the mortage, it'll cost me £1,000 per year of the mortgage remaining - which is roughly what I'm losing anyway, so that seems a bad idea.   I can overpay by up to £500 per month. However, doing this doesn't help pay down the mortgage at all: the total is just added up and will cause the mortgage to end early, by a period dependent on the overpayment total.   This seems to me to be a very bad idea because hoping interest rates rise over the next five years is the only hope I have of making good on some of the losses that I've made.   Is this sensible thinking? If so, is there anything at all I can do to try and ameliorate the financial pain this product is causing me? I've been trying to wrap my head around the basic concepts of category theory, and I thought I would attempt to illustrate what I understand with the category of sets, probably the easiest example. Particularly, I've been trying to prove that $id_A$ (the identity morphism on $A$, for all $A \in Obj(\mathbf{Set})$) is $1_A \colon A \rightarrow A, x \mapsto x$.  This is a very intuitive and reasonable statement, and it's trivial to prove that $1_A$ is indeed an identity morphism on $A$, and I suppose uniqueness of $id_A$ can be demonstrated analogously to uniqueness of the identity element in a monoid (considering the subcategory which has $A$ as its only object, and endofunctions on $A$ as its only morphisms).  In this manner, it is not hard to prove that the proposition in the title is true, but this demonstration requires to make an assumption or guess as to what could $id_A$ be. Specifically, the scheme of the proof is: assume $id_A$ = $1_A$, see that it works with the definition of an identity morphism, show that the identity morphism is unique, and, in conclusion, $id_A$ can only be $1_A$. What I'm looking for, nonetheless, is a somehow more direct proof, that doesn't assume $id_A$ = $1_A$ at the start. I want to place myself in a state of little or no knowledge about sets and functions, and under this assumption, why would I assume $id_A$ = $1_A$ at first? Why not try with $id_\mathbb{Z}$ = $f \colon \mathbb{Z} \to \mathbb{Z}, x \mapsto x^2 + 1$, for example? It wouldn't work, but I don't have any reason to think that $1_\mathbb{Z}$ is a better guess for $id_\mathbb{Z}$.  I suppose that the proof for which I'm asking would work for categories of sets with additional structure, and probably for posets as well, although I'm not clear as to what modifications it would require to work.  Thanks. Faithful group actions for singleton group or for empty set Let $G$ be a group, possibly a singleton. Let $M$ be a set, possibly empty. Let $\mu: M \times G \to M$ be a right group action. Let $1_G$ be the identity of $G$.  I understand 's second definition of faithful as follows:     $\mu$ is faithful if for each $g \in G$ such that $g \ne 1_G$, there exists $x \in M$ such that $\mu(x,g) \ne x$. $\tag{1}$   Later  says if $\mu$ is free and $M$ is a non-empty set, then $\mu$ is faithful.  Question: Given the idea that we can have $M$ as an empty set, I would like to clarify: Are these correct?   If $G$ is a singleton, then every action $\mu$ is faithful, whether or not $M$ is empty. If $G$ is not a singleton, but $M$ is empty, then every action $\mu$ is not faithful. Why does the aorta spray blood when atmospheric pressure is higher than blood pressure? It seems i'm not gonna find an answer for this question which does not use LHopital's rule. How do you prove limit of (lnx)/x approaches 0 as x moves toward infinity WITHOUT using LHopital's rule? Too big of a sofa Convolution is uniformly continuous and bounded Suppose $f\in L^\infty(\mathbb{R})$ and $K\in L^1(\mathbb{R})$ with $\int_\mathbb{R}K(x)dx=1$. Show that the convolution $f\ast K$ is a uniformly continuous and bounded function.  The definition of the convolution is $(f\ast K)(x)=\int_\mathbb{R}f(x-y)K(y)dy$.   There is the inequality $\|f\ast K\|_\infty\leq\|f\|_\infty\|K\|_1$, which yields that $f\ast K$ is bounded. But what about uniform continuity? Disable ohead on a single page How do I log in if my OpenID is not available, or maybe even no longer exists? Can I restore my lost account, or do I need to start over?  See also: