相关论文: Congruences on Stirling numbers and Eulerian numbe…
General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic normality of these procedures.
We define statistical Ces\`{a}ro and statistical logarithmic summability methods of sequences in intuitionistic fuzzy normed spaces($IFNS$) and give slowly oscillating type and Hardy type Tauberian conditions under which statistical…
Motivated by the work of David Singmaster, we study the number of times an integer can appear among the Stirling numbers of both kinds. We provide an upper bound for the occurrences of all the positive integers, and present certain…
We prove that the constellation of Weierstrass points characterizes the isomorphism-class of double covering of curves of genus large enough.
In this paper we announce some results obtained for certain algebraic functions, which we call of cyclotomic type. The main results properly resemble von Staudt-Clausen's theorem and Kummer's congruence for the Bernoulli numbers, and such…
We solve two conjectures of Ceken-Palmieri-Wang-Zhang concerning discriminants and give some applications.
Guillera and Zudilin proved three "divergent" Ramanujan-type supercongruences by means of the Wilf-Zeilberger algorithmic technique. In this paper, we prove $q$-analogues of two of them via the $q$-WZ method. Additionally, we give…
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
In this paper, we give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.
Preliminary results about Lie and potential symmetries of a class of Korteweg-de Vries type equations are presented. In order to prove existence of potential symmetries three different systems of so called determining equations are…
Stirling numbers of both kinds are linked to each other via two combinatorial identities due to Schl\"afli and Gould. Using q-analogs of Stirling numbers defined as inversion generating functions, we provide q-analogs of the two identities.…
In this paper, by using some families of special numbers and polynomials with their generating functions, we give various properties of these numbers and polynomials. These numbers are related to the well-known numbers and polynomials,…
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
By introducing a new point of view in Algebraic Topology relating elliptic curves in $\mathbb{R}^2$ and suitable bordism groups, the congruent number problem is solved showing that the Tunnell's theorem is also sufficient. This could be…
In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian…
In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.
We derive several symmetric identities for Bernoulli and Euler polynomials which imply some known identities. Our proofs depend on the new technique developed in part I and some identities obtained in [European J. Combin. 24(2003),…
We introduce the $B$-Stirling numbers of the first and second kind, which are the coefficients of the potential polynomials when we express them in terms of the monomials and the falling factorials, respectively. These numbers include, as…