How to copy file with a different name, but same extension?
Extracting extension from filename in Python
Intersection of powers of an ideal in a Noetherian ring Given a Noetherian ring $R$ and a proper ideal $I$ of it.  Is it true that $$\bigcap_{n\ge 1} I^n=0$$ as $n$ varies over all natural numbers? If not, is it true if $I$ is a maximal ideal? If not, is it true if $I$ is the maximal ideal of a local ring $R$? If not, is it true under additional assumptions on $R$ (like $R$ is regular)? Ubuntu 19.04 and Gnome desktop icons Automatically put PGFPlots xtick scale label in x axis label CloudPagesURL() value not showing in HTML I am trying to pass the email value from a data extension to HTML. I am using the CloudPagesURL() in my email in attempt to grab the subscriber's email.  Here is my code syntax that I am attempting to use:  Email Code:  &lt;p&gt;&lt;a title="MyPage" href="%%=RedirectTo(CloudPagesURL(505,'Email Address',@EmailAddress))=%%" alias="ThisAlias" conversion="false"&gt;Click to unsubscribe page 505&lt;/a&gt;&lt;/p&gt;   CloudPage AMPScript Code:  %%[  VAR @emailAddress  SET @emailAddress = RequestParameter("emailaddr")  ]%%   Cloudpage HTML Code:  &lt;td width='155' valign='bottom'&gt;&lt;input type='text' name='Name1' value='%%=v(@emailAddress)=%%' id='Name1' /&gt;&lt;/td&gt;   Any reason as to why this doesn't work? My syntax might just be wrong or I might be using the CloudPagesURL() function incorrectly. Autodesk Maya symbol lookup error on start after installing AMD proprietary driver on Ubuntu 18.04 I've installed Maya 2018 on Ubuntu 18.04 and tested it with the amdgpu driver (open source) and it launched without problems, but some components were not working with the open source driver so I tried amd gpu pro 18.20 (amd closed-source driver). I ran  ./amdgpu-pro-install   but since then Maya won't work and gives this warning message:  ./maya.bin: symbol lookup error: /usr/autodesk/maya2018/bin/.. /lib/libOGSDeviceOGL4-16.so: undefined symbol: EVP_CIPHER_CTX_init   My card is hd7770 and it's supported by the amd closed driver, so what am I doing wrong? The currently proposed Gravitational wave detection apparatus consists of Michelson Interferometer which is supposed to measure distances of the order of $10^{-22}$m. But the wavelength of the light used is in the order of micrometers ($10^{-6}$m). How is this possible? The conventional way to measure distance is by counting the interference fringes. But for path difference smaller than wavelength of laser light this is not possible. When to use self references or composition? How to make a ISO file out of a folder containing Windows setup files I copied the Windows 8 CD to my HDD. I want to convert that folder to an ISO and use that to create a bootable USB.  Please tell me how I can make an ISO image out of that folder containing files.  This is my folder which I want to convert to a ISO file: Drupal out of the box comes with a page (which is the default homepage) that is assigned to the node path.  How do I avoid users reach it, and redirect them to the actual homepage of the site? What's the name for the relativistic paradox with the train/car travelling over a gap? There is a relativistic paradox I was introduced by a friend in Ithaca (Courtenay Footman). It involves a vehicle travelling over a ravine relativistically, so it's in the general family of ladder paradoxes. There are many ways to phrase it, but here's a simple one.   A three-car train with each car of length $L$ is travelling over a bridge across a ravine. (Assume that the couplings between cars are stiff: this train does not bend.) Unfortunately, some evil genius has precisely removed a length $6L$ of the track. The train however is relativistic, travelling at a speed such that $\gamma \approx 12$.  In the reference frame of the ground, the train should appear to be 1/24th the size of the gap, which suggests that it will fall a little and should crash into the bridge opposite. But in the reference frame of the train, each car of the train is at least twice as long as the gap and aside from the very front wheel and the very back wheel, which need to be supported by rigidity, everything is constantly well-supported. This suggests that the train makes it. Who is right?  I vaguely remember that as an undergraduate knowing only a little relativity, I trusted the train's perspective because it's at rest in that perspective, and Courtenay said that this was ultimately correct after a lot of details got resolved. But I do not remember all of these details such that I could work it out for myself. So I'm looking for some discussion that's a little more well-sourced or authoritative.  What is this paradox called, and what literature has addressed the issue? Is leaving airport at a stop before the final destination illegal? There are tricks such as  or  which involve booking a ticket composed of several connecting flights, then leaving the airport at a stop, possibly even "hopping off" a plane (intermediate landing). Rationale: Sometimes these tickets are cheaper than a ticket to one of the stops. So one adds an additional leg and discards it.  