The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.

 Penicillium expansum produced the toxin patulin in pome fruits. To evaluate the molecular mechanism by which the treatment of probiotic bacteria Bifidobacterium breve and Lactobacillus salivarius could modulate patulin production, three genes involved in the biosynthesis of patulin were measured using real time-PCR technique. The result of this study found that the supplementation with B. brave and L. salivarius down-regulate the relative expression of 6-methylsalicylic acid synthase (msas), ATP binding cassette transporter (ABC) and putative cytochrome P450 monooxygenases (P450-1) as well. Although, there is no effect of some strains on this expression. However, these finding suggested that these bacteria decreased patulin product

The aims of the paper are to present a modified symmetric fuzzy approach to find the best workable compromise solution for quadratic fractional programming problems (QFPP) with fuzzy crisp in both the objective functions and the constraints. We introduced a modified symmetric fuzzy by proposing a procedure, that starts first by converting the quadratic fractional programming problems that exist in the objective functions to crisp numbers and then converts the linear function that exists in the constraints to crisp numbers. After that, we applied the fuzzy approach to determine the optimal solution for our quadratic fractional programming problem which is supported theoretically and practically. The computer application for the algo

The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

Abstract

       The current study was carried out to reveal the plasma parameters such as ,the electron temperature ( ), electron density (n_e) , plasma frequency (fp), Debye length ( ) , Debye number (   for  CdS to employ the LIBS for the purpose of analyzing and determining spectral emission lines using . The results of electron temperature for CdS range (0.746-0.856) eV , the electron density(3.909-4.691)×10¹⁸ cm^-3. Finally ,we discuss plasma parameters of CdS  through  nano second  laser generated plasma .

In the past two decades, maritime transport traffic has increased, especially in the case of container flow. The BAP (Berth Allocation Problem) (BAP) is a main problem to optimize the port terminals. The current manuscript explains the DBAP problems in a typical arrangement that varies from the conventional separate design station, where each berth can simultaneously accommodate several ships when their entire length is less or equal to length. Be a pier, serve. This problem was then solved by crossing the Red Colobuses Monkey Optimization (RCM) with the Genetic Algorithm (GA). In conclusion, the comparison and the computational experiments are approached to demonstrate the effectiveness of the proposed method contrasted with other