Asian Research Journal of Mathematics

Structural Characterization of T-Normal Graphs

Seena V — 2025-11-21

Graph-theoretic properties pertaining to topological separation are important in order to understand how graph elements are structurally related. In this paper, we introduce the concept of T-normal graphs and investigate some of their basic properties. Specifically, we derive conditions under which the complete graph K_n is T-normal, and consider how the T-normal aspect behaves under the union and Cartesian product of two graphs. Finally, we provide a characterization of T-normal graphs using complements of graphs, providing a more in-depth understanding of their structural and topological behavior.

A Note on Stability (Hyers-Ulam) of Functional Equations in 2-Banach Spaces

Bhavin Mansukhlal Patel — 2025-11-25

In this research artricle, we present modifications to the results reported in the paper of Chung and Park (2012). The modifieded theorems strengthen the theoretical framework of functional equations in 2-Banach spaces and ensure consistency in their applications to stability theory.

Hyperbolic Extensions of Generalized Pandita Numbers

Fatih Zahid Kalca — 2025-11-25

This paper introduces the framework of generalized hyperbolic Pandita numbers constructed over the bidimensional Clifford algebra of hyperbolic numbers, contributing a novel class of structured sequences to the expanding domain of number theory. Anchored in the principles of hyperbolic systems, these constructs pave the way for exploring algebraic symmetries and recursive behaviors beyond classical formulations. Special attention is devoted to notable cases, including the hyperbolic Pandita and hyperbolic Pandita-Lucas numbers, whose properties are meticulously examined. To deepen understanding and facilitate computation, we derive explicit closed-form representations using Binet-type formulas, construct generating functions through formal power series, and establish summation expressions with broad applicability. Additionally, matrix-based representations are developed to offer an algebraic lens through which structural dynamics can be modeled and analyzed. These formulations not only enrich the theoretical foundations of discrete mathematics and symbolic computation but also highlight promising applications in engineering disciplines— particularly in the modeling of iterative systems, signal transformations, the analysis of complex networks, and cryptographic systems. The insights presented herein lay the groundwork for future exploration into hybrid sequence systems and their role in interdisciplinary problem solving.

Queueing Inventory Model for Optimized Material Allocation in Multistation Shipbuilding Assembly Operations

ANUSHA AK — 2025-12-05

Shipbuilding involves highly complex multi-station assembly operations where the timely availability of materials is critical for maintaining production flow and preventing bottlenecks. Traditional inventory management in shipyards relies heavily on deterministic planning and static ordering policies, which often fail to capture system uncertainties associated with stochastic material demand and the sequential nature of multi-station operations. This paper develops a pure theoretical queueing-inventory model to optimize material allocation among assembly stations in a shipbuilding environment. Each workstation is modeled as an M/M/1 queue, and material inventory replenishment follows an (s, S) policy. The interaction between queueing dynamics (arrival and service rates) and inventory control (reorder point and replenishment level) is formulated using a continuous-time Markov chain. The state space is defined as a two-dimensional process based on inventory level and queue length at each station. The transition probability matrix (TPM) is derived to compute steady-state probabilities, enabling quantitative assessment of performance measures including stockout probability, average number of jobs in queue, expected inventory levels, and utilization rates of assembly stations. The model provides analytical insights into minimizing holding costs, reorder frequencies, and production delays. The contribution of this work lies in integrating queueing theory with stochastic inventory control specifically tailored for shipbuilding operations, providing a foundation for future simulation or optimization-based studies.

Additive Optional Scrambled Randomized Response Model for Estimating Population Mean and Sensitivity Level of Sensitive Variable

I. B. Okafor — 2025-12-06

The paper proposed an additive optional randomized response technique model that improves upon Gjestvang and Singh (2009) model by effectively balancing respondents privacy protection and statistical estimation efficiency. The proposed model establishes an unbiased estimator of the population mean under both simple random sampling and probability proportional to size sampling schemes. The proposed model effectively balances the privacy protection with statistical efficiency – a key trade-off in survey design involving sensitive variable. For all values of scrambling parameters and sensitivity level, the proposed model recorded high gain in efficiency and the relative efficiency of the proposed model under both sampling scheme is greater than one. As sensitivity level increases, the relative gain in efficiency decreases which is in agreement with theoretical expectations. Nevertheless, even at high sensitivity level W = 0.9, the proposed model maintained acceptable efficiency and unbiasedness. The weighted privacy-efficiency measure established that proposed model out-performed Gjestvang and Singh (2009) model.

Graph-theoretic Modeling of Multi-echelon Queueing-inventory Systems with Node and Edge Dependencies

ANUSHA A K — 2025-12-06

Multi-echelon supply chains and inventory networks are inherently complex, characterized by stochastic demand, variable lead times, and interdependent transportation links. Traditional queueing–inventory models often assume independence among nodes and edges, limiting their applicability in realistic, interconnected supply networks. In this study, we develop a graph-theoretic framework for multi-echelon queueing–inventory systems, where nodes represent warehouses, suppliers, or retailers and edges represent stochastic transportation or information flows with temporal correlations.

By integrating queueing theory, stochastic inventory control, and graph spectral analysis, the framework captures propagation of demand signals, stockouts, and service delays throughout the network, enabling the identification of critical bottlenecks and optimization of inventory allocation. Simulation results demonstrate that the model effectively accounts for node and edge dependencies, reflecting how upstream disruptions or fluctuating lead times influence downstream inventory levels and service performance.

The proposed methodology provides actionable insights for complex logistics systems, including shipyards, multi-warehouse distribution networks, and manufacturing supply chains, supporting resilient, efficient, and responsive inventory management strategies under uncertainty.