Realization by a Differential Operator of the Annihilation Operator for Generalized Chebyshev Oscillator

SOLVING A CLASS OF GENERALIZED LYAPUNOV OPERATOR DIFFERENTIAL EQUATIONS WITHOUT THE EXPONENTIAL OPERATOR FUNCTION A bstract

Bi-concave Functions Defined by Al-Oboudi Differential Operator

The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

Some Subclasses of Analytic Functions Defined by Generalized Differential Operator

Let A denote the class of analytic functions in the open unit disk U = {z : |z| < 1} normalized by f(0) = f ′(0) − 1 = 0. In this paper, we introduce and study certain subclasses of analytic functions. Several inclusion relations of various subclasses of analytic functions, coefficient estimates , growth and distortion theorems, Hadamard Product, extreme points, integral means and inclusion pro...

Differential Evolution with Generalized Mutation Operator

Differential Evolution (DE) proved to be one of the most successful evolutionary algorithms for global optimization purposes in continuous problems. The core operator in DE is mutation which can provide the algorithm with both exploration and exploitation. In this article, a new notation for DE is proposed which has a formula that can be utilized for generating and extracting novel mutations an...

Creating Quanta with 'annihilation' Operator

The non-symmetric nature of the boson 'destruction' operatorâ and its 'creation' partnerâ † is made apparent by applying them to a quantum state |ψ different from the Fock state |n. We show that it is possible to increase (by many times or by any quantity) the mean number of quanta in the new 'photon-subtracted' statê a|ψ. Moreover, in certain cases the mean number of quanta in the (normalized)...