Some people say that when using such tricks, one enters a legal gray area. But I wonder:  Could leaving the airport at a stop really be illegal, i.e. violating an airline's or a travel agency's terms?  Also there are suggestions that one should not request an upgrade, because then the trick may be discovered by the airline. Here I wonder:  How can they know that one will throw away the last leg? How to make sense out of the $\epsilon-\delta$ definition of a limit? The informal intuition for the limit of a function is this:     What is the value of the function $f$ as $x$ gets infinitely close to $c$?   How on earth does this monster  $$ \lim_{x \to c} f(x) = L  \iff  (\forall \varepsilon &gt; 0)(\exists \ \delta &gt; 0) (\forall x \in D)(0 &lt; |x - c | &lt; \delta \ \Rightarrow \ |f(x) - L| &lt; \varepsilon)$$ capture our intuition?  I want the answer to explain and motivate every bit of this formal statement. Remember: I am able to parse the statement, I just don't see how it captures our informal intuition. Yesterday, Asaf Karagila's  sparked an extensive discussion on ways of proving that all countable ordinals are embeddable in $\Bbb Q$, and whether particular solutions to this use the Axiom of Choice.  Since the arguments used to prove this can be shady on their use of Choice when formulated tersely, fully fleshed out answers are appreciated.  To be concrete, this question asks for proofs of the following fact:     All countable ordinals $\alpha &lt; \omega_1$ are order-embeddable in the rationals $\Bbb Q$.   Especially answers avoiding the Axiom of Choice are appreciated.    Of relevance and related interest is  (but it's not a duplicate, since that question asks for explicit embeddings). Why do electrons around nucleus radiate light according to classical physics As I navigate through physics stackexchange, I noticed .  Electrons radiate light when revolving around nucleus? Why is it so obvious?  Note that I do not know anything about quantum mechanics - and I just want classical stories. Is $\lim\limits_{n\rightarrow\infty} n$ comparable to $\aleph_0$? For example, can we say: $\infty=\lim\limits_{n\rightarrow\infty} n &lt; \aleph_0$?  These are two different types of structures. The limit being like the length, extension, or just generic magnitude and the other being cardinality of a set. Can we compare magnitude to cardinality?  Intuitively, we can reach $\aleph_0$ by counting the natural numbers on the number line and in the process will be approaching $\infty$. Which leads me to believe $\infty\leq\aleph_0$. But I can't see why it should be a strict inequality. I feel like they should be of equal magnitude.  I saw on a recent comment that $2^\infty=\infty$, but are those infinities really the same? It seems not to me. Of course we (usually) have that  $2^{\aleph_0}=\aleph_1$ where ${\aleph_0}$ and $\aleph_1$ are clearly two very distinct infinities, countable vs uncountable at least. Maybe one might argue that as far as the concept of magnitude is concerned, all infinities are "equal". How was this answer posted after this question was closed? How can I be a good reviewer? Someday, as strange as it feels to me right now, I might be asked to review an article for publication. A while ago my advisor and I were talking about this, and it hit me that I don't really know how to be a good reviewer, beyond the basics:   Respond timely to things, Make your report clear and detailed, Have actually read the paper, Etc.   Beyond this, though, I'm completely in the dark. So I'd like to ask:     What's some good advice for a first-time reviewer?   My field is math, but I'm really interested in general advice (although advice specific to math, or another field, would also be interesting and useful).    I'd like to make this question "community wiki" or analogous, but I can't seem to figure out how - if someone can do so, please do, and then I will delete this paragraph. Are there examples of third-(or higher)-order linear differential equations in physics or applied mathematics? The classical second-order linear ordinary differential equation is that named after Sturm and Liouville: formally, \begin{equation} (pu')'=ru. \end{equation} It arises naturally in many physical situations, for example through radial considerations of Schrödinger's equation. A higher-order "analogue" of it is the Orr$-$Sommerfeld equation, which, after relabelling the coefficients, may be written as \begin{equation} (\phi u'')''=\psi u. \end{equation} It also arises naturally, namely from certain simplifications applied to Navier$-$Stokes' (in)famous equation, and describes to great accuracy the cross-stream behaviour of channel fluid flow.  I have been thinking long and hard about whether there are additional higher-order linear differential equations that emerge naturally from our mathematical models of the world. It even seems pretty much all of the linear partial differential equations (heat, wave, Schrödinger, etc.) are of second order. Does anybody know of higher-order examples? shebang line not working with cr-lf Anyone can comment this ruby code?