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This sandbox is intended for a collective collaboration to edit posts which would require a lot of effort and a lot of time, in particular, $\LaTeX$ifying images. It serves to localize to one thread the front-page "bumps" caused by edits, so that they may be easily ignored and mainly to facilitate that procedure. (Since if everyone attributed only a small amount of time, we would then together finish them without loosing too much time) Also, it helps to guard against losing longly-composed edits due to system crashes.

If you wish to take the time to format one of your own posts, please use this thread instead.

At the top of each post, type a link to the post you wanna edit followed with what should be edited in the post itself (directly copied from the code of the post), followed by a small space. $\text{($\star$)}$

Proper Use of the Sandbox

Look for a post which indicates that it is free and then edit it to your heart's content. If you want to edit a post that is not in the list of answers, create a new one with the requirements mentioned in $\text{($\star$)}$.

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  • $\begingroup$ If you didn't understand the purpose of this sandbox well, see the answers below. Thanks. $\endgroup$
    – user93957
    Dec 14, 2013 at 15:14
  • $\begingroup$ I wiki-fied this entire question, and so removed your first two rules (since they are obsolete by virtue of all posts being CW). $\endgroup$ Dec 16, 2013 at 9:39
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    $\begingroup$ Could the four downvoters explain their act? $\endgroup$
    – user93957
    Dec 20, 2013 at 11:47
  • $\begingroup$ @Adobe Are you aware that such a sandbox already exists? The point of having a unique sandbox is that it minimizes the noise on the front page. Multiple sandboxes increase the noise, since they both can be simultaneously on the front page. As such, I recommend deleting this one to avoid this problem. $\endgroup$ Jan 6, 2014 at 17:06
  • $\begingroup$ @BillDubuque I don't that the sandbox you linked to is similar to this one, since one is about answers and the other about edits, one is personal (only the one who wants to post an answer use it) the other is non-personal. $\endgroup$
    – user93957
    Jan 6, 2014 at 18:37
  • $\begingroup$ @Aðøbe When I created the other sandbox the intent was that it would be used for all such purposes (except for TeX testing, for which there is already a sandbox, which is better not reused for this because of the TeX torture tests there) I don't understand why you think that the original sandbox does not suffice. Could you please elaborate. $\endgroup$ Jan 6, 2014 at 18:41
  • $\begingroup$ @BillDubuque I didn't know the intent of the first sandbox since I though it was only for answers. If it is the case, then it is more convenient to delete this sandbox. However, is it permissible to post like this answer: meta.math.stackexchange.com/a/12055/93957 in that sandbox? $\endgroup$
    – user93957
    Jan 6, 2014 at 18:47
  • $\begingroup$ @Aðøbe Having been away I was not sure if there might have been other motivations for a new sandbox. We can amend the other sandbox description to specifically state any protocols for specialized uses, e.g. maybe adding a banner to an answer stating any special purpose of the answer, e.g. inviting collaboration, or whatever other specific purpose it is intended to be used for. Does that sound ok to you? I mentioned similar things when I created the sandbox, but maybe it was in a comment that never made it into the thread. $\endgroup$ Jan 6, 2014 at 18:54
  • $\begingroup$ @BillDubuque "Does that sound ok to you?" - Yes, perfect. $\endgroup$
    – user93957
    Jan 6, 2014 at 18:56
  • $\begingroup$ @Aðøbe Ok, great. Please be sure that no one is actively using this box before closing it. $\endgroup$ Jan 6, 2014 at 19:03
  • $\begingroup$ @BillDubuque Sure. ${}{}$ $\endgroup$
    – user93957
    Jan 6, 2014 at 19:05
  • $\begingroup$ @Adobe Hmm, closing it doesn't stop people from using it. It seems we need mod intervention to lock it. Since you are the author, it probably makes more sense for you to flag with such a request. $\endgroup$ Jan 10, 2014 at 19:03
  • $\begingroup$ @BillDubuque Done. ${}{}{}{}$ $\endgroup$
    – user93957
    Jan 10, 2014 at 19:07
  • $\begingroup$ @Aðøbe Do you think we should add some remarks to the original sandbox to make it clearer that its intent is universal? (except for LaTeX torture tests) $\endgroup$ Jan 10, 2014 at 19:13
  • $\begingroup$ @BillDubuque Of course. $\endgroup$
    – user93957
    Jan 10, 2014 at 19:15

