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.

A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to wall-crossing formulas for the Donaldson-Thomas type invariants of M. Kontsevich and Y. Soibelman, in particular confirming their integrality.

In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted (h, q)-extension of Euler polynomials and numbers, by using p-adic q-deformed fermionic integral on Zp. By applying their generating functions, they derived the complete sums of products of the twisted (h, q)-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new q-extension o...

In Einstein-Æther theory, the Lorentz symmetry is locally broken in high-energy regime due to presence of Æther field. This shall leave significant imprint on astronomical observation. this paper, we investigate optical appearance two types static and spherically symmetric black holes theory. Via Euler-Lagrange equation, obtain equations motion photon calculate total deflection angle trajectory...