Asian Research Journal of Mathematics

Fostering Inquiry and Creativity in Mathematics Using Math Fair as a Pedagogical Tool

Suryakanta Behera — 2026-03-21

Mathematics often has a less-than-stellar reputation in the field of teaching. Traditional methods like lectures turn math into a chore, stifling creativity and conflicting with the modern approach of constructivist pedagogy. A math fair shifts learning responsibility to students, making teachers to guide in constructive learning, thereby having the students construct their own mathematical knowledge. This study attempts to explain the various facets of a math fair as well as examine its positive effects on the students. The study concludes that the conduction of a mathematics fair yields positive learning outcomes and increases the interest of students in the subject, along with teaching them other important skills.

Distinguishing Labellings of Cartesian Powers and Wreath Product Actions

Salihu Lawan Aliyu — 2026-03-20

The distinguishing number is an important invariant used to measure the extent to which symmetries of graphs and permutation group actions can be broken by vertex labelings. In this paper, we investigate distinguishing labelings arising from permutation group actions with particular emphasis on Cartesian power constructions and wreath product actions. We establish structural bounds for distinguishing numbers in terms of orbit structure, stabilizers, and base size of permutation groups. Furthermore, we analyze the behavior of distinguishing numbers under Cartesian powers of sets and derive bounds for wreath product actions of the form G ≀ S_m acting on X^m.

Spectral and Energy Analysis of the Rook Hypergraph Derived from the 8 × 8 Chessboard

S. G. Jakkewad — 2026-03-20

Graph and hypergraph models derived from chessboard movements provide an effective framework for studying structural and spectral properties of discrete mathematical systems. In this work, we investigate the Rook hypergraph associated with the standard 8×8 chessboard. In this construction, each square of the chessboard is considered as a vertex, while hyperedges are formed by combining all vertices lying in the same row and column as a given square, reflecting the legal movement of a Rook. We develop the adjacency, Laplacian, and Seidel matrix representations corresponding to this hypergraph and examine their spectral characteristics. The eigenvalues and their multiplicities are obtained through numerical computation using Python. Based on these spectra, the adjacency energy, Laplacian energy, and Seidel energy of the Rook hypergraph are determined. The analysis shows that the structure is regular of degree 14 and highly symmetric due to the row–column configuration of the chessboard. In particular, the adjacency and Laplacian energies are both equal to 196, while the Seidel energy is 364. These results illustrate how chessboard-based constructions yield structured spectral behavior and provide a useful model for studying grid-based networks and combinatorial structures.

Spectral and Energy Analysis of the Queen Hypergraph Derived from the 8 × 8 Chessboard

S. G. Jakkewad — 2026-03-21

In this paper, we study the spectral properties of the Queen hypergraph HQ associated with the standard 8 × 8 chessboard. Each square of the board is represented as a vertex, and adjacency is defined according to the legal movements of the queen along rows, columns, and diagonals. The structural characteristics of this hypergraph are analyzed through three matrix representations: the adjacency, Laplacian, and Seidel matrices. The adjacency spectrum reflects the dense connectivity produced by the queen’s movement, while the Laplacian spectrum confirms the connectivity and describes the variation in vertex degrees. The computed energy values are adjacency energy EA ≈ 245.54, Laplacian energy EL ≈ 259.15, and Seidel energy ES ≈ 455.10. These results provide insight into the algebraic structure of chessboard-based graphs and offer a foundation for further studies on generalized n×n chessboard configurations and related combinatorial models.

Tempered FDTM–bell Framework with Hybrid Laplace–sumudu Rules for Fractional Delay Systems

Saiganesh R. Yadav — 2026-03-21

This work introduces a semi-analytical approach for nonlinear fractional delay differential equations governed by tempered Caputo memory. The proposed framework combines the Fractional Differential Transform Method (FDTM) with partial ordinary Bell polynomials to efficiently manage composite nonlinear terms, while a hybrid Laplace–Sumudu formulation ensures that tempering enters the coefficient recursion as an analytic multiplier. On the theoretical side, we establish existence and uniqueness results with bounds independent of the tempering parameter , and further prove geometric convergence of the truncabridhyted FDTM–Bell expansions under mild analyticity assumptions, uniformly valid in both and on compact subsets of . From an algorithmic perspective, we design a dynamic-programming Bell engine and propose an adaptive truncation criterion that balances accuracy with efficiency. Numerical experiments on three benchmark problems—a proportional delay, a time-varying delay, and a two-dimensional neutral-type system—demonstrate the stabilizing influence of tempering over long time intervals and verify the theoretically predicted error–truncation trends. The framework is modular in design and can be extended to tempered Caputo–Fabrizio kernels with only minor modifications.

