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5
votes
1
answer
921
views
Space of metrics with positive sectional curvature
Hello;
We know that the space of riemannian metrics on a compact manifold is an open cone in the space of symmetric 2-tensors.
Is it reasonable to think that metrics with positive sectional curvatur …
1
vote
2
answers
891
views
Concrete examples concerning standard deviations and mean absolute deviations
Once again stackexchange is not responding to one of my questions (so far no comments, no answers, two up-votes). Hence this "crossposting":
Is there a simple (or not simple?) algorithm that will ch …
2
votes
1
answer
350
views
is there a way to solve the following equation?
(I tried asking that on math.stackexchange.com, but did not get a satisfying answer. I am trying here as well, in case someone here will have more insight. The question was eventually abandoned there. …
3
votes
1
answer
205
views
A minimum problem of the CoV
I have the following minimum problem:
$$\tag{1} \min_{u\in W^{1,1}(0,B)} \int_0^B (\sqrt{1+|u^\prime (t)|^2} -a)\ u^{k-1} (t) t^{h-1}\ \text{d} t $$
(where $B>0$, $0 < a < 1$, $h,k\in \mathbb{N}$ a …
3
votes
1
answer
454
views
A Bessel integral
Today I came across the integral
$\int_a^\infty e^{-bx} I_n(x) dx$
where $I_n$ is the modified Bessel function of the first kind. There is a solution for $a=0$, provided in Gradshteyn and Ryzhik, bu …
8
votes
1
answer
365
views
Counting copies of a BA within a BA: arbitrarily many vs infinitely many
Informally, I am wondering if a Boolean algebra $\mathcal{B}$ contains infinitely many disjoint copies of a Boolean algebra $\mathcal{A}$ whenever it contains arbitrarily many disjoint copies of $\mat …
1
vote
2
answers
313
views
Automorphisms of locally finite countable posets-2
Given is a locally finite countable connected poset which satisfies further the following properties:
Let $C$ be any maximal chain ( i.e. inextendible chain) and $A$ be any antichain. Then $A$ is …
14
votes
1
answer
2k
views
What is the limit of the "knight" distance on finer and finer chessboards?
Consider the "infinite chessboard" on the plane. Think of it as the lattice $X_1:=\mathbb{Z}^2$, and also finer chessboards $X_n$ corresponding to $\frac{1}{n}\cdot \mathbb{Z}^2$, $n\geq 1$. Given two …
2
votes
1
answer
456
views
Giambelli and Porteous Formula
I was looking at the formula to compute the schubert class of a grassmanian in terms of a more elementary schubert cycles via giambelli's formula, and on the other hand Porteous formula tells us how t …
5
votes
1
answer
474
views
When are constructible points closed?
Let $X$ be a scheme. What technical hypotheses must be imposed on $X$ to assure that a point $p \in X$ is closed if and only if the 1-point set $\{p\}$ is constructible?
3
votes
3
answers
5k
views
Show that holomorphic functions are infinitely differentiable without complex analysis [duplicate]
Possible Duplicate:
Is there an integration free proof (or heuristic) that once differentiable implies twice differentiable for complex functions?
Is there a way to show that holomorphic func …
4
votes
0
answers
167
views
A fast way to test whether a partial function can be extended to a chirotope of rank 3 ?
Hello,
What is a fast way to test whether a partial function can be extended to a chirotope of rank 3 ? That is: I have a domain
$E = \{1,...,n\}$
and a partial function
$f: E^3 \to \{-1, 0, 1\}$
…
4
votes
2
answers
476
views
Lens-shaped vs globally hyperbolic
The theorem of uniqueness of solutions of first order, quasilinear, symmetric hyperbolic systems is naturally formulated in terms of so-called lens-shaped domains. Roughly, a domain is lens-shaped if …
11
votes
2
answers
1k
views
Is [mD] very ample if D is ample?
Let D be an ample R-divisor, is the round down [mD] very ample for any sufficiently divisible number m?
I think it's true. But I do not know how to arrange an argument.
4
votes
2
answers
674
views
When is a class function on a group G (finite abelian) into the rational numbers Q an elemen...
Given a class function $f: G \to \mathbb Q$, where $G$ is a finite abelian group, is there an easy way to decide whether $f$ is an element of the rational representation ring $R_{\mathbb Q}(G)$, i.e. …