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 ...

It is recently conjectured that phase-shift errors occur with high probability than qubitflip errors, hence phase-shift errors are more disturbing to quantum information than qubit-flip errors. This leads to construct asymmetric quantum error-correcting codes (AQEC) to protect quantum information over asymmetric channels, PrZ ≥ PrX. In this paper we present two generic methods to derive asymmet...

We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function.We have the generating function of h, q -Genocchi polynomials. We define the Cangul-Ozden-Simsek’s type twisted h, q -Genocchi polynomials and numbers. We also have the generalized twisted h, q -Genocchi numbers attached to the Dirichlet’s character χ. F...

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...

We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...

Using a simple factorization scheme we obtain the recurrence-shift relations of the polynomial functions of Aldaya, Bisquert and Navarro-Salas (ABNS), F N n (ω c √ N x), i.e., one-step first-order differential relations referring to N , as follows. Firstly, we apply the scheme to the polynomial degree confirming the recurrence relations of Aldaya, Bisquert and Navarro-Salas, but also obtaining ...

In this paper, we define a new form of Carlitz’s type degenerate twisted (p,q)-Euler numbers and polynomials by generalizing the Euler polynomials, q-Euler polynomials. Some interesting identities, explicit formulas, symmetric properties, connection with are obtained. Finally, investigate zeros using computer.

Using computer, a realistic study for new analogs of weighted q-Euler numbers and polynomials is very interesting. It is the aim of this paper to observe an interesting phenomenon of ‘scattering’ of the zeros of the weighted q-Euler polynomials E (α) n,q (x). The outline of this paper is as follows. In Section 2, we study weighted q-Euler polynomials E (α) n,q (x). In Section 3, we describe the...