141 papers
This paper proposes a novel, computationally efficient algorithm for constructing discrete Green's functions in two-dimensional linear elasticity systems, demonstrating its validity and applicability to methods like the finite element method through numerical analysis and examples.
This paper establishes the global convergence and explicit convergence rates of a block coordinate descent method augmented with a gradient consistency penalty for non-convex composite optimization, demonstrating that the penalty acts as an implicit regularizer to prevent high-curvature regions while validating these theoretical findings through numerical experiments.
This paper develops a deterministic mathematical model to analyze the transmission dynamics of wheat mosaic virus, establishes stability conditions based on the basic reproduction number, and demonstrates through optimal control theory that combining prevention and removal of infected plants is the most effective strategy for reducing disease prevalence.
This conceptual paper introduces AI-EPE, a comprehensive framework that integrates policy, pedagogy, and assessment to guide the ethical and effective use of generative AI in undergraduate mathematics by defining key constructs like ethical competency and epistemic agency while offering level-specific guidelines and assessment strategies.
This paper mathematically proves that the Multi-Sphere Shape Generator's placement strategy effectively identifies centers of maximal inscribed spheres by demonstrating that local maxima of its feature-enhanced residual field correspond to the medial axis of the target shape.
This paper presents a unified mathematical framework integrating Physics-Informed Neural Networks with metaheuristic optimization to create a scalable, real-time digital twin for sustainable engineering that guarantees convergence and stability while significantly reducing computational complexity and energy consumption compared to classical numerical methods.
This paper develops a novel four-compartment epidemiological model for addiction dynamics that demonstrates how treatment-capacity saturation, rather than incidence saturation, uniquely drives backward bifurcation and bistability, creating a critical policy gap where the basic reproduction number fails to capture the risk of long-term persistence even below traditional thresholds.
This paper establishes a coordinate-free Lie derivative criterion for the synchronization of fiber bundle sections with identical internal dynamics on connected manifolds, proving that vanishing Lie derivatives of section differences imply flow-equivariant diffeomorphism without requiring Laplacian diagonalization or a drive-response setup.
This paper characterizes holomorphic retracts through the center of polyballs with strictly convex factors as either biholomorphic to linear retracts of individual factors or products thereof, a result that establishes the essential uniqueness of their product representations by proving they cannot be biholomorphically equivalent to other product domains with differing factor counts or dimensions.
This paper proposes a modified assignment method for the FIFA World Cup 2026 knockout bracket that treats the allocation of third-place qualifiers as a capacitated bipartite matching problem to ensure that no two teams from the same group meet before the semi-finals, thereby improving fairness and tournament appeal compared to the official schedule which fails this condition in 70 out of 495 scenarios.