All Questions

271 views

Primary structures in $\mathbb Q$

I'll formulate a topic restricted here to the positive rational numbers $\ \mathbb Q_{_{>0}},\$, then will pose a question (Q2) plus some related, to which I don't know the answers nor reference. ...
27 views

Stochastic Pontryagin Principle with a final state constraint

I am searching for information about the Stochastic Pontryagin Principle with a final state constraint. Someone knows a paper or a book where this case is treated in depth?
42 views

Global dimension of matrix algebra [on hold]

Let $k$ be a field, and $A=T_{n}(k)$. $gldim(A) = 1$, and if $B = A/rad(A)^{2}$, then $gldim(B) = n-1$. Some indication!! How can I prove that $gldim(A) = 1$, and $gldim(B) = n-1$ ? Thank you!
113 views

Example to $2^\kappa\nrightarrow (3)^2_\kappa$, plus closed walks of odd length?

Let $\kappa$ be an infinite cardinal. Consider the following example to $2^\kappa\nrightarrow (3)^2_\kappa$. $V$ is a set of vertices, each of which is an element of $2^\kappa$. Color the edge ...
16 views

Upper bound on the number of convex connected components of the complement of the zero set of a polynomial

The classic Milnor-Thom upper bound on the sum of the Betti numbers of real algebraic sets (for a nice exposition and references, see e.g. N.R. Wallach, On a Theorem of Milnor and Thom, in S. Gindikin ...
24 views

Multivariate analogue of Jackson's inequality's modulus of continuity form

According to Jackson's inequality, there is $c > 0$ s.t. for any continuous function $f: S^1 \rightarrow \mathbb{R}$ (where $S^1 := \mathbb{R} / \mathbb{Z}$ is the circle) and integer $n$ there is ...
139 views

Why should intersection cohomology and quantum cohomology be related for a symplectic resolution?

In http://arxiv.org/pdf/1410.6240.pdf M. McBreen and N. Proudfoot conjectured a precise relationship between the quantum cohomology of a symplectic resolution and the intersection cohomology of the ...
94 views

Additional condition to the Bollobas theorem (Sperner's therorem) in extremal set theory

The Bollobas'1965 theorem is the following: If $A_1,...,A_n$ and $B_1,...,B_n$ are two sequences of subsets of $X=\{1,...,r\}$ such that $A_i\cap B_j = \emptyset$ if and only if $i=j$, then ...
69 views

Twisted Hodge numbers in a family

It is well known (e.g. Voisin's book) that for a smooth family $\pi: \mathcal{X} \to B$ of smooth projective varieties (and projectively normal) over $\mathbb{C}$, the Hodge numbers $h^{p,q}(X_b)$ are ...
143 views

Calabi-Yau theorem on Arithmetic Variety

Let $\mathcal X\to Spec(\mathcal O_K)=C$ be an arithmetric projective variety over $C$ , where $\mathcal O_K$, ring of number filed $K$. Let $\omega$ be a Kaehler current of $\mathcal X(\mathbb C)$. ...
9 views

Understanding the steps taken in a calculation of the maximum profile likelihood of a simple ODE, given some data [on hold]

I'm trying to understand a calculation made in a paper (section 2 from the supplementary contents of ...
35 views

Uniform convergence of long geodesic to Liouville measure

Here is the set up : let $(S,g)$ an hyperbolic surface and $L_g$ the associated volume measure. By the shadowing lemma there exist sequences of long closed geodesics, $\gamma_n$ which approximate the ...
70 views