Afrika Matematika最新文献

In this paper, we study the positive solution to the Finslerian Yamabe-type equation

We give the Hamilton-type gradient estimate on compact Finsler metric measure spaces with the celebrated (CD(-K,N)) condition. Besides, on forward complete noncompact Finsler metric measure spaces with the mixed weighted Ricci curvature bounded below, the new comparison theorem established by the third author (Shen in Operators on nonlinear metric measure spaces I: A new Laplacian comparison theorem on Finsler manifolds and a traditional approach to gradient estimates of Finslerian Schrödinger equation arXiv:2312.06617v2 [math.DG], 2024) allows us to give the gradient estimate under the assumption of certain bounded non-Riemannian tensors. Finally, we prove the Liouville-type theorem and the Harnack inequality for such solutions as applications.

The degree distribution is one of the characteristic features of the topology of networks. This distribution describes the in-degree and out-degree of nodes in systems. In genetic networks, the in-degree or arriving connectivity represents the number of links coming to a target gene, while the out-degree or departing connectivity represents the number of links leaving the target gene. For biological networks, the in-degree distribution can be modeled by the exponential distribution, whereas the power-law distribution generally models the out-degree distribution. However, truncated power-law, generalized Pareto, stretched exponential, geometric, or combinations of these distributions may serve as robust alternative out-degree models, satisfying the centrality and small-world properties even without scale-free behavior. The Pearson curve is a fundamental tool for categorizing distributions based on the characteristics of their first four moments. In this study, we aim to describe the out-degree of biological systems through an alternative approach. This approach ensures that the previously mentioned out-degree densities are treated as special cases within the Pearson curve framework. Their distributional similarities are evaluated using the three-moment Chi-square and four-moment F approximations. As a result, we assess the effectiveness of our proposed method in accurately classifying these distributions. The findings reveal that the degree distributions satisfying the scale-free property mainly fall within the Pearson Type I family, with only a few in Type VI. In contrast, clustered and hub networks do not align with Pearson distributions. The scale-free networks demonstrate the applicability of the four-moment F approximation, highlighting the robustness of Pearson curves in modeling biological networks. This study suggests that fitting a plausible distribution in the Pearson families provides realistic choices for the degree distribution in biological networks, addressing limitations in existing methodologies and opening pathways for further research on various biological network types and distribution systems.

In this paper, we consider the existence of infinitely many consecutive cube-free numbers in Piatetski-Shapiro sequences. We prove that, for any fixed (1<c<2), there exist infinitely many consecutive cube-free integers in Piatetski-Shapiro sequences.

We introduce the finite variable cubic functional equation of the form

where (m ge 4) is a fixed integer, and we establish the Hyers–Ulam–Rassias stability results in paranormed spaces and matrix paranormed spaces.

In this work we model a compact star in simultaneosuly comoving and isotropic coordinates. Using a transformation first developed by Kustaanheimo and Qvist [republished: Gen Relat Grav 30, 663 (1998)] we recast the Einstein field equations into a simple, albeit, nonlinear system. We further impose a linear equation of state of the form, ({p_{r}} = alpha rho -beta), which we integrate in general. We reduce the problem of finding exact solutions of the Einstein field equations to quadratures relating the metric functions. We complete the gravitational description of the model by choosing one of the metric functions by appealing to physics. A complete physical analysis of our model is carried out to test its robustness as a viable description of compact objects within the framework of general relativity.

Using the concept of the symmetric difference formula of the Dunkl operator, a new fractional integral iteration of symmetric Schur functions is constructed in the open unit disk. That will be referred to as the fractional Schur–Dunkl operator. When applying the fractional Schur–Dunkl operator to the normalized class of holomorphic functions in the open unit disk, we take it into consideration. Some geometric criteria for the convexity and starlikeness of the envisaged operator are investigated. Furthermore, we declare a series of requirements for the fractional Schur–Dunkl operator to be in the domains of Symmetric Piatetski–Shapiro. Using Mathematica 13.3, figures are shown for the proposed fractional Schur–Dunkl operator.

Open sets are regarded natural offshoots as they are the basic tool for structuring a topology in any environment and these are generating different generalizations whereas a few are stronger than the same and it is noteworthy that the open sets are lying in the center of the line of open like sets in any form. Fuzzy open set neither implies nor is implied by fuzzy (gamma ^*)-open sets. Even more, the family of all fuzzy (gamma ^*)-open sets generates a new fuzzy topology which is an independent structure that is beyond compare. In this treatise, it is claimed and established that there is a stronger form of fuzzy open set that contained in fuzzy open set as well as its associated independent fuzzy open set simultaneously for any given fuzzy topological space. Existence of strongly fuzzy independent topological space is shown in the light of fuzzy (delta ^*)-open set. This study may be applicable in fuzzy bags connecting with relational database analysis.

The purpose of this article is to put forth the idea of multivalued weak Suzuki Type ((mathcal {theta },{hat{{mathcal {R}}}})) contractions whose single valued version is also novel in literature. A fixed point result in the frame of metric space endowed with binary relation for such a mapping is established and some examples are provided. Data dependence of fixed points and existence of solution of matrix equations are also discussed as an application of our results.

We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these generating functions we evaluate several infinite series in closed form. In addition, we offer some combinatorial sum identities involving Catalan numbers, harmonic numbers and odd harmonic numbers. Finally, we analyze a special log-integral with Fibonacci numbers and odd harmonic numbers.