276 papers
This paper determines the first-order asymptotic behavior of the proportion of losing positions among integer partitions of N. The proportion tends to zero on the scale 1/(√N log N), but after normalization by its natural scale it does not converge; instead, it exhibits a dyadic sawtooth pattern with a Poisson-parity transition near dyadic boundaries.
This paper analyzes the random geometry and total correlation of the K smallest values in a dependent chi-square sequence, establishing that selected sites become asymptotically uncorrelated for sub-critical selection sizes while exhibiting Poisson-distributed adjacent pairs and positive correlation at the critical square-root threshold.
This paper proposes a numerically stable and efficient partial singular value decomposition method for dual quaternion matrices using the Lanczos algorithm with thick-restart and one-sided reorthogonalization, demonstrating its superior accuracy and computational performance in applications such as color face recognition and video compression.
This paper introduces a novel, higher-precision cubature rule (SM 2 4) derived by optimizing the combination of Anti-Gaussian, Fejer's second, and Lobatto rules, which demonstrates superior accuracy and efficiency over its constituent methods in both theoretical analysis and numerical experiments.
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.