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bio website thatsmathematics.com
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visits member for 5 years, 3 months
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33m
comment How do we respond to the question, “What is mathematics?”?
From the help center: "Your questions should be reasonably scoped. If you can imagine an entire book that answers your question, you’re asking too much." See Courant and Robbins 1941, et seq.
18h
comment Is Zsigmondy's Theorem utilized in Sociology to the extent that a lay person might be familiar with its use?
A Google search for "Zsigmondy's theorem sociology" shows nothing relevant. I can't think of any reason why they should be related at all.
1d
answered Maximum principle for the heat equation with Dirichlet conditions
2d
comment Construction of a path of quadratic variation
Suggestion: Try to construct a "sawtooth" path $x_0$ which at least has finite positive quadratic variation on any neighborhood $[0, \epsilon]$, by giving it smaller and smaller "teeth" of appropriate size near 0. Then construct $x$ with rational translates of $x_0$, like $x(t) = \sum_{n=1}^\infty 2^{-n} x_0(t-q_n)$.
2d
comment A question of Erdos on entire functions
1. What's the full citation of the Erdős paper? 2. Have you checked MathSciNet or a similar database for papers that cite this one?
Jul
4
comment Is a specific sequentially closed subset of $M([0,1])$ closed?
@ChristianRemling: Yes, I understand that the class of functions of the form $f(x,y) = g_1(x) h_1(y) + \dots + g_n(x) h_n(y)$ is dense. And I can see that if $f$ is of this form then the set $A$ is closed. What I do not understand is how we conclude that if $f$ is a uniform limit of such functions, then $A$ is again closed.
Jul
4
comment Ergodicity property for continuous-time Harris positive Markov process
I don't understand the downvote and close vote. I think this is a perfectly reasonable research-level question.
Jul
4
comment Is a specific sequentially closed subset of $M([0,1])$ closed?
@BillJohnson: I had the same idea but the details were not immediately clear to me, particularly the density argument. If I can work it out, I will post an answer, otherwise I might ping you again with questions (unless you are inclined to write a more detailed answer anyway).
Jun
21
comment Dense subsets in tensor products of Banach spaces
No, certainly not for any choice of the norm $\|\cdot\|_B$: it could be totally unrelated to the $B_1, B_2$ norms. The usual assumption for the norm on a tensor product of Banach spaces is that it should satisfy $\|f \otimes g\|_B = \|f\|_{B_1} \|g\|_{B_2}$, see ncatlab.org/nlab/show/tensor+product+of+Banach+spaces, and in that case your claim is true.
Jun
20
comment Proof of no bound for stochastic integral
Oh, when you wrote $f(t)$ I assumed $f$ was deterministic. Of course if $f$ is a process then what I said does not apply.
Jun
20
comment Proof of no bound for stochastic integral
By the way, I wouldn't expect your $\sim$ statement to be true in any reasonable sense. The "infinitesimal increments" $dW(t)$ can be both positive and negative, so there's no reason why an inequality like $f > \epsilon$ should be preserved in any way when integrating.
Jun
20
comment Proof of no bound for stochastic integral
Do you know anything else about $f$? For example, if $f \in L^2([0,T])$ then $X$ is normally distributed with mean 0 and variance $\int_0^T |f(t)|^2\,dt$, so your desired statement follows and you don't need the lower bound on $f$, except to exclude the trivial case where $f = 0$ a.e. If you don't have any control on the integrability of $f$, you may have trouble guaranteeing that the Ito integral exists.
Jun
20
comment Proving a differential inequality without performing iteration
If you set $f = \sqrt{g}$ you immediately get $f' \le \frac{1}{2}$. I guess you do have to account for points where $f=g=0$ but that should not be hard.
Jun
19
comment Infinitesimal generator is bounded
@MichaelRenardy: Strictly speaking, that itself is not the issue: for each $t > 0$ the operator $(S(t)-I)/t$ is bounded. The issue is that the uniform boundedness principle argument requires the pointwise limit to exist for every $x$ in a Banach space (completeness is essential), and here it only exists for $x$ in an (incomplete) dense subspace.
Jun
19
comment Which topological properties are preserved under taking box products?
@KConrad: I took a shot at writing it out in prose.
Jun
19
revised Which topological properties are preserved under taking box products?
less logical symbology
Jun
19
comment What lets the Square of Opposition fail in Intuitionistic Logic?
I believe in some sense, once you have posted the question, it belongs to the community, not to you. Evidently, although you think it's silly, other people have found it interesting and useful, and answerers have spent their time writing answers that were also found interesting and useful. It's against the rules of the site to "vandalize" your own question by editing out the content.
Jun
19
revised What lets the Square of Opposition fail in Intuitionistic Logic?
rolled back to a previous revision
Jun
18
answered When do Borel $\sigma$-algebras generated by the total variation norm and the weak* topology coincide?
Jun
16
answered Is it possible to prove concentration bounds from optional stopping theorem?