Afrika Matematika最新文献

The basic tool for studying the ageing and associated characteristics of any lifetime equipments is the reliability/survival function. It is common practice that while estimating the parameters of a model, one usually adopt maximum likelihood estimation method as the starting point as a classical method of estimation. In this paper, we consider maximum product of spacing estimation, besides using maximum likelihood method for estimating the reliability characteristics, such as, mean time to system failure (MTSF), reliability function (RF) and hazard rate function (HF) at a specified time point (t_0) for logistic-exponential distribution. In addition, three bootstrap methods are considered for obtaining confidence intervals of MTSF, RT and HF. Besides, Bayesian estimation method is considered under symmetric as well as asymmetric loss functions using gamma priors for both shape and scale parameters for the considered model. Further, highest posterior density credible intervals are obtained by using a Markov chain Monte Carlo method with Gibbs sampler under Metropolis–Hastings sampling procedure. Average widths and coverage probabilities for each confidence intervals are computed. A Monte Carlo simulation study is carried out to compare the performance of the proposed estimates. Finally, two real data sets have been re-analyzed for illustrative purposes.

In this paper, we aim to discuss several results associated with conical domains and some general properties. By utilizing some conical sections, we introduce a new class of analytic functions with respect to (j, m)-ply symmetric points, (j=0,1,ldots ,m-1) and (m in mathbb {N}). Also, we formulate certain k-uniformly convex starlike functions influenced by the principle of the differential subordinations. In addition, we derive coefficient bounds for various functions in the given classes of analytic functions and evaluate certain sufficiency criteria in a form of convolutions. Over and above, we derive interesting results involving starlike functions as well.

In this paper, first we present two new integral representations of the Gauss hypergeometric function in the form of double integrals obtained recently by us Chammam et al. (Bull Belgian Math Soc 31(3), 336–340, 2024). Two specific cases of our representations allow for an alternative proofs of the well-known Gauss summation theorem and Watson summation theorem. Additionally, as an application, we introduce a new class of double integrals and provide interesting integral representations for Catalan–Qi numbers and Fuss–Catalan–Qi numbers.

Recently Yang–Roh–Jun introduced the notion of OBCI-algebras as a generalization of BCI-algebras. Here we introduce homomorphisms and kernels of OBCI-algebras and investigate related properties. More exactly, we first define the homomorphism and kernel of OBCI-algebras. We then investigate properties related to (ordered) subalgebras, (ordered) filters and direct products of OBCI-algebras.

In the paper, we consider differential nonsymmetric T-Riccati equations. So far, it presents an unexplored problem in numerical analysis, theoretical results, and computational methods, which are lacking in the literature. The method we consider is based on an extended block Krylov subspace and Rosenbrock method. The implementation of the algorithm requires only the solution of small-scale differential matrix equations in each time step. Some theoretical results are presented such as an accurate expression of the remaining criteria. The main advantage of the proposed method is that by using this method differential nonsymmetric T-Riccati equation reduces to two T-Sylvester matrix equations. Then report some numerical experiments to show the effectiveness of the proposed method for large-scale problems.

In this paper, we consider compatible Hom-associative algebras as a twisted version of compatible associative algebras. Compatible Hom-associative algebras are characterized as Maurer–Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-associative algebras generalizing the classical case. As applications of cohomology, we study abelian extensions and deformations of compatible Hom-associative algebras.

Evolutionary game theory offers an interesting avenue of exploration for populations that are subdivided into smaller groups based on shared traits. Despite being self-contained, interactions between individuals within each group are crucial. These interactions lead to a game with a block-diagonal payoff matrix having blocks of order two or three. A constant negative payoff is assigned to each player, while the background fitness function is inversely proportional to the density of players in the given territory. Through the lens of reaction–diffusion systems, we examine the circumstances necessary for diffusion-driven instability or Turing instability. We derive a set of necessary conditions for Turing instability around the interior equilibrium state. These results reveal that Turing instability occurs when some diagonal elements are positive, or diagonal cofactors of 3-order blocks are negative in the payoff matrix of the game. In summary, this article explores the dynamics of group interactions in population games and identifies key conditions that lead to instability.

In the present article, we prove a Shapiro uncertainty principle for the directional short-time Fourier transform. Next, we introduce the notion of Toeplitz operators associated with the directional short-time Fourier transform. Particularly, we study the trace class properties of such operators and prove that they belong to the Schatten–von Neumann class. Next, we investigate the boundedness and compactness of these Toeplitz operators in the (L^{p})-spaces. Finally, we introduce and study the generalized spectrogram associated with these Toeplitz operators.

In this article, we discuss the geometry of gradient Ricci-Bourguignon solitons (GRB) and then we characterize the general relativistic space-time with Ricci-Bourguignon (RB) and GRB solitons. First, we obtain the expression for the scalar curvature of a compact GRB soliton. Then, we prove that the gradient of the potential function of GRB soliton is bounded if its scalar curvature satisfies a boundedness condition. Then the Riemannian curvature of a 4-dimensional GRB soliton and its derivative are investigated whenever the Weyl tensor is harmonic. It is proven that if the potential vector field is torse-forming, then a compact RB soliton becomes perfect fluid space-time. We also discuss the bounds of the first eigenvalue of Laplacian. A volume formula for GRB soliton is obtained. Further, we study the application of conformal vector field on a RB soliton and obtain the expression for the Ricci curvature. Next, we find when RB soliton is expanding, shrinking and steady, if relativistic perfect fluid space-time admits a RB soliton with conformal vector field. We also construct a non-trivial example of GRB soliton equipped with a conformal potential vector field.

First, we prove a new alternative fixed point theorem in generalized gauge (or generalized uniformizable) spaces. This is a generalization of a famous result of Diaz-Margoli. Next, using this theorem, we show the stability of a delay differential equation where the unknown mapping takes its values in a locally convex space (in particular into a Banach space). Examples are given to support our results. We also point out some gaps in the literature and fix them.