Afrika Matematika最新文献

In this manuscript, we expand some functions of a q-discrete variable as linear combination of the q-Laguerre polynomials. The recurrence relations satisfied by the expansion coefficients are derived and in many cases, explicit solutions of these recurrence relations are computed. We show how our results can be used to solve some q-difference equations and to illustrate this, we solve the connection problem between classical q-orthogonal polynomials and the q-Laguerre polynomials.

In this work, we explore the defocusing nonlinear Schrödinger equation known as the Camassa–Holm–Nonlinear Schrödinger (CH–NLS) model, which is newly derived in the sense of deformation of hierarchies of integrable systems. This equation captures important features of nonlinear wave propagation in shallow water dynamics, plasma physics, and nonlinear optics. A comprehensive Lie symmetry analysis is carried out to determine the symmetry generators and to derive similarity reductions of the equation. These reductions enable us to construct several exact group-invariant solutions. In addition, we employ Ibragimov’s conservation theorem to derive associated conservation laws based on the identified symmetries. The study also includes an investigation of modulational instability using the framework of linear stability analysis to assess the stability properties of continuous wave solutions. The results provide analytical insights into the interplay between symmetry, conservation, and stability in the CH–NLS model, thereby contributing to the broader understanding of nonlinear dispersive wave phenomena.

In a K-causal spacetime M, we know that the manifold topology can be recovered from the (K^+) order relation and therefore the chronological or causal future (past) of an event can be expressed in terms of K-causal order. In this article, we prove a conjecture put forward by R. D. Sorkin et al., which states that the chronological future (I^+(p)) of an event (pin M) can be characterized in terms of K-causal order: (K^+(p){setminus } S=I^+(p)), where (S=lbrace rin K^+(p)mid)every ’full chain’ from p to r meets (partial K^+(p)rbrace) and the same is true for (I^-(p)); that is, (I^pm (p)) can be viewed as an order theoretic set instead of a set of events which are connected through a future (resp. past) directed time-like curves to p. In the same vein we show that if M is a continuous dcpo and (tilde{M}) be its covering space, then the lift of a K-causal curve is also a K-causal curve.

In general, the property of being an ideal-whether left, right, or two-sided-is not transitive in rings, a fact that has motivated significant research. In this paper, we introduce and investigate a new class of rings, denoted by (mathcal {K}_{1}), defined by the condition that if J is a left ideal of a left ideal L of a ring R, and also a right ideal of a right ideal K of R, then J is a left ideal of R. We show that (mathcal {K}_{1}) is distinct from the Veldsman classes (mathcal {K} (x,y;z)) by Veldsman (Publ Math Debrecen 38(3–4):297–309, 1991) and we establish its position relative to them through strict inclusion relations. Several characterisations and properties of the rings in (mathcal {K}_{1}) are given. In particular, we present analogues of known results for the Veldsman classes: for example, we describe rings in (mathcal {K}_{1}) that are direct sums of copies of a ring, investigate their Baer radical and identify and study some properties of the largest subclass of (mathcal {K}_{1}) that is closed under direct sums.

In this article, we study transcendental entire solutions of certain non-linear q-shift differential equations in higher-dimensional complex fields. Such equations in the same settings have not been considered so far. The paper focuses on the formulation and analysis of these equations and examines the structure of their solutions. The results are illustrated by explicit examples and are presented in relation to existing work.

This research article develops the exponential type estimators for estimating the population mean using conventional and non-conventional auxiliary parameters under ranked set sampling (left( {RSS} right)) technique. The bias and mean square error of the developed estimators have been calculated up to the linear approximation. The conditions have been derived for optimizing the value of mean square error and then the minimum value of mean square has been obtained. Theoretical comparisons have been made with the relevant literary estimators in terms of efficiency and conditions have been derived under which the developed estimators perform more efficiently. Empirically by using real data sets, the effectiveness of the developed estimator over the literary estimators has been justified. Also, the preference of ranked set sampling over simple random sampling without replacement (SRS_wor) is recommended on the basis of empirical results.

This article will focus on establishing the existence of renormalized solution for the subsequent parabolic equation

In this context, the operator (textrm{H}(w)=-operatorname {div}{mathcal {H}}(x,tau ,w,nabla w)) corresponds to a Leray-Lions operator defined on the inhomogeneous Orlicz–Sobolev space (W_0^{1,x} L_A(Q )) into its dual (W^{-1,x} L_{{bar{A}}}(Q )), A and ({bar{A}}) are two N-functions related to the growth of ({mathcal {H}}).

A Hom-Lie supertriple system L is (mathbb {Z}_2)-graded generalization of a Hom-Lie triple system. The purpose of this paper is to investigate the superderivation algebra Der(L), the generalized superderivation algebra GDer(L), the quasisuperderivation algebra QDer(L), the central superderivation algebra ZDer(L), and the supercentroid C(L) of a Hom-Lie supertriple system. We give some useful properties and connections between these superderivations. Furthermore, we show that the quasisuperderivation of L can be embedded as a superderivation in a larger Hom-Lie supertriple system and (Der(tilde{L})) has a direct sum decomposition when the center of L is equal to zero where (tilde{L}={sum (z_1otimes t +z_2otimes t^3)|z_1,z_2in L}) and t is an indeterminate. Later, we obtain some structural results on supercentroids of Hom-Lie supertriple systems.

In this paper, we introduce the concept of approximate Connes I-biprojectivity for Banach algebras, where I is a (w^*)-closed ideal on A. We explore several hereditary properties associated with this notion and provide illustrative examples that distinguish it from classical concepts. Finally, we offer a characterization of approximate Connes biprojectivity for upper triangular matrix Banach algebras and certain semigroup algebras.

In this paper, we provide a correct and complete proof of a result obtained by K. El Fahri and M. Moussa [Domination by positive Dunford–Pettis completely continuous operators. Afr. Mat. 27, 1311–1319 (2016)]. Moreover, we present a refinement of some other results. Among other things, we establish that the convex solid hull of each almost Dunford Pettis set of a Banach lattice E is also almost Dunford Pettis set. Additionally, we establish that the convex solid hull of each Dunford–Pettis set of E is Dunford–Pettis if and only if one of the equivalent conditions is satisfied: (1) The order intervals of E are Dunford–Pettis sets; (2) Every almost Dunford–Pettis set of E is a Dunford–Pettis set.