12 Answers 12

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Confusion related to the tractability of an integral - FREE


https://i.stack.imgur.com/6LTWa.png


  • Let's try to compute it. First, we can take advantage of the conditional independence of the $z_i$'s given the cluster centers, $$p(x_{1:n})=\int_{\mu_1: \text{Which symbol here?}}$$
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find the general integrals of the given P.D.E - FREE


Could someone please check this? I don't understand what that thing that looks like $+y$ is supposed to be about, and I'm a little confused about some of the variables.


I tried to find the general integrals of the given P.D.E in the yellow box.

And I found $c_1$. But I cannot find another one, say $c_2$.

Please help me finding $c_2$. Thank you.

$$\color{#F3D159}{\boxed{\displaystyle\,\,\color{black}{px(z-2y^2)=(z-9y)(z-y^2-2x^3)}\,\,}}$$ \begin{gather*} P=x(x-2y^2)\\ Q=+y(z-y^2-2x^3)\\ R=z(z-y^2-2x^3) \end{gather*} $$\frac{\mathrm dx}{x(z-2y^2)}=\frac{\mathrm dy}{+y(z-y^2-2x^3)}=\frac{\mathrm dz}{z(z-y^2-2x^3)}$$ $$\frac{\mathrm dy} y = \frac {\mathrm dz} z \implies \ln y = \ln z + \ln c_1$$ $$\frac y z = c_1$$

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Can an algorithm be part of a proof? - FREE


enter image description here


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This space is free. Anyone can use it.

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  • $\begingroup$ @GEdgar what are you doing?? $\endgroup$
    – user93957
    Dec 18, 2013 at 20:37
  • $\begingroup$ I found one that says FREE and used it. I guess it wasn't FREE after all? $\endgroup$
    – GEdgar
    Dec 18, 2013 at 21:20
  • $\begingroup$ FREE in this context doesn't mean anyone could use it rather it means anyone could edit it. $\endgroup$
    – user93957
    Dec 18, 2013 at 21:25
  • $\begingroup$ @GEdgar, if it were free free, all content would have been deleted. The terminology is non-optimal. "Free" currently means something akin to "not checked out" in a revision control system. $\endgroup$
    – dfeuer
    Dec 19, 2013 at 6:25
  • $\begingroup$ @GEdgar By the way here is a free to use post: meta.math.stackexchange.com/a/12054/93957 $\endgroup$
    – user93957
    Dec 19, 2013 at 12:30
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    $\begingroup$ @dfeuer: What? Confusing terminology defined by a mathematician? That's a first! $\endgroup$
    – GEdgar
    Dec 19, 2013 at 15:26
  • $\begingroup$ @KarlKronenfeld Now that you edited that post here, you can directly edit it in the original post (math.stackexchange.com/questions/509831/…). $\endgroup$
    – user93957
    Dec 22, 2013 at 12:03
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    $\begingroup$ @Adobe Do you recommend replacing the image? $\endgroup$ Dec 22, 2013 at 12:11
  • $\begingroup$ @KarlKronenfeld Yes in the original post. (math.stackexchange.com/questions/509831/…) $\endgroup$
    – user93957
    Dec 22, 2013 at 12:12
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This space is free for rent...

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This space is free for use. $\text{}\text{}$

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This space is free for use. ${}{}{}{{}{}{}}{}{}$

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Questions that are pending edits:


Clairuts' Equation

Which of the following double integrals would correctly solve this problem?

Changing lower limits integral.

Complete representative set of squares modulo $15$.

Questions about the book linear algebraic groups by Springer.

