Asian Journal of Mathematics and Computer Research

Development of a Generalized Quadrature Formula Using Anti-gaussian Methods

Sanjit Kumar Mohanty — 2026-05-25

In this paper, we propose a novel generalized quadrature rule, denoted by SM₁₅ (f), constructed by combining the Anti-Lobatto 4-point rule and the Anti-Gauss 3-point rule through a generalized quadrature framework. A detailed theoretical investigation of the proposed rule is carried out, including convergence analysis and the derivation of appropriate truncation error estimates. The analytical results reveal that the proposed quadrature rule possesses a higher degree of precision and significantly improved accuracy compared with its constituent quadrature rules. To assess the practical performance of the method, several numerical experiments are performed on a variety of test integrals. The obtained results demonstrate that the proposed rule yields highly accurate approximations with considerably reduced truncation errors, thereby confirming its reliability, stability, and computational efficiency. Comparative error analysis and numerical illustrations further establish the superiority of the proposed quadrature rule over the existing component rules. Consequently, the generalized quadrature rule SM₁₅ (f) emerges as an efficient and powerful technique for high-precision numerical integration problems arising in applied mathematics and scientific computing.

Polynomially Stable of a Thermoelastic Timoshenko System with Cattaneo Heat Conduction Law

Hui Chang — 2026-05-27

This paper investigates the polynomial stability of a thermoelastic Timoshenko system with Cattaneo’s heat conduction law. The system consists of coupled hyperbolic-parabolic equations governing the transverse displacement, rotation angle, temperature, and heat flux. Previous work established the lack of exponential stability regardless of the equal wave speeds (EWS) condition. It is proved in this paper that when the EWS condition is satisfied, the associated C0-semigroup exhibits polynomial stability. Specifically, it is demonstrated that solutions decay at a rate of t^−1/4 as t → ∞, with the decay rate uniform for initial data in the domain of the generator. The analysis employs energy methods combined with semigroup theory, leveraging the structural properties induced by the EWS condition to establish polynomial decay estimates. This result extends previous stability analyses and highlights the critical role of wave speed matching in stabilizing Timoshenko systems with second-sound thermal effects.

Eco-Performance Analytics: A Multi-Objective Optimization Framework for Sustainable Sports Engineering

S. Ranjith Kumar — 2026-05-30

The sports engineering domain has traditionally emphasized performance maximization, often overlooking environmental sustainability and long-term ecological impact. With increasing global attention toward climate responsibility and sustainable product design, there is a pressing need for engineering frameworks that simultaneously address athletic performance and environmental efficiency. This paper proposes Eco-Performance Analytics (EPA), a multi-objective optimization framework that integrates performance metrics, biomechanical efficiency, material sustainability, and energy consumption into a unified decision-making model. The framework employs data-driven analytics, life-cycle assessment (LCA), and evolutionary multi-objective optimization algorithms to identify optimal trade-offs between performance enhancement and environmental impact. A conceptual implementation is demonstrated through a sustainable sports equipment design and athlete–equipment interaction model. The proposed framework aims to support designers, coaches, and sports technologists in developing high-performance yet environmentally responsible sports systems.

Properties of ΔLG Transformation via Optimal Bounds on Connectivity, Independence and Domination

Ghadeer Khudhair Obayes — 2026-06-01

In this study, we present a balanced graph (L_Δ (G)), which is an edge-based graph transformation that improves classical linear graphs by incorporating the vertex degree as a structural node in (L_Δ (G)). The two edges are adjacent only if they are not adjacent and have a length distance of 2 and are connected via an intermediate vertex w of deg(w)≥3.Through this formula, adjacencies mediated by vertices with reduced degrees are excluded, making \(\bar{L(G}\)) is a sub graph. It is clear to us from the definition that (L_Δ (G)), is continuous if and only if δ(G) ≥ 3, which reflects on the adjacency property, which is very weak, giving it a special uniqueness not found in traditional linear Apleyan graphs. We also define lower limits for the dominance number: γ(L_Δ (G)) ≥ \(\frac{|E(G)|}{2(Δ(G)−1)^2+1}\)

An upper bound on the matching number: μ(L_Δ (G)) ≤|E(G)|- α(L_Δ (G)) and for the independence number α(L_Δ (G))≥ μ(G)

The results obtained for these limits are accurate for third-order regular graphs, confirming that (L_Δ (G)), embodies the correlation between degree heterogeneity and edge independence. This transformation provides a solid foundation for the design of global networks, communication systems, and performance, and addresses the fundamental shortcomings of L_Δ (G)and (\(\bar{L(G}\))) linear graph models, which fail to accommodate the structural heterogeneity based on the degree of the vertex. It provides the first solid foundation for modeling structurally constrained systems where local degree centrality is a critical factor making it uniquely suitable for designing nested networks.

Tchebychev Polynomials of Second Kind on the Ellipse and Approximations

Abdelhamid Rehouma — 2026-06-05

We study the orthogonality of Tchebychev polynomials of second kind {U_n (z)}_{n=0,1,2,3,...}with respect to the Lebesgue planar measure concentrated on the ellipse D: b²x² + a²y² < a²b²where a > b,a system of orthogonal polynomials, given by : \(U_n(z)=\frac{T_{n+1}^{\prime}(z)}{n+1}=\frac{\sin \left((n+1) \cos ^{-1} z\right)}{\sqrt{1-z^2}},\) n = 0, 1, 2, 3, ...

where Tn (z) = cos ( n cos⁻¹ z ) , n = 0, 1, 2, 3, ...is a polynomial of degree n . T_n (z) is called the Tchebychev polynomial of degree n of first kind.They satisfies

\(\iint\limits_D U_n(z) \overline{U_m(z)} d x d y=\frac{4(n+1)}{\pi\left(\rho^{n+1}-\rho^{-n-1}\right)} \delta_{n, m}\) , n,m = 0, 1, 2, 3, ...

where δ_n,m , is the symbol of Kronecker and (a + b)² = ρ.

We study extremal properties and minimization and Fourier development involving of these orthogonal Tchebychev polynomials of second kind with respect to the Lebesgue planar measure concentrated on the ellipse.General expressions are found for the kernels polynomials associated to orthonormalized Tchebychev polynomials of second kind on the ellipse.These kernel polynomials can be used to describe the approximation of continuous functions and to solve some area extremal problems by Tchebychev polynomials of second kind on the ellipse .They can be used for the representation of the n-th partial sum of the Fourier series expansion of orthonormalized Tchebychev polynomials of second kind in the form of an integral.

Convergence Analysis of Generalized Non-Smooth Equations Using Gauss-Type Proximal Point Method

Md. Asraful Alom — 2026-06-05

This work discusses the Gauss-type proximal point algorithm for solving non-smooth generalized equations like 0 ∈ q(x) + Q(x), where a set-valued mapping Q : X ⇉ 2^Y acting between two real or complex Banach spaces X and Y with closed graph and q: U ⊆ X→Y is a single-valued mapping. In order to ensure the existence as well as convergence of any sequence produced by this algorithm under appropriate circumstances, we develop the convergence criteria of this approach by utilize metric regularity condition and point-based approximation. Lastly, we present a numerical example to validate the semi-local convergence of this algorithm.