Abstract:
By using the ordinary fermionic -adic invariant integral on ？, we derivesome interesting identities related to the Frobenius-Euler polynomials.

Abstract:
This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikg z et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised. It is point out that the generating function for the q-Bernoulli numbers and polynomials is unreasonable. By using the theorem of Kim (Kyushu J Math 48, 73-86, 1994) (see Equation 9), some new generating functions for the q-Bernoulli numbers and polynomials are shown. Mathematics Subject Classification (2000) 11B68, 11S40, 11S80

Abstract:
In this paper we consider the q-extension of the generating function for the higher-order generalized Genocchi numbers and polynomials attached to Dirichlet's character.

Abstract:
In this paper we give some interesting equation of p-adic q-integrals on Zp. From those p-adic q-integrals, we present a systemic study of some families of extended Carlitz q-Bernoulli numbers and polynomials in p-adic number field.

Abstract:
By the properties of -adic invariant integral on ？,we establish various identities concerning the generalized Bernoulli numbers andpolynomials. From the symmetric properties of -adic invariant integral on ？, we give some interesting relationship between the power sums and the generalizedBernoulli polynomials.

Abstract:
A compact multiband handset antenna including MIMO antenna operation for LTE 13 band (746~787 MHz) applications is proposed. The proposed antennas are separately located on the top and bottom portions of a mobile handset in order to use the antenna area more effectively. The proposed antenna achieves isolations of higher than 14 dB, enveloped correlation coefficients (ECC) of less than 0.25, and total efficiencies of greater than 40%. The operating frequency bands of Antenna 1 and Antenna 2 include the LTE 13 (746~787 MHz)/DCS/PCS/UMTS (1710~2170 MHz) bands and the LTE 13 (746~787 MHz)/GSM850/900 (824~960 MHz) bands, respectively.

Abstract:
Properties of -extensions of Euler numbers and polynomials which generalize those satisfied by and are used to construct -extensions of -adic Euler measures and define -adic --series which interpolate -Euler numbers at negative integers. Finally, we give Kummer Congruence for the -extension of ordinary Euler numbers.

Abstract:
Properties of q-extensions of Euler numbers and polynomials which generalize those satisfied by Ek and Ek(x) are used to construct q-extensions of p-adic Euler measures and define p-adic q- -series which interpolate q-Euler numbers at negative integers. Finally, we give Kummer Congruence for the q-extension of ordinary Euler numbers.