NSDictionary Key For Value/Object?
How to get the key for a given object from an NSMutableDictionary?
Is there a way to determine which features / variables of the dataset are the most important / dominant within a k-means cluster solution? Check for Process if Same is Running Is there a script or a way in linux that when I try to execute a shell script/process, if the same is running, it will prompt that same is running and will exit otherwise it will continue. What is mathematical existence? Determinant of matrix "viruses" or "virii"? Does League of Legends have a tournament that is recognized as the 'Most Important'? I have been editing an answer on , with some considerable amount of effort, and when I hit on Save Edits, the edit gets rejected with the following error. I got to know the meaning of this from .     The edit queue is full at the moment - try again in a few minutes!     I tried in a few mins, and still it didn't work. I believe that some edits might be valuable and this resists the users from doing so.   Main Question: Is there a way to show the queue limit at the beginning of the editing process? (So that we won't spend time on doing the edit, knowing it will fail) How do you display a photo map tip in QGIS 3 on Windows?  As a new user I'm not sure if this is my lack of experience or a bug, so I've tried to simplify it as far as I can:  This is the contents of the Layer Display properties.    &lt;div style="width:400;height:400"&gt; &lt;p&gt;test&lt;/p&gt; &lt;div&gt;&lt;img src="C:\Local\aa.jpg" width="350" /&gt;&lt;/div&gt; &lt;/div&gt;   and this is how it appears:    C:\Local\aa.jpg is real file I'm using to try to figure out what the problem is. What am I doing wrong? A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing. I would like to prove the statement in the title.  Proof: We prove that if $f$ is not strictly decreasing, then it must be strictly increasing. So suppose $x &lt; y$.  And that's pretty much how far I got.  Help will be appreciated. Remove a marker from a GoogleMap Background: I'm making a retro style game for both fun, and an unofficial contest.   I have bought a song, song X. However, I then found notation for song X, and all the instruments. So basically, it's a program recreating song X in a sense.  I took the notation, and used another program to make it sound like a chiptune does (just for the fun of it, and it sounds good :P). However, I would like to use this in my game. It's non-commercial, but is this allowed? I would've said yes, because I'm not actually using the original, copyrighted song.  I think the main point is can I:   Use the music with no reference to the author Use the music with a reference, since it's non-profit. Not use the music at all since the melody and rhythm is copyright. How to insert strings containing slashes with sed? How to forbid keyboard shortcut stealing by websites in Firefox Many websites, especially everything involving rich text editing (this site is guilty as well), steal keyboard shortcuts normally used to control Firefox and make them do something else instead. It is totally infuriating when I press something like Cmd-number, Cmd-L, Cmd-T, or Cmd-K and it doesn't do what I want it to. Can I make it stop?  Actually, it would probably be for the best if I could forbid stealing of all Cmd-* shortcuts. I've never seen them used for anything useful. Is it possible? Consider the space of continuously differentiable functions, $$C^1([a,b]) = \{f:[a,b]\rightarrow \mathbb{R}\mid f,f' \text{ are continuous}\}$$ with the $C^1$-norm $$\lVert f\rVert := \sup_{a\leq x\leq b}|f(x)|+\sup_{a\leq x\leq b}|f'(x)|.$$ Prove that $C^1([a,b])$ is a Banach Space.   This was the proof we were given: Assuming $C^1([a,b])$ is a normed linear space all we need to show is completeness. Let $(f_n)$ be a Cauchy Sequence in $C^1([a,b])$ with respect to the $C^1$-norm. Then each $f_n,f'_n\in (C([a,b]),\|\cdot\|_{\sup})$. We know that $C([a,b])$ is complete and thus there exists $f,g\in C([a,b])$ such that $f_n\rightarrow f$, and $f'_n\rightarrow g$ (uniformly) with respect to $\|\cdot\|_{\sup}$. If we let  $$ F_n(x) = \int_a^x f_n(t)dt, \hspace{2mm}  F(x) = \int_a^x f(t)dt $$ then $F_n\rightarrow F$ uniformly because  $$\lVert F_n-F\rVert_{\sup}\leq \sup_{a\leq x\leq b}\int_a^x|f_n(t)-f(t)|dt\leq \lVert f_n-f\rVert_{\sup}&lt;\epsilon.$$ From the fundamental theorem of calculus: $$f_n(x)-f_n(a) = \int_a^x f'_n(t)dt $$ Since $f'_n\rightarrow g$ uniformly then  $$ \int_a^xf'_n(t)dt\rightarrow \int_a^x g(t)dt $$ Since we know that $f_n\rightarrow f$ uniformly, $$f(x)-f(a) = \int_a^x g(t) dt $$ which by the fundamental theorem of calculues implies $f'=g$. So we know have $f_n\rightarrow f$ and $f'_n\rightarrow g=f'$ which mean $f_n\rightarrow f\in C^1([a,b])$ with respect to $C^1$-norm. So every cauchy sequence converges. Hence $C^1([a,b])$ is a Banach Space.   So I understand most of the proof. Where I get confused is that how did we actually show this satisfies the $C^1$-norm? Maybe I don't understand what this norm actually does.   Thank you for any help, comments and advice! Extra slash added to the chat room URLs in the side bar How do I create a dynamic key to be added to a JavaScript object variable How to be sure API calls are using TLS 1.2 We are using .Net to make web service calls the Salesforce API. Is there a way to know for sure that the calls are using TLS 1.2? Are there any API logs or records of the protocol is use in Salesforce we can review to be confident the change is working? Why was the Holdo manoeuvre not used earlier? This question is related to "The Last Jedi":  The maneuvre that vice admiral Holdo (with the purple hair) uses towards the end of the film seems remarkably effective.   It seems that it would have worked pretty well much earlier. Especially as two other ships were just allowed to run out of fuel and be destroyed.  It seems doing it earlier with different assets would have incurred less losses. Yet nobody seemed to consider it. Any in universe reason why? How long does a ban or suspension on an SE site last? I've tried to make some searches about ban and suspension but the data I found doesn't seem to correspond to my experience. I also cannot find a FAQ on the help section.  Can you explain me how these mechanics work?   I've just found  for a review ban duration to be extended automatically at every new suspension . But it's speaking of 2, 7, 30 days.  I've heard from a moderator that the suspension duration is 7, 30, 365 days. Is that correct? Can a moderator change the duration of a suspension? Definition of the Pauli group and the Clifford group There seem to be two definitions of the Pauli group. In Nielsen and Chuang, the Pauli group on 1 qubit is defined as \begin{align*} \mathcal{P}_1 = \{\pm I, \pm iI, \pm X, \pm iX, \pm Y, \pm iY, \pm Z, \pm iZ\} = \langle X, Y, Z\rangle. \end{align*} But in other references, such as ,  \begin{align*} \mathcal{P}_1 = \{\pm I, \pm X, \pm iY, \pm Z\} = \langle X, Z\rangle. \end{align*} The second definition makes more sense in the stabilizer formalism, since we usually only consider the action of Pauli strings of $X$ and $Z$. What bothers me is that by the second definition, the phase gate $S$, which is an element of the Clifford group, results in \begin{align*} SXS^\dagger = Y \notin \mathcal{P}_1. \end{align*} I know that the prefactor $\pm i$ somehow doesn't matter, but can someone justify it from a more mathematical/group-theoretical perspective?