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A nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets
strong law of large numbers nonconventional ergodic averages
2011/1/21
We provide conditions which yield a strong law of large num-bers for expressions of the form 1/N PN n=1 FX(q1(n)), · · · ,X(qℓ(n)) where X(n), n 0’s is a sufficiently fast mixing ve...
Betti numbers of toric varieties and eulerian polynomials
Betti numbers of toric varieties eulerian polynomials
2010/12/3
It is well-known that the Eulerian polynomials, which count permutations in Sn by their number of descents, give the h-polynomial/h-vector of the simple polytopes known as permutohedra, the convex hul...
q-Bernstein polynomials associated with q-stirling numbers and Carlitz's q-Bernoulli numbers
q-Bernstein polynomial Bernoulli numbers and polynomials
2010/12/8
Recently, T. Kim([4]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips([12]). In this paper, we give p-adic q-integral representation for Kim’s q-Bernstein po...
Some identities of Bernoulli numbers and polynomials associated with Bernstein polynomials
Bernstein polynomials Bosonic p-adic integrals
2010/11/26
We investigate some interesting properties of the Bernstein poly-nomials related to the bosonic p-adic integrals on Zp.
The Distribution of Unbounded Random Sets and the Multivalued Strong Law of Large Numbers in Nonreflexive Banach Spaces
distribution of random sets multivalued strong law of large numbers set convergence measurable multifunctions convex sets
2009/1/20
In the first part, we introduce appropriate tools concerning the distribution of random sets. We study the relation between the distribution of a random set, whose values are closed subsets of a Banac...
The Limiting Distribution of the Coefficients of the q-Catalan Numbers
Bernoulli number q-Catalan number unimodality log-concavity moment generating function
2014/6/3
We show that the limiting distributions of the coefficients of the q-Catalan numbers and the generalized q-Catalan numbers are normal. Despite the fact that these coefficients are not unimodal for sma...
Two Kinds of Numbers and Their Applicatins
combinatorial sequence Hankel determinant combinatorial identity
2007/12/12
computational formula of Hankel determinants on some classical combinatorial sequences such as Catalan numbers and polynomials, Bell polynomials, Hermite polynomials, Derangement polynomials etc. From...
The n-point functions for intersection numbers on moduli spaces of curves
n-point functions intersection numbers moduli spaces curves
2018/4/20
We derive from Witten's KdV equation a simple formula of the $n$-point functions for intersection numbers on moduli spaces of curves, generalizing Dijkgraaf's two-point function and Zagier's three-poi...