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.

Closed-Form Solutions of Leonardo-Type Sequences: Pell-Padovan, Jacobsthal-Padovan, and Narayana Families as Homogeneous Counterparts

Yüksel Soykan — 2026-06-06

Recurrence sequences are widely used mathematical models with applications across many disciplines. Beyond classical second-order sequences, higher-order families such as Tribonacci, Tetranacci, and Pentanacci reveal richer algebraic structures, with the study of their characteristic roots and recurrence relations advancing symbolic recurrence theory.

In this paper, we present unified closed-form solutions for third-order nonhomogeneous linear recurrence relations of Leonardo-type sequences, where the input term is taken as a polynomial. By decomposing each recurrence into homogeneous and particular components, we obtain explicit formulas that depend jointly on the multiplicity of the characteristic roots and the degree of the input polynomial. Although the general framework accounts for resonance phenomena arising from repeated roots, our illustrative examples focus on the non-resonant case r = 0, where all three roots of the characteristic equation are distinct from 1.

Within this setting, we investigate several notable families of generalized Tribonacci numbers, which appear as homogeneous analogues of the original nonhomogeneous relations. Classical sequences such as the adjusted Pell-Padovan, third-order Lucas-Pell, third-order Fibonacci-Pell, Pell-Perrin, Pell-Padovan, adjusted Jacobsthal-Padovan, Jacobsthal-Perrin (Jacobsthal-Perrin-Lucas), Jacobsthal-Padovan, Narayana, and Narayana-Lucas numbers arise naturally as special cases of the Leonardo-type framework. These examples illustrate how closed-form expressions clarify the interaction between characteristic roots, polynomial inputs, and resonance effects, while also providing templates for applications in discrete mathematics, combinatorics, computational number theory, algorithmic analysis, cryptography, and discrete models in physics and biology. A further illustration is given by considering the case where the input polynomial has degree s = 3, which serves as a natural extension of the classical situations with s = 0. Under identical initial conditions, the homogeneous dynamics reproduce the well-known Pell-Padovan, Lucas-Pell, Fibonacci-Pell, Pell-Perrin, and Pell-Padovan sequences, while the cubic input enriches the particular solution. This demonstrates the continuity of the framework across polynomial degrees and emphasizes the role of initial values in shaping the resulting closed forms.

Beyond their theoretical contribution, the explicit constructions offer pedagogical value by enabling students to engage directly with nonhomogeneous recurrences through accessible formulas rather than lengthy computations. Thus, the study demonstrates both the novelty and interdisciplinary reach of generalized Leonardo-type sequences, furnishing researchers with extended tools for higher-order recurrence analysis and educators with clear examples for teaching advanced recurrence methods.

Existence of Solutions for a Class of \(p\)-biharmonic Equations with Navier Boundary Conditions

Sha-Sha Liao — 2026-06-09

The p-biharmonic equation with Navier boundary conditions is an important class of higher-order nonlinear elliptic equations that arises in applications such as beam vibration theory and suspension bridge dynamics. Extensive research has employed variational methods and critical point theory to establish the existence and multiplicity of solutions, highlighting its significance in both mathematical analysis and engineering applications. This paper studies the existence of solutions for a class of p-biharmonic equations with Navier boundary conditions. Using Morse theory, critical point theory and the G-link theorem, we establish the existence and multiplicity of solutions under the nonquadratic type conditions and the asymptotic noncrossing condition.

A Novel 4D Nonlinear Interaction Football Model: Stability Analysis

I. C. Nwokike — 2026-06-13

A novel nonlinear mathematical model is formulated to study the effects of defense, midfield, and attack on an overall football team performance. Bilinear inhibitory effects are considered for match-based factors such as defensive breakdown under attacking pressure, midfield congestion, and failure to convert attacking opportunities into match outcomes. Qualitative analysis is carried out to confirm positivity, boundedness, and well-posedness of solutions. Equilibrium points corresponding to stable tactical configurations are obtained and analyzed. Local stability analysis is carried out through analysis of the Jacobian, while global stability is established with the use of a Lyapunov function and LaSalle’s Invariance Principle. Analytical results indicate that nonlinear inhibitory factors are a major force in maintaining control over football tactics, as they ensure that none of the considered aspects are able to grow unbounded. In fact, it is demonstrated that synergy between effective defense, midfield, and attack leads to more sustainable tactics and higher rates of team performance.

Quantum Search using Grover’s Algorithm: Principles, Performance, and Applications

Anggit Gusti Nugraheni — 2026-06-23

Quantum search is one of the most important algorithmic developments in quantum computing because it demonstrates how quantum principles can improve the efficiency of solving unstructured search problems. Grover’s algorithm provides a quadratic speed-up over classical linear search by reducing query complexity from O(N) to O(√N), where N represents the size of the search space. This review examines the principles, performance, and applications of Grover’s algorithm, with emphasis on its theoretical foundation and practical relevance. The discussion covers the roles of superposition, quantum interference, oracle operations, diffusion operators, and amplitude amplification in increasing the probability of measuring a desired solution. The manuscript also reviews the computational performance of quantum search in comparison with classical search methods and considers its relevance to database searching, combinatorial optimisation, cryptography, machine learning, bioinformatics, quantum chemistry, and materials science. The review highlights that Grover’s algorithm is not limited to database retrieval, as many computationally intensive problems can be reformulated as search or optimisation tasks. However, practical implementation remains constrained by current quantum hardware limitations, including decoherence, quantum noise, limited qubit availability, circuit depth, and the difficulty of designing efficient oracles. Despite these challenges, continuing progress in quantum hardware, error correction, cloud-based quantum platforms, and hybrid quantum-classical architectures suggests that quantum search will remain an important area of research. Overall, Grover’s algorithm represents a foundational quantum algorithm with significant theoretical value and potential long-term application in computational domains involving large and unstructured search spaces.

Fixed Point Theory in Partial Ordered Metric Spaces and Their Generalizations: A Systematic Review

Chandni Byapari — 2026-06-10

Fixed point theory has emerged as a fundamental area of modern functional analysis due to its significant role in establishing the existence, uniqueness, and approximation of solutions to a wide range of linear and nonlinear mathematical problems. Over the past two decades, substantial progress has been made in extending the classical Banach contraction principle through the introduction of generalized contractive conditions, novel metric structures, and auxiliary control functions. This review systematically examines recent developments in fixed point theory with particular emphasis on partial order metric spaces and their important generalizations, including partial metric, partial cone metric, partial b-metric, partial cone b-metric, and partial Aᵦ-metric spaces. Relevant literature published between 2000 and 2025 was identified through a structured literature review approach using major academic databases and predefined inclusion and exclusion criteria. The review is organized into four thematic areas: the role of fixed point theory in functional analysis; advances in generalized metric spaces; fixed point results in partial order metric spaces and their extensions; and recent developments in hybrid, integral-type, and generalized contraction mappings. The synthesis highlights significant theoretical advancements and their applications to differential equations, integral equations, optimization, and dynamic programming. Furthermore, several research gaps are identified, including the lack of a unified framework for partial-type spaces, limited investigations in partial Aᵦ-metric spaces, insufficient development of constructive iterative methods with convergence guarantees, and relatively few applications to fractional and Volterra-type integral equations. The review concludes by outlining promising directions for future research aimed at unifying existing theories and expanding the applicability of fixedpoint techniques to emerging mathematical and applied problems.