Oscillatory Behavior and Stability Switching in Fourth-Order Nonlinear Delay Differential Equations

Umar Ado — 2026-03-24

This Paper investigates the oscillatory behavior and stability transitions in three-dimensional fourth-order delay differential equations (DDEs), which are crucial for modeling complex systems with memory or timedelay effects. The primary aim is to establish sufficient conditions under which solutions exhibit oscillations and to identify criteria for stability switches driven by varying delay parameters. The methodology employs analytical techniques including characteristic equation analysis, normal form reduction, and integrability conditions to derive precise criteria for oscillation and bifurcation. The results reveal that under specific growth and delay conditions, the system exhibits sustained oscillatory behavior and transitions in stability can occur at critical parameter values. These findings deepen the understanding of delay-induced dynamics in higher-order systems and provide a rigorous theoretical foundation for future analysis and application in fields such as engineering, biology, and physics.

Fuzzy Autoregressive Modeling and Parameter Estimation for Electrical Power Distribution Systems

Christian Mpeti Benimi — 2026-03-24

In this article, we analyzed the operating voltage of a substation in Kinshasa by transforming its classical distribution into a fuzzy distribution. This approach allowed us to estimate fuzzy stochastic parameters, which we classified as total and partial parameters. Total parameters, such as fuzzy expectation and variance, have a maximum membership degree of 1. Partial parameters, such as fuzzy autocovariance and autocorrelation, have membership degrees less than 1. This study formalized a fuzzy distribution approach based on Zadeh arithmetic, providing a rigorous framework for imprecision modeling. The integration of fuzzy numbers into the estimation methods led to a more robust evaluation of the model parameters. Furthermore, the stationarity criteria were re-examined in this fuzzy context, highlighting their theoretical consistency and practical applicability. The results obtained confirm the relevance of this approach for the analysis of random phenomena tainted by epistemic uncertainty.

The results show that the fuzzy expectation and variance have a maximum degree of membership equal to 1, while the autocorrelation functions reach a maximum degree of 0.332, confirming the partial nature of the estimated model.

Existence, Uniqueness, Boundedness and Continuous Dependence of Solutions for Fractional Order Fredholm Difference Equations

B. U. Lavhare — 2026-03-24

In this paper, we investigate the existence and uniqueness of solutions to certain fractional-order Fredholmtype difference equation involving an iterated sum. In addition, we examine the boundedness and continuous dependence of solutions under various assumptions imposed on the associated functions. The results are established using finite difference inequalities with explicit estimates, and offer fundamental insights that may serve as a valuable reference for future research.

Generalized Lyapunov-and Hartman–Wintner-type Inequalities for Mixed Fractional Differential Equations with Advanced Fractional Operators

Sukalwad Umesh Ramrao — 2026-03-25

Fractional differential equations model systems with memory and nonlocal effects, with applications across many scientific fields. Lyapunov and Hartman–Wintner type inequalities help analyze solution existence, eigenvalues, and oscillatory behavior, but their extension to modern fractional operators remains limited. Current research lacks a unified framework for these inequalities across different advanced operators. In this paper, we investigate Lyapunov- and Hartman–Wintner-type inequalities for a class of fractional boundary value problems involving non-singular kernels. The analysis is carried out using Caputo–Fabrizio and Atangana–Baleanu fractional operators. We establish new bounds under suitable assumptions and derive conditions for the existence of nontrivial solutions. The obtained inequalities generalize several known results in the literature. Illustrative examples are provided to validate the theoretical findings and to demonstrate the applicability of the proposed approach.

Binary Relations in Friendship Networks: A Mathematical Framework for Reflexivity, Symmetry, Transitivity and Community Formation

Hitesh Choudhury — 2026-03-26

Friendship networks provide a clear and intuitive framework for analyzing binary relations and understanding their structural properties. This paper presents a mathematical framework for representing social networks using binary relations on finite sets, with an emphasis on reflexivity, symmetry, transitivity and their role in community formation. In this framework, individuals are represented as elements of a finite set A, while the friendship relation is modeled as a subset of the Cartesian product A×A. Its structural properties - reflexivity, symmetry, and transitivity are examined in detail. The study formulates fundamental propositions that connect relational properties with their graph-theoretic representations, showing that reflexivity corresponds to self-loops, symmetry to undirected edges, and transitivity to the formation of direct connections from indirect paths. When the friendship relation forms an equivalence relation, it naturally partitions the population into disjoint communities. Expanding the framework further, social connectivity is analyzed using measures such as degree, paths, reachability, and connected components to interpret influence, cohesion, and community formation. A comparative analysis of real-world social networks highlights the differences between directed and undirected networks and shows that, although strict global transitivity is rare, actual networks often exhibit high clustering, reflecting local or near transitivity.