Splitting a string with numbers and letters
How to split strings into text and number?
Extended Euclidean Algorithm: backward vs. forward How much hard drive space do I need to install Windows 7 on my Mac via Boot Camp? I have a Macbook Air and would like to install Windows 7 on it via Boot Camp. How much hard drive space should I make sure to have free before doing this? Do multi-use keys get discarded when finished with? As with many resident evil games, you sometimes needs to collect certain keys to open certain doors, and resident evil 7 has plenty of these around.  Some keys are clearly single use, and get left in the lock in which you use them. However, there are a number of keys that can be used on multiple doors. For example, the Scorpion Key.  I am concerned that I might end up carrying these around needlessly and using up valuable inventory space, so...  Do these multi-use keys get discarded when you use them on all the doors they apply to? Or do you get a warning saying the key is no longer needed? (like previous games are known to do) New navigation doesn't appear to alert of question changes when watching a tag I am watching the  tag on Stack Overflow. My filter looks like this:    I do not receive notification of new questions. Previously I'd get notifications like this:    This notification does work when watching the  page of Meta.   Are notifications only active for a certain set of filter options? If so, what are they? If not, can we get them back when watching pages other than the main page? Why is my fire simulation so light? I have been struggling to get a match tip to actually look like it's on fire and no matter what material shaders I try, I can't seem to achieve what everyone else does, I can in other scenes, just not this one. :( Does iCloud Drive automatically download all files? I am using OS X 10.10 with iCloud Drive. I am thinking of upgrading to a bigger storage plan (at the moment: 5GB).   I am running this Version on a MacBook Air with 128GB.      If I buy the 500GB package, does it mean that I fill up my local hard   drive automatically when I upload things to the iCloud Drive?   iTunes has the Option of stream the music i didn't download yet.   How does iCloud Drive behave? Is there any Online Document? Drawing cross section in QGIS? Does anyone have a simple work-flow for drawing cross sections of earth features in QGIS?   My thing is that QGIS is being used to present the plan view, but we have a little interest in some elevations as well. All the data is one set and is simply an elevation value in the attribute table, I don't want to have to move all that to CAD.  One logical workaround is to present the z value as the y.  I am a dunce in paper space in CAD, and would be more comfortable with the QGIS Composer. Can markdown icons be available on the iPad? As you can see by the screenshot below, neither buttons nor even the live-preview is available on the iPad.    StackExchange is great on mobile devices, maybe it can be full available in mobile safari as well.  The same thing happens with the tags autocomplete, there is no options for it! we need to check previous questions to know what tags are available to use. Every Artinian ring is isomorphic to a direct product of Artinian local rings Proposition. Let $R$ be commutative ring with $1_R$. We assume that $R$ is an Artinian ring and $M_1,\dots,M_n$ its maximal ideals. Then         $R/\mathrm{Jac}(R)\cong (R/M_1)\times \dotsb \times (R/M_n)$.   The ring $R$ is isomorphic to the direct product of a finite number of Artinian local rings.      Proof. 1. It's obvious that $M_i+M_j=R,\ \forall 1\leq i \neq j \leq n$. So, from Chinese Remainder Theorem, we have  $$R/\bigcap_{i=1}^{n}M_i = R/\mathrm{Jac}(R) \cong (R/M_1)\times \dotsb \times (R/M_n),$$ as we wanted.    Since $R$ is an Artinian ring, we have $\mathrm{Jac}(R)^m=\{0_R\}$, for some $m\in \Bbb Z^+$. But,  $$\{0_R\}\subseteq M_1^m\dotsb M_n^m=(M_1\dotsb M_n)^m\subseteq (\bigcap_{i=1}^{n}M_i=\mathrm{Jac}(R))^m=\{0_R\}.$$ So, if we apply CRT we will take  $$R\cong R/\{0_R\}\cong R/M_1^m\dotsb M_n^m\cong (R/M_1^m)\times \dots \times (R/M_n^m).$$   Questions.   1) Are these thoughts complete and correct?  2) Why $R/M_i^m$ are artinian local rings?  3) Could you please elaborate some examples as an application? PhD thesis without acknowledgements During the process of writing my PhD thesis, I was close to falling out with my adviser, the advice I received from other staff at the lab (including the director) was unhelpful at best. I have since made up with my adviser and have successfully defended the thesis. I now have to publish my thesis.  The department says that one can include acknowledgements. All of the theses I have seen in my lab and in my department feature acknowledgements. Due to this special situation,  I don't quite feel that acknowledgements are called for. Yes, my adviser helped during the first half of the project but then almost completely reverted his stance. In terms of contribution, it is my opinion that he comes out at 0%.  I do not want to address any of the issues in the acknowledgements. I do not think that this is the right place. Likewise, I do not feel like thanking any of the involved people. Therefore, I would just leave out the acknowledgements completely. In academia, is this considered worse than lukewarm acknowledgements? Should I actually care about the acknowledgement, because others do? How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$? Let $a\geq 0$ and $ b\geq 0$. Prove that $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$. [Hint: Use the identity $(a^n -b^n)=(a-b)(\sum_{i=0}^{n-1}a^ib^{n-1-i})$]    I need some help! I cannot do it even with the hint... :( How to read dash files How can I read a dash file from the terminal other than delimiting it with ./  For example to read a - file we can read it by   cat ./-file_name  Q: Is there an alternative way to achieve the same thing? How to print object content in correct way? Equivalent of "both" when referring to three or more items? In the same way as you can currently render the active viewport in Open GL? Some aspects of the Workbench renderer look as if they will be very useful for NPR people. Graduate school admission with a degree in a different field Remotely changing hard drive boot order, windows 7 I have one workstation chassis with two hard drives.  Depending on which one I boot from, I get one of two different operating systems: both are windows 7, but they have different static IPs, serve totally different purposes, etc.    The workstation has a modern asus motherboard, core i7 intel CPU, 32 GB ram.   Is there a way to remotely change which hard drive is booted from on a reboot?  Both systems have remote users, and i'd like a solution that is more elegant than being physically present and selecting boot order manually. How can I separate multiple quote blocks? I have a series of quotes which I want to display in two separate quote blocks.  &gt; Are questions about Microsoft Word Online on-topic here? I don't &gt; really see any posted here, but perhaps I am not searching correctly. &gt; - mweiss &gt;  &gt; Yes, they are. We even have a specific tag: [tag:word-online]. -ale &gt;  &gt; Thanks! I'm sorry I missed that tag. -mweiss   When I try to add these to my post, they display as a single combined quote.     Are questions about Microsoft Word Online on-topic here? I don't   really see any posted here, but perhaps I am not searching correctly.   - mweiss      Yes, they are. We even have a specific tag: . -ale      Thanks! I'm sorry I missed that tag. -mweiss   How can I separate quotes so that they aren't combined into a single quote block? For example an electron radiates when accelerated. So does a positron. But is the radiation emitted by accelerated positronium the sum of the radiation emitted by each separately? If not, why not? If so, does this provide a way of testing whether a given neutral particle is composite? For example, does a neutron bremsstrahlung when decelerated? Characterization of weak convergence in $\ell_\infty$ Is there some simple characterization of weak convergence of sequences in the space $\ell_\infty$? If yes, is there some similar claim for nets?   I was only able to come up with a characterization of sequential weak convergence using limit along ultrafilters, which I will describe below. I wonder whether there is some insight into this characterization. (E.g. whether there is some simple reformulations which does not use ultralimits.) Moreover, I do not know whether at least this characterization works for nets, too.  We have the following result describing weak convergence in $C(K)$, see e.g. Corollary 3.138,  in Banach Space Theory by Fabian, Habala et al. (It is a consequence of Rainwater theorem and characterization of extreme points of unit ball in $C(K)^*$.)     Let $K$ be a compact topological space. Let $\{f_n\}$ be a bounded sequence in $C(K)$ and $f\in C(K)$. Then, if $f_n\to f$ pointwise, we have $f_n\overset{w}\to f$.   Moreover we have isometric isomorphism between $\ell_\infty$ and $C(\beta\mathbb N)$, which is described e.g. in the Wikipedia article on  or in  of Carothers' book A short course on Banach space theory. This isomorphism assigns to each bounded sequence $(x_n)$ the continuous function $\overline x$ on $\beta\mathbb N$ defined by $$\overline x(\mathscr U) = \operatorname{\mathscr U-lim} x_n,$$ where $\operatorname{\mathscr U-lim} x_n$ denotes the  of $x_n$ w.r.t the ultrafilter $\mathscr U$.  Combining the above results we get the following characterization:      Let $f^{(n)},f\in\ell_\infty$. The sequence $f^{(n)}$ converges to $f$ weakly if and only if for every ultrafilter $\mathscr U$    $$\lim_{n\to\infty} \operatorname{\mathscr U-lim} f^{(n)}= \operatorname{\mathscr U-lim} f.$$   (The above claim for principal ultrafilters is just a pointwise convergence. But in the above claim the equality is required for free ultrafilters, too.)