Taylor's Theorem Problem

transition function DFA, PDA

$\mathbb{E}[\mathbb{E}[e^{Yt} \mid X]]$

Ray intersection with generic sphere. Not understanding something fundamental

find the general integrals of the given P.D.E

Evaluate the following using Simpson's rule

The arithmetic mean of $X$ when arithmetic mean of $X^2 = 29$.

Clairuts' Equation

Proving that f is monotonic

Homework -graph theory

Find the area of these 2 specific regions

A simple question about the domain of a PDE

Second fundamental form question.

How to deduce the results of response time by this trajectory approach?

https://math.stackexchange.com/questions/509831/how-to-compute-the-coefficient-of-t

Varying an action

Question on relative homology

Confusion related to the tractability of an integral

What does SVD Entropy Capture?

Method Recovery and Uncertainty

Can anyone explain me this proof about a Brownian Motion?

Why the kernel of $\phi_0: Der_R(B, N) \to Der_R(A, N)$ is $Der_{A}(B, N)$?

2nd order differential

The proof of an abelian tower admits a cyclic refinement --New question

Prove an trigonometric identity. Can someone help me by solving it?

What is wrong with the following proof?

Calculus III boat problem

Does Whitehead and Russells' PM distinguish Proof from Demonstration?

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    $\begingroup$ Many of these seem to be quite old and should not be edited just for the sake of removing images. For example math.stackexchange.com/questions/548511/… is from November $\endgroup$ Dec 14, 2013 at 22:37
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    $\begingroup$ @CarlMummert, it's from November of this year. That's pretty recent in my book. Personally, I think images of text are bad enough to justify editing them away in posts of any age. $\endgroup$
    – dfeuer
    Dec 15, 2013 at 0:33
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    $\begingroup$ @dfeuer: is there really any significant benefit, particularly when the question is already answered? $\endgroup$ Dec 15, 2013 at 0:44
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    $\begingroup$ @CarlMummert, in my opinion, the ability of people who have disabilities preventing them from accessing images to use this site is very important. That includes being able not only to ask questions and get answers but also to read others' questions, vote, perform moderation functions, etc. Obviously, the SE platform has some unfortunate inherent limitations (e.g., not supporting xyjax or any function graphing system), but that does not free us from the responsibility to do what we can within those constraints. $\endgroup$
    – dfeuer
    Dec 15, 2013 at 0:57
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    $\begingroup$ @CarlMummert See this topic: Should I edit a question/answer every-time I see an image in it? meta.math.stackexchange.com/questions/11696/… $\endgroup$
    – user93957
    Dec 15, 2013 at 10:56
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Clairuts' Equation - FREE


enter image description here


$\displaystyle\left(x\dfrac{\mathrm dy}{\mathrm dx}-y\right)^2=a\left(1+\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2\right)(x^2+y^2)^{3/2}$

$\displaystyle \begin{cases}x=\rho \cos(\theta) \\ y=\rho \sin(\theta)\end{cases}\,\to\,\begin{cases}\mathrm dx=\mathrm d\rho\cos(\theta)-\rho\sin(\theta)\mathrm d\theta \\ \mathrm dy=\mathrm d\rho\sin(\theta)+\rho\cos(\theta)\mathrm d\theta\end{cases}$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\dfrac{\mathrm d\rho}{\mathrm d\theta}\sin(\theta)+\rho\cos(\theta)}{\dfrac{\mathrm d\rho}{\mathrm d\theta}\cos(\theta)-\rho\sin(\theta)}$

$\left( \rho \cos(\theta) \dfrac{\dfrac{\mathrm d\rho}{\mathrm d\theta}\sin(\theta)+\rho\cos(\theta)}{\dfrac{\mathrm d\rho}{\mathrm d\theta}\cos(\theta)-\rho\sin(\theta)}-\rho\sin(\theta) \right)^2=a\left[1+\left(\dfrac{\dfrac{\mathrm d\rho}{\mathrm d\theta}\sin(\theta)+\rho\cos(\theta)}{\dfrac{\mathrm d\rho}{\mathrm d\theta}\cos(\theta)-\rho\sin(\theta)}\right)^2\right]\rho^3$

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This space is free for rent...

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