Annals of Communications in Mathematics

AbstractMalaria is one of the serious life-threatening diseases with negative effects on both the social and economic aspects of human life. Researching into its curtailment or eradication is necessary for elevating human health and social-economic status. In thisregard, this study focuses on the spatial non-linear mathematical model to investigate how vector control strategies are correlated with the dynamics of malaria transmission. The study employs a non-linear partial differential equations (NPDE) mathematical model to investigate malaria transmission. The model system incorporates human (host), mosquito (vector), and invasive alien plant populations. Some applicable epidemiological mathematical analyses were carried out on the model system, such as critical points, stability, the basic reproduction number, local asymptotic stability (LAS), bifurcation, global as- ymptotic stability (GAS), wave speed, and numerical analyses using relevant data were extensively analysed. Using the sharp threshold conditions imposed on the basic reproduction number, we were able to show that the model exhibited the backward bifurcation phenomenon and the DFE was shown to be globally asymptotic stable (GAS) under certain conditions. It was found that the invasive alien plants have significant effects on malaria transmission. This study suggests that mosquito repellent plants should be planted around the human environment to replace the invasive plants so as to reduce mosquito shelters andfeeding opportunities for mosquitoes.

Abstractn this section, we introduce the notions of a left and a right translational invariant fuzzy subsets of a Γ−semigroup M, as well as the concept of a unit with respect to a fuzzy subset, and study their properties. We also prove that if μ is a translational invariant fuzzy subset of a commutative Γ−semigroup with unity, then the principal ideal generated by an element and μ that contains a unity element is a prime ideal of the Γ−semigroup.

AbstractFor a wide class of infinite boundaries and the zero boundary condition, a simple proof is given for the absence of the positive eigenvalues of the Laplacian. The objective of this work is to prove Theorem 1 in which such conditions are formulated.

AbstractBI-algebra was introduced in 2017 by A. Borumand Saeid, H. S. Kim and A. Rezaei. Then this class of logical algebras was the focus of many researchers. In this paper, we register an additional property of ideals in right distributive BI-algebras. Then, in this paper we discuss the following two things: the definition of the concept of atoms in right distributive BI-algebras and the registration of many properties of such a designed concept of atoms. In addition to the previous one, the paper designs an extension of the right distributive BI-algebra A = (A, ·, 0) by adding one element w /∈ A such that w is an atom in A.

AbstractA new proof is given for the uniqueness theorem for inverse obstacle scattering with non-overdetermined scattering data. It is proved that the knowledge of the scattring amplitude for a fixed wave number, fixed direction of the incident field and all directions of the scattered field in an arbitrary small cone determine the boundary of the obstacle uniquely for the Dirichle boundary condition on the obstacle.

AbstractThis article’s main goal is to introduce and investigate several new neutrosophic normed spaces of I-convergence of the triple sequences. By using the compact operator, these spaces are defined. These spaces have several basic characteristics, such as fuzzy topology and verifiable inclusion relations.

AbstractIn this paper, we introduce the notion of a tri-quasi ideal and a fuzzy tri-quasi ideal as a further generalization of ideals, left ideals, right ideals, bi-ideals, quasi ideals, and interior ideals. We characterize the regular semigroup in terms of tri-quasi ideals, fuzzy tri-quasi ideals and study some of their properties. This generalization enables mathematicians to explore new relationships and enhancing the understanding of these structures. We establish that, a semigroup is a regular semigroup if and only if B ∩ I ∩ L ⊆ BIL, for any tri-quasi ideal B, ideal I and left ideal L of a semigroup, and for a semigroup, if μ is a fuzzy left tri-ideal of a semigroup then μ is a fuzzy tri-quasi ideal.

AbstractIn this paper, as a further generalization of ideals, we introduce the notion of a bi-quasi-interior ideal as a generalization of ideals, right ideals, left ideals, quasi ideals, bi ideals, interior ideals and quasi interior ideals of a Γ−semigroup and study the properties of bi-quasi-interior ideals of a Γ−semigroup.