Afrika Matematika最新文献

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.

In this paper, we introduce the concept of soft GE-algebras within the framework of GE-algebra theory, extending existing approaches by incorporating principles of soft set theory. We investigate the structural properties of soft GE-algebras, define operations on these structures, and establish criteria for identifying soft subalgebras. Furthermore, we present key theorems that relate the properties of soft GE-algebras to operations such as intersection, union, and mapping, particularly emphasizing the role of GE-morphisms. These findings lay the groundwork for further exploration of soft structures in the context of GE-algebras and their potential applications in decision-making and computational logic.

In this paper, we revisit the concept of proximal groups, which are generalization of topological groups. Further, we prove Kuratowski–Mrówka theorem for proximity spaces which motivate us to define categorically compact proximal groups. Finally, we prove Tychonoff theorems for proximal groups. The study is supported by various examples.

Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of transformations that leaves the differential equation invariant. It is now known that this differential equation method plays the same role when it comes to the study of difference equations. Difference equations can be used to model various phenomena where the changes occur in discrete manner. The use of symmetries on recurrence equations, usually, leads to reductions of order and hence eases the process of finding their solutions. One of the aims of this work is to employ symmetries to generalize some results in the literature. We present new generalized formula solutions of a class of difference equations and we investigate the periodicity and behavior of these solutions.

In this paper, we investigate the concept of topological (Gamma)-semihypergroups as a generalization of topological semihypergroups. Also, we present the new connection between topological (Gamma)-semihypergroups and topological semihypergroups by special equivalence relation. Furthermore, we define and consider (Gamma)-hyperideals and selection function on (Gamma)-semihypergroups. Additionally, we consider separation axioms((T_1) to (T_4)) for topological (Gamma) -semihypergroup and we present a connection between topological (Gamma) -semihypergroups and topological semihypergroups(semigroups). Finally, we prove that topological (Gamma)-semihypergroup H is (T_i,) for (1le i le 4) if and only if (mid H mid =1.)

This research investigates the Bianchi type-I Barrow holographic dark energy model within the framework of Brans-Dicke gravity theory, incorporating logarithmic scalar fields. We formulate the field equations for a spatially homogeneous and anisotropic spacetime characterized by a configuration of pressure-less matter and dark energy. The Hubble function for the model is derived and constrained using a joint analysis of the cosmic chronometers and Pantheon datasets to obtain values for the model parameters (H_{0}) and (vartheta _{3}) at (1sigma ) and (2sigma ) confidence levels. Based on these parameter values, we compute derived parameters and discuss the results by illustrating the geometrical behavior of cosmological quantities. In this context, we analyze the graphical behavior of the cosmological and dynamical parameters of the proposed model. Stability is examined through the squared sound speed criterion. The proposed framework may potentially address the cosmic coincidence problem. Furthermore, we assess the validity of our model by analyzing thermodynamic quantities. All cosmological evaluations suggest that a suitable choice of model parameters results in an accelerating universe. The suggested model exhibits stability in the early and present epochs but becomes unstable in the later stages.

We examine a popular extension of the classical Susceptible-Infected-Recovered (SIR) model within a network-based framework, where node degrees follow a Poisson distribution. First, we review the properties of this extension, its connection to the classical SIR model, and its relationship with the pairwise closure condition for stochastic epidemics on networks. We then apply it to data analysis. This network-based formulation introduces an additional parameter representing the mean node degree, allowing for the incorporation of heterogeneity in contact patterns. Using the extended SIR model, we analyze epidemic data from the 2018–2020 Ebola outbreak in the Democratic Republic of the Congo, employing a survival approach combined with the Hamiltonian Monte Carlo method. Our findings suggest that network-based models more accurately capture epidemic heterogeneity than traditional compartmental models, without introducing unnecessary additional complexity.

In 2010, Dieulefait and Urroz considered the notion of malleability of an RSA modulus. They proved that, given some information on the factors of numbers coprime to n, where n is an RSA modulus, there exists an algorithm that finds a proper factor of n in time (O(log n)). As a particular case of their algorithm, just some knowledge of the factors of (2^npm 1) is enough to factor n except possibly when n is a base-2 pseudoprime. They went on to prove that the set of these exceptional RSA moduli with prime factors between z and 2z has size at most (O(z^2/(log z)^3)). In the present paper, we improve this bound significantly and show that the counting function for these RSA moduli is bounded above by (O(z^{8/5}/(log z)^2)). In addition, as a related problem, we prove an upper bound of (O(z^{4/5}/(log z)^{2/5})) for the number of base-2 pseudoprimes up to z that are products of two primes.

The ensemble learning algorithm is a statistical method that is unknown in HEA(s)'s prediction phase. The ensemble learning algorithm is used to check on the phase selection principles, utilizing a large experimental case study on 401 distinct HEAs, comprising 174 SS, 54 IM, and 173 SS + IM phases. Random forest(RF) has the highest accuracy compared with other ensemble learning algorithms i.e. its certainty is about 10% higher than support-vector machines(SVM) and K-nearest neighbors(KNN) for allocating HEA(s). The validity and reliability of the proposed algorithms are announced as results of the paper. Therewith, findings show two main advantages to allocating HEAs: First deduction of decision trees and improving the carefulness, and second automating missing values. In addition, to check the practical accuracy of the machine learning results, the XRD results of the TiZrNbCrV, TiZrNbFeCr, and Ti ZrNbFeV alloys are presented. All alloys are in solid solution statues without any intermetallic phases. The practical results show the ensemble learning algorithms have suitable consistency in real conditions and can be a great help to design new high entropy alloys.