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In this paper, we study partially degenerate Bell numbers and polynomials by using umbral calculus. We give some new identities for these numbers and polynomials which are associated with special numbers and polynomial. [ABSTRACT FROM AUTHOR]

We consider the Witt-type formula for the nth twisted Daehee numbers and polynomials and investigate some properties of those numbers and polynomials. In particular, the nth twisted Daehee numbers are closely related to higher-order Bernoulli numbers and Bernoulli numbers of the second kind. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some identities of q-extensions of special polynomials which are derived from the fermonic q-integral on ℤp and the bosonic q-integral on ℤp. [ABSTRACT FROM AUTHOR]

Recently, some interesting and new identities are introduced in the work of Kim et al. (2012). From these identities, we derive some new and interesting integral formulae for Bernoulli and Genocchi polynomials. [ABSTRACT FROM AUTHOR]

We give some interesting identities on the Bernoulli numbers and polynomials, on the Genocchi numbers and polynomials by using symmetric properties of the Bernoulli and Genocchi polynomials. [ABSTRACT FROM AUTHOR]

We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. Let Pn = {p(x) ∈ Q [x] | deg p(x) ≤ n} be the (n + 1)-dimensional vector space over Q. Then we show that {H0(x),H1(x), . . . , Hn(x)} is a good basis for the space Pn for our purpose of arithmetical and combinatorial applications. [ABSTRACT FROM AUTHOR]

We will give the Lebesgue-Radon-Nikodym theorem with respect to weighted p-adic q-measure on Zp. In special case, q = 1, we can derive the same result as Kim, 2012; Kim et al., 2011. [ABSTRACT FROM AUTHOR]

We give some interesting identities on the twisted (h, q)-Genocchi numbers and polynomials associated with q-Bernstein polynomials. [ABSTRACT FROM AUTHOR]

We give some new identities on the Bernoulli and Euler numbers by using the bosonic p-adic integral on 핫p and reflection symmetric properties of Bernoulli and Euler polynomials. [ABSTRACT FROM AUTHOR]

Recently, many authors have studied twisted q-Bernoulli polynomials by using the p-adic invariant q-integral on Zp. In this paper, we define the twisted p-adic q-integral on Zp and extend our result to the twisted q-Bernoulli polynomials and numbers. Finally, we derive some various identities related to the twisted q-Bernoulli polynomials. [ABSTRACT FROM AUTHOR]

We derive the modified p-adic q-measures related to q-Nasybullin's type lemma. [ABSTRACT FROM AUTHOR]

Recently, many mathematicians have studied various kinds of the q-analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105- 112, 2009.", Kim defined new generating functions of q-Genocchi, q-Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type qzeta function. This function interpolates q-Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials. [ABSTRACT FROM AUTHOR]

By the properties of p-adic invariant integral on Zp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties of p-adic invariant integral on Zp, we give some interesting relationship between the power sums and the generalized Bernoulli polynomials. [ABSTRACT FROM AUTHOR]

Recently, many mathematicians have studied various kinds of the q-analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105-112, 2009.", Kim defined new generating functions of q-Genocchi, q-Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type q-zeta function. This function interpolates q-Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the distribution of Genocchi polynomials. Finally, we construct the Genocchi zeta function which interpolates Genocchi polynomials at negative integers. [ABSTRACT FROM AUTHOR]

For an ordinal α, a modular lattice L with 0 and 1 is α-atomic if L has dual Krull dimension α but each interval [0,x] with x < 1 has dual Krull dimension <α. The properties of α-atomic lattices are presented and applied to module theory. The endomorphism ring of certain types of α-atomic modules is a local domain and hence there is a Krull–Schmidt type theorem for those α-atomic modules. [ABSTRACT FROM AUTHOR]