Afrika Matematika最新文献

This paper aims to study some topological properties of Cesàro function spaces on rooted trees. We also characterize bounded, compact, invertible and Fredhlom multiplication operators on these spaces.

We provide a new theorem which asserts that any analytic n-dimensional pseudo-Riemannian manifold can be locally and isometrically embedded into (n+2)-dimensional pseudo-Euclidean spacetimes with at least two possible signatures (mathbb {E}^{n+1,1}) and (mathbb {E}^{n,2}). Hence, such manifolds are at most of embedding class two. This theorem may be viewed as a direct consequence of the Dahia–Romero embedding theorem for embeddings into (n+1)-dimension pseudo-Riemannian space, in the context of vacuum and constant non-zero curvature. As consequence of this embedding theorem, we note that it resolves the open problem concerning the embedding class of the Gödel metric. We recapitulate the known Euclidean embedding results for FLRW geometries into pseudo-Euclidean spaces, and make some corrections to the possible signature. We also provide an explicit example demonstrating this.

In this paper, we introduce the notion of a vague near-algebra over a vague field. We also define the concepts of the image and pre-image of a vague near-algebra. Based on these foundations, we analyse several properties and results that contribute to the development of the theory of vague near-algebras. Illustrative examples are provided to support and clarify the theoretical results.

Lie symmetries play a central role in the analysis and solution of differential equations, offering systematic techniques for order reduction and integration. However, many differential equations do not admit classical Lie point symmetries, limiting the applicability of this approach. To address this limitation, various generalisations have been developed, among which the notion of (lambda)-symmetries (also known as (C^{infty })-symmetries) has proven particularly effective. These (lambda)-symmetries extend the symmetry framework, enabling the reduction of order and the derivation of first integrals even in the absence of classical symmetries. In this paper, we investigate the Painlevé–Ince equation within the context of (lambda)-symmetries for the first time. We identify the conditions under which the equation admits such symmetries and employ them to obtain a novel reduction of order. This analysis yields new insights into the structural properties and integrability of the equation.

In this paper, we introduce a new class of Bazilevič bi-univalent functions with complex order, defined in the open unit disk by employing bounded analytic functions. We establish precise bounds for the second and third Taylor–Maclaurin coefficients of functions in this class. Our results generalize several known coefficient estimates in geometric function theory. Furthermore, we examine important special cases that demonstrate the practical implications of our findings.

This paper is motivated by the emerging framework of rough ideal convergence which provides a tolerance parameter that allows sequences to converge within a certain margin and is studied in the context of fuzzy sequences. We introduce detailed notations for rough ideal convergence of fuzzy sequences and define the corresponding rough ideal limit sets. We then explore their fundamental properties and relationships, and present counterexamples to illustrate the concepts more clearly.

In this paper, we investigate the properties of a specialized class of lacunary sequences defined through the Euler transform within the framework of an n-normed space, employing the Musielak–Orlicz function of order ((alpha , beta )). By constructing these spaces through Euler and matrix transformations of order ((alpha , beta )), we aim to develop the structural and topological characteristics that govern the behavior of these sequences and analyse some inclusion relations. Our analysis focuses on how such transformations influence convergence behaviors, embedding new perspectives on functional interactions within n-normed spaces. These insights contribute to a deeper understanding of convergence and stability phenomena, broadening the applicability of Musielak–Orlicz function theory in advanced functional analysis and sequence spaces over order ((alpha , beta )).

From the era of Black–Scholes, European options have dwelt on pay-offs that are a linear function of the asset price. In this paper, we will look at a special case of exotic options - power options - whose payoffs are nonlinear functions of the underlying asset price. Exotic options are derivatives which have features that makes them more complex than commonly traded products - thus finding their fair value is not an always easy task. Previous analyses of the power option partial differential equation (PDE) have only obtained closed form solutions either by guessing solutions, similarity methods or the martingale approach [8, 9, 25]. Using Lie symmetry analysis we obtain an optimal system of the Lie point symmetries of the power option PDE and demonstrate an algorithmic method for finding solutions to the equation. In addition, we find a new analytical solution to the asymmetric type of the power option.

Ismail Mohamed’s major contributions, which were in collaboration with Hermann Heineken, was to provide a procedure for constructing groups with prescribed characteristics. In particular, they constructed examples of non-nilpotent groups in which every subgroup is subnormal and nilpotent. These have become known as the Heineken–Mohamed groups. This construction led to settling a few questions posed, in the 1940s, by Kurosh and Cernikov in their survey of various generalisations of nilpotency. He also studied properties of series of subgroups of a group G that are constructed from arbitrary subgroups of automorphisms of a group.

This study explores the relationship between a specific type of graph and the Fibonacci sequence by introducing and analyzing the Fibonacci numbers graph, denoted as (G_{f_n}). We delve into the structural properties of (G_{f_n}) and establish new bounds for the first Zagreb index (M_1(G_{f_n})), relating it to the number of vertices n, the number of edges m, the maximum vertex degree (Delta), the minimum vertex degree (delta), and the clique number (omega). Additionally, we investigate the domination number specific to Fibonacci graphs. Furthermore, we introduce two matrices: the equi-degree Laplacian matrix and the equi-degree signless Laplacian matrix, and examine their spectral characteristics to gain deeper insights into the eigenvalues of these matrices associated with connected graphs corresponding to Fibonacci numbers. This research not only broadens the theoretical understanding of Fibonacci graphs but also contributes to the field of algebraic graph theory by examining these new matrices.