Afrika Matematika最新文献

As an extension of the fuzzy set, linear Diophantine fuzzy set (LDFS) was recently introduced. In this paper, we apply the concept of LDFS in ordered semigroups by introducing some new related concepts. More precisely, we study LDF-ideals and LDF-interior ideals of ordered semigroups, illustrate non-trivial examples on each, and present some of their properties. Finally, and using LDFS, we discuss the simplicity of an ordered semigroup.

In this paper, we delve into the fascinating realm of analytic mappings within the open unit disc, focusing on functions that are standardly normalized. Our research is centered on determining the sharp upper bound of the third Hankel determinant for a kth-root transformation applied to a specific subclass of these analytic functions.

In this existing paper, we examine a connection between certain class of harmonic univalent functions with starlike and convex harmonic functions define in the open unit disk by applying the convolution operator defined by Mittag-Leffler function. Several corollaries and consequences of the main results are also obtained.

This paper presents a study on the univalence extension of a specific class of functions defined by an integral operator. The research provides sufficient conditions for determining this univalence extension, which depend on two arbitrary analytic functions defined in the unit disk, alongside three complex numbers. The main result of the study includes these functions and parameters, and by specializing them, it leads to various well-known univalent conditions. The paper showcases examples to demonstrate how these conditions can be applied.

The coordinated search method for a one-dimensional Brownian particle in the fluid is investigated in this paper. This technique helps to remove pollutants and impurities from the fluid. To locate a Brownian particle that moves along one of n disjoint real lines, we have 2n cooperative nano-sensors coordinate their efforts such that each line contains two of them. All of these nano-sensors begin their searches at the origin. Because of random travelled distances right and left of the origin, we have a random sequence of distances on each line. Due to this uncertainty, we are able to integrate the discounted effort-reward search as a parameter in the distance function. By doing this, the expected value of the first meeting time between one of the nano-sensors and a Brownian particle will be reduced. We determine the approximate value of this expected value in addition to identifying the conditions under which it is finite. We use an example to illustrate the usefulness and application of this model.

This work investigates the well-posedness and stability outcomes of the one-dimensional Cauchy problem within a system involving swelling-porous elastic soils and thermal effects. The heat conduction in this system is described by the Lord–Shulman theory. By the energy method, we establish the existence of solutions and then prove an exponential stability result under suitable hypotheses. Our results were achieved without the need for the condition of equal velocities, and it is also considered a good improvement to our work in the paper (Choucha et al. in Mathematics 11(23):4785, 2023), completely dispensing with any damping term.

In this paper we study the direct sums of subspaces and some constructions of quotient spaces of near-vector spaces, as defined by André. In particular, for near-vector spaces constructed by taking copies of finite fields, we characterise the quasi-kernels of their quotient spaces, find their cardinality and determine when they are regular. In the case of non-regular quotient spaces, we show how they decompose into maximal regular subspaces. We show how the theory of finite-dimensional near-vector spaces constructed from finite fields allows us to reconstruct near-vector spaces with certain quotient spaces.

In order to study the invariant approximation in 2-Banach spaces, we define the concept of ( H^{+} ) type nonexpansive mapping to investigate the existence and uniqueness of approximation. Using ( H^{+} ) type non expansive multi-valued mapping in 2-Banach spaces to obtain a generalization of the classical Nadler’s fixed point theorem, also discuss the invariant approximation and prove several new results by replacing multi-valued mapping with ( H^{+} ) mapping in 2-Banach space.

In this paper, we introduce the bi-bases of a ternary semigroup. The results of this paper are based on the bi-ideals generated by a non-empty subset of a ternary semigroup. Moreover, we define the quasi-order relation of a ternary semigroup and study some of their interesting properties.

Let M be a smooth manifold and A a Weil algebra. We introduce and discuss the symplectic structure in the Weil bundle ((M^A,pi ,M)) and we establish the link between the symplectic structure in M and that in (M^A.) As applications, we discuss Hamiltonian vector fields, symplectic vector fields and poisson structures in both cases.