Authors:N.H. Sweilam; I.A. Soliman; S.M. Al-Mekhlafi Abstract: Publication date: Available online 25 November 2016 Source:Journal of the Egyptian Mathematical Society Author(s): N.H. Sweilam, I.A. Soliman, S.M. Al-Mekhlafi In this paper, numerical studies for the mathematical model of tuberculosis (TB), that incorporates three strains, i.e., drug - sensitive, emerging multi - drug resistant(MDR) and extensively drug - resistant (XDR), are presented. Special class of numerical methods, known as nonstandard finite difference method (NSFDM) is introduced to solve this model. Numerical stability analysis of fixed points are studied. The obtained results by NSFDM are compared with other known numerical methods such as implicit Euler method and fourth-order Runge–Kutta method (RK4). It is concluded that NSFD scheme preserves the positivity of the solution and numerical stability in larger region than the other methods.
Authors:Taher S. Hassan Abstract: Publication date: Available online 25 November 2016 Source:Journal of the Egyptian Mathematical Society Author(s): Taher S. Hassan In this paper, we deal with the oscillation of the solutions of the higher order quasilinear dynamic equation with Laplacians and a deviating argument in the form of ( x [ n − 1 ] ) Δ ( t ) + p ( t ) ϕ γ ( x ( g ( t ) ) ) = 0 on an above-unbounded time scale, where n ≥ 2, x [ i ] ( t ) : = r i ( t ) ϕ α i [ ( x [ i − 1 ] ) Δ ( t ) ] , i = 1 , 2 , … , n − 1 , with x [ 0 ] = x . By using a generalized Riccati transformation and integral averaging technique, we establish some new oscillation criteria for the cases when n is even and odd, and when α > γ, α = γ , and α < γ, respectively, with α = α 1 ⋯ α n − 1 and without any restrictions on the time scale.
Authors:A.A. Azzam Abstract: Publication date: Available online 25 November 2016 Source:Journal of the Egyptian Mathematical Society Author(s): A.A. Azzam The grill Nano generalized closed sets is an expansion of Nano generalized closed sets in grill Nano topological spaces, which is the frame of reference measurement, inference and reasoning in many applications such as computer science and information systems. So, this paper aims to study and analyze this expansion through the topological structure via the concept of grill. Some important characteristics and main properties which are related with these sets are obtained.
Authors:Kandil Amr; Zakaria Abstract: Publication date: Available online 17 October 2016 Source:Journal of the Egyptian Mathematical Society Author(s): A. Kandil, Amr Zakaria In this note, we show that Examples 3.1, 3.3, 3.4, 3.5, 3.8, 3.9, 3.10 and 3.11 in [1] are incorrect, by giving remarks and comments on these examples. Finally, reasonable reasons to improve some of the incorrect examples have been mentioned.
Authors:Abd El-Mohsen; Badawy Ragaa. El-Fawal Abstract: Publication date: Available online 13 October 2016 Source:Journal of the Egyptian Mathematical Society Author(s): Abd El-Mohsen Badawy, Ragaa. El-Fawal Decomposable MS-algebras were introduced and characterized by Badawy et al. [1] in terms of decomposable MS-triple (M, D, φ), where M is a de Morgan algebra, D is a distributive lattice with unit and φ is a bounded lattice homomorphism of M into the lattice of filters of D. In this paper we study homomorphisms, subalgebras and solve the “Fill-in” problem for such decomposable MS-algebras.
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