Research Article
Strong Hub Sets and Strong Hub Number of Hypergraphs
Shama Kochuthundiyil Syed*,
Ramakrishnan Thekkan Veetil,
Divya Pookulath Madhavan
Issue:
Volume 14, Issue 1, February 2026
Pages:
1-9
Received:
29 October 2025
Accepted:
8 November 2025
Published:
15 January 2026
Abstract: This paper introduces and investigates the concepts of strong hub sets and the strong hub number in hypergraphs, extending the notion of hub sets defined for graphs. For a hypergraph H = (V, E), a subset S ⊆ V (H) is said to be a strong hub set if, for every pair of distinct vertices u, v ∈ V (H) − S, either u and v are adjacent or there exists a strong S-hyperpath joining them. The minimum cardinality of such a set is called the strong hub number of H, denoted by h∗(H). Fundamental properties of strong hub sets are established, and relationships between the strong hub number and various hypergraph parameters such as the domination number and connectivity are explored. The effects of vertex deletion and weak deletion on h∗(H) are studied, leading to several sharp bounds and recursive characterizations. In particular, it is shown that under weak deletion of a non cut vertex, the strong hub number remains invariant, while deletion of a cut vertex reduces it according to the structure of the resulting components. Special attention is devoted to hypertrees, where structural simplicity allows a precise characterization. This characterization provides an exact formula for h∗(H) in acyclic hypergraphs and establishes the foundational link between connectivity and hub-based path structure in hypertrees.
Abstract: This paper introduces and investigates the concepts of strong hub sets and the strong hub number in hypergraphs, extending the notion of hub sets defined for graphs. For a hypergraph H = (V, E), a subset S ⊆ V (H) is said to be a strong hub set if, for every pair of distinct vertices u, v ∈ V (H) − S, either u and v are adjacent or there exists a s...
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Research Article
A Unified Framework for Stochastic Differential Equations Driven by H ö lder Continuous Functions with Applications to Senegalese Groundwater Management
Issue:
Volume 14, Issue 1, February 2026
Pages:
10-13
Received:
25 October 2025
Accepted:
4 November 2025
Published:
15 January 2026
Abstract: This research develops an innovative mathematical framework that unifies classical and modern approaches to stochastic differential equations (SDEs) driven by irregular paths. We introduce a novel Newton-Cotes integration method that bridges Young integration and rough path theory, providing comprehensive solutions for processes with Hölder continuous sample paths. The theoretical foundation establishes existence, uniqueness, and regularity results across the entire roughness spectrum. Our methodology offers practical advantages through adaptive numerical schemes with proven convergence rates and robust parameter estimation techniques combining maximum likelihood and Bayesian approaches. The framework’s real-world utility is demonstrated through a detailed case study of groundwater management in Senegal, where our model achieves a 52%improvement in prediction accuracy over traditional methods. This enhancement enables more reliable drought early warnings and sustainable water resource planning in semi-arid regions facing climate uncertainty. The unified approach has broad applicability across scientific domains dealing with irregular data patterns, including finance, environmental science, and engineering.
Abstract: This research develops an innovative mathematical framework that unifies classical and modern approaches to stochastic differential equations (SDEs) driven by irregular paths. We introduce a novel Newton-Cotes integration method that bridges Young integration and rough path theory, providing comprehensive solutions for processes with Hölder continu...
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Research Article
Versatility of the Generalized Lagrange Interpolation Formula in the Matrix Form
Issue:
Volume 14, Issue 1, February 2026
Pages:
14-26
Received:
13 October 2025
Accepted:
8 November 2025
Published:
20 January 2026
DOI:
10.11648/j.ajam.20261401.13
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Views:
Abstract: In this paper, a generalized Lagrange interpolation formula expressed in matrix form is developed to systematically expand a sampled function with enhanced flexibility and computational rigor. The proposed formulation employs appropriate coordinate functions that not only satisfy prescribed boundary conditions but also exploit the symmetry or anti-symmetry inherent in the function under consideration. When such conditions are absent, the coordinate functions naturally degenerate into polynomial bases, thereby reproducing the classical Lagrange interpolation as a special case. The expansion coefficients are efficiently obtained through the collocation method, ensuring numerical simplicity and stability. The matrix-based generalized Lagrange interpolation exhibits substantial versatility beyond traditional interpolation tasks. It can be readily applied to numerical differentiation and integration under both uniform and non-uniform sampling schemes. Moreover, the approach proves useful in solving ordinary differential equations with specified boundary constraints, as well as in problems involving root-finding and extremum detection of functions. Numerical experiments demonstrate the accuracy and robustness of the proposed method, revealing a marked reduction in the Runge phenomenon even when the number of sampling points is limited. The results further indicate that computational efficiency and precision improve progressively as the number of samples increases. Overall, the generalized interpolation framework developed herein provides a unified and reliable computational tool for interpolation, differentiation, integration, and boundary-value problems, thereby offering broad potential for applications in numerical analysis and scientific computing.
Abstract: In this paper, a generalized Lagrange interpolation formula expressed in matrix form is developed to systematically expand a sampled function with enhanced flexibility and computational rigor. The proposed formulation employs appropriate coordinate functions that not only satisfy prescribed boundary conditions but also exploit the symmetry or anti-...
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,
Wei-Chau Xie
