In this paper, we consider Poisson-Charlier and poly-Cauchy mixed type polynomials and give various identities of those polynomials which are derived from umbral calculus. 424 Dae San Kim, Dmitry V. Dolgy, Taekyun Kim and Jong-Jin Seo

Extensions of Sherman’s theorem to convex functions of higher order and to real weights are obtained by using Taylor’s formula. New upper bounds for Sherman’s difference and generalized inequalities are established. Some related Cauchy-type means are discussed.

The research is Supported by Natural Science Foundation of Fujian Province, China (2007J0183). Abstract Under the condition of arc-wise smooth path of integration, the Plemelj formula of Cauchy-type integral on random process with second order moment is obtained.

We review some results about the computational power of several computational models. Considered models have in common to be related to continuous dynamical systems. 1 Dynamical Systems and Polynomial Cauchy Problems A polynomial Cauchy problem is a Cauchy problem of type { x′ = p(x, t) x(0) = x0 where p(x, t) is a vector of polynomials, and x0 is some initial condition. The class of functions ...

In this paper, we present certain results concerning the location of the zeros of lacunarytpye polynomials which generalize and refine some known Cauchy type bounds for the zeros of polynomials.

We present an affirmative answer to Stanley’s zrank problem, namely, the zrank and rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices are nonsingular and furthermore, the signs depend on the number of zero entries. Similar to notion of the jrank of a skew partition, we give a characterization of the rank in terms of the Giambelli type matrices of t...

Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers.