In 2010, Long and Zeng introduced a new generalization of the Bernstein polynomials that depends on a parameter  and called -Bernstein polynomials. After that, in 2018, Lain and Zhou studied the uniform convergence for these -polynomials and obtained a Voronovaskaja-type asymptotic formula in ordinary approximation. This paper studies the convergence theorem and gives two Voronovaskaja-type asymptotic formulas of the sequence of -Bernstein polynomials in both ordinary and simultaneous approximations. For this purpose, we discuss the possibility of finding the recurrence relations of the -th order moment for these polynomials and evaluate the values of -Bernstein for the functions ,  is a non-negative integer

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near topological spaces over B. Also, we introduce the concepts of fibrewise near closed and near open topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

The bandwidth requirements of telecommunication network users increased rapidly during the last decades. Optical access technologies must provide the bandwidth demand for each user. The passive optical access networks (PONs) support a maximum data rate of 100 Gbps by using the Orthogonal Frequency Division Multiplexing (OFDM) technique in the optical access network. In this paper, the optical broadband access networks with many techniques from Time Division Multiplexing Passive Optical Networks (TDM PON) to Orthogonal Frequency Division Multiplex Passive Optical Networks (OFDM PON) are presented. The architectures, advantages, disadvantages, and main parameters of these optical access networks are discussed and reported which have many ad

      Long memory analysis is one of the most active areas in econometrics and time series where various methods have been introduced to identify and estimate the long memory parameter in partially integrated time series. One of the most common models used to represent time series that have a long memory is the ARFIMA (Auto Regressive Fractional Integration Moving Average Model) which diffs are a fractional number called the fractional parameter. To analyze and determine the ARFIMA model, the fractal parameter must be estimated. There are many methods for fractional parameter estimation. In this research, the estimation methods were divided into indirect methods, where the Hurst parameter is estimated fir

The theoretical analysis depends on the Classical Laminated Plate Theory (CLPT) that is based on the Von-K ráman Theory and Kirchhov Hypothesis in the deflection analysis during elastic limit as well as the Hooke's laws of calculation the stresses. New function for boundary condition is used to solve the forth degree of differential equations which depends on variety sources of advanced engineering mathematics. The behavior of composite laminated plates, symmetric and anti-symmetric of cross-ply angle, under out-of-plane loads (uniform distributed loads) with two different boundary conditions are investigated to obtain the central deflection for mid-plane by using the Ritz method. The computer programs is built using Ma

In this paper, we generalized the principle of Banach contractive to the relative formula and then used this formula to prove that the set valued mapping has a fixed point in a complete partial metric space. We also showed that the set-valued mapping can have a fixed point in a complete partial metric space without satisfying the contraction condition. Additionally, we justified an example for our proof.

This paper examines a new nonlinear system of multiple integro-differential equations containing symmetric matrices with impulsive actions. The numerical-analytic method of ordinary differential equations and Banach fixed point theorem are used to study the existence, uniqueness and stability of periodic solutions of impulsive integro-differential equations with piecewise continuous functions. This study is based on the Hölder condition in which the ordering ,  and  are real numbers between 0 and 1.

In this paper, we derive and prove the stability bounds of the momentum coefficient µ and the learning rate ? of the back propagation updating rule in Artificial Neural Networks .The theoretical upper bound of learning rate ? is derived and its practical approximation is obtained

In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

     In this paper, one of the Machine Scheduling Problems is studied, which is the problem of scheduling a number of products (n-jobs) on one (single) machine with the multi-criteria objective function. These functions are (completion time, the tardiness, the earliness, and the late work) which formulated as . The branch and bound (BAB) method are used as the main method for solving the problem, where four upper bounds and one lower bound are proposed and a number of dominance rules are considered to reduce the number of branches in the search tree. The genetic algorithm (GA) and the particle swarm optimization (PSO) are used to obtain two of the upper bounds. The computational results are calculated by coding (progr