Afrika Matematika最新文献

To solve all types of Fredholm integro-differential equations, we develop a computational automation based on the collocation method. (gamma )-spline basis functions are employed to compute an approximate solution of these linear integral equations. In addition, Pocklington’s integro-differential equation is studied in this work. Accordingly, the signal reconstruction in the wire antennas is treated using these equations. Several techniques based on quadrature computational automation methods are involved to determine the computed solutions of the considered integro-differential equations. Moreover, the (gamma )-spline interpolation function is proposed to solve the Fredholm equation. Some examples are presented to indicate the numerical convergence orders (mathcal {O}(h^{gamma +1})), accuracy, effectiveness, and robustness of the method.

In this paper, firstly, for one operator, later for multiple operators, the continuity properties of the joint (k, p)-numerical radii and the joint (k, p)-Crawford numbers of operators are investigated.

Construction of partially balanced incomplete block (PBIB)-designs from a strongly regular graph with given set of parameters is a difficult problem. In literature only three such constructions are available. In this paper, we address this nearly impossible case by constructing PBIB-designs arising from strongly regular graphs with given parameter set for orders from 51 to 100, viz., Sims–Gewirtz graph, (text {M}_{22}) or Mesner graph, Brouwer’s graph, Brouwer and Haemer’s graph, Higman–Sims graph, Hall–Janko graph, Paley graphs—(P_{53},~P_{61},~P_{73},~P_{81},~P_{89},~P_{97}) and Hamming graphs H(2, 8) and H(2, 10) using vertices of diametral paths as blocks. In each case we provide the composition of blocks. All these designs are constant block sum designs.

A finite group G is called (l, m, n)-generated, if it is a quotient group of the triangle group (T(l,m, n) = left<x, y, z|x^{l} = y^{m} = z^{n} = xyz = 1right>.) In [23], Moori posed the question of finding all the (p, q, r) triples, where (p, q) and r are prime numbers, such that a non-abelian finite simple group G is a (p, q, r)-generated. In answering this question, we establish all the (p, q, r)-generations for the group (G_{2}(3).) We mainly used the structure constant method together with other results to establish the generation and non-generation of the (G_{2}(3)) by the triples (p, q, r). The Groups, Algorithms and Programming, GAP [21] and the Atlas of finite group representations [27] are used in our computations.

In this article, we establish the Bohr inequalities for the sense-preserving K-quasiconformal harmonic mappings defined in the unit disk (mathbb {D}) associated with the subclasses of Ma-Minda starlike and convex univalent functions denoted by (mathcal {S}^*(psi )) and (mathcal {C}(psi )) respectively, and for (log (f(z)/z)) where f belongs to the Ma-Minda classes or satisfies certain differential subordination. We also estimate the Logarithmic coefficient’s bounds for the functions in the subclass (mathcal {C}(psi )) when (psi (mathbb {D})) is convex, which complement the result for starlike functions.

In this paper, using some elements of the q-harmonic analysis associated to the q-Dunkl operator introduced in [3], for fixed (0<q<1), some new estimates useful in applications are proved for the generalized q-Dunkl transform in the space (L^{2}_{q,alpha }(mathbb {R}_{q})) as applied to some classes of functions characterized by a generalized modulus of continuity.

This study uses a q-derivative operator and q-Bernoulli numbers to establish the subclass ({mathcal {S}}mathfrak {B}_{q,lambda }^{s,b}left( mathcal {F}_{0}right) ) of Sakaguchi type functions. We obtained constraints for the initial coefficients (vert a_2 vert ) and (vert a_3 vert ) through our analysis, providing insight into the characteristics and behavior of functions in this subclass. Furthermore, we derive the Fekete-Szegö inequality that is peculiar to this class, along with a number of corollaries that expand on our results and enhance our comprehension of their implications.

A new model involving the equations of isotropic thermoviscoelastic diffusion under a multi-phase-lags medium (ITDM) has been proposed in this study. The model is developed by modifying the classical Fourier’s (Theorie Analytique de la Chaleur. Oeuvres de Fourier, Paris, 1822) and Fick’s (Ann Phys 94:59–86, 1855) laws to incorporate higher-order time derivatives of the heat flux vector and the mass flux, along with gradients of temperature and chemical potential. These modifications enable the model to more accurately capture memory and non-local effects in heat and mass transport. The governing equations are employed to establish uniqueness and reciprocity theorems, which are essential for validating the well-posedness and symmetric properties of the system. The reciprocity theorem is applied to cases involving instantaneous and moving sources of heat, mass, and body forces, demonstrating how system responses are influenced by parameter variations and the sensitivity of field variables. The methodology adopted in this work allows for the derivation of generalized theoretical results and their validation through special and limiting cases, offering a sturdy theoretical framework for further study. Several unique cases are also derived and shown to correlate well with previously established results, thereby confirming the reliability of the proposed model. Although the study is theoretical, it lays the groundwork for future exploration of fundamental problems in thermoelastic continua involving multiple coupled field variables. The developed model has applications in material science, geomechanics, soil dynamics, and the electronic industry, where complex interactions between thermal, mechanical, and diffusive processes are prevalent.

In this paper, we explore square-mean asymptotically (varkappa)-periodic mild solutions from square mean (varkappa)-periodic limit for a stochastic integro-differential equations driven by Brownian motion, utilizing Grimmer’s resolvent and a version of Darbo’s fixed point theorem based on the degree of nondensifiability. Additionally, an example is given to illustrate our results.

The prupose of the present paper is to study an application of a Miller and Mocanu’ theorem for the Dziok–Raina operator.