Afrika Matematika最新文献

In this paper, we introduce the concept of Denjoy-Wolff set in rational semigroups. We show that for finitely generated Abelian rational semigroups, the Denjoy-Wolff like set is countable. Some results concerning the Denjoy-Wolff like set and the Julia set are also discussed. Then we consider a special class of rational semigroups and discuss various properties of the Denjoy-Wolff like set for this class. We use the concept of Denjoy-Wolff like set to classify the class into three sub-classes. We also show that for any semigroup in this class, the semigroup can be partitioned into k partitions where k is the cardinality of the Denjoy-Wolff like set.

Let ({mathcal {G}}(alpha )) denote the family of functions f(z) in the open unit disk ({mathbb {D}} :={zin {mathbb {C}}: |z|<1}) that satisfy (f(0)=0=f'(0)=1) and

We determine the disks (|z|<rho _n) in which sections (s_n(z;f)) of f(z) are convex, starlike, and close-to-convex of order (beta ;(0le beta < 1)). Further, we obtain certain inequalities of sections in the considered class of functions.

Neutrosophic soft sets are a potent tool for data modeling and have therefore been the focus of extensive research, both in practical applications and from a theoretical mathematical perspective. This study aims to determine a numerical characteristic of neutrosophic soft sets that parallels the concept of energy found in graph theory and fuzzy soft set theory. This study aims to develop a decision-making algorithm that surpasses the efficiency of existing algorithms. The energy of graphs and fuzzy soft sets is determined using the singular values of a matrix, with the sum of these values representing a norm function, known as the nuclear norm in optimization problems. This concept inspires the introduction of neutrosophic soft set energy and an exploration of its potential applications. The created algorithm has been compared with a large number of existing algorithms, and in all these comparisons, the advantages of the energy-based algorithm have been highlighted.

The Solow-Swan equation is a cornerstone in the development of modern economic growth theory and continues to attract significant scholarly attention. This study incorporates memory effects into the classical Solow-Swan model by introducing a formulation based on the Caputo fractional derivative. A comparative analysis is conducted between the integer-order and fractional-order versions of the model to examine the influence of fractional dynamics on capital accumulation. The findings reveal that the inclusion of a fractional-order derivative significantly affects the trajectory and long-term stability of capital, offering a more flexible and comprehensive framework for modeling economic growth processes.

An (unrooted) d-ary tree is a tree in which every internal vertex has degree (d+1). In this paper, we show for every fixed (dge 2) that d-ary caterpillars have the minimum number of dominating sets among d-ary trees of a given order. We also determine the maximum number of dominating sets in binary trees (the special case (d=2)) and classify the extremal trees, which are also unique.

This paper examines a genetic frequency model, governed by a second-order differential equation that includes a migration mean and variance parameters. Such a model is critical for understanding how gene flow affects genetic variation across migrating populations. We prove how to reduce the equation to a solvable expression, and thereafter apply Lie symmetries to obtain exact solutions. Finally, a case study of the CCR5-(triangle)32 mutant gene which provides resistance to HIV, is discussed.

In this paper, we study the generalized heat equation associated with the Heckman-Opdam-Jacobi operator (Delta _{textrm{HJ}}) on ({mathbb {R}}^{d+1}). Specifically, we show that the extension of this operator on the space of continuous functions on ({mathbb {R}}^{d+1}) and which tend towards 0 to infinity, is the generator of a positive strongly continuous contraction semi group. This is ensured by a maximum principle for the Heckman-Opdam-Jacobi operator (Delta _{textrm{HJ}}). The explicit solution to the corresponding Cauchy problem incorporates a generalized heat kernel (h_t), which is demonstrated to be nonnegative for real arguments.

Let (G:=Kltimes N) be the semidirect product with Lie algebra (mathfrak {g},) where N is a simply connected nilpotent Lie group, and K is a subgroup of the automorphisms group, Aut(N),  of N. We say that the pair (K, N) is a nilpotent Gelfand pair when the set (L_K^1(N)) of integrable K-invariant functions on N forms an abelian algebra under convolution. According to Lipsman, the unitary dual (widehat{G}) of G is in one-to-one correspondence with the space of admissible coadjoint orbits (mathfrak {g}^ddag /G) of G. Under some assumptions on the pair (K, N) we will show in this paper and its sequel (part II), that the Kirillov–Lipsman bijection

is a homeomorphism for a class of Lie groups associated with the nilpotent Gelfand pairs (K, N). Part I (this paper) concerns generalities and the study of the convergence in the quotient space (mathfrak {g}^ddag /G.) More precisely, we give a necessary and sufficient conditions when a sequence of admissible coadjoint orbits converges in (mathfrak {g}^ddag /G.)

In this paper, we consider regular discrete Sturm–Liouville problems with transmission conditions. Some fundamental properties are studied concerning self-adjointness, orthogonality of eigenfunctions, and eigenfunction expansions.

Process capability analysis is a vital tool in quality management that enables organizations to evaluate and enhance their processes. Real-world data are mostly non-normal, they often deviate from the assumption of normality. The estimators of process capability indices (PCIs) for normal processes are not sufficient to characterize non-normal processes and can give misleading results. The Marshall-Olkin inverse log-logistic (MO-ILL) distribution is a flexible distribution that can effectively model data exhibiting positive skewness, asymmetry and heavy tails. In this paper, we derived the process capability indices (PCIs) based on the MO-ILL distribution when the process is assumed to be in a state of statistical control. Two PCIs based on MO-ILL mean and variance, and MO-ILL quantiles are proposed. The proposed PCIs were compared with the traditional PCIs and percentile-based PCIs using two real life data and data generated from MO-ILL distribution. Moreover, the effect of the sample size and parameters of the MO-ILL distribution on the PCI measures is also investigated. The results showed that PCIs values based on the proposed MO-ILL mean and variance, and MO-ILL quantiles are respectively lower and better than the traditional PCIs and percentile-based PCIs. This is an indication that MO-ILL distribution-based methods developed have narrow margin of error and are more appropriate in assessing the performance of a skewed process.