The stress(Y) – strength(X) model reliability Bayesian estimation which defines life of a component with strength X and stress Y (the component fails if and only if at any time the applied stress is greater than its strength) has been studied, then the reliability; R=P(Y<X), can be considered as a measure of the component performance. In this paper, a Bayesian analysis has been considered for R when the two variables X and Y are independent Weibull random variables with common parameter α in order to study the effect of each of the two different scale parameters β and λ; respectively, using three different [weighted, quadratic and entropy] loss functions under two different prior functions [Gamma and extension of Jeffery

This paper deals with the F-compact operator defined on probabilistic Hilbert space and gives some of its main properties.

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a

      Faintly continuous (FC) functions, entitled faintly S-continuous and faintly δS-continuous functions have been introduced and investigated via a -open and -open sets. Several characterizations and properties of faintly S-continuous and faintly -Continuous functions were obtained. In addition, relationships between faintly s- Continuous and faintly S-continuous function and other forms of FC function were investigated. Also, it is shown that every faintly  S-continuous is weakly S-continuous. The Convers is shown to be satisfied only if the co-domain of the function is almost regular.

This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabi

Decision making is vital and important activity in field operations research ,engineering ,administration science and economic science with any industrial or service company or organization because the core of management process as well as improve him performance . The research includes decision making process when the objective function is fraction function and solve models fraction programming by using some fraction programming methods and using goal programming method aid programming ( win QSB )and the results explain the effect use the goal programming method in decision making process when the objective function is
fraction .

Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

The objective of this paper is to study the stability of SIS epidemic model involving treatment. Two types of such eco-epidemiological models are introduced and analyzed. Boundedness of the system is established. The local and global dynamical behaviors are performed. The conditions of persistence of the models are derived.