A. This paper focuses on the bifurcation behavior of physiological control system by the nonstandard finite difference method.By using the Hopf bifurcation theory of discrete system, we prove that a series of Hopf bifurcations appear at the positive equilibrium point with the increase of time delay.At the same time, the existence of local Hopf bifurcations is investigated.Moreover, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are verified.Finally, some numerical examples are given to illustrate the theoretical results.

. In this article, we study the asymptotic behavior of a linear advanced difference equation. The idea used here is to construct appropriate mapping. Then we apply the Banach fixed point theorem to obtain sufficient conditions satisfying stability, asymptotic stability and exponential stability of the considered equation.

. In this paper, we established a differentiable results leading to analytic function thereby laying special emphasis on equicontinuous and uniformly differentiable semigroup on a special class of C 0 -Semigroup called -order preserving partial contraction mapping in semigroup of linear operator. We were able to obtained some differentiable and analytic results

A. A mathematical model to describe the dynamics of COVID-19 was formulated and analysed.The model is aimed at addressing the peculiarities of the dynamics of COVID-19 as identified by researchers as much as possible.Standard analysis indicates the existence of a disease-free equilibrium for the model which is locally-asymptotically stable when the basic reproduction number is less than unity.Conditions for the existence and stability of the endemic equilibria were determined.A backward bifurcation was found to be possible and triggered by the clinical progression of symptoms from asymptomatic to mild and to severe symptoms.Numerical simulation shows no significant difference in the dynamics of the asymptomatic and those with mild symptoms.The result also also shows that strict enforcement of quarantine can help contain the disease.

. Fixed points approximation is a very important aspect of complex Hilbert spaces in fixed point theory. This paper discusses approximation of nonexpansive operators on Hilbert spaces in terms of fixed points especially when the operators are norm-attainable. In particular, we prove that for an invariant subspace H 0 of a complex Hilbert space H, there exists a unique nonexpansive retraction R of H 0 onto (Q) and x H 0 such that the sequence { n } generated by n = n f ( n ) + (1n )T n n is strongly convergent to Rx for all n N .

A . Soft set theory was first introduced by Molodtsov [10] in the year 1999, as a general mathematical tool for dealing with problems that contain uncertainty. Soft set theory has a rich potential for applications in several directions. The notion of soft topological spaces was formulated by Shabir et al [5] and Cagman et al [2] separately in 2011. Robert and Pious Missier [13, 14] defined semi*-open and semi*-closed sets using generalized closure operator. Many researchers defined some basic notions on soft topology and studied many properties see [ [1], [5], [9], [11], [16]]. In this paper, we introduce and study soft semi*-connectedness and soft semi*-compactness using soft semi*-open sets.

. In this paper, as a further generalization of ideals, we introduce the notion of quasiinterior ideals and weak -interior ideals as a generalization of quasi ideal, bi-ideal and interior ideal of semigroups.We study the properties of weak-interior ideals of semigroup and characterize the weak-interior simple semigroup, regular semigroup using quasi-interior ideals weak-interior ideal ideals of semigroups.

. This paper aimed to study fuzzy regression models including Tanaka model, Tanaka modified model and other models, and build a fuzzy regression model using fuzzy and nonfuzzy data. In this paper, a prediction model was constructed based on the application of the Sanli and Apaydin idea which adopted the Shapiro proposal based on the square distances provided by Diamond. It compared fuzzy regression model and regression model by using normal least square model. The research found that the fuzzy regression is clearer and easier to calculate, and does not differ much from the classical regression, which supports the idea of fuzzy regression prediction, especially with regard to fuzzy data.

. Here, we consider the Bell experiment for a system described by multipartite states in the case where n-

. The objective of this paper is to find the closed form of summation theorem for Appell's double hypergeometric function second kind with suitable convergence conditions. In this paper, we find summation theorems of F 2 [A; B, C; A, A; x, y], where